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Published in Vadose Zone Journal 3:1367-1379 (2004)
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

ORIGINAL RESEARCH

Impact of Within-Field Variability in Soil Hydraulic Properties on Transpiration Fluxes and Crop Yields

A Numerical Study

F. Hupeta,*, J. C. van Damb and M. Vancloostera

a Université Catholique de Louvain, Department of Environmental Sciences and Land Use Planning, Croix du Sud 2, BP 2, B-1348 Louvain-la-Neuve, Belgium
b Wageningen Agricultural University, Department of Environmental Sciences, Nieuwe Kanaal 11, 6709 PA Wageningen, The Netherlands
* Corresponding author (hupet{at}geru.ucl.ac.be)

Received 22 February 2004.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSIONS
 CONCLUSIONS
 REFERENCES
 
By means of numerical modeling we investigate the impact of within-field variability in the soil hydraulic properties on actual transpiration and dry matter yield for three different climate scenarios. We first show that the sensitivity of the simulated actual transpiration and dry matter yield to soil hydraulic parameters increases with the dryness of the climate. The numerical simulations with soil independent stress factors further demonstrate that the impact of the within-field variability in soil hydraulic properties on the simulated transpiration and dry matter yield can be very large. The generated spatial variability in transpiration and dry matter yield increases systematically with the dryness of the climate, with coefficients of variation increasing from 7 to 14.6% for actual transpiration and from 6.7 to 16% for dry matter yield. In a subsequent analysis, all agrohydrological simulations are rerun considering that the water stress parameters are spatially variable and soil dependent. While the results obtained with the adjusted water stress parameters are quite different, the spatial variability in simulated transpiration and dry matter yield still increases for drier conditions. The different results obtained, although not validated experimentally, illustrate that the use of an agrohydrological simulation model in a stochastic mode requires accurate estimates of the water stress parameters, which should be soil dependent. Finally, we show that simultaneous estimation of water stress and soil hydraulic parameters cannot be robustly performed using measurements of transpiration or dry matter yield alone. Consequently, the use of an agro-hydrological model in a stochastic mode for a vegetated surface requires alternative strategies for specifying reliable water stress parameters. Adjustment of water stress parameters from reference unsaturated hydraulic conductivity values seems attractive, but needs more research.

Abbreviations: MRC, moisture retention curves


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIAL AND METHODS
 RESULTS AND DISCUSSIONS
 CONCLUSIONS
 REFERENCES
 
ACCURATE ESTIMATION OF transpiration and crop growth is important for many hydrological and agricultural studies. Indeed, transpiration is a major component of the hydrological cycle, while the yield of crops and their optimization is the major objective of agricultural operations. Transpiration and crop yield can be directly measured within fields, but measurements are often expensive, time-consuming, very local in space and time, and generally destructive. Consequently, the use of simulation models has become widespread because they allow predictions in space (where measurements are generally not available) and into the future (where measurements are not possible) (e.g., Vanclooster et al., 2002). Models are also relevant tools for evaluating alternative management strategies within agronomic and/or environmental contexts (e.g., Otegui et al., 1996). One category of models allows for the simultaneous estimation of transpiration and crop growth and includes such agrohydrological and ecohydrological models as WAVE (Vanclooster et al., 1996) and SWAP (van Dam et al., 1997). These models describe in detail the prevailing physical soil processes, while crop growth is generally represented only very approximately using climatic factors, physiological characteristics, and water stress parameters. A second category includes more detailed crop simulation models, such as CERES-maize (Jones and Kiniry, 1986) and MACROS (Penning de Vries et al., 1989), which are primarily focused on crop development. This second category of models generally allows the simulation of yields at several production levels by considering additional parameters, such as the N balance, P and K uptake, and the effects of weeds and pests. While agrohydrological and crop simulation models can be very powerful tools, their use may be subject to limitations due to the large number of parameters that often need to be specified (Boote et al., 1996). Among these are the soil hydraulic properties, which are key parameters since they govern soil water flow and as such affect the amount of soil water available for transpiration and crop growth.

Besides issues related to soil hydraulic property estimation, additional problems arise because of the variability of these characteristics. Soil hydraulic parameters are known to be highly variable in space, even for small agricultural fields within one soil textural class (e.g., Rawls et al., 1983; Mohanty et al., 1994; Shouse et al., 1995). Since the spatial scale at which soil hydraulic properties are estimated is generally very local, and since the number of replicates is often limited, field-scale estimates of these parameters and subsequent predictions of transpiration and crop yield are often vulnerable to errors. The magnitude of these errors strongly depends both on the spatial variability in the soil hydraulic properties and the sensitivity of the model output to the hydraulic properties. The sensitivity depends further on climatic conditions. The sensitivity is generally low in humid climates where transpiration is controlled mainly by the evaporating demand of the atmosphere. Conversely, the sensitivity may be relatively high in very dry climates where transpiration is more controlled by the soil. In that case, the within-field variability in soil hydraulic properties is likely to generate spatially variable transpiration rates and crop growth.

The effects of variability in the soil hydraulic properties have been studied extensively for infiltration and runoff (e.g., Merz and Plate, 1997; Kim et al., 1997), drainage (e.g., Mallants, 1996; Vachaud and Chen, 2002), and soil evaporation (e.g., Lewan and Jansson, 1996; Zhu and Mohanty, 2003). With regard to transpiration and crop yields, the effects of soil hydraulic variability were investigated within the context of precision farming by Paz et al. (1998) and Batchelor et al. (2002), among others. These latter studies were performed with crop simulation models in which soil water flow processes were highly simplified. Additionally, these studies mostly focused on within-field variability of transpiration and crop yield by considering simultaneously the complex nonlinear interactions of several different stresses (e.g., Paz et al., 2001). Consequently, elucidating the effects of soil hydraulic variability is not immediately obvious. A few studies have tackled this problem by decoupling the modeling of transpiration from that of vegetation development, such as by making use of an approximate vegetation growth module (e.g., Dagan and Bresler, 1983; Hopmans and Stricker, 1989; Droogers, 1997; Kim et al., 1997; Vachaud and Chen, 2002). Still, a clear feedback exists between vegetation development and transpiration. Furthermore, some of the latter studies considered only the soil hydraulic properties to be spatially variable. Such an approach ignores the fact that water stress parameters, governing the magnitude of actual transpiration and crop growth, also are likely to depend in some way on soil type (Hopmans and Guttièrez-Ravé, 1988). Reductions in the potential root water uptake rate, and hence potential transpiration, within agrohydrological and ecohydrological models are generally assumed to be controlled by water flow within the soil surrounding the root, rather than within the root tissue only (e.g., Molz, 1981). To account for this, water stress functions have been proposed that make the actual root water uptake and transpiration rates dependent on soil water content (Feddes et al., 1976), soil water pressure head (Feddes et al., 1978), or the soil hydraulic conductivity (Selim and Iskandar, 1978). Consequently, to rigorously investigate the effect of within-field soil hydraulic variability on transpiration and crop yield, it seems appropriate to adjust the water stress parameters according to the basic soil properties as well. Unfortunately, such an adjustment is not straightforward because water stress parameters cannot be directly measured and their indirect estimation is also very difficult (e.g., Musters et al., 2000).

The main objective of this study was to numerically investigate the impact of within-field variability in soil hydraulic properties on transpiration and crop yield. We used a comprehensive data set of soil hydraulic properties measured within a small agricultural field. The combined use of measured hydraulic properties and numerical simulations allowed us to address some of the abovementioned issues. The specific objectives of the study were to:

  1. Perform a sensitivity analysis to investigate the sensitivity of cumulative actual transpiration and crop yield to the measured soil hydraulic properties.
  2. Study the effects of soil hydraulic variability on transpiration and crop yield for cases where water stress parameters are and are not soil dependent.
  3. Investigate the feasibility of estimating spatially variable soil hydraulic and water stress parameters from actual transpiration and crop yield measurements.


   MATERIAL AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
RESULTS AND DISCUSSIONS
 CONCLUSIONS
 REFERENCES
 
Numerical Simulations
For transpiration and crop yield modeling, we used both the soil water flow and crop growth modules of the agrohydrological SWAP model (van Dam et al., 1997). One-dimensional vertical transient water flow in this model is based on the Richards equation combined with a sink term:

[1]
where C(h) = {partial}{theta}/{partial}h is the soil water capacity (L–1); h is the soil water pressure head (L); t is time (T); z is the vertical coordinate (L), being positive upward; K(h) the hydraulic conductivity (L T–1); and S(z) is a sink term describing water uptake by plant roots (T–1). In this study we assumed that the soil hydraulic properties can be described with the closed-form van Genuchten (1980) relationships:

[2]

[3]
in which {theta}r and {theta}s are the residual and saturated volumetric water content, respectively; {alpha} (L–1), n, and m = (1 – 1/n) are empirical parameters; Ks is the saturated conductivity (L T–1); and {lambda} is the pore-connectivity factor. In this study we fixed {theta}r and {lambda} to 0 and 0.5, respectively. Soil water flow was simulated using Eq. [1] subject to specified lower and upper boundary conditions, which in our study were a free drainage with a unit gradient at the 160-cm depth, and measured rainfall and crop potential evapotranspiration (ETp), respectively. ETp was obtained by multiplying the reference evapotranspiration (ETo) calculated according to Allen et al. (1998) by an appropriate crop coefficient. ETp was subsequently partitioned into potential soil evaporation (Ep) and transpiration components (Tp) by using

[4]
in which LAI is the leaf area index and c = 0.6 a crop specific parameter. Potential transpiration is then back-calculated by subtracting Ep from ETp.

The sink term S(z,h) in Eq. [1] was defined by Feddes et al. (1978) as

[5]
where Smax(z) is the maximal root water uptake (RWU) distribution as a function of depth (T–1), and {gamma}(h) is a dimensionless reduction function that simulates the effects of soil moisture stress. In the SWAP model, the maximum possible RWU rate, Smax(z), integrated over the rooting depth, is equal to the potential transpiration, and defined as follows:

[6]
where RLD(z) is the root length density at depth z (L L–3). In this study we will use a linear root density profile vs. depth. The reduction function {gamma}(h) is characterized by different pressure head values h1, h2, h3 (low and high according to the climatic demand), and h4 (Feddes et al., 1978). Above h1, {gamma}(h) is zero, between h2 and h3(l or h){gamma}(h) is 1, and between h3 and h4 the value of the reduction function is given by

[7]

The actual root water uptake distribution given by Eq. [5] is subsequently integrated over the whole rooting depth to yield the actual transpiration rate, Ta.

Crop growth in the SWAP model is simulated using a detailed crop growth routine derived from WOFOST 6.0. (Spitters et al., 1989). Using the absorbed radiation and taking into account photosynthetic leaf characteristics, the crop growth model calculates the potential assimilation rate. This rate is reduced due to water stress as quantified by the relative transpiration rate (i.e., Ta/Tp) to yield the daily actual gross assimilation rate. For further details about the crop growth routine, the reader is referred to van Dam et al. (1997).

In this study, numerical runs were generated for three contrasted climatic scenarios, namely a very wet (1998), a normal (1999), and a very dry (1990) crop season. These scenarios are based on climatic data recorded by a meteorological station in Louvain-la-Neuve (50° N, 4° E, 120 m above mean sea level), Belgium. Details about the meteorological station and the sensors can be found in Hupet and Vanclooster (2001). Table 1 summarizes the climatic conditions encountered during the agricultural season (5 May–30 October) of the 3 yr in terms of rainfall, evaporative demand (ETo), and their ratio. Maize (Zea mays L.) was chosen as the crop of interest for all numerical scenarios. All maize-related parameters were derived from the literature (Wesseling, 1991; Boons-Prins et al., 1993); relevant parameters for our study are provided in Table 2. The numerical simulations started at maize emergence on 5 May each year (i.e., 10 d after sowing), and were terminated at maturity (i.e., at development stage equal to 2). The simulations were generated for a 160-cm-deep soil profile, which was considered homogeneous in terms of its soil hydraulic properties. The flow domain was discretized into 40 compartments using a nodal distance of 1 cm for the first 10 compartments and a nodal distance of 5 cm for the remaining soil profile.


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  		Table 1. Values of rainfall, reference evapotranspiration (ETo), and their ratio (ETo/rainfall) for the three climatic scenarios considered. The values are cumulative totals for 5 May through 30 October.

 

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  		Table 2. Maize crop parameters used for the numerical simulations.

 
Soil Hydraulic Properties
Numerical simulations were run using soil hydraulic properties measured within a small experimental field located in Louvain-la-Neuve, Belgium. Water retention measurements were made on undisturbed 8.4-cm-diameter soil cores collected in PVC tubes from 0 to 125 cm depth on a regular sampling grid of 28 sampling locations within an area of 6300 m2 centered in the experimental field (for details see Hupet and Vanclooster, 2002). The PVC tubes were obtained with a hydraulic auger mounted on a four-wheel vehicle. Afterwards, all PVC tubes were opened to yield, within each long soil column, three undisturbed 5.1-cm-long, 5-cm-diameter soil cores from depths of 45, 75, and 105 cm. For each of the 84 soil cores we determined the drying part of the water retention curve by means of a sandbox apparatus for soil water pressures of 1, 10, and 100 cm and with a pressure cell for soil water pressures of 300, 1000, 2500, and 15000 cm (Dane and Topp, 2002, p. 675–697).

Saturated hydraulic conductivity measurements were made using the constant head permeameter method. Six undisturbed soil samples were collected at two different locations and three different depths (25, 50, and 75 cm) within the 6300-m2 area. Each sample of 1440 cm3 (10 cm long, with a cross section of 144 cm2) was brought back into the laboratory and subjected to a constant head of 10 cm on top of the samples. The flow rate through the soil sample was measured by collecting water at the bottom during a set period of time. Saturated hydraulic conductivity values were obtained using Darcy's Law with water flow measured at steady state.

The experimental field where all soil hydraulic properties were measured in 2000 was part of an extensive study aimed at investigating the within-field variability of water fluxes. As part of that study, soil water contents were measured at all 28 sampling locations using a neutron probe at five different depths (25, 50, 75, 100, and 125 cm) and with TDR in the top 20 cm of the soil profile during the 1999 agricultural season for which the experimental field was cropped with maize (for details see Hupet and Vanclooster, 2002).

Sensitivity Analysis
For the sensitivity analysis, we generated a reference run for the three different climatic conditions using soil hydraulic properties averaged for the three investigated depths and 28 sampling locations. The three depths were treated together since their soil properties were very similar (Table 3). Next, the averaged soil hydraulic parameters were successively and independently perturbed by 5% to quantify the sensitivity of the cumulative actual transpiration and the final dry matter yield to the perturbed parameter. Sensitivity coefficients were calculated with the following expressions:

[8]

[9]
where {Omega}Ta and {Omega}DMY(pj) are, respectively, the relative changes (in percentages) in cumulative actual transpiration and dry matter yield corresponding to a 5% change in parameter pj ({Delta}p = 0.05p). This formulation of the sensitivity coefficients allows a comparison of the sensitivities to different parameters, independent of the invoked units or their absolute values. While the parameters were systematically changed by +5% of the nominal value, additional changes of between –10 and +10% were performed for several cases to test linearity of model outputs to the perturbed parameters. In our sensitivity analysis we choose to modify all soil hydraulic parameters, plus the water stress parameters and the time series of the driving forces (i.e., ETo and rainfall).


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  		Table 3. Variability in soil hydraulic properties measured within the experimental field. The presented values are averages over the three investigated depths.

 
Impact of Within-Field Soil Hydraulic Variability
To investigate the influence of soil hydraulic spatial variability on simulated transpiration rates and crop yield, we performed numerical simulations for all 28 sampling locations using depth-averaged soil hydraulic parameters. Since saturated hydraulic conductivity values were not available, for each location we generated 40 stochastic simulations in which Ksat was randomly sampled from a uniform distribution bounded by the lowest and highest measured values (i.e., 13.39 and 48.96 cm d–1). It is important to note that all of the 1120 (28 x 40) simulations generated for each climatic scenario used one of the 28 measured moisture retention parameter sets. The methodology hence accounted for cross correlations between the different moisture retention parameters, which would have been ignored if they had been sampled randomly and independently from probability distributions generated using the moments presented in Table 3. All simulations assumed that the parameters of the water stress function were constant (see reference values in Table 2 derived from the literature).

All simulations were next rerun while considering the dependence between the spatially variable soil hydraulic parameters and the water stress parameters. Before rerunning each simulation, the water stress parameters (i.e., the critical pressure heads h3l, h3h, and h4) were adjusted relative to three "reference" unsaturated hydraulic conductivity values. This was done since the water stress function by Feddes (Feddes et al., 1978) explicitly assumes that reductions in the potential root water uptake occur from some critical pressure head, even though this function already implicitly assumes that the unsaturated soil hydraulic conductivity governs this reduction. It is generally acknowledged that the critical pressure heads depend on soil type and that the reduction occurs much earlier for a coarse-textured than a medium- or fine-textured soil (i.e., that |hcrit|sand < |hcrit|loam; e.g., Musters et al., 2000) since the unsaturated hydraulic conductivity curve drops much faster. This concept is used here to adjust the critical pressure heads according to our spatially variable measured hydraulic properties. We assumed that the critical pressure head values used during the simulations of the previous step (i.e., h3 = –600 cm, h3h = –325 cm, and h4 = –8000 cm) were effectively valid for the 1998 run for which the soil hydraulic properties generated the least water stress (i.e., {theta}s = 0.403, {alpha} = 0.0051 cm–1, n = 1.275, and Ksat = 14.1 cm d–1). This assumption seems very realistic since the 1998 climate was relatively wet (Table 1) and pronounced water stress likely did not develop for the considered loamy soil. We estimated the three reference unsaturated hydraulic conductivity values corresponding to the above critical pressure head values from the literature. The reference values were K3l = 0.0156 cm d–1 (for h3l = –600 cm), K3h = 0.0791 cm d–1 (for h3h = –325 cm), and K4 = 2.15 x 10–5 cm d–1 (for h4 = –8000 cm). Reductions in the potential root water uptake were subsequently adjusted relative to these three reference hydraulic conductivity values for all simulations. Before each run, critical pressure heads were adjusted using the reference hydraulic conductivity values. Following Feddes et al. (1974) and Nimah and Hanks (1973), we assumed that the critical pressure value for h4 could not be less than –15000 cm. Figure 1 schematically illustrates the adjustment procedure of the reference critical pressure head h3h (i.e., –325 cm) from the reference hydraulic conductivity value K3h. The adopted adjustment procedure hence explicitly considers that reductions in the potential root water uptake occur from some threshold unsaturated hydraulic conductivity value.



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  		Fig. 1. Schematic of the adjustment procedure for the critical pressure head h3h. Figure 1a shows the reference moisture retention curve ({alpha} = 0.0051) and that of a similar soil with {alpha} = 0.002. Figure 1b presents the two corresponding hydraulic conductivity curves and the K3ref value used for the adjustment.

 
Estimation of Soil Hydraulic Properties from Water Stress Parameters
In a fourth step, we investigated whether knowledge of transpiration and crop yields can be used to simultaneously estimate spatially variable soil hydraulic and water stress parameters. For this purpose we performed the process using the two following objective functions (OF):

[10]

[11]
where b is the model parameter vector; T*a and Ta(b) are the "measured" (in our case generated with a reference run) and simulated cumulative transpiration rates, respectively; and DMY* and DMY(b) are the "measured" and simulated final dry matter yields, respectively. After generating a reference run for the averaged hydraulic properties of the experimental field (similar to the reference run of the sensitivity analysis for the reference water stress parameters derived from the literature), the simulations were rerun for every combination of two parameter sets (including systematically a water stress and a hydraulic parameter set) within a predefined parameter space discretized into 50 discrete increments. For each of the 2500 (50 x 50) runs, values of the OF were calculated with Eq. [3] and [4]. The feasibility of the identification process was subsequently evaluated by visual inspection of two-dimensional OF surface responses for different combinations of parameters.


   RESULTS AND DISCUSSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSIONS
CONCLUSIONS
 REFERENCES
 
Sensitivity Analysis
Results of the sensitivity analyses are summarized in Table 4 in terms of absolute values and sensitivity coefficients (SC), respectively, for the three different climatic scenarios. Table 4 clearly shows that the sensitivity of the cumulative actual transpiration rate and the final dry matter yield is quite variable according to the hydraulic parameters. For the three climatic scenarios, a higher sensitivity was found for the saturated water content ({theta}s) and the shape parameter (n). An increase in these two parameters leads to increases in both the actual transpiration rate and the final dry matter yield. An increase of {theta}s results in an upward shift of the moisture retention curve (MRC), leading to an increase in the available water between saturation and the critical pressure head where the potential root water uptake rate starts to decrease. The effect for n is similar since an increase in this parameter induces a steeper slope of the MRC, and consequently an increase in available water. In terms of absolute values, the impact of the modified hydraulic parameters on actual transpiration is not very pronounced, showing a maximum of 5 mm for the parameter n. On the other hand, an increase in n of 5% induces an increase of >500 kg in the final dry matter yield for the very dry 1990 agricultural season. Note that such an effect on the final yield is quite important, especially considering the high level of uncertainty generally associated with field-scale soil hydraulic parameter estimates. The effect is far less important for the wetter years (i.e., 1998 and 1999). The transpiration and the dry matter yield are less affected by the soil hydraulic parameters for those two years than for the dry 1990. This stems from the fact that transpiration and crop production are much more controlled by the soil than by the atmosphere for relatively dry conditions.


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  		Table 4. Results of the sensitivity analysis for the three considered climatic scenarios. Shown are absolute values of both cumulative transpiration (Ta) and the final dry matter yield (DMY) for the reference run and for runs with adjusted parameters. Also shown are the corresponding sensitivity coefficients calculated with Eq. [1] and [2].

 
The differences between the dry year and the wetter years are well illustrated in Table 4, which shows that SC for n decreases from 2.88 to 0.85 and from 3.45 to 0.75 for transpiration and crop yield, respectively. Similar distinct differences in the sensitivity were previously observed by St'astna and Zalud (1999) using two different crop simulation models, but the sensitivity in that case also markedly depended on the invoked model. In our study, transpiration and crop yield were not very sensitive to the saturated hydraulic conductivity (Ksat), with SC values ranging between –0.59 and –0.2. These small negative values indicate that an increase in Ksat leads to only a small decrease in both the transpiration rate and crop yield. An increase in Ksat reduces soil control on the potential soil water evaporation, in this way leaving a smaller quantity of water for transpiration. This is consistent with results obtained by Diels (1994). Note that in our study all rainfall reaching the soil surface is assumed to infiltrate into the soil (no runoff occurs) since the daily rainfall values are evenly distributed over the whole day (i.e., instantaneous rates are relatively low). Perturbations in Ksat hence should not affect the amount of water infiltrating into the soil. As such it may seem surprising that the data in Table 4 suggest that perturbation in the soil hydraulic properties has a marked effect on the transpiration rates and the crop yields of 1998 since this is very wet year (ratio ETo/rainfall = 0.69). This possibly biased result may be explained by the fact that potential correlations between soil hydraulic parameters and water stress parameters are not taken into account. Finally, we note that the effects of the soil hydraulic properties on transpiration and crop yield are very similar (see sensitivity coefficients in Table 4. This is inherent to the conceptual agrohydrological model used in our study, which links actual transpiration to dry matter production.

Compared with the soil hydraulic parameters, perturbations in the critical pressure heads have only limited impact on the cumulative actual transpiration rate and the final dry matter yields. However, the ranges of uncertainty related to the critical pressure head parameters may be much larger than those of the soil hydraulic parameters (Homaee, 1999). However, this does not mean that the water stress parameters are less important within the calibration process.

Transpiration and crop yield are both sensitive to the driving forces (ETo and rainfall) but vary differently according to the actual climatic scenarios. For the very dry year (1990), the increase in ETo only produced a slight increase in cumulative transpiration (+4.4 mm), but strongly affected crop yield (–494 kg). The significant decrease in yield is due to the fact that an increase in ETo involves a proportional increase in the potential crop transpiration rate, and therefore in case of a dry year, increased water stress. Note that the selected perturbation in ETo is similar to the value of the error in ETo caused by a poor temporal sampling frequency of meteorological variables (Hupet and Vanclooster, 2001). On the other hand, for the 1998 and 1999 agricultural seasons, the effect of the modification is more marked for the actual transpiration rates than for the crop yields. Indeed, for wet years, the actual transpiration rate is more controlled by the evaporating demand than by the soil. However the increase in ETo for both years leads to a slight lower yield, which is indicative of water stress. The impact of rainfall on transpiration is more limited, and the sensitivity is more pronounced for drier years, with SC equal to 0.37, 0.87, and 1.44 for 1998, 1999, and 1990, respectively (for absolute values see Table 4). The sensitivity of transpiration and crop yield to the driving forces is rarely investigated in classical sensitivity analyses. We are not aware of other sensitivity analyses comparable to our study. Nevertheless, the model structure, (especially the soil water flow module in crop growth simulation models) is generally so different that such comparisons would be difficult to interpret (see results of St'astna and Zalud, 1999).

Finally, we present results obtained for the case where the soil hydraulic parameters ({alpha} and n) are perturbed by 10% around their nominal values. Results for the very dry year (1990) for cumulative actual transpiration and crop yield are shown in Fig. 2a and 2b , respectively. The figures show that the model response can be very linear to some parameters (e.g., for {alpha}) and very nonlinear in other cases (e.g., for n). This is an obvious consequence of the nonlinearity of the Richards equation and the equations governing crop growth. While not surprising (e.g., see results by Brooks et al., 2001), these results suggest that a classical sensitivity analysis that ignores correlation between the perturbed parameters and assumes relatively arbitrary changes in the parameters can only provide a limited view of model response within parameter space. Furthermore, to quantify the true impact of the spatially variable soil hydraulic properties on the variables of interest, the sensitivity coefficients should be combined with the measured spatial variability of each soil hydraulic parameters. The agrohydrological model could then be run in a stochastic mode using the measured spatial variability in soil hydraulic properties.



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  		Fig. 2. Impact of perturbations in {alpha} and n on the actual cumulative transpiration rate (Fig. 2a) and on crop yield (Fig. 2b) for the dry 1990 climatic scenario.

 
Impact of Within-Field Variability in Soil Hydraulic Properties
Table 3 summarizes the spatial variability in the soil hydraulic properties measured within the experimental field. The presented values are typical for a medium-fine textured soil (loam) with {theta}s values close to 0.4 cm3 cm–3 and with small values for both the n and {alpha} parameters. The magnitude of the observed variability is very similar to that found in other studies (e.g., Shouse et al., 1995; Mallants, 1996), except for Ksat. The observed spatial variability for this parameter is smaller, which can be explained by the limited number of replicates (i.e., 6) and by the relatively large support volume used in the measurements (Mallants et al., 1997). The variability observed for {alpha} is more than one order of magnitude larger than that observed for n and {theta}s. Accounting for this difference in variability in the sensitivity analysis may well strongly modify our previous results obtained by perturbing each parameter in a similar value. Figures 3a, 3b, and 3c show the variability in the MRCs for the first (45 cm), second (75 cm), and third (105 cm) soil depths, respectively. Figure 3d shows the 28 MRC averaged for the three depths. These latter results were used in our agrohydrological simulations.



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  		Fig. 3. (a–c) The measured spatial variability in the moisture retention curves (MRC) for the first (45 cm), second (75 cm), and third (105 cm) depths, respectively; (d) the 28 MRCs with soil hydraulic properties averaged for the three investigated depths.

 
Figure 4 presents simulation results for the very dry 1990 (Fig. 4a, 4c, and 4e) and very wet 1998 growing seasons (Fig. 4b, 4d, and 4f). Figures 4c and 4d show the cumulative actual transpiration, and Fig. 4e and 4f show the dry matter yield, with the whiskers indicating the minimum and maximum values of the 1120 runs. Differences in temperature caused maize to reach maturity within 163 d in 1990 and 147 d in 1998. Notice that the results in Fig. 4 are markedly different for the two climatic scenarios. For the 1990 and 1998 agricultural seasons, the simulated cumulative actual transpiration rates ranged between 92.8 and 202.9 mm and between 132.8 and 198.3 mm, with mean values of 166.9 and 182.68 mm, respectively. Differences in simulated dry matter yields were also very pronounced, giving mean values of 14.76 and 20.39 t ha–1 for 1990 and 1998, respectively. The 1999 growing season produced intermediate results for both yield and transpiration (Table 5). The data in Table 5 show that the spatial variability in the simulated transpiration and crop yield progressively increased with the dryness of the agricultural season. Coefficient of variation values for the wet 1998 to very dry 1990 agricultural seasons increased from 7 to 14.6% and from 6.7 to 16% for transpiration and dry matter yield, respectively. These results suggest that the dryness of a climate does not only affect the mean values, but also governs the effects of spatial variability in the soil hydraulic properties on transpiration and crop yield variability. The effect of climate on transpiration variability is similar to results obtained by Braud et al. (2003) at a larger scale. A corollary of these results is that incomplete capture of within-field variability in the soil hydraulic properties likely will bias field-scale estimates of the transpiration rate and crop yield during dry years. Our numerical results also corroborate previous findings (e.g., Jhorar, 2002) that showed using information about measured spatially variable crop growth or transpiration rates to retrieve the structure of the underlying soil spatial variability will be successful only for relatively dry climates. Finally, we note that the variability in the simulated transpiration fluxes and crop yields is in the range of the measured spatial variability in soil hydraulic parameters. The variability in simulated transpiration rates ranged between 9.5 and 14.6% (in terms of CV), while the variability in the soil hydraulic properties ranged between 2.67% (n parameter) and 57% (Ksat). In terms of transpiration fluxes and crop yields, this means that the model tends to exaggerate the variability of some parameters ({theta}s and n), while lowering the variability of other parameters (Ksat and {alpha}).



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  		Fig. 4. Impact of the within-field variability in soil hydraulic properties on (c, d) the actual transpiration rate and (e, f) the dry matter yield for the relatively (a, c, e) dry 1990 and (b, d, f) wet 1998 climatic scenarios. Whiskers indicate the maximum and minimum simulated values. (a, b) Rainfall rates for the two climatic scenarios.

 

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  		Table 5. Numerical simulation results for the three climatic scenarios.

 
Results for the 1999 climatic scenario agreed well with the field-measured soil water contents, especially since the model was not previously calibrated nor validated. Figure 5 shows for four different depths (0–20, 25, 50, and 75 cm) the mean field measured soil water content (dots), and the mean and the extremes (continuous and dotted lines) of the 1120 simulations. Root mean square errors (RMSE) between the mean measured and simulated soil water contents ranged between 0.02 and 0.036 cm3 cm–3 (for the 25- and 75-cm depth, respectively). The slightly larger RMSE for the 0- to 20- and 25-cm depths can be explained by the location of the soil water content sensors in the middle of the maize rows (Hupet and Vanclooster, 2004).



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  		Fig. 5. Comparison between simulated and measured soil water contents for the 1999 climatic scenario for the different depths: (a) 0–20 cm, (b) 25 cm, (c) 50 cm, and (d) 75 cm. Dots indicate the average of the field measured soil water contents, continuous and dotted lines the mean and the extremes of the 1120 simulated soil water contents, respectively.

 
Despite the good correspondence between simulated and measured soil water contents for 1999, some results (especially those for the wet 1998 agricultural season) appear questionable for three reasons. First, we found that several locations within the field experienced severe water stress (Ta,min/Ta,max = 0.66), even though water stress presumably should not have occurred for a maize crop growing in such wet conditions (ratio ETo/rainfall = 0.69, with only one long 16-d dry spell without any rainfall) (Otegui et al., 1995). Second, the results presented in Fig. 4d suggest that water stress was highly variable within the loamy field for which the measured soil hydraulic variability was relatively small (Table 3). This is surprising since this soil type is generally considered optimal in terms of soil water availability. Also, the minimum cumulative actual transpiration values obtained for the dry 1999 season (92.8 mm) seem much too low since they corresponded to a daily mean transpiration value of barely 0.66 mm d–1. These findings caused us to suspect that the water stress parameters were not correctly specified (although derived from reference literature values; see Table 2), at least for those locations where the literature parameters exacerbate the effects of water stress. By comparison, several sampling locations (i.e., several combinations of hydraulic parameters) showed more normal behavior with very limited water stress.

As a consequence, we decided to rerun all numerical simulations after adjusting the water stress parameters as explained in the Materials and Methods section. This was done according to the three reference unsaturated hydraulic conductivity values (K3l = 0.0156 cm d–1 for h3l, K3h = 0.0791 cm d–1 for h3h, and K4 = 2.15 x 10–5 cm d–1 for h4) derived from the less water stressed 1998 run. Figure 6 presents the 1120 combinations of h3h and h3l (arrows in this figure indicate the original values, i.e., –325 and –600 cm) obtained using this strategy. The adjusted water stress parameters for h3h ranged between –136 and –2176 cm (the vast majority between –220 and –840 cm), for h3l between –431 and –4301 cm (the vast majority between –580 and –1460 cm) and for h4 between –5626 and –24996 cm (the vast majority between –7500 and –14600 cm). Table 6 summarizes the agrohydrological simulation results obtained with the modified water stress parameterization procedure. Notice that, the simulated values for both transpiration and dry matter yield are now higher than those obtained previously (for comparison, see values in Table 5). The mean actual transpiration values increased by 13, 18, and 25% for 1998, 1999, and 1990, respectively. Such increases, progressively larger with the drier years, were also observed for the simulated dry matter yield. These increases, both for transpiration and crop yields, reflect less accurate water stress, obviously a consequence of the adjustments in the water stress parameterization. The simulated spatial variability was now also more limited (CV values ranged between 1.55 and 5.4%), although the variability still increased systematically with the dryness of the considered climatic scenario. The 1990 dry year, now also produced much more realistic minimum values for the actual transpiration (i.e., 164.7 instead of 92.1 mm).



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  		Fig. 6. Scatter plots of the adjusted critical pressure heads h3l and h3h. Arrows indicate reference values of –325 and –600 cm for h7h and h3l, respectively.

 

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  		Table 6. Results of the numerical simulations for the three climatic scenarios, rerun with the adjusted critical pressure heads.

 
Results of the above simulation reruns using the modified water stress parameters cannot be easily validated experimentally. Comparisons between measured and simulated soil water contents (using adjusted water stress parameters) show only a very slight decrease in the RMSE values (results not shown), which is not surprising since the soil water dynamics is relatively insensitive to the water stress parameters (Hupet et al., 2003), and since 1999 was not the driest climatic scenario. To be effective, a comparative study should include accurate measurements of transpiration and dry matter yield within the field. Dry matter yield measurements in our case were only available for the 1999 agricultural season, although the measurements were not performed on the exact same 28 locations where soil hydraulic properties were determined (±50 cm apart). Additionally, the agrohydrological model we used was not previously calibrated and did not consider various other stresses that inevitably occur at the field scale.

Our numerical results, while partially validated only for soil moisture, show that the use of water stress parameters derived from the literature can be very problematic. Our findings show that these parameters can strongly affect the simulated transpiration and the crop yield, even during a wet year. Furthermore, the results show that adjustments in the water stress parameters influence not only the mean simulated transpiration rate and crop yield, but also the spatial variability in these variables. Results obtained with the sensitivity analysis may therefore be somewhat limited since the perturbations in the hydraulic parameters were performed independently of the water stress parameters, which seems physically inconsistent. Introducing some correlations between the soil hydraulic and the water stress parameters during the perturbation process could well lead to somewhat different results. Our results also reinforce the fact that it is very important to develop water stress parameterization procedures that include realistic representations of the soil water retention and hydraulic conductivity functions.

Estimation of Water Stress and Hydraulic Parameters
Figure 7 shows two-dimensional response surfaces of object functions (OF) obtained when h4 is simultaneously optimized with n (Fig. 7a, 7b, 7e, and 7f) and {alpha} (Fig. 7c, 7d, 7g, and 7h) for the 1990 (Fig. 7a–7d) and 1998 (Fig. 7e–7h) agricultural season. The left (Fig. 7a, 7c, 7e, 7g) and the right figures (Fig. 7b, 7d, 7f, 7h) give OF response surfaces calculated using the actual cumulative transpiration rate and the final dry matter yield, respectively. True values (i.e., n = 1.204, {alpha} = 0.00408, and h4 = –8000 cm) are marked with a star. Figure 7 reveals in all cases strong parameter interactions between h4 and n or {alpha}. Notice that many pairs of parameter values give very similar goodness of fits for both the actual transpiration rate and the dry matter yield. For example in Fig. 7a, perfect fits can be obtained for some combinations of parameters across the entire selected parameter space (i.e., –15000 < h4 < –5000 and 1.05 < n < 1.8). Similar results were obtained for each combination of parameters and for both climatic scenarios. Note, however, that the response surfaces are much flatter for the wet 1998 scenario than for the dry one. Figure 7e and 7f show quite extreme cases where very good fits are obtained almost everywhere in parameter space for the simultaneous optimization of {alpha} and h4. This is a consequence of the low sensitivities of actual transpiration and dry matter yield to the water stress and soil hydraulic parameters as compared with a dry year. The different results clearly point out that simultaneous estimation of water stress and soil hydraulic parameter is inherently difficult. Indeed, although very good fits can be obtained in terms of transpiration or actual dry matter yield, the derived parameter values may not be physically realistic. Such a calibration exercise is also problematic since the derived hydraulic parameters can be strongly biased, possibly leading to unrealistic model responses for other processes (e.g., drainage or runoff predicted during wetter periods).



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  		Fig. 7. Two-dimensional response surfaces of objective functions (OFs) obtained when h4 is simultaneously optimized with (a, b, e, f) n and (c, d, g, h) {alpha} for the (a–d) 1990 and (e–h) 1998 agricultural seasons. The left (a, c, e, g) and the right figures (b, d, f, h) show OF response surfaces calculated using actual cumulative transpiration rates and final dry matter yields, respectively.

 
Furthermore, simultaneous estimation of spatially variable water stress and soil hydraulic parameters (e.g., using spatially measured crop yields) could severely exaggerate or underestimate the variability in these parameters. The feasibility of simultaneously estimating water stress and soil hydraulic parameters was not tested for h3h, h3l, {theta}s, and Ksat, but similar results are very likely. In this paper we showed parameter estimation results for cases where the final actual cumulative transpiration rate and dry matter yield were used. Very similar results were obtained when the entire time series of daily variables was incorporated in the OFs of Eq. [3] and [4] (results not shown). In view of the results obtained in this section, we note that the water stress concept used in the SWAP model is quite basic compared with several other codes where more biophysical processes are considered, such as stomatal response to environmental conditions and resistances to water flow in the soil toward the root and/or within the root (e.g., Santini, 1992). The use of more comprehensive concepts, although giving a more realistic picture of the underlying processes, is very likely to lead to results more poor than those presented here since they contain more parameters (e.g., Franks et al., 1997), unless very specific identification strategies are implemented to avoid parameter nonuniqueness problems (e.g., Dekker et al., 2001).

From this study we can conclude that alternative strategies are needed to estimate both the hydraulic and water stress parameters. The soil hydraulic parameters could be estimated first by means of a series of direct or indirect measurement techniques (Dane and Topp, 2002). The water stress parameters could then be estimated next by fixing the soil hydraulic parameters at those estimated values. This strategy is certainly more robust since the OF minimum should be more easily found (at least in case of a dry year; see Fig. 7a–7d), while the uncertainty related to the water stress parameters should be smaller. Note that in this study we did not test the possibility of simultaneously estimating several water stress parameters (e.g., h3l and h4), although one may suspect that additional correlations will occur for this type of parameter combinations.

Results presented in this section show that very good fits can be obtained by fitting water stress and hydraulic parameters to actual transpiration rates and dry matter yields measured within a given experimental site. Notwithstanding the apparently good results, the derived parameters may not at all be physical. Therefore, it is very problematic to consider such derived water stress parameters as reference values for a given crop, and to subsequently use them in modeling exercises for other sites with relatively similar soil hydraulic parameters. Unfortunately, such a methodology is often the only alternative that can be used, and many examples of this can be found in the literature (e.g., Droogers, 1997; Meiresonne et al., 1999; Droogers, 2000; Ritter et al., 2003). In view of the disappointing results presented in Fig. 7, we encourage researchers to develop alternative strategies for estimating water stress parameters needed in agrohydrological models.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSIONS
 CONCLUSIONS
REFERENCES
 
We investigated the impact of within-field variability in soil hydraulic properties on cumulative actual transpiration and dry matter yield for three contrasted climatic scenarios by combining measurements and agrohydrological simulations. In a first step, a sensitivity analysis was performed to quantify the sensitivity of the actual transpiration rates and the dry matter yield to the soil hydraulic properties. The results show that the sensitivity is very variable. Some parameters have a marked effect (e.g., {theta}s and n), while others (e.g., Ksat) have only a weak effect. The effect of soil hydraulic properties on the actual transpiration and the dry matter yield was found to generally increase when dryness increase. This result reflects an increase in the soil control on water fluxes and on dry matter production in dry conditions. The sensitivity of the actual transpiration rate and the dry matter yield to the soil hydraulic parameters was often very similar, being a direct consequence of conceptualizations used in agrohydrological models to reduce the daily potential gross CO2 assimilation rate.

In a second step we investigated the impact of within-field variability in soil hydraulic properties on the simulated actual transpiration rate and dry matter yield by considering the water stress parameters to be constant for all simulations. The measured variability in the soil hydraulic parameters was typical of what is generally observed within agricultural fields, showing coefficients of variation between 2.67 and 57.7%. The results of the agrohydrological simulations were very different according to the climatic scenarios. For the dry 1990 and wet 1998 agricultural seasons, the simulated cumulative actual transpiration ranged between 92.8 and 202.9 mm and between 132.8 and 198.3 mm, with mean values of 166.9 and 182.68 mm, respectively. The results show that the spatial variability in the simulated transpiration rate and crop yield increases progressively with the dryness of the agricultural season. From the wet 1998 to the very dry 1990 agricultural season, CV values increased from 7 to 14.6% and from 6.7 to 16% for the transpiration rate and the dry matter yield, respectively. This means that incomplete capture in the within-field variability of the soil hydraulic properties likely biased the field-scale estimates of the transpiration rate and crop yield during dry years.

In a third step, all simulations were rerun after adjusting the water stress parameters according to three reference soil hydraulic conductivity values. Compared with the earlier results, the adjusted mean actual transpiration values increased by 13, 18, and 25% for 1998, 1999, and 1990, respectively. Similar increases, progressively larger with drier years, were also obtained for the simulated dry matter yields. The simulated spatial variability was then also less extensive (CV values ranged between 1.55 and 5.4%), but still increased systematically with the dryness of the considered climatic scenario. These results show that accurate estimation of water stress parameters is important for studies dealing with the effect of the soil hydraulic variability on transpiration and dry matter yield. They also show the importance of developing more effective procedures for estimating soil specific water stress parameters.

Finally, we investigated whether or not soil hydraulic and water stress parameters can be accurately estimated simultaneously using only measurements of transpiration and the dry matter yield. Visual observations of two-dimensional response surfaces in all cases revealed strong interactions between the soil hydraulic and water stress parameters. This showed that simultaneous estimation of water stress and soil hydraulic parameters is generally not feasible, and may lead to physically inconsistent water stress parameters. Consequently, the use of an agrohydrological model in a stochastic mode for a vegetated surface will require alternative strategies for estimating reliable water stress parameters.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIAL AND METHODS
 RESULTS AND DISCUSSIONS
 CONCLUSIONS
 REFERENCES