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DIVISION S-6-SOIL & WATER MANAGEMENT & CONSERVATION

Comparison of Inverse and Direct Evaporation Methods for Estimating Soil Hydraulic Properties under Different Tillage Practices

Institut National de la Recherche Agronomique, Unité d'Agronomie de Laon-Péronne, 02007 Laon Cedex, France

Corresponding author(richard{at}laon.inra.fr)

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIAL AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Tillage and traffic modify soil porosity and pore-size distribution, leading to changes in the unsaturated hydraulic properties of the tilled layer. These modifications are difficult to characterize although they can greatly affect evaporation. This study was conducted to compare field and laboratory methods for estimating the unsaturated hydraulic properties of two soils under different tillage practices. Soils freshly tilled, soils tilled 6 mo earlier that received winter rainfall (340–380 mm), and soils compacted by wheel tracks, were created in loess (Typic Hapludalf) and calcareous (Typic Rendoll) soils to obtain a wide range of soil bulk densities (1.0–1.6 g cm^-3). The Wind laboratory method (direct evaporation) was compared with an inverse modeling method applied to field measurements of water content and water potential during dry periods in spring. The soil samples were saturated with water from the top (full saturation) or from the bottom (partial saturation) before conducting the laboratory evaporation experiment. The Wind method overestimated water retention, except in the compacted soils, when the soil samples were initially fully saturated with water. On the contrary, there was good agreement between the Wind method and field data for tilled soils with a low bulk density when the samples were only partially saturated from the bottom. In that case, the hydraulic conductivity obtained with the Wind and the inverse modeling methods were similar. The Wind method can be used to estimate the unsaturated hydraulic properties of tilled soils, but care must be taken to saturate the soil cores with water: full saturation (saturation fraction of the total pore space >0.9 m³ m^-3) for the cores from compacted soils with a low structural void ratio (<0.3 m³ m^-3), partial saturation (saturation fraction of the total pore space around 0.7 m³ m^-3) for the cores from the tilled soils with a high structural void ratio (>0.5 m³ m^-3).

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIAL AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
ONE of the objectives of tillage is to manipulate the structure of the tilled layer to control evaporation when the soil is bare, that is, during crop establishment and the intercropping period. Linden (1982) used simulated data to show that the effect of soil bulk density on unsaturated hydraulic properties is very important for predicting changes in evaporation caused by tillage. However, the effect of tillage-induced soil structure on unsaturated hydraulic properties is still difficult to predict (Ehlers, 1977; Tamari, 1994; Horton et al., 1994). Several methods are now available to determine unsaturated hydraulic properties. Inverse modeling techniques (Kool et al., 1987) and various laboratory methods (Stolte et al., 1994) can be used. Inverse solution techniques are interesting because they can be applied to field evaporation experiments, but the identifiability, uniqueness and stability of the results are often questioned (Abbaspour et al., 1999). The Wind laboratory method (Wind, 1968) is a direct evaporation technique that provides estimates of retention and conductivity curves in the tensiometric range and is quite easy to use. It has been intensively studied in recent years (Tamari et al., 1993; Wendroth et al., 1993; Stolte et al., 1994; Morath et al., 1997; Simunek et al., 1998), but its results have not been compared with field estimations of hydraulic properties, particularly within the tilled layer. This method, like most laboratory methods, also requires prior saturation of the soil sample with water. This step is difficult to define because it must simulate field conditions of water-saturated soil, which are not well known (Wessolek et al., 1994). This study was therefore carried out to determine the unsaturated hydraulic properties of soils under different tillage practices, comparing an inverse modeling method applied to field data with the Wind method and several saturation strategies.

	MATERIAL AND METHODS

TOP ABSTRACT INTRODUCTION MATERIAL AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Tillage Experiment
Two field experiments were conducted in spring to obtain changes in water content due to evaporation, one in March through June 1995 for the loess soil and the other in March through June 1996 for the calcareous soil (the two main soils in northern France). The experiments were performed on a 750-m² field at the Research Centre of INRA, Mons en Chaussée (Somme) for the loess soil (Soil Type I), and at the Research Centre of INRA, Châlons (Marne) for the calcareous soil (Soil Type II). The loess soil (silt loam, Typic Hapludalf) was a Luvisol Orthique (FAO classification), whereas the calcareous soil (Typic Rendoll) was a Rendzina (FAO classification). The physical properties of the ploughed layers are shown on Table 1. Four soil samples were taken to be sure of the textural homogeneity of the field in each experimental site.

Soil Property Measurements
The dry bulk density profile was measured using a gamma probe with six replications per treatment. Measurements were made every 5 cm in the 5- to 30-cm layer. The total void ratio (e) at a depth (z) was calculated as a function of soil bulk density () and soil particle bulk density (_s) using the formula

(1)

The soil particle density was established for each treatment in the laboratory using a pycnometer with four replications per treatment (Table 1). Within the total pore space, the structural pore space was distinguished from the textural pore space as proposed by Monnier et al. (1973) and Fiès and Stengel (1981). The structural pore space results from the arrangement of structural elements created by tillage and weathering, while the textural pore space results from packing of the elementary particles. The structural void ratio (e_S) was calculated with the following formula:

(2)

where e_t(w) is the textural void ratio for the gravimetric water content w measured at the same time as the bulk density. The textural void ratio was measured as a function of soil water content on calibrated aggregates (2–3 mm diam.) by the method of Monnier et al. (1973). The volume of the aggregates at each water content was measured in kerosene using Archimedes' principle.

Changes in soil profile gravimetry water content were measured at 2- to 3-d intervals during dry periods between March and June. Measurements were made every 1 cm in the 0- to 5-cm layer and every 5 cm in the 5- to 30-cm layer (6 replications per layer). The water ratio () and volumetric water content () were calculated from the gravimetric water content (w), soil particle bulk density (_s), bulk density measurements (), and water density (_w) using the expressions

(3)

(4)

Changes in water potential profiles were measured daily using tensiometers (13-mm diam.; Objectif K, Tours, France) equipped with mercury manometers installed at 2-, 5-, 10-, 17-, and 25-cm depths (3 replicates per depth). We considered the water content on a soil particle volume basis (e.g., water ratio), although it is not the most common method. The use of the water ratio allows the water content to be expressed on the basis of the same mass of soil, whatever the bulk density.

Field Assessment of Hydraulic Properties
The relationships between soil water matric potential (h) and soil water ratio was established from field data of pairs of values (h_i,j, _i,j), where the subscripts i and j refer to the depth and time, respectively. We used the mean water potential measurements and gravimetric water content within the same layer at the same time (e.g., tensiometers at 2, 5, 10, 17, and 25 cm and water content of the 1- to 3-, 4- to 6-, 6- to 15-, 15- to 20-, 20- to 30-cm layers, respectively). Data were fitted to the following analytical equation proposed by van Genuchten (1980) to describe water-retention properties

(5)

where S_e is the effective water content, h is the soil matric water potential (m), and (m^-1) and n are fitting parameters. S_e can also be expressed using volumetric water content or water ratio

(6)

where _r and _s denote residual and saturated water ratio, and _r and _s denote residual and saturated volumetric water content, respectively. For each soil, the four parameters _s, _r, , and n were estimated by minimizing the sum of square differences between the measured and calculated water ratio for each measured water potential.

The relationships between soil water content and hydraulic conductivity were obtained using field changes in water potential as a function of soil depth by inverting a mechanistic model that describes the water transfer within a soil. This model was described in Witono and Bruckler (1989). It is based on heat and mass flow theory in partially saturated porous media (Philip and de Vries, 1957). The corresponding equations for one-dimensional vertical flows are (see Witono and Bruckler [1989] for details)

(7)

(8)

where t is the time (s), z is the depth (m), T is the temperature (K), C_h is the capillary capacity, D_hh is the isothermal moisture conductivity (m s^-1), D_hT is the thermal moisture conductivity (m² s^-1), K is the hydraulic conductivity (m s^-1), C_T is the heat capacity (J m^-3 K^-1), D_vh is the isothermal vapor conductivity (m s^-1), * is the apparent heat conductivity (W m^-1 K^-1), is the specific mass of the water vapor (kg m^-3), and L is the latent heat of vaporization (J kg^-1).

The nonlinear partial differential equations of the model describing changes in water potential and temperature were solved by a Galerkin finite element method with 30 linear elements. Time steps (<600 s) were automatically calculated according to the magnitude of changes in temperature and water content. The model was applied to the 2- to 25-cm layer of each treatment during dry periods of several days. Boundary conditions consisted of the soil water potential and soil temperature measurements at 2 and 25 cm using a linear interpolation between two measurements. The initial conditions were obtained from field measurements. The 2- to 25-cm layer of each soil was described by its mean dry bulk density, thermal, hydraulic, and gas diffusion properties. Mean dry bulk density was deduced from field measurements (Table 2). Heat capacity and thermal conductivity were estimated using the models of de Vries (1963) as a function of soil water content, bulk density, and the thermal properties of quartz, clay minerals, organic matter, water and air given by de Vries (1963). Water vapor diffusion coefficient (D_v) was calculated as a function of the air-filled porosity (n_a) using the relationships of Bruckler et al. (1989)

(9)

where D₀ is the coefficient of diffusion of the water vapor in air.

(10)

The K() relationship was derived from the corresponding K() and the dry bulk density and particle density of each soil. The K() relationship was the only soil property unknown to run the model of heat and water transfer. Therefore, the four coefficients of the Eq. [10] were obtained by minimizing the sum of square difference between the observed values of water potential at 5-, 10-, and 17-cm depths during a 7-d dry period and the calculated water potential at the same depth (least-square fitting procedure, Marquart [1963]).

Direct measurements of hydraulic conductivity at the 5-cm depth were performed using a disc infiltrometer (TRIMS, Objectif K). Measurements at a water potential of -0.05 m were done with two disc diameters (8 and 25 cm), with five replicates per disc diameter. Hydraulic conductivity was calculated with the method of Scotter et al. (1982).

Laboratory Assessment of Hydraulic Properties
We used the laboratory method proposed by Wind (1968), which was recently evaluated by Tamari et al. (1993) and Simunek et al. (1998) from a theoretical point of view, and by Stolte et al. (1994) and Morath et al. (1997) from a practical point of view. It is an evaporation method based on the measurements of the water potential profile and the mean water content of a soil column during a free evaporation period. Sample weight and water potential profiles are recorded periodically. The water retention characteristics, described by a single curve of Van Genuchten (Eq. [5]), are determined by an iterative procedure. The water content of the compartments around each tensiometer at each measurement time is calculated from measured water potential and the estimated water retention characteristics. The mean water content of the soil core is calculated using the water content of each compartment. The four parameters describing the water retention curve are obtained by minimizing the sum of square differences between the observed and calculated water content of the core at each measurement time.

The hydraulic conductivity is calculated directly using Darcy's law

(11)

where q_z is the water flux density through the depth z (m s^-1).

The water flux density through depth z is calculated from decrease in water contents of the compartments

(12)

where q_z and q_z+1 are the water fluxes at two consecutive depths z and z+1 (z₀ and z_max correspond with the top and the bottom of the soil core, respectively), S (m³) is the change in water storage in a finite elementary soil layer having a surface S_col (m²) between times t and t + t. S is calculated from the soil moisture profiles given by the Wind algorithm as a function of the water potential profile. The water potential gradient (h/z) is estimated from a three-point approximation as a function of the change in water potential at three consecutive depths, z - 1, z, and z + 1, between two consecutive times of measurement, t and t + t (see Morath et al. [1997] for details). Hydraulic conductivity cannot be estimated near saturation because the hydraulic gradients are too small (Wendroth et al., 1993). Hydraulic conductivity was normalized to a temperature of 20°C according to the dynamic viscosity of liquid water (Morath et al., 1997). The method gives a set of pairs of (K_i,j, _i,j) estimates, where the subscripts i and j refer to the water potential probe depth within the soil core and time, respectively. This set of values is used to fit any hydraulic conductivity–water content relationship.

Soil cores must be saturated with water before conducting the evaporation experiment. Two methods of saturation of the soil cores were used. The first method (Method 1) consisted of applying a zero water potential to the bottom of the soil core for 1 wk and then progressively applying the zero water potential to the top of the soil core for 8 h. This procedure, which is generally adopted for laboratory measurements, leads to a high initial saturation fraction of the pore space. A second method was used in the most porous soils (Method 2). The zero water potential was only applied to the bottom of the soil core, in order to obtain a lower initial saturation fraction. After the saturation step, the bottom of the soil sample was waterproofed once free drainage of water had stopped. Then, five microtensiometers (2.2-mm diam., SDEC, Tours, France) were installed in the soil core, at 1, 2, 3, 4 and 5 cm below the top of the sample. Water potential and core weight were measured every 20 min. The experiment took 1 wk at a room temperature of 18 to 25°C. Each experiment was discontinued when the tensiometer at 1-cm depth indicated a water potential lower than -8 m. The maximum range of water potential applied for each sample was between -8 and -0.5 m. The hydraulic conductivity–water content relationship of a single soil core was described using the log-polynomial equation (Eq. [10]) combining all the compartments.

Several undisturbed cores (15-cm diam., 7-cm height), taken from the 5- to 22-cm layer, were used to characterize each soil (a total of 35 cores from the six soils). The retention curve obtained for each core was discretized every 0.1 m of water potential. A set of (h_l, _l) values was obtained, where the subscript l refers to a list of n values of water potential equally spaced. Then a van Genuchten curve (Eq. [5]) was fitted mixing the pairs of (h_l,k, _l,k) values obtained with the different soil cores, where the subscript k refers to the soil core, to obtain the mean retention curve of each soil. The mean hydraulic–water content curve of each soil was obtained by fitting a log-polynomial equation to the pairs of (K_i,j,k, _i,j,k) values obtained with the different soil cores, where the subscripts i, j, and k refer to the probe depth within the soil core, the time, and the soil core, respectively.

Comparison of the Methods
Coefficient of determination (r²) and root mean square error (RMSE) were calculated for the two methods used in each soil. The results of the field and laboratory methods were compared by calculating, for each soil, the mean difference (MD) and root mean square difference (RMSD) between the retention curve, or the hydraulic conductivity–water ratio curve, obtained with the field method and the different retention curves, or respectively hydraulic conductivity–water ratio curves, obtained from the Wind method.

(13)

(14)

where h_l is a list of n_k values of water potential in the range between -8 and -0.5 m with , k refers to the soil cores used for each soil and method of saturation, _F is the water ratio calculated from the retention curve fitted on the field data, _W,k is the water ratio calculated from the retention curve obtained from the soil core k with the Wind method. The mean difference and root mean square difference were calculated using the water ratio difference at a given water potential rather than the water potential difference at a given water ratio because the different methods could give totally different ranges of water ratios.

(15)

(16)

where _l is a list of n_k values of water ratio in the range of water ratio measured during the field experiment with , K_F is the hydraulic conductivity calculated from the equation obtained with the inverse method on the field data, K_W,k is the hydraulic conductivity deduced from the Wind method on soil core k.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIAL AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Ploughed Layer Structure
Significant increase of bulk density, or decrease of void ratio, was obtained after soil compaction due to field traffic (Table 2). The difference in bulk density between compacted plots (IA and IIA) and fall-tilled plots (IB and IIB) was 0.4 Mg m^-3 in the two soil types. A structural void ratio nearly zero was obtained in the compacted loess soil (IA). The calcareous soil was more porous than the loess soil before compaction, and the structural void ratio remained 0.3 m³ m^-3 in the compacted calcareous soil (IIA). Bulk density of the fall-tilled soils (IB and IIB) was only slightly higher than that of the spring-tilled soils (IC and IIC), indicating that winter rainfall had little effect on soil structure in the two soil types (the crust formation at the soil surface was not taken into account in this study). The mean bulk density of each soil calculated from the bulk density of soil cores used for the Wind method was essentially the same as that obtained from field measurements (Table 2): there was no bias in sampling the soil cores for the Wind method, except for soil IIC.

Water Retention Curve
Field Method
The four parameters of the van Genuchten curve (Eq. [5]) fitted to the set of pairs of values (h, ) obtained in each soil (Fig. 1) are given on Table 3. Higher variation of the water retention properties was obtained in the compacted soils (r² between 0.51 and 0.63) than in the tilled soils (r² between 0.83 and 0.93) in spite of similar variation coefficients of the bulk density. The root mean square error, which has the same unit as the water void ratio, was lower than 0.011 m³ m^-3 in the six soils. The fitted saturated water ratios (Table 3) were much lower than the total void ratios (Table 2), particularly in the tilled soils, because of the lack of field measurements near saturation.

View larger version (33K): [in this window] [in a new window]   Fig. 1. Relationships between water ratio and water potential in the six soils. Field data of simultaneous measurements of water potential and water ratio during dry periods at different depths (2, 5, 10, 17, and 25 cm) (filled diamonds). Retention curve (Eq. [5]) fitted to field data (one fitted curve per soil) (thick line). Retention curve obtained with the Wind method after full saturation (Method 1) (one curve corresponds with one soil core) (thin line). Retention curve obtained with the Wind method after partial saturation (Method 2) (one curve corresponds with one soil core) (line with plus signs)

View larger version (15K): [in this window] [in a new window]   Fig. 2. Change in core mean water ratio measured during a Wind experiment (squares) or simulated (line) after fitting the water retention curve using the Wind algorithm

View this table: [in this window] [in a new window]   Table 5. Mean difference (MD, Eq. [13]) and root mean square difference (RMSD, Eq. [14]) between the retention curve obtained with the field method and that obtained with the Wind method after full saturation (Method 1) or partial saturation (Method 2) of soil cores

Hydraulic Conductivity Curve
Field Method
Table 6 gives the parameters of the log-polynomial equation for the six soils obtained by minimizing the difference between the measured water potential at different depths during a dry period in the field and the corresponding simulated change in water potential. Figure 3 illustrates the change in observed and calculated water potential after fitting the hydraulic conductivity–water content relationships in soil IB. The correlation between the measured and simulated water potential within the tilled layer during a dry period was always high in the six soils (>0.95, Table 6). The root mean square error, which had in this case the same unit as a water potential, was always <0.2 m. Using the same model of water and heat transfers, Witono and Bruckler (1989) showed the very great sensivity of this model to hydraulic properties and its lower sensivity to thermal properties or water vapor diffusion. Finally, a good agreement between observed and calculated water potential was obtained in the six soils in spite of the uncertainty of the thermal properties of each soil (estimated by the model of de Vries) and precise locations of the tensiometers and of water content sampling in the field conditions. Similar results were obtained by Chanzy and Bruckler (1994) calibrating the same model for change in water content in the 0- to 20-cm layer of loamy or clayey soils.

View larger version (20K): [in this window] [in a new window]   Fig. 3. Change in water potential with time at 2, 5, 10, 17, and 25 cm during a field experiment in the 2- to 25-cm tilled layer of soil IB or simulated at 5, 10, and 17 cm using the model of soil water transfer after fitting the relationships between hydraulic conductivity and water ratio (inverse field method)

View larger version (24K): [in this window] [in a new window]   Fig. 4. Relationships between hydraulic conductivity and water ratio obtained by the Wind method (same core as Fig. 2). Each point represents a pair of values (K, ) obtained with the Wind method from each depth at each measurement time. The solid line represents the log-polynomial curve after fitting

View larger version (24K): [in this window] [in a new window]   Fig. 5. Relationships between hydraulic conductivity and water ratio in the six soils. Relationships obtained by inverting the soil water transfer model (thick line). Relationships obtained from the Wind method after full saturation (Method 1) (each curve corresponds with one soil core) (thin line). Relationships obtained from the Wind method after partial saturation (Method 2) (each curve corresponds with one soil core) (line with plus signs)

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIAL AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
This study was done under field conditions to estimate the unsaturated hydraulic properties of tilled layers. We have compared the Wind method, an evaporation laboratory method that is quite easy to perform in the laboratory, with a field method based on measurements of soil water content and water potentials during dry periods. Both methods were used in the tensiometric range of water potential. The retention curve was directly established from field measurements while it was estimated by an inverse procedure using the Wind method. The hydraulic conductivity–water content curve was estimated by an inverse procedure using field measurements and directly with the Wind method. Two methods of saturating soil cores were tested before conducting the evaporation experiment in the laboratory: full or partial saturation. The results obtained by the field and Wind methods were consistent under our conditions if the saturation of soil cores, before conducting the Wind experiment, was adapted to the structural porosity of the soil. Full saturation of the cores (saturation fraction of the total pore space >0.9 m³ m^-3) for soils with a low structural void ratio (<0.3 m³ m^-3), partial saturation of the cores (saturation fraction of the total pore space around 0.7 m³ m^-3) for soils with a high structural void ratio (>0.5 m³ m^-3). A full saturation of the soil cores with a high structural porosity led to overestimation of the retention curve and underestimation of the hydraulic conductivity. These results confirm the usefulness of the Wind method for assessing soil hydraulic properties, as mentioned by Stolte et al. (1994), and emphasize the problem of saturation before performing laboratory measurements. Perhaps soil should be sampled in wet conditions and the laboratory evaporation experiment begun immediately without a saturation step to avoid this problem. This strategy would not reduce the range of water content for which the hydraulic properties can be estimated because the Wind method cannot be used to estimate the hydraulic properties near saturation.

	ACKNOWLEDGMENTS

 
The work was done as part of the requirements for the Ph.D. by J.F. Sillon and was partially supported by the Chambre d'Agriculture de la Marne and the Conseil Régional de Picardie. The authors thank O. Parkes and B. Lowery for checking the English text.

Received for publication April 20, 1999.

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