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DIVISION S-1-SOIL PHYSICS

Measurement of Hydraulic Properties During Constant Flux Infiltration

Field Average

^a Land Resource Dep., Univ. of Guelph, Guelph, ON N1G 2W1 Canada
^b College of Graduate Studies and Research, Univ. of Saskatchewan, 3 Campus Drive, Saskatoon, SK S7N 5A4 Canada

gary.kachanoski{at}usask.ca

	ABSTRACT

TOP ABSTRACT INTRODUCTION Theory Materials and methods Results and discussion Summary REFERENCES

 
Accurate measurement of in situ soil hydraulic properties is important for developing, testing, and applying water and solute transport theory. A method of measuring hydraulic conductivity (K), soil matric pressure head (), and water content () relationships is presented. The procedure uses a series of multipurpose time domain reflectometry (TDR) probes that measure both and . The TDR probes are installed vertically and measure the rate of change of local soil water storage (q) along the probe during constant rate water application. The values of q are equal to local soil water flux, and assuming unit gradient, are set equal to K at the steady state and measured at long times. The measured values of K, , and from different water application rates are combined to obtain average K() and () functions. To test the procedure, multipurpose TDR probes were installed vertically in a sandy soil every 0.15 m in a 7.5-m-long transect for a total of 50 probes per depth. This was repeated in parallel transects 0.1 m apart for four depths (0.2 m, 0.4 m, 0.6 m, 0.8 m) and a total of 200 probes. Six different water application rates were applied with subsequent drainage. Average K() and () functions were obtained and used in an analytical solution for constant rate infiltration. Transient water storage changes were accurately predicted for all application rates.

Abbreviations: GP, Guelph permeameter • GPI, Guelph pressure infiltrometer

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Theory Materials and methods Results and discussion Summary REFERENCES

 
Accurate field measurements of soil hydraulic properties are necessary to understand water balance, irrigation, movement of chemicals, and, more generally, transport processes occurring in surface soils. Analytical solutions of Richards' equation for constant flux water infiltration into homogeneous soil profiles have been developed using integral procedures (Parlange, 1972; Philip and Knight, 1974; White et al., 1979), Kirchhoff, Hopf-Cole, and Storm transformations (Broadbridge et al., 1988; Broadbridge and White, 1988; Warrick et al., 1990), and by reciprocal Bäcklund transform (Sander et al., 1988; Barry and Sander, 1991). These analytical solutions are very useful for assessing the accuracy of numerical models and estimating soil hydraulic properties by inverse procedures (Broadbridge and White, 1988). Analytical solutions can also be used to test inverse techniques for nonuniqueness and identifiability of hydraulic parameters of interest.

Significant advances have recently been made in the measurement technology for field infiltration experiments. Time domain reflectometry is potentially useful for measuring both volumetric water content (Topp et al., 1980) and vertical solute mass flux in a nondestructive and rapid fashion during field infiltration experiments (Kachanoski et al., 1992). Vertically installed TDR probes measure the volume-averaged water content or the water storage from the surface to bottom of the probes. Parkin et al. (1992, 1995a) presented quasi-analytical solutions for cumulative water storage in a fixed depth of soil by integration of the parametric water content–depth relationships presented by Broadbridge and White (1988) for constant flux infiltration and those demonstrated by Warrick et al. (1990) for drainage. However, the solutions require particular forms of the hydraulic conductivity vs. water content () function, K(), and diffusivity function, D().

Parkin et al. (1995b) used TDR probes installed vertically at the soil surface beneath a constant-rate rainfall simulator to measure cumulative water storage with time. They estimated the local infiltration rate from the slope of water storage vs. time during early time, before the wetting front reached the bottom of the TDR probe. Assuming a unit gradient and utilizing the spatial variability in local infiltration rate, they directly estimated the unsaturated hydraulic conductivity for a wide range of water contents, using only two water application rates. However, they also concluded that unique estimates of K() and () functions with three unknown parameters were not possible from measurements of only soil water storage with time. Additional measurements of are an obvious choice to reduce nonuniqueness. However, spatial variability may limit the usefulness of measurements taken at spatial locations different from the soil water measurements. Baumgartner et al. (1994) developed a soil water TDR probe that measures and soil water storage at the same horizontal location, yet the probe has not been used in field applications to our knowledge.

The objectives of this paper are to extend the method of Parkin et al. (1995b) to estimate not only the field average K(), but also the field-average water retention characteristic, (), during constant flux infiltration. In addition, utilizing the estimated field averaged parameters, we compare the solution of Parkin et al. (1992) to in situ measured values of soil water storage as a function of time during constant flux infiltration. The new multipurpose TDR probes of Baumgartner et al. (1994) were used in a field experiment with a rainfall simulator to fulfill the goals of the study.

	Theory

TOP ABSTRACT INTRODUCTION Theory Materials and methods Results and discussion Summary REFERENCES

 
Measurement of Unsaturated Hydraulic Properties
The cumulative storage of water (m³ m^-2) to depth L, W(L,t), is measured by vertically installed TDR probes and is given by

(1)

where is the average water content (m³ m^-3) over the probe length, L (m). The abrupt change of water content at the wetting front does not have significant effect on the measurement of water storage (Topp et al., 1982).

Before the wetting front first reaches L under constant water application, the derivative of cumulative storage of water measured by TDR with respect to time should approximately equal the local water flux at the soil surface, q_w|0 (Parkin et al., 1995b). Assuming conservation of mass, one-dimensional flow, and that the applied water has not yet reached depth L, then

(2)

Equation [2] allows us to calculate the local water flux during the early stage of constant flux infiltration. After a long time, the average water content from the soil surface to depth L reaches a constant value and a corresponding steady state measurement can be taken from the multipurpose TDR probe.

The Solution of Parkin et al. (1992)
Broadbridge and White (1988) (BW) and Sander et al. (1988) independently developed an analytical solution for constant flux infiltration. The BW solution is based on the following parameterization of hydraulic conductivity and diffusivity functions:

(3)

(4)

where . The terms _s and _r are the saturated water content and residual water content, respectively. K_s, , and C are the saturated hydraulic conductivity, inverse capillary length scale (Philip, 1985), and a constant introduced by BW. By definition,

(5)

Thus,

(6)

Substitution of Eq. [3] and Eq. [4] into Eq. [6] and integration yields

(7)

where ₀ is an integration constant. Using , the integration constant .

We consider nonhysteretic vertical flow and seek to find an expression for time dependence for water storage to a fixed depth. The flow of water may be described in this process by the nonlinear Richards' equation used to describe one-dimensional nonhysteretic flow in ideal soil:

(8)

The initial and boundary condition considered here are

(9)

(10)

where R = water application rate (R K_s).

Utilizing Eq. [1] and Eq. [2], through a series of transforms (i.e., Kirchhoff, Hopf-Cole, and Storm transforms), BW derived an analytical solution as

(11)

and

(12)

where is a parameter connecting Eq. [11] and Eq. [12], u(,t) is given by Eq. [43] of BW, and

(13)

By a change of variable of integration, Parkin et al. (1992) obtained an analytical solution for water storage to depth L for constant flux infiltration:

(14)

A more versatile hydraulic model is the van Genuchten form (Eq. [15]) for soil water characteristic and Burdine form (Eq. [16]) for hydraulic conductivity (van Genuchten, 1980).

(15)

with , and

(16)

where _g and n are fitting parameters.

	Materials and methods

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Site Description
The field infiltration measurements were conducted at the Canadian Forces Base, Borden, Ontario, Canada. The spatial variability of saturated hydraulic conductivity (K_s) in the saturated zone has been characterized in detail by Sudicky (1986), who used 1275 undisturbed cores, and has been reexamined by Woodbury and Sudicky (1991). Turcke and Kueper (1996) used 642 undisturbed cores sampled near the site of Sudicky (1986). The study site at Borden is an area where the water table is >4.5 m below the surface.

The site was prepared by removing the top 0.5-m thick layer of surface soil over an area 4 x 9.5 m². The area was covered with a greenhouse to prevent effects of wind, precipitation, and evaporation. Within the sampling area, multipurpose TDR probes for a given depth were installed every 15 cm in a 7.5-m-long transect for a total of 50 probes per depth. This was repeated in parallel transects 10 cm apart for each of four depths (20, 40, 60, and 80 cm) for a total of 200 TDR probes (Fig. 1) . The probes were easily pushed or lightly tapped into the soil using hand vice-grip tools and a small hammer.

View larger version (15K): [in this window] [in a new window]   Fig. 1 Diagram of wetted sample area (2 x 9 m2) and locations of multipurpose TDR probes

Water Applications
The water application system produced a uniform wetted area 2 m wide by 9 m long that was centered over the TDR instrumented transects (Fig. 1). A linear array of eight flat spray nozzles was constructed. The spray pattern of a single nozzle suspended 50 cm above the surface approximates a narrow rectangle 120 x 20 cm². The nozzles were installed on the linear array at 10-cm intervals with their spray axes aligned. This produced a uniform, narrow wetted area of approximately 20 x 200 cm². The nozzle array was attached 50 cm above the soil surface to a commercially available, programmable water application system designed for greenhouses (model DCA, Monorail Boom Spray System, Waterford, ON). The system has a single pressure regulator, electric solenoid valve, and microprocessor unit attached to a hanging track and conveyor belt. The hanging track is mounted to the top of the greenhouse and allows the nozzle array to go smoothly back and forth along a straight line (9 m long) with programmable delay time at either end of the line. The water can be turned on or off at either end of the line.

Six different application rates were applied during a 60-d period in a random sequence (Table 1) . After each rate the soil was allowed to drain until daily changes in soil water storage were negligible relative to the next infiltration rate. Measurements were also taken during drainage, but they are not described in this paper. The uniformity of the water application system was checked by placing 100 cups (1.2 cm high x 0.9 cm i.d.) along the transects and by collecting applied water for 1 h. The water application was very uniform with the coefficient of variation <1.5%. For example, at the rate of 0.9 cm h^-1, the minimum and maximum measured rates were 0.87 cm h^-1 and 0.92 cm h^-1, respectively.

Measurement of Water Storage and

The pressure head measurements were taken using two tensimeters (Soil Measurement Systems, Tucson, AZ) after the wetting front was beyond the 80-cm depth and all measurements indicated little or no change with time. The measurements were taken for the application rates of 0.21, 0.9, and 3.3 cm h^-1 for the 20-cm and 40-cm probes. Measurements of were also taken at the initial condition before the application rate of 6.22 cm h^-1. Measurements of were not taken at the 60-cm and 80-cm depths because of time constraints. In addition, the steady state measurements (discussed later) indicated a significant change in hydraulic properties for depths >40 cm. Thus, the major focus of the paper is confined to the 0- to 40-cm depth interval.

Estimation of the Hydraulic Parameters
The optimization of the hydraulic parameters utilized simultaneous fit of model predictions to measured values of () and K(). The objective function is:

(17)

where b is the parameter vector (K_s, , C, _s) for the BW model or (K_s, _g, _s and n) for van Genuchten and Burdine model (VGB). The _i (b|) and _j (b|) are the predicted average and K for given and b. The variable M and N are the number of observations of and K, respectively, and G is the weight assigned to the hydraulic conductivity in order to prevent from dominating the K data solely because of its larger numerical values. Since (cm) values were generally ten times bigger than K (cm h^-1), we set . The value of _r was set equal to 0.05 based on measurements using a standard pressure plate apparatus with = -15000 cm. Several nonlinear programs, such as secant, Gauss-Newton, Marquardt, steepest decent methods (SAS Inst., 1994) were adopted, and different initial values were tried to ensure a global minimum. We assumed the correlation between measurement errors in K() and () was negligible, because they were measured by different equipment (i.e., TDR, tensimeter) and at different times.

	Results and discussion

TOP ABSTRACT INTRODUCTION Theory Materials and methods Results and discussion Summary REFERENCES

 
An example of measured water content as a function of time for individual TDR probes is shown in Fig. 2 . Generally, there existed a linear relationship between soil water storage, W (L, t), and t for early time measurements (i.e., before the wetting front moved beyond the ends of the probes) (Fig. 3) . This suggests local water flux was relatively constant with depth for a particular probe. For one-dimensional infiltration, the value of the measured water flux should equal the applied water application rate and be the same for all TDR probes. The average water fluxes along the transect for different rates were calculated using two different methods and both were very similar to the applied rates (Table 1); however, there was significant horizontal variability of the water flux for individual probes (Table 1). The variance of local water flux increased as the water application rate increased for all the four depths, but the coefficients of variations did not increase with increasing rate.

View larger version (15K): [in this window] [in a new window]   Fig. 2 Water content vs. time for 40-, 60-, and 80-cm probes at position 3.4 m

View larger version (15K): [in this window] [in a new window]   Fig. 3 Example of the linear relationship of water storage vs. time, at early time, for application rate 2.59 cm h-1 and TDR probe (20 cm) at position 3.4 m. The first five points were used in the regression

The average steady state soil water content decreased, as expected, with a decrease in application rate (Table 2) . The variance of local steady state water content first increased, then decreased with increasing water application rate. This is similar to predictions based on theoretical analysis given by Yeh (1989) for steady state flow in heterogeneous soils with positively correlated saturated hydraulic conductivity, K_s, and inverse macroscopic capillary length scale, .

In a manner similar to Parkin et al. (1995b), the variability in measured local water fluxes is utilized to estimate the field average hydraulic conductivity. Constant water flux along each TDR probe is assumed to represent an individual stream tube with local but different one-dimensional flow. At long times a unit gradient is assumed along each TDR probe and the measured local water flux (from early time measurements) is set equal to the hydraulic conductivity value associated with the steady state local soil water content and pressure head measurements for each multipurpose TDR probe. Average values indicate a hydraulic gradient very close to unity for two of the three measured rates (Table 2). The lower gradient for the 0.9 cm h^-1 rate is unexplained and attributed to measurement error. The () and K() measurements (L = 20 cm) are graphed in Fig. 4 and Fig. 5 , respectively. The fitted curves for the VGB (Eq. [15] and Eq. [16]) and the BW models (Eq. [3] and Eq. [4]) are very similar. The parameters for the BW model are K_s = 7.18 cm h^-1, = 0.09 cm^-1, C = 1.27 and _s = 0.42 cm³ cm^-3. The parameters for the VGB model are K_s = 8.94 cm h^-1, _g = 0.056 cm^-1, n = 1.64, m = 0.76, and _s = 0.45 cm³ cm^-3.

View larger version (19K): [in this window] [in a new window]   Fig. 4 Measured and fitted water retention curves for 0- to 20-cm depth

View larger version (20K): [in this window] [in a new window]   Fig. 5 Measured and fitted hydraulic conductivity curves for 0- to 20-cm depth

View larger version (19K): [in this window] [in a new window]   Fig. 6 Average hydraulic conductivity as a function of average soil water content calculated for separate depth increments

The estimated BW parameters were used in the BW solution (Eq. [16]) to predict field average water storage vs. time for the 0- to 20- and 0- to 40-cm depth during constant flux infiltration for the five application rates. The applied water rates were used in the predictions. The predicted water storage was very similar to measured values (Fig. 7 and 8) . Regression of predicted vs. measured storage using data from all rates were highly significant (r² 0.95). The average prediction error for water content was ± 0.005, which is less than the measurement error of the TDR method (Topp et al., 1980). The predictions for the 0- to 60-cm and 0- to 80-cm depths (not given) were not accurate, as we expected from the apparent change in hydraulic properties for depths >40 cm.

View larger version (25K): [in this window] [in a new window]   Fig. 7 Measured and predicted water storage (0–20 cm) vs. time for different application rates

View larger version (25K): [in this window] [in a new window]   Fig. 8 Measured and predicted water storage (0–40 cm) vs. time for different application rates

	Summary

TOP ABSTRACT INTRODUCTION Theory Materials and methods Results and discussion Summary REFERENCES

Received for publication April 29, 1998.

	REFERENCES

TOP ABSTRACT INTRODUCTION Theory Materials and methods Results and discussion Summary REFERENCES

 

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