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Univ. of Hohenheim, Inst. of Soil Science and Land Evaluation, 70593 Stuttgart, Germany
* Corresponding author (jingwer{at}uni-hohenheim.de)
Received 22 March 2005.
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ABSTRACT |
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 TOPEXECUTIVE SUMMARY ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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Abbreviations: AEV, air entry value • BVG, bimodal van Genuchten • Eact, actual evaporation • Epot, potential evaporation • ETo, potential reference evapotranspiration • IPM, Instantaneous Profile Method • LAC, low activity clay • MVG, modified van Genuchten • PSD, pore size distribution • PTF, podotransfer function • SWRC, soil water retention curve • TFE, transient flow experiment • VG, van Genuchten • ZFP, zero flux plane
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INTRODUCTION |
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TOPEXECUTIVE SUMMARYABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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). However, several studies have shown that the pore size distribution of soils is often bi- or multimodal. In the tropics, for example, bimodal pore size distributions have been shown for Ferralsols of Cuba (Medina et al., 2002) or Brazil (Teixeira 2001). Compared with soils from temperate regions, general differences exist in texture (less silt content), mineralogy, and structure (Hodnett and Tomasella 2002). Low-silt-soils feature pore size maxima in the representative sand and clay ranges (Tomasella et al., 2000). In structured soils even three pore systems are possible (Mallants et al., 1997).
Deriving Kr() from an inappropriate SWRC parameterization inevitably results in poor predictions, even with an in-principle suitable prediction model (Durner 1994). To encounter these problems, in the last decade several approaches have been developed to describe bi- or multimodal SWRCs. An x-modal SWRC superimposes x unimodal functions, in which each of them describes one pore size maximum in the soil (Othmer et al., 1991, Durner 1994, Ross and Smettem 1993). In studies using these more flexible functions, the pore space was mostly regarded as a dual system, with one pore size maximum near saturation, representing the interaggregate pores and the other maximum in a suction range of intraaggregate pores (Othmer et al., 1991, Coppola 2000, Schneider 2001). By this approach water flow near saturation could be treated more independently, which yielded in increased accuracy when predicting water fluxes and solute transports.
Own previous studies at an Umbric Acrisol (according to the World reference base for soil resources, FAO 1998) in the tropical northern Thailand suggested also bimodal retention functions (Spohrer et al., 2002). The research was embedded in the Uplands Program "Sustainable Land Use and Rural Development in mountainous regions of Southeast Asia" and focused on water balance modeling during dry season to control irrigation. Because of the bimodal SWRC the question for the applicability of unimodal retention function arose. The aim of the present study was therefore to investigate whether the unimodal van Genuchten retention function (1980) is sufficient to simulate the soil water regime of the Umbric Acrisol. The model was parameterized and tested by solving the inverse problem of a one-dimensional transient flow experiment (TFE). The unimodal approach was compared with the bimodal SWRC of Durner (1994) and the modified van Genuchten parameterization of Vogel and Cislerova (1988) for fine textured soils. Pressure head and water content data of the TFE, as well as on site measured hydraulic conductivities near saturation were included in the optimization. Hydraulic conductivities calculated according to the Instantaneous Profile Method (IPM) (Dirksen 1999) were used to verify the accuracy of the optimized conductivity functions.
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MATERIALS AND METHODS |
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TOPEXECUTIVE SUMMARYABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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2°) a skeleton-free soil block of 3.2 by 2.4 m down to a depth of 1 m was separated from the surrounding soil with a plastic sheet. According to the findings of Abbaspour et al. (2000), who emphasized the importance of an accurate soil system description for water flow modeling in field soils, the horizons (down to 0.15, 0.30, 0.50, 0.75, and 1 m) were identified based on a foregoing detailed bulk density study and soil analysis (Table 1). For the bulk density study, 80 soil cores, taken by grid sampling from a soil pit wall (0.4 by 1 m), were investigated. The results showed that a loose Ap horizon is followed by a transition horizon (AB) with compactions due to tillage practices. Below, the soil appears more homogeneous in the Bt horizons and the averaged bulk density slightly decreases. Bulk density as well as texture, porosity, and total C analyses of mixed samples were conducted according to laboratory guidelines at University of Hohenheim (Herrmann 2001).
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The measurements started 1 d after the end of water ponding at pressure heads of h 
–35 cm to avoid inaccurate pressure head measurements due to preferential water flow along the tensiometer tubes. Pressure head measurements were conducted with a portable needle pressure transducer. The signals of the TDR probes were read out with a Tektronix 1502C cable tester and transformed to water content values using the composite dielectric approach of Roth et al. (1990). The TDR readings were calibrated with gravimetric water content measurements. Temperature dependency of the time domain reflectometry was neglected because of the small significance for field measurements with small soil temperature changes (Persson and Berndtsson 1998). Water loss of the self-made tensiometers at lower pressure heads and its impact on current measurements as well as the response time of the tensiometers were investigated in an accompanying experiment. It showed that under the prevailing technical conditions, precise pressure head measurements in the field were only possible down to about –400 cm. Therefore, pressure head measurements below –400 cm were not considered. After 116 d the soil and plastic sheet cover was removed to enable evaporation. Subsequently, measurements went on for additional 185 d, in which direct sunlight on the experimental plot was avoided by a metal roof and transpiration was prevented by suppressing vegetation using herbicides.
In the following, averaged water content and pressure head values of each horizon were used to obtain representative SWRCs. This aggregation was justified because of the rather small measurement variability. From the upper to the lower horizon, the average CV of the water content and pressure head measurements were 2.1, 4.8, 5.3, 5.2% and 10.2, 9.2, 7.7, and 14.7%, respectively.
Boundary Conditions
The experimental setup allowed one-dimensional calculation of the water drainage fluxes in the enclosed soil block. Although measurements comprised five horizons down to 100 cm, only four horizons were further investigated. The lowermost served as a "buffer" for disturbing influences from lower horizons and aside.
For modeling purposes, the lower boundary condition was therefore set as equal to the averaged tensiometer measurements of the fourth horizon at 70-cm depth. The upper boundary condition was set as "no flux" for the first experimental phase of 116 d. For a second period of additional 75 d the plastic sheet cover was removed and the potential evaporation (Epot) was measured with two self-made first-stage evaporimeters. For a third phase of 110 d Epot values were estimated based on on-site measured potential reference evapotranspirations (ETo) (Clarke et al., 1992) (Fig. 1 ).
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 | [1] |
(1) denotes the effective water content. The volumetric water content is symbolized by 
(h). The terms r and s are the residual and saturated water content (all in m3 m–3). Through the introduction of two dimensionless shape parameters n (n > 1) and m (= 1 – 1/n), the width of the pore size distribution both toward large and small pores can be described. Depending on the m/n ratio, the reciprocal of 
[ (1/cm) > 0] describes the air entry value (AEV) of the soil (at low m/n), the pressure head at the point of inflection (at high m/n), or a pressure head in-between. s. The MVG function can be expressed as
 | [2] |
s is the pressure head at the retention function break and m the fictitious water content without any break.
 | [3] |
wi = 1,) is the weighting factor for the ith of k unimodal functions. In this study, a bimodal approach, by superposition of two van Genuchten functions (BVG) was applied.
To achieve realistic data for the SWRC near saturation, measurements of the volumetric water content at h = –3.75cm (NS) were added to the inverse simulation as fit points (Table 2). The measurements were done with 7.5-cm-high soil cores according to Klute (1986). Subsequently, the volumetric water content was determined in a high resolution for additional pressure heads near saturation (h = –5, –10, –20, –30, and –40 cm). Fit points for the dry region at wilting point pF 4.2 (WP) were calculated using a pedotransfer function (PTF) for tropical low activity clay (LAC) soils (Gaiser et al., 2000).
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) is defined as "conductivity over water-filled pores/conductivity over all pores" and is based on statistical pore bundle assumptions. It can be expressed as
 | [4] |
). The combination of [3] and [4] has to be solved numerically. By treating the parameters Ks and l as unknown when solving the inverse problem, greatest flexibility is given for the determination of the unsaturated hydraulic conductivity function Ku(h) (Durner 1994). However, to obtain realistic data for Ks, hydraulic conductivities at h = –2 cm (k2) were included in the objective function. The measurements were performed in representative depths (0, 20, 40, and 60 cm) close to the experimental plot with a Hood Infiltrometer (UGT, Germany) (Table 2). The conductivity measurements (infiltration area = 201 cm2) revealed a rather large variability (CVs varied between 34 and 92%). Because they did not clearly indicate normal or skewed distributions, averages were computed for TFE simulations.
To check the plausibility of the determined Ku(h) functions, they were tested against hydraulic conductivity data (kIPM) derived from the IPM experiment. Because of lacking pressure head measurements near the soil surface, conductivity calculations in the upper horizon were based on the assumption of a constant pressure head gradient dh/dz = 1. The IPM calculations were limited to pressure heads between –40 and –100 cm. Thus, potentially large errors in the wet and dry pressure head ranges, which result from inaccurate hydraulic gradient or water content measurements (Flühler et al., 1976) could be avoided.
Parameter Optimization
The HYDRUS-1D code (Simunek et al., 1998) was used for parameter optimization in the upper four horizons. However, not all parameters of the SWRCs and Ku(h) functions were included in the optimization procedure. They will be discussed in the following. The optimization was performed by minimizing the objective function with a nonlinear least-squares optimization approach. Normalization of different data types was done with the "weighting by standard deviation" procedure.
Following data sets were included in the objective function:
WP data) from pedotransfer function (Table 2) Initial parameters were set within realistic ranges to successfully reach the global minimum when solving the objective function. Initial values of the SWRC parameters were estimated by fitting SWRCs to the measured retention data by using the SHYPFIT code of Durner (1995). Initial guesses of Ks were obtained by matching the relative hydraulic conductivity functions [Kr(h) function] to the k2 data.
The determination of an accurate initial guess for l proved to be difficult. During preliminary parameter optimization runs, different positive initial l estimates converged to different local minima. Even though statistics (narrow 95% confidence intervals and very low degrees of parameter correlation) indicated acceptable optimization conditions, TFE predictions were poor. For that reason further investigations were done. It was found that negative initial l values were necessary to match the observed drainage.
To yield the best overall fit, all hydraulic property parameters should be optimized simultaneously (Durner 1994). However, for practical reasons in this study, r and s values were not included in the optimization procedure. Moreover, Ks values of MVG and BVG were excluded from a further optimization. For MVG, the AEV are always defined at h < –2 cm. Then Ks = k2, which makes a Ks optimization needless. For BVG, Ks optimization could be neglected because Ks k2. This originates from the shape of the asymptotic SWRC near saturation. In contrast, the VG-SWRC shapes near saturation necessitated to optimize Ks. The reason for this lies in the SWRC shape near saturation as will be discussed later.
In total, 16 parameters of VG, 17 of MVG, and 25 parameters of BVG were finally considered in the objective functions (Table 3). When the number of parameters exceeded the maximum number (15) in the objective function, the optimization was conducted stepwise by which the parameters were alternately included with upper and lower limits slightly different from the initial values before.
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The meaningfulness of standard errors for this study was additionally limited, because they neither properly reflect the physical accuracy of retention functions nor they accurately assess the performance of SWRC approaches with different numbers of parameters (Durner 1995). Therefore, this statistical measure was not used to compare the applicability of the investigated retention functions.
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RESULTS AND DISCUSSION |
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TOPEXECUTIVE SUMMARYABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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–30 cm. The inflection point of the SWRC determines the AEV, where the pores start to drain. Laboratory data agreed here with field measurements of Kahl (2003), and pointed to an AEV between h = –10 and –20 cm (Fig. 2
). Based on the Laplace equation and assuming a mean interfacial tension of 
= 72.7 10–3 N m–1, as well as complete wetting of the pores (contact angle 0), the pressure head h can be roughly related to a pore radius r by r (µm) = 1500/h (cm) (Gisi et al., 1997). Consequently, the equivalent diameters of the largest pores in the soil matrix lie between 300 and 150 µm. Preferential flow in macropores happens in pores with diameters >500 µm and equivalent pressure heads larger than 6 cm (Scheinost, 1995; Coppola, 2000). Even though retention measurements near saturation did not indicate the existence of pores that contribute to preferential flow in macropores, it must be stressed that the number of replicates was not sufficient to prove this statement.
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In the pressure head range of the field measurements, the estimated VG and MVG SWRCs are subject to systematic errors. Thus, water contents are either over- or underestimated. The BVG SWRC is more flexible. Hence, the course of the retention data could be described quite accurate. A measure for the goodness of the SWRC description is the averaged absolute water content deviation [AWCD (m3 m–3)] of predictions from measurements (Durner, 1995). In this study, the calculated AWCD values (Table 3) are based on field measurements and demonstrate the goodness of the BVG fit. Values for BVG (0.0033–0.0035) are less than half of those obtained with the unimodal function (0.0071–0.0108). An exception is the BVG fit in 25 cm. It almost perfectly describes the shape of the measured data. The bad AWCD value comes from an overall shift of the SWRC toward saturation which is mainly caused by a too large estimated 1 value (Fig. 2).
Below pressure heads of –400 cm, tensiometer measurements became inaccurate and were stopped. When SWRCs were fitted to measured retention data with SHYPFIT unrealistic high r values (>30%) were obtained. Therefore it was necessary to add an additional fit point. Comparison of retention data estimates with pedotransfer functions of Schaap (2000) and Gaiser et al. (2000) showed clear differences at field capacity but agreed well at pF 4.2. At this pF range, water content predictions are merely influenced by texture (or rather surface area) and not by structural peculiarities (Hillel, 1998). Therefore, the pedotransfer function of Gaiser et al. (2000) was seen as suitable for the calculations of additional fit points at pF 4.2 (WP).
Between end of field measurements at pF 2.6 and fit point at pF 4.2, the shapes of the SWRCs are uncertain. However, the effect of this uncertainty on moisture regime modeling should be small within this pressure head range. Even an additional pore size maximum should not significantly change modeling results. For example, usual relative hydraulic conductivities at pressure heads >pF 2.6 are <0.0001 for fine-textured soils (Schaap, 2000). Even with unrealistic high Ks values of 50 cm d–1, the actual conductivity is still very low (<50 µm d–1).
Because varying pressure heads are related to different pore diameters, the pore density at a given pressure head can be expressed with the SWRC. The pore size distribution (PSD) in the soil is the first derivative of the retention curve d/dlog h. For a better visualization, pressure heads are plotted logarithmically (Durner, 1994). The PSDs derived from the optimized retention curves are given in Fig. 2. Depending whether uni- or the bimodal approaches were used the obtained PSDs differed distinctly.
With VG as well as with its modification (MVG), the pore size maxima are always located near h = –100 cm. In the lower two horizons a distinct pore size maximum is hardly to detect, because the distribution is very broad (Fig. 2). Contrary to the unimodal approaches, PSDs of BVG show a clear first pore size maximum at h –90 cm. They are well described by measurements both toward larger and smaller pores (Fig. 2). A second distinct pore size maximum follows in the dry range. Because of lacking measurements, however, neither its exact location nor its spread toward smaller pores can be exactly determined. Nevertheless, as discussed by Tomasella et al. (2000), this bimodality goes well together with texture analysis. Assigning pore radii of 5 to 25 µm and equivalent pressure heads of –63 to –316 cm (pF 1.8–2.5) to the silt fraction (Blume et al., 2002), the pore size minima at about h = –200 cm can be explained by the low silt content of the tropical Acrisol. In contrast, PSD with VG and MVG rather indicate an even particle-size distribution with no silt deficit. However, it must be pointed out, that all above-mentioned pore-size related information were inferred from measured SWRCs and thus are blurred due to pore topology (Vogel, 2000). Since not all equally sized pores are emptied at a certain pressure head, PSD derived from measured SWRC reflect the "effective" geometric radii rather than the real geometry of the pores.
Near saturation, the slope of the VG SWRC is steeper than those of MVG or BVG and causes considerable pore spaces even at pressure heads >–10 cm. With BVG, the estimated pore volume near saturation are distinctly smaller and approach zero at h > –5 cm. For MVG, the pore space is zero above the SWRC break.
Without a break, all continuous retention functions describe an asymptotic slope of the SWRC at h 
0. The way how this asymptotic SWRC slope approaches saturation is a crucial point in predicting the relative hydraulic conductivity when Mualem's conductivity model is used (Vogel et al., 2001). With VG, the SWRC shape at h 0 is mainly determined by m or indirectly by n when m is expressed through n (m = 1 – 1/n) (m1 and n1 for BVG, respectively). The smaller n the steeper the slope of the SWRC at h 0 and thus the larger estimated pore spaces. The larger the pore spaces at h 0 the more increases the relative hydraulic conductivity (Kr()) toward saturation. The reason for it lies in the mathematical expression of the Mualem-conductivity model, that is, in the integral in Eq. [4], by which Kr() is obtained by integrating over the inverse of h. The larger h is when the water content is changed by a certain volume unit, the bigger is the contribution to this integrand (Durner, 1994). Vogel et al. (2001) defined a n value threshold of 1.3. Below this threshold, Kr() functions are mostly unrealistic and the numerical solution is susceptible to stability problems. While n1 values of BVG are always >2, all n values of VG are below the threshold of 1.3. The effect of it will be discussed in the following section together with the hydraulic conductivity functions.
Hydraulic Conductivities
It was tried to achieve realistic Ks values by including k2 data in the objective function (Durner, 1994). However, the k2 value of the lower horizon (70 cm) were neglected because optimized values became too small for a realistic TFE modeling (Fig. 3
). The reason might be that pores were smeared during digging in the harder subsoil.
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If Ku(h) is derived by the model of Mualem (1976), its shape is mostly defined by the respective SWRC. The parameter l, which accounts for tortuosity and pore connectivity in the soil, also affects the shape of Ku(h). In many studies its value is fixed to 0.5; an average for many soils (Mualem, 1976). However, the smaller l, the gentler the shape of Ku(h) or rather the smaller the decrease of Ku with decreasing h. Consequently, l can be seen as a specific characteristic of the pore system. A shortcoming of the used bimodal approach is therefore the use of only one l value for both pore systems, which appears less realistic. In unimodal approaches, l values may vary from –16 to 10 (van Genuchten et al., 1989, cited in: Kutilek and Nielsen, 1994; Wösten and van Genuchten, 1988). In principle negative l values are only restricted by a certain threshold that is influenced by the SWRC. Below this threshold, the slope of dk/dh becomes negative. As a consequence, the hydraulic conductivity would unrealistically increase with decreasing pressure head. In this study, the empirically determined l thresholds for all SWRC approaches and horizons were between –5 and –12.
The parameter optimization revealed negative l values for all investigated horizons and SWRC descriptions. On the one hand, these results fit well with findings of Schaap and Leij (2000) who also often found negative l values for finer-textured soils in 235 investigated soil samples. On the other hand, a physical reasoning of negative l values is difficult. Negative l values mean that tortuosity decreases with decreasing water content. This has been shown for cylindrically shaped pores in network models (Vogel, 2000) but never in natural soils yet. Therefore, l is treated here as a pure fitting factor and, in a broader sense, "considered as an integral over all uncertainties" (Vogel, 2000).
The kIPM data (Fig. 3) served to assess the goodness of the predicted Ku(h) functions. No marked differences between the investigated retention functions could be detected in 12 and 45 cm. They fitted well to k2 and kIPM data. In 70 cm, Ku(h) functions matched well kIPM data but as discussed above, overestimated k2 data. Only for 25 cm, larger differences in kIPM prediction were observed. They are smallest for BVG whose deviations might be explained by the worse SWRC fit (Fig. 2). In general, possible reasons for the deviations are manifold. On the one hand, problems with soil compactions (Table 1) are likely. On the other hand, they also might be attributed to the optimization procedure itself. Because all parameters of all horizons were optimized simultaneously, inaccuracies in terms of water content, pressure head, and hydraulic conductivity measurements were balanced between the horizons to get a parameter combination with which the TFE could be modeled best. Thus, bad Ku(h) functions in 25 cm might also be related to inaccuracies in other horizons.
Among the unimodal approaches, kIPM data could be described better with VG but most Ks values were out of range of realistic values. Therefore, similar to results of Vogel et al. (2001), this study showed that MVG bears advantages over VG and should be preferred for modeling the water regime of fine-textured soils. In the end, the applicability of the investigated retention functions will be assessed not only by the goodness of the hydraulic property descriptions but also by how accurate the TFE could be simulated.
Water Flux Modeling with Optimized Hydraulic Properties
In the first "drainage phase" (0–116 d), the upper boundary condition of the soil block was "no flux." Measured hydraulic potentials indicated downward water fluxes.
Modeling results of this first phase with unimodal retention functions (VG, MVG) showed always accurate predictions of the pressure head measurements (Fig. 4
). Contrary to this, respective water contents were precisely predicted only in the upper horizon. In the second and third horizons (25 and 45 cm) the model overestimated measured values already at the beginning of the experiment when the soil was close to saturation (h –35 cm). This error became continuously larger (up to 2% and more) in the course of the experiment. In the lowermost horizon, water content predictions rather reflect the goodness of the applied SWRC. For modeling, the measured pressure heads in 70-cm depth were set as lower boundary condition. Hence, inaccurate SWRCs resulted inevitably in inaccurate simulated water contents. When comparing the accuracy of VG and MVG, overall differences are small although water content deviations are clearly smaller in 25 cm with VG.
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–100 cm (Fig. 2). Fitting of a three-modal SWRC with SHYPFIT (Durner, 1995) failed probably because of the small size of this pore system. It was therefore decided to neglect it, since problems for the inverse parameter determination were expected, too (Zurmühl and Durner, 1998). In addition, the amount of needed SWRC parameters would increase from 7 to 10 for each horizon. Even if r, s, and Ks are excluded from the optimization, there are still 36 unknown parameters. The simultaneous optimization of these 36 parameters is fraught with problems (e.g., increase of possibly correlated parameters) and bears no relation to the expected improvements. Additional error sources for inverse modeling of field problems might stem from design and implementation of the experiment, the underlying flow process, and the formulation of the objective function (Abbaspour et al., 2000). Also the problem of soil heterogeneity must be encountered. Because effective parameters at the horizon-scale were used, the model did not take into account the intra-horizontal variability.
After 116 d, at the beginning of the second TFE phase, the plastic sheet and soil cover was removed to enable evaporation. With beginning of evaporation water fluxes were directed upward. The depth from where water flows upward is determined by the zero flux plane (ZFP). The ZFP is defined as the point where the vertical hydraulic gradient is zero. Below, water moves still downward. Depending on the initial water content, soil hydraulic properties and Epot, the actual evaporation (Eact) equals Epot or is lower. In this study evaporation rates were modeled by Hydrus 1D (Simunek et al., 1998) with Epot measurements or predictions as predefined upper boundary condition. In Fig. 1 the course of the modeled Eact with BVG is depicted. In the first 8 d, Eact equaled Epot, which resulted in a fast decrease of pressure head and water content in the upper horizon. Subsequently, Eact decreased exponentially and approached after 200 d Eact,min, which was mainly maintained by water vapor transport in the upper soil (Ritchie, 1972). During the same time, the ZFP moved downward. After 26 d of evaporation (Day 144), pressure head measurements detected the ZFP in 70-cm depth. From that time on, water fluxes were exclusively directed upward in the investigated soil block. Modeling results based on BVG agreed best with this and predicted the ZFP in 76 cm depth. With VG the ZFP reached a soil depth of 53 cm, while for MVG a soil depth of 40 cm was noticed after 144 d (not depicted).
After 200 d, water flows definitely upward in the investigated soil block. The prevailing evaporation rates are small due to small water contents and hydraulic conductivities. Thus, water content losses from the soil block are also small. The optimized hydraulic property parameters revealed for all approaches similar and quite accurate water content predictions with averaged deviations smaller than 0.5%. However, already after 141 d, the inverse problem was ill-posed, because pressure head measurements in the upper horizon were missing. After 177 d, even the pressure head measurements in the third horizon were stopped. Consequently, modeling results after 141 d were not brought to discussion.
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SUMMARY AND CONCLUSIONS |
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TOPEXECUTIVE SUMMARYABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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Measured SWRC gave evidence for the existence of at least two main pore size maxima. At h = –100 cm data suggested a third small pore size maximum, but which was not further considered in this study.
The BVG parameterization of Durner (1994) described best the measured retention data. Hydraulic conductivity functions, which were derived from the SWRC by using Mualems conductivity model (Mualem, 1976) also matched well independently calculated conductivity data (kIPM). Thus, also the best simulation results of the TFE were obtained with this approach.
The retention measurements of the investigated Acrisol could not be described properly with the unimodal MVG parameterization of Vogel and Cislerova (1988). Averaged deviations of predicted water content from measurements were more than double of those obtained with BVG. Nevertheless, both Ku(h) and TFE simulation results were still acceptable. If not enough measurements for sound parameterizations of bimodal SWRC descriptions are available, MVG is an acceptable alternative.
Even though the van Genuchten parameterization resulted in similar SWRCs, Ku(h) and TFE predictions, the underlying Ku(h) parameterizations near saturation were out of range of reasonable values. Unrealistically high Ks values were estimated due to the fine texture of the investigated Acrisol. Hence, in case of fine-textured soils optimized VG-Ks values should be considered as fitting and not as physical parameters.
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ACKNOWLEDGMENTS |
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TOPEXECUTIVE SUMMARYABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONSUMMARY AND CONCLUSIONSREFERENCES |
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