special section: soil–plant– uncertainties of water fluxes...

www.VadoseZoneJournal.org

Uncertainties of Water Fluxes in Soil–Vegetation–Atmosphere Transfer Models: Inverting Surface Soil Moisture and Evapotranspiration Retrieved from Remote SensingEffective hydraulic parameters of soil–vegetation–atmosphere transfer (SVAT) models can be derived by inverting observed surface soil moisture, qobs, and evapotranspiration, ETobs, retrieved from remote sensing. We investigated the uncertainties in simulating the water fluxes of contrasting hydroclimatic scenarios for which it was assumed that qobs had a RMSE of 0.04 m3 m−3 (Dqobs) and ETobs had a relative error of 20% (DETobs). The correlation of the uncertainties in the simulated water fluxes (DWFsim) with Dqobs and DETobs was derived with the proposed Uncertainty Simulator Algorithm. The results show that DWFsim is influenced by climate and increases when the climate is drier. The uncertainty in esti-mated root-zone q was found to be correlated with Dqobs. The prediction of evaporation contained large uncertainties and was correlated with the actual/potential evapotranspira-tion ratio. The uncertainties in transpiration under dry climates were high and were cor-related with DETobs; however, the uncertainty under wet climates was insignificant. The uncertainties in groundwater recharge under dry climates were large but were reduced under wet climates. Furthermore, uncertainties in groundwater recharge were correlated with DETobs but not with Dqobs. In general, the DWFsim increases as (i) climate gets drier, (ii) texture gets coarser, or (iii) roots grow deeper. The uncertainty in recharge is explained by soil moisture and transpiration decoupling. Soil moisture decoupling occurs when the information provided by surface q is no longer representative of root-zone q. Transpiration decoupling occurs when there is substantially more water storage at depth. We propose methodology to reduce the nonuniqueness of the inverted hydraulic parameters.

Abbreviations: AI, aridity index; LAI, leaf area index; SCE-UA, Shuffled Complex Evolution Algorithm–Uni-versity of Arizona; SVAT, soil–vegetation–atmosphere transfer; SWAP, Soil–Water–Atmosphere–Plant model; SWAPinv, modified Soil–Water–Atmosphere–Plant model; UnSA, Uncertainty Simulator Algorithm.

Large-scale hydrologic models require representative effective soil hydraulic parameters at the scale of interest to compute effective water fluxes composed of groundwater recharge, evapotranspiration, evaporation, transpiration, and surface and root-zone soil moisture. Effective soil hydraulic parameters are traditionally derived by upscaling point measurements, which requires the collection of an extensive soil hydraulic data set (e.g., Nielsen et al., 1973; Stolte, 1994), thus limiting the accuracy of deriving effec-tive hydraulic parameters. An increasingly attractive, cost-efficient alternative is to derive the effective hydraulic parameters by inverting one-dimensional Richards’ model, with observed top 5-cm volumetric water content, qobs [L3 L−3], and observed actual evapo-transpiration, ETobs [L T−1], time series retrieved from remote sensing (e.g., Gutmann and Small, 2010; Ines and Mohanty, 2008a; Mohanty and Zhu, 2007).

The algorithms to retrieve top soil moisture from remote sensing have been validated with field campaigns (under low vegetated area [e.g., Jackson and Schmugge, 1991]) with an average accuracy of root mean square error (RMSE) of 0.04 m3 m−3 volumetric soil moisture (e.g., Choi et al., 2008; Das and Mohanty, 2008; Das et al., 2008; Friesen et al., 2008; Ines and Mohanty, 2009; Sahoo et al., 2008; Vischel et al., 2008). The algorithms to retrieve actual evapotranspiration from remote sensing have been also validated from field campaigns and given an average relative error of 20% (e.g., Bashir et al., 2009; Gao and Long, 2008; Kalma et al., 2008; Opoku-Duah et al., 2008; Ramos et al., 2009; Su et al., 2007; Teixeira et al., 2009).

The uncertainties in inverting the water fluxes from topsoil moisture and evapotranspiration retrieved from remote sensing increases as the climate gets drier, soil texture gets coarser, roots grow deeper, and the water table rises. This is due to soil moisture and transpiration decoupling. A methodology is given to reduce the nonuniqueness of the hydraulic parameters.

J.A.P. Pollaco and B.P. Mohanty, Dep. of Bio-logical and Agricultural Engineering, Texas A&M Univ., College Station, TX 77843-2117; J.A.P. Pollaco now at Dep. of Bioenvironmen-tal Systems Engineering, National Taiwan University, Taipei, Taiwan. *Corresponding author ([email protected]).

Vadose Zone J. doi:10.2136/vzj2011.0167Received 14 Nov. 2011.

Special Section: Soil–Plant–Atmosphere Continuum

Joseph A. P. Pollacco*Binayak P. Mohanty

© Soil Science Society of America 5585 Guilford Rd., Madison, WI 53711 USA.All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including pho-tocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.


Until now, there has been no comprehensive study to estimate the uncertainties in the modeled water fluxes determined by inverting the hydraulic parameters of SVAT water flow models from surface qobs and ETobs retrieved from remote sensing (see the reviews of Vereecken et al., 2007, 2008). Performing measurements to estimate the uncertainties in the inverted water fluxes at such a large scale is considered infeasible because typically soil moisture and evapo-transpiration are retrieved at a scale of several square kilometers (e.g., Jackson et al., 1995; Njoku et al., 2003). A method of estimating the uncertainties in water fluxes of a one-dimensional SVAT model, without taking into account the discrepancy in measurement scales between qobs and ETobs, would be to invert ETobs values retrieved from the water balance of weighing lysimeters (e.g., Abbaspour et al., 1999; Durner et al., 2008; Kosugi and Katsuyama, 2001, 2004; Scanlon et al., 2005) and the surface qobs determined (for example) by neutron probe or time-domain reflectometer (e.g., Haverkamp et al., 1984; Pollacco, 2003; Sinclair and Williams, 1979). To mimic the uncertainties in retrieving qobs and ETobs from remote sensing, noise can be introduced into the measurements of surface qobs and lysimeter ETobs.

Nevertheless, before designing costly experiments, it is important to have a good understanding of how the uncertainties in qobs and ETobs impact the predictions of the water fluxes under contrast-ing hydroclimate conditions because Teuling et al. (2009) and van Werkhoven (2008) showed that the sensitivity of hydrologic parameters is highly dependent on the hydroclimate. Thus, we chose to perform numerical studies for which all the parameters, water fluxes, and uncertainties in qobs and ETobs (as defined above) were known beforehand (e.g., Durner et al., 2008; Hupet et al., 2003; Pollacco et al., 2008a, 2008b).

Eighteen contrasting hydroclimate scenarios were selected for the numerical experiments, which were composed of a combination of three climates (across the United States), three soil textures, and two rooting depths. Contrasting rooting depths were tested because Ines and Mohanty (2008a) maintained that the predic-tions of the hydraulic parameters are sensitive to the rooting depth. In this study, the vegetation parameters were not the subject of investigation since they can be retrieved from MODIS (Moderate Resolution Imaging Spectroradiometer) (e.g., Huete et al., 2002; Nagler et al., 2005; Simic et al., 2004).

One of the drawbacks of using physically based SVAT models is that they require as much as five hydraulic parameters per hydro-logic unit to describe the soil water characteristics and the unsatu-rated hydraulic conductivity curve (e.g., Brooks and Corey, 1964; Kosugi, 1996; van Genuchten, 1980). This results in a nonunique inverted hydraulic parameter set (e.g., Abbaspour et al., 1999; Bey-doun and Lehmann, 2006; Binley and Beven, 2003; Jhorar et al., 2002; Pollacco et al., 2008b; Ritter et al., 2003) and uncertain-ties in the inverted water fluxes, as was determined in this study. The other concern is that upscaling and downscaling require the

comparison of a nonunique effective parameter set retrieved via inverse modeling with unique effective physically based hydraulic parameters derived by scaling point measurements (e.g., Braud et al., 2005a; Kosugi and Hopmans, 1998; Leij et al., 2007; Saito et al., 2009). Pollacco et al. (2008b) found that when the hydraulic parameters are inverted from the time series of soil moisture profile, for which the uncertainties in the observed soil moisture are taken into account, similar water fluxes are obtained with contrasting combinations of four van Genuchten (1980) hydraulic parameter sets (residual soil moisture is forced to zero and the shape factor is kept constant). They also found that all the feasible combinations of the four hydraulic parameters that produce similar values of the objective function can be derived with two equations. Conse-quently, they concluded that for most hydroclimates, two hydraulic parameters are sufficient to simulate water fluxes. In this study, we investigated whether reducing the number of hydraulic param-eters would cause an increase in the uncertainties in the predicted water fluxes when they were calibrated with surface qobs and ETobs. The choice of the least sensitive van Genuchten (1980) hydraulic parameters is not widely accepted by all researchers, as shown by the divergence of the results described in Table 1, and therefore the two least sensitive hydraulic parameters in the computation of the water fluxes were investigated in this study.

The uncertainties in the estimated water fluxes and the inverted hydraulic parameters were derived by using the proposed Uncer-tainty Simulator Algorithm (UnSA) methodology, which is an improvement of the Linking Test (Pollacco et al., 2008a, 2008b). The UnSA simulates qsim and ETsim within the error bars of the observations (described above). A common inverse methodology to derive the uncertainties would be to use multiobjective algo-rithms to compute the Pareto front (nondominated solutions) (e.g., Efstratiadis and Koutsoyiannis, 2008; Tang et al., 2007; Vrugt et al., 2003; Yapo et al., 1998) and to extract the subset of behavioral water flux solutions to compute the uncertainties. Nevertheless, when using synthetic data, the use of multiobjective algorithms is only possible when the distribution of the uncertainties in the observations are known or else the Pareto front would just follow

Table 1. Literature review of the most insensitive van Genuchten (1980) hydraulic parameters: saturated volumetric water content (qs), air-entry matric potential (hae), shape parameter n, and saturated hydraulic conductivity (Ks). This table depicts the divergence of the results.

Reference qs hae n Ks

Pollacco et al. (2008b) X X

Beydoun and Lehmann (2006) X

Abbaspour et al. (1999) X X

Binley and Beven (2003) X X

Ritter et al. (2003) X X

Ines and Droogers (2002) X X

Ines and Mohanty (2008b) X X


the x and y axes (of qsim and ETsim), which is not desirable. To date, the distribution of the uncertainties in qobs and ETobs retrieved from remote sensing is not well understood (e.g., Fernandez-Galvez, 2008), and therefore multiobjective algorithms were not used in this study. The commonly used Generalized Likelihood Uncer-tainty Estimation (GLUE) developed by Beven and Binley (1992) to estimate the uncertainties in the parameters was also not selected because the GLUE method uses subjective criteria to differentiate the behavioral simulators from the nonbehavioral ones (e.g., Efstra-tiadis and Koutsoyiannis, 2010) and in our case study, the limits of behavioral and nonbehavioral parameter sets were well defined (within the error bars of measured qobs and ETobs).

In this study, the uncertainties in the water fluxes and the hydraulic parameters were determined by a Monte Carlo approach. Because there are a large number of simulations that need to be performed, however, the strictly Monte Carlo approach is highly computa-tional. An efficient alternative is to keep in memory all the trials performed by a global optimization (Pollacco et al., 2008a, 2008b; van Griensven and Meixner, 2006) and to select the behavioral parameters such that the errors between observed and simulated soil moisture are not greater than a RMSE error of 0.04 m3 m−3 and the maximum relative error between observed and simulated evapotranspiration is <20%. The advantage of this methodology is that the optimizer samples solutions around the global minima.

For each hydroclimate, the modeled uncertainties in the water fluxes were selected from the behavioral (feasible) parameter set such that it gives the maximum uncertainties. The rationale for selecting the greatest uncertainties in the water fluxes can be justified due to the uncertainties in the hydrologic model, which assumes that the Richards’ equation of the SVAT model is also valid at a large scale (e.g., Beven and Binley, 1992; Beven et al., 2008; Engeland et al., 2005; Vereecken et al., 2008; Verstraeten et al., 2008). To increase our understanding of the behavior of the uncertainties in the inverted water fluxes of SVAT models, we investigated the correlations between the uncertainties in the water fluxes and the uncertainties in qobs and ETobs by using the UnSA algorithm.

In this study, we assumed that the soils were homogeneous, which inevitably is a source of errors in the predicted water fluxes. Nev-ertheless, this assumption can be to a certain degree acceptable because Jhorar et al. (2004) found that, in most cases, a reliable water balance can be computed by replacing a heterogeneous soil profile with an equivalent single homogeneous soil profile.

The motivation for this study was to have an understanding of the hydrologic processes that cause uncertainties. The specific objectives of this research were therefore to: (i) determine how the uncertainties in the predicted water fluxes are correlated with soil textures, rooting depths, and climates; (ii) understand what hydrologic processes cause uncertainties in the water fluxes; and (iii) establish if the nonuniqueness of the inverted soil hydraulic

parameters can be reduced to compare these parameters with the effective unique set of physically based soil hydraulic parameters determined by scaling point measurements.

6 Uncertainty Simulator Algorithm

The proposed UnSA performs numerical experiments to correlate the uncertainties in the observed top 5-cm surface soil moisture, qobs [L3 L−3], and evapotranspiration, ETobs [L T−1], with the uncertainties in the simulated water fluxes (WFsim). The WFsim of interest is composed of groundwater recharge Q [L T−1], evapora-tion E [L T−1], transpiration T [L T−1], and root-zone soil moisture qrz [L3 L−3]. The approach taken by the UnSA was discussed above and therefore only the algorithm is presented below. The uncer-tainties in the simulated water fluxes (DWFsim) are derived by gen-erating different sets of behavioral (feasible) hydraulic parameters of the SVAT model presented below. To mimic the uncertainties in retrieving soil moisture and evapotranspiration from remote sensing, the behavioral qsim and ETsim are selected such that they are encompassed in the errors bars of qobs and ETobs. The UnSA is performed in three successive steps.

Step 1: Computing Synthetic ObservationsThe UnSA uses synthetic data and therefore requires for each hydroclimate scenario that qobs, ETobs, and WFobs are known. The WFobs values are computed by inputting known sets of hydraulic parameters (HYDRAULICobs in Fig. 1) and vegetation param-eters (VEGETATIONobs in Fig. 1) and forcing data on precipi-tation and potential evapotranspiration into a SVAT hydrologic model (Fig. 1, Loop 1). In this study, as discussed above, the vegeta-tion parameters were not the subject of investigation.

Step 2: Generating UncertaintiesFor each hydroclimate scenario, an ensemble of qsim and ETsim are simulated to reproduce the uncertainties in retrieving qobs and ETobs from remote sensing. This is performed by generating differ-ent sets of simulated hydraulic parameters (HYDRAULICsim in Fig. 1) and the corresponding time series WFsim, qsim, and ETsim by optimizing the “unknown” constrained hydraulic parameters by minimizing a weighted objective function (Fig. 1, Loop 2). The Shuffled Complex Evolution Algorithm–University of Arizona (SCE-UA) developed by Duan et al. (1992, 1994) was used as a global optimization routine. We modified the SCE-UA such that during the search of the global minima, all the different trials of HYDRAULICsim and the corresponding WFsim are stored in the STORAGE. The customized global optimization can be seen as a restrained Monte Carlo simulation that searches different combi-nations of behavioral parameter sets, which produces values of the objective function in the vicinity of the global minimum (Pollacco et al., 2008a, 2008b; van Griensven and Meixner, 2006).


Step 3: Selecting the Maximum Uncertainties in the Water FluxesThe behavioral hydraulic parameters and the WFsim are selected from the STORAGE (Fig. 1, Loop 3) in order that the following condition is satisfied:

( )2obs sim

sim 1N

Nq

q

q -qDq = å [1a]

et

et

obs sim1sim

obs1

ET ETET

ET

N

N

-D =

åå

[1b]

Uncertainties in retrieving soil moisture and evapotranspiration, respectively, from remote sensing are derived:

sim rs sim rsAND ET ETDq £Dq D £D [1c]

For comparison purposes, we also derived the uncertainties in retrieving soil moisture and evapotranspiration, respectively, from the field:

sim f sim fAND ET ETDq £Dq D £D [1d]

where the subscripts obs and sim indicate the daily observed values and simulations, respectively; Nq is the number of qobs and Net is the number of ETobs; Dqrs and DETrs are typical uncertainties in retrieving soil moisture and evapotranspiration, respectively, from remote sensing; and Dqf and DETf are typical uncertainties in retrieving soil moisture and evapotranspiration, respectively, from the field (in situ observations).

Thus, simulations that do not comply with Eq. [1c] or [1d] are rejected (depending on whether we are interested in the uncertain-ties in retrieving the data from remote sensing or from the field). The Dqrs is given a RMSE of 0.04 m3 m−3 volumetric soil moisture (e.g., Crow et al., 2005a, 2005b; Davenport et al., 2005; Kerr et al., 2001; Simmonds et al., 2004), and DETrs is given a relative error

Fig. 1. Flowchart of the Uncertainty Simulator Algorithm (UnSA). The UnSA computes the uncertainty of the water flux outputs (DWF) by using a soil–vegetation–atmosphere transfer (SVAT) hydrologic model, where WOF is the weighted objective function, q is soil moisture, ET is evapotranspiration, subscripts obs and sim are observed and simulated, respectively, and Dqrs and DETrs are the uncertainties in the soil moisture and evapotranspiration, respectively, retrieved from remote sensing. The UnSA is performed in three separate steps: Step 1 (solid line) generates synthetic data; Step 2 (dashed line) generates uncertainties; Step 3 (square dots) selects the maximum uncertainties, DWFmax.


of 20% (e.g., Kalma et al. [2008] from a compilation of 30 studies). For comparison purposes, the DWFsim are also filtered with the uncertainties in measuring soil moisture and evapotranspiration from the field. The Dqf is given a RMSE value of 0.02 m3 m−3 volu-metric soil moisture, which is a typical uncertainty in measuring soil moisture with a neutron probe (e.g., Haverkamp et al., 1984), and DETf is given a relative error of 12% of evapotranspiration from eddy-covariance measurements (e.g., Tomlinson, 1996, p. 15).

The average yearly residuals DWFsim are computed for each water flux Q, ET, T, and E (%) by computing the differences between sim-ulated and observed water fluxes using the following relationship:

sim

1 1 1 1

WF

WFobs WFsim WFobsy y yt t tY

t t tt t t

Y= = =

D =

é ùê ú-ê úê úë û

å å å å [2]

where Y corresponds to 3 yr of simulations and ty corresponds to 365 d.

The residual Dqrz is computed in the same manner as Dqsim as described in Eq. [1a].

The commonly used objective function (coefficient of efficiency) is derived from Nash and Sutcliffe (1970). Nevertheless, accord-ing to Schaefli and Gupta (2007) and Schaefli et al. (2005), the Nash–Sutcliffe coefficient does not measure how efficient a model is in absolute terms and can be a very poor predictor for strongly seasonal data. This is the case for time series soil moisture and evapotranspiration, which fluctuate seasonally around a mean value. Therefore, we adopted the following weighted objective function (WOF) for which the uncertainties in q are computed from Eq. [1a] and the uncertainties in ET are computed with Eq. [1b] and normalized by the maximum uncertainties in deriving Dqsim and DETsim (Eq. [1c] and [1d]):

et et

obs sim rs1

obs sim rs obs1 1

WOF2

ET ET ET ET

2

N

N N

Nqqq -q Dq

=

- D+

å

å å [3]

In summary, the model outputs are the correlations of DWFsim with Dqobs and DETobs. The maximum DWFsim values are com-puted with Eq. [1c] and [1d], respectively.

6Materials and MethodsSoil–Water–Atmosphere–Plant Hydrologic ModelThe Soil–Water–Atmosphere–Plant (SWAP3.2) model is a physi-cally based SVAT water flow model that is used to simulate the unsaturated-zone soil water fluxes of vegetated land (e.g., Kroes et al., 2000; van Dam et al., 2008, 1997). The governing equation of SWAP solves the mixed form of the Richards’ equation, combined with a sink term for root extraction to simulate variably saturated soil moisture movement in the soil profile:

( )( )( )

1K h zS h

t z

é ù¶ q ¶ ¶ +¶q ê úë û= -¶ ¶

[4]

where q is the volumetric water content [L3 L−3] or the fraction of water-filled pore space; h is the capillary pressure head [L]; t is time [T]; z is the vertical coordinate [L] defined as positive upward; K(q) is the unsaturated hydraulic conductivity [L T−1]; and S(h) is the rate of soil water extraction by plant roots [L3 L−3 T −1].

Soil Water Retention and Unsaturated Hydraulic ConductivityThe accuracy of modeling groundwater recharge depends on the knowledge of two functions: the soil moisture characteristic curve, h(q), and the unsaturated hydraulic conductivity curve, K(q). The analytic h(q) function is commonly described by the van Genu-chten model (1980), and the unsaturated hydraulic conductivity function K(q) is modeled by the Mualem (1976)–van Genuchten (1980) model. The h(q) relationship is computed as

( )r

es r

ae

1

1mn

S h h

q-q= =

q -q é ù+ê úë û

[5]

where h is the capillary pressure head [L]; Se denotes the normal-ized volumetric water content [L3 L−3]; qr and q s [L3 L−3] are residual and saturated water contents respectively, with 0 £ qr < q

< qs < 1 [L3 L−3]; hae (1/a) is associated with the air-entry matrix potential [L−1]; n (>1) is a shape parameter related to the pore-size distribution; and m is a shape parameter. The parameters m and n are related via the expression m = 1 − 1/n following the assumption of the hydraulic conductivity model of Mualem (1976).

The unsaturated hydraulic conductivity function, K(q), is described by the Mualem–van Genuchten model and computed as

( ) ( )2

1/s e 1 1

mL meK K S Sé ù

q = - -ê úê úë û [6]

where L is a connectivity parameter and is commonly kept fixed and equal to 0.5, and Ks is the saturated hydraulic conductivity [L T−1].


The residual water content (qr) is often set to 0 because qr does not greatly affect the goodness-of-fit of the characteristic curve (e.g., Boufadel et al., 1998; Ines and Droogers, 2002; Luckner et al., 1989; Russo, 1988; Schaap and Leij, 1998b; Tietje and Tapken-hinrichs, 1993). As a compromise, we set qr = 0.05 m3 m−3, which is the minimum value of qr taken from the compiled data set of Schaap and Leij (1998a).

The feasible range of the hydraulic parameters for large-scale mod-eling were derived from Schaap and Leij (1998a) and are described in Table 2, except for the minimum value of qs, which was com-puted for each hydroclimate from the maximum values of qobs:

( )s,min obsmaxq = q [7]

Sink Term and Evaporation Module of the Parsimonious Modified SWAP ModelBuilding parsimonious hydrologic models by reducing the number of input vegetation parameters of the SWAP model without alter-ing the physical concepts of the model and without decreasing the accuracy of predicting the water fluxes is challenging. Consequently, we modified the evaporation, root water uptake, transpiration, and rainfall interception modules of SWAP, termed SWAPinv, such that it uses only the leaf area index (LAI) [L3 L−3], which could be retrieved from remote sensing (e.g., Garrigues and et al., 2008), the extinction coefficient of solar radiation (Kg) that was set to 0.5 (Varado et al., 2006; Wang et al., 2009), the rooting depth information, and the hydraulic parameters qs and qr as input parameters.

Below are described the computation of the potential evapotrans-piration, the sink term, and the evaporation modules of SWAPinv, which are substantially different than the those implemented in SWAP. The interception module is described in the Appendix because it does not influence the results significantly.

Potential Evapotranspiration

We selected the potential evapotranspiration, ETp [L T−1], computed by Priestley and Taylor (1972), which is termed reference crop evapo-transpiration by Jensen et al. (1990) and Maidment (1992). This is

because Weiß and Menzel (2008) compared, in a global application, four different potential evapotranspiration equations, which included Priestley and Taylor (1972), Penman–Monteith (Allen et al., 1998), Kimberly–Penman (Wright, 1982), and Hargreaves et al. (1985). Weiß and Menzel (2008) concluded that the use of the radiation-based Priestley–Taylor ETp gave the most accurate calculation of water balance. In this synthetic study, the Priestley–Taylor ETp was computed by following the procedure of Jarvis (2011):

( ) ( )npET

R Gé ùa D D+g -ë û=l

[8a]

To compute the net radiation, Rn (MJ m−2 d−1), from the total incoming shortwave solar radiation Rs (MJ m−2 d−1), we used the linear Jensen et al. (1990) equation:

n sR R b=b + [8b]

The slope of vapor pressure curve, D (kPa °C−1), is expressed by

( )

( )mean mean

2mean

2504 exp 17.27 237.2

237.2

T T

T

é ù+ë ûD=+

[8c]

where the mean daily air temperature Tmean (°C) is computed by averaging the maximum and minimum temperatures of the day (Tmax + Tmin)/2; g is a psychrometric constant and is given a constant value of 0.054 kPa °C−1; l = 2.501 − 0.002361 Tmin (MJ kg−1) is the latent heat of vaporization given by Harrison (1963); G (MJ m−2 d−1) is the soil heat flux, which is negligible at the land surface and is equal to 0; b is an empirically determined dimensionless correction taken as 1.26; a = 0.61 and b = −1.0, were obtained by Jensen et al. (1990), who averaged data from 14 locations worldwide.

The value of ETp is partitioned into potential evaporation from a wet canopy Epw (L T−1), potential soil evaporation Ep (L T−1), and potential transpiration Tp (L T−1). The partitioning is performed by using the Beer–Lambert law (e.g., Belmans et al., 1983; Goudri-aan, 1982; Ritchie, 1972), which uses the LAI and Kg parameters by assuming that the net radiation inside the canopy decreases exponentially. The ETp decreases with increasing Kg and increasing LAI. For further information on the evapotranspiration partition-ing, see the SWAP manual (http://www.swap.alterra.nl/).

Sink Term

To take into account tree physiology and the reduction of transpi-ration by soil water stress, the actual transpiration T is distributed by the sink term S(hi) across the whole root zone and is calculated

Table 2. Feasible range of van Genuchten (1980) hydraulic parameter space, including saturated and residual water content (qs and qr, respectively), air-entry matric potential (hae), shape parameter n, and saturated hydraulic conductivity (Ks), for soils of all textures (derived from Schaap and Leij, 1998a), where Pmin and Pmax are the upper and lower bounds, respectively, of the feasible parameter space.

Bound qs qr hae n Ks

———— m3 m−3 ————— cm cm d−1

Pmin qs,min (Eq. [7]) 0.05 25 1.2 4

Pmax 0.52 0.05 230 2.3 230


for each cell by the method of Feddes et al. (1978) and by the com-pensation term of Li et al. (2001), which was added to SWAPinv. The sink term is computed by

( ) ( ) ( )c p Rdf , Rdfi i i i iS h K T G h C G= D D [9]

where Kc is the transpiration fraction or crop factor, Tp [L T−1] is the potential transpiration estimated for short grass; DRdfi is the vertical fraction of the root density function for the ith cell (%); G(hi) is the reduction of root water uptake at pressure head h for the ith cell, and C(G,DRdfi) accounts for the compensation mechanism.

Root Density Function

In SWAP, the vertical fraction of the root density function for the ith cell (DRdfi), which defines the general shape of the roots, is entered manually in tabular form. In SWAPinv, the root distribu-tion is modeled with an empirical function of Gale and Grigal (1987) that was modified further by Pollacco et al. (2008a). The model requires the rooting depth and the percentage of root den-sity in the top 30 cm (DRdf30). The fraction of roots in the ith cell, DRdfi, between the top and the bottom of the ith cell is computed as

updown max

root

c c

1c

Rdf with Rdf 11

zz i i

i iz

E E

E

=-D = D =

-å [10]

where zup and zdown are the top and bottom depths, respectively, of each cell, which are positive downward (cm); Ec is an “exten-sion coefficient” parameter, zroot is the rooting depth (cm), and imax is the last cell of the root zone. The value of Ec varies between 0.7 and 0.9999 such that when Ec is close to 0.7, all the roots are distributed in the top cell, and when Ec is close to 1, the roots are distributed evenly within the root zone. The value of Ec is com-puted from the percentage of roots (for example) in the top 30 cm, DRdf30, by solving the following equation numerically:

root root

0 30 30c c c

30c c

1Rdf

1 1Z Z

E E E

E E

- -D = =

- - [11]

It is interesting to note that the use of the compensation mecha-nism causes the predictions of the water fluxes to be more sensitive to zroot than to Ec

(results not shown).

Root Water Uptake

When the capillary pressure head in the ith node (hi) is reduced, the vegetation closes its stoma and decreases transpiration by using the stress function shown in Fig. 2. The limits of G(hi) are computed as

( )( )

4 1

2 3

0 IF OR

1 IF AND i

i

G h h h h h

G h h h h h

ìï = > <ïíï = > <ïî [12]

Water uptake below |h1| (O2 deficiency, anaerobiosis point) and above |h4| (wilting point) is set to zero. Between |h2| and |h3|, G(hi) = Tp maximal. The value of h3 varies with Tp. For different values of Tp, h3 is linearly interpolated between h3low and h3high.

Compensation Mechanism of the Root Water Uptake Module

We introduced in SWAPinv a root water uptake compensation mechanism that improves the prediction of transpiration by enabling water uptake from deeper layers when the upper layers are depleted, although the percentage of roots at deeper depth is limited (e.g., Adiku et al., 2000; English and Raja, 1996; Jarvis, 2011; Skaggs et al., 2006; Stikic et al., 2003; Taylor and Klepper, 1978). The compensation mechanism of Li et al. (2001), validated by Braud et al. (2005b) and Varado et al. (2006), was introduced into SWAPinv. The Li et al. (2001) model requires one parameter. The compensation mechanism C accounts for the general soil moisture profile before computation of the water uptake for each individual cell and is computed as

( )( )max

1

1

Rdf

Rdfi i

i i ii ii

G hC

G h

l-

= l=

D=

Då [13]

where DRdfi (Eq. [10]) is the vertical fraction of the root density function for the ith cell (%); G(hi) (Eq. [12]) is the reduction of root water uptake at pressure head h for the ith cell; and l is a parameter for which when l = 1 the model is not compensated and

Fig. 2. Schematic of the plant water stress response function as a function of pressure head and potential transpiration rate, Tp (Eq. [12]) (adopted from Feddes et al., 1978).


when l = 0 the DRdfi becomes constant throughout the whole root-zone depth. Li et al. (2001) and Braud et al. (2005b) found an optimal value of l = 0.5, which was used in this study.

Evaporation Module

The evaporation module of SWAP was simplified. Under wet soil con-ditions, the actual soil evaporation E [L T−1] equals the potential soil evaporation Ep. During a period between storms, SWAP computes E by using the empirical evaporation method of Black et al. (1969), which requires two fitting parameters. Nevertheless, Eagleson (1978), Milly (1986), and Romano and Giudici, (2007, 2009) showed that good results can be achieved by relating evaporation to soil moisture. We therefore used the Romano and Giudici (2007, 2009) evaporation model, which does not require any extra parameters:

0r5

ps r

maxE E

q -q=

q -q [14]

where the maximum soil moisture is selected between the surface and the depth of 5 cm, and Ep is the potential evaporation com-puted with the Beer–Lambert law. Consequently, the sharing of the hydraulic parameters, which compute soil moisture and evaporation, increases the sensitivity of the hydraulic parameters when they are inverted simultaneously from soil moisture and evapotranspiration.

Boundary Conditions and DiscretizationThe soil column was discretized for (i) deep roots with a total depth of 1.80 m and (ii) shallow roots with a total depth of 0.90 m. The discretization starting from the top cell was, for the deep roots, 0.25, 0.25, 0.5, 1.5, 2.5, and 5 (for the following 35 cells) cm, and for the shallow roots, 0.25, 0.25, 0.5, 1.5, 2.5, and 5 (for the fol-lowing 17 cells) cm. For all the scenarios, the soil columns were initialized uniformly at h = −100 cm and SWAPinv was run 90 d (spin-up time) ahead of the experiment to tune the state of the initial soil moisture profile. For the bottom boundary condition of the soil columns, free drainage condition was selected. The upper boundary condition was determined by daily net precipitation and daily potential evapotranspiration. The potential evapotrans-piration was partitioned into potential transpiration, potential soil evaporation, and potential evaporation from a wet canopy by

using the Beer–Lambert law (e.g., Belmans et al., 1983; Goudriaan, 1982; Ritchie, 1972). A maximum of 2 cm of ponding water was permitted, with any overflow lost as runoff.

Reference Climate, Soil Hydraulic Properties, Vegetation Parameters, and Water FluxesWe selected 18 hydroclimatic scenarios, which were composed of the combinations of three soil textures, two rooting depths, and three climates. The three contrasting climates, summarized in Table 3, were selected from the data set compiled by Jarvis (2011), who obtained the raw data from the Solar and Meteorological Surface Observational Network (SAMSON; http://www7.ncdc.noaa.gov/CDO/cdo). Each data set was composed of daily precipitation and weather data used to compute the Priestley–Taylor potential evapo-transpiration (Eq. [8]) for a period of three water years (1 Oct. 1987–30 Sept. 1990). The selected contrasting climates corresponded to typical mainland southern United States climates for which snowfall is scarce. The climates were classified according to the Aridity Index (AI) (or dryness index) of Budyko (1974), which is calculated as the ratio of annual potential evaporation to precipitation. Regions where AI is >1 are approximately classified as dry because the evaporative demand cannot be met by precipitation. Similarly, regions with AI

< 1 are roughly classified as wet (Arora, 2002).

The data for three contrasting benchmark soils (Table 4) were taken from Twarakavi et al. (2010), who classified the soils based on their hydraulics. Pure sand and clay were not selected because they are rarely encountered on a large scale.

Table 3. Sources of selected reference hydroclimate data compiled by Jarvis (2011), who obtained the raw data from the Solar and Meteorological Surface Observational Network (SAMSON; http://www7.ncdc.noaa.gov/CDO/cdo).

Aridity Index Location Latitude Longitude

2 Dodge City, KS 37°45¢ N 101°1¢ W

1 Oklahoma City, OK 35°26¢ N 97°28¢ W

0.5 Asheville, NC 35°26¢ N 82°32¢ W

Table 4. Reference values of contrasting van Genuchten hydraulic parameters, including saturated and residual water content (qs and qr, respectively), shape factor (L), air-entry matric pressure (hae), shape parameter n, and saturated hydraulic conductivity (Ks). The soils are classified based on their hydrologic features (Twarakavi et al., 2010).

Abbreviation Texture Classification qs qr L hae n Ks

——— m3 m−3 ————— cm cm d−1

Cl clay loam–clay Clay4 0.5 0.07 0.5 77 1.4 21

L silty loam Loam2 0.43 0.05 0.5 190 1.6 52

S loamy sand Sand2 0.38 0.05 0.5 30 1.9 124


Two contrasting benchmark rooting depths (shallow and deep roots) were used in the numerical experiments. The rooting depths and the percentage of roots in the top 30 cm are given in Table 5. The deep rooting depths was selected to depict shrubs. Forested land was not modeled in this study because currently soil moisture cannot be retrieved using remote sensing under a dense canopy (e.g., Jackson and Schmugge, 1991).

The values of the constant vegetation parameters for each climate (AI), including water uptake parameters, LAI, extinction coeffi-cient of solar radiation, and crop factor, are provided in Table 6.

6ResultsReference Water FluxesThe summary of the 18 reference water fluxes that were used in this numerical study and computed with SWAPinv are described in Fig.

3. The selected scenarios had contrasting groundwater recharge that ranged from 19 to 651 mm yr−1, transpiration from 195 to 474 mm yr−1, and evaporation from 52 to 266 mm yr−1.

Uncertainties in the Predicted Water FluxesThe UnSA computed for the each hydroclimate the relation-ships between Dqobs, DETobs, DQsim, DTsim, DEsim, DETsim, and Dqrz_sim (described in Eq. [1] and Eq. [2]). The correlations between DQsim and Dq sim, DETsim, DTsim, DEsim, DETsim, Dqrz_sim are depicted in Fig. 4 for six representative hydrocli-mates. For each hydroclimate and WFsim depicted in Fig. 4, the maximum DWFsim is reported in Table 7 for the following two conditions: (i) Dq sim £ Dqrs and DETsim £ DETrs (Dqrs and DETrs are typical uncertainties in retrieving soil moisture and

Table 5. Scenarios of the percentage of roots in the top 30 cm, DRDF30 (Jackson et al., 1996) and the maximum rooting depth, Zroot (Schenk and Jackson, 2002) for shallow and deep roots.

Acronym Description Zroot DRDF30 Vegetation type

cm %

SR shallow roots 40 80 meadow

DR deep roots 130 50 semi-desert

Table 6. Values of the vegetation parameters that remain constant, where h1, h2, h3high, h3low, and h4 are the matric potentials that regulate the water uptake described in Fig. 2, LAI is the leaf area index, b is the crop factor, and Kg is the extinction coefficient of solar radiation.

Aridity index h1 h2 h3high h3low h4 LAI Kg b

————————— cm —————————— m3 m−3

2 −1 −22 −1000 −2200 −16,000 1.50 0.5 0.7

1 −1 −22 −1000 −2200 −16,000 2.25 0.5 0.8

0.5 −1 −22 −1000 −2200 −16,000 3.00 0.5 0.9

Fig. 3. Yearly groundwater recharge Q, transpiration T, evaporation E, interception Pint, potential evapotranspiration ETp, computed with the modified Soil–Water–Atmosphere–Plant model (SWAPinv) for the 18 hydroclimate condition scenarios. For visualization, the gross precipitation was computed as Pg = Q + T + E + Pint, with the long-term storage computed to 0. The acronyms include climate (Aridity Index: AI_2 dry, AI_1 moderate, or AI_0.5 wet), soil type (clay Cl, loam L, or sand S), and rooting (shallow SR or deep DR).


evapotranspiration from remote sensing), and (ii) Dqsim £ Dqf and DETsim £ DETf (Dqf and DETf are typical uncertainties in retrieving soil moisture and evapotranspiration from the field or in situ). The results summarized in Table 7 show that there is a good agreement between DWFsim computed with Dqrs and DETrs and DWFsim computed with Dqf and DETf because in this case study Dqrs ? 2Dqf and DETrs ? 2DETf..

Uncertainties in Predicting Groundwater RechargeThe predictions of DQsim for which the AI was >1.5, as described in Table 7, had large uncertainties, with DQsim of 38 to 917% for

Dqrs and DETrs and DQsim of 19 to 789% for Dqf and DETf. The high DQsim found in regions with AI > 1.5 is not surprising because, according to Herczeg and Leaney (2011), in such regions the residual error when subtracting rainfall from evapotranspira-tion is much larger than the net recharge. But for climates with AI

< 1.5, the uncertainties were reduced substantially, with DQsim £ 22% for Dqrs and DETrs and DQsim £ 16% for Dqf and DETf. The dependency found of parameter sensitivity of water fluxes to climate conditions is in line with several studies (e.g., Bastidas et al., 1999; Teuling et al., 2009). Figure 4 shows that for all hydro-climates, DQsim was strongly correlated with DETsim but poorly

Fig. 4. Output of the Uncertainty Simulator Algorithm, which correlates the uncertainties in groundwater recharge DQ with the uncertainties on the y axis of evaporation DE, evapotranspiration DET, transpiration DT, root-zone soil moisture Dqrz, and surface soil moisture Dq for dry climate (left) and wet climate (right). For visual purposes, we multiplied Dqrz and Dq by 10.


correlated with Dqsim. Table 7 shows for climates with AI > 1.5 that DQsim increased under finer texture soils and deeper rooted vegetation. These uncertainties are explained by the combination of soil moisture decoupling and evapotranspiration decoupling, as described below. Soil moisture and evapotranspiration decou-pling occur when there is significant drying of the soil profile, as occurs under climates with AI > 1.5 where the soil moisture profile becomes heterogeneous, but, as described below, the mechanism that drives soil moisture decoupling is substantially different than the mechanism that drives evapotranspiration decoupling.

Soil moisture decoupling is driven by a high evaporation rate caused by prolonged hot, dry, and windy conditions, which yields a relatively strong nonlinear effect between the surface and the shallow root-zone layers, giving rise to a quasi-decoupled soil moisture scenario between the surface and the lower layers. This effect, known as decoupling, reduces the near-surface hydraulic conductivity and mainly occurs under coarse-texture soils that are in the drying phase (e.g., Capehart and Carlson, 1997; Walker et al., 2002; Wilson et al., 2003). Soil moisture decoupling, which is

more pronounced under sandy soils, can be seen in Fig. 5. Figure 5 shows that under dry conditions, the subsurface soil moisture does not respond to the dynamics of the surface time series soil moisture caused by rainfall events. Therefore, when soil moisture decou-pling occurs, the information provided by surface soil moisture is no longer representative of the root-zone soil moisture, causing uncertainties in the prediction of the WFsim.

The transpiration decoupling concept is introduced in this study and occurs when ETobs is no longer representative of the root zone, causing uncertainties in the prediction of the WFsim. The transpira-tion decoupling mechanism differs from the soil moisture decou-pling mechanism due to the fact that it is driven by the deep root water uptake of vegetation rather than surface evaporation. Thus, soil moisture decoupling is representative of the shallower root zone and transpiration decoupling is a signature of the deeper root zone. Transpiration decoupling increases under fine-texture soils (soil moisture decoupling occurs under coarser texture), where there is substantially more water storage at depth, as depicted in Fig. 5 for clay and loam soils. Transpiration decoupling of subsurface and

Table 7. Maximum uncertainties in the predicted water fluxes for surface soil moisture (Dq), evapotranspiration (DET), root-zone soil moisture (Dqrz), evaporation (DE), transpiration (DT), and groundwater recharge (DQ) described in Fig. 4 for each hydroclimate by using the Uncertainty Simulator Algorithm for scenarios where the uncertainties in simulated soil moisture and evapotranspiration (Dqsim and DETsim, respectively) are less than or equal to the uncertainties in the observed soil moisture and evapotranspiration retrieved from remote sensing (Dqrs and DETrs, respectively) and where Dqsim and DETsim are less than or equal to the uncertainties in the observed soil moisture and evapotranspiration retrieved from the field (Dqf and DETf, respectively).

Aridity Index Roots Texture

Dqsim £ Dqrs and DETsim £ DETrs Dqsim £ Dqf and DETsim £ DETf

Dq DET Dqrz DE DT DQ Dq DET Dqrz DE DT DQ

———————————————————————————————— % ——————————————————————————————————

2 deep sand 4 20 4 57 6 38 2 12 2 35 2 23

silt 4 19 5 46 28 111 2 12 2 40 23 74

clay 4 11 5 25 23 917 2 9 3 20 12 789

shallow sand 4 20 4 68 10 31 2 12 2 41 6 19

loam 4 20 4 54 40 83 2 12 2 43 32 52

clay 4 12 5 32 36 138 2 9 3 24 23 111

1 deep sand 4 14 4 94 5 21 2 9 2 58 3 13

loam 4 10 4 41 9 22 2 7 2 29 8 16

clay 4 7 4 22 12 19 2 5 2 15 5 13

shallow sand 4 20 4 91 12 20 2 12 2 54 9 12

loam 4 12 4 43 19 19 2 7 2 30 13 12

clay 4 9 4 29 18 20 2 5 2 17 9 11

0.5 deep sand 4 8 4 67 3 7 2 6 2 49 3 5

loam 4 7 4 43 6 7 2 5 2 27 6 5

clay 4 4 4 19 5 5 2 4 2 14 5 5

shallow sand 4 10 4 78 5 8 2 7 2 48 3 5

loam 4 7 4 46 8 7 2 5 2 32 6 5

clay 4 6 4 23 9 7 2 4 2 15 6 5


deeper root-zone soil moisture increases when the compensation mechanism (Eq. [13]) is used and when the vegetation roots are deep, enabling water to be extracted at depth when the surface soil moisture is depleted. This explains why Ines and Mohanty (2009) found that DWFsim values are higher under a shallow water table.

Uncertainties in Predicting TranspirationThe DTsim is climate driven and decreases exponentially as the AI decreases (Table 7). For Dqrs and DETrs when AI = 2, DTsim was 6 to 40%, when AI = 1, DTsim was 5 to 19%, and when AI = 0.5, DTsim was 3 to 9%, with similar results for Dqf and DETf. For AI = 2, DTsim increased as the texture became finer due to transpi-ration decoupling (see above). Nevertheless, it is not understood why DTsim under loam was slightly higher than under clay soils. Another explanation for why DTsim decreased when AI decreased is because when AI < 1.5, Table 7 shows that Dqsim ? Dqrs but DETsim << DETrs, and Dqsim ? Dqf but DETsim < DETf. This suggests that selecting the feasible parameter set such that Dqrs £ Dqsim or Dqf £ Dqsim is a stronger criterion than filtering the data with DETrs £ DETsim. Thus, these results indicate that calibrat-ing simultaneously with qobs and ETobs is more beneficial under drier climates than under wetter climates. Subsequently, under a wet climate, to further reduce DWFsim, DETrs must be <5% to compete with the uncertainties in Dqrs. These results are in line with those obtained by Ines and Droogers (2002), Jhorar et al. (2002, 2004), and Ines and Mohanty (2008b), who found that using multiple objective calibration with soil moisture and evapo-transpiration was not beneficial under all hydroclimates. This can be understood because under wet climates, there is little stress and the hydraulic parameters are directly related to soil moisture rather than evapotranspiration.

Uncertainties in Predicting EvaporationUnder all hydroclimatic conditions, Table 7 shows that the pre-dicted evaporation contained large uncertainties for all hydrocli-mates such that for Dqrs and DETrs when AI = 2, DEsim was 25 to 68%, when AI = 1, DEsim was 22 to 94%, and when AI = 0.5, DEsim was 19 to 78%. Table 7 shows that for all hydroclimates, DEsim was higher under clay soils than under sandy soils, which have a lower evaporation rate due to faster drainage compared with clay soils. Figure 6 shows that DEsim is inversely correlated with Eobs/ETp and therefore DEsim increased as Eobs decreased. There-fore for small Eobs, uncertainties in the observations (Dqrs and DETrs) caused large DEsim. It would be expected that DEsim be correlated with Dqobs because Eobs was computed from soil mois-ture (Eq. [14]). Nevertheless, as shown in Fig. 4, DEsim is strongly correlated with DETobs (uncertainties in predicting the climatic demands) because actual evaporation, E, was also computed from Ep, which was derived from ETp by using the Beer–Lambert law.

Fig. 5. Observed time series of soil moisture plotted at different depths: average 5-cm q (THETAtop) as seen by the satellite and 65 and 130 cm for sand, loam, and clay soils for a selected period of 12 mo under a Mediterranean climate. As expected, the average soil moisture increases as the soil texture becomes finer. These plots show where THETAtop decouples from the deeper layers (q decoupling) and where transpiration decoupling (ET decoupling) occurs due to more water storage at depth than at the surface.


Uncertainties in Predicting Root-Zone Soil MoistureThe Dqrz_sim described in Table 7 was found for all hydroclimate to be ?5% (for Dqrs and DETrs) and Dqrz ? 3% (for Dqf and DETf), which follows a similar pattern to Dqrs = 4% and Dqf = 2%, respectively. Figure 4 shows that for all hydroclimates there was a high correlation between Dqrz_sim and Dqrs (R2 = 0.95) because in this study the soil column was homogeneous. Future work will determine if Dqrz_sim and Dqsim will still be correlated in heterogeneous soils, as in the experiments undertaken by Jhorar et al. (2004).

Reducing Correlation of the Inverted Hydraulic ParametersWe also investigated whether the nonuniqueness of the inverted hydraulic parameters could be reduced. The reduction of the nonuniqueness would enable a comparison of the inverted effec-tive hydraulic parameters with the effective hydraulic parameter set obtained by scaling the hydraulic parameters (e.g., Braud et al., 2005a; Kosugi and Hopmans, 1998; Leij et al., 2007; Saito et al., 2009) determined in situ. To perform this study, the choice of the least sensitive hydraulic parameters needed to be resolved because it is not widely accepted by all researchers, as shown by the wide divergence of the results in Table 1. Subsequently, the impact of using reduced correlated parameters on the uncertainties in the water fluxes was investigated.

Least Sensitive Hydraulic ParametersThe feasible range of the parameters of qs, hae, n, and Ks computed with UnSA such that qsim £ Dqrs and ETsim £ DETrs or qsim £ Dqf and ETsim £ DETf are plotted in Fig. 7. The feasible range of each parameter was taken from Table 2 and is described in Fig.

7 by the upper (Pmax) and lower limits (Pmin) of the y axis. The results highlight the strong nonuniqueness of the inverted hydrau-lic parameters even when the uncertainties in the observations are taken from the field (Dqf and DETf), which is half the uncertain-ties in retrieving soil moisture and evapotranspiration from remote sensing (Dqrs and DETrs). The finding of strong nonuniqueness of the inverted hydraulic parameters has been reported by many researchers (e.g., Abbaspour et al., 1999; Beydoun and Lehmann, 2006; Binley and Beven, 2003; Jhorar et al., 2002; Pollacco et al., 2008b; Ritter et al., 2003). Therefore, the inverted hae, qs, n, and Ks parameters can no longer be seen as physical but as functional hydraulic parameters (hae,func, qs,func, nfunc, and Ks,func) due to the strong nonuniqueness. This signifies that different sets of func-tional parameters produce similar ETsim and qsim within the error bars of Dqf and DETf or Dqrs and DETrs.

The parameter n, statistically speaking, is the most sensitive param-eter because Fig. 7 shows that the maximum and minimum range does not cover the whole feasible parameter space, as within the plots of hae and Ks. This result is not surprising because, according to Haverkamp et al. (2005), the parameter n is the only van Genu-chten parameter that is representative of the soil texture. The next most sensitive parameter for all hydroclimates is q s. The uncer-tainty band of qs is narrower for finer texture soils than for coarser soils. This is because the lower value of the degree of freedom of qs (Pmin) was computed from the highest value of qobs (Eq. [7]) and clay soils reach saturation faster than sandy soils, as shown in Fig. 5. The final least sensitive parameters are hae and Ks because they cover practically the full range of the prescribed degrees of freedom.

The results shown in Fig. 7 highlight the problem of the intercor-relation of the hydraulic parameters, which is shown in Fig. 8. As an example of the intercorrelation of the hydraulic parameters, we selected a loamy soil from Fig. 7. Figure 8 shows that when we select the data set such that Dq £ 0.002 m3 m−3 and DET £ 2% (for visualization purposes), we can see correlations between qs and n, hae and n, hae and Ks, and n and Ks, which explains the wide ranges shown in Fig. 7. For further discussion on the subject, see Pollacco et al. (2008b).

Impact of Functional Hydraulic Parameters on Uncertainties in the Water FluxesPollacco et al. (2008b) found that the functional parameters are strongly linked (correlated), and therefore while performing optimization, any two parameters can remain constant and the optimized parameters will correct for any mismatch of the fixed parameters. Nevertheless, Pollacco et al. (2008b) calibrated the hydraulic parameters only with the soil moisture profile and did not determine the optimal values of the fixed parameters. The values of the fixed hae,func = 126 cm and Ks,func = 117 cm d−1, valid for all hydroclimates, were taken from Fig. 7 such that they encompass the uncertainties in all hydroclimates, preferably for Dqf and DETf (because they are smaller than Dqrs and DETrs).

Fig. 6. Correlation between the uncertainty of evaporation DE and the ratio of the annual actual evaporation over annual potential evapotranspiration (E/ETp), showing that DE is negatively correlated with E/ETp.


To determine the errors introduced by fixing hae,func = 126 cm and Ks,func = 117 cm d−1, qs,func and nfunc were optimized (with the SCE-UA), and the global optima of qs,func and nfunc are reported in Table 8 for all hydroclimates. Table 8 shows that for all hydro-climates the use of functional parameters gives the following max-imum errors: DEsim £ 12%, DTsim £ 8%, and DQsim £ 45%, which is considered acceptable. The results show that DWFsim values are lower for coarser texture soils, which may be due to the choice of the fixed parameters. For each soil texture, the optimal nfunc determined for different climates and rooting depths is very stable at ±0.035. This highlights that n is not influenced by the erroneous values of the other parameters. The value of qs is also very

stable at ±0.02, but it is noted that this may be due to the use of Eq. 7 to reduce the feasible parameter space described in Table 2.

To determine if using functional parameters would reduce the uncertainties in the water f luxes, the UnSA was run by forc-ing hae,func to 126 cm and Ks,func to 117 cm d−1; the increase or decrease of uncertainties in using functional parameters are reported in Table 9 and summarized for each climate for Dqrs, DETrs, Dqf, and DETf. Table 9 shows that the use of functional parameters did not substantially improve or decrease DWFsim, which gives room for improvement because this analysis shows that the selected Ks,func and hae,func values are not very sensitive on DWFsim.

Fig. 7. The Uncertainly Simulator Algorithm computations of the feasible range of the hydraulic parameters saturated volumetric water content qs, air-entry matric potential hae, shape parameter n, and saturated hydraulic conductivity Ks for simulated qsim £ uncertainty in observed Dqf and simulated evapotranspiration ETsim £ DETf symbolized by Min1 − Max1, and when qsim £ uncertainty in remotely sensed Dqrs and ETsim £ DETrs, the feasible range is symbolized by Min2 − Max2. The true value of each parameter is symbolized by the circle. The maximum and minimum values for each parameter described on the y axis are taken from Table 2. The graphs suggest that the least sensitive parameter is hae followed by Ks, and the most sensitive parameter is n. The horizontal dash-dotted line in hae and Ks represents the value at which these parameters were kept constant in the other simulations. The acronyms include climate (aridity index: AI_2 dry, AI_1 moderate, or AI_0.5 wet), soil type (clay Cl, loam L, or sand S), and rooting (shallow SR or deep DR).


Fig. 8. Intercorrelation of the saturated volumetric water content qs, saturated hydraulic conductivity Ks, shape parameter n, and air-entry matric potential hae hydraulic parameters by selecting the data from the simulation for Aridity Index 1 (moderate climate), loam soil, and deep rooting plants (AI_1/L/DR) simulated by the Uncertainty Simulator Algorithm such that the uncertainty in the volumetric water content Dq £ 0.002 m3 m−3 and the uncertainty in evapotranspiration DET £ 2%. This explains why in Table 7 we find such large uncertainties in the optimized water fluxes.

Table 8. Uncertainties in the water fluxes for evapotranspiration (DET), soil evaporation (DE), transpiration (DT), and groundwater recharge (DQ) by forcing the air-entry matric potential hae to 126 cm and the saturated hydraulic conductivity Ks to 117 cm d−1 and by optimizing the saturated volu-metric water content qs and shape parameter n with the Shuffled Complex Evolution Algorithm–University of Arizona (SCE-UA). The minimum and maximum values are classified for each texture, which encompasses the three climates and the two rooting depths.

Texture Roots hae Ks qs n DET DE DT DQ

cm cm d−1 m3 m−3 ———————————————— % ————————————————

Sand observed 30 124 0.4 1.9 0 0 0 0

min. 126 117 0.41 2.23 0.6 3.0 0.0 0.9

max. 126 117 0.44 2.30 3.0 11.7 2.6 5.6

Loam observed 190 52 0.40 1.60 0 0 0 0

min. 126 117 0.47 1.56 1.8 8.7 0.0 1.7

max. 126 117 0.48 1.60 4.8 11.3 1.5 25.7

Clay observed 77 21 0.40 1.40 0 0 0 0

min. 126 117 0.52 1.27 0.7 1.9 0.7 0.9

max. 126 117 0.52 1.33 2.9 4.5 7.7 45.0


6Future ResearchThe DWFsim obtained in this study without considering the scale issues needs to be validated. This can be performed with precise weighing lysimeters for which all the water fluxes are measured (storage, drainage, and evapotranspiration) (e.g., Abbaspour et al., 1999; Durner et al., 2008; Kosugi and Katsuyama, 2001, 2004; Scanlon et al., 2005). The results of this study suggest that the different experiments should contain contrasting textures with unvegetated and vegetated lysimeters to enable the partitioning of evaporation and transpiration. The climates with AI > 1.5 are the most problematic and can be omitted. The selected lysimeters should not have a water table because it has been found that when plants can extract water at depth, the uncertainties increase.

Minimum Time Length of MeasurementsThe time length of the experiment is hydroclimatic specific and ideally the data set should encompass data for which the normal-ized root-zone volumetric water content, Se, would range from 0 to 1 (Eq. [5]). This is because Pollacco et al. (2008b) showed that to have a unique set of solutions, the root-zone soil moisture data must range from dry to wet, which is rarely met in situ. Research is required, by using, for example, lysimeter experiments, to deter-mine for a specific hydroclimate the uncertainties caused by the limited range in measuring Se. It should also be taken into account that non-daily information for observed soil moisture and evapo-transpiration is retrieved from thermal-band land surface tempera-ture retrievals, which to date are limited to cloud-free atmospheric conditions (e.g., Anderson et al., 2011). This implies that the col-lected data from remote sensing is skewed toward drier conditions.

Reducing the Feasible Parameter SpaceThe results suggest that the selection of Ks,func and hae,func is not very sensitive for the predictions of DWFsim. Alternatively, a more accurate way of obtaining Ks,func and hae,func would be to scale hae and Ks derived from point measurements (e.g., Braud et al., 2005a; Kosugi and Hopmans, 1998; Leij et al., 2007; Saito et al., 2009). This procedure will be useful to downscale the parameters, enabling the comparison of a nonunique effective parameter set retrieved via inverse modeling with unique, effective, physically based hydraulic parameters derived by scaling point measurements.

Making Usage of Transpiration and Soil Moisture Decoupling ConceptsFuture research is required to make usage of the soil moisture and transpiration decoupling concepts to reduce DWFsim by assigning more weight to the objective function (q based or ET based) during the period when soil moisture or transpiration decoupling does not occur. Soil moisture and transpiration decoupling may also be used as a drought metric comparable to the Palmer (1965) drought severity index to assess agricultural drought, reflecting root-zone soil moisture deficits.

One question that must be addressed is to what extent transpira-tion and soil moisture decoupling can be retrieved from remote sensing. Transpiration decoupling is better derived from vegetation stress (ET/ETp). The value of ET/ETp can be retrieved by using thermal imaging, which uses time-differential land surface tem-perature measurements derived from satellite imagery collected, for example, by the Geostationary Operational Environmental Satellites (e.g., Anderson et al., 2007a, 2007b, 2011; Moran, 2003).

Assessing the periods when transpiration and soil moisture decou-pling occur is not trivial, and models can be derived from lysimeter experiments. Transpiration and soil moisture decoupling occur after different drying soil moisture thresholds (at different depths) are met and need to be defined from lysimeter experiments. The threshold values would depend on the integrative memory of prior moisture conditions.

6ConclusionsIn this numerical study, we estimated the uncertainties in the simulated water fluxes (DWFsim) of a one-dimensional Richards’ model when the hydraulic parameters were inverted from the time series of top 5-cm soil moisture and evapotranspiration retrieved from remote sensing. The DWFsim values were derived by perform-ing numerical experiments with the UnSA, which was developed on the basis of previous studies (Pollacco et al., 2008a, 2008b). It was assumed that the uncertainties in the observed soil moisture had a RMSE of 0.04 m3 m−3 and the observed evapotranspiration had a relative error of 20%. For comparison purposes, DWFsim was also computed with uncertainties in retrieving soil moisture and evapotranspiration from the field. The water fluxes of interest

Table 9. The average decrease or increase in the uncertainty of soil evap-oration (DE), transpiration (DT), and groundwater recharge (DQ) for each Aridity Index (AI), which encompasses the three textures and the two rooting depths, determined with the Uncertainty Simulator Algo-rithm using the uncertainty in water content and evapotranspiration retrieved from either remote sensing (Dqrs and DETrs, respectively) or field observations (Dqf and DETf, respectively) and by forcing the air-entry matric potential hae to 126 cm and the saturated hydraulic conductivity Ks to 117 cm d−1.

AI Dq source DET source

Change in uncertainty

DE DT DQ

——————— % —————————

2 Dqrs DETrs−5 −7 −16

Dqf DETf−1 −1 −49

1 Dqrs DETrs−6 −2 −4

Dqf DETf4 3 −3

0.5 Dqrs DETrs−8 −1 −2

Dqf DETf−1 −1 −11


included groundwater recharge, evaporation, actual transpiration, and root-zone soil moisture. The DWFsim values were investigated under 18 contrasting hydroclimatic scenarios composed of the combinations of three climates from the United States, three soil textures, and two rooting depths, which are summarized in Fig. 3.

The uncertainty of computing the root-zone soil moisture was found, for all hydroclimatic conditions, to be correlated to the uncertainties in the top 5-cm soil moisture because in this study the soil column was homogeneous. Under all hydroclimatic con-ditions, the prediction of evaporation contained large uncertain-ties and was negatively correlated to the ratio of the annual actual evaporation with the potential evapotranspiration. The uncertain-ties in predicting transpiration were high under climates with AI > 1.5 and reduced when the AI decreased. The uncertainties in predicting groundwater recharge under climates with AI > 1.5 had large errors, but under climates with AI < 1.5, the uncertainties were reduced. For all hydroclimates, the uncertainties in ground-water recharge were strongly correlated with the uncertainties in observed evapotranspiration but not with the uncertainties in observed soil moisture. The results show that the uncertain-ties in groundwater recharge increased under (i) dry climate, (ii) coarse-texture soil, (iii) deep-rooted vegetation, and (iv) when water was preferentially taken up at depth due to the root com-pensation mechanism. The uncertainty of groundwater recharge was explained by the combination of soil moisture decoupling and evapotranspiration decoupling. Soil moisture decoupling occurs when the information provided by the surface soil moisture is no longer representative of the root-zone soil moisture due to strong evaporation. Transpiration decoupling of surface and root-zone soil moisture was introduced here and occurs when there is sub-stantially more water storage at depth and when the vegetation has deep roots (or can tap water from the water table) so that it can extract water at depth when the surface soil moisture is depleted.

To compare the inverted effective hydraulic parameters with a unique hydraulic parameter set obtained by scaling the measured physical hydraulic parameters, the nonuniqueness of the inverted hydraulic parameters needs to be reduced. For this study, the choice of the least sensitive hydraulic parameters needed to be determined. It was found by analyzing contrasting hydroclimates that hae and Ks are the least sensitive van Genuchten hydraulic parameters and n is the most sensitive parameter. It was shown that the high nonuniqueness of the inverted hydraulic parameters is due to the intercorrelation of the hydraulic parameters. Acceptable errors are reported in Table 8 when hae and Ks were kept constant and n and qs were optimized. We showed by running the UnSA that fixing these two parameters did not significantly reduce or increase DWFsim. Alternatively, a more accurate way of obtain-ing Ks and hae would be to scale hae and Ks derived from point measurements. This methodology would facilitate the downscal-ing of the parameters, enabling the comparison of a nonunique effective parameter set retrieved via inverse modeling with unique,

effective, physically based hydraulic parameters derived by scaling point measurements. It is also expected that more accurate results will be obtained if Ks is computed from parameters describing the characteristic curves by abiding soil physics principles (e.g., Guar-racino, 2007; Han et al., 2008).

6AppendixRainfall Interception ModelThe SWAP model computes rainfall interception following Braden (1985) and von Hoyningen-Huene (1981). These interception models, however, require extra parameters and do not use the potential evaporation of a wet canopy, Epw [L T−1]. We introduced in SWAPinv a physically based interception model, shown in Fig. 9, based on the work of Noilhan and Lacarrere (1995) and Varado et al. (2006) that uses Epw as a predictor and LAI and Kg as param-eters. The values of the LAI and Kg are provided in Table 6. The gross precipitation, Pg (mm d−1), defined as the amount of water that reaches the canopy, is computed following Rutter et al. (1971):

g int freeP P P= + [1A]

where Pfree (mm d−1) is the free throughfall, which is the fraction of precipitation that reaches the ground surface through gaps in the canopy, and Pint (mm d−1) is the intercepted precipitation.

Fig. 9. Description of rainfall interception model introduced in the modified Soil–Water–Atmosphere–Plant model (SWAPinv), where Pg is gross precipitation, Pint is intercepted precipitation, Pfree is free throughfall, Pnet is net precipitation, Pover is overflow of water from the reservoir, LAI is leaf area index, Lg is the extinction coefficient of solar radiation, Wmax is the maximum storage capacity of the water reservoir, Wr is the current level of the water reservoir, and EAw is the maximum quantity of water that can be evaporated.


The foliage of the canopy is considered as a water reservoir filled up to a depth Wr (mm), with a maximum storage capacity Wmax (mm). When the canopy is fully saturated (Wr = Wmax), any excess of Pint overflows, Pover (mm), to the ground such that, according to Valente et al. (1997):

( )over int r maxmax ;0P P W W= + - [2A]

The amount of water that reaches the ground is the net precipita-tion, Pnet (mm d−1):

net over freeP P P= + [3A]

A fraction of the water from the reservoir Wr will be evaporated at the rate of the actual evaporation of a wetted canopy, EAw (mm d−1) during and after a rainfall event. The value of Wr is calculated following Deardorff (1978):

rint over wEA

WP P

t¶

= - -¶

[4A]

The maximum quantity of water that can be evaporated during a time step is computed as

rw pw wEA min ;

dW

E Ft

æ ö÷ç= ÷ç ÷çè ø [5A]

where Epw is the potential transpiration of a wet canopy.

According to Rutter et al. (1971), evaporation from wet canopies is assumed to be proportional to the fraction of the canopy that is wet, Fw (0–1), which is computed following Deardorff, (1978):

2/3r

wmax

WF

W

æ ö÷ç ÷=ç ÷ç ÷çè ø [6A]

The value of Wmax is related to the LAI based on the empirical relationship of Varado et al. (2006) and von Hoyningen-Huene (1981). Varado et al. (2006) assumed that the interception of water of a canopy is similar to the interception of solar radiation Fs (0–1). Combining Varado et al. (2006) and von Hoyningen-Huene (1981), Wmax can be computed as

( )( )2max s0.935 0.498LAI 0.00575LAI 1W F= + - - [7A]

The value of Wmax increases with increasing LAI and Kg. The par-titioning of Pg and Pfree is similar to the Beer–Lambert law:

free s gP F P= [8A]

( )int s g1P F P= - [9A]

( )s gexp LAIF K= - [10A]

6NomenclatureHydraulic Parameters h(q) soil moisture characteristic curve K(q) unsaturated hydraulic conductivity h matric potential, m qr residual volumetric water content, m3 m−3

qs saturated volumetric water content, m3 m−3

hae air-entry matrix potential, cm Ks saturated hydraulic conductivity, cm d−1

n shape parameter related to pore-size distribution L shape factor

Vegetation Parameters h1, h2, h3high, h3low, h4 matric potentials that regulate water uptake, cm Kg extinction coefficient of solar radiation LAI leaf area index Zroot maximum rooting depth, cm Kc crop factorDRdf30 percentage of roots in the top 30 cm

Water Fluxes q top soil moisture, m3 m−3

qrz root-zone soil moisture, m3 m−3

E actual soil evaporation, m d−1

ET actual evapotranspiration, m d−1

Q groundwater recharge, m d−1

T actual transpiration, m d−1

UncertaintiesDqrs uncertainties in the observed soil moisture retrieved

from remote sensing, m3 m−3

DETrs uncertainties in the observed evapotranspiration retrieved from remote sensing, m3 m−3

Dqf uncertainties in the observed soil moisture retrieved from the field, m3 m−3

DETf uncertainties in the observed evapotranspiration retrieved from the field, m3 m−3


AcknowedgmentsWe acknowledge the partial support of the National Science Foundation (CMG/DMS Grants 062113 and C10-00021) and NASA THPs (NNX08AF55G and NNX09AK73G) grants. We are thankful for Joop Kroes (Alterra, the Netherlands), Jos van Dam (Alterra, the Netherlands), and Isabelle Braud (CEMAGREF, France) for their help with the development of SWAPinv; Martha Anderson (USDA) for her assistance with questions on remote sensing; and Nicholas Jarvis (SLU, Sweden), who provided us with the raw data from SAMSON. Finally we would like to thank Dr. Emanuel Pollacco (CEA, France) for his numerous suggestions during the course of this study. We wish also to thank the three anonymous reviewers, who provided valu-able critiques on the original manuscript.

ReferencesAbbaspour, K.C., M.A. Sonnleitner, and R. Schulin. 1999. Uncertainty in es-

timation of soil hydraulic parameters by inverse modeling: Example lysimeter experiments. Soil Sci. Soc. Am. J. 63:501–509. doi:10.2136/sssaj1999.03615995006300030012x

Adiku, S.G.K., C.W. Rose, R.D. Braddock, and H. Ozier-Lafontaine. 2000. On the simulation of root water extraction: Examination of a minimum energy hy-pothesis. Soil Sci. 165:226–236. doi:10.1097/00010694-200003000-00005

Allen, R.G., L.S. Pereira, D. Raes, and M. Smith. 1998. Crop evapotranspiration: Guidelines for computing crop water requirements. Irrig. Drain. Pap. 56. FAO, Rome.

Anderson, M.C., C. Hain, B. Wardlow, A. Pimstein, J.R. Mecikalski, and W.P. Kus-tas. 2011. Evaluation of drought indices based on thermal remote sensing of evapotranspiration over the continental United States. J. Clim. 24:2025–2044. doi:10.1175/2010JCLI3812.1

Anderson, M.C., W.P. Kustas, and J.M. Norman. 2007a. Upscaling flux observa-tions from local to continental scales using thermal remote sensing. Agron. J. 99:240–254. doi:10.2134/agronj2005.0096S

Anderson, M.C., J.M. Norman, J.R. Mecikalski, J.A. Otkin, and W.P. Kustas. 2007b. A climatological study of evapotranspiration and moisture stress across the continental United States based on thermal remote sensing: 1. Model for-mulation. J. Geophys. Res. 112:D10117. doi:10.1029/2006JD007506

Arora, V.K. 2002. The use of the aridity index to assess climate change effect on annual runoff. J. Hydrol. 265:164–177. doi:10.1016/S0022-1694(02)00101-4

Bashir, M.A., H. Tanakamaru, and A. Tada. 2009. Spatial and temporal analy-sis of evapotranspiration using satellite remote sensing data: A case study in the Gezira scheme, Sudan. J. Environ. Inform. 13:86–92. doi:10.3808/jei.200900143

Bastidas, L.A., H.V. Gupta, S. Sorooshian, W.J. Shuttleworth, and Z.L. Yang. 1999. Sensitivity analysis of a land surface scheme using multicriteria methods. J. Geophys. Res. 104(D16):19481–19490. doi:10.1029/1999JD900155

Belmans, C., J.G. Wesseling, and R.A. Feddes. 1983. Simulation model of the water balance of a cropped soil: SWATRE. J. Hydrol. 63:271–286. doi:10.1016/0022-1694(83)90045-8

Beven, K., and A. Binley. 1992. The future of distributed models: Model calibra-tion and uncertainty prediction. Hydrol. Processes 6:279–298. doi:10.1002/hyp.3360060305

Beven, K.J., P.J. Smith, and J.E. Freer. 2008. So just why would a modeller choose to be incoherent? J. Hydrol. 354:15–32. doi:10.1016/j.jhydrol.2008.02.007

Beydoun, H., and F. Lehmann. 2006. Drainage experiments and parameter esti-mation in unsaturated porous media. C. R. Geosci. 338:180–187.

Binley, A., and K. Beven. 2003. Vadose zone flow model uncertainty as conditioned on geophysical data. Ground Water 41:119–127. doi:10.1111/j.1745-6584.2003.tb02576.x

Black, T.A., W.R. Gardner, and G.W. Thurtell. 1969. Prediction of evaporation, drainage, and soil water storage for a bare soil. Soil Sci. Soc. Am. Proc. 33:655–660.

Boufadel, M.C., M.T. Suidan, A.D. Venosa, C.H. Rauch, and P. Biswas. 1998. 2D variably saturated flows: Physical scaling and Bayesian estimation. J. Hydrol. Eng. 3:223–231. doi:10.1061/(ASCE)1084-0699(1998)3:4(223)

Braden, H. 1985. Ein Energiehaushalts- und Verdun-stungsmodell für Wasser- und Stoffhaushaltsuntersuchungen landwirtschaftlich genutzter Einzugsge-biete. Mitt. Dtsch. Bodenkdl. Ges. 42:294–299.

Braud, I., D. De Condappa, J.M. Soria, R. Haverkamp, R. Angulo-Jaramillo, S. Gal-le, and M. Vauclin. 2005a. Use of scaled forms of the infiltration equation for the estimation of unsaturated soil hydraulic properties (the Beerkan meth-od). Eur. J. Soil Sci. 56:361–374. doi:10.1111/j.1365-2389.2004.00660.x

Braud, I., N. Varado, and A. Olioso. 2005b. Comparison of root water uptake modules using either the surface energy balance or potential transpiration. J. Hydrol. 301:267–286. doi:10.1016/j.jhydrol.2004.06.033

Brooks, R.H., and A.T. Corey. 1964. Hydraulic properties of porous media. Hy-drol. Pap. 3. Colorado State Univ., Fort Collins.

Budyko, M.I. 1974. Climate and life. Academic Press, Orlando, FL.Capehart, W.J., and T.N. Carlson. 1997. Decoupling of surface and near-sur-

face soil water content: A remote sensing perspective. Water Resour. Res. 33:1383–1395. doi:10.1029/97WR00617

Choi, M., J.M. Jacobs, and D.D. Bosch. 2008. Remote sensing observatory vali-dation of surface soil moisture using Advanced Microwave Scanning Ra-diometer E, Common Land Model, and ground based data: Case study in SMEX03 Little River Region, Georgia, U.S. Water Resour. Res. 44:W08421. doi:10.1029/2006WR005578

Crow, W.T., S. Chant, D. Entekhabi, A. Hsu, T.J. Jackson, E. Njoku, et al. 2005a. An observing system simulation experiment for HYDROS radiometer-only soil moisture and freeze–thaw products. In: Proceedings of the International Geoscience and Remote Sensing Symposium, Seoul, South Korea. 25–29 July 2005. Vol. 4. p. 2737–2740.

Crow, W.T., R.D. Koster, R.H. Reichle, and H.O. Sharif. 2005b. Relevance of time-varying and time-invariant retrieval error sources on the util-ity of spaceborne soil moisture products. Geophys. Res. Lett. 32:L24405. doi:10.1029/2005GL024889

Das, N.N., and B.P. Mohanty. 2008. Temporal dynamics of PSR-based soil mois-ture across spatial scales in an agricultural landscape during SMEX02: A wavelet approach. Remote Sens. Environ. 112:522–534. doi:10.1016/j.rse.2007.05.007

Das, N.N., B.P. Mohanty, M.H. Cosh, and T.J. Jackson. 2008. Modeling and as-similation of root zone soil moisture using remote sensing observations in Walnut Gulch watershed during SMEX04. Remote Sens. Environ. 112:415–429. doi:10.1016/j.rse.2006.10.027

Davenport, I.J., J. Fernandez-Galvez, and R.J. Gurney. 2005. A sensitivity analy-sis of soil moisture retrieval from the tau-omega microwave emission model. IEEE Trans. Geosci. Remote Sens. 43:1304–1316. doi:10.1109/TGRS.2005.845640

Deardorff, J.W. 1978. Efficient prediction of ground surface temperature and moisture, with inclusion of a layer of vegetation. J. Geophys. Res. 83:1889–1903. doi:10.1029/JC083iC04p01889

Duan, Q., S. Sorooshian, and V. Gupta. 1992. Effective and efficient global optimization for conceptual rainfall–runoff models. Water Resour. Res. 28:1015–1031. doi:10.1029/91WR02985

Duan, Q., S. Sorooshian, and V.K. Gupta. 1994. Optimal use of the SCE-UA global optimization method for calibrating watershed models. J. Hydrol. 158:265–284. doi:10.1016/0022-1694(94)90057-4

Durner, W., U. Jansen, and S.C. Iden. 2008. Effective hydraulic properties of lay-ered soils at the lysimeter scale determined by inverse modelling. Eur. J. Soil Sci. 59:114–124.

Eagleson, P.S. 1978. Climate, soil and vegetation: I. Introduction to wa-ter balance dynamics. Water Resour. Res. 14:705–712. doi:10.1029/WR014i005p00705

Efstratiadis, A., and D. Koutsoyiannis. 2008. Fitting hydrological models on mul-tiple responses using the multiobjective evolutionary annealing-simplex approach. In: R.J. Abrahart et al., editors, Practical hydroinformatics: Com-putational intelligence and technological developments in water applica-tions. Water Sci. Technol. Lib. 68. Springer-Verlag, Berlin. p. 259–273.

Efstratiadis, A., and D. Koutsoyiannis. 2010. One decade of multiobjective calibration approaches in hydrological modelling: A review. Hydrol. Sci. J. 55:58–78. doi:10.1080/02626660903526292

Engeland, K., C.Y. Xu, and L. Gottschalk. 2005. Assessing uncertainties in a con-ceptual water balance model using Bayesian methodology. Hydrol. Sci. J. 50:45–63.

English, M., and S.N. Raja. 1996. Perspectives on deficit irrigation. Agric. Water Manage. 32:1–14. doi:10.1016/S0378-3774(96)01255-3

Feddes, R.A., P.J. Kowalik, and H. Zaradny. 1978. Simulation of field water use and crop yield. Simul. Monogr. 189. Pudoc, Wageningen, the Netherlands.

Fernandez-Galvez, J. 2008. Errors in soil moisture content estimates induced by uncertainties in the effective soil dielectric constant. Int. J. Remote Sens. 29:3317–3323. doi:10.1080/01431160701469115

Friesen, J., C. Rodgers, P.G. Ogunrunde, J.M.H. Hendrickx, and N. van de Gie-sen. 2008. Hydrotope-based protocol to determine average soil moisture over large areas for satellite calibration and validation with results from an observation campaign in the Volta Basin, West Africa. IEEE Trans. Geosci. Remote Sens. 46:1995–2004. doi:10.1109/TGRS.2008.916638

Gale, M.R., and D.F. Grigal. 1987. Vertical root distributions of northern tree species in relation to successional status. Can. J. For. Res. 17:829–834. doi:10.1139/x87-131

Gao, Y., and D. Long. 2008. Intercomparison of remote sensing-based models for estimation of evapotranspiration and accuracy assessment based on SWAT. Hydrol. Processes 22:4850–4869. doi:10.1002/hyp.7104

Garrigues, S., R. Lacaze, F. Baret, J.T. Morisette, M. Weiss, J.E. Nickerson, et al. 2008. Validation and intercomparison of global leaf area index prod-ucts derived from remote sensing data. J. Geophys. Res. 113:G02028. doi:10.1029/2007JG000635

Goudriaan, J. 1982. Crop meteorology: A simulation study. Simul. Monogr. 683. Pudoc, Wageningen, the Netherlands.

Guarracino, L. 2007. Estimation of saturated hydraulic conductivity Ks from the van Genuchten shape parameter . Water Resour. Res. 43:W11502. doi:10.1029/2006WR005766

Gutmann, E.D., and E.E. Small. 2010. A method for the determination of the hy-draulic properties of soil from MODIS surface temperature for use in land-sur-face models. Water Resour. Res. 46:W06520. doi:10.1029/2009WR008203


Han, H., D. Giménez, and A. Lilly. 2008. Textural averages of saturated soil hydraulic conductivity predicted from water retention data. Geoderma 146:121–128. doi:10.1016/j.geoderma.2008.05.017

Hargreaves, G.L., G.H. Hargreaves, and J.P. Riley. 1985. Agricultural benefits for Senegal river basin. J. Irrig. Drain. Eng. 111:113–124. doi:10.1061/(ASCE)0733-9437(1985)111:2(113)

Harrison, L.P. 1963. Fundamentals concepts and definitions relating to humid-ity. In: A.E. Wexler, editor, Humidity and moisture. Vol. 3. Reinhold Publ. Co., New York. p. 3–70.

Haverkamp, R., F.J. Leij, C. Fuentes, A. Sciortino, and P.J. Ross. 2005. Soil water retention: I. Introduction of a shape index. Soil Sci. Soc. Am. J. 69:1881–1890. doi:10.2136/sssaj2004.0225

Haverkamp, R., M. Vauclin, and G. Vachaud. 1984. Error analysis in estimating soil water content from neutron probe measurements: I. Local standpoint. Soil Sci. 137:78–90. doi:10.1097/00010694-198402000-00002

Herczeg, A.L., and F.W. Leaney. 2011. Review: Environmental tracers in arid-zone hydrology. Hydrogeol. J. 19:17–29. doi:10.1007/s10040-010-0652-7

Huete, A., K. Didan, T. Miura, E.P. Rodriguez, X. Gao, and L.G. Ferreira. 2002. Overview of the radiometric and biophysical performance of the MO-DIS vegetation indices. Remote Sens. Environ. 83:195–213. doi:10.1016/S0034-4257(02)00096-2

Hupet, F., S. Lambot, R.A. Feddes, J.C. van Dam, and M. Vanclooster. 2003. Esti-mation of root water uptake parameters by inverse modeling with soil wa-ter content data. Water Resour. Res. 39:1312. doi:10.1029/2003WR002046

Ines, A.V.M., and P. Droogers. 2002. Inverse modelling in estimating soil hydrau-lic functions: A genetic algorithm approach. Hydrol. Earth Syst. Sci. 6:49–65. doi:10.5194/hess-6-49-2002

Ines, A.V.M., and B.P. Mohanty. 2008a. Near-surface soil moisture assimilation for quantifying effective soil hydraulic properties under different hydrocli-matic conditions. Vadose Zone J. 7:39–52. doi:10.2136/vzj2007.0048

Ines, A.V.M., and B.P. Mohanty. 2008b. Near-surface soil moisture assimi-lation for quantifying effective soil hydraulic properties using genetic algorithm: 1. Conceptual modeling. Water Resour. Res. 44:W06422. doi:10.1029/2007WR005990

Ines, A.V.M., and B.P. Mohanty. 2009. Near-surface soil moisture assimilation for quantifying effective soil hydraulic properties using genetic algorithms: 2. Using airborne remote sensing during SGP97 and SMEX02. Water Resour. Res. 45:W01408. doi:10.1029/2008WR007022

Jackson, R.B., J. Canadell, J.R. Ehleringer, H.A. Mooney, O.E. Sala, and E.D. Schulze. 1996. A global analysis of root distributions for terrestrial biomes. Oecologia 108:389–411. doi:10.1007/BF00333714

Jackson, T.J., D.M. Le Vine, C.T. Swift, T.J. Schmugge, and F.R. Schiebe. 1995. Large area mapping of soil moisture using the ESTAR passive microwave radiom-eter in Washita’92. Remote Sens. Environ. 54:27–37. doi:10.1016/0034-4257(95)00084-E

Jackson, T.J., and T.J. Schmugge. 1991. Vegetation effects on the microwave emission of soils. Remote Sens. Environ. 36:203–212. doi:10.1016/0034-4257(91)90057-D

Jarvis, N.J. 2011. Simple physics-based models of compensatory plant water uptake: Concepts and eco-hydrological consequences. Hydrol. Earth Syst. Sci. 15:3431–3446. doi:10.5194/hess-15-3431-2011

Jensen, M.E., R.D. Burman, and R.G. Allen. 1990. Evapotranspiration and irriga-tion water requirements. Am. Soc. Civ. Eng., New York.

Jhorar, R.K., W.G.M. Bastiaanssen, R.A. Feddes, and J.C. van Dam. 2002. In-versely estimating soil hydraulic functions using evapotranspiration fluxes. J. Hydrol. 258:198–213. doi:10.1016/S0022-1694(01)00564-9

Jhorar, R.K., J.C. van Dam, W.G.M. Bastiaanssen, and R.A. Feddes. 2004. Calibra-tion of effective soil hydraulic parameters of heterogeneous soil profiles. J. Hydrol. 285:233–247. doi:10.1016/j.jhydrol.2003.09.003

Kalma, J.D., T.R. McVicar, and M.F. McCabe. 2008. Estimating land surface evap-oration: A review of methods using remotely sensed surface temperature data. Surv. Geophys. 29:421–469. doi:10.1007/s10712-008-9037-z

Kerr, Y.H., P. Waldteufel, J.P. Wigneron, J.M. Martinuzzi, J. Font, and M. Berger. 2001. Soil moisture retrieval from space: The Soil Moisture and Ocean Salinity (SMOS) mission. IEEE Trans. Geosci. Remote Sens. 39:1729–1735. doi:10.1109/36.942551

Kosugi, K. 1996. Lognormal distribution model for unsaturated soil hydraulic properties. Water Resour. Res. 32:2697–2703. doi:10.1029/96WR01776

Kosugi, K., and J.W. Hopmans. 1998. Scaling water retention curves for soils with lognormal pore-size distribution. Soil Sci. Soc. Am. J. 62:1496–1505. doi:10.2136/sssaj1998.03615995006200060004x

Kosugi, K., and M. Katsuyama. 2001. Measurements of groundwater recharge rate and unsaturated convective chemical fluxes by suction controlled ly-simeter. In: H. Gehrels et al., editors, Impact of Human Activity on Ground-water Dynamics: Proceedings of a Symposium held during the Sixth IAHS Scientific Assembly, Maastricht, the Netherlands. 18–27 July 2001. IAHS Publ. 269. IAHS Press, Wallingford, UK. p. 19–24.

Kosugi, K., and M. Katsuyama. 2004. Controlled-suction period lysimeter for measuring vertical water flux and convective chemical fluxes. Soil Sci. Soc. Am. J. 68:371–382.

Kroes, J.G., J.G. Wesseling, and J.C. van Dam. 2000. Integrated modelling of the soil–water–atmosphere–plant system using the model SWAP 2.0: An overview of theory and an application. Hydrol. Processes 14:1993–2002. doi:10.1002/1099-1085(20000815/30)14:11/123.0.CO;2-#

Leij, F.J., A. Sciortino, R. Haverkamp, and J.M. Soria Ugalde. 2007. Aggregation of vertical flow in the vadose zone with auto- and cross-correlated hydrau-lic properties. J. Hydrol. 338:96–112. doi:10.1016/j.jhydrol.2007.02.032

Li, K.Y., R. De Jong, and J.B. Boisvert. 2001. An exponential root-water-up-take model with water stress compensation. J. Hydrol. 252:189–204. doi:10.1016/S0022-1694(01)00456-5

Luckner, L., M.Th. van Genuchten, and D.R. Nielsen. 1989. A consistent set of parametric models for the two-phase flow of immiscible fluids in the sub-surface. Water Resour. Res. 25:2187–2193. doi:10.1029/WR025i010p02187

Maidment, D. 1992. Handbook of hydrology. McGraw-Hill, New York.Milly, P.C.D. 1986. Event-based simulation model of moisture and energy flux-

es at a bare soil surface. Water Resour. Res. 22:1680–1692. doi:10.1029/WR022i012p01680

Mohanty, B.P., and J. Zhu. 2007. Effective hydraulic parameters in horizontally and vertically heterogeneous soils for steady-state land–atmosphere inter-action. J. Hydrometeorol. 8:715–729. doi:10.1175/JHM606.1

Moran, M.S. 2003. Thermal infrared measurement as an indicator of plant eco-system health. In: D.A. Quattrochi and J. Luvall, editors, Thermal remote sensing in land surface processes. CRC Press, Boca Raton, FL. p. 257–282.

Mualem, Y. 1976. New model for predicting the hydraulic conductivity of un-saturated porous media. Water Resour. Res. 12:513–522. doi:10.1029/WR012i003p00513

Nagler, P.L., J. Cleverly, E. Glenn, D. Lampkin, A. Huete, and Z. Wan. 2005. Predicting riparian evapotranspiration from MODIS vegetation indices and meteorological data. Remote Sens. Environ. 94:17–30. doi:10.1016/j.rse.2004.08.009

Nash, J.E., and J.V. Sutcliffe. 1970. River flow forecasting through con-ceptual models: I. A discussion of principles. J. Hydrol. 10:282–290. doi:10.1016/0022-1694(70)90255-6

Nielsen, D.R., J.W. Biggar, and K.T. Erh. 1973. Spatial variability of field-mea-sured soil-water properties. Hilgardia 42:215–259.

Njoku, E.G., T.J. Jackson, V. Lakshmi, T.K. Chan, and S.V. Nghiem. 2003. Soil mois-ture retrieval from AMSR-E. IEEE Trans. Geosci. Remote Sens. 41:215–229. doi:10.1109/TGRS.2002.808243

Noilhan, J., and P. Lacarrere. 1995. GCM grid-scale evaporation from mesoscale modeling. J. Clim. 8:206–223. doi:10.1175/1520-0442(1995)0082.0.CO;2

Opoku-Duah, S., D.N.M. Donoghue, and T.P. Burt. 2008. Intercomparison of evapotranspiration over the savannah Volta basin in West Africa using re-mote sensing data. Sensors 8:2736–2761. doi:10.3390/s8042736

Palmer, W.C. 1965. Meteorological drought. Res. Pap. 45. U.S. Gov. Print. Office, Washington, DC.

Pollacco, J.A.P. 2003. Constructing and optimising a parsimonious groundwater recharge model using neutron probe data. In: D.A. Post, editor, Proceedings of the MODSIM Conference, Townsville, QLD, Australia. 14–17 July 2003. Modelling and Simulation Society of Australia and New Zealand, Perth, WA, Australia, p. 195–200.

Pollacco, J.A.P., I. Braud, R. Angulo-Jaramillo, and B. Saugier. 2008a. A Linking Test that establishes if groundwater recharge can be determined by opti-mising vegetation parameters against soil moisture. Ann. For. Sci. 65:702. doi:10.1051/forest:2008046

Pollacco, J.A.P., J.M.S. Ugalde, R. Angulo-Jaramillo, I. Braud, and B. Saugier. 2008b. A Linking Test to reduce the number of hydraulic parameters nec-essary to simulate groundwater recharge in unsaturated soils. Adv. Water Resour. 31:355–369. doi:10.1016/j.advwatres.2007.09.002

Priestley, C.H.B., and R.J. Taylor. 1972. On the assessment of surface heat flux and evaporation using large-scale parameters. Mon. Weather Rev. 100:81–92. doi:10.1175/1520-0493(1972)1002.3.CO;2

Ramos, J.G., C.R. Cratchley, J.A. Kay, M.A. Casterad, A. Martinez-Cob, and R. Dominguez. 2009. Evaluation of satellite evapotranspiration estimates us-ing ground-meteorological data available for the Flumen District into the Ebro Valley of N.E. Spain. Agric. Water Manage. 96:638–652. doi:10.1016/j.agwat.2008.10.001

Ritchie, J.T. 1972. Model for predicting evaporation from a row crop with incomplete cover. Water Resour. Res. 8:1204–1213. doi:10.1029/WR008i005p01204

Ritter, A., F. Hupet, R. Muñoz-Carpena, S. Lambot, and M. Vanclooster. 2003. Using inverse methods for estimating soil hydraulic properties from field data as an alternative to direct methods. Agric. Water Manage. 59:77–96. doi:10.1016/S0378-3774(02)00160-9

Romano, E., and M. Giudici. 2007. Experimental and modeling study of the soil–atmosphere interaction and unsaturated water flow to estimate the recharge of a phreatic aquifer. J. Hydrol. Eng. 12:573–584. doi:10.1061/(ASCE)1084-0699(2007)12:6(573)

Romano, E., and M. Giudici. 2009. On the use of meteorological data to as-sess the evaporation from a bare soil. J. Hydrol. 372:30–40. doi:10.1016/j.jhydrol.2009.04.003


Russo, D. 1988. Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties. Water Resour. Res. 24:453–459. doi:10.1029/WR024i003p00453

Rutter, A.J., K.A. Kershaw, P.C. Robins, and A.J. Morton. 1971. A predictive model of rainfall interception in forests: 1. Derivation of the model from observations in a plantation of Corsican pine. Agric. Meteorol. 9:367–384. doi:10.1016/0002-1571(71)90034-3

Sahoo, A.K., P.R. Houser, C. Ferguson, E.F. Wood, P.A. Dirmeyer, and M. Kafatos. 2008. Evaluation of AMSR-E soil moisture results using the in-situ data over the Little River Experimental Watershed, Georgia. Remote Sens. Environ. 112:3142–3152. doi:10.1016/j.rse.2008.03.007

Saito, H., K. Seki, and J. Šimůnek. 2009. An alternative deterministic method for the spatial interpolation of water retention parameters. Hydrol. Earth Syst. Sci. 13:453–465. doi:10.5194/hess-13-453-2009

Saleh, K., J.-P. Wigneron, P. de Rosnay, M.J. Escorihuela, Y. Kerr, J.C. Calvet, et al. 2008. Estimates of surface soil moisture in prairies using L-band passive microwaves. In: Proceedings of the International Geoscience and Remote Sensing Symposium, Barcelona, Spain. 23–28 July 2007. IEEE, Piscataway, NJ. p. 1200–1203.

Scanlon, B.R., D.G. Levitt, R.C. Reedy, K.E. Keesec, and M.J. Sully. 2005. Ecologi-cal controls on water-cycle response to climate variability in deserts. Proc. Natl. Acad. Sci. 102:6033–6038. doi:10.1073/pnas.0408571102

Schaap, M.G., and F.J. Leij. 1998a. Database-related accuracy and uncertainty of pedotransfer functions. Soil Sci. 163:765–779. doi:10.1097/00010694-199810000-00001

Schaap, M.G., and F.J. Leij. 1998b. Using neural networks to predict soil wa-ter retention and soil hydraulic conductivity. Soil Tillage Res. 47:37–42. doi:10.1016/S0167-1987(98)00070-1

Schaefli, B., and H.V. Gupta. 2007. Do Nash values have value? Hydrol. Pro-cesses 21:2075–2080. doi:10.1002/hyp.6825

Schaefli, B., B. Hingray, M. Niggli, and A. Musy. 2005. A conceptual glacio-hy-drological model for high mountainous catchments. Hydrol. Earth Syst. Sci. Discuss. 2:73–117. doi:10.5194/hessd-2-73-2005

Schenk, H.J., and R.B. Jackson. 2002. The global biogeography of roots. Ecol. Monogr. 72:311–328. doi:10.1890/0012-9615(2002)072[0311:TGBOR]2.0.CO;2

Simic, A., R. Fernandes, R. Brown, P. Romanov, and W. Park. 2004. Validation of VEGETATION, MODIS, and GOES + SSM/I snow-cover products over Canada based on surface snow depth observations. Hydrol. Processes 18:1089–1104. doi:10.1002/hyp.5509

Simmonds, L.P., C. Antolin, J.C. Calvet, A. Chanzy, K.C. Saleh, H. Douville, et al. 2004. Soil moisture retrieval by a future space-borne earth observation mission. Eur. Space Agency, Noorwijk, the Netherlands.

Simmons, C.S., and P.D. Meyer. 2000. A simplified model for the transient water budget of a shallow unsaturated zone. Water Resour. Res. 36:2835–2844. doi:10.1029/2000WR900202

Sinclair, D.F., and J. Williams. 1979. Components of variance involved in esti-mating soil water content and water content change using a neutron mois-ture meter. Aust. J. Soil Res. 17:237–247. doi:10.1071/SR9790237

Skaggs, T.H., M.Th. van Genuchten, P.J. Shouse, and J.A. Poss. 2006. Macroscop-ic approaches to root water uptake as a function of water and salinity stress. Agric. Water Manage. 86:140–149. doi:10.1016/j.agwat.2006.06.005

Stikic, R., S. Popovic, M. Srdic, D. Savic, Z. Jovanovic, L. Prokic, and J. Zdravkovic. 2003. Partial root drying (PRD): A new technique for growing plants that saves water and improves the quality of fruit. Bulg. J. Plant Physiol. 29(3–4):164–171.

Stolte, J. 1994. Comparison of six methods to determine unsaturated soil hydraulic conductivity. Soil Sci. Soc. Am. J. 58:1596–1603. doi:10.2136/sssaj1994.03615995005800060002x

Su, H., E.F. Wood, M.F. McCabe, and Z. Su. 2007. Evaluation of remotely sensed evapotranspiration over the CEOP EOP-1 reference sites. J. Meteorol. Soc. Jpn. 85A:439–459. doi:10.2151/jmsj.85A.439

Tang, Y., P.M. Reed, and J.B. Kollat. 2007. Parallelization strategies for rapid and robust evolutionary multiobjective optimization in water resources applications. Adv. Water Resour. 30:335–353. doi:10.1016/j.advwa-tres.2006.06.006

Taylor, H.M., and B. Klepper. 1978. The role of rooting characteristics in the supply of water to plants. Adv. Agron. 30:99–125. doi:10.1016/S0065-2113(08)60704-X

Teixeira, A.H.C., W.G.M. Bastiaanssen, M.D. Ahmad, and M.G. Bos. 2009. Re-viewing SEBAL input parameters for assessing evapotranspiration and wa-ter productivity for the Low–Middle São Francisco River basin, Brazil: A. Cal-ibration and validation. Agric. For. Meteorol. 149:462–476. doi:10.1016/j.agrformet.2008.09.016

Teuling, A.J., R. Uijlenhoet, B. van den Hurk, and S.I. Seneviratne. 2009. Pa-rameter sensitivity in LSMs: An analysis using stochastic soil moisture models and ELDAS soil parameters. J. Hydrometeorol. 10:751–765. doi:10.1175/2008JHM1033.1

Tietje, O., and M. Tapkenhinrichs. 1993. Evaluation of pedo-trans-fer functions. Soil Sci. Soc. Am. J. 57:1088–1095. doi:10.2136/sssaj1993.03615995005700040035x

Tomlinson, S.A. 1996. Comparison of Bowen-ratio, eddy-correlation, and weighing-lysimeter evapotranspiration for two sparse-canopy sites in east-ern Washington. Water-Resour. Invest. Rep. 96-4081. USGS, Tacoma, WA.

Twarakavi, N.K.C., J. Šimůnek, and M.G. Schaap. 2010. Can texture-based classi-fication optimally classify soils with respect to soil hydraulics? Water Resour. Res. 46:W01501. doi:10.1029/2009WR007939

Valente, F., J.S. David, and J.H.C. Gash. 1997. Modelling interception loss for two sparse eucalypt and pine forests in central Portugal using reformulated Rutter and Gash analytical models. J. Hydrol. 190:141–162. doi:10.1016/S0022-1694(96)03066-1

van Dam, J.C., P. Groenendijk, R.F.A. Hendriks, and J.G. Kroes. 2008. Advances of modeling water flow in variably saturated soils with SWAP. Vadose Zone J. 7:640–653. doi:10.2136/vzj2007.0060

van Dam, J.C., J. Huygen, J.G. Wesseling, R.A. Feddes, P. Kabat, P.E.V. van Wal-sum, et al. 1997. Theory of SWAP version 2.0. Rep. 71. Dep. Water Resour., Wageningen Agric. Univ., Wageningen, the Netherlands.

van Genuchten, M.Th. 1980. Closed-form equation for predicting the hy-draulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892–898. doi:10.2136/sssaj1980.03615995004400050002x

van Griensven, A., and T. Meixner. 2006. Methods to quantify and identify the sources of uncertainty for river basin water quality models. Water Sci. Tech-nol. 53:51–59.

van Werkhoven, K., T. Wagener, P. Reed, and Y. Tang. 2008. Characterization of watershed model behavior across a hydroclimatic gradient. Water Resour. Res. 44:W01429. doi:10.1029/2007WR006271

Varado, N., I. Braud, and P.J. Ross. 2006. Development and assessment of an efficient vadose zone module solving the 1D Richards’ equation and in-cluding root extraction by plants. J. Hydrol. 323:258–275. doi:10.1016/j.jhydrol.2005.09.015

Vereecken, H., J.A. Huisman, H. Bogena, J. Vanderborght, J.A. Vrugt, and J.W. Hopmans. 2008. On the value of soil moisture measurements in vadose zone hydrology: A review. Water Resour. Res. 44:W00D06. doi:10.1029/2008WR006829

Vereecken, H., R. Kasteel, J. Vanderborght, and T. Harter. 2007. Upscaling hy-draulic properties and soil water flow processes in heterogeneous soils: A review. Vadose Zone J. 6:1–28. doi:10.2136/vzj2006.0055

Verstraeten, W.W., F. Veroustraete, and J. Feyen. 2008. Assessment of evapo-transpiration and soil moisture content across different scales of observa-tion. Sensors 8:70–117. doi:10.3390/s8010070

Vischel, T., G.G.S. Pegram, S. Sinclair, W. Wagner, and A. Bartsch. 2008. Compar-ison of soil moisture fields estimated by catchment modelling and remote sensing: A case study in South Africa. Hydrol. Earth Syst. Sci. 12:751–767. doi:10.5194/hess-12-751-2008

von Hoyningen-Huene, J. 1981. Die Interzeption des Niederschlags in land-wirtschaftlichen Pflanzenbeständen. Schriftenr. Dtsch. Verb. Wasserwirtsch. Kulturbau 57:1–53.

Vrugt, J.A., H.V. Gupta, W. Bouten, and S. Sorooshian. 2003. A Shuffled Com-plex Evolution Metropolis algorithm for optimization and uncertainty as-sessment of hydrologic model parameters. Water Resour. Res. 39(8):1201. doi:10.1029/2002WR001642

Walker, J.P., G.R. Willgoose, and J.D. Kalma. 2002. Three-dimensional soil moisture profile retrieval by assimilation of near-surface measurements: Simplified Kalman filter covariance forecasting and field application. Water Resour. Res. 41:38.

Wang, T., V.A. Zlotnik, J. Šimůnek, and M.G. Schaap. 2009. Using pedo-transfer functions in vadose zone models for estimating groundwa-ter recharge in semiarid regions. Water Resour. Res. 45:W04412. doi:10.1029/2008WR006903

Weiß, M., and L. Menzel. 2008. A global comparison of four potential evapo-transpiration equations and their relevance to stream flow modelling in semi-arid environments. Adv. Geosci. 18:15–23. doi:10.5194/ad-geo-18-15-2008

Wilson, D.J., A.W. Western, R.B. Grayson, A.A. Berg, M.S. Lear, M. Rodell, et al. 2003. Spatial distribution of soil moisture over 6 and 30 cm depth, Mahurangi river catchment, New Zealand. J. Hydrol. 276:254–274. doi:10.1016/S0022-1694(03)00060-X

Wright, J.L. 1982. New evapotranspiration crop coefficients. J. Irrig. Drain. Div. 108:57–74.

Yapo, P.O., H.V. Gupta, and S. Sorooshian. 1998. Multi-objective global opti-mization for hydrologic models. J. Hydrol. 204:83–97. doi:10.1016/S0022-1694(97)00107-8

special section: soil–plant– uncertainties of water fluxes...

Documents