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Dipartimento di Agronomia, Selvicoltura e Gestione del Territorio, Università di Torino, 44, via Leonardo da Vinci, 10095 Grugliasco, Italy
Corresponding author (zavattaro{at}agraria.unito.it)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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–
function approach. The soil water content at saturation was not consistent with the total porosity calculated from measured bulk and particle densities. The water retention curve (RC) measured in the laboratory and the conductivity curve measured in the field were described using modified Campbell functions that were separately parameterized, and results were then compared. The optimized values obtained for the – curve were remarkably different from those for the K– curve. Considering the physical nature of a model and the measurability of its parameters as the basic requirements for extending model predictions to sites where validation cannot be provided, possible solutions are to derive all soil properties simultaneously on the same sample and/or with a cofitting procedure, to adjust the measured values of the soil properties to the functional values, in order to combine the measured soil properties with the code requirements, and to modify the code to allow a separate parameterization of the two curves.
Abbreviations: ID, internal drainage method • RC, retention curve • TI, tension infiltrometer
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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A common solution to the problem of searching for parameters is the use of empirical functions (pedotrans-fer functions) to relate the soil behavior to information that is easily obtainable through routine analyses, though the predictive capacity of these functions may be found to be acceptable only for certain types of soil or specific horizons. However, when a more precise description of phenomena is required, specific experiments should be carried out to derive physically based parameter values for model input. Specific measurements are needed to derive the hydrological characteristics of the soil, in particular the soil bulk density, the porosity, the RC, and the conductivity curve.
The applicability of a model lies in the assumption that such soil properties are measurable and can be described with simple coefficients that are consistent and obtainable through specific measurements. Unfortunately, linking all the information together to derive parameter values may not be straightforward. A possible reason for this is the distortion due to spatial variability of sampling. As several soil properties are (or are frequently approximated as) lognormally distributed (Hillel, 1980), the number of samples required to estimate the mean and standard deviation is in fact high. An inadequate sample size at field scale may result in a low predictive capacity of pure deterministic models (Addiscott and Wagenet, 1985). Another possible reason is the time dependency of soil properties. Not all measurements can be made at the same time, and long-term experiments may suffer from the approximation of extending in time information acquired only once. Some models, such as MACRO (Jarvis, 1994), include an option for changing the soil properties since specified dates in the simulation period. An important source of error in modeling is that, in the absence of local specific measurements, the user, in some cases, accepts the model default value as an input parameter; this often involves unquestioned assumptions, such as the soil particle density, or the pore-interaction parameter p in Campbell's conductivity equation. A certain degree of subjectivity is introduced by the user into nonmeasurable options (for instance the computation time step and the soil layer thickness). Brown et al. (1996) demonstrated, with a ring test performed by expert model users, that the subjectivity of values assigned to nonmeasured parameters may lead to very different model outputs. This also affects the reproducibility of model predictions.
The sampling scale is another crucial point, which often depends on the methodology used. Laboratory methods are possible only at the point or local scale. Sometimes it might seem unrealistic to try to measure soil hydraulic and biological parameters in the laboratory, on discrete and small samples, even though undisturbed (Hillel et al., 1972; Marion et al., 1994). Nevertheless, disadvantages such as the higher cost and the larger level of uncertainty due to the field conditions (because the measurement error is larger and the uncontrolled variables more numerous) may encourage laboratory experiments. It is well known that the scale at which measurements are made, fixed by the instrument used, should be the same at which the conceptual model used for interpretations was developed, and the same at which results are discussed (Cushman, 1986). Nevertheless, models based on the Richards equation and the convection–dispersion equation, which were developed on single-dimensional soil columns, are commonly applied at the field scale without verifying the underlying assumptions (Jury and Flühler, 1992; Corwin, 1996). Moreover, applications of physical deterministic models at an even larger scale, through the means of interpolations, or simply through the extension of point measurements to a whole soil mapping unit, are frequent in literature (Tiktak and van der Linden, 1996; Hack-ten Broeke et al., 1999). Some authors studied the impact of spatial variability on the model results (Finke, 1993; Djurhuus et al., 1999). More frequently, simpler water storage models have been used for regional estimates (Jansson and Andersson, 1988; Shaffer et al., 1995; Rogowski, 1999).
The precision required in measurements is high because when all the information on a soil is linked together, small measurement errors may multiply, add up with the inner approximations in the code, and lead to large overall simulation errors (Kemptorne and Allmaras, 1986; Mishra and Parker, 1989). Combining parameters found using various procedures to set up a model input file is a crucial step in modeling, although it is often poorly described in literature.
The objectives of this study were (i) to derive hydrological parameter values to input into a model applied at the plot scale, through the analysis of measured data—the LEACHM model (Hutson and Wagenet, 1992) was used as a case study, with the constraint of respecting the model assumptions and the code, as most of model users would do; (ii) to highlight possible inconsistencies and contrasts among parameter values obtained with various procedures; and (iii) to suggest some criteria for choosing the most suitable input values, respecting the physical meaning of the model as much as possible.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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1000 m apart, with no significant difference in elevation between the two sites (234 m above sea level). The Tetto Frati soil evolved on the inside of an ancient meander (now abandoned). The Molinasso soil is on the trace of another ancient meander that was abandoned as well and filled with sediments. The groundwater level is 6 m deep, with scarce seasonal variations, and has no or little influence on the water movement of the upper part of the soil at both sites (Zavattaro, 1998), as the deep coarse material in the subsoil suggests. Tetto Frati was cultivated with maize (Zea mays L.) for grain, while Molinasso was a permanent meadow.
The texture class at the surface is loam for both soils and ranged from sand to silt loam in deeper horizons. The particle-size distribution at each horizon is reported in Table 1.
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Soil Bulk and Particle Density
The soil dry bulk density was measured with the cylindrical sampler method (Blake and Hartge, 1986a). The cores were 50.4 mm in diameter and 50.0 mm high (100 cm3). The number of replicates varied between 2 and 20 (Fig. 1)
. Samples were taken in spring following both criteria (pedological horizons and 0.2-m grid). The particle density was measured with the picnometer method (Busoni, 1997; Blake and Hartge, 1986b) on samples from the laboratory analysis of the RC.
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– Relation) and the volumetric water content () was derived in the laboratory and in the field. Laboratory analyses were conducted in desorption, with a tension chamber and a pressure plate apparatus, following the methodology proposed by Klute (1986). Four undisturbed cylindrical soil samples (58 mm in diameter and 30 mm in height) were extracted, weighed at saturation and after equilibration at various pressures, and then oven-dried (105°C, 24 h) to determine the volumetric water content. Tensions of -1, -2, -5, and -10 kPa were achieved in a tension chamber, whereas pressure plates were used to measure the water content at 20, 33, 80, 200, 500, and 1500 kPa. Further details are reported in Zavattaro (1998).
Paired measurements of the soil volumetric water content and the corresponding matric potential were also determined in the field, for tensions within the working range of tensiometers. Eleven tensiometers were placed in a row in both profiles, every 0.2 m from 0.2 to 1.8 m in depth, and at 2.2 and 2.6 m. The gravimetric soil water content of a sample extracted with an auger was multiplied by a fixed value of the soil bulk density at each depth to obtain the volumetric water content. The bulk density values were those described above and reported in Fig. 1.
Deriving the Water Retention Function Parameters
A water retention function in the form proposed by Campbell (1974)( 1985) and modified by Hutson and Cass (1987) was used to describe the – paired data.
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s is the saturated water content, a is a shape parameter that was originally defined by Campbell as the "air entry value", b is a shape parameter, and the point of intersection of the exponential and parabolic curve (c, c) is defined and calculated as
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This is a two-parameter Brooks–Corey type function, with the residual water content set to zero. The modification by Hutson and Cass (1987) consists of describing the range near saturation with a parabolic curve, which encompasses the discontinuity at a potential greater than the air entry value of the original function.
The fitting procedure minimized the sum of the squared difference between the measured and predicted . The volumetric water content at saturation was set to the measured value and was not optimized.
K– Relation at the Soil Surface
The surface near-saturated hydraulic conductivity was measured with tension infiltrometers (TI) with a 148-mm-diam. bottom plate. The steady-state infiltration rate was measured manually at three different supply pressure heads (-10, -50, and -100 mm). A layer of fine sand 5 mm thick was applied to the soil surface, with an area equal to that of the infiltrometer, to smooth out any surface unevenness and to improve the contact between the infiltrometer and the soil (Jarvis and Messing, 1995; Zavattaro et al., 1999). Although some authors reported that the contact material may affect measurements, other studies confirm that the influence of the contact sand is negligible if the water permeability of the contact material is greater than that of the soil. For discussions see, for instance, Everts and Kanvar (1993) and Bagarello et al. (2000). The steady-state infiltration rate was converted to one-dimensional hydraulic conductivity following the method proposed by Ankeny et al. (1991). With this procedure, involving a linear interpolation between measurements, four pairs of K–h values at -100, -75, -30, and -10 mm were calculated. Four replicated measurements were carried out at Tetto Frati, three at Molinasso.
K– Relation in the Soil Profile
The instantaneous profile method (Watson, 1966; Hillel et al., 1972; Ahuja et al., 1980; Vachaud et al., 1990; Marion et al., 1994) was used to determine the soil hydraulic conductivity at various degrees of saturation. It is a direct inversion method based on the solution of Richards' equation with respect to K, during internal drainage. Field measurements of the hydraulic gradients and of the volumetric water contents are required.
The plot was submerged in water in order to saturate it to a great depth; then the soil water content and potential were recorded for 30 (Tetto Frati) and 44 d (Molinasso), until variations were negligible. The water potential was measured with the set of 11 tensiometers described above. At Molinasso, a second set of tensiometers, parallel to the first one and spaced 1 m, was used as a replicate. The water content was measured on soil cores extracted with an auger to a depth of 1.6 m, with two replicates. The gravimetric moisture was multiplied by the soil bulk density (Fig. 1) to calculate the volumetric water content. At depths >1.6 m, the soil water content was calculated from the matric potential through the laboratory water retention function.
Data analysis was conducted following the procedure described by Vachaud et al. (1990) and Reichardt et al. (1998), as a modification of the methods reported by Hillel et al. (1972) and Green et al. (1986). Further details can be found in Zavattaro (1998).
Deriving the Conductivity Function Parameters
A conductivity function was fitted to data both from the TI measurements and from the internal drainage experiment, with a least squares procedure. Campbell's K() function (Campbell, 1974, 1985)
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(where b is the power of Campbell's retention function, p is a pore interaction parameter, and Ks is the hydraulic conductivity at saturation), was calculated and converted into the form K() through the retention function modified by Hutson and Cass (1987). Consequently, the K() relation was continuous and expressed as a function of the three parameters a, b, and Ks. In the fitting procedure Ks, a, and b were optimized, whereas s was set to the measured value and p was set to the fixed value of 1.
In this study, the K() and the () curves were parameterized independently, and results were then compared.
The LEACHM Model
The LEACHM model (Hutson and Wagenet, 1992) was used as an example of a physically based, deterministic model that requires common values for the parameters of the retention and the conductivity curve. The constraint of respecting the model assumptions and the code requirements was followed in all data analyses.
It was developed to predict the movement and transformation of water, solutes, N, organic matter, pesticides, and microbial biomass in soils. The water section of the model solves, in one dimension, a finite-difference form of Richards' equation. The implemented water retention function is derived from Campbell's equation with the modification proposed by Hutson and Cass (1987), as mentioned above.
The conductivity function is the Campbell equation, which was also previously reported. The LEACHM model code allows one to use a paired K– value instead of Ks, which will be treated as a matching point for the conductivity curve. In this case, the Ks parameter is automatically calculated from the other parameter values at the matching potential.
The water content at saturation is not required as an input parameter, as it is calculated from the soil bulk density with the following formula
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Validation Data Set
The model prediction was compared with measured values of matric potential at various depths. The tensiometer sets were those that were described for the internal drainage experiment. They were manually monitored every 2 wk, from February 1996 (Tetto Frati) or July 1996 (Molinasso) to October 1997. Further details were reported by Zavattaro (1998).
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The soil bulk density varied in the two examined profiles, as reported in Fig. 1. Samples were taken at various occasions, therefore the number of samples at each depth may be different, as Fig. 1 shows. All sampling events occurred in spring, hence the error bars in the figure indicate the sum of time (max. 2 mo) and small-scale space variability (3–5 m).
In Tetto Frati (maize-cropped field), the bulk density was 1.40 Mg m-3 near the surface and increased to a maximum value of 1.52 Mg m-3 at 0.5 m in depth. This increase of 10% indicates a soil compaction that is probably due to tillage. The bulk density was stable around 1.30 Mg m-3 between 0.6 and 2.5 m, with a coefficient of variation of 2.6%, on average. Instead, the coefficient of variation in the tilled layer was higher, of 4.8%.
In Molinasso (in permanent meadow for several decades), the low bulk density near the surface (1.18 Mg m-3) may be due to the high organic matter content and to the incidence of macropores, especially earthworm (Lumbricus terrestris) channels, as both factors are typical of permanent meadows. At greater depths, data spreading along the profile and within replicates indicate a remarkable heterogeneity, which derives from the complexity of the river depositions on which this young soil evolved, with numerous lenses of contrasting texture. The variability was particularly large (coefficient of variance > 6%) at the 0.7- to 0.8-, 1.6-, and 2.0-m depths.
In both cases the measured soil bulk density was much lower than could be expected from the particle-size distribution analysis. For instance, using the pedotransfer function proposed by Baumer (1994) the estimated soil bulk density was 15 and 10% higher than the measured ones, as an average of all horizons in the two soils, respectively, whereas the pedotransfer function proposed by Rawls (1983) estimated values of 18 and 7% higher than the measured ones.
Volumetric Water Content at Saturation
The water content at saturation was directly measured on undisturbed cores 58 mm in diameter and 30 mm high (76.6 cm3). The results are reported in Table 2. The variability of s across four replicates ranged between 0.2 and 10%, with the larger dispersion in the tilled layer of Tetto Frati.
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s and the total pore space: (i) swelling, which also occurs to a lesser extent in coarse-textured soils; (ii) an underestimation of the dry weight for soil losses between weighing at saturation and after oven-drying, as the soil samples passed through a sequence of 11 wetting cycles in the tension and pressure apparatus; (iii) an overestimation of the weight at saturation due to a water film at the core surface and along the cylinder walls; and (iv) an incorrect measurement of the effective soil core volume. However, none of these hypotheses could exhaustively explain the mentioned discrepancy, which remained unsolved.
When the total pore space is estimated from the bulk density, the particle density is usually set to the conventional value of 2.65 Mg m-3, this being typical for quartz sand, but not appropriate for solid particles with a different mineralogical composition. Despite the large sand content in the examined soils, the average particle density along the profiles was in fact 2.79 Mg m-3, and was identical for the two soils (as they evolved on deposits with the same mineralogical composition), but significantly (P < 0.01) higher than the standard value. If the total porosity were estimated assuming the particle density to be equal to 2.65, it would be underestimated by 5%, on average (Table 2). In addition, discrepancies with the measured s would be even larger, with a difference varying between 0.03 and 0.14 mm3 mm-3 in the different horizons. An even greater underestimation of s would be obtained if the soil bulk density were calculated through the mentioned pedotransfer functions.
The method implemented in the LEACHM model to convert the bulk density into the saturated water content may account for the contribution of organic C and clay, which have a lower particle density than that of sand and silt. The estimation was smaller than measurements even when the measured particle density of mineral compounds was used, and that of the organic fraction was set to the default value of 1.10 Mg m-3. The difference ranged from 0.01 to 0.12 mm3 mm-3 (Table 2).
These observations have an important consequence: when the soil bulk density required in a model is used to calculate the water content at saturation, as in the LEACHM model, the estimated s may be quite different from the real one. If a direct measurement is available, but is not directly used as an input variable, such as in LEACHM, the code may be forced to use the measured s by using a functional bulk density calculated by rearranging the equation that relates the bulk density to s. Another possible correction is to adjust the particle density to a value so that the measured s is met. This deprives the modified input variable of its physical meaning, but preserves the physical nature of the model algorithms. This is of course possible only if the modified variable is not used in other subroutines of the code, in which case more severe errors may be caused. However, the simplest solution would certainly be to modify the code, but this may not be feasible for all model users.
As both the retention and the conductivity curves are expressed as a function of the relative saturation, an incorrect s may cause biased prediction of the soil behavior, especially near saturation, where the error on the ratio /s is proportionally greater.
In subsequent analyses, the reference value for s was that obtained from direct measurements.
– Relation
In most cases, a good agreement was found between laboratory and field determination of the – relation (Fig. 2 and 3)
, although the sampling criteria were different (every 0.2 m in the field method, and at the pedological horizons in the laboratory method). However, the agreement was better in shallow horizons than in deep ones. The soil cores used in the laboratory procedure were sampled in a narrow distance and within apparently homogeneous pedological horizons; hence the spatial variability explored was very limited. Nevertheless, some outlier samples were detected, such as at horizon Cg2 at Molinasso, as a consequence of the irregular layering of this soil.
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/s ratio >1 in some samples (Fig. 2 and 3). Another source of error in the field measurements might be the contamination of the soil core by the upper layers when extracting the auger, in particular when the soil was very wet and sampling was deep. This was probably the main reason why the agreement between field and laboratory measurements was better at shallow depths. In addition, the high scatter at horizon C2 in Tetto Frati could be explained if one considers that it corresponds with a sandy lens, and that field measurements were made during an infiltration–redistribution process. Water funneling into preferential channels in the sand (fingering) probably resulted in a remarkable horizontal heterogeneity in the soil moisture. Laboratory measurements were considered more reliable and were used for subsequent analyses. The corresponding water retention function parameters are reported in Table 3.
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), was used to describe the data. The results of the two soils are shown in Fig. 4
and the fitting parameters are reported in Table 4.
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No clear relation was found between the variability of the replicates and the supply water pressure head in the TI measurements. The coefficient of variation of the hydraulic conductivity (calculated for a lognormal variable according to Gilbert, 1987) increased from -100 to -10 mm of water pressure head in Tetto Frati, whereas it decreased at Molinasso. The largest variability was found in Tetto Frati at a pressure head of -75 and -100 mm, where the hydraulic conductivity ranged across almost one order of magnitude among replicates (Fig. 4).
Hydraulic Conductivity Function from the Internal Drainage Method
The ID was applied to both soils, but several difficulties were encountered. Neither of the two profiles was completely saturated in the experiment owing to technical reasons, therefore the data analysis was limited to a certain depth. The soil layering caused discontinuities in the soil behavior and complicated the data analysis. Good performances of this method have in fact been obtained in literature for shallow, fast-draining soils, with scarce layering and after complete saturation has been achieved.
The profile of the hydraulic head for selected dates and for both soils is shown in Fig. 5a and 5b .
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The coefficient of variation for the water content data ranged from 0 to 29% and was larger at the beginning of the recording period, when the soil moisture rapidly changed. This is noteworthy as these recordings are the most important, both because they have a higher relative influence on the interpolating function and because their physical relevance is higher, as the soil behavior in the near-saturated range greatly affects the water flow.
The Campbell conductivity equation was fitted to paired K–h data, optimizing the three parameters Ks, a, and b independently from the retention function discussed above. The resulting conductivity at saturation in the Tetto Frati soil was 71 mm d-1 near the surface and increased with depth to 1000 mm d-1 at 1.3 m in depth (Fig. 4 and Table 4). The increase of Ks of about one order of magnitude contrasted with the substantial homogeneity of the particle-size distribution and of the RCs in the same interval.
In Molinasso, the water content of all the soil layers decreased in time during the experiment. Already at the beginning, the soil layers between 1.0 and 1.8 m showed a tendency of reaching a zero-gradient equilibrium over the depth of 2.2 m (Fig. 5b). In contrast, a strong gradient remained, during the whole recording period, between 2.2 and 2.6 m in depth. This can be explained by the particularly low hydraulic conductivity of horizon Cg4 between 2.0 and 2.5 m in depth (see Table 4), and by the sharp texture discontinuity with the coarse and stony subsoil, which created a perched water body. Such impediments reduced drainage and slowed down the loss of water from the upper horizons.
The two series of tensiometers in Molinasso recorded quite different redistribution patterns, although they were spaced only 1 m apart. The coefficient of variation between the two replicates of the hydraulic head was even 320%, while the variability in measurements was higher than at Tetto Frati, ranging from 0 to 40%.
Falleiros et al. (1998) reported that variations in with a maximum of 5.4% led to CVs of up to 170% in the estimation of the soil hydraulic conductivity. Hence, the results obtained at both sites, but in particular in Molinasso, may be questionable because of the remarkable horizontal variability.
The conductivity at saturation (Table 4) was higher near the surface (20 mm d-1) and lower at the deepest Cg4 horizon (0.5 mm d-1), and in general was two orders of magnitude lower than at Tetto Frati. The marked difference between Tetto Frati and Molinasso, in both the retention and the conductivity curves, notwithstanding their rather similar texture class, origin and age, was probably due to different depositional patterns in the meander plain, which favored the deposition of finer particles in the Molinasso site.
At both sites the gradient remained significantly different from unity throughout the internal drainage process. Therefore, simplifications in data analysis proposed by several authors (Black et al., 1969; Libardi et al., 1980; Chong et al., 1981; Vachaud et al., 1990) based on the unit-gradient assumption, could not be applied. Ahuja et al. (1988) found that appreciable discrepancies resulted from the approximation of the unit-gradient in the complex layered profile they studied. In particular, larger errors were observed in the part of the curve that has greater influence on water flow, that is, at low suctions. Reichardt (1993) and Reichardt et al. (1998) also criticized the unit-gradient assumption, from a theoretical point of view, when applied to layered and nonhomogeneous profiles.
Comparison of the Hydraulic Conductivity in the First Two Layers
The relation between the water pressure head and hydraulic conductivity from the TI measurements at the soil surface was compared with that derived from the internal drainage experiment for the soil layer between 0.2 and 0.4 m. The results are shown in Fig. 4.
In Tetto Frati, the difference between the two layers in the near-saturated range was about one order of magnitude, that is, the same variability that was observed for replicated measurements with TIs at a supply pressure head of -100 mm. The hydraulic conductivity at saturation, extrapolated from the fitting curve, differed by less than one order of magnitude. It was in fact 350 mm d-1 for the surface layer and 71 mm d-1 for the 0.2- to 0.4-m horizon. The difference between the two layers was not high, if one also considers that the data were obtained using methods based on different principles and have a measurement scale that is slightly different (Cushman, 1986).
In Molinasso, the hydraulic conductivity at the soil surface was similar to that of the 0.2- to 0.4-m layer in the drier range (potentials smaller than -100 mm), but large discrepancies were found near saturation (Fig. 4). The extrapolated hydraulic conductivity at saturation Ks was 1383 mm d-1 at the soil surface and 20 mm d-1 for the 0.2- to 0.4-m layer. The difference between the two layers was more marked in the non-tilled permanent meadow soil than in the Tetto Frati tilled soil.
Combining the Water Retention and the Conductivity Function Parameters
Campbell's a and b values obtained from the () and the K() curves are summarized in Tables 3 and 4. Large differences were observed in parameter a, which originally, in Campbell's approach, is the air entry value and is generally smaller (in absolute value) in porous media with larger pores. The absolute value of a from the conductivity curve was smaller than that from the RC in all the horizons of both soils. Such a discrepancy may be due to the fact that the two characteristic curves were derived in different ranges of tensions. The RC was in fact explored in the 0.1 to 1500 kPa range, while the conductivity curve was explored between 0 and 15 kPa, with the ID, and between 0.01 and 0.1 kPa, with the TI method. In other words, and with the terminology of geostatistics, the two measurements have a different support. Both a and b parameter values at the surface layer of the two soils were rather similar when derived from the conductivity measurements, but were different when derived from the RC. Notwithstanding the limitations due to the use of different methods, this would suggest that the behavior of the two soils was more similar in the near-saturated range (namely in the macropore system) than in the dry range (the micropore system).
Although K() and () were considered in this study as being independently parameterized, the two curves may be expressed in terms of the same a and b parameters. If this holds theoretically, several studies have shown that parameters that better describe the retention function are not necessarily appropriate for the conductivity curve (Yates et al., 1992; Messing, 1993; Jarvis and Messing, 1995), especially when the hydraulic conductivity is measured in the near-saturated range, and the RC in a wider range of tension, as frequently occurs in laboratory analyses. Nevertheless, most hydrological models favor simplicity and require only three parameters to predict water flow. The LEACHM model is in this group, while AdHydra (Ferraris, 1997) is an example of a model that may use five parameters to describe the K–– relation.
If the parameter values from the RC are used to describe K(), such a calculated curve may deviate from experimental data. Two examples are provided in Fig. 6a and 6b
. In the former, the conductivity curve calculated using the parameter values from the RC was compared with that using the parameters from TI measurements in the surface layer. In both cases, the Ks was that from the TI measurements (Table 4). The discrepancy between the two curves was remarkable, and this suggests that the experimental K() cannot be properly described with the parameters that optimize (), either in Tetto Frati or Molinasso. This observation indicates that the model code could be modified so that the two characteristic curves may be independently parameterized when a measure of the soil conductivity in a certain range of tensions, and not only at saturation, is available. Another possibility is to adjust parameters used as inputs to optimize the model performance.
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paired datum may be declared as a matching point to calculate the Ks parameter. This may be used to adjust the RC to the TI curve within a certain range. An example of shifting the matching point from saturation to a potential of -75 mm is also shown in Fig. 6a. In this environment, the saturated condition is rather uncommon in soil, so a perfect match of a measured Ks (supposing that this is a stable and measurable soil property) would not be very important. Conversely, a more precise description of the near saturated range is recommendable. The matching point could then be used to calibrate or adjust the RC curve to the range of the TI curve that is thought to be the most important for a determined situation. This procedure is clearly far from satisfactory. Other possible solutions could be changing the code so that different parameters can be used for the K– and the – curves, or respecting the original code and measuring the RC and the conductivity curve only in the near-saturated range. Similarly, Fig. 6b shows two possible conductivity curves for the 0.2- to 0.4-m-deep layer. One was experimental and was obtained from the ID; the second was calculated using parameters from the RC with the same Ks as in ID. The similarity is remarkable, at least in the pressure head range between 0 and 1.0 m. In this case, shifting the matching point from saturation to a potential of -75 mm would not significantly modify the RC curve.
Example of Model Application
The LEACHM model was parameterized according to what was described above, and the predicted matric potentials were compared with measured values at the plot scale (Fig. 7)
. The model performance in the long period was rather good in Tetto Frati at all depths and potential ranges. On the contrary, in Molinasso the model prediction was acceptable in deep layers, but poor near the surface, where the simulated matric potentials were much smaller than measured. According to Zavattaro (1998), this was due to the fact that the hydraulic conductivity at the soil surface (Fig. 6, dotted line) correctly predicted the water supply to subsurface layers during flood irrigation, but it was too high when simulating the soil supply to the evapotranspirative demand. Consequently, in the first 0.4 m, the model predicted frequent drought conditions that were not recorded by tensiometers.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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In this study, the soil water content at saturation could not be completely predicted from the total porosity calculated from measured soil bulk and particle densities, and, in addition, the use of the standard particle density value led to biased predictions. Even larger errors would be introduced by the use of a pedotransfer function to estimate the soil bulk density. However, an accurate prediction of the soil total porosity might be of little practical importance if the soil seldom reaches saturated or near-saturated conditions in the period of interest for the simulation.
The RC was derived in the laboratory, and the conductivity curve in the field. The sampling method of the former was at pedological horizons, that of the latter at a fixed grid. The explored range of tensions was 0.1 to 1500 kPa in the RC, and 0 to 15 kPa in the conductivity curve. Moreover, the hydraulic conductivity was studied using two different methods, one (TI) applied at the soil surface, and one (ID) in the bulk soil. Notwithstanding the fact that all studies were carried out in a small plot, every measurement was valid at the local or point scale, and problems arose when they were all referred to the same soil column. The inconsistencies were partly due to a small-scale spatial variability, and partly to the different sample size (support) of the various methods. Consequently, the parameter values that produced the best fit with measured data in a methodology did not always match those from another method. More consistent results would probably be obtained if measurements were carried out (i) on a single sample, (ii) limited to the tension range of interest, and (iii) with a co-fitting procedure to match the whole K–– relation, such as in the Wind evaporation experiment (Wind, 1968). This would also encompass the problem of dealing with spatial variability; however, it would not necessarily improve model performance to meet an independent field data set for validation purposes.
We have shown that an adjustment may be required in measured soil properties to force the code to use a given value. For instance, the soil particle density can be adjusted so that the calculated total porosity will match the measured water content at saturation. Another example is the choice of a matching point for the hydraulic conductivity function so that the calculated conductivity curve will meet the measured values at a tension range frequently encountered in a given situation. Such adjustments, which preserve the integrity of the code, involve depriving the measured properties of their physical meaning, but should not be confused with a black-box calibration, as the aim of such adjustments is not to match an independently measured dataset (for instance a time series of soil water contents or matric potentials), but rather to combine the measured soil properties with the code requirements. Consequently, such a transformation of the model inputs can be applied a priori and is not necessarily site-specific.
Although these results confirm once again that the nature of parameters Ks, a, and b in Campbell's functions is numerical rather than physical, we think that model results can be used for practical applications and in the absence of validation only if the model is physically based and the input parameters are measurable. Consequently, objective solutions are necessary to fill the gap between the measurements of soil properties and the compilation of a model input file.
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ACKNOWLEDGMENTS |
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Received for publication May 5, 2000.
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