eddy covariance measurements in the po valley ... · eddy covariance measurements in the po valley:...
TRANSCRIPT
1
POLITECNICO DI MILANO
Department of Civil and Environmental Engineering
PhD course in Environmental and Infrastructure Engineering
EDDY COVARIANCE MEASUREMENTS IN THE PO
VALLEY: REPRESENTATIVENESS AND ACCURACY
Chair of the doctoral program:
Prof. Fernando Sansò
Tutor:
Doctoral dissertation of:
Daniele Masseroni
Matr. 753709
Year 2013 – Cicle XXV
2
3
Index
General Abstract ........................................................................................................... 6
General Introduction .................................................................................................... 8
Eddy covariance technique ....................................................................................... 8
References .............................................................................................................. 10
(Chapter 1) - Impact of data corrections on turbulent flux measurements ........ 11
Abstract .................................................................................................................. 11
Introduction ............................................................................................................ 11
Data collection ........................................................................................................ 13
Preliminary processes for correction procedure ..................................................... 13
Axis rotation for tilt correction ............................................................................... 13
Double rotation method .......................................................................................... 14
Spike removal ......................................................................................................... 14
Time lag compensation .......................................................................................... 14
Covariance maximization method .......................................................................... 15
Detrending .............................................................................................................. 15
Linear detrending ................................................................................................... 15
Calculating fluxes ................................................................................................... 16
Uncorrected fluxes – level 0 ................................................................................... 16
Spectral correction factors – level 1 ....................................................................... 17
Corrected fluxes – level 2 and 3 ............................................................................. 19
Results .................................................................................................................... 20
Effect of the preliminary processes on raw data .................................................... 20
Effect of the preliminary processes on uncorrected fluxes .................................... 22
Effect of the spectral corrections on turbulent fluxes ............................................ 24
Flux loss in function of air temperature and relative humidity .............................. 25
Flux loss in function of wind velocity and friction velocity .................................. 27
Flux loss in function of stability parameter ............................................................ 27
Daily and seasonal trend of flux losses .................................................................. 28
Effect of the WPL and VD corrections on fluxes at level 3 ................................... 29
Quality of fluxes ..................................................................................................... 31
Energy balance closure ........................................................................................... 34
Fluxes directly obtained from 30 minutes averaged data ....................................... 35
PEC software features ............................................................................................ 36
PEC fluxes in comparison with Eddy Pro 4.0 fluxes ............................................. 36
Energy balance closure with PEC fluxes ............................................................... 38
Conclusion .............................................................................................................. 38
References .............................................................................................................. 39
(Chapter 2) – Energy balance closure of an eddy covariance station: limitations and
improvements ........................................................................................................... 43
Abstract .................................................................................................................. 43
Introduction ............................................................................................................ 43
Instruments, data collection and site description ................................................... 45
The energy balance closure problem ...................................................................... 46
4
Effect of data corrections ....................................................................................... 47
Effect of storage terms ........................................................................................... 48
Effect of time aggregation ...................................................................................... 51
Effect of scale differences in fluxes measurement ................................................. 52
Effect of turbulent mixing ...................................................................................... 54
Effect of vegetation ................................................................................................ 56
Effect of seasonality ............................................................................................... 57
Random error ......................................................................................................... 59
Conclusion ............................................................................................................. 60
References .............................................................................................................. 61
(Chapter 3) – Experimental data about the spatial variability of scalar fluxes across maize
field in Po Valley and comparison with theoretical footprint model predictions66
Abstract .................................................................................................................. 66
Introduction ............................................................................................................ 66
What is the importance of this experiment? ........................................................... 69
Theoretical background .......................................................................................... 69
Hsieh Model ........................................................................................................... 70
Kormann Model ..................................................................................................... 71
Study site, instruments and data ............................................................................. 71
Site characteristics.................................................................................................. 71
Instruments ............................................................................................................. 72
Data corrections ..................................................................................................... 72
Fixed eddy covariance stations (A1 and A2) ......................................................... 73
Experimental execution .......................................................................................... 74
Results .................................................................................................................... 76
Flux measurements across the fields ...................................................................... 76
Experimental data compared with footprint model predictions ............................. 78
Discussions............................................................................................................. 80
Conclusion ............................................................................................................. 81
References .............................................................................................................. 81
General Conclusion .................................................................................................... 85
Acknowledges ............................................................................................................ 86
5
6
General Abstract
This PhD work is mainly focused on researching utilities for increasing the micrometeorological
flux reliabilities. Micrometeorological stations, which use the eddy covariance technique to
estimate turbulent fluxes in the surface layer, are generally located in different agricultural fields
to assess evapotranspiration and carbon dioxide fluxes between soil (or vegetation) and
atmosphere. Evapotranspiration and carbon dioxide fluxes of the SVAT (Soil – Vegetation –
Atmosphere) systems, have to be correctly estimated if a sustainable and parsimonious water
resources management would be made. Moreover energy and mass balances model outputs (e.g.
latent heat flux and soil moisture) can be compared with micrometeorological measurements, if
and only if micrometeorological data are rigorously processed and their qualities are assessed.
Micrometeorological technique was born about 30 years ago and, subsequently, a large
contribution about data corrections was rapidly given by many scientists. However, many
aspects about measurement proprieties and flux reliabilities are only now investigated. In the
first part of this work, starting from high frequency measurements of the three wind components
and carbon dioxide/water concentrations, eddy covariance data are processed using an open
source program and the results are compared with those obtained by a simple software
implemented at the Politecnico of Milan for averaged data for real time water management.
Thanks to this comparison the main correction procedures which have to be necessarily
implemented to obtain reliable turbulent fluxes from micrometeorological data, are shown.
The reliability of the micrometeorological measurements is usually assessed with the energy
balance closure. Moreover, the use of energy data to validate land surface models requires that
the conservation of the energy balance closure is satisfied. However, the unbalance problem is an
important issue which has not yet been resolved. In the second part of this work, many aspects
which could cause underestimation in turbulent flux measurements are shown. The factors which
could influence the energy balance colure are separately investigated and the energy balance
closure improvements or worsening are shown in order to understand the number of factors
which could play a fundament role into energy balance closure problem.
One of these problems is represented by flux scale proprieties. In fact, net radiation, latent,
sensible and ground heat fluxes (which represent the four components of the energy balance)
have different representative source areas which covers different sectors of the field: from few
centimeters for ground heat flux, to a hectare for latent and sensible heat fluxes. Therefore,
several errors in energy balance closure can be related to the difficulty to match footprint area of
eddy covariance fluxes with the source areas of the instruments which measure net radiation and
ground heat flux. In the third part of this work, representative source area for turbulent fluxes
measured by eddy covariance station is investigated through modeling and experimental
campaigns in totally different field situations: bare and vegetated soils. A revisited simple
method based on mobile and fixed eddy covariance stations is found to be helpful in intra-field
spatial variability investigations of turbulent fluxes also over homogeneous canopy such us
maize fields. The results of these experiments lead to interesting improvements about turbulent
flux representative source area knowledge increasing literature results.
This PhD thesis has been conceived as a collection of three strongly connected papers, which
constitute the nucleus of the author research activities. One introduction, at the beginning of the
7
thesis, has been added to briefly explain eddy covariance technique and its mathematical basis.
The PhD thesis is subdivided in three macro chapters which are independently built in order to
simplify the comprehension of the text, giving to the reader the possibility to read each chapter
separately from each others. Each chapter is built with a quite standard structure which is
constituted by a synthetic abstract, an introduction which gives to the reader an overview about
the problems which are developed in the chapter, a theoretical background which is widely
referred to literature works, a site-instrument-data description, result discussions and finally a
conclusion remark. Other author works, which have been developed during his PhD research
period, are quoted in the text and they constitute parallel efforts which allowed completing this
thesis. Here, only the papers which have already been published are shown, while other works
which are in review or in press processes have not been quoted in the reference subparagraphs.
Subparagraph, equation and figure enumerations restart at each chapter to improve the
comprehension of the text. It is an author’s choice to use, into the equations, symbols which are
usually founded in literature articles also if they could be utilized several times into the text with
different meanings which, however, are widely explained in order to prevent any
misunderstanding.
8
General Introduction
In this paragraph a theoretical background about the eddy correlation theory, with reference to
three scientific works (Baldocchi et al. (1988), Verma (1990) and Papale et al. (2006)) is shown.
It does not want to be an exhaustive dissertation about the micrometeorological method but only
a general introduction about the mathematical basis which governs the turbulent flux calculus
methodology focusing on limitations and problems connected to this approach.
Eddy covariance technique
Micrometeorological techniques provide for direct measurements of carbon dioxide, water and
energy flux exchanges between biosphere and the atmosphere. Micrometeorological techniques
have many advantages:
1) They are in situ and do not disturb the environment around the plant canopy.
2) These techniques allow continuous measurements.
3) Time averaged micrometeorological measurements at point provide an area-integrated,
ensemble average of the exchange rates between the surface and the atmosphere.
Defining as net ecosystem exchange the mass or energy quantity exchanged from ecosystem to
atmosphere trough an imaginary surface of interface in a determinate range of time, the
objectives of micrometeorological technique are:
1) To find a simple formulation about net ecosystem exchange which can be applied starting
from measurements carry out using not many expensive instruments;
2) To find a net ecosystem exchange general formulation so that the results can be
considered representative of the ecosystem behavior.
The conservation equation provides the basis framework for measuring and interpreting
micrometeorological flux measurements. In concept, the conservation equation states, which are
represented by the variation at fixed point of a chemical constituent in time, are equal to the sum
of the mean horizontal and vertical advection, mean horizontal and vertical divergence or
convergence of the turbulent flux, molecular diffusion and any source or sink as described by
Eq.1.
cScut
c 2 (1)
Where
t
c is the variation of the concentration (c) of a generic passive scalar in time;
cu
is the turbulent transport of c generated by a wind field described by the vector u
;
S is a source or sink of c in a fixed point in space;
c2 is the molecular diffusion and represents the gas diffusivity in air.
While Eq. 1 represents the instantaneous transport equation, Eq. 2 describes the evolution in time
of the mean concentration of the scalar c (Garrat, 1993).
9
cScut
c 2 (2)
Applying the Reynolds’s decomposition (Foken, 2008) which converts a generic instantaneous
value as a sum of mean component and fluctuant component, in accordance with Reynolds’s
mean proprieties law, it is possible to obtain Eq. 3.
cSz
cw
y
cv
x
cu
z
cw
y
cv
x
cu
t
c 2''' (3)
Where
z
cw
y
cv
x
cu is the advection transport term generated by the mean wind flow;
z
cw
y
cv
x
cu ''' is the advection transport term generated by the turbulent flow.
Eddy correlation theory is based on ideal conditions which permit to simplify Eq. 3 in
accordance with technical objectives described before. Supposing that:
1) Molecular diffusion can be neglected in a turbulent flow;
2) Mean variation of the scalar quantity in horizontal directions can be neglected;
3) Mean vertical velocity can be neglected;
4) The turbulence is homogenous in horizontal directions;
5) The concentration of the constituent does not vary significantly with time;
it is possible to obtain Eq. 4.
z
cwS
t
c '' (4)
As described by Eq. 4, the variation of the mean concentration of gas in time is equal to the
difference between what enters or leaves the controlled volume and turbulent vertical flux.
Integrating Eq. 4 from surface to measurement height (zm) and considering the sum of what
enters or leaves the controlled volume as the net ecosystem exchange (F), it is possible to obtain
Eq. 5.
dzt
ccwF
mz
z 0
'' (5)
Eq. 5 says that the net ecosystem exchange is the sum of turbulent vertical flux and storage term.
The turbulent vertical flux is also called eddy covariance flux, while the storage term represents
gas or energy quantities which are not carried by turbulent flow and remain stored under the
10
measurement point. In first approximation storage term can be neglected and Eq. 5 is simplified
in Eq. 6.
''cwF (6)
The equations of the turbulent fluxes can be summarized in:
1) Sensible heat flux (Eq. 7)
''TwCH pa (7)
2) Latent heat flux (Eq. 8)
''qwLE a (8)
3) Momentum flux (Eq. 9)
''uwa (9)
Where a is the air density, pC is the specific heat capacity of air and is the vaporization latent
heat of water. T’ represents air temperature while q’ water vapor turbulent concentration in the
atmosphere.
For other discussion on the conservation equation, as related to micrometeorological
measurements, the reader should refer to the work of Kanemasu et al. (1979) and Businger
(1986).
References
Baldocchi, D., Hincks, B., & Meyers, T. (1988). Measuring biosphere-atmosphere exchanges of biologically related
gases with micrometeorological methods. Ecology , 69: 1331-1340.
Businger, J. (1986). Evaluation of the accuracy with which dry deposition can be measured with current
micrometeorological techniques. Journal of Climate and Applied Meteorology , 25: 1100-1124.
Foken, T. (2008). Micrometeorology. Berlin: Springer, pp. 306, ISBN 978 3 540 74665 2.
Garratt, J. (1993). The atmospheric boundary layer. Cambridge: Cambridge university press, pp.316, ISBN 0 521
38052 9.
Kanemasu, E., Wesely, M., Hicks, B., & Heilman, J. (1979). Techniques for calculating energy and mass fluxes.
Michigan, USA: Pages 156-182 in B.L. Barfield and J.F.Gerber editors.
Papale, D., Reichstein, M., Aubinet, M., Canfora, E., Bernhofer, C., Kutsch, W., et al. (2006). Towards a
standardized processing of net ecosystem exchange measured with eddy covariance technique: algorithms and
uncertainty estimation. Biogeosciences , 3 : 571-583.
Verma, S. (1990). Micrometeorological methods for measuring surface fluxes of mass and energy. Remote Sensing
Reviews , 5: 99-115.
11
(Chapter 1) - Impact of data corrections on turbulent flux measurements
Abstract
Reliable estimation of evapotranspiration and carbon dioxide fluxes is based on a correction
procedure due to eddy covariance methodology and instrumental characteristics. Literature
standardized methods for data processing are defined for analyzing the quality of high frequency
measurements. However, for operative applications, linked to real time irrigation water
management, high frequency data are difficult to manage. So the objective of this paper is to
verify the possibility of using eddy covariance data in an operative way in order to understand if
averaged data at 30 minutes are still of good quality in relation to those obtained from high
frequency measurements.
Data have been collected by an eddy covariance station over a maize field at Livraga (Lodi,
Italy) for the year 2012. High frequency data (20 Hz) and averaged data (30 minutes) are
collected separately in a PCMICA of 2Gb capacity and data logger memory respectively. High
frequency data are analyzed with Eddy Pro 4.0 open source software. Effects of different types
of corrections, from axis rotation to density fluctuations, are shown. Spectral correction factors
have been calculated and flux losses are estimated. Quality of corrected fluxes and energy
balance closure are also shown.
Averaged data have been analyzed with Polimi Eddy Covariance software (PEC) which accounts
only a portion of the correction procedures which can be applied to high frequency data, where
the major difference is linked to the absence of the spectra correction.
Evapotranspiration and carbon dioxide fluxes from high frequency and average data are then
compared and cumulated trends over the growing season are assessed and a small difference is
found. So these comparisons highlight the possibility of using averaged data for operative water
management without drastically decreasing the quality of fluxes.
Introduction
Energy fluxes developed in a SVAT (Soil-Vegetation-ATmosphere) system are important for a
wide range of applications at different spatial and temporal scales: from flood simulation at basin
scale to water management in agricultural areas. Reliability of eddy covariance measurements
has to be studied before using them in hydrological simulations (Aubinet et al., 2000).
Eddy covariance stations measure turbulent fluxes of sensible and latent heat, net radiation and
heat flux in the soil at agricultural field-scale, having the objective to estimate the correct water
requirement for a crop. The main instruments, which give the name to the eddy covariance
technique, are gas analyzer and tridimensional sonic anemometer. They provide for estimate
turbulent fluxes into surface layer (Stull, 1988), thanks to the covariance between vertical wind
velocity and concentration of a scalar passive (for example: air/water, temperature or carbon
dioxide). Flux estimations are obtained through complex series of steps starting from raw data
acquired with high frequencies of about 10-20 Hz. The quality of these measurements is mainly
influenced by problems of sensor configuration, place of the tower and stability of the
12
atmosphere (Baldocchi, 2001; Foken and Wichura, 1996; Fuehrer and Friehe, 2002). As
described in Moncrieff at al. (1997), eddy covariance technique should be viewed as a 'system' of
measurement, i.e. which includes not only the hardware but also the method of analysis, whether
in real-time or off-line, and the algorithms used to filter or detrend the raw data and to apply
calibrations and corrections. An example of the details and considerations which are necessary in
a typical eddy covariance system is revealed in a series of papers (Shuttleworth et al., 1982,
Shuttleworth et al., 1988 Moore, 1983, Moore, 1986; Lloyd et al., 1984; Shuttleworth, 1988)
which describe not only the used instrumentation, including sensors and microcomputer control,
but also the corrections required for real-time analysis.
The problem of a correct implementation of data correction procedures is strongly connected
with micrometeorological measurements which are often not able to close the surface energy
balance equation (Foken, 2008). Uncertainties in the post-field data processing of eddy
covariance measurements of the turbulent fluxes are suspected to be crucial (Massman and Lee,
2002). Lee et al. (2004) formulate recommendations related to the eddy covariance technique for
estimating turbulent mass and energy exchange, and give a comprehensive overview on the
current state of the art regarding micrometeorological issues and methods.
Eddy Pro 4.0 is an open source software used to calculate turbulent fluxes from high frequency
measurements of wind velocity and gas concentrations. It can be founded at the WEB page
http://www.licor.com/env/products/eddy_covariance/software.html and it has been implemented
by University of Tuscia and Li-Cor industry. In recent decades, other softwares, implemented by
different universities in the world, can be found in literature (TK3, EdiRe, EddySoft, Alteddy)
with the main objective to standardize the correction procedure of eddy covariance
measurements. These softwares have been widely validated and they are all based on five
fundamental points:
1) Measured data are opportunely selected in function of quality tools;
2) Data are calibrated or corrected if necessary;
3) Data are aggregated in statistic tools as mean, variance or covariance;
4) Data are converted in averaged fluxes;
5) Reliability of fluxes is evaluated.
To provide a complete data correction procedure high frequency data are needed because they
can be used to find the reason for possible errors into flux measurements (Ueyama et al., 2012).
However, only averaged data are available sometimes (for example in real time application).
High frequency data acquisition is not practical, considering that data loggers internal memories
are not sufficient to store big quantities of data. Usually, a PCMCIA card allows expanding data
logger memory capacity, so that, high frequency data are stored on this memory card while
averaged data are stored on internal data logger memory. High frequency measurements could be
directly downloaded trough Ethernet or Wi-Fi but in many case eddy covariance system location
does not permit these types of connections. Typically through the use of GSM modem
connection data logger memory could be downloaded on a personal computer which could be
many kilometers away from the station, while the PCMCIA card has to download in situ using a
personal computer and a compact flesh reader, leading to a non operative procedure. In order to
overcome these complications, PEC software which uses directly averaged data to calculate
turbulent fluxes has been implemented (Corbari et al., 2012) and in this work comparison
between Eddy Pro 4.0 and PEC software results are shown.
13
In the first part of this work, an overview of correction procedures which are necessary to obtain
reliable turbulent fluxes is described in reference to Eddy Pro 4.0. Only practical formulas are
shown, while mathematical approaches are quoted in literature. In the second part, the impact of
the various steps of post-field data processing on turbulent flux assesses is investigated. In the
third part, fluxes performed by PEC are compared to the fluxes computed by Eddy Pro 4.0 in
order to understand if reliable latent heat and carbon dioxide fluxes can still be obtained for an
operative use of irrigation water management.
Data collection
Eddy covariance data are measured by a tridimensional sonic anemometer (Young 81000) and
open path gas analyzer (LICOR 7500) located at the top of a tower 5 m high. The tower is placed
in a maize field at the city of Livraga (LO) in the Po Valley. High frequency (20 Hz)
measurements are stored in a compact flesh of 2 Gb connected with the data logger Campbell
CR5000 and downloaded in situ weekly. On compact flash only three wind velocity components,
sonic temperature, vapor and carbon dioxide concentrations are stored (raw data). Data logger
program is directly set to calculate averaged data over a time step of 30 minutes, and these data
are collected into data logger internal memory. Contemporaneously, net radiation, measured by
CNR1 Kipp&Zonen radiometer, soil heat flux, measured by HFP01 Campbell Scientific flux
plate, and soil temperature measurements are stored on data logger in different memory tables.
While high frequency data are directly used by Eddy Pro 4.0 software, 30 minutes averaged data
are the starting point for the fluxes computation using PEC software.
Experimental measurements were carried out from 21 May 2012 to 7 September 2012 but the
dataset is composed by only 3103 averaged data because some gaps due to malfunctioning of
instrumentations or rainfall days are shown into the data sequences. From 131 to 241 Julian days
the field is covered by vegetation, while the remaining days of the year, the field is characterized
by bare soil.
Preliminary processes for correction procedure
Before calculating fluxes, high frequency data have to be adjusted and if necessary neglected.
The different types of corrections are now analyzed.
Axis rotation for tilt correction
Each anemometer model adopts a customized convention for providing wind components in an
orthogonal coordinate system, so that the user is able to retrieve the actual wind direction with
respect to geographic north. Anemometer north is shown on Young 81000, by an “N” on
junction box. Wind components are indicated with u (positive if wind from East), v (positive if
wind from North), and w (positive if wind from below) and they represent x,y,z directions
respectively.
Tilt correction algorithms are necessary to correct wind statistics for any misalignment of the
sonic anemometer with respect to the local wind streamlines. In particular, this implies that
14
fluxes which are evaluated perpendicular to the local streamlines are affected by spurious
contributions from the variance of along-streamlines components. Wilczak et al. (2001),
proposes three typologies of correction algorithms: double rotation, triple rotation, and the planar
fit method. For Livraga 2012 dataset a double rotation method has been used.
Double rotation method
With this method, the anemometer tilt is compensated by rotating raw wind components to
nullify the average cross-stream and vertical wind components, evaluated on the time period
defined by the flux averaging length (30 minutes). The rationale is that cross and perpendicular
wind components are averaged to zero during such time period. In the first rotation, the
measured wind vector is rotated about the z axis with objective to nullify v component.
Successively, a second rotation is performed on a new y axis with the objective to nullify w
component (for mathematical implementation of this method see Wilczak et al., 2001).
Spike removal
The so called despiking procedure consists in detecting and eliminating short term outranged
values in the time series. Following Vickers and Mahrt (1997), for each variable a spike is
detected as up to three consecutive outliers with respect to a plausibility range defined within a
certain time window, which moves throughout the time series. The rationale is that if more
consecutive values are found to exceed the plausibility threshold, an unusual physical trend can
be identified. The width of the moving window is defined as one sixth of the current flux
averaging period and the plausibile range is quantified differently for each variable. Tab. 1
provides default values used in Eddy Pro 4.0. The window moves forward half its length at a
time. The procedure is repeated up to twenty times or until no more spikes are found for all
variables. Detected spikes are counted and replaced by linear interpolation of neighboring
values.
Tab. 1. Plausibility range for spike detection for each sensitive variable.
Variable Plausibility Range
u,v Window mean +/- 3.5 standard deviation
w Window mean +/- 5.0 standard deviation
CO2,H2O Window mean +/- 3.5 standard deviation
Temperatures, Pressures Window mean +/- 3.5 standard deviation
Time lag compensation
In open path system the time lag between anemometric variables and variables measured by gas
analyzer is due to the physical distance between the two instruments, which are usually placed
several decimeters or less apart to avoid mutual disturbances. The wind field takes some time to
15
travel from one instrument to the other, resulting in a certain delay between the moments the
same air parcel is sampled by the two instruments.
It is a common practice to compensate for time lags before calculating covariances between
anemometric variables and gas analyzer measurements.
In literature four different alternative methods for detecting and compensating time lags exits:
constant time lag, covariance maximization, covariance maximization with default and automatic
time lag optimization (Runkle et al., 2012; Fan et al., 1990; Eddy Pro 4.0 manual, 2012). For
Livraga 2012 dataset covariance maximization method has been used.
Covariance maximization method
The variability of wind regimes (in open path systems) suggests an automatic time lag detection
procedure, normally performed for each flux averaging period. Typically the detection is
accomplished via the covariance maximization procedure, consisting in the determination of the
time lag that maximizes the covariance of two variables, within a window of plausible time lags
(Fan et al., 1990).
Using the covariance maximization procedure a plausible time lag window has to be defined
with the minimum and maximum time lags, which constitute the end points of the plausibility
window. A too narrowed plausible window might lead to frequent use of the default (covariance
maximization with default) or either endpoint (covariance maximization) time lag, because the
actual time lag is often found to be outside the defined plausibility range. This situation leads to
systematic flux underestimations. Conversely, imposing a too broad plausibility window, the
possibility that unrealistic time lags are detected increases, especially when covariances are small
and vary erratically with the lag time. These cases often result in flux overestimations. A trade-
off must be reached between the two contrasting needs.
Detrending
Eddy correlation method of calculating fluxes requires that the fluctuating components of the
measured signals are derived by subtracting them from the mean signals. In steady-state
conditions simple linear means would be adequate, but steady state conditions rarely exist in the
atmosphere and it is necessary to remove the long term trends in the data which do not contribute
to the flux (Gash and Culf, 1996).
Different methods are described in literature for extracting turbulent fluctuations from time
series data. The most commonly applied, in the context of eddy covariance, are the block-
averaging, linear detrending (Gash and Culf, 1996) and two types of high-pass filters, namely the
moving average (Moncrieff et al., 2004) and the exponentially weighted average (McMillen,
1988; Rannik and Vesala, 1999). For Livraga 2012 data set the linear detrending is used.
Linear detrending
Gash and Culf (1996) show that it is possible to apply a linear detrend to eddy correlation data
and calculate variances and fluxes in a single pass operation, accumulating an appropriate
16
combination of the sum of fluctuating variables and their cross products. Linear detrending
method is generally done retrospectively using a two-pass method. The data are first divided into
blocks each long normally 20-30 minutes, and a linear regression of the measured signal on time
is then calculated. The fluctuations with respect to the regression line are then calculated during
a second pass through the data. An alternative approach, proposed by Gash and Culf (1996), is to
calculate the fluxes with respect to a filtered “mean”, which is derived by feeding the measured
signal through a low-pass filter. Since this is a single pass method it can be used in real-time to
calculate the fluxes as the data are collected.
Calculating fluxes
After completing the preliminary processes, it is possible to calculate turbulent fluxes, starting
from uncorrected fluxes. Uncorrected fluxes represent gas, energy, and momentum fluxes which
are obtained by merely adjusting units of relevant covariances, in order to match the desired
output units.
This operation may imply the inclusion of some previously calculated physical parameters
described in Eddy Pro manual. These fluxes are uncorrected because some effects are not
accounted in their calculation, notably the effects of air density fluctuations, of spectral losses,
and effects of humidity on air temperature estimation through the sonic anemometer.
Uncorrected fluxes – level 0
The uncorrected fluxes are calculated according to the following equations:
1) Sensible heat flux
''0 spa TwcH (1)
2) CO2 flux, if CO2 is measured as molar density with an open path analyzer
''10 2
3
2,0 COCO dwF (2)
3) H2O flux, if H2O is measured as molar density with an open path analyzer
'' 22,0 OHOH dwF (3)
4) Latent heat flux
OHOH MFLE 22,0
3
0 10 (4)
5) Evaporatranspiration flux
OHOH MFE 22,0
3
0 10 (5)
6) Momentum flux
22
0 '''' wvwuT a (6)
Where
0H is the uncorrected sensible heat (W m-2
).
a is the air density (Kg m-3
).
pc is the air heat capacity at constant pressure (J Kg-1
K-1
).
17
'' sTw is the covariance between turbulent vertical wind velocity ( m s-1
) and sonic temperature
(°C).
2,0 COF is the uncorrected CO2 flux (micromol m-2
s-1
)
'' 2COdw is the covariance between turbulent vertical wind velocity ( m s-1
) and moles of CO2 per
unit of volume (millimol m-3
).
OHF 2,0 is the uncorrected H2O flux (millimol m-2
s-1
).
'' 2OHdw is the covariance between turbulent vertical wind velocity ( m s-1
) and moles of H2O per
unit of volume (millimol m-3
).
0LE is the uncorrected latent heat (W m-2
).
is the latent heat of water vaporization (J Kg-1
).
OHM 2is the molecular weight of H2O (Kg mol
-1).
0E is the uncorrected evapotranspiration flux (Kg m-2
s-1
).
0T is the uncorrected momentum flux (Kg m-2
s-1
).
''wu and '' wv is the covariance between horizontal turbulent wind velocities and vertical
turbulent wind velocity, both calculated in m s-1
.
The subscript “0” indicates the level of correction.
Spectral correction factors – level 1
Spectral corrections compensate flux underestimations due to two distinct effects. The first is
referred to the fluxes which are calculated on a finite averaging time, implying that longer-term
turbulent contributions are under-sampled at some extent, or completely. The correction for these
flux losses is referred to as high-pass filtering correction because the detrending method acts
similarly to a high-pass filter, by attenuating flux contributions in the frequency range close to
the flux averaging interval. The second is connected with instrument and setup limitations that
do not allow sampling the full spatiotemporal turbulence fluctuations and necessarily imply
some space or time averaging of smaller eddies, as well as actual dampening of the small-scale
turbulent fluctuations. The correction for these flux losses is referred to as low-pass filtering
correction. Mathematical approach to calculate spectral corrections can be found in Moncrieff et
al. (1997).
For any given flux, the spectral correction procedure requires a series of conceptual steps which
can be found in Ibrom et al. (2007) and Massman (2004) works:
1) Calculation or estimation of a reference flux cospectrum, representing the true spectral
content of the investigated flux as it would be measured by a perfect system.
2) Estimation of the high-pass and low-pass filtering properties implied by the actual
measuring system and the chosen averaging period and detrending method.
3) Estimation of flux attenuation.
4) Calculation of the spectral correction factor (SCF) and application of the correction.
Spectral corrections are implemented on Livraga 2012 dataset. High-pass filtering correction is
applied following Moncrieff et al. (2004) while for low-pass filtering correction a fully analytic
method described in Moncrieff et al. (1997) is applied.
18
SCF is defined as the ratio between the integral of theoretical cospectrum model and the integral
of measured co spectrum (Moncrieff et al., 1997). Measured co spectrum can be obtained
starting from theoretical co spectrum multiplied for a transfer function which describes the
proprieties of the measurement system (Eq. 7).
dffTfCo
dffCoSCF
F
Theo
i
Theo
i
i)()(
)( (7)
Where Theo
iCo is the theoretical co spectrum of the flux i, FT is the transfer function and f is the
frequency. SCF is always major of 1 because it has to compensate flux underestimations caused
by the problems described in section 4.2. The most widely used theoretical co spectral models
are those from Kaimal et al. (1972). Moore (1986) proposes a scheme whereby a series of
transfer functions could be defined for each of the correction terms required in an eddy
covariance system. The transfer function defines the system reliance on different factors as
digital recursive running mean, dynamic frequency response of the sensors, sensors response
mismatch, scalar path averaging and so on, each connected with the typology of anemometer and
gas analyzer used on the eddy covariance tower (Massman, 2000).
Starting from SCF, it is possible to calculate the fractional error on the measured flux as Eq.8
(Moncrieff et al., 1997).
1001
1(%)i
iSCF
lossFlux (8)
Where Flux loss defines the whole system flux losses.
Spectral corrections are applied first to open path fluxes. This is because sensible and latent heat
fluxes used in the Webb-Pearman-Leuning (WPL) correction (Webb et al., 1980) are the
“environmental ones”, those actually present in the atmosphere and affecting measurements of
molar densities in open path analyzer.
Marking as 1 the fluxes obtained after spectral corrections, CO2, H2O latent heat and
evapotranspiration fluxes are described by Eq. 9, Eq. 10, Eq. 11 and Eq.12 respectively.
2,2,02,1 COwCOCO SCFFF (9)
OHwCOOH SCFFF 2,2,02,1 (10)
OHwSCFLELE 2,01 (11)
OHwSCFEE 2,01 (12)
Where 2,COwSCF and OHwSCF 2, are the spectral correction factors calculated for CO2 and H2O
respectively.
Furthermore, uncorrected momentum flux is corrected using the relevant spectral correction
factor wuSCF , (Eq. 13).
19
wuSCFTT ,01 (13)
Corrected fluxes – level 2 and 3
After the spectral correction, evapotranspiration flux is at first corrected with the WPL term,
following the formulation proposed in Webb et al. (1980) (Eq.14).
apa
w
Tc
HEE 0
12 )1()1( (14)
Where
is the ratio between molar density of dry air and molar density of the water ( non
dimensional).
is the water to dry air density ratio (non dimensional).
aT is the ambient air temperature (°C).
wis the water density (Kg m
-3).
Sonic temperature and sensible heat flux are corrected for humidity effects following van Dijk et
al. (2004), revising Schotanus et al. (1983) (Eq. 15). In next sections, this correction is simply
called VD.
''202 s
a
spa TwQE
TcHH (15)
Where is a constant equals to 0.51 and Q is the specific humidity (non dimensional).
H2 is then spectrally corrected to get the first fully corrected flux (Eq. 16).
TswSCFHH ,23 (16)
Where TswSCF , is the spectral correction factor calculated for sonic temperature. When CO2 and
H2O molar densities are measured with an open path gas analyzer in cold environmental (with
low temperature below -10 °C) H0 has to be corrected to account for the additional instrument-
related sensible heat flux, due to instrument surface heating/cooling. This correction is fully
described and tested in literature (Burba et al., 2008).
Now that sensible heat is fully corrected, evapotranspiration flux is corrected again, adding the
WPL terms with the revised H (Eq. 17).
apa
w
Tc
HEE 3
13 )1()1( (17)
Water vapor and latent heat fluxes are easily determined:
20
OHOH MEF 23
3
2,3 10 (18)
33 ELE (19)
Now that evapotranspiration and sensible heat fluxes are fully corrected, fluxes of other gases
such as carbon dioxide can be corrected for air density fluctuations, according to Webb et al.
(1980). For carbon dioxide we get the Eq. 20.
apa
CO
d
COCOCO
Tc
dHC
dEBFAF 232
12,12,2 1 (20)
Where A, B and C are multipliers described in Webb et al. (1980). Finally, corrected fluxes of
CO2 (F3,CO2) in a system with open path instrument, coincide with fluxes at level 2.
Results
As shown in the previous paragraphs, correction procedures can be summarized in three groups:
preliminary processes, spectral corrections, WPL and VD corrections. In this section the impact
of correction procedures in half-hourly measurements is quantified. With the expectation of the
corrected fluxes calculation, results of the standardized processing procedure described above
are performed. In general, to quantify the impact of each correction procedure, the slope and
intercept values between the post-processed fluxes and pre-processed fluxes from a regression
analysis on half hourly basis, have been calculated. The slope represents a difference in
proportion to flux magnitude, and the intercept represents a constant difference on all flux range.
Effect of the preliminary processes on raw data
Preliminary processes should be applied on raw data measurements to prepare the dataset for
fluxing calculation. In Fig.1 the effect of different correction methods on each u, v, w, H2O and
CO2 averaged component is shown.
A B
-6
-4
-2
0
2
4
6
218 218.2 218.4 218.6 218.8 219
Win
d v
elo
city
(m
s-1
)
Julian day
u (raw data)
u (raw data+despiking+double
rotation+time lag+detrending)
0
200
400
600
800
1000
1200
1400
215 215.2 215.4 215.6 215.8 216
Ga
s co
nce
ntr
ati
on
(m
illi
mo
l m
-3)
Julian day
H2O (raw data)
H2O (raw data+despiking+double
rotation+time lag+detrending)
21
C D
-6
-4
-2
0
2
4
6
218 218.2 218.4 218.6 218.8 219
Win
d v
elo
city
(m
s-1
)
Julian day
v (raw data)
v (raw data+despiking+double
rotation+time lag+detrending)
5
10
15
20
25
30
227.5 227.7 227.9 228.1 228.3 228.5
Ga
s co
nce
ntr
ati
on
(m
illi
mo
l m
-3)
Julian day
CO2 (raw data)
CO2 (raw data+despiking+double
rotation+time lag+detrending)
E
-0.4
-0.3
-0.2
-0.1
0
0.1
218 218.2 218.4 218.6 218.8 219
Win
d v
elo
city
(m
s-1
)
Julian day
w (raw data)
w (raw data+despiking+double
rotation+time lag+detrending)
Fig. 1. Effects of the preliminary correction methods on wind velocities (A, C, E) and gas
concentrations (B, D).
Double rotation method produces a modification of the anemometer coordinate system (x,y,z) in
respect to the local wind streamlines. The consequence of these rotations is that v and w wind
components are led to zero (Fig. 1C and E) while u turns out to be characterized only by positive
terms (Fig. 1A). This effect is also shown Fig. 2A where the dots, which represent modulus of u
after double correction, take place only in first and fourth sectors. The effect of double rotation is
major in correspondence of weak wind intensity. The modulus of u is subject to slight variations
in a range of wind velocity between -3 m s-1
and 3 m s-1
; while no variation are present for high
values of modulus of u, and the dots stay on bisectors of first and fourth sectors (grey line). CO2
and H2O concentrations are not particularly affected by preliminary corrections procedures (Fig.
2B and C), and only in correspondence of the raw data peaks, data corrections are relevant (Fig.
1B and D). This behavior could be a good indicator of the reliability of the gas analyzer
measurements. In fact, calculating over the experimental period the mean differences between
CO2 and H2O raw data concentrations and CO2 and H2O corrected concentrations (after the
application of the preliminary processes), the results are quite similar and equal to -0.0274
millimol m-3
and 0.118 millimol m-3
respectively.
22
A B
0
1
2
3
4
5
6
7
8
9
-8 -6 -4 -2 0 2 4 6 8
u -
win
d c
orr
ecte
d v
elo
city
(m
s-1
)
u - wind raw data velocity (m s-1)
0
200
400
600
800
1000
1200
1400
1600
0 200 400 600 800 1000 1200 1400 1600
H2O
co
rrec
ted
co
nce
ntr
ati
on
(mil
lim
ol
m-3
)
H2O raw data concentration (millimol m-3) C
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30 35 40
CO
2co
rrec
ted
co
nce
ntr
ati
on
(mil
lim
ol
m-3
)
CO2 raw data concnetration (millimol m-3)
Fig. 2. Comparison between mean raw data of u (A), H2O (B) and CO2 (C) concentrations before
and after preliminary correction procedures.
Effect of the preliminary processes on uncorrected fluxes
When fluxes directly obtained by raw data covariances and those calculated after preliminary
processes (uncorrected – level 0) are compared, slight differences are found, and in Fig.3 the
results are shown. The differences are quantified as slope between uncorrected fluxes and raw
data fluxes from a regression analysis on half-hourly basis. The (1-slope) and intercepts
quantities measure the difference in flux magnitude after the application of correction procedure
while R2 represents the dots dispersion around the regression line which describes the
amplification of the random error (Ueyama et al., 2012).
A
0.20
0.40
0.60
0.80
1.00
1.20
0.20
0.40
0.60
0.80
1.00
1.20
FH2O FCO2 LE H
R2
(-)
Slo
pe
(-)
Slope
R2
23
B C
-2.40
-2.00
-1.60
-1.20
-0.80
-0.40
0.00
0.40
FH2O FCO2*
Inte
rcep
t (m
illi
mo
l m
-2s-1
)
-6.00
-4.00
-2.00
0.00
2.00
4.00
LE H
Inte
rcep
t (W
m-2
)
Fig. 3. A. Slope and R2 determined by regression of half-hourly fluxes before and after
preliminary corrections. B and C. Intercepts of the regression lines. In FCO2* the intercept is
represented as (millimol m-2
s-1
)103.
As shown in Fig. 3A, preliminary corrections produce a decrease of flux intensities which varies
from 8% for latent heat and H2O to 36% for CO2. Only sensible heat has a slight increase of
about 6%. For momentum flux (not shown in figure) slope is equal to 0.86 while intercept is
about -0.01 Kg m-2
s-1
, therefore preliminary processes produce a decrease of about 14% in its
flux magnitude. Evaluating mean slope performed over the whole preferable fluxes (from vapor
to momentum), the preliminary corrections produce a decrease of turbulent flux intensities of
about 12%. R2 deviates from 1 of about 18% on all fluxes, except for CO2 where R
2 is equal to
0.47, indicating that, for this flux, application of preliminary processes create random error
amplification. Moderated shifts of turbulent flux mean intensities are shown Fig.3B and C,
where the range of intercept values vary from -5 W m-2
for sensible heat to 1.71 W m-2
for latent
heat. For CO2 flux the intercept is equal to -2.3 micromol m-2
s-1
while for H2O flux preliminary
processes do not play a substantial role in the alteration of its mean intensity.
As shown in Fig. 4, where the trend of fluxes over an experimental day is shown, spike removal
correction leads to the elimination of some peaks of data. However, the remaining peaks in the
flux series may be due to particular physical phenomena related with atmospheric or field events.
A B
-100
-80
-60
-40
-20
0
20
40
60
80
100
217 217.2 217.4 217.6 217.8 218
CO
2fl
ux
(m
icro
mo
l m
-2s-1
)
Julian day
Fo,CO2 (from raw data)
Fo,CO2 (uncorrected)
-30
-20
-10
0
10
20
30
217 217.2 217.4 217.6 217.8 218
H2O
flu
x (
mil
lim
ol
m-2
s-1)
Julian day
Fo,H2O (from raw data)
Fo,H2O (uncorrected)
24
C D
-200
-100
0
100
200
218.0 218.2 218.4 218.6 218.8 219.0
Sen
sib
le h
eat
flu
x (
W m
-2)
Julian day
Ho (from raw data)
Ho (uncorrected)
-500
-250
0
250
500
218.0 218.2 218.4 218.6 218.8 219.0
La
ten
t h
eat
flu
x (
W m
-2)
Julian day
LEo (from raw
data)
Fig. 4. Comparison between mean raw data fluxes before and after preliminary correction
procedures.
Effect of the spectral corrections on turbulent fluxes
n Fig.5, spectral correction impact over uncorrected turbulent fluxes is shown. In this case, slope
represents the ratio between fluxes at level 1 and fluxes at level 0. Only for sensible heat the ratio
is calculated between H3 and H2 because the spectral correction is applied after the WPL and VD
equations. Spectral correction factor is a value always greater than 1, and this produce, on all
turbulent fluxes (including momentum flux), a systematic growth in slope of about 10%
(Fig.5A). The regression coefficient (R2) is closed at about 0.99 on all fluxes. The maximum
intercept values are in correspondence with CO2 and latent heat fluxes where the difference
before and after the application of the spectral correction is equal to 0.61 micromol m-2
s-1
and
0.60 W m-2
respectively (Fig. 5B and C), while H2O and sensible heat intercepts are near to zero.
A
0.8
0.9
1.0
1.1
1.2
0.6
0.8
1
1.2
1.4
FH2O FCO2 LE H
R2 (-)
Slo
pe
(-)
Slope
R2
B C
0
0.2
0.4
0.6
0.8
FH2O FCO2*
Inte
rcep
t (m
illi
mo
l m
-2s-1
)
0
0.2
0.4
0.6
0.8
LE H
Inte
rcep
t (
W m
-2)
Fig. 5. A. Slope and R2 calculated by regression of half-hourly fluxes before and after the application of SCF on uncorrected
fluxes. B and C. Intercepts of the regression lines. In FCO2* the intercept is represented as (millimol m-2 s-1
) 103.
25
In the next sessions flux losses for the whole range of turbulent fluxes are investigated with the
objective to understand if some atmospheric or turbulent characteristics could influence the
spectra or cospectra information losses. In Fig. 6 the flux losses (for water vapor, carbon dioxide,
latent heat, sensible heat and momentum fluxes), in function of the main atmospheric proprieties,
are shown.
Flux loss in function of air temperature and relative humidity
Minimum value of flux loss for momentum and sensible heat is about 0.7% while maximum
value of flux loss is about 30%. For latent heat, CO2 and H2O minimum flux loss is about 7%
while the maximum flux loss is about 87%. This is probably due to the proprieties of transfer
function ( FT ) which is calculated as a product of different transfer functions connected with
characteristics of the systems used to measure eddy covariance variables (Moore, 1986).
Sensible heat and momentum fluxes can be calculated starting only from data measured by sonic
anemometer instrument, so that transfer function has to take into account only anemometer
signal losses. Instead, latent heat, H2O and CO2 fluxes are calculated using sonic anemometer
and gas analyzer contemporaneously. In this case, the transfer function has to take into account
flux information losses derived by anemometer and gas analyzer with a consequent rising in the
turbulent flux loss. For all fluxes, the flux loss is not particularly influenced by air temperature.
In general, a random distribution of the dots is shown in correspondence with a range of
temperature which varies from 10 °C to 30 °C. Major dispersion of dots is shown in association
with latent heat, CO2 and H2O fluxes with a standard deviation in flux loss of about 9%. Air
humidity plays a modest role on flux loss. For high values of relative humidity, dispersion of
dots and flux loss tend to increase up to maximum values of 30% (for sensible heat and
momentum fluxes) and 87% (for latent heat, H2O and CO2 fluxes). As shown in Runkle et al.
(2012), relative humidity plays a fundamental role on time lag of close-path gas analyzers, where
the time lag is a parameter included in the transfer function implementation (Massman, 2000).
Fig. 6 results show that high air humidity concentrations (also in an open path gas analyzer)
could influence transfer function with a consequent increase in flux loss.
26
Mo
men
tum
flu
x
Sen
sib
le h
eat
Lat
ent
hea
t
CO
2 f
lux
H2O
flu
x
Air Temperature Relative humidity Wind velocity Friction velocity Stability parameter
Fig. 6. Flux loss in function of atmospheric characteristics.
0
10
20
30
40
50
60
70
80
90
10
0
05
10
15
20
25
30
35
Flux loss (%)
Air
te
mp
era
ture
(C
)
0
10
20
30
40
50
60
70
80
90
10
0
05
10
15
20
25
30
35
Flux loss (%)
Air
te
mp
era
ture (
C)
0102030405060708090100
05
1015
2025
3035
Flux loss (%)
Air
te
mp
era
ture
(C
)
0
10
20
30
40
50
60
70
80
90
10
0
05
10
15
20
25
30
35
Flux loss (%)
Air
te
mp
era
ture
(C
)
0
10
20
30
40
50
60
70
80
90
10
0
01
02
03
04
05
06
07
08
09
01
00
Flux loss (%)
Rea
ltiv
e h
um
idit
y (%
)0
10
20
30
40
50
60
70
80
90
10
0
01
02
03
04
05
06
07
08
09
01
00
Flux loss (%)R
ealt
ive
hu
mid
ity
(%
)
0102030405060708090100
010
2030
4050
6070
8090
100
Flux loss (%)
Rea
ltiv
e h
um
idit
y (%
)
0
10
20
30
40
50
60
70
80
90
10
0
01
02
03
04
05
06
07
08
09
01
00
Flux loss (%)
Rea
ltiv
e h
um
idit
y (%
)
0
10
20
30
40
50
60
70
80
90
10
0
01
02
03
04
05
06
07
08
09
01
00
Flux loss (%)
Rea
ltiv
e h
um
idit
y (%
)
0.11
10
10
0
02
46
81
0
Flux loss (%)
Win
d v
elo
city
(m
s-1
)0
.11
10
10
0
02
46
81
0
Flux loss (%)
Win
d v
elo
cit
y (m
s-1
)110100
02
46
810
Flux loss (%)
Win
d v
elo
city
(m s
-1)
1
10
10
0
02
46
81
0
Flux loss (%)
Win
d v
elo
city
(m
s-1
)
1
10
10
0
02
46
81
0
Flux loss (%)
Win
d v
elo
city
(m
s-1
)
1
10
10
0
00
.51
1.5
2
Flux loss (%)
Fri
ctio
n v
elo
city
(m
s-1
)1
10
10
0
00
.51
1.5
2
Flux loss (%)
Fri
ctio
n v
elo
city
(m
s-1
)
110
10
0
00
.51
1.5
2
Flux loss (%)
Fri
ctio
n v
elo
city
(m
s-1
)
0.11
10
10
0
00
.51
1.5
2
Flux loss (%)
Fric
tio
n v
elo
cit
y (
m s
-1)
0.11
10
10
0
00
.51
1.5
2
Flux loss (%)
Fri
ctio
n v
elo
city
(m
s-1
)
0
10
20
30
40
50
60
70
80
90
10
0
-50
-30
-10
10
30
50
Flux loss (%)
Sta
bil
ity
pa
ram
eter
(-)
0
10
20
30
40
50
60
70
80
90
10
0
-50
-30
-10
10
30
50
Flux loss (%)
Sta
bil
ity
pa
ra
mete
r (-)
010
2030405060708090
10
0
-50
-30
-10
103
050
Flux loss (%)
Sta
bil
ity
pa
ram
eter
(-)
0
10
20
30
40
50
60
70
80
90
10
0
-50
-30
-10
10
30
50
Flux loss (%)
Sta
bil
ity
pa
ram
eter
(-)
0
10
20
30
40
50
60
70
80
90
10
0
-50
-30
-10
10
30
50
Flux loss (%)
Sta
bil
ity
pa
ram
eter
(-)
0
10
20
30
40
50
60
70
80
90
10
0
05
10
15
20
25
30
35
Flux loss (%)
Air
te
mp
era
ture
(C
)
27
Flux loss in function of wind velocity and friction velocity
In Po Valley wind velocity intensities are not particularly elevated. During unfavorable weather
conditions maximum velocities can be up to about 10 m s-1
. As shown in Moncrieff et al. (1997),
low wind speed, which favors a greater proportion of large eddies, produces a flux
underestimation. In Fig. 6 graphs of flux loss in function of wind velocity and friction velocity
are shown in a semi logarithmic Cartesian plane to highlight the negative effect of slow wind
velocities. For wind velocities of about 2.5 m s-1
, flux loss tends to be stabilized at about 10%.
Analyzing the trend with wind velocities higher than 4 m s-1
, flux underestimation tends to
increase slightly in a linear way. However, the experimental design for a limited range of wind
intensity does not permit to understand if also high velocities could add flux losses. Moncrieff et
al. (1997) show that in a close-path gas analyzer, errors occur with high wind speed and when
the instruments are near the ground leading to a flux loss up to 40% with a wind velocity of
about 8 m s-1
. Even if an open path anlyzer is a completely different instrument in respect to a
close path, it is constituted as well by an optical window which should modify wind flow during
its passage through it with a consequent slight increase of information loss.
Friction velocity is a characteristic parameter of mechanical turbulence (Foken, 2008).
Turbulence is an important issue connected with the correct measurement obtained by eddy
covariance stations. Eddy covariance technique is based on measurement of wind and gas
concentrations turbulent variables in atmospheric surface layer (Foken, 2008; Garrat, 1993).
Laminar flows or advection conditions represents negative situations where the eddy covariance
station is not able to measure correctly fluxes. As shown in Fig.6, for small values of friction
velocity, flux loss increases drastically. In many different literature works (Aubinet et al., 2000;
Falge et al., 2001), friction velocity is used as a threshold which indicates the level of turbulence
in a site. Reichstein et al. (2002) assumes that all eddy covariance data with u* < 0.2 m s-1
should
be excluded from the analysis, as it is likely that under these conditions storage and advection
can reduce gas fluxes through the boundary layer. However, as shown in Barr et al. (2006), 0.2
m s-1
can not be used as a universal threshold value, but it has to be estimated starting from
micrometeorological parameters measured by the tower at each site. From results shown in Fig.
6, optimal u* threshold definition could not be individuated. To provide the u* threshold, Papale
et al. (2006) method should be applied but, it is not an objective of this work.
Flux loss in function of stability parameter
Stability parameter is defined as the ratio between measurement height (taking into account
about displacement height) and Monin-Obukhov length (Obukhov, 1946). It is a dimensionless
parameter that characterizes turbulent processes in the surface layer, and it is described by Eq.21.
L
dz )( (21)
Where
is the stability parameter (non dimensional).
z is the measurement height (m)
28
d is the displacement height described in Foken (2008) (m).
L Monin-Obukhov length (m).
Monin-Obukhov length is defined as the ratio between mechanical and convective forces as
shown in Eq. 22.
''
*3
Twkg
uTL a (22)
Where
Ta is the main air temperature (K).
u* is the friction velocity (m s-1
).
k is the Von Karman constant (0.4) (non dimensionaless).
g is the gravity acceleration (m s-2
).
Starting from Monin-Obukhov length, it is possible to define if the atmosphere is in convective,
stable or adiabatic conditions (Foken, 2008). When L<0 ( ''Tw >0 and 0 ) atmosphere is in a
convective condition, L>0 ( ''Tw <0 and 0 ) atmosphere is in a stable condition and |L| =
( ''Tw and tend to 0) atmosphere is in adiabatic condition.
Spectral and co spectral theoretical models are described with different formulations respect to
the stability characteristics of the atmosphere (Kaimal et al., 1972) and, as a consequence of this
reason, stability parameter plays an important role on flux loss with a substantial difference
between stable or convective conditions. As shown in Fig. 6, during convective conditions flux
loss is constant (about 8%), while in stable conditions flux loss tends to increase rapidly (up to
80%). That being so, turbulence generated by convective and mechanical forces
contemporaneously is necessary to guarantee a minimum flux loss. Starting from all
experimental data set, assuming that convective conditions is verified when 1.0 , stable
conditions when 1.0 and near adiabatic conditions when 1.01.0 (Foken, 2008), 43%
of data is in convective conditions, 33% in stable conditions and 25% is in adiabatic conditions.
Daily and seasonal trend of flux losses
In Fig. 7 daily and seasonal trend of flux losses are shown. During daytime the averaged flux
losses are smaller than night time of about 10% (Fig. 7A). From 6 A.M. to 18 P.M. for latent
heat, carbon dioxide and air vapor fluxes, flux loss is about 8%. Form 18 P.M. to 6 A.M. the flux
loss is about 17%. Considering the effect of stability conditions on flux losses, these results are
in accordance with those obtained in many literature works and in Masseroni et al. (2011) which,
starting from eddy covariance data sets measured in Landriano and Livraga in the year 2011,
shows that convective situations are prevalent during day time while in the night time the stable
conditions are dominant. Sensible heat and momentum fluxes are characterized by a small flux
loss of about 2% for the entire day. This marked difference in flux loss between latent heat,
carbon dioxide, air vapor fluxes and sensible heat, momentum fluxes is probably due to the
proprieties of the transfer functions. Combination of several instruments to measure a flux give a
contribute to increase flux loss.
29
A peak of flux loss (of about 15% for latent heat, CO2 and H2O fluxes) is located at July but, as
shown in Fig. 7B, a seasonal trend is not definable.
A B
0
2
4
6
8
10
12
14
16
18
20
0-6 6-12 12-18 18-24
Flu
x lo
ss (
%)
Time (h)
Momentum flux
Sensible heat flux
Latent heat flux
Carbon dioxide flux
Water vapour flux
0
2
4
6
8
10
12
14
16
18
20
Flu
x lo
ss (
%)
Momentum flux
Sensible heat flux
Latent heat flux
Carbon dioxide flux
Water vapour flux
Fig. 7. Daily (A) and seasonal (B) trends of flux losses.
Effect of the WPL and VD corrections on fluxes at level 3
After the application of the preliminary processes and spectral corrections, turbulent fluxes need
to be corrected for density fluctuation and humidity effects trough the WPL and VD algorithms
(Leuning, 2004). VD correction impact on sensible heat (Eq. 15) produces a decrease in its
uncorrected value (H0) as a consequence of the humidity effect on sonic temperature, while WPL
correction is an additive terms for the uncorrected fluxes of latent, vapor and carbon dioxide as
shown by Eq. 14 and Eq. 20.
All flux estimations, with the exception of momentum flux, change in magnitude after the
application of these corrections (as shown in Fig. 8A). The slope is calculated as the ratio
between corrected fluxes at level 3 and fluxes at level 1 (after the spectral corrections), while for
sensible heat the ratio is performed between H2 and H0. From H2O flux to latent heat, an
important increase in magnitude of fluxes is caused by WPL correction, while for sensible heat
VD correction produces a decrease of the mean intensity. Magnitude of the differences is about
20% for H2O, CO2 and latent heat, while for sensible heat the examined difference is about -
15%. A constant increase of flux is presented in CO2 terms where the intercept is 2.2 micromol
m-2
s-1
(Fig. 8B). On the contrary, sensible heat is subjected to a decreasing of flux of about -4 W
m-2
(Fig. 8C).
A
0.8
0.9
1
1.1
1.2
0.8
1
1.2
1.4
FH2O FCO2 LE H
R2(-
)
Slo
pe(-
)
30
B C
0
0.6
1.2
1.8
2.4
FH2O FCO2*
Inte
rcep
t (m
illi
mo
l m
-2s-1
)
-5.6
-3.6
-1.6
0.4
2.4
LE H
Inte
rcep
t (W
m-2
)
Fig.8. A. Slope and R2 calculated by regression of half-hourly fluxes before and after the
application of WPL and VD corrections on fluxes at level 1. B and C. Intercepts of the regression
lines. In FCO2* the intercept is represented as (millimol m-2
s-1
) 103.
To quantify the impact of WPL and VD corrections over the whole experimental days,
cumulated evapotranspiration and carbon dioxide fluxes are calculated, and the results are shown
in Fig. 9. Impact of correction procedures, which permit to obtain reliable values of turbulent
fluxes, is shown taking into account the divergence between fluxes at level 1 and the corrected
fluxes. At the end of the growing season, uncorrected evapotranspiration results are
underestimated with respect to corrected fluxes with a difference of about 34 mm (Fig. 9A).
After a brief period of time where CO2 cumulated flux is positive, due to the absence of
vegetation in the field, plant photosynthesis effects play an essential role in the reduction of CO2
concentration in the air (Fig. 9B). Correction procedures permit to estimate correctly CO2
cumulated flux which is distant from uncorrected flux of about 443 g m-2
. If the WPL and VD
corrections are not applied, CO2 sequestration is overestimated. Another important issue
connected with the necessity to apply the WPL and VD corrections for the correct estimation of
CO2 flux, is shown in reference with the first period of growing season which come from 140 to
160 Julian days. This period of time, which is characterized by a heterogeneous surface, fluxes
between soil and atmosphere are exchanged. When the vegetation is sufficiently high to cover
completely the soil, respiration effects, characteristics of a bare soil, are substituted by
photosynthesis processes produced by the vegetation. If WPL and VD corrections are not
applied, physical process of respiration that occurs in the first part of growing season is not
evidenced with a drastic consequence over the physical interpretation of the flux measurements.
A B
0
50
100
150
200
250
300
140 160 180 200 220 240 260
Ev
ap
otr
an
spir
ati
on
(m
m)
Julian day
ET_uncorrected
ET_corrected
-1.8E+03
-1.5E+03
-1.2E+03
-9.0E+02
-6.0E+02
-3.0E+02
0.0E+00
3.0E+02
140 160 180 200 220 240 260
CO
2cu
mu
late
d f
lux
(g
m-2
)
Julian day
CO2_uncorrected
CO2_corrected
Fig. 9. Evapotranspiration (A) and carbon dioxide (B) cumulated fluxes over growing season.
31
Quality of fluxes
Quality of fluxes is evaluated through two different automatic tests implemented in Eddy Pro
4.0: statistical tests applied directly on high frequency measurements (Vickers and Mahrt, 1997)
and micrometeorological tests (Foken et al., 2004; Mauder and Foken, 2004).
Statistical screen for high frequency data is obtained applying six statistical tests described in the
work of Vickers and Mahrt (1997): spike, amplitude resolution, drop-out, absolute limits,
discontinuities, skewness and kurtosis.
Family of micrometeorological tests is constituted by two tests which are known as steady state
test and developed turbulent conditions test (Foken et al. 2004; Foken and Wichura, 1996;
Gockede et al., 2008). As described in Foken and Wichura (1996) stationary test and developed
turbulence test are summarized in a classification scheme defined above 9 levels of averaged
data quality. 1 corresponds to good quality, 9 bad quality of data which should be discarded from
the dataset. In Mauder and Foken (2004), quality of fluxes is based on a flag which can be 0, 1 or
2 from best quality to worst quality respectively. 0 quality flag corresponds with a range of
steady state and developed turbulence test levels which vary from 1 to 2; 1 quality flag
corresponds with a range which is up to 5 and 2 quality flag corresponds with a range from 6 to
7. Eddy Pro 4.0 shows these flags in association with each flux value (latent, sensible heat,
momentum and carbon dioxide flux) in order that the user can decide if the flux should be
discarded from results dataset.
Steady state test is based on idea to compare covariances determined for an averaging period
with the same parameters evaluated in short intervals within this period, using the method
explained in Gurjanov et al. (1984). A time series is considered to be in steady state if the
difference between both covariances (that are the covariance calculated over whole period and
the mean of covariances obtained in short intervals within this period) is lower 30% (Foken and
Wichura, 1996). In Fig. 10A, frequency of '','','' 2COwTwuw s and '' 2OHw covariance data for
each degree of quality, are shown. About 45% of data are included in 1 degree of quality
highlighting the good agreement of quality of measurements in respect to the stationary
condition control. From class 2 to 6 there are about 10% of data (for each class) and from class 7
to 9 about 5% of data.
A B
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9
Fre
qu
ency
(%
)
Degree of quality
Stationary test (Foken and Wichura, 1996)
w/u
w/Ts
w/CO2
w/H2O
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9
Fre
qu
ency
(%
)
Degree of quality
Developed turbulence test (Foken and Wichura, 1996)
u
w
Ts
Fig. 10. Percentage of data for each degree of quality using two different tests: stationary test (A)
and developed turbulent test (B).
32
The so called flux variance similarity, which is explained in many textbooks as Foken (2008), is
a good measure to test the development of turbulent conditions. This similarity means that the
ratio of standard deviation of a turbulent parameter and its turbulent flux is nearly constant or
function of the stability conditions of atmosphere through Monin-Obukov length parameter and
measurement height. This ratio called integral turbulence characteristic (ITC) is the basic
parameter to describe atmospheric turbulence. Foken (1991) classify ITC functions in three
groups related to u, w and Ts parameters, and a well developed turbulence can be assumed if the
modulus of relative error between modeled ITC and measured ITC is lower than 30%. In Fig.
10B frequency of ITCu, ITCw and ITCTs values for each degree of quality are shown. The results
evidence a discrete percentage of data (about 15%) which stay in class 9 of quality, showing that
well developed turbulence is not always guarantee.
Assuming the Mauder and Foken (2004) classification of data quality (Fig. 11) about 25% of
turbulent fluxes over the total data set should be neglected because they are included in the class
2 of quality sectors. This is probably due to the fact that, in general, nighttime data are flagged
because developed turbulence test is failed while during dawn and dusk the steady test fails.
0
10
20
30
40
50
60
0 1 2
Fre
qu
ency
(%
)
Degree of quality
Quality test (Mauder and Foken, 2004)
H
LE
CO2_flux
Fig. 11. Percentage of data for each quality class using Mauder and Foken (2004) quality test.
In Fig. 12, turbulent fluxes are shown using dots with different shape in relation with their
quality class. Bad quality of data is shown mainly during night time, while during day time the
fluxes measured by eddy station can be considered of good quality. Dawn and dusk represent
intermediate conditions where it is not always possible to define the good or bad quality of data.
A B
-100
-50
0
50
100
150
200
227 227.5 228 228.5 229
Sen
sib
le h
eat
flu
x (
W m
-2)
Julian day
0_(good quality)
1_(sufficient quality)
2_(bad quality)
-100
0
100
200
300
400
500
227 227.5 228 228.5 229
La
ten
t h
eat
flu
x (
W m
-2)
Julian day
0_(good quality)
1_(sufficient quality)
2_(bad quality)
33
C
-60
-40
-20
0
20
40
227 227.5 228 228.5 229
CO
2fl
ux
(m
icro
mo
l m
-2s-1
)
Julian day
0_(good quality)
1_(sufficient quality)
2_(bad quality)
Fig. 12. Turbulent fluxes representation in function of their quality class. (A) Sensible heat. (B)
Latent heat. (C) Carbon dioxide flux.
Quality of data is strongly connected with atmospheric stability as shown in Fig. 13. Data are
subdivided in convective, adiabatic and stable conditions and their quality flag has been
examined. The results shown in Fig. 13 indicate that the bad quality of fluxes is mainly
concentrated during stable condition of the atmosphere while for adiabatic and convective
situations quality of fluxes is often guaranteed. However, it is not possible to eliminate
completely fluxes in stable conditions because it should cause a loss of data of about 10%,
calculated as the sum of stable fluxes which belong to 0 and 1 quality classes.
A B
0
10
20
30
40
01
2
Fre
qu
ency
(%
)
Degree of quality
Quality test for sensible heat flux
Convective
Adiabatic
Stable
0
10
20
30
40
01
2
Fre
qu
ency
(%
)
Degree of quality
Quality test for latent heat flux
Convective
Adiabatic
Stable
C
0
10
20
30
40
01
2
Fre
qu
ency
(%
)
Degree of quality
Quality test for CO2 flux
Convective
Adiabatic
Stable
Fig. 13. Quality test for data subdivision in convective, adiabatic and stable conditions. (A)
Quality test for sensible heat. (B) Quality test for latent heat. (C) Quality test for carbon dioxide
flux.
34
Energy balance closure
The turbulent fluxes of sensible and latent heat, net radiation, ground heat flux and energy
balance closure are calculated before and after the whole correction procedures. In Fig. 14A and
B, ensemble means of diurnal variations of turbulent fluxes over the whole experimental period
are shown. Correction procedures play an important role on all turbulent fluxes of latent and
sensible heat, and also ground heat has to be corrected for storage term to obtain a reliable flux
estimation. For ground heat flux the correction procedure (not described in this work) is required
to account for the heat storage that occurs in the layer between the soil surface and the heat flux
plate (Kustas and Daughtry, 1990). As shown in Fig.14A, if correction procedures are not
applied, during daytime, latent, sensible and ground heat fluxes collapsed to zero, while in
nighttime overestimations of latent and sensible heat leads to an unsatisfactory flux
interpretations. In Fig.14B, corrected fluxes have a typical trend described in literature, with
latent heat greater then sensible heat because the field is covered by the vegetation for a wide
range of the experimental period. In Fig. 14C, residual flux calculated as Rn-LE-H-G is shown.
Residual magnitude for uncorrected fluxes is characterized by peaks in daytime and nighttime,
with maximum values of about 400 W m-2
at 12 A.M and -300 W m-2
at 2 A.M.. Residual trend
for corrected fluxes is close to zero with the exception of some hours in the morning, where the
mean residual value is about 50 W m-2
.
A B
-100
0
100
200
300
400
500
600
0 3 6 9 12 15 18 21 24
Flu
xes
(W m
-2)
Hours
Rn
LE_uncorrected
H_uncorrected
G_uncorrected
-100
0
100
200
300
400
500
600
0 3 6 9 12 15 18 21 24
Flu
xes
(W m
-2)
Hours
Rn
LE_corrected
H_corrected
G_corrected
C
-300
0
300
600
0 3 6 9 12 15 18 21 24
Rn
-LE
-H-G
(W
m-2
)
Hours
Residual_uncorrected fluxes
Resudual_corrected fluxes
Fig. 14. Ensemble means of diurnal variation of turbulent (A, B) and residual (C) fluxes for the
whole period of the experimental campaign.
35
The energy balance closure using all corrected fluxes (Fig. 15A) or only fluxes related to 0 and 1
quality classes (Fig. 15B), is shown. Even if the increase in energy balance closure is only of
about 4%, quality check permits to eliminate data which could be cause of major dispersion of
dots in respect 1:1 ideal line with R2 which comes from 0.75 to 0.80. Energy budget is typically
not closed when measuring energy fluxes with an eddy covariance station, available energy is
usually bigger than the sum of turbulent vertical heat fluxes with a ratio that varies between 70
and 98% (Jacobs et al., 2008; Meyers and Hollinger, 2004; Wilson et al., 2002; Foken et al.,
2006). As shown in Fig. 15A the slope of linear regression is 0.81 which is included in the range
of values which are usually described in literature. However, there are several aspects which
could give a relevant improvement in energy balance closure: the contribution of additional
storage fluxes such as photosynthesis flux, crop, air enthalpy changes (Jacobs at al., 2008;
Meyers and Hollinger, 2004), footprint shape and the representativeness of measured fluxes as a
function of scale (Shmid, 1997) to make mention of some problems. Usually for homogeneous
area it is considered valid the assumption that source areas are the same for all fluxes. However
these areas can be significantly different, if the footprint of turbulent fluxes is compared to the
source area of ground heat flux. So a portion of the error in energy balance closure can be related
to the difficulty to match footprint area of eddy covariance fluxes with the source areas of the net
radiation and heat flux plate instruments (Wilson et al., 2002).
A B
y = 0.81x
R² = 0.75
-200
0
200
400
600
800
-200 0 200 400 600 800 1000
LE
+H
(W
m-2
)
Rn-G (W m-2)
y = 0.85x
R² = 0.80
-200
0
200
400
600
800
-200 0 200 400 600 800 1000
LE
+H
(W
m-2
)
Rn-G (W m-2)
Fig. 15. Energy balance closure with all data set (A) and only with 0 and 1 quality fluxes (B).
Fluxes directly obtained from 30 minutes averaged data
As explained in Ueyama et al. (2012), in literature, it is unstill clear which data processing steps
are influential in the calculation of half-hourly and annual fluxes. According to results shown in
previous sections, WPL and VD corrections provide for a substantial fluxes modification,
influencing drastically cumulated evapotranspiration and carbon dioxide flux annual budgets.
These corrections are the heart of PEC software (Corbari et al., 2012), which is designed to
answer question of real time data management. With the objective to verify the possibility of
using eddy covariance station in an operative way for water irrigation management, so to
understand if averaged data at 30 minutes are still of good quality in respect to high frequency
data, the results obtained by PEC software are compared with those obtained by Eddy Pro 4.0.
36
PEC software features
Data logger program has to be compiled to convert electrical signals, originated from sensors, in
physical measurements. Moreover, choosing an appropriated averaged interval, it can be set to
perform some elementary mathematical operations as mean, variance or covariance among
different measured variables. High frequency data will be lost but on the data logger memory
aggregated data which are at 30 minutes will be stored. Time step (averaged time) has been
chosen in accordance with results shown in different literature works as Lumley and Panofsky
(1964), Lenschow et al. (1994) and Gluhovsky and Agee (1994). According to these authors,
averaged time can not be less than 30-60 minutes if means, variances and covariance have to be
assessed with an accuracy of about 5-15%. The complete procedure implemented in PEC for real
time data management is reported in Corbari et al. (2012). Steps which describe the procedure
for turbulent fluxes calculation, can be summarized in four points:
1) Starting from averaged data, uncorrected fluxes (level 0) are calculated;
2) WPL and VD corrections are implemented;
3) Rainfall days are discarded;
4) Elimination of spikes is applied.
While points 1 and 2 are implemented with a programming language, points 3 and 4 are
performed manually by the operator. During rainfall periods the data are completely discarded
and if the rain falls during night time the data until the net radiation is greater than 0 W m-2
are
discarded. Despiking is applied on turbulent fluxes of latent, sensible heat and carbon dioxide in
accordance with the experience of the operator. Deep knowledge of site, cultivation typology and
literature data are the basic information which give to the operator the possibility to exclude, for
the analysis, turbulent fluxes which are not representative of the physical phenomena in the field.
In Tab. 2 the plausibility ranges for latent, sensible heat and carbon dioxide are shown.
Preliminary processes and spectral corrections have not been applied.
Tab. 2. Plausibility range for turbulent fluxes of latent, sensible heat and carbon dioxide
Min Max
Latent heat (W m-2
) -50 850
Sensible heat (W m-2
) -150 600
Carbon dioxide (millimol m-2
s-1
) -80 50
PEC fluxes in comparison with Eddy Pro 4.0 fluxes
In Fig. 16 two simple schemes which describe the levels of flux intensities applying the
sequences of correction procedures for Eddy Pro 4.0 and PEC software, are shown. Starting from
raw flux of latent heat (LE0), spectral correction factor is multiplied for LE0 obtaining LE1 and
subsequently WPL correction is added for the calculation of the definitive corrected flux LE3.
Using PEC software, LE3 is directly calculated applying only the WPL correction, and a flux loss
is shown as a consequence of spectral information losses. VD correction algorithm produces a
decrease of the raw flux of sensible heat from H0 to H2. Subsequently, it is multiplied for the
37
spectral correction factor for sonic temperature, to obtain H3. Also in this case, using PEC
software, the data has not been opportunely corrected for spectral losses.
A B
In
ten
sit
y o
f la
ten
t h
ea
t (W
m-2
)
Eddy Pro 4.0 Averaged dataset
LE0
LE1
LE3
LE0
LE3Flux loss
In
ten
sit
y o
f sen
sib
le h
ea
t (W
m-2
) Eddy Pro 4.0 Averaged dataset
H0
H2
H3
H0
H3Flux loss
Fig. 16. Intensities of latent(A) and sensible(B) heat fluxes before and after the application of the
correction procedures using Eddy Pro 4.0 and PEC softwares.
The consequences of the spectral losses are remarked in the slope of linear regression between
PEC and Eddy Pro fluxes. Flux losses, for latent and sensible heat, produce a mean decrease in
flux magnitude of about 8%, with slopes equal to 0.95 for latent heat and 0.90 for sensible heat.
Intercepts are near closed to zero while R2 is about 0.9 for both fluxes.
Usually, engineering applications need to know evapotranspiration flux overall growing season.
Cumulated evapotranspiration flux and carbon dioxide trend could be used to define the
characteristics of canopy comportment from sowing to reaping time. In Fig.17, cumulated
evapotranspiration flux and carbon dioxide trend over growing season of maize field are shown.
In black, the fluxes calculated using Eddy Pro 4.0, and in grey the fluxes obtained by PEC
software are shown. As shown in Fig. 17A, the divergence among two fluxes starts at the
beginning of the growing season and it remains constant on all experimental period. As shown in
Fig. 17B, the divergence begins more or less at 200 Julian day and increases until the end of the
cultivated season. At the end of growing season the difference among the fluxes is about 10 mm
for the cumulated evapotranspiration and 90 g m-2
for CO2.
A B
0
50
100
150
200
250
300
140 160 180 200 220 240 260
Ev
ap
otr
an
spir
ati
on
(m
m)
Julian day
ET_from_averaged_data
ET_from_EddyPro
-1.2E+03
-9.0E+02
-6.0E+02
-3.0E+02
0.0E+00
3.0E+02
140 160 180 200 220 240 260
CO
2cu
mu
late
d f
lux
(g
m-2
)
Julian day
CO2_from_averaged_data
CO2_EddyPro
Fig. 17. Comparison between cumulated evapotranspiration (A) and carbon dioxide (B) fluxes
obtained by PEC and Eddy Pro 4.0 softwares.
38
Energy balance closure with PEC fluxes
In order to complete the analysis over fluxes obtained by PEC software, energy balance closure
is shown in Fig. 18. The slope of the linear regression is quite differenced by that shown in Fig.
15A (obtained by Eddy Pro 4.0). In this case the slope is equal to 0.74, while the dispersion of
the dots is reduced and R2
value is about 0.89. This result is probably due to the moderated
influence of preliminary processes and spectral losses which have not been considered into the
PEC software corrections.
y = 0.74x
R² = 0.89
-200
0
200
400
600
800
-200 0 200 400 600 800
LE
+H
(W
m-2
)
Rn-G (W m-2)
Fig. 18. Energy balance closure using latent and sensible heat fluxes calculated by PEC software.
Conclusion
In this work the impact of different correction procedures on turbulent flux measurements
collected by an eddy covariance station, are described. Starting from high frequency data a
complex series of processes have to be implemented to extract reliable turbulent fluxes of latent,
sensible heat, carbon dioxide and water vapor from raw data measurements.
In the preliminary processes, the double correction procedure play a fundamental role to adjust
the orientation of the Cartesian system of axis respect to streamlines. Spectral corrections are
necessary to define flux losses due to the specific transfer functions which characterize the
measurement system. Turbulent fluxes need to be corrected for density fluctuation and humidity
effect on sonic temperature using WPL and VD corrections. These corrections should not be
considered as corrections, but a normal step to calculate turbulent fluxes. In fact, if the WPL and
VD corrections are not applied, turbulent fluxes do not reproduce correctly the physical aspects
of the experimental site. A final control based on micrometeorological tests of steady state and
developed turbulence permits to highlight the quality of calculated fluxes advising the operator if
flux data should be neglected.
High frequency (10-20 Hz) measurements of the three components of wind velocity and gas
concentrations have to be stored to obtain reliable turbulent fluxes at different scale. It is widely
known in literature, but in some cases, impossibility to have high frequency data do not permit to
apply the whole categories of correction procedures. Moreover, some engineering applications
which for example refer to the possibility to estimate evapotranspiration fluxes over a growing
season could not require for the accuracy developed in the previous analysis. For these problems,
a simple method which permits to the operator the possibility to calculate turbulent fluxes from
39
an averaged dataset has been shown. In fact, in PEC software only WPL and VD corrections are
implemented and these corrections could be defined as essential ingredients to covert
measurements in reliable fluxes. As shown in Fig. 17A the difference between PEC software
results and Eddy Pro 4.0 fluxes is small and PEC fluxes underestimates Eddy Pro
evapotranspiration fluxes only for 10 mm. Reducing the number of corrections, the algorithm
implementations in a programming language appear to be of easy application also for operators
which are not expert in software engineering. In general it is possible to conclude that turbulent
fluxes could be approximately assessed starting from averaged data, but if the flux accuracies are
rigorously required, the whole range of corrections should be taken into account.
References
Aubinet, M., Grelle, A., Ibrom, A., Rannik, U., Moncrieff J., Foken, T., et al. (2000). Estimates of the annual net
carbon and water exchange of forests: the euroflux methodology. Advanced in Ecological Research , 30: 113-175.
Baldocchi, D., Falge, E., Gu, L., Olsen, R., Hollinger, D., Running, S., et al. (2001). FLUXNET: a new tool to study
the temporal and spatial variability of ecosystem scale carbon dioxide, water vapor, and energy flux densities.
Bulletin of American Meteorological Society , 82: 2415-2434.
Barr, A., Morgenstern, K., Black, T., McCaughey, J., and Nesic, Z. (2006). Surface energy balance closure by the
eddy-covariance method above three boreal forest stands and implications for the measurement of CO2 flux.
Agricultural and Forest Meteorology, 140: 322-337.
Burba, G., McDermitt, D., Grelle, D., Anderson, D., and Xu, L. (2008). Addressing the influence of instrument
surface heat exchange on the measurements of CO2 flux from open path gas analyzer. Global Change Biology, 14:
1854-1876.
Corbari C., Masseroni,D.,Mancini, M., (2012). Effetto delle correzioni dei dati misurati da stazioni eddy covariance
sulla stima dei flussi evapotraspirativi. Italian Journal of Agrometeorology,1:35-51.
Fan, S., Wofsy, S., Bakwin, P., Jacob, D., and Fitzjarrald, D. (1990). Atmosphere-biosphere exchange of CO2 and
O3 in the Central Amazon Forest. Journal of Geophysical Research , 95: 16851-16864.
Foken, T. (1991). Informationen uber das internationale experiment TARTEX-90, torevere bei tartu, estland, 28.05
bis 13.07.1990. Zeitschrift fur Meteorologie , 41: 227.
Foken, T. (2008). Micrometeorology. Berlin: Springer, pp. 306, ISBN 978 3 540 74665 2.
Foken, T., and Wichura, B. (1996). Tools for quality assessment of surface-based flux measurements. Agricultural
and Forest Meteorology. , 78: 83-105.
Foken, T., Gockede, M., Mauder, M., Mahrt, L., Amiro, B., and Muger, J. (2004). A guide for surface flux
measurements. Kluwer Academic, Dordrecht 81-108.
Foken, T., Wimmer, F., Mauder, M., Thomas, C., and Liebhetal, C. (2006). Some aspects of the energy balance
closure problem. Atmospheric Chemistry and Physics, 6: 4395-4402.
Fuehrer, P.L. and Friehe, C.A. (2002) Flux correction revised. Boundary Layer Meteorology, 102: 415-457.
Garratt, J. (1993). The atmospheric boundary layer. Cambridge: Cambridge university press, pp.316, ISBN 0 521
38052 9.
40
Gash, J., and Culf, A. (1996). Applying linear de-trend to eddy correlation data in real time. Boundary Layer
Meteorology, 79: 301-306.
Gluhovsky A. and Agee E. (1994): A definitive approach to turbulence statistical studies in Planetary Boundary
Layer. Journal of Atmospheric Sciences, 51: 1682-1690.
Gockede, M., Foken, T., Aubinet, M., Aurela, M., and Banza, J. (2008). Quality control of CarboEurope flux data -
Part1: Coupling footprint analysis with flux data quality assesment to evaluate sites in forest ecosystems.
Biogeosciences, 5: 433-450.
Gurjanov AE, Zubkovskij SL and Fedorov MM (1984) Mnogokanalnaja avtomatizirovannaja sistema obrabotki
signalov na baze EVM (Automatic multi-channel system for signal analysis with electronic data processing). Geod
Geophys Veröff, R II. 26:17-20.
Ibrom, A., Dellwik, E., Larse, E., and Pilegaard, K. (2007). On the use of the Webb-Pearman_Leuning theory for
closed-path eddy correlation measurements. Tellus Series B-Chemical and Physiscal Meteorology , 59: 937-946.
Jacobs, A., Heusinlveld, B., and Holtslag, A. (2008). Towards closing the energy surface budget of a mid-latitude
grassland. Boundary Layer Meteorology ,126:125-136.
Kaimal, J., Wyngaard, J., Izumi, Y., and Cotè, O. (1972). Spectral characteristics of surface-layer turbolence.
Quarterly Journal of the Royal Meteorological Society, 98: 563-589.
Kustas, W., and Daughtry, C. (1990). Estimation of the soil heat fluxnet radiation ratio from spectral data.
Agricultural and Forest Meteorology: 49: 205-223.
Lee, X., Massman, W., and Law, B. (2004). Handbook of Micrometeorology: A Guide for Surface Flux
Measurement and Analysis. Kluwer Academic Press, Dordrecht, 250 pp.
Lenschow D.H., Mann,J., and Kristensen, L. (1994): How long is long enough when measuring fluxes and other
turbulence statistics? Journal of Atmospheric and Oceanic Technology, 11: 661-673.
Leuning, R. (2004). Measurements of trace gas fluxes in the atmosphere using eddy covariance : WPL correction
revisited. Kluwer, Dordrecht, pp.119-132.
Lloyd, C., Shuttleworth, W., and Gash, J. T. (1984). A microprocessor system for eddy-correlation. Agricultural and
Forest Meteorology, 33: 67-80.
Lumley, H.H., and Panofsky, H.A. (1964): The structure of atmospheric turbulence. John Wiley&Sons.
Masseroni, D., Ravazzani, G., Corbari, C., and Mancini, M. (2011). Correlazione tra la dimensione del footrpint e le
variabili esogene misurate da stazioni eddy covariance in Pinura Padana, Italia. Italian Journal of Agrometeorology ,
1: 25-36.
Massman, W. (2000). A simple method for estimating frequency responce corrections for eddy covariance systems.
Agricoltural and Forest Meteorology , 104: 185-198.
Massman, W. (2004). Concerning the measurement of atmospheric trace gas fluxes with open and closed path eddy
covariance system: The WPL terms and spectral attenuation, in Handbook of micrometeorology: a guide for
surfacem flux measurements. Kluwer Academic, Netherlands,133-160.
Massman, W., and Lee, X. (2002). Eddy covariance flux corrections and uncertainties in long-term studies of carbon
and energy exchanges. Agricultural Forest Meteorology, 113: 121-144.
41
Mauder, M. and Foken, T. (2004). Documentation and instruction manual of the eddy covariance software package
TK2. Arbeitsergebn, Univ Bayreuth, Abt Mikrometeorol, ISSN 1614-8916. 26: 42 pp.
Mauder, M., and Foken, T. (2006). Impact of post field data processing on eddy covariance flux estimates and
energy balance closure. Meteorologische Zeitschrift , 15: 597-609.
McMillen, R. (1988). An eddy correlation technique with extended applicability to non-simple terrein. Boundary
Layer Meteorology , 43: 231-245.
Moncrieff, J., Clement, R., Finnigan, J., and Meyers, T. (2004). Averanging and filtering of eddy covariance time
series, in Handbook of micrometeorology: a guide for surface flux measurements. Kluwer Academic, Dordrecht, 7-
31.
Moncrieff, J., Massheder, J., De Bruin, H., Ebers, J., Friborg, T., Heusinkveld, B., et al. (1997). A system to
measure surface fluxes of momentum, sensible heat, water vapor and carbon dioxide. Journal of Hydrology , 188-
189: 589-611.
Moore, C. (1983). On the calibration and temperature behaviour of single-beam infrared hygrometer. Boundary
Layer Meteorology, 25: 245-269.
Moore, C. (1986). Frequency response corrections for eddy correlation systems. Boundary Layer Meteorology, 37:
17-35.
Obukov, A. (1946). Turbolance in an atmosphere with a non-uniform temperature. Trudy Ins. Theor. Geofiz. AN
SSSR , 1:95-115.
Rannik, U., and Vesala, T. (1999). Autoregressive filtering versus linear detrending estimation of fluxes by the eddy
covariance method. Boundary Layer Meteorology , 91: 258-280.
Reichstein, M., Tenhunen, J., Roupsard O., Orcival, J., Rambal, S., Dore S., and Valentini R. (2002). Ecosystem
respiration in two Mediterranean evergreen holm oak forests: drought effects and decomposition dynamic.
Functional Ecology , 16: 27-39.
Runkle, B., Wille, C., Gazovic, M., and Kutzbach, L. (2012). Attenuation correction procedures for water vapor
fluxes from closed-path eddy covariance systems. Boundary Layer Meteorology , 142: 1-23.
Schmid HP (1997) Experimental design for flux measurements: matching scales of observations and fluxes.
Agricultural and Forest Meteorology. 87: 179-200.
Schotanus, P., Nieuwstadt, F., and De Bruin, H. (1983). Temperature meaurement with a sonic anemometer and its
application to heat and moisture fluxes. Boundary Layer Meteorology, 26: 81-93.
Shuttleworth, W. (1988). Corrections for the effect of background concentrations change and sensor drift in real
time eddy correlation systems. Boundary Layer Meteorology , 42:167-180.
Shuttleworth, W., Gash, J., Lloyd, C., McNeil, D., Moore, C., and Wallance, J. (1988). An integrated
micrometeorological system for evaporation measurement. Agricultural and Forest Meteorology, 43: 295-317.
Shuttleworth, W., McNeil, D., and Moore, C. (1982). A switched continuous-wave sonic anemometer for measuring
surface heat fluxes. Boundary Layer Meteorology , 23: 425-448.
Stull, R. (1988). An introduction to boundary layer meteorology. Dordrecht, Boston, London, 666: Kluwer
Academic Publisher.
42
Treviño G., E.L. Andreas (2000): Averaging interval for spectral analysis of non stationary turbulence - Bound.
Layer Meteor., 95: 231-247.
Ueyama, M., Hirata, R., Mano, M., Hamotani, K., Harazono, Y., Hirano, T., Miyata, A., Takagi, K., and Takahashi,
Y., (2012). Influences of various calculation options on heat, water and carbon fluxes determined by open- and
closed –path eddy covariance methods. Tellus B, 64: 1-26.
Van Dijk, A., Kohsiek, W., and De Bruin, H. (2003). Oxygen sensitivity of krypton and Lyman-alfa Hygrometer.
Journal of Atmospheric and Oceanic Technology , 20: 143-151.
Vickers, D., and Mahrt, L. (1997). Quality control and flux sampling problems for tower and aircraft data. Journal of
Atmospheric and Oceanic Technology , 14: 512-526.
Webb, E., Pearman, G., and Leuning, R. (1980). Correction of the flux measurements for density effects due to heat
and water vapour transfer. Boundary Layer Meteorology, 23: 251-254.
Wilczak, J., Oncley, S., and Stage, S. (2001). Sonic anemometer tilt correction algorithms. Boundary Layer
Meteorology , 99: 127-150.
Wilson, K., Goldstein, A., Falge, E., Aubinet, M., Baldocchi, D., Berbigier, P., et al. (2002). Energy balance closure
at FLUXNET sites. Agricultural and Forest Meteorology, 113: 223-243.
43
(Chapter 2) – Energy balance closure of an eddy covariance station: limitations and improvements
Abstract
The use of energy fluxes data to validate land surface models requires that the conservation of
the energy balance closure is satisfied; but usually this condition is not verified when, measuring
energy components with an eddy covariance station, available energy is bigger than the sum of
turbulent vertical fluxes. In this work, a comprehensive evaluation of the energy balance closure
problems is performed on Livraga 2012 data set which is obtained by a micrometeorological
eddy covariance station located in a maize field in Po Valley. Energy balance closure is
calculated by statistical regression of turbulent energy fluxes and soil heat flux against available
energy. Generally, the results indicate a lack of closure with a mean imbalance in the order of
20%. Storage terms are the main reason for the unclosed energy balance but also the turbulent
mixing conditions play a fundamental role in the reliable turbulent flux estimations. Recently
introduced in literature, the energy balance problem has been studied as a scale problem.
Representative source area for each flux of the energy balance has been analyzed and the closure
has been performed in function of turbulent flux footprint areas. Surface heterogeneity and
seasonality effects have been studied with objective to understand the influence of canopy
growth on energy balance closure. High frequency data have been used to calculate co-spectral
and ogive functions which suggest if averaging period of 30 minutes may miss temporal scales
that contribute to the turbulent fluxes. Finally, latent and sensible heat random error estimations
are computed to give information about measurement system and turbulence transport
deficiencies.
Introduction
Surface energy fluxes are important for a huge range of application over different spatial and
temporal scales: from flash flood simulation at basin scale to water management in agricultural
area. It is then important to understand the quality of measured fluxes before using them for land
– atmosphere simulations.
The quality of eddy covariance measurements is influenced not only by possible deviations from
the theoretical assumptions but also by problems of sensor configurations and meteorological
conditions (Foken and Wichura, 1996). However, it is difficult to isolate the causes of
measurements errors. Instrumental errors, uncorrected sensor configurations, problem of
heterogeneities in the area and atmospheric conditions are the main problems that afflict the data
quality (Jacobs et al., 2008; Wilson et al., 2002; Foken et al., 2006; Foken, 2008a). Eddy
covariance method produces reliable results when the theoretical assumptions in the surface
layer are respected (Baldocchi et a. 2001; Foken and Wichura, 1996; Fisher et al., 2006). In
particular, the theoretical requirements, such as steady-state condition, horizontal homogeneity
of the field, validity of the mass conservation equation, negligible vertical density flux, turbulent
44
fluxes constant with height and flat topography, should be satisfied. Moreover, sensors
configuration should be analyzed in relation to the sampling duration and frequency, separation
of sonic anemometer and gas analyzer, sensor placement within the constant flux layer, but out
of the roughness sub-layer. Meteorological conditions, such as precipitation events and low
turbulence, especially at night time, can lead to errors in fluxes measurement.
The unbalance of the energy budget has been widely studied in the last decade due to the fact
that the use of energy fluxes to validate land surface models requires that the closure of the
energy balance is satisfied. Energy budget is typically not closed when, measuring energy fluxes
with an eddy covariance station, available energy is usually bigger than the sum of turbulent
vertical heat fluxes with a ratio that varies between 70 and 90% (Jacobs et al., 2008; Wilson et
al., 2002; Foken et al., 2006; Ma et al., 2009). Thus, it is important to understand the different
factors that can lead to an improvement of the energy balance closure.
The first cause of the lack of energy balance closure is liked to an uncorrected implementation of
a complete set of instrumental and flux corrections as described in Aubinet et al. (2000). Axis
rotation, spike removal, time lag compensation and detrending are the preliminary correction
processes which should be applied on high frequency raw data set measured by sonic
anemometer and gas analyzer. Subsequently, spectral information losses, air density fluctuations
and humidity effects have to be taken into account to obtain reliable fluxes of latent and sensible
heat (Moncrieff et al. 1997,Webb et al. 1980; Van Dijk et al. 2004).
However, later studies discuss unbalance problem as an effect of the fractional coverage of
vegetation and the influence of the soil storage (Foken, 2008b). Additional storage terms, like the
ones linked to the photosynthesis processes or vegetation canopy, give a relevant improvement
in energy balance closure (Meyers and Hollinger, 2004).
Different time aggregation could reduce the effect of storage terms because they have an
opposite behavior during day time and night time (Papale et al., 2006). Some recent works
(Finnigan et al., 2003; Oncley et al., 1993) have suggested that averaged time (generally 30
minutes) which is chosen to calculate covariances could be inadequate for assessing turbulent
fluxes. Ogive function for each half hour data set can be a good indicator for measurement errors
associated to such energy balance problems (Oncley et al., 1993).
Moreover, energy balance closure can be seen as a scale problem, because the representativeness
of a measured flux is a function of scale. Usually, for homogeneous areas, the assumption that
source areas are the same for all fluxes is considered valid. However, these areas can be
significantly different if the footprint of turbulent fluxes is compared to the source area of ground
heat flux. So a portion of the error in energy balance closure can be related to the difficulty to
match footprint area of eddy covariance fluxes with the source areas of the instruments which
measure net radiation and ground heat flux (Wilson et al., 2002; Schmid, 1997; Hsieh et al
2000).
Eddy flux measurements can be underestimated during periods with low turbulence and air
mixing. This underestimation acts as a selective systematic error and it generally occurs during
the night time. Massman and Lee (2002) listed the possible causes of the night-time flux error.
There is now a large consensus to recognize that the most probable cause of error is the presence
of small scale movements associated with drainage flows or land breezes that take place in low
turbulence conditions and create a decoupling between the soil surface and the canopy top. In
these conditions, advection becomes an important term in the flux balance and cannot be
neglected anymore. It has been recently suggested (Finnigan et al., 2006) that, contrary to what
45
was thought before, advection probably affects most of the sites, including also flat and
homogeneous ones. Direct advection fluxes measurements are difficult to measure as they
require several measurement towers at the same site. Attempts are notably made by Aubinet et
al. (2003), Feigenwinter et al. (2004), Staebler and Fitzjarrald (2004) and Marcolla et al. (2005).
They find that advection fluxes are usually significant during calm weather conditions. However,
in most cases, the measurement uncertainty is too large to allow their precise estimation. In
addition, such direct measurements require a too complicated set up to allow routine
measurements at each site. In practice, flux problem is by-passed by discarding the data
corresponding to low mixed periods. The friction velocity is currently used as a criterion to
discriminate low and high mixed periods. This approach is generally known as the “u∗
correction”. Although being currently the best and most widely used method to circumvent the
problem, the u∗ correction is affected by several drawbacks and must be applied with care.
Factors connected with growing vegetation and seasonality have been investigated. As shown in
Panin et al. (1998) the unbalance could be attributed to the influence of the surface heterogeneity
and vegetation height in respect to sensors position.
Different sources of uncertainties in flux measurements can be sometimes difficult to assess.
Random measurement errors in flux data, including errors due to measurement system and
turbulence transport, have been assessed by Hollinger and Richardson (2005), comparing the
measurements from two towers with the same flux source area (“footprint”) and by Richardson
et al. (2006), comparing pair of measurements made on two successive days from the same tower
under equivalent environmental conditions. A simple method described in Moncrieff et al.
(1996) can be used to quantify the influence of random error on momentum, latent and sensible
heat calculating a degree of uncertainty for each turbulent flux.
In this work relevant findings on energy balance closure problem over maize field in Po Valley
are summarized mainly on the basis of recent investigation works as Foken (2008b), Oncley et
al. (2007) and Wilson et al. (2002). Turbulent fluxes from a raw data set of high frequency
measurements, are obtained using Eddy Pro 4.0 software with the main objective to standardize
the correction procedure of eddy covariance measurements. Impacts of each investigated factor
is quantified by the slope and intercept values between turbulent vertical heat fluxes (latent heat,
sensible heat and ground heat fluxes) and available energy (net radiation) from a regression
analysis of half hourly basis. Each examined factor is separately studied to each other to improve
understanding of its impact on energy balance closure. Theoretical backgrounds are not
summarized in a separate chapter but they are included in each sub-paragraph to improve the
description of the exanimate problems. Only practical formulas are shown, while mathematical
approaches are quoted in literature.
Instruments, data collection and site description
Experimental campaign was carried out over a maize field at Livraga (LO) in Po Valley during
the year 2012. The field is about 10 hectare large and the local overall topography is flat. In the
middle of the field an island of about 50 m2 is designed to include agro-micrometeorological
instruments and devices.
Eddy covariance data are measured by a tridimensional sonic anemometer (Young 81000) and
open path gas analyzer (LICOR 7500) located at the top of a tower at an height of about 5 m.
46
High frequency (20 Hz) measurements are stored in a compact flesh of 2 Gb connected with the
data logger Campbell CR5000 and downloaded in situ weekly. On compact flash only three wind
velocity components, sonic temperature, vapor and carbon dioxide concentrations are stored (raw
data). Contemporaneously net radiation, measured by CNR1 Kipp&Zonen radiometer (4.5 m
high), soil heat flux, measured by HFP01 Campbell Scientific flux plate, and soil temperature
measurements are stored on data logger in different memory tables. Into the island also soil
moisture at different levels and rain are measured. Averaged fluxes are calculated over a time
step of 30 minutes.
Experimental measurements were carried out from 21 May to 7 September but the dataset is
composed by only 3103 averaged data because some gaps due to malfunctioning of
instrumentations or rainfall days are shown into the data sequences. From 131 to 241 Julian day
the field is covered by vegetation, while the remaining days of the year, the field is characterized
by bare soil. Vegetation height varies from zero to 320 cm and the canopy grew during the
project can be spatially considered homogeneous across the field.
Wind direction is quite steady, generally from West during day time and East during night time
but in some days this convention is not always respected. Considering each wind direction, the
eddy tower position is compatible with the constant flux layer (CFL) (Elliot, 1958). CFL is
defined as 10-15% of internal boundary layer (Baldocchi and Rao, 1995), and it represents a
space area where measured fluxes by the eddy tower are constant. Applying Elliot’s (1958)
formula in unfavourable conditions of bare soil, with a calculated aerodynamic roughness of
about 0.04 m (Garrat, 1993), the CFL depth at the tower is about 6 meters ensuring that the eddy
covariance instruments (tridimentional sonic anemometer and gas analyser) are included into the
CFL.
During the summer period the site is typically characterized by a cloud-free sky in association
with a quit high evapotranspiration and net radiation values of about 600 and 700 W m-2
respectively. Cumulated rain over the experimental period is about 200 mm, while soil moisture
measured at a depth of 10 cm varies between maximum and minimum peaks of about 0.4 and
0.15 respectively.
The energy balance closure problem
Energy balance closure, a formulation of the first law of thermodynamic, requires that the sum of
the estimated latent (LE) and sensible (H) heat and ground heat flux (G) has to be equivalent to
all other energy sink or source (Eq. 1).
nRGHLE (1)
Where Rn is the net radiation. Generally, fluxes are typically integrated over periods of half hour
building the basis to calculate energy balance to annual time scales. The slope (defined as
(LE+H+G)Rn-1
) and intercept values of the regression line quantify the reliability of the energy
balance closure which is close to 1 in an ideal case. In the following sections the relevant
findings on the energy balance closure are summarized and data processing results using the
experimental measurements are shown.
47
Effect of data corrections
In this paragraph the procedures necessary to obtain reliable fluxes starting from high frequency
raw data set are briefly described (see Chapter 1).
Eddy covariance measurements have to be corrected to obtain reliable turbulent fluxes of latent
and sensible heat. Before calculating fluxes, two groups of corrections should be implemented:
“instrumental” and “physical” corrections.
Instrumental corrections can be considered as preliminary processes which have to be directly
applied on high frequency measurements to prepare the data set for fluxes calculation.
Axis rotation for tilt correction. Tilt correction algorithms are necessary to correct wind statistics
for any misalignment of the sonic anemometer with respect to the local wind streamlines.
Wilczak et al. (2001), proposes three typologies of correction algorithms, and for Livraga 2012
dataset a double rotation method has been used. Using this method, the anemometer tilt is
compensated by rotating raw wind components to nullify the average cross-stream and vertical
wind components.
Spike removal. The so called despiking procedure consists in detecting and eliminating short
term outranged values in the time series. Following Vickers and Mahrt (1997), for each variable
a spike is detected as up to three consecutive outliers with respect to a plausibility range defined
within a certain time window, which moves throughout the time series.
Time lag compensation. In open path system the time lag between anemometric variables and
variables measured by gas analyzer is due to the physical distance between the two instruments,
which are usually placed several decimeters or less apart to avoid mutual disturbances. The wind
field takes some time to travel from one instrument to the other, resulting in a certain delay
between the moments the same air parcel is sampled by the two instruments (Runkle et al.,
2012).
Detrending. Eddy correlation method of calculating fluxes requires that the fluctuating
components of the measured signals are derived by subtracting them from the mean signals. In
steady-state conditions simple linear means would be adequate, but steady state conditions rarely
exist in the atmosphere and it is necessary to remove the long term trends in the data which do
not contribute to the flux (Gash and Culf, 1996).
After completing the preliminary processes, physical corrections have to be implemented.
Spectral information losses, air density fluctuation and humidity effects on sonic temperature are
taken into account in accordance with the procedure described in Ueyama et al. (2012).
Spectral correction. Spectral corrections compensate flux underestimations due to two distinct
effects. The first is referred to the fluxes which are calculated on a finite averaging time,
implying that longer-term turbulent contributions are under-sampled at some extent, or
completely. The correction for these flux losses is referred to as high-pass filtering correction
because the detrending method acts similarly to a high-pass filter, by attenuating flux
contributions in the frequency range close to the flux averaging interval. The second is connected
with instrument and setup limitations that do not allow sampling the full spatiotemporal
turbulence fluctuations and necessarily imply some space or time averaging of smaller eddies, as
well as actual dampening of the small-scale turbulent fluctuations (Moncrieff et al., 1997).
WPL correction. The open-path gas analyzer does not measure nondimensional carbon dioxide
and water vapor concentrations as mixing ratios but it measures carbon dioxide and water vapor
densities. For this reason, the trace gas flux using this analyzer needs to correct for the mean
48
vertical flow due to air density fluctuation. Webb et al. (1980) suggested that the flux due to the
mean vertical flow cannot be neglected for trace gases such as water vapor and carbon dioxide.
To evaluate the magnitude of the influence by the mean vertical flow, Webb et al. (1980)
assumed that the vertical flux of dry air should be zero. Practically, sensible and latent heat
fluxes evaluated by the eddy covariance technique are used to calculate water vapor and carbon
dioxide fluxes by the mean vertical flow (WPL correction).
VD correction. Sonic anemometer measures wind velocity components and sonic temperature.
Sonic temperature, which is the basis of the sensible heat calculation, is affected by both
humidity and velocity fluctuations. Van Dijk et al. (2004), revising the experiment carried out by
Schotanus et al. (1983), defines a correction term to apply on sensible heat formula to obtain
reliable flux (VD correction).
Corrections impact on turbulent fluxes as a consequence of the procedure described above, can
be founded in the work of Ueyama et al. (2012) and also in Chapter 1 of this thesis. As shown in
Chapter 1, where ensemble means of diurnal variations of turbulent fluxes over the whole
experimental period are computed, if correction procedures are not applied, during daytime,
latent, sensible and ground heat fluxes collapsed to zero, while in nighttime overestimations of
latent and sensible heat brings to an unsatisfactory flux interpretations.
The energy balance closure calculated after the correction procedures only applied on latent and
sensible heat flux components is equal to 0.75 with a correlation coefficient (R2) of about 0.8 and
intercept of about 10 W m-2
.
Effect of storage terms
Eddy covariance measurements are based on turbulent air mixing and vertical flux exchanges.
Sometimes, portion of latent and sensible heat could be stored below measurement point and
these concentrations are not measured by anemometer and gas analyzer devices. Usually, when
the canopy covers the field, the effect of the canopy heat storage and photosynthesis flux
increase drastically. The best way to compute storage flux is to deduce it from a concentration
profile method inside the canopy (Papale et al, 2006). However, at many sites, a discrete
estimation based only on concentration at the tower top is used (Meyer and Hollinger, 2004).
Moreover, a correction is required to account for the heat storage that occurs in the layer between
the soil surface and the heat flux plate (Mayocchi and Bristow, 1995), so Eq. 1 can be rewritten
adding the storage terms (Eq. 2).
npcg RSSSGHLE (2)
Where Sp is the energy flux for photosynthesis, Sc is the canopy heat storage in biomass and
water content and Sg is the ground heat storage above the soil heat plate.
The heat storage terms for the local surface energy balance are calculated by computing the total
enthalpy change over a given time interval ( t ) which is 30 minutes. For the canopy, the rate
change in enthalpy is described by Eq.3.
t
cmcmS bbww
c (3)
49
Where is the temperature exchange over the canopy directly measured by radiometer. In
fact, CNR1 Kipp & Zonen radiometer permits to measure directly long wave and short wave
radiation incoming and outgoing the surface. Starting from long wave radiation outgoing the
surface, considering the surface as a bleakbody, temperature can be calculated inverting Stefan-
Boltzmann law. Plant water mass (mw), biomass (mb) density, specific heat for plant water (cw)
and biomass (cb) are directly estimated by Meyers and Hollinger (2004) work, where the maize
plant were weighed, dried, and weighed again in order to assess the plant water content and
biomass density.
A similar procedure for heat storage in the soil surface is followed (Eq. 4).
t
zcmcTS ssswww
g (4)
Where T is the temperature exchange in the soil, msw is the density of water, w
is the measured
volumetric content measured by soil moisture probe at 10 cm depth, z is the depth above the
soil heat plate to the ground surface, sis the soil bulk density and cs is the specific heat capacity
of soil (Kustas and Daughtry, 1990).
The light energy transformed in the photosynthetic process to carbon bond energy in biomass has
long been ignored when compared to the other terms in the surface energy balance. However, as
researchers continue to be plagued by a lack of closure in the surface energy balance (Meyer and
Hollinger, 2004) all of the data processing methods and terms should be reevaluated.
Analyzing the formation of glucose in its chemical reaction (Eq.5), an estimate of the energy
used in photosynthesis is obtained from the net sum of the energy that is required to break the
bonds of the reactants and those in forming glucose and oxygen.
6H2O + 6CO2 ⇒ 6O2 + C6H12O6 (5)
This is the solar energy that is now stored in the bonds of carbohydrate and is ≈422 kJ of energy
per mole of CO2 fixed by photosynthesis (Nobel, 1974). A canopy assimilation rate of 2.5 mg
CO2 m−2
s−1
equates to an energy flux of 28 W m−2
. This conversion factor is used to compute the
measured photosynthesis rates from the eddy covariance measurements to an equivalent energy
flux.
In accordance with Meyers and Hollinger (2004) procedure, storage terms are computed for the
daytime period only and the data are grouped into 2 hours bins beginning at 6:00 and ending to
18:00. The averaged daytime storage fluxes for the whole experimental period are shown in Fig.
1. As shown in Fig.1A, heat storage in the soil is grater then the other storage fluxes. Its trend is
characterized by a peak of about 34 W m-2
in correspondence with the midday. During the
morning, heat storage in the soil increases while in the afternoon it decreases up to 10 W m-2
.
Photosynthesis storage term have a similar behavior with a peak of about 10 W m-2
, while the
canopy heat storage term tend to decrease during the day. In Fig. 1B the ratio between the sum of
storage terms (Total storage) and net radiation, which represents the available energy in the
ecosystem, is shown. The storage fluxes constitute a significant fraction of the available energy
50
with a ratio of about 10% which is quite constant from 8:00 to 14:00, while it tends to decrease
in the late afternoon.
A B
-10
0
10
20
30
40
6-8 8-10 10-12 12-14 14-16 16-18
En
erg
y f
lux
( W
m-2
)
Hours
Sc
Sp
Sg
-5
0
5
10
15
6-8 8-10 10-12 12-14 14-16 16-18
To
tal st
ora
ge/
Rn
(%)
Hours
Fig. 1. A. The average daytime cycle for each storage term for the whole experimental perid. B.
Fraction of net radiation that is portioned to storage for maize plants.
The effect of storage terms on surface energy balance is examined by comparing the sum of H,
LE and G with and without each storage flux against Rn for the daytime periods over the whole
experimental campaign. For the maize filed, without including the storage terms, the slope from
simple linear regression is 0.75 with an R2 of about 0.8 (Fig. 2). When the storage terms, in the
surface energy balance, are included the slope of the linear regression tends to increase up to
0.86 with a R2
of about 0.8 and an intercept of about 1.8 W m-2
. If in the energy balance closure
storage terms are included, the systematic error in fluxes, described by linear regression
intercept, is characterized by a drastic decreasing from 10 W m-2
to 1.8 W m-2
. As explained in
Foken (2008a), the ground heat storage has to be added into soil heat flux to obtain reliable G
flux estimation. In fact, as shown in Fig. 2, ground storage term plays a fundament role into the
energy balance closure improvement having a positive influence of about 6% which is equal to
about 54% over the total energy balance improvement if the whole storage terms are considered.
0
4
8
12
0.68
0.72
0.76
0.8
0.84
0.88
Inte
rcep
t (
W m
-2)
Slo
pe
an
d R
2(-
)
Slope
R2
Intercept
Fig. 2. Energy balance closure adding storage terms.
Although the daytime energy balance with total storage terms is on average closed within 14%,
closure deficit may be a consequence of an inaccurate G flux estimation which is extremely
different in the spatial contest as described in Wilson et al. (2002). Moreover, storage fluxes
51
obtained by a single point measurement can be underestimated in respect to the more
complicated profile methods.
In the common practice, heat soil flux (measured by heat soil plate) is usually corrected with
ground storage term, so that, in the following paragraphs, in G flux the ground heat storage term
is already included.
Effect of time aggregation
As described in Foken (2008b), an energy transport with large eddies which cannot be measured
with the eddy covariance method is assumed as one of the main reasons of the closure problems.
In literature, several methods are discussed to investigate this problem (Sakai et al. 2001,
Finnigan et al. 2003, Foken et al. 2006). About 15 years ago, the ogive function was introduced
into the investigation of turbulent fluxes (Oncley et al. 1990, Friehe 1991). This function was
proposed as a test to check if all low frequency parts are included in the turbulent flux measured
with the eddy covariance method (Foken et al. 1995). The ogive function is the cumulative
integral of the co-spectrum starting with the highest frequencies as described by Eq.6.
0
)()( 0
f
wxwx dffCofOg (6)
where Cowx is the co-spectrum of a turbulent flux, w is the vertical wind component, x is the
horizontal wind component or scalar, and f is the frequency. In Fig. 3 sensible and latent heat
flux cospectrums and their ogive functions are respectively shown. In Fig. 3A example of a
ogive function and co-spectrum for ''Tw in 20 July at 14:00 is shown, while in Fig. 3B example
of a ogive function and co-spectrum for '' 2OHw in 11 August at 03:30 is shown.
A B
-2
0
2
4
6
0.00010.0010.010.1110
0
30
60
90
120
0.00010.0010.010.1110
Co
WT
Og
WT
Frequency (Hz)
Ogive (WT)
Cospectrum (WT)
-20
-10
0
10
20
30
40
0.00010.00100.01000.10001.000010.0000
-30
0
30
60
90
120
150
0.00010.00100.01000.10001.000010.0000
Co
WH
2O
Og
WH
2O
Frequency (Hz)
Ogive (WH2O)
Cospectrum (WH2O)
Fig. 3. Example of a ogive function and cospectrum for ''Tw (A) and '' 2OHw (B) in 20 July at
14:00 and 11 August at 03:30 respectively.
In the convergent case (Fig.3A), the ogive function increases during the integration from high
frequencies to low frequencies until a certain value is reached and remains on a more or less
constant plateau before a 30 minutes integration time. If this condition is full-filled, the 30
52
minutes covariance is a reliable estimate for the turbulent flux, because it is possible to assume
that the whole turbulent spectrum is covered within that interval and that there are only
negligible flux contributions from longer wavelengths (Case 1). But it can also occur that the
ogive function shows an extreme value and decreases again afterwards (Case 2- Fig.3B) or that
the ogive function doesn’t show a plateau but increases throughout (Case 3). Ogive functions
corresponding to Case 2 or 3 indicate that a 30 minutes flux estimate is possibly inadequate.
Foken et al. (2006) define thresholds about ogive characteristic behaviors in order to prescribe if
a ogive belongs to Case 1, 2 or 3.
From the ogive analysis performed for latent and sensible heat fluxes over the whole
experimental period, 30 minutes averaging interval appears to be sufficient to cover all relevant
flux contributions with about 80% of cases included in the Case 1, while only 20% of cases
belongs to Case 2 and 3.
Finnigam et al. (2003) propose a site specific extension of the averaging time up to several hours
to close the energy balance. In Fig. 4 energy balance closures with reference to energy flux
aggregations at different temporal scales, are shown.
-50
-30
-10
10
30
0.7
0.75
0.8
0.85
0.9
0.95
0.5 hour 6 hour 24 hour
Inte
rcep
t (W
m-2
)
Slo
pe
an
d R
2(-
)
Slope
R2
Intercept
Fig. 4. Energy balance closure with different aggregation times.
The slope tends to increase if large size of averaging time are considered, but if an aggregation
period of 6 hours is examined, the linear regression (0.76) is quite similar to that calculated with
half-hourly data (0.75). Instead, with an aggregation time period equal to 24 hours, the slope has
a large improvement (0.83). This is probably due to the effect of storage terms which can be
considered negligible at daily scale as shown in Foken (2008b).
Effect of scale differences in fluxes measurement
The energy balance closure can also be seen as a scale problem, because each flux is
representative of an area (Fig.5). In fact net radiometer source area is the field of view of the
instrument at nadir related to sensor height and it doesn’t change with time. In Fig.5A the net
radiometer source area described by Schmid’s (1997) equation using the radiometer
configuration on the tower for this experimental campaign, is shown. Radiometer is located on a
arm (b) of about 2.5m long, attached on the tower at the height of about 4.5 m (zr). Its orientation
is from North to South to receive the whole solar radiation during the daily hours. Its source area
has a circular shape with a maximum radius of about 4 m, and the major representativeness of
53
the short and long wave measurement, which are coming from the surface, are in correspondence
with the projection of the radiometer on the ground (red zones).
The flux footprint of turbulent fluxes varies in space and time depending mainly on wind
velocity and direction, surface roughness, stability condition of the atmosphere and measurement
height (Hsieh et al., 2000). According to Hsieh et al. (2000) definition, the footprint represents a
weight function (for unit of length) of different contribution that is coming from the surface area
at a certain distance away for the instruments (anemometer and gas analyzer - EC station). This
function change in space and in time and it is different for each 30 minutes measurement. In Fig.
5B footprint source area of the eddy covariance station considering the whole experimental data
from May to September, is shown. Bi-dimensional footprint is computed using Hsieh et al.
(2000) and Detto et al. (2006) models for the longitudinal and lateral spreads respectively. The
mathematical approach to match Hsieh et al. (2000) and Detto et al. (2006) models is not
described in this work but it is widely discussed in the recent article of van de Boer et al. (2013).
The footprint area obtained for each half-hourly data has been oriented in respect to the wind
directions, and performing this procedure on the whole experimental data set, the footprint shape
represented in Fig. 5B has been obtained. In general, the major representativeness of the latent
and sensible heat flux measurements is confined in an area of about 450m2 on the right of the
tower (West direction). This is probably due to the limited magnitude of the wind intensities in
Po Valley which are not exceeded 10 m s-1
.
A B
zr
b
projection of the
radiometer center
Radiometer
footprint (m-2)
zm
EC station
EC station
footprint (m-1)
zm
Fig. 5. A. Radiometer source area. B. Footprint source area for eddy covariance instruments. (b)
arm length , (zr) radiometer height, (EC station) eddy covariance instruments (gas analyzer and
sonic anemometer), (zm) eddy covariance instrument heights.
The effect of flux spatial scales on energy balance closure is evaluated considering the peak
location of the footprint function inside the field. As shown in Fig. 6, the peak data have been
subdivided into four percentile groups (each with 25% of the data) so that turbulent fluxes of
latent and sensible heat connected to each peak are used to compute the energy balance closure.
54
0
2
4
6
8
10
12
0.4
0.6
0.8
1.0
6 - 25% 10- 50% 22 - 75% 628 - 100%
Inte
rcep
t (
W m
-2)
Slo
pe
an
d R
2(-
)
xpeak (m) - percentile
Slope
R2
Intercept
Fig. 6. Energy balance closure for four 25 percentile groups of footprint function peak location
(xpeak).
The energy balance closure tends to increase when the peak location is far from the eddy
covariance station up to 22 m. The maximum value of the linear regression slope is 0.88 in
correspondence with 75 percentile group, i.e. with the footprint peak far from the tower which
varies between 10 and 22 meters. However, when the peak exceeds 22 m the slope tends to
decrease probably because representative source area of eddy covariance measurements exceed
the field dimension. Instead, when the peak location is near the station the heterogeneity of the
island surface (which is sown by hand) and devices influence could create alteration in turbulent
flux measurements. The systematic error defined by intercept, increases linearly with the
percentile groups up to 9.7 W m-2
.
Ground heat flux is usually very small in respect to the other energy fluxes, ranging from 5 to 40
% of net radiation but this flux is the one with the highest uncertainty in its estimate that can
reach an error up to 50% (Foken, 2008a). Moreover, it is measured with an instrument with the
smallest source area that can be up to two orders of magnitude lower than latent and sensible
heat fluxes footprints. So that it can be very changeable in a field due to different soil
characteristics or soil moisture conditions as shown in Kustas et al. (2000), where they found
that, measuring G with 20 instruments in a small site, mean differences in soil heat flux are of
about 40 W m-2
but they can deviate in some occasion also of 100 Wm-2
. Investigation of
variation of heat soil flux across the field and its influences on energy balance closure, is an
important issue which has been studied by many scientists. In the current state, G is assumed
uniform on the field and its strong variability across the field is in first approximation neglected.
Effect of turbulent mixing
The effect of turbulent mixing is evaluated in respect to friction velocity (u*). Friction velocity
typically changes with stability of atmosphere and time of day as explained in Wilson et al.
(2002). The change in energy balance closure could also be the direct result of changes in
friction velocity. In accordance with Wilson et al. (2002), a simple method used to isolate the
effects of friction velocity on energy balance improvement, is shown. Data are separated into
four 25 percentile groups, and each group contains data when the friction velocity is included
among two consecutive friction velocity percentile values. Slope of the linear regression, R2 and
intercept are also evaluated during daytime and night time as shown in Fig.7. As explained in
55
Fig. 7A, during daytime the slope increases from 0.73 to 0.85 and the intercept varies from -1 to
2 W m-2
. Only when friction velocity is included between 0.28 and 0.83 m s-1
, intercept
collapsed on a value of about 0.7 W m-2
. During nighttime (Fig. 7B) energy balance closure is
drastically worsen with a mean slope of about 0.06. Intercept is quite closed to 0 W m-2
while R2
considerably varies among the percentile groups. This is probably due to low wind velocities
which, during nighttime, prevent the well turbulent mixed conditions of the atmosphere
increasing the advection transport of scalar fluxes and worsening the eddy covariance
measurements.
A B
-2
0
2
4
6
0.4
0.6
0.8
1.0
0.14-25% 0.21-50% 0.28-75% 0.83-100%
Inte
rcep
t (W
m-2
)
Slo
pe
an
d R
2(-
)
u* (m s-1) - percentile
Slope
R2
Intercept
-6
-4
-2
0
2
4
6
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.06-25% 0.09-50% 0.15-75% 0.69-100%
Inte
rcep
t (W
m-2
)
Slo
pe
an
d R
2(-
)
u* (m s-1) - percentile
Slope
R2
Intercept
Fig. 7. Energy balance closure for four 25 percentile groups of u* friction velocities. A. Daytime.
B. Nighttime.
In Fig. 8, friction velocity influence on energy balance closure globally evaluated for the whole
experimental data set, is shown. The slope constantly increases up to 0.82 when the data are
included in a friction velocity range between 0.24 and 0.83 m s-1
. The systematic errors defined
by the intercept values tend to decrease, and in correspondence with a closure of 0.82 the
intercept value is about 4.3 W m-2
. Literature results (Wilson et al., 2002; Barr et al., 2006) are
also confirmed from the analysis performed at Livraga station, given that with the increase of
friction velocity the closure of the energy budget tends to increase as well. In fact when the
friction velocity is low, the turbulence is softened and the fluxes are usually underestimated. The
problem related to the use of friction velocity as an indicator of good measured data is linked to a
u* threshold definition. In Alavi et al. (2006) a value of 0.1 m s-1
is considered, while Oliphant et
al. (2004) use 0.3 m s-1
and Barr et al. (2006) 0.35 m s-1
, showing that the choice of this limit on
u* seems to be site dependent.
0
2
4
6
8
10
0
0.2
0.4
0.6
0.8
1
0.08 - 25% 0.15 - 50% 0.24 - 75% 0.83 - 100%
Inte
rcep
t (W
m-2
)
Slo
pe
an
d R
2(-
)
u* (m s-1) - percentile
Slope
R2
Intercept
Fig. 8. Energy balance closure for four 25 percentile groups of u* friction velocities for the
whole experimental dataset.
56
Effect of vegetation
Many experimental results about energy balance problems above low and tall vegetations are
available in literature (Wilson et al., 2002; Aubinet et al., 2000; Panin et al., 1998). Here, the
influence of the vegetation height and heterogeneity on energy balance closure is studied
subdividing the experimental data set into five classes from C1 to C5. Each class contains data
with different vegetation height (Tab. 1) in function of canopy growth.
Tab. 1. Vegetation height classis.
Class Vegetation height (cm)
C1 From 0 to 30
C2 From 30 to 60
C3 From 60 to 90
C4 From 90 to 150
C5 From 150 to 320
For each class the energy balance closure is calculated and the results are shown in Fig. 9A. The
slope tends to decrease, with an increase of vegetation height, up to 0.76 for a canopy height
between 150 and 320 cm. The maximum slope value is about 0.98 in correspondence with C1
class when the surface heterogeneity is particularly accentuated. Intercept changes its plus sign
in correspondence with C5 class, where the intercept value is about -3.4 W m-2
. To better
understand how these results are possible, the storage terms should be taken into account. In Fig.
9B, the slopes of the linear regression is compared with the percentage storage weights defined
by Eq.7. Storage weight is the ratio between the averaged storage fluxes for each class and the
sum of these averages on the whole class subdivisions.
1001
1
5
1 1
1
j j
N
i
i
N
i
i
x
SxN
SxN
weightStorage (7)
Where S is the storage term for the x flux (soil heat ground, photosynthesis or canopy storages),
N is the number of data for each class and j is a class indicator so that when it is equal to 1 it
represents C1 class, when it is equal to 2 it represents C2 class, and so on.
As shown in Fig. 9B, the slope trend is opposite to canopy and photosynthesis storage weight
terms. In fact, when the canopy is tall the weights of Sc and Sp are particularly relevant reaching
the value of about 35% in correspondence with C5 class. Instead, the soil heat ground storage
weight term drastically decreases when the vegetation is tall, moving it from 25% to 5% when
the class changes from C4 to C5. The presence of vegetation which covers the field play a
fundamental role in energy balance closure. In particular way, during the canopy growth, the Sp
and Sc storage terms increase their influence on energy balance closure and if they are not
considered the energy unbalance is accentuated. When the vegetation is lowed Sp and Sc effects
can be neglected while Sg becomes relevant reaching the weight value of about 30% (C1 class).
57
A B
-4
-3
-2
-1
0
1
0.7
0.8
0.9
1
1.1
C1 C2 C3 C4 C5
Inte
rcep
t (W
m-2
)
Slo
pe
an
d R
2(-
)
Slope
R2
Intercept
0
10
20
30
40
50
60
0.6
0.7
0.8
0.9
1
1.1
C1 C2 C3 C4 C5
Sto
rag
e w
eig
ht
(%)
Slo
pe
(-)
Slope
Sg
Sc
Sp
Fig. 9. A. Energy balance closure for five class of vegetation height. B. Slope and storage weight
terms in function of vegetation height classes.
Effect of seasonality
To clearly describe the partition of energy balance components during different seasons, the
daily patterns of the 30 minutes averages of Rn, LE, H and G in May, June, July and August are
plotted in Fig.10. Net radiation maximum peak is quite constant from May to August oscillating
between 500 and 600 W m-2
. Latent and sensible heat have a strong variability trough the
months, showing a quite similar trend from May to June while in July and August latent heat is
about 3 times greater than sensible heat. The soil heat flux accounts for a small proportion of the
available energy, in particular way, when the vegetation covers the field surface. In fact, in May
at 12:00 it can also reach the maximum value of about 100 W m-2
, while in July and August the
soil heat flux is equal to few tens of watt to meter square.
The partitioning of net radiation into sensible heat and latent heat fluxes is strongly influenced by
change in vegetative characteristics. Specifically, when the vegetation is tall, the dominant
component of the energy budget is represented by latent heat with a peak in July of about 450 W
m-2
. Sensible heat is the main energy component when the vegetation is absented. It tends to
decrease during the canopy growth but, as shown in August, when the vegetation is fully
developed, it returns to be similar to values shown in May. One special phenomenon, called the
“oasis effect” can be noted in July when latent heat is the main component which takes the
largest portion of Rn and sensible heat is very small. In the case of optimum conditions for
evaporation, i.e. high soil moisture and well turbulent conditions (Foken, 2008a), the evaporation
process will be greater than the sensible heat flux. In such cases, sensible heat changes its sign 1-
3 hours before sunset and sometimes in the shortly afternoon, occurring in the atmosphere a
temperature gradient inversion and a downwarded sensible heat transfer.
58
A B
-100
0
100
200
300
400
500
600
0 3 6 9 12 15 18 21 24
Flu
xes
( W
m-2
)
Hours
Rn
LE
H
G
-100
0
100
200
300
400
500
600
0 3 6 9 12 15 18 21 24
Flu
xes
( W
m-2
)
Hours
Rn
LE
H
G
C D
-100
0
100
200
300
400
500
600
700
0 3 6 9 12 15 18 21 24
Flu
xes
( W
m-2
)
Hours
Rn
LE
H
G
-100
0
100
200
300
400
500
600
0 3 6 9 12 15 18 21 24
Flu
xes
( W
m-2
)
Hours
Rn
LE
H
G
Fig. 10. Seasonal variation of energy fluxes. A. May. B. June. C. July. D. August.
Energy balance closure for each month is shown in Fig. 11. The slope of the linear regression is
particularly influenced by the canopy growth. When the field is completely covered by the
vegetation and it can be considered as an homogenous surface, energy balance closure decreases
up to 0.77 with an intercept value of about -1.4 W m-2
. This is probably due to the effect of
canopy and photosynthetic storage terms which become important when the vegetation is tall and
the surface is homogenously covered by the plants. Analyzing each flux of the energy balance
over the whole experimental period (Fig. 10) it is possible to realize that over a field covered by
dense vegetation, latent heat is the main dominant component of the energy budget (respect to
sensible heat and soil heat ground) and a lack of the energy balance closure corresponds to an
underestimation of the canopy evapotranspiration fluxes. In water management practices this
problem assumes a dominant role in irrigation procedure given that a correct estimation of the
evapotranspiration fluxes corresponds to an efficacious and sustainable management of the water
resource.
59
-1.5
-1
-0.5
0
0.5
1
0.4
0.6
0.8
1
1.2
May June July August
Inte
rcep
t (W
m-2
)
Slo
pe
an
d R
2(-
)
Slope
R2
Intercept
Fig. 11. Energy balance closure evaluated for each month.
Random error
Reliability of turbulent fluxes can be obtained only if theoretical assumption of the eddy
covariance technique, described in Moncrieff et al. (1996), are followed. Non steady-state
conditions, random noise of the signal, inadequate length of sampling interval, size variation of
flux footprint and surface heterogeneity, single point measurement of turbulence and inadequate
sensor response could cause random uncertainty in fluxes measurements. Random errors have
been mainly studied by Hollinger and Richardson (2005) comparing flux measurements obtained
by two identical micrometeorological stations located in the same place with the same flux
footprint, or by Richardson et al. (2006) comparing pair of measurements made on two
successive days from the same tower under equivalent environmental conditions. Using
Lenschow et al. (1994) method to detect random uncertainty in sensible and latent heat fluxes, it
is possible to realize that errors in estimated means, variances and co-variances diminish
increasing the size of data set (as long as the data set is not enlarged that, for example, seasonal
trends become important) and the random uncertainty magnitude proportionally increases with
the growth of sensible and latent heat flux intensities (Fig. 12).
A B
0
10
20
30
40
50
-200 -100 0 100 200 300
Ra
nd
om
un
cert
ain
ity
(W
m-2
)
Sensible heat ( W m-2)
0
20
40
60
80
100
-100 0 100 200 300 400 500
Ra
nd
om
un
cert
ain
ity
(W
m-2
)
Latent heat ( W m-2)
Fig. 12. Random uncertainty in function of sensible (A) and latent (B) heat flux magnitudes.
Some authors as Bernardes and Dias (2010) include error bars when reporting measured values
of turbulent fluxes. It is not a common micrometeorological practice but to realize how random
60
errors affects latent and sensible heat fluxes, in Fig. 13 the mean daily turbulent flux intensities
jointed with their range of confidence, are shown. The maximum uncertainty is associated with
daytime when maximum latent and sensible heat magnitudes are shown. During daytime, the
maximum range of confidence is about 40 W m-2
for sensible heat and 80 W m-2
for latent heat,
while during the nighttime it tends to zero.
A B
-20
10
40
70
100
130
0 3 6 9 12 15 18 21 24
Sen
sib
le h
eat
(W m
-2)
Hours
H
Random uncertainity
-20
60
140
220
300
380
0 3 6 9 12 15 18 21 24L
ate
nt
hea
t (W
m-2
)
Hours
LERandom uncertainity
Fig. 13. Range of confidence obtained from random error estimation for sensible (A) and latent
(B) heat fluxes.
Generally, some random error sources could be solved trying to apply rigorously practical rules
described in many literature works which have been written starting from the birth of the eddy
covariance technique (Foken, 2008a; Schmid, 1997). However, the energy balance closure is
affected by these errors which can not be completely eliminated. Filtering methods based on a
spatially decomposition of turbulent fluxes (Salesky et al., 2012) tries to quantify rigorously the
random errors with the objective, in the common practice for the authors, to include an estimate
of random errors magnitude when micrometeorological measurements are shown.
Conclusion
Livraga 2012 measurements have been an excellent data set for evaluating the surface energy
balance problems. All findings about the flux error sources cannot completely explain the
problem of the unclosed surface energy balance. It is founded that crucial attention to calibration,
maintenance and software correction of data is essential to obtain half-hourly reliable fluxes.
Despite this effort, data set contains an unbalance of about 25% which has been studied taking
into account different turbulent flux problems.
Storage terms play a fundamental role to improve the energy balance closure and they are about
10% of the daily available radiation energy. Photosynthesis and canopy storage terms are
prevalent in the field when the vegetation covers the soil surface and the canopy is fully
developed. Ground heat storage is greater than the other storage terms and it can reach up to 50%
of the soil heat flux. Canopy growth and seasonality effects are strongly connected with storage
terms. When the vegetation is lowed the energy balance closure is almost equal to 1 because only
ground heat storage term exists with a percentage weight of about 30%. From class C1 to class
C5 the energy balance closure decreases if the vegetation storage terms (canopy and
61
photosynthesis terms) are not considered. Similarly, energy balance closure decreases from May
to August in accordance with the increasing of the vegetation storage terms. Energy balance flux
partitioning highline how the available energy (net radiation) is subdivided in latent, sensible and
soil heat fluxes, detecting the flux which could mainly contribute to the unbalance problem.
During experimental campaign the results show that latent heat is the main component of the
energy budget, and, in some months, it is grater then 40% of the available energy.
Atmospheric turbulence characteristics play a fundamental role in flux reliable estimations. In
some cases, half-hourly averaged time is not sufficiently longed to take into account the long-
wave terms of the turbulent flux measurements. Studying the ogive functions, the results show
that about 20% of data are partially corrected because their aggregation time covers only a
portion of turbulent eddies which stay in the surface layer (Garrat, 1993). Some authors
(Lenschow et al., 1994) suggests to change the averaged aggregation time of the eddy covariance
flux measurements in function of the atmospheric turbulence characteristics, but increasing
drastically the complexity of the common practice measurements. State of turbulent mixing is an
important aspect against to the advection phenomenon. One of the theoretical assumption of the
eddy covariance technique is that advection terms can be neglected. Friction velocity is used to
give a threshold which discerns the existing probability of the advection transport. Energy
balance closure in developed turbulent mixing conditions is greater than the cases with low
turbulence, and the closure is about 0.8 if friction velocity is confined between 0.24 and 0.83 m
s-1
.
In the past the researches on the energy balance closure problems was mainly directed on
measuring errors, and only a few results underline the scale hypothesis. The results shown in this
work underline the complexity of the source area footprint definition for each flux of the energy
budget. Atmospheric stability conditions, measurement height, surface roughness and wind
velocity are some common parameters which govern the footprint models. In Po Valley, the
weak wind velocities and strong convective forces during summer months provoke the
movement of footprint peak in direction of the tower, so that the major representativeness of
source area is certainly confined inside the field. Site specific new experiments should be made
to understand how the representative source area for eddy covariance measurements change in
function of atmospheric, physical and geometrical characteristics of the field. It should be a
subject of further researches to recalculate eddy covariance experimental results again using a
new experimental plan and a specialized measuring setup calibrated for the scale problem. LES
modeling studies could be used to support these researches.
Despite this overview cannot be a final work, this paper shows important results about the
energy balance closure problem. Moreover, this work is one of the few researches on maize field
in Po Valley which are presented in literature, increasing the knowledge on the energy balance
problems at international scale.
References
Alavi, N., Warland, J., and Berg, A. (2006). Filling gaps in evapotranspiration measurements for water budget
studies: Evalutation of a Kalman filtering approach. Agricultural and Forest Meteorology , 141: 57-66.
Aubinet, M., Grelle, A., Ibrom, A., et al. (2000). Estimates of the annual net carbon and water exchange of forests:
the euroflux methodology. Advanced in Ecological Research , 30: 113-175.
62
Aubinet, M., Heinesch, B., and Yernaux, M. (2003). Horizontal and vertical CO2 advection in a sloping forest.
Boundary Layer Meteorology , 108: 397-417.
Baldocchi, D., Falge, E., Gu, L., Olsen, R., Hollinger, D., Running, S., et al. (2001). FLUXNET: a new tool to study
the temporal and spatial variability of ecosystem scale carbon dioxide, water vapor, and energy flux densities.
Bullettin of the American Meteorological Society , 82: 2415-2434.
Baldocchi, D. and Rao K.S. (1995). Intra field variability of scalar flux densities across a transition between a desert
and an irrigated potato field. Boundary Layer Meteorology, 76: 109-136.
Barr, A., Morgenstern, K., Black, T., McCaughey, J.,and Nesic, Z. (2006). Surface energy balance closure by the
eddy-covariance method above three boreal forest stands and implications for the measurement of CO2 flux.
Agricultural and Forest Meteorology , 140: 322-337.
Bernardes, M., and Dias, N. (2010). The alignment of the mean wind and stress vectors in the unstable surface layer.
Boundary Layer Meteorology , 134: 41-59.
Detto, M., Montaldo, N., Alberston, J., Mancini, M., and Katul, G. (2006). Soil moisture and vegetation controls on
evapotranspiration in a eterogeneus Mediteranean ecosystem on Sardinia,Italy. Water Resources Research , 42: 1-
16.
Elliot, W. (1958). The growth of the atmospheric internal boundary layer. Transaction American Geophysic Union,
50: 171-203.
Feigenwinter, C., Bernhofer, C., and Vogt, R. (2004). The influence of advection on the short term CO2- budget in
and above a forest canopy. Boundary Layer Meteorology , 113: 201-224.
Finnigan, J., Clement, R., Malhi, Y., Leuning, R., and Cleugh, H. (2003). A re-evaluation of long term flux
measurement techniques part I: averaging and coordinate rotation. Boundary Layer Meteorology , 107: 1-48.
Finningam, J., Aubinet, M., Katul, G., Leuning, R., and Schimel, D. (2006). Report of a specialist workshop on
"Flux measurements in difficult conditions",26-28 January, Boulder Colorado. Bullettin of the American
Meteorological Society , in press.
Fisher, J., Baldocchi, D., Misson, L., Dawson, T., and Goldstein, A. (2007). What the towers don't see at night:
nocturnal sap flow in trees and shrubs at two AmeriFlux sites in California. Tree Physiology , 27: 597-610.
Foken, T. (2008a). Micrometeorology. Berlin: Springer, pp. 306, ISBN 978 3 540 74665 2.
Foken, T. (2008b). The energy balance closure problem:an overview. Ecological Applicatons, 18: 1351-1367.
Foken, T., and Wichura, B. (1996). Tools for quality assessment of surface-based flux measurements. Agricultural
and Forest Meteorology , 78: 83-105.
Foken, T., Dlugi, R., and Kramm, G. (1995). On the determination of dry deposition and emission og gaseous
compounds at biosphere-atmosphere interface. Meterologische Zeitschrift , 4: 91-118.
Foken, T., Wimmer, F., Mauder, M., Thomas, C., and Liebhetal, C. (2006). Some aspects of the energy balance
closure problem. Atmososperich and Chemistry Physics, 6,4395-4402.
Friehe, C. (1991). Air-sea fluxes and surface layer turbulence around a sea surface temperature front. Journal of
Geophysical Research , C96: 8593-8609.
63
Garratt, J. (1993). The atmospheric boundary layer. Cambridge: Cambridge university press, pp.316, ISBN 0 521
38052 9.
Gash, J., and Culf, A. (1996). Applying linear de-trend to eddy correlation data in real time. Boundary Layer
Meteorol. , 79: 301-306.
Hollinger, D., and Richardson, A. (2005). Uncertainity in eddy covariance measurements and its application to
physiological models. Tree Physiology, 25: 791-873.
Hsieh, C., Katul, G., and Chi, T. (2000). An approximate analytical model for footprint estimation of scalar fluxes
in thermally stratified atmospheric flows. Advanced Water Resource , 23: 765-772.
Jacobs, A., Heusinlveld, B., and Holtslag, A. (2008). Towards closing the energy surface budget of a mid-latitude
grassland. Boundary Layer Meteorology , 126: 125-136.
Kustas, W.,and Daughtry, C. (1990). Estimation of the soil heat fluxnet radiation ratio from spectral data .
Agricultural and Forest Meteorology , 49: 205-223.
Kustas, W., Prueger, J., Hatfieldb, J., Ramalingamc, K., and Hippsc, L. (2000). Variability in soil heat flux from a
mesquite dune site. Agricultural and Forest Meteorology , 103: 249-264.
Lenschow, D., Mann, J., and Kristensen, L. (1994). How long is long enough when measuring fluxes and other
turbulence statistics? Journal of Atmospheric and Oceanic Technology , 11: 661-673.
Ma, Y., Wang, Y., Wu, R., Hu, Z., Yang, K., Ma, W., et al. (2009). Recent advances on the study of atmosphere-
land interaction observations on the Tibetan Plateau. Hydrology Earth System Sciences, 13: 1103-1111.
Marcolla, B., Cescatti, A., Montagnani, L., Manca, G., Kerschbaumer, G., and Minerbi, S. (2005). Importance of
advection in atmospheric CO2 exchanges of an alpine forest. Agricultural and Forest Meteorology, 130: 193-206.
Massman, W., and Lee, X. (2002). Eddy covariance flux corrections and uncertainties in long-term studies of carbon
and energy exchanges. Agricultural and Forest Meteorology , 113: 121-144.
Mayocchi, C., and Bristow, K. (1995). Soil surface heat flux: some general questions and comments on
measurements. Agricultural and Forest Meteorology , 75: 43-50.
Meyers, T., and Hollinger, S. (2004). An assessment of storage terms in the surface energy balance of maize and
soybean. Agricultural and Forest Meteorology , 125: 105-115.
Moncrieff, J., Malhi, Y., and Leuning, R. (1996). The propagation of errors in long term measurements of land
atmosphere fluxes of carbon and water. Global Change Biology , 2: 231-240.
Moncrieff, J., Massheder, J., De Bruin, H., Ebers, J., Friborg, T., Heusinkveld, B., et al. (1997). A system to
measure surface fluxes of momentum, sensible heat, water vapor and carbon dioxide. Journal of Hydrology , 188:
589-611.
Nobel, P. (1974). Introduction to biophysical physiology. New York: Freeman.
Oliphant, A., Grimmond, C., Zutter, H., Schmid, H., H.B., S., Scott, S., et al. (2004). Heat storage and energy
balance fluxes for a temperate deciduos forest. Agricultural and Forest Meteorology , 126:185-201.
Oncley, S., Businger, J., Itsweire, C., Friehe, J., LaRue, J., and Chang, S. (1990). Surface layer profiles and
turbulence measurements over uniform land under near-neutral conditions. American Meteorological Society
Washinton D.C., USA , Pages 237-240 in 9th Symposium on Boundary Layer and Turbulence.
64
Oncley, S., Delany, A., Horst, T., and Tans, P. (1993). Verification of flux measurement using relaxed eddy
accumulation. Atmospheric Environment , 27: 2417-2426.
Oncley, S., Foken, T., Vogt, R., Kohsiek, W., DeBruin, H., Bernhofer, C., et al. (2007). The energy balance
experiment EBEX-2000. Part I: overview and energy balance. Boundary Layer Meteorology , 123: 1-28.
Panin, G., Tetzlaff, G., and Raabe, A. (1998). Inhomogeneity of the land surface and problems in the
parameterization of surface fluxes in natural conditions. Theoretical and Applied Climatology , 60:163-178.
Papale, D., Reichstein, M., Aubinet, M., Canfora, E., Bernhofer, C., Kutsch, W., et al. (2006). Towards a
standardized processing of net ecosystem exchange measured with eddy covariance technique: algorithms and
uncertainty estimation. Biogeosciences , 3: 571-583.
Richardson, A., Hollinger, D., Burba, G., Davd, K., Flanagan, L., Katul, G., et al. (2006). A multi site analysis of
random error in tower-based measurements of carbon and energy fluxes. Agricultural and Forest Meteorology , 136:
1-18.
Runkle, B., Wille, C., Gazovic, M., and Kutzbach, L. (2012). Attenuation correction procedures for water vapor
fluxes from closed-path eddy covariance systems. Boundary-Layer Meteorology , 142: 1-23.
Sakai, R., Fitzjarrald, D., and Moore, K. (2001). Importance of low frequency contributions to eddy fluxes observed
over rough surface. Journal of Applied Meteorology , 40: 2178-2192.
Salesky, S., Chamecki, M., and Dias, N. (2010). Estimating the random error in eddy covariance based fluxes and
other turbulence statistics: the filtering method. Boundary Layer Meteorology, 144: 113-135.
Savelyev, S., and Taylor, P. (2005). Internal Boundary Layer: I. Height formulae for neutral and diabatic flows.
Boundary Layer Meteorology , 115: 1-25.
Schmid, H. (1997). Experimental design for flux measurements: matching scales of observations and fluxes.
Agricultural and Foest Meteorology , 87: 179-200.
Schotanus, P., Nieuwstadt, F., and De Bruin, H. (1983). Temperature meaurement with a sonic anemometer and its
application to heat and moisture fluxes. Boundary Layer Meteorology , 26: 81-93.
Staebler, R., and Fitzjarrald, D. (2006). Observing subcanopy CO2 advection. Agricultural and Forest Meteorology ,
122: 139-156.
Ueyama, M., Hirata, R., Mano, M., Hamotani, K., Harazono, Y., Hirano, T., Miyata, A., Takagi, K., and Takahashi,
Y., (2012). Influences of various calculation options on heat, water and carbon fluxes determined by open- and
closed –path eddy covariance methods. Tellus B, 64: 1-26.
Van de Boer A., A.F. Moene, D. Schuttemeyer, A. Graf (2013). Sesnitivity and uncertainity of analytical footprint
models according to a combined natural tracer and ensemble. Agricultural and Forest Meteorology, 169: 1-11.
Van DijK, A., Kohsiek, W., and De Bruin, H. (2003). Oxygen sensitivity of krypton and Lyman-alfa Hygrometer.
Journal of Atmospheric and Oceanic Technology , 20: 143-151.
Vickers, D and Mahrt, L. (1997). Quality control and flux sampling problems for tower and aircraft data. Journal of
Atmospheric and Oceanic Technology , 14: 512-526.
Webb, E., Pearman, G., and Leuning, R. (1980). Correction of the flux measurements for density effects due to heat
and water vapour transfer. Boundary Layer Meteorology , 23: 251-254.
65
Wilczak, J., Oncley, S., and Stage, S. (2001). Sonic anemometer tilt correction algorithms. Boundary Layer
Meteorology , 99: 127-150.
Wilson, K., Goldstein, A., Falge, E., Aubinet, M., Baldocchi, D., Berbigier, P., et al. (2002). Energy balance closure
at FLUXNET sites. Agricultural and Forest Meteorology , 113: 223-243.
66
(Chapter 3) – Experimental data about the spatial variability of scalar fluxes across maize field in Po Valley and
comparison with theoretical footprint model predictions
Abstract
Representative source area for turbulent flux measurements by eddy covariance stations is an
important issue which has not yet been fully investigated. In particular way, the validation of the
analytical footprint models is generally based on the comparison with Lagrangian model
predictions, while experimental results are not largely diffused in literature. In this work, latent,
sensible heat and carbon dioxide flux measurements across two experimental fields in Po Valley
are shown, and two totally different scenarios at bare and vegetated soils are analyzed.
Experiments are performed using two eddy covariance systems: one fixed station which is
located about in the middle of the field and a mobile station which is placed at various distances
from the field edge to investigate the horizontal variation of the vertical scalar fluxes. The
measured fluxes of latent, sensible heat and carbon dioxide are compared with the predictions of
two analytical footprint models. There is a good agreement between measurements and one of
the two analyzed model predictions. The results have also shown that the spatial distribution of
turbulent fluxes is strongly influenced by the presence of vegetation in the field. Moreover, each
turbulent flux is characterized by its own representative source area which could be extremely
different from the others increasing the complexity of the footprint problem determinations for
eddy covariance measurements.
Introduction
Eddy covariance measurements are widely applied to continuously monitor turbulent exchange
of mass and energy at the vegetation-atmosphere interface (Aubinet et al., 2000). Moreover, the
eddy covariance method is one of the most accurate and direct approaches available in literature
to measure turbulent exchanges over field areas with different sizes (Baldocchi et al., 2001). The
eddy covariance method is a statistical tool which, stating from high-frequency data of wind
components and scalar densities, provides to assess latent, sensible heat and carbon dioxide
turbulent fluxes (Baldocchi, 2003). The fluxes are calculated as a covariance among turbulent
components of vertical wind velocity and scalar concentration (vapor, air temperature or carbon
dioxide). The main micrometeorological instruments which give the name to the eddy covariance
technique are the tridimensional sonic anemometer and gas analyzer respectively. The reliability
of flux measurements depend on certain theoretical assumptions of the eddy covariance
technique (Kaimal and Finnigan, 1994; Foken and Wichura, 1996), the most important of which
are horizontal homogeneity, stationarity and mean vertical wind speed equal to zero during the
averaging period. Eddy covariance method was used in micrometeorology for over 30 years, and
now, modern instruments and software make this method easily available and widely used in
67
different research fields, such as in ecology, hydrology, environmental and industrial monitoring
(Baldocchi et al., 1988; Papale et al., 2006).
In the past years a global network of micrometeorological tower sites which use eddy covariance
methods to measure carbon dioxide, water vapor and energy exchanges between soil-vegetation
and atmosphere systems was constituted. Its name is Fluxnet and as of January 2009, there are
over 500 tower sites in continuous long-term operation
(http://www.fluxnet.ornl.gov/fluxnet/overview.cfm, Wilson et. al., 2002; Sanchez et. al., 2010).
The proliferation of eddy covariance flux systems in a variety of conditions and ecosystems,
often violating some the theoretical requirements of the methodology, has created an increasing
interest in footprint analysis (Schmid, 1997; Rannik et al., 2000). Schuepp et al. (1990) specify
the term ‘footprint’ as the relative contribution from each element of the upwind source area to
the measured concentration or vertical flux. It can be interpreted as the probability that a trace
gas, emitted from a given elemental source, reaches the measurement point. Mathematically, flux
and footprint are related by Eq. 1 as explained in Hsieh et al. (2000).
x
mm dxzxfxSzxF ),()(),( (1)
Where F is the scalar flux, f is the footprint function, S is the source strength, zm is the
measurement height and x represents the horizontal coordinate along wind direction.
As described in Vesala et al. (2008), the determination of the footprint function is not a
straightforward task and several theoretical approaches have been derived over the previous
decades. They can be classified into four categories: (i) analytical models, (ii) Lagrangian
stochastic particle dispersion models, (iii) large eddy simulations, and (iv) ensemble-averaged
closure models. Additionally, parameterizations of some of these approaches have been
developed, simplifying the original algorithms for use in practical applications (e.g., Horst and
Weil, 1992; Schmid, 1994). The criterion of a 100:1 fetch to measurement height ratio was long
held as the golden rule guiding internal boundary layer (IBL) estimation and nowadays is still
used as a rule-of- thumb to crudely approximate the source area of flux measurements over short
canopies in daytime conditions. However, the unsatisfactory nature of the 100:1 ratio and the
related footprint predictions were explicitly discussed by Leclerc and Thurtell (1990).
The dramatic increase of publications that address footprint modeling, applications or related
issues of fetch and spatial representativeness for flux measurements in recent years, demonstrates
the growing need for practical footprint models. The development of a growing number of long-
term trace gas exchange studies over complex forest canopies and in often topographically
challenged terrain, underlines the fact that the requirements for future footprint models are
divergent: on the one hand, practical footprint models must be easy to use, if ever possible in the
field, where the availability of computer resources (and time) is limited. The recent
developments in analytical footprint models satisfy this need, but these models are limited to
homogeneous surface layer similarity conditions (Horst and Weil, 1992; Schuepp et al., 1990;
Hsieh et al. 2000; Kormann and Meixner, 2001). On the other hand, footprint models should
produce realistic results in real-world situations for measurements over (or below) tall canopies,
spatially heterogeneous turbulence, stability conditions from extremely stable to free-convective,
and instationarity. Backward Lagrangian models and the large eddy simulation-based footprint
68
studies provide for the analysis of the representativeness source area in real-world situations but
also if they are considered promising, computational time and extreme complexity restrict their
application field (Kljun et al., 2002; Rodean, 1996; Wilson and Sawford, 1996; Thomson, 1987).
There is a general need for footprint model validations. According to Foken and Leclerc (2004)
only a few experimental data set are available for validation proposes. Lagrangian dispersion
models are tested against dispersion experiments of artificial traces for different turbulence
regimes (Thomson, 1987; Kurbanmuradov and Sabelfeld, 2000; Kljun et al., 2002; Leclerc et al.,
2003). Measurements in complex flow fields, as dispersion inside and above high vegetation
canopy, may not be ideal for evaluation and validation of footprint models. Kljun et al. (2004)
suggest the validation under ideally controlled conditions that can be reproduced in wind tunnels.
Generally, analytical footprint predictions are often evaluated using results of Lagrangian
footprint models. Nowadays, only sites with short vegetation and an accurate selection of
measured data, according to the quality check criteria by Foken and Wichura (1996), allow the in
situ validation of analytical footprint models in “nearly ideal” conditions. In Marcolla and
Cescatti (2005) a new approach for the determination of the relative contribution of a source area
to the measured turbulent flux is shown. In their study areas at different distances from the
measuring point are cut at different times, thus generating spatial and temporal variability in the
sink strength. Light response curves at three different time periods, characterized by
homogenous or heterogeneous surface coverage, are used to quantify the contribution of the area
within a certain distance from the measuring system to the total flux. Gockede et al. (2005)
approach is constituted by two flux stations over bare soil and a meadow. A third station, with a
footprint area covering both surfaces, is used to validate the footprint model, because the
contributions of both surfaces changed with the stability and wind velocity. Earlier investigations
used a similar approach: Soegaard et al. (2003) operated five ground-level eddy covariance
systems over five different crop fields together with a sixth set-up on top of a higher mast to
enable landscape-wide flux measurements. The agreement between high-level values and those
integrated from ground-level using a re-formulated version of the models of Gash (1986) and
Schuepp et al. (1990) is good. Van de Boen et al. (2013) use a data set obtained by three eddy
covariance stations located in landscape with different land use typologies, to test the
performance of the Hsieh et al. (2000) and Kormann and Meixner (2001) footprint models using
an experimental methodology widely described in Neftel et al. (2008). In literature, only one
experiment which investigates the horizontal variation of the vertical turbulent fluxes over a
potato field is shown (Baldocchi and Rao, 1995). The experiment is performed by placing a
mobile eddy covariance station at various distances from the upwind field edge versus a fixed
eddy covariance station located in the middle of the field. The results are used by Hsieh et al.
(2000) to validate their footprint model starting from natural traces.
In this paper Baldocchi and Rao (1995) methodology to validate Hsieh et al. (2000) and
Kormann and Meixner (2001) footprint models has been proposed again but, for the first time, it
is applied over two experimental fields located in Po Valley: one characterized by bare soil and
another one covered by maize plants. Particular wind condition regimes, atmospheric turbulence
characteristics and field geometrical shapes, which occur in Po Valley, make of this experiment
an interesting footprint model validation proof. This paper describes experimental set up and its
execution, furthermore, the results about intra-field spatial variability of latent, sensible and
carbon dioxide fluxes are compared with Hsieh et al. (2000) and Kormann and Meixner (2001)
69
footprint models to verify their reliability also for eddy covariance station placed over Padana
region cultivations.
What is the importance of this experiment?
In this paragraph many different improvement connected with a correct definition of the
representative source area for turbulent flux measurements are briefly summarized.
1) Representative source area for turbulent fluxes has to be confined inside the field if the
eddy covariance flux measurements are used to characterize water management practices
or canopy phenological growth. In Po Valley, where the field shapes are quite small (in
the order of ten hectares), rigorous footprint modeling predictions are necessary to reduce
uncertainty over the evapotranspiration flux representative source areas. Footprint model
validations could also contribute to improve the reliability of turbulent flux
measurements by eddy covariance stations decreasing the uncertainty about
evapotranspiration annual budget over cultivated fields.
2) This experiment actively contributes to improve literature results about footprint model
validation experiments with a scenario totally different by the other presented nowadays
in literature. Moreover, as highlighted by Foken and Leclerc (2004), many experimental
campaigns to validate footprint models are expensive, and hence prohibitive for the vast
majority of university researches. Increasing literature experimental results, which try to
resolve this problem, a common database could be developed so that it can be consulted
by the researcher for their experiments.
3) Flux spatial distribution results above the canopy or on bare soil can be used in some
mathematical models, from Lagrangian stochastic dispersion to large eddy simulation, to
describe in an accurate way the field-domain turbulent real conditions, comparing output
model results with the experimental measurements.
4) The knowledge about representative source areas for latent and sensible heat fluxes could
contribute to resolve the energy unbalance problem which can be seen as a scale problem
about sensor measurements as widely discussed in Foken (2008).
5) Another practical implication about footprint model validations is connected with the
correct definition of the eddy covariance tower position in the field. In fact, it has to be
located sufficiently far from the field edge to avoid the influence of the neighbor fields.
However, eddy covariance measurements which are performed in fields where the
heterogeneity is particularly accentuated, need to known the footprint shape and its size
to understand the weight of fluxes which come from the neighbor fields.
These points explain five macro-areas which could be affected by the results of this experiment,
making a list about the problems which many scientists met in their researches.
Theoretical background
Estimation of flux footprint from experimental data is compared with predictions of two
analytical footprint models proposed by Hsieh et al. (2000) (called Hsieh model) and Kormann
and Meixner (2001) (called Kormann Model). The choice of these footprint models is a
70
compromise between reliability and simplicity, following the suggestion by Foken and Leclerc
(2004) on the necessity of easy-to-use footprint models.
Hsieh et al. (2000) model is constituted by a combination of Lagrangian stochastic model results
and dimensional analysis. It analytically relates atmospheric stability, measurement height and
surface roughness length to obtain an approximated analytical expression which accurately
describes the footprint function. The results are organized in non-dimensional groups and related
to the input variables by regression analysis. The advantages of this model are evident: the
hybrid model can be expressed by a set of explicit algebraic equations, while some of the
complexity and skill of the full model is retained through the regression. However, the pitfall of
any approximation or parameterization is that its validity is strictly limited to the range of
conditions over which it is developed.
Kormann and Meixner (2001) model belongs to the class of the Eulerian analytic flux footprint
models which explore several approaches to approximately resolve the advection-diffusion
equation. Schuepp et al. (1990) are the first scientists that have taken a purely analytical
approach, based on an approximate solution of the diffusion equation given by Calder (1952) for
thermally neutral stratification and a constant wind velocity profile. As stated by the authors, it
suffers from the restriction to neutral stratification. Their suggestion, to correct the wind velocity
in the footprint calculation based on thermal stability, has no mathematical basis. Instead,
Kormann and Meixner (2001) model includes parameterizations of power law for wind velocity
and eddy diffusivity extending the applicability of their footprint model to the whole atmospheric
stability range. However, some model limitations are present, such as its usage in areas where
wind velocity and eddy diffusivity profiles are horizontally homogeneous, and at heights where
the effects of a finite mixing depth are negligible. In addition, this model assumes that turbulent
diffusion in streamwise direction is small compared to advection, a form of Taylor’s hypothesis,
and are thus confined to flow situations with relatively small turbulence intensities.
Hsieh Model
Hsieh et al. (2000) develops an approximate analytical model to estimate the flux footprint in
thermally stratified flows. This is a hybrid approach combining elements from Calder’s
analytical solution (1952) with the results of Thompson’s Lagrangian model (1987). In the
analysis of their results, they scaled Gash (1986) effective fetch with the Obukhov length and
accounted for the effect of stability introducing two similarity parameters D and P, obtaining the
Eq. 2.
P
u
L
zD
SFkL
x
||)/ln(
1
|| 0
2 (2)
Where zu is a length scale, function of measurement height and surface roughness. k is the Von
Karman constant , L the Obukhov length and D and P depends on stability conditions of the
atmosphere . F/S0 is the ratio between scalar flux and source strength always confined between 0
and 1 (Hsieh et al., 2000).
The footprint function is expressed by Eq. 3.
71
PPu LDz
xkPP
um eLDzxk
zxf
1
2||
1
1
22||
1),( (3)
Kormann Model
The Kormann Model is based on a modification of the analytical solution of the advection-
diffusion equation of Van Ulden (1978) and Horst and Weil (1992) for power low profiles of the
mean wind velocity and the eddy diffusivity. To allow for the analytical treatment, the model
assumes homogenous and stationary flow conditions over homogeneous terrain, it represents the
vertical turbulent transport as a gradient diffusion process and it considers only advection in
along wind direction. Assuming that vertical and crosswind dispersion are independent, the
continuity equation reduces to a two-dimensional advection-diffusion equation.
In the Kormann Model the footprint function is expressed by Eq. 4.
xr
z
xr
z
r
mx
zxfK
r
mur
m
K
r
mum 2
1
2exp
1
1),( (4)
Where is the gamma function, r the shape parameter related to the exponents of the power
laws as r=2+m-n (Van Ulden, 1978) and Ku , are proportionally constants determined by
fitting the power laws for u ( m
u zu ) and K ( n
K zK ) to Monin-Obukhov similarity theory
(Garrat, 1993).
Study site, instruments and data
In this paragraph, filed characteristics, instruments necessary to perform the experiments and
data corrections are briefly shown.
Site characteristics
The experiments are carried out in two fields destined for maize cultivations at Landriano (Pavia,
Italy) and Livraga (Lodi, Italy) respectively. Fields geographic coordinates are (45.19 N, 9.16 E,
87 m a.s.l.) and (45.11 N, 9.34 E, 61 m a.s.l.) for Landriano (Field 1) and Livraga (Field 2)
respectively. The experiments are performed in two different situations: after reaping time (Field
1) and during maximum phenological development of the homogenous maize canopy (Field 2).
Both fields have a polygonal shape with a flat area of about ten hectares large. Field 1 is
completely surrounded by tall row plants which generate a strong discontinuity with the
neighbouring fields, while Field 2 is surrounded on three sites by other maize fields and in
South-West direction it forms a border with an uncultivated zone.
72
Instruments
With objective to investigate evapotranspiration and carbon dioxide fluxes over maize
cultivation in Po Valley, in the middle of Field 1 and 2, fixed eddy covariance towers A1 (for the
Field 1) and A2 (for the Field 2) are installed, and here, instruments are briefly summarised.
The stations are equipped with the following sensors: one three-dimensional sonic anemometer
(Young 81000), which measures sonic temperature and three components of wind speed at the
height of 5 m; one open-path gas analyzer (LICOR 7500) which measures water vapour and
carbon dioxide concentrations at the height of 5 m too. Both these instruments have been set with
an acquisition frequency of 10 Hz, so that the data can be used to calculate latent, sensible heat
and carbon dioxide fluxes trough eddy covariance method. One net radiometer (CNR1 by Kipp
& Zonen) is located on an arm (2.5 m long) attached on the tower at the height of 4 m. One
thermo-hygrometer (HMP45C Campbell Scientific) is located at the height of 3.5 m to measure
air humidity and temperature. In the soil, two thermocouples (by ELSI) and a heat flux plate
(HFP01 by Hukseflux) are placed at a depth of about 10 cm. Contemporaneously, soil moisture
is detected by three humidity probes (CS616 by Campbell Scientific) at different depths. Finally,
one rain gauge (AGR100 by Campbell Scientific) is separately located by the tower and, at the
height of about 1.5 m, it measures the precipitation intensity.
Data logger CR5000 (Cambpell Scientific) is used to store all data with an averaged time step of
5 minutes. This averaged time is designed to ensure that the eddy flux measurement system
captures most of the flux-containing eddies. This goal was accomplished by sampling
anemometer and gas analyzer sensors rapidly and averaging data over a time step of 5 minutes.
This averaged time is also justified by the results obtained by Masseroni et al. (2012) which,
studying surface layer turbulent characteristics over the Field 1, show that eddy integral lengths
in convective situations tends to be stationary for a time major of 300 s (about 5 minutes).
Data corrections
Energy fluxes have been corrected applying the whole range of correction procedures described
in many different literature works (Aubinet et al., 2000; Foken et al., 2004; Mauder and Foken,
2004). Before calculating fluxes, two groups of correction have been applied: “instrumental” and
“physical” corrections. Axis rotation for tilt corrections, spike removal, time lag compensation
and detrending represent preliminary processes which have to be directly applied on high
frequency measurements to prepare the data set for fluxes calculation. Spectral information
losses as a consequence of measurement system typologies trough transfer function
characteristics and sampling errors, have to be opportunely corrected to compensate the
underestimation of the turbulent fluxes (Moncrieff et al., 1997). Moreover, air density
fluctuations and air humidity effects on sonic temperature have to be necessarily corrected
trough Webb et al. (1980) and Van Dijk et al. (2004) procedures respectively.
These instrumental and physical corrections are automatically implemented in a PEC (Polimi
Eddy Covariance) software which has been opportunely developed for this experiment by
Corbari et al. (2012). The core of software is based on four substantial points:
a) Data stored into the data logger are sent on specific computer at the Politecnico of Milan
using a GSM modem;
73
b) Automatically, correction algorithms are activated and turbulent fluxes are calculated;
c) Some statistic indexes are generated to control the micrometeorological variables;
d) Turbulent flux and micrometeorological variable graphics are plotted at the web page
http://geoserver.iar.polimi.it.
Fixed eddy covariance stations (A1 and A2)
Energy flux measurements are proper to the cultivation if eddy covariance station is correctly
positioned inside the field. It has to be opportunely located far from the field edges, so that flux
measurements do not belong to the neighboring fields. Moreover, anemometer and gas analyzer
have to be compatible with the constant flux layer (Savelyev and Taylor, 2005). The constant
flux layer represents a space area where eddy covariance station measurements are constant, and
it is defined as 10-15% of internal boundary layer (Baldocchi and Rao, 1995). Considering the
whole wind direction ranges and analyzing the bare soil unfavourable conditions where
aerodynamic roughness for both fields is about 0.041 m, the constant flux layer depth at the
towers A1 and A2, calculated trough Elliot (1958)’s formula, is about 6 m ensuring that
anemometer and gas analyser are included into the constant flux layer. Moreover, several
conditions should be met before eddy correlation method can be applied to measure the fluxes of
mass and over an experimental field. First, the site should be flat. Second, vertical velocity
should be measured normal to the surface streamlines. Third, the crop should be homogeneous
and sufficiently extensive. Finally, no intermediate or advective sources or sinks should be exist
for the scalar under inverstigation (Baldocchi et al., 1988).
A method which is generally used to confirm the reliability of turbulent flux measurements of an
eddy covariance station is the energy balance closure (Foken et al., 2006). However, energy
balance issue is still unresolved problem and the closures which are present in literature
generally vary from 0.5 to 0.98 (Foken, 2008). The slope of the regression line between latent
and sensible heat turbulent fluxes and ground heat flux against available energy (net radiation) is
performed over Field 1 and 2 and the results are shown in Fig. 1.
0.84
0.91
0.98
1.05
1.12
1.19
0.72
0.76
0.80
0.84
0.88
A1 A2
Inte
rcep
t (W
m-2
)
Slo
pe
an
d R
2(-
)
Slope
R2
Intercept
Fig. 1 Energy balance closure for fixed eddy covariance stations A1 and A2.
Intercept and correlation coefficient (R2) are also included in Fig. 1, to highlight the presence of
systematic or random errors. The energy balance closure for A1 and A2 stations is about equal to
0.8 with a low dots dispersion around the regression line and a negligible systematic error of
about 1 W m-2
.
74
Experimental execution
Experimental campaigns were carried out in two consecutive years: 2011 and 2012 respectively.
For the Field 1 the experiment was performed over a range of nine days, from 15 September to
23 September in the year 2011, while for the Field 2 the experiment was performed over a range
of six days, from 2 August to 8 August in the year 2012.
In Tab.1 and 2 four daily averaged atmospheric parameters measured by the eddy covariance
stations over the experimental periods, are shown. The fields, which are at a distance of about 50
Km, are characterized by similar atmospheric turbulent conditions. Weak wind velocities, which
are typical in Po Valley, have a range which vary between 0.7 and 3 m s-1
. Friction velocities are
quite constant at a value of about 0.1 m s-1
. Air temperatures are greater than 20 °C in
accordance with the seasonal mean temperatures. Net radiations are grater then 200 W m-2
except for 261 and 262 Julian days of the year 2011 where the sky were particularly covered by
clouds.
Tab. 1. Meteorological conditions measured by A1 eddy covariance station in the year 2011.
Julian
day
Mean
velocity
(m s-1
)
Friction
velocity
(m s-1
)
Air
Temperature
(°C)
Wind
direction
(°)
Net
radiation
(W m-2
)
258 0.71 0.085 22.15 212 269
259 0.79 0.090 22.45 239 236
260 1.40 0.16 21.34 251 298
261 1.59 0.15 19.14 197 93
262 2.84 0.26 15.04 250 186
263 1.13 0.12 15.33 202 291
264 1.02 0.11 16.86 225 284
265 0.79 0.10 18.43 206 292
266 1.65 0.23 21.91 122 243
Tab. 2. Meteorological conditions measured by A2 eddy covariance station in the year 2012.
Julian
day
Mean
velocity
(m s-1
)
Friction
velocity
(m s-1
)
Air
Temperature
(°C)
Wind
direction
(°)
Net
radiation
(W m-2
)
215 1.01 0.12 25.69 230 310
216 0.93 0.10 25.42 210 301
217 1.09 0.15 24.73 250 297
218 1.11 0.13 24.98 239 285
219 1.81 0.17 25.97 247 307
220 1.16 0.16 25.01 290 304
To investigate the horizontal variation of turbulent fluxes across the fields, the experiments are
performed by placing a mobile eddy covariance station (B1 for the Field 1 and B2 for the Field
75
2) at various distances from the field edge, moving it versus the fixed stations (A1 or A2) placed
about in the middle of the fields. The mobile stations (Fig. 2A and B) are equipped by a sonic
anemometer (Young 81000) as well as the open-path gas analyzer (LICOR 7500) which are
attached at the top of an extensible tripod. To verify if mobile station measurements are equal to
those obtained by fixed stations, both stations have been placed close together for some days
before the experiments. Moreover, the clock among two data loggers (CR5000 for B1 and
CR23X for B2) has been set to obtain measurements at the same time.
A B
Fig. 2. Mobile stations in the Field 1 (A) and in Field 2 (B). In (A) fixed tower A1 is also shown.
In the Field 1, the mobile system (B1) is placed at nominal distances of 0 (P1_1), 15 (P2_1) and
65 (P3_1) meters from the field edge along a reference line inclined of about 191° in respect to
North. In the Field 2, the mobile system (B2) is placed at nominal distances of 0 (P1_2), 14
(P2_2) and 50 (P3_2) meters from the field edge along a reference line inclined of about 236° in
respect to North. The fixed towers (A1 and A2) are placed at a distance of the field edge of about
184 and 188 meters respectively (Fig. 3).
76
A B
North
South
East West (A1)
(B1)
191
40
North
East West
South
(A2) 236
(B2)
40
Fig. 3. Maps of the experimental sites. (A) Field 1 and (B) Field 2. The circle indicates the fixed
stations (A1 or A2) while the triangles the mobile station positions. The dotted line indicates the
reference line.
Latent, sensible heat and carbon dioxide flux measurements performed by mobile stations are
compared with those which are contemporaneously obtained by the fixed stations, but only a
range of data is taken into account for the analysis. Data are selected only when wind directions
are included in a range of 40° in respect to the reference line (Fig. 3) and net radiation is greater
than 0 W m-2
(Baldocchi and Rao, 1995). For this reasons, the experimental period cover several
days because mobile towers can not be moved as long as a sufficient number of data have been
stored.
The experiment success is guarantee if the field has at least one border site with a strong
discontinuity in respect to the examined field typology, and the reference line has to be
orientated in respect to this discontinuity zone (Fig. 3). Moreover, the fluxes which come from
the upwind zones in respect the discontinuity border should be quite constant during the whole
experimental period. To verify this condition, mobile station has been stayed on field border for
some days before the experimental campaign and the results have shown that daily averaged
fluxes does not drastically change from day to day.
Results
In this paragraph experimental measurements are compared with theoretical footprint models,
and some considerations about footprint model reliabilities have been discussed.
Flux measurements across the fields
To investigate latent, sensible heat and carbon dioxide spatial distribution across the Filed 1 and
2, eddy covariance measurements performed by B1 and B2 mobile stations have been compared
with those obtained by A1 and A2 fixed stations. In practice, mobile station measurements have
been normalized with fixed station measurements for each steady point of the experimental
77
design. Moreover, experimental data have to be rigorously processed with the goal to compare
experimental measurements with theoretical footprint model results.
The starting point for experimental data processing is dictated by the slope determination of the
regression line for the ratios between mobile and fixed station measurements for each
measurement point. For example, when the mobile station B1 stays at P1_1 point, on a Cartesian
plane B1 and A1 station measurements are plotted together in order to calculate the regression
line between mobile and fixed measurements. The slope of the regression line which has been
determined trough this method, represents the first point in the Fig. 4A and B. F can be
considered as a mean latent heat (Fig. 4A) or carbon dioxide (Fig. 4B) flux measurement
performed by the mobile system for the whole period where the station stays in a specific point,
while SA is that performed by the fixed station for the same period. F/SA ratio is a variable which
theoretically varies from zero to one. However, at P1 points (both in the Field 1 and 2), the
upwind fluxes are not zero and the F/SA ratio always starts with a value which is about 0.4 for
latent heat and carbon dioxide concentrations. Only in one case (Field 1) carbon dioxide
experimental measurements lead to having regression line with a slope near to zero. The last
point in Fig. 4A and B, which corresponds at P3_1 or P3_2 position, is equal to one because
mobile and fixed station are in the same position and the flux measurements are equivalent.
A B
0.0
0.4
0.8
1.2
0 50 100 150 200
F/S
A(-
)
Distance from the field edge (m)
LE_Field 1
LE_Field 2
0.0
0.4
0.8
1.2
0 50 100 150 200
F/S
A(-
)
Distance from the field edge (m)
f_CO2_Field 1
f_CO2_Field 2
Fig. 4. Turbulent flux measurements across the fields. (A) latent heat (LE), (B) carbon dioxide
flux (f_CO2). F/SA represents the ratio between mobile and fixed station flux measurements.
In the Field 1 and 2 the upwind zones have a sensible heat major then experimental fields, so that
the slope of the regression line is certainly greater than one. Therefore, to obtain the F/SA ratio
point distributions as shown in Fig. 5, the ideal case where mobile and fixed measurements are
equivalent with a slope of the regression line equal to 1, has been subtracted from the real value
of the slope (major then 1) and successively this result is again subtracted to 1. As shown in Fig.
5, sensible heat at the field border is quite different from Field 1 to 2. In bare soil F/SA ratio is
near to 0.4 as similarly shown for latent and carbon dioxide fluxes in Fig. 4A and B respectively,
while when high vegetation is opposed with an uncultivated zone, at the transition point (P1_2),
mobile and fixed station measurements are totally different and the F/SA ratio is about equal to
zero.
78
0.0
0.4
0.8
1.2
0 50 100 150 200F
/SA
(-)
Distance from the field edge (m)
H_Field 1
H_Field 2
Fig. 5. Sensible heat flux measurement across the fields. F/SA represents the ratio between
mobile and fixed station flux measurements.
The results obtained in these experimental campaigns and globally summarized in Fig. 4 and 5,
have shown that flux distributions across the fields are in accordance with the prediction
described in Baldocchi and Rao (1995)’s work. In the Field 2 latent, sensible heat and carbon
dioxide fluxes have a quite standard logarithmic behavior, while in the Field 1 this trend is
verified only for the latent heat. In the Field 1, sensible heat is quite influenced by the boundary
conditions, given that F/SA ratio at P2_1 point is very similar to that in P1_1 position, while for
carbon dioxide flux a linear growth trend is shown. When the canopy homogeneously covers the
field, boundary condition effects can be neglected if the mobile station is beyond from the field
edge of about 50 meters where the F/SA ratio values are already constant and near to 1. For latent
and sensible heat fluxes a similar behavior is also verified in bare soil while the carbon dioxide
flux constantly increases across the field.
Experimental results have shown that turbulent flux magnitudes rapidly increase in a transition
region which is about 50 meters large and then the F/SA ratios can be considered constant to 1 up
to the position of the fixed towers. However, the flux spatial distribution across the field is quite
different for latent, sensible and carbon dioxide fluxes, and it is strongly influenced by the
presence of the canopy on the soil.
Experimental data compared with footprint model predictions
In this subparagraph footprint model predictions are matched with latent, sensible heat and
carbon dioxide flux measurements across the experimental fields. In both sites the upwind fluxes
outside the fields are not zero and the source strength shown in Eq. 1 is simply approximated by
the Eq. 5.
0
0)(
1
xforS
xforSxS
A
(5)
Where S1 and SA are the fluxes measured by eddy stations at zero meters and at the position of
the fixed towers respectively. By superposition, it is possible to calculate the flux ratio using the
methodology widely described in Hsieh et al. (2000) and synthetically explained by Eq. 6.
79
x
m
x
m
AA
m dxzxfdxzxfS
S
S
zxF
0
1 ),(),(),(
(6)
In this way, theoretical footprint models can be compared with experimental measurements, and
the results are globally shown in Fig. 6 and 7. Each averaged data of flux is characterized by its
own representative source area which is defined by the F/SA ratio which is calculated trough Eq.
6. The data which are used into Eq. 6 have been measured by the fixed stations over the whole
period of time of the two experimental campaigns. The range of F/SA values which are obtained
by the fixed station experimental measurements is subdivided in groups each of which covers a
period of time which corresponds to the time period where the mobile station stays at P1, P2 or
P3 positions in the field. Subsequently, the mean of F/SA values for each group has been
calculated, so that F/SA measured and calculated results can be compared.
Fig. 6 and 7 are subdivided in two parts, the first (A, B, C) where the theoretical footprint model
results are matched to the experimental measurements, and the second part (D, E, F) where a
scatter plot defines if the footprint models are in a good agreement with the experimental results.
A B C
0.0
0.4
0.8
1.2
0 50 100 150 200
F/S
A(-
)
Distance from the field edge (m)
Experimental data
Hsieh Model
Kormann Model
0.0
0.4
0.8
1.2
0 50 100 150 200
F/S
A(-
)
Distance from the field edge (m)
Experimental data
Hsieh Model
Kormann Model
0.0
0.4
0.8
1.2
0 50 100 150 200
F/S
A(-
)
Distance from the field edge (m)
Experimental data
Hsieh Model
Kormann Model
D E F
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2
F/S
AM
od
eled
(-)
F/SA Measured (-)
Hsieh Model
Kormann Model
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2
F/S
AM
od
ele
d (
-)
F/SA Measured (-)
Hsieh Model
Kormann Model
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2
F/S
AM
od
eled
(-)
F/SA Measured (-)
Hsieh Model
Kormann Model
Fig. 6. Variation of latent, sensible heat and carbon dioxide fluxes in the Field 1 with the
distance from the field edge, and comparison with theoretical footprint models (A, B, C).
Comparison between measured and modeled model predicted footprint (F/SA). The 1:1 line is
also shown.
80
A B C
0.0
0.4
0.8
1.2
0 50 100 150 200
F/S
A(-
)
Distance from the field edge (m)
Experimental data
Hsieh Model
Kormann Model
0.0
0.4
0.8
1.2
0 50 100 150 200
F/S
A(-
)
Distance from the field edge (m)
Experimental data
Hsieh Model
Kormann Model
0.0
0.4
0.8
1.2
0 50 100 150 200
F/S
A(-
)
Distance from the field edge (m)
Experimental data
Hsieh Model
Kormann Model
F E D
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2
F/S
AM
od
eled
(-)
F/SA Measured (-)
Hsieh Model
Kormann Model
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2
F/S
AM
od
eled
(-)
F/SA Measured (-)
Hsieh Model
Kormann Model
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.2 0.4 0.6 0.8 1.0 1.2
F/S
AM
od
eled
(-)
F/SA Measured (-)
Hsieh Model
Kormann Model
Fig. 7. Variation of latent, sensible heat and carbon dioxide fluxes in the Field 2 with the
distance from the field edge, and comparison with theoretical footprint models (A, B, C).
Comparison between measured and modeled model predicted footprint (F/SA). The 1:1 line is
also shown.
In the Field 1, the latent, sensible heat and carbon dioxide variation in spatial distribution, leads
to an unsatisfactory definition of a unique footprint model which can be used to describe the
representative source area for the whole range of turbulent fluxes. In fact, while the agreement
between Kormann model and experimental data of latent heat flux is good, the same could not be
said for sensible heat and carbon dioxide fluxes. Evaluating the errors between model and
experimental results trough the regression line of the dots in the scatter plots, Kormann Model
can be considered the best one for latent heat flux with a slope of the regression line equal to
0.98. However, both models are inadequate to describe footprint shape for sensible heat and
carbon dioxide fluxes with an estimated error of about 10% and 30% respectively.
In the Field 2, latent, sensible heat and carbon dioxide spatial distribution are quite similar. F/SA
ratios have a rapidly increase versus the maximum admissible value of 1 which has been reached
in a transition zone of about 50 meters. Hsieh Model underestimates footprint shape for the
whole range of turbulent fluxes with an error which varies from 5% al 27% for latent and
sensible heat fluxes respectively. Korman Model is in a good agreement with latent heat and
carbon dioxide experimental data with a slight error of about 2%, while for sensible heat Korman
Model underestimates the representative source area with an error of about 20%.
Discussions
Spatial distribution of turbulent fluxes across the field is particularly influenced by the presence
of vegetation which covers the ground surface. In bare soil, boundary condition effects can
81
remain for several meters away the field edge while, when the vegetation cover the field, the
homogeneity effect of the canopy produces a rapid change in flux distribution leading to 1 the
F/SA ratio at a distance of about 50 meters from the field edge.
The results obtained in Field 1 and 2, have shown that representative source area is not equal for
each flux. Generally, footprint models describe the representative source area for turbulent flux
without specifying if it is latent, sensible heat or carbon dioxide. Experimental results show that,
especially in bare soil, intra-field spatial distribution of turbulent fluxes change from a
logarithmic behavior for latent heat to a linear growth for carbon dioxide. On the other hand, in
Field 2, the F/SA logarithmic growth profile is guaranteed for the whole range of turbulent fluxes,
but the F/SA ratio values are not identical.
Kormann Model could be considered the best one for the whole range of turbulent fluxes,
however also Hsieh Model is in a good agreement with latent heat flux distributions. In the other
cases, Hsieh Model underestimates the footprint area and this is probably due to the simplified
parameterizations which form the model structure. On the other hand, Kormann Model, which
derives from a direct analytical solution of the diffusion equation, approximates footprint area of
the turbulent fluxes in a good way also if, in some cases, it result to be underestimated in respect
to the experimental measurements. The good agreement of the Kormann Model can be due to
atmospheric and turbulent conditions which are typical in Po Valley and which are in accordance
to the limitations and basic hypothesis which govern the theoretical model.
Conclusion
In this work a simple method which is quite different from those recently presented in literature
is used to analyze horizontal variability of vertical scalar fluxes across bare and vegetated soils in
Po Valley. One mobile eddy covariance station is moved from the field edge to the center of the
field where a fixed station is located. Comparing flux measurements obtained by the both
stations, latent, sensible heat and carbon dioxide flux intra-field distributions are investigated and
two footprint model perditions have been compared. A good agreement of the Kormann model is
verified with experimental measurements while Hsieh Model could be used to define footprint
shape only for latent heat flux. Variability of scalar fluxes across the fields is particularly
influenced by the presence of the vegetation and in bare soil turbulent flux spatial distributions
are highly differenced from flux to flux.
These results have contributed to improve the knowledge about the reliability of analytical
footprint model predictions in order to understand the model behaviours over a wide variety of
natural situations where eddy covariance stations could be located. Po valley and its typical
cultivations such as maize or rice are still poorly investigated, but the improvement in eddy
covariance technique, and its applications over a wide range of fields, needs to know more
accurately the representative source areas of the evapotranspiration or carbon dioxide fluxes to
improve management practice in water irrigation or plant care.
References
Aubinet, M., Grelle, A., Ibrom, A., et al. (2000). Estimates of the annual net carbon and water exchange of forests:
the euroflux methodology. Advanced in Ecological Research , 30: 113-175.
82
Baldocchi, D. (2003). Assessing the eddy covariance technique for evaluating carbon dioxide exchange rates of
ecosystems: past, present and future. Global Change Biology, 9:1-14.
Baldocchi, D. and Rao, K. (1995). Intra-field variability of scalar flux densities across a transition between desert
and an irrigated potato field . Boundary Layer Meteorology. 76: 109-136.
Baldocchi, D., Falge, E., Gu, L., Olsen, R., Hollinger, D., Running, S., et al. (2001). FLUXNET: a new tool to study
the temporal and spatial variability of ecosystem scale carbon dioxide, water vapor, and energy flux densities.
Bullettin of the American Meteorological Society , 82: 2415-2434.
Baldocchi, D., Hicks B.B. and Meyers T.P. (1988). Measuring biosphere atmosphere exchange of biologically
related gases with micrometeorological methods. Ecology, 69:1331-1340.
Calder, K. (1952). Some recent british work on the problem of diffusion in the lower atmosphere. New York: Mc
Graw-Hill, pp. 787-792.
Corbari C., Masseroni,D. and Mancini, M., (2012). Effetto delle correzioni dei dati misurati da stazioni eddy
covariance sulla stima dei flussi evapotraspirativi. Italian Journal of Agrometeorology,1:35-51.
Elliot, W. (1958). The growth of the atmospheric internal boundary layer. Trans. Am. Geophys. Un. 50, 171-203.
Foken, T. (2008). The energy balance closure problem:an overview. Ecological Applicatons, 18: 1351-1367.
Foken, T. and Leclerc, M.Y. (2004). Methods and limitations in validation of footprint models. Agricultural and
Forest Meteorology. 127: 223-234.
Foken, T. and Wichura, B. (1996). Tools for quality assessment of surface-based flux measurements. Agricultural
and Forest Meteorology. , 78: 83-105.
Foken, T., Gockede, M., Mauder, M., Mahrt, L., Amiro, B., and Muger, J. (2004). A guide for surface flux
measurements. Kluwer Academic, Dordrecht 81-108.
Foken, T., Wimmer, F., Mauder, M., Thomas, C., and Liebhetal, C. (2006). Some aspects of the energy balance
closure problem. Atmososperich and Chemistry Physics, 6,4395-4402.
Garratt, J. (1993). The atmospheric boundary layer. Cambridge: Cambridge university press, pp.316, ISBN 0 521
38052 9.
Gash, J.H.C. (1986). A note on estimating the effect of a limited fetch on micrometeorological evaporation
measurements. Boundary-Layer Meteorology. 35: 409-413.
Göckede, M., Markkanen, T., Mauder, M., Arnold, K., Leps, J.-P. and Foken, T. (2005). Validation of footprint
models using natural tracer measurements from a field experiment. Agricultural and Forest Meteorology. 135: 314-
325.
Horst, T. and Weil, J. (1992). Footprint estimation for scalar flux measuraments in the atmospheric sourface layer.
Boundary Layer Meteorology, 59: 279-296.
Hsieh, C., Katul, G., and Chi, T. (2000). An approximate analytical model for footprint estimation of scalar fluxes in
thermally stratified atmospheric flows. Advanced Water Resource , 23: 765-772.
Kaimal, J. C. and Finnigan, J. J. (1994) Atmospheric Boundary Layer Flows – Their Structure and Measurement,
Oxford University Press, New York, 289 pp.
83
Kljun, N., P. Kastner-Klein, E. Fedorovich, M.W. Rotach (2004): Evaluation of a Lagrangian Footprint Model
Using Data from a Wind Tunnel Convective Boundary Layer. Special Issue on Footprints of Fluxes and
Concentrations, Agricultural and Forest Meteorology. 127: 189-201.
Kljun, N., Rotach, M. and Schmid, H. (2002). A 3D bacward Lagrangian footprint model for a wide range of
buondary layer stratifications. Boundary Layer Meteorology. 103: 205-226.
Kormann, R. and Meixner, F. (2001). An analytical model for non-neutral stratification. Boundary Layer
Meteorology. 103: 205-224.
Kurbanmuradov, O.A. and Sabelfeld, K.K. (2000). Lagrangian stochastic models for turbulent dispersion in the
atmospheric boundary layer. Boundary Layer Meteorology. 97: 191-218.
Leclerc, M.Y. and Thurtell, G.W., (1990). Footprint prediction of scalar fluxes using a Markovian analysis.
Boundary-Layer Meteorology. 52: 247−258.
Leclerc, M.Y., Meskhidze, N. and Finn, D. (2003). Comparison Between Measured Tracer Fluxes and Footprint
Model Predictions Over a Homogeneous Canopy of Intermediate Roughness. Agricultural and Forest Meteorology,
117: 145-158.
Marcolla, B. and Cescatti, A. (2005). Experimental analysis of flux footprint for varying stability conditions in an
alpine meadow. Agricultural and Forest Meteorology. 135: 291-301.
Masseroni, D., Ravazzani, G., Corbari, C. and Mancini, M.(2012). Turbulance integral length and footprint
dimension with reference to experimental data measured over maize cultivation in Po Valley, Italy. Atmosfera, 25:
183-198.
Mauder, M. and Foken, T. (2004). Documentation and instruction manual of the eddy covariance software package
TK2. Arbeitsergebn, Univ Bayreuth, Abt Mikrometeorol, ISSN 1614-8916. 26: 42 pp.
Moncrieff, J., Clement, R., Finnigan, J., and Meyers, T. (2004). Averanging and filtering of eddy covariance time
series, in Handbook of micrometeorology: a guide for surface flux measurements. Kluwer Academic, Dordrecht, 7-
31.
Neftel A., Spirig C. and Ammann C. (2008). Application and test of a simple tool for operational footprint
evaluations. Environmental Pollution. 152: 644-652.
Papale, D., Reichstein, M., Aubinet, M., Canfora, E., Bernhofer, C., Kutsch, W., et al. (2006). Towards a
standardized processing of net ecosystem exchange measured with eddy covariance technique: algorithms and
uncertainty estimation. Biogeosciences , 3: 571-583.
Rannik, U., Aubinet, M., Kurbanmuradov, O., Sabelfeld, K. K., Markkanen, T., and Vesala, T. (2000). Footprint
analysis for measurements over a heterogeneous forest, Boundary-Layer Meteorology, 97: 137–166.
Rodean, H. 1996. Stochastic lagrangian models of turbolent diffusion. Boston: American Meteorological Society
pp.84.
Sanchez J.M., Caselles V. and Rubio E.M. (2010). Analysis of the energy balance closure over a FLUXNET boreal
forest in Finland. Hydrology Earth System Sciences Discussion, 7: 2683–2707, 2010.
Savelyev, S. and Taylor, P. (2005). Internal Boundary Layer: I. Height formulae for neutral and diabatic flows.
Boundary Layer Meteorology. 115: 1-25.
84
Schmid, H. (1994). Source areas for scalars and scalar fluxes. Boundary Layer Meteorology, 67, 293-318.
Schmid, H. (1997). Experimental design for flux measurements: matching scales of observations and fluxes.
Agricultural and Foest Meteorology , 87: 179-200.
Schuepp, P., Leclerc, M., Macpherson, J. and Desjardins R (1990). Footprint prediction of scalar fluxes from
analytical solutions of the diffusion equation. Boundary Layer Meteorology. 50: 353-373.
Soegaard H., Jensen, N.O., Boegh, E., Hasager, C.B., Schelde K. and Thomsen A. (2003). Carbon dioxide exchange
over agricultural landscape using eddy correlation and footprint modelling. Agricultural and Forest Meteorology.
114: 153-173.
Thomson, D. (1987). Criteria for the selection of stochastic models of particle trajectories in turbolent flows. Journal
of Fluid Mechanic, 180: 529-56.
Van de Boer, A., Moene A.F., Schuttemeyer D. and Graf A. (2013). Sensitivity and uncertainty of analytical
footprint models according to a combined natural tracer and ensemble approach. Agricultural and Forest
Meteorology, 2013: 1-11.
Van Dijk, A., Kohsiek, W., and De Bruin, H. (2003). Oxygen sensitivity of krypton and Lyman-alfa Hygrometer.
Journal of Atmospheric and Oceanic Technology , 20: 143-151.
Van Ulden, A. (1978). Simple estimates for vertical diffusion from cources near the ground. Atmospheric
Environmental. 12: 2125-2129.
Vesala, T., Kljun, N., Rannik, U., Rinne, J., Sogachev, A., Markkanen, T., Sabelfeld, K., Foken T. and Leclerc, M.
Y. (2008). Flux and concentration footprint modeling: State of the art. Environmental Pollution, 152: 653–666,
2008.
Webb, E., Pearman, G., and Leuning, R. (1980). Correction of the flux measurements for density effects due to heat
and water vapour transfer. Boundary Layer Meteorology, 23: 251-254.
Wilson, J. and Sawford, B. (1996). Review of lagrangian stochastic models for trajectories in the turbolent
atmosphere. Boundary Layer Meteorology, 78: 191-210.
Wilson, K., Goldstein, A., Falge, E., Aubinet, M., Baldocchi, D., Berbigier, P., et al. (2002). Energy balance closure
at FLUXNET sites. Agricultural and Forest Meteorology , 113: 223-243.
85
General Conclusion
In this PhD thesis, the complexity of the eddy covariance measurements for turbulent flux
estimations has been investigated with the objective to improve evapotranspiration and carbon
dioxide flux reliabilities. Experimental data corrections, energy balance closure and turbulent
fluxes scales are the main problems which have been widely discussed in literature from the birth
of the eddy covariance technique. Despite the scientific community efforts, some of these
problems have not yet been resolved, and the research in micrometeorological fields should try
to give response on these key points.
The results of this research have shown some important considerations about the possibility to
directly use 30 minutes averaged data to obtain evapotranspiration and carbon dioxide reliable
fluxes. Although the eddy covariance technique requires high frequency data to obtain reliable
covariances and successively turbulent fluxes, PEC software implemented at the Politecnico of
Milan gives the possibility to directly obtain reliable flux estimation starting from the averaged
data in output from data logger. Corrections for air density fluctuations and humidity effects
represent the core of the PEC software and they could be considered the main basis for accurate
flux estimation.
Energy balance closure is generally used to verify the reliability of latent and sensible heat flux
measurements by an eddy covariance station. In an ideal ecosystem, the sum of turbulent fluxes
and ground heat flux should be equal to the available energy (net radiation), but in the real case
the energy balance closure is always lower than one. The results have shown that storage terms
are the main factors which play a substantial role in eddy flux underestimations, and when the
field is homogeneously covered by the canopy, their effect can not be neglected. Ground heat
storage plays a fundamental role in energy balance closure when the field is in bare soil
conditions, while when the vegetation covers the field, photosynthetic and canopy storage terms
are dominant. Despite the efforts to improve the energy balance closure, it is still an unsolved
problem which leads to a maximum closure, for the data collected in this work, of about 90%.
Another problem linked to the impossibility to perfectly close the energy balance is represented
by the difficult to match the footprint areas for the instruments which measure latent and sensible
heat fluxes, net radiation and ground heat flux. Latent and sensible heat fluxes have a
representative source area on the order of hundred meters, while for net radiometer it is equal to
about ten meters and for heat flux plate it is equal to about one meter.
Experimental campaigns to study the spatial scale of turbulent fluxes across bare and vegetated
soils have been performed in order to validate two analytical footprint models from literature.
These experiments have shown that the intra-field spatial distribution of latent, sensible and
carbon dioxide fluxes can be strongly differenced among them and, in bare soil, it is extremely
complicated to define a unique footprint model which accurately describes the representative
source area for the whole range of fluxes. Generally, in literature, footprint area is assumed to be
the same for the whole range of turbulent fluxes while, thanks to these experiments, it has been
possible to increase the knowledge about the latent, sensible heat and carbon dioxide spatial
variability which is the main feature analyzed in the footprint model.
86
Acknowledges
This work was funded in the framework of the ACQWA EU/FP7 project (grant number 212250)
“Assessing Climate impacts on the Quantity and quality of WAter” , the framework of the
ACCA project funded by Regione Lombardia “Misura e modellazione matematica dei flussi di
ACqua e CArbonio negli agro-ecosistemi a mais” and PREGI (Previsione meteo idrologica per
la gestione irrigua) funded by Regione Lombardia.
The author thanks the University of Milan (Faculty of Agricultural and Food Sciences) for the
collaboration given in managing Landriano and Livraga eddy covariance stations.
Special thanks to Dr. Alessandro Ceppi, Ing. Chiara Corbari, Ing. Giovanni Ravazzani and Prof.
Marco Mancini for their help in setting up the experiments and their precious advices. Special
thanks also to the whole group of PhD students which are my colleagues and precious friends.