Published in Vadose Zone Journal 2:400-408 (2003)
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH PAPER
A Transient Evaporation Method for Determining Soil Hydraulic Properties at Low Pressure
Haruyuki Fujimaki*,a and
Mitsuhiro Inoueb
a Institute of Agricultural and Forest Engineering, University of Tsukuba, 1-1-1 Tennohdai, Tsukuba, Ibaraki 305-8572, Japan
b Arid Land Research Center, Tottori University, 1390 Hamasaka, Tottori 680-0001, Japan
* Corresponding author (fujimaki{at}sakura.cc.tsukuba.ac.jp).
Received 10 December 2002.
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ABSTRACT
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A two-stage laboratory method is presented for rapid estimation of the soil water retention function 
(
) and the hydraulic conductivity function K() from near saturation to air dry. The pressure head, h, at the bottom of an initially saturated soil core was stepwise decreased whenever the outflow rate had essentially ceased. After attaining this near-equilibrium at = -160 cm, the bottom boundary was sealed, the soil surface was uncovered, and the evaporation rate at a controlled constant temperature was measured. The () was determined by curve-fitting of the equilibrium outflow and psychrometric data obtained from soil samples after evaporation, while the K() was estimated inversely using cumulative evaporation amounts and the final water content profile. The simulated cumulative evaporation and final water content profiles from the optimized parameter values agreed well with the measured data. The root mean square errors for evaporation and the final water content profile were less than 0.022 cm and 0.011, respectively. In addition to close agreement with the simulation, agreement with independent K() data obtained from a steady-state, direct method confirm the reliability of the method presented here.
Abbreviations: SDFM, steady-state downward flow method • SEM, steady-state evaporation experiment • TEM, transient evaporation method
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INTRODUCTION
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KNOWLEDGE OF SOIL hydraulic properties that consists of the soil water retention and hydraulic conductivity functions is a prerequisite for predicting solution transport in soils, as well as the evapotranspiration rate. Many methods for determining hydraulic properties have been developed since the early days of soil physics (Bruce and Klute, 1956; Gardner and Miklich, 1962). In the last two decades, several inverse methods that optimize parameters in predetermined soil hydraulic functions have been developed to make the measurements of hydraulic properties faster and less laborious. However, most inverse methods are limited to relatively wet ranges of the pressure head. Outflow methods (Kool et al., 1985; van Dam et al. 1994; Eching et al., 1994) for rapid estimation are restricted by practical considerations to pressure heads higher than approximately -1000 cm because a porous plate that remains saturated at these low pressures cannot have high conductivity. The applicable range of evaporation methods that use tensiometers (Tamari et al., 1993; Wendroth et al., 1993; Wessolek et al., 1994; Simunek et al., 1998; Romano and Santini, 1999; Richard et al., 2001) is also limited to pressure heads higher than about -700 cm.
Determination of the unsaturated hydraulic conductivity at a low pressure head (less than -800 cm in this study), where most existing inverse methods cannot be applied, is essential for predicting the evaporation rate from soil surfaces. However, most studies that have predicted the evaporation rate have used the predicted hydraulic conductivity function suggested by Campbell (1974) without sufficient verification (Camillo and Gurney, 1986; Mihailovic et al. 1993; Daamen and Simmonds, 1996; Yakirevich et al., 1997; Nassar and Horton, 1999). This implies that there is a lack of a suitable method for determining drying hydraulic conductivity functions at low pressures.
The Boltzmann transform method of Bruce and Klute (1956) or the sorptivity method of Dirksen (1979) give estimates of the hydraulic conductivity in the low pressure range during wetting. However, it is still uncertain whether hysteresis in the hydraulic conductivity in the low pressure range is negligible.
Arya et al. (1975) developed a hot air method for determining the water diffusivity in the low pressure range during the drying process. However, this method imposes an extreme temperature gradient that induces considerable water vapor flow that is not included in the analysis. Additionally, evaporation losses from hot samples during sampling can cause large errors. Nimmo et al. (1992) measured the hydraulic conductivity at low water contents from steady-state flow in a centrifugal field. Undesired compaction due to the centrifugal force is the chief limitation of this method. Mehta et al. (1994) applied the instantaneous profile method to an evaporating process with zero flux at the bottom of a column. They also considered isothermal vapor flow. This method yields a drying hydraulic conductivity function in the low pressure range within a reasonable time. However, the validity of taking the arithmetic mean of widely different hydraulic gradients between two adjacent sampling times has not been verified. Globus and Gee (1995) proposed a heat pipe method for estimating the hydraulic conductivity of moderately dry soil. This method relies heavily on the accuracy of the enhancement factor for thermal vapor flow, which is also difficult to determine.
The purpose of this study was to develop a relatively rapid laboratory method for determining drying soil water retention and hydraulic conductivity functions for a wide range of water contents, including nearly air-dry states. The experimental phase consists of two stages for a single soil core: a multistep outflow stage and an evaporation stage. The data analysis involves the inverse estimation of parameter values.
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THEORY
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The one-dimensional water balance equation in the combined liquid and gaseous phases is given by
 | [1] |
where is the volumetric water content (cm3 cm-3), t is the time (s), q
is the liquid water flux (cm s-1), qv is the water vapor flux (cm s-1), z is the depth (cm), and Sw is the sink term, which is zero in this study. The liquid water flux, q, is described by Darcy's Law:
 | [2] |
where K is the hydraulic conductivity (cm s-1), and is the pressure head (cm). Note that K does not contain a water vapor component. On the other hand, when the temperature gradient and osmotic potential are negligible, the water vapor flux, qv, can be expressed as follows (Campbell, 1985; Mehta et al., 1994):
 | [3] |
where a is the air-filled porosity (cm3 cm-3), 
is the tortuosity, Dva is the diffusion coefficient of water vapor in free air (g cm-2 s-1), 
v* is the saturated water vapor density (g cm-3), hr is the relative humidity, w is the density of water (0.997 g cm-3 at 25°C), Rv is the gas constant for water vapor (4697 cm K-1), and T is the temperature (K). We used a value of 0.66 for the tortuosity (Penman, 1940; Cass et al., 1984, Daamen and Simmonds, 1996). Dva is a function of temperature and can be described as (Kimball et al., 1976)
 | [4] |
v* is also temperature dependent and is given by (Kimball et al., 1976)
 | [5] |
hr can be calculated using the following equation, assuming thermodynamic equilibrium between the liquid and gaseous phases (Philip and de Vries, 1957):
 | [6] |
The evaporation rate, E (g cm-2 s-1), from soil surfaces may be described by the bulk transfer equation (Milly, 1984; Lascano and van Bavel, 1986; Daamen and Simmonds, 1996):
 | [7] |
where ra is the aerodynamic resistance (s cm-1), and subscripts "s" and "a" denote soil surface and air at the reference height, respectively. We tested the validity of the aerodynamic equation in a laboratory column experiment and found it to be valid for our experimental conditions.
The equations presented here were used in the inverse parameter estimation approach and in a steady-state method described below.
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MATERIALS AND METHODS
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Masa loamy sand (Udorthent) and Tohaku loam (Fulvudand) were used in this study. Both soils were taken from the Tottori prefecture, Japan. Results of particle-size analyses, bulk densities, and saturated hydraulic conductivities are presented in Table 1. The soils were well leached and air-dried before packing. All experiments described below were conducted at 25 ± 1°C. Saturated hydraulic conductivities were measured using the falling head method. In this study we used disturbed soil samples to enable comparison with other methods.
Transient Evaporation Experiment
Each soil was packed as uniformly as possible to predetermined bulk densities in soil columns 3.8 cm in diameter and 5.2 cm tall. The walls of the columns were made of acrylic rings either 0.5 or 1.0 cm high, with small air-exit holes and a porous plate (5.0 mm thick) at the bottom. A thermocouple was inserted horizontally at a depth of 0.2 cm. Because slight shrinkage due to both desorption and evaporation was observed in the preliminary experiments, the soil was added such that the soil surfaces were raised to about 1 (Masa loamy sand) or 1.5 mm (Tokaku loam) higher than the top of the column wall. The hydraulic conductivity of the porous plate was 0.3 cm h-1.
Before the initiation of evaporation, a stepwise outflow experiment (i.e., hanging water method) was conducted to reduce the duration of the evaporation experiment and to obtain the retention data in the low suction range. Figure 1a illustrates the experimental setup in the outflow stage. The soil samples were initially saturated with distilled water from the soil surface at the flow rate of the saturated hydraulic conductivity for each soil to ensure leaching of the solutes while maintaining a pressure head of -160 cm at the bottom. When the wetting front arrived at the bottom, the pressure head at the bottom was increased to 0 cm. After near saturation, the pressure head at the bottom, bot, was decreased in steps to -10, -40, and -160 cm, each time lowering the dripping point after confirming that the outflow had practically ceased, as shown in Fig. 2. The criterion for changing bot was when the outflow rate decreased to below 0.5 mm d-1. The outflow amounts were measured by weighing the outflow reservoir with an electronic balance. To prevent balance fluctuation caused by wind and evaporation from the outflow reservoir, we placed a transparent curtain around all of the apparatus, and the humidity inside was kept high. Evaporation from the soil surface was prevented at this stage by covering the soil surface with a plastic bag.
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Fig. 1. (a) Experimental setup for the outflow stage; (b) experimental setup for the evaporation stage.
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After attaining near-equilibrium at bot = -160 cm, the soil sample and column wall were simultaneously removed from the porous plate using a sharp spatula, and placed on another foundation having an impermeable bottom boundary (Fig. 1b). The soil surface was then uncovered to start evaporation under conditions that were nearly constant, except for the radiation, which was automatically regulated using a thermostat so that the soil temperature remained constant and uniform at 25°C. Preliminary experiments showed that without a lamp, the surface temperature decreased to about 20°C, 5°C lower than air temperature. The porous plate was removed and the lower boundary was made impermeable at this stage. Evaporation was prompted by blowing air across the soil surface with an electric fan. The wind velocity and the relative humidity of the ambient air are listed in Table 2. The outside of the column was wrapped with 2.0-cm-thick polystyrene foam for heat insulation and a doughnut-shaped brim was placed around the top so that air would flow smoothly over the soil surface. The white, doughnut-shaped brim was made of polyvinyl chloride, and was 1 mm thick and 45 mm wide.
The evaporation amounts were manually measured with an electronic balance. It was expected that the relative humidity just above the soil surface would not be uniform since the water vapor evaporated from the upstream surface is transported downstream. For this reason, the columns were manually turned 180° at every weighing. After the evaporation rate had decreased to below 10% of its constant rate stage, the soil core was sectioned to determine the water content profile. These water contents were determined by oven drying at 105°C. The durations from the initiation of the outflow until sampling were only 17 h for the Masa loamy sand and 30 h for the Tohaku loam.
The water content profiles are shown in Fig. 3. Six soil samples taken from 0.5-cm depth increments in the upper 3 cm were placed in a thermocouple psychrometer (SC-10A Decagon Device Inc., Pullman, WA) to measure the water potential, to be used as the retention data. Since it is difficult to completely leach solutes, the electrical conductivities of the 1:20 soil/water (w/w) solution extracts of the soil samples were measured, and osmotic potentials were subtracted from the water potentials, assuming that the solute was sodium chloride. The osmotic potential, o (cm), of a dilute solution can be estimated from van't Hoff's Law:
 | [8] |
where is a unit-conversion factor (10.2 cm kg J-1), 
is the number of ions per molecule (i.e., two for NaCl), c is the concentration of the solute (mol kg-1), R is the universal gas constant (8.31 J mol-1 K-1). Concentration in the 1:20 solution, cdil, was converted to that in the soil solution, c, from the following mass relationship:
 | [9] |
where ms is mass of soil particles placed in the chamber of the thermocouple psychrometer, and b is the bulk density of the soil. The left-hand side of the above equation represents the mass of solute in the sample placed in the chamber, and the right-hand side expresses that in the diluted solution. Table 3 presents the estimated osmotic potential values from electrical conductivity of the 1:20 diluted solution, indicating the osmotic potential is not negligible even if preliminary leaching was conducted, and thus highlights the importance of preliminary leaching.
Steady-State Evaporation Experiment
To check the reliability of the hydraulic conductivity function determined with the method presented, steady-state evaporation experiments (SEMs) for measuring hydraulic conductivity under low pressures were performed. Each soil was packed as uniformly as possible to a predetermined bulk density in soil columns 3.8 cm in diameter and 15.0 cm high with a hypodermic needle and small air-exit holes at the bottom. The outlet of the hypodermic needle was located at the center of the ring. Distilled water was applied to the soil surface at the flow rate of the saturated hydraulic conductivity for each soil to ensure leaching of the solutes. Shrinkage of a few millimeters occurred for both soils during the infiltration. The Masa loamy sand was refilled to the top of the column wall. Because additional shrinkage during evaporation was expected for the Tohaku loam, soil was added such that the soil surfaces were raised to about 1 mm higher than the top of the column wall. After saturation, the soil surface was uncovered to start evaporation under conditions that were nearly constant, except for the radiation that was automatically regulated for the same reason as in the two-stage experiment. At the same time, a continuous and steady injection of distilled water into the bottom was started using a peristaltic pump at a constant rate of 10.2 mm d-1 for the Masa loamy sand and 11.9 mm d-1 for the Tohaku loam. The wind velocity and the relative humidity of the ambient air are listed in Table 2. The outside of the upper 5 cm of the column was wrapped with 2.0-cm-thick polystyrene foam for heat insulation, and a doughnut-shaped brim was placed around the top. A thermocouple was inserted horizontally to a depth of 0.2 cm.
Some time after the start of each run when the soil surface was sufficiently wet to meet the atmospheric evaporation demand (which exceeds the water supplement rate), the column weights decreased linearly with time. The evaporation rate then decreased as the pressure head at the soil surface dropped until the evaporation rate equated the water supplement rate. An end to the decrease in column weight meant the establishment of a steady state. When the decrease had nearly leveled off, the soil column was sectioned to measure the water content profile. The water contents were determined by oven drying at 105°C. The water content profiles are shown in Fig. 4. The total shrinkage for the Tohaku loam was about 2 mm. Deformation to this extent does not violate the assumption of a rigid porous medium invoked in the water flow equation (Eq. [1]). Sampling increments were 0.5 cm in the upper 3 cm and 1.0 cm in the lower 12 cm. The durations from the initiation of outflow until sampling were 45 h for the Masa loamy sand and 120 h for the Tohaku loam.
Steady-State Downward Flow Experiment
Hydraulic conductivities at higher water contents ranging from saturation to a pressure head of -200 cm were measured by the steady-state downward flow method (SDFM; Klute and Dirksen, 1986). Tensiometers were inserted horizontally into a 25-cm-high soil column at depths of 10 and 20 cm. Water was applied with a peristaltic pump while negative pressure was applied through a porous plate at the bottom. The hydraulic conductivities at the average pressure heads between the pair of tensiometers were obtained under nearly unit hydraulic gradients at successive steady-state conditions during drainage from saturation. Pressure gradients were obtained by linear approximation of the tensiometer readings. The retention curves determined with the two-stage experiment were used to convert from pressure head to water content.
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DATA ANALYSIS
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Soil Water Retention Function
The soil water retention functions were determined independently by curve fitting the retention data. In the low suction range, retention data were obtained from the near-equilibrium outflow data at successive pressure steps, assuming that hydraulic equilibrium was attained when the outflow had materially stopped. In the low pressure head range, the retention data were obtained with a thermocouple psychrometer from the six samples in the upper 3 cm, except for several samples that were too wet for determination of the water potential with the thermocouple psychrometer. These data are plotted in Fig. 5.
The empirical equation used to describe the soil water retention curves is
 | [10] |
where is the volumetric water content, is the pressure head (cm), sat is at = 0, and 
, 
, n, and m are fitting parameters. 0 is the pressure head where becomes nearly zero (i.e., oven dry) if [(1 + (-0)n)]-m 
0. In this study, 0 was set to -107 cm and m was handled as an independent fitting parameter. This equation is a modification of the retention function by Mehta et al. (1994), such that becomes nearly zero at = 0 and the water capacity becomes zero at = 0.
The curve fitting was accomplished using the Levenberg–Marquardt nonlinear method (Marquardt, 1963). Average water contents at bot = 0 cm were used as initial estimates of sat. The initial was set at the average at a depth of 2.5 to 3.0 cm at the final sampling. The initial estimates of and n were iteratively determined with the bisection method so that the function satisfies two retention data ( at = -42.6 and -162.6 cm) obtained from the outflow stage with m = 1 - 1/n. Figure 5 shows the fitted curve using this equation. The fitted curves are in excellent agreement with the retention data. Table 4 lists the parameter values. Note that the sat values of the soils were lower by several percent than their porosities. This may be because of the initial wetting from the top and immediate start of outflow after "saturation," leaving a nonnegligible amount of entrapped or dissolved air. However, disagreement between sat and porosity is often reported even if the initial wetting was conducted from the bottom and the soil samples were kept near = 0 for several days (Wessolek et al., 1994; Hollenbeck and Jensen, 1998; Richard et al., 2001). Also, full saturation (i.e., sat = porosity) in the laboratory may be rather unrealistic (Campbell, 1985).
Campbell (1974) proposed that when the retention function can be described as
 | [11] |
where a and b are fitting parameters, the hydraulic conductivity can be predicted by
 | [12] |
where K is the hydraulic conductivity (cm s-1). This prediction scheme is widely used in evaporation studies (Camillo and Gurney, 1986; Mihailovic et al., 1993; Daamen and Simmonds, 1996; Nassar and Horton, 1999). To test the validity of this scheme on our soils, curve fitting with Eq. [11] was also performed with retention data, except for those at near saturation. The curve fittings were performed in two fitted pressure head ranges for each soil. For a narrower fitted range, good agreement was obtained for both soils. However, for a wider fitted range, the discrepancy increased for both soils, although only one pair of ( and ) was added to the fitting. The parameter values obtained are listed in Table 5.
Hydraulic Conductivity Function
After determining the water retention function, the parameter 
in Eq. [12] was inversely estimated using the golden section method (Press et al., 1989), combined with a one-dimensional numerical solution of the water flow equation. The objective function to be minimized in the algorithm is
 | [13] |
where j denotes the different sets of measurements, nj are the numbers of measurements within particular sets, wj,i are the weights associated with a particular measurement point (which are all set at one), pj,i* are the measurements of type j at time ti, pj,i() are the corresponding model predictions using , and 
j are the variances of the measurements of data type j. The coefficients (nj,, j)-1 are used as weighting factors to adjust for both the numbers of measurements and the measurement scales. In this study, type j = 1 was the cumulative evaporation, and j = 2 was the final water content profile. We did not include the outflow data in the objective function since the hydraulic resistance in the interface between the soil and the porous plate may neither be stable nor predictable (Gee et al., 2002). The value from Campbell's prediction scheme was used as the initial parameter and 0.1 times was used as the initial step for the initial bracketing search required in the golden section method.
The water flow equation (Eq. [1]) including isothermal vapor movement was solved by the finite difference method based on the mass-conservative iterative scheme proposed by Celia and Bouloutas (1990). Space increments, 
z, were set constant at 0.1 cm. Time steps were controlled automatically so that the number of iterations in each time step was around five and the maximum change of ln() in each time step was <0.693 [= ln(2)]. Since the outflow data were not used in the inverse parameter estimation, only the second (evaporation) stages were simulated. The initial conditions were thus the equilibrium pressure head profiles at bot = -160 cm. The lower boundary condition was zero flux, while the upper boundary condition was the atmospheric boundary condition where the evaporation rates at each time increment were calculated using Eq. [7].
The aerodynamic resistance, ra, was determined from the evaporation rate during the first hour using the bulk transfer equation, because the evaporation rate is nearly constant and relative humidity at the soil surface, hrs, is kept at approximately 1.0 for some time after the start of a run. The values were 0.45 s cm-1 for the Masa loamy sand and 0.43 s cm-1 for the Tohaku loam.
Steady-State Evaporation Method
If the water flux (q = q + qv), temperature, water content (or pressure head), and pressure head gradient are known at a particular depth, the hydraulic conductivity at that depth can be calculated by combining Eq. [2] and [3] and rearranging to
 | [14] |
In steady-state one-dimensional flow, water flux, the sum of liquid (q), and vapor flux (qv), at any depth is the same as the flux at the soil surface:
 | [15] |
where E is the evaporation rate (g cm-2 s-1). Since no tensiometer was used in this experiment, the pressure gradient in Eq. [14] was obtained from the water content gradient using the following relationship:
 | [16] |
The water content gradients were obtained by differentiating the following empirical equation that was used to fit the water content profile.
 | [17] |
 | [18] |
where aw, bw, cw, dw, and ew are empirical parameters. The fitted curves are in excellent agreement with the data shown in Fig. 4. The retention functions determined with the two-stage experiment (Eq. [10] and Table 4) were used in Eq. [16]. Because the retention function, Eq. [10], cannot be solved algebraically for the pressure head, the bisection method was used for converting water content to pressure head. The hydraulic conductivity data were obtained at each sampling boundary.
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RESULTS AND DISCUSSION
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Hydraulic Conductivity Function
Shown in Fig. 6 are the optimized hydraulic conductivity curves, K*(). Numerical solutions with fitted water retention functions and optimized hydraulic conductivity functions are shown in Fig. 7 and 8. The observed data and numerical solutions are in close agreement for both soils. The root mean square errors between the measured and optimized evaporations and final water content profile are presented in Table 6.
K*() agreed well with the hydraulic conductivity data from the SEM for both soils. This agreement with a contrast method (i.e., transient vs. steady state and indirect vs. direct) indicates the reliability of the transient evaporation method (TEM). Thus, the SEM can provide hydraulic conductivity in the low pressure range as well. The SEM invokes fewer assumptions than the TEM, such as the applicability of the bulk transfer equation or predetermined hydraulic functions. Also, the SEM is less laborious, since it does not require frequent manual weighing as in the TEM. Even if an automatic weighing device was introduced for the TEM, it might be expensive since the fan has to be stopped during weighing. However, the need for the peristaltic pump and its longer time consumption are shortcomings compared with the TEM.
Not only do the K*() values match the SEM data, but they are also in fair agreement with data obtained using the SDFM. These results indicate that even if hydraulic conductivities at higher water contents are not available, the interpolation between the optimized K() at low pressure and the saturated hydraulic conductivity may be reasonable.
Predicted hydraulic conductivity curves with = 2b + 3 are also shown in Fig. 6. We used the b values determined from narrower pressure head range fitting, which showed better agreement. While the predicted K() function is in excellent agreement with measured data for the Tohaku loam, it is underestimated for the Masa loamy sand data. However, if we use the b value from the wider fitted range, the predicted K() for Tohaku loam is also underestimated. The dependency on the rather arbitrarily chosen range where the retention data were included in the fitting may be a shortcoming of Campbell's scheme.
To investigate the sensitivity of the simulated evaporation rate and water content profiles under the soil regulated evaporation stage, the direct problem for the evaporation stage was solved using the underestimated (= 2b + 3) value for the Masa loamy sand. While the deviation of the predicted K() from the measured K() is not so large, numerical solutions of (= 2b + 3) apparently underestimate the cumulative evaporation amount in the latter stage under a reduced evaporation rate and overestimate the final water contents, as shown in Fig. 7 and 8. These large discrepancies indicate the high sensitivity of the simulated evaporation amount and water content profile to hydraulic conductivity in the low pressure range. Since the dependence of on b has not been calibrated within the range, more empirical studies are required to refine (b).
Usability of Outflow Data for Estimating Hydraulic Conductivity in the Wet Range
As mentioned above, outflow data were not used in the TEM. However, if this data could be used in the numerical inversion, output would be more reliable in the wet range. We thus tested the usability of outflow data for estimating hydraulic conductivity. The outflow stage is essentially the same as a version of the widely used multistep outflow experiment (van Dam et al., 1994).
The average water content in the soil sample at the end of the outflow stage and the cumulative outflow amount were used in the objective function. Space increments, z, were set to be constant at 0.2 cm. The initial conditions were that of hydraulic equilibrium with -5.2 cm at the soil surface. The upper boundary condition was set to zero flux, while the lower one was controlled by the pressure head, considering the bulk hydraulic conductance (0.6 h-1) of the porous plate and the subsequent tubing.
For the numerical inversion of the multistep outflow, the soil hydraulic functions were assumed to be described by the widely used equations presented by van Genuchten (1980), since its linkage of the parameter (m = 1 - 1/n) reduces the number of parameters to be optimized.
 | [19] |
 | [20] |
where r is residual water content and is an empirical parameter. Since this multistep outflow experiment did not use a tensiometer, the number of parameters should be reduced to enhance the uniqueness of each parameter. Therefore, the l was fixed at -1, which is the value suggested by Schaap and Leij (2000) found through an empirical method. Also, r was fixed at zero. Unlike the TEM, Ksat was also optimized.
The resulting retention curves are presented in Fig. 5, showing good agreement with those from equilibrium data. On the other hand, the determined K() were obviously smaller than those from the SDFM as shown in Fig. 6, although the fitted outflow agrees with observed data (Fig. 9). These results imply the existence of a hydraulic resistance in the soil–plate interface. Therefore, we could not use outflow data in determining K(). The optimized parameter values are listed in Table 7.
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CONCLUSIONS
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We presented a new laboratory method for determining drying soil water retention and hydraulic conductivity functions for a wide range of water contents, including near air dry. The experimental phase consisted of two stages for a single soil core: a multistep outflow stage and an evaporation stage. The durations from the initiation of outflow until sampling were <30 h under our experimental conditions. The retention function was determined by curve-fitting the equilibrium outflow and psychrometric data obtained from final soil samples, while the K() function is estimated inversely using the cumulative evaporation amounts and the final water content profile.
The determined K() functions were compared with data measured with the more reliable, but time-consuming, steady-state evaporation method. In addition to the excellent agreement between measured and simulated cumulative evaporation amounts and final water content profiles, agreements with data obtained from a steady-state, direct method confirm the reliability of the present method. A widely used K() prediction scheme by Campbell (1974) was also tested. For the two soils, the predicted K() gave fair agreement with the measured data, but numerical solutions with the K() deviated from the measured values for the loamy sand. This indicates the high sensitivity of the simulated evaporation amount to hydraulic conductivity and the importance of actual measurements.
Since the present method assumes that the soil is undeformable and the aerodynamic resistance is constant, it is not applicable for a highly shrinkable clayey soil. Also, in applying this method to sand, the preliminary multistep outflow procedure should be omitted, since low water content at the initiation of the evaporation experiment disables the determination of aerodynamic resistance.
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ABSTRACT
INTRODUCTION
