Reducing uncertainty in NEE estimates from flux measurements

D. Hollinger, L. Mahrt, J. Sun,

and G.G. Katul

Ameriflux Meeting, Boulder CO., October 20, 2005

Organizing Framework

Uncertainty in flux measurements (random and systematic errors) over sampling intervals needed to average out turbulence.

Gap-filling missing data when averaging over extended time scales (relevant to impact of carbon allocation on ecosystem properties).

Linking measured fluxes to biological sources and sinks (main issues – stable flows; topography).

All recent reviews concerning measurements and

modeling of surface-atmosphere mass, energy, and

momentum exchange expressed the need to confront

the problem of turbulent flows within plant canopies

on non-flat terrain.

Background

Field Studies [Mainly forests, stable flows, mild topography]

Aubinet et al. (2003; 2005);Yi et al. (2004);Staebler and Fitzjarrald, (2004); Feigenwinter et al., (2004);Fokken et al., (2005);

Laboratory Studies: [steep topography]

Finnigan and Brunet (1995)

Previous Studies

Results from Recent Field Experiments

CO2 advection study at the Niwot Ridge AmeriFlux site by Yi et al. (2004) suggested that:

1) Both longitudinal and vertical advective fluxes are

important and often larger than the turbulent flux.

2) They often act in opposite direction

Feigenwinter et al1. (2004)

“The opposite sign of horizontal and vertical advection supports the idea that the two fluxes will cancel out each other in the long-term carbon balance”.

“The mean advective fluxes at night have magnitudes comparable to the daily NEE”.

1Feigenwinter et al., 2004, Boundary-Layer Meteorology.

Aubinet et al1. (2005)

“The advective fluxes strongly influence the nocturnal CO2 balance, with the exception of almost flat and highly homogeneous sites”.

Storage - significant “only during periods of both low turbulence and low advection”.

“All sites where advection occurs show the onset of a boundary layer characterized by a downslope flow, negative vertical velocities and negative vertical CO2 concentration gradients during nighttime”.

1Aubinet et al., 2004, Boundary-Layer Meteorology.

Hill Properties:Four hill modulesHill Height (H) = 0.08 mHill Half Length (L) = 0.8 m

Canopy PropertiesCanopy Height = 0.1 mRod diameter = 0.004 mRod density = 1000 rods/m2

Flow Properties:Water Depth = 0.6 mBulk Re > 1.5 x 105

Polytechnic of Turin (IT) Flume Experiments

Velocity MeasurementsSampling Frequency = 300 Hz

Sampling Period = 300 sLaser Doppler Anemometer

Displaced Coordinates

Coordinate Systems

Mean Velocity (m/s)

Turbulent Stress (m2/s2)

0

z

W

x

U

),(1

cd hzFz

wu

x

P

z

UW

x

UU H

Model Formulation: 2-D Mean Flow

Fluid Continuity:

Mean Momentum Equation:

Two equations with two unknowns – after appropriate parameterization

Produced by the Hill

CanopyDrag

Finnigan and Belcher (2004)Analytical Model

2' 'U U

u w lz z

Closure for Reynolds StressConstant mixing length insidecanopy:

d d bF C aU U

Linearized Adv.:bb

UU U UU W U W

x z x z

Closure for Linearized Drag:

2 U Uu w l

z z

Mixing Length Model

Linearized Advective Term

Linearized Drag Force

Deep Inside the Canopy

AdvectionDrag

Turbulent Stress Pressure Gradient

MeanMomentumBalance

4 2o

u w u wS

u w

w

u

EJECTIONS

SWEEPS

Ejection-Sweep Cycle

Canopy Surface

Smooth Surface (no canopy)

Advective fluxes are opposite in sign

They are often larger than Photosynthesis (Sc)

Advective terms are (individually) of the same order of magnitude as photosynthesis, consistent with field experiments to date. Note that the model does not consider atmospheric stability.

The effects of advective terms on CO2 fluxes at a particular point can be as large as 100%. Both advective terms must be considered in any flux-correction treatment due to topography.

Conclusions

~1 km

(b): Tower relief mapTumbarumba, AU

(a): SLICERData from Duke Forest

(c): Eucalyptus vegetationTumbarumba, AU

Gap-Filling

What new information is being added in the Gap-filling?

How much are the distributional and spectral properties altered by gap-filling?

Distributional and Autocorrelation Properties

fBm process with Hurst exponent=1/3

Shannon-Entropy

1

log( )m

i ii

E p p

p=Empirical probability density function OR Energy distribution (e.g. from spectral analysis)

Maximum Entropy:1

; ( ) log( )ip Max E mm

Entropy = Information Content (Shannon, 1948)

Wavelet-Based Spectra

Haar wavelet, localizedin time domain – can remove gaps fromspectral calculations.

Schimel & others – use Entropy measures for assessing New information injected by gap-filling.

PP = Pine PlantationOF = Old Field

HW = Hardwood Forest

Duke Forest Ameriflux Sites

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

OF PP HW OF PP HW

Shan

non

Ent

ropy

__

_

raw

gapfilled

SpectraProbability

Entropy, Gap filling, ET

Entropy, Gap filling, Daytime NEE

Daytime

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

OF PP HW OF PP HW

Sh

ann

on E

ntr

opy

___

raw

gapfilled

SpectraProbability

Night-time NEE

Nighttime

00.10.20.30.40.50.60.70.80.9

OF PP HW OF PP HW

Sh

ann

on E

ntr

opy

___

raw

gapfilled

SpectraProbability

Remarks

If after gap-filling, the

log( )raw gapfilledE E

Em

is large (>20%), the ‘long-term’ estimates of NEE are going to be sensitive to gap-filling and are likely to have significant artificial correlation with the gap-filling drivers.

Extra References

Katul et al., 2001, Advances in Water Resources , 24, 1119.

Katul et al., 2001, Geophysical Research Letters, 28, 3305.

Katul et al., 2001, Physics of Fluids, 13, 241.

Wesson et al., 2003, Boundary-Layer Meteorology, 106, 507.

Mahrt et al., 1999, Journal of the Atmospheric Sciences, 48, 472.