Parameter estimation using the falling head infiltration model: Simulation and field experiment

Transcription

1 WATER RESOURCES RESEARCH, VOL. 41,, doi: /2004wr003407, 2005 Parameter estimation using the falling head infiltration model: Simulation and field experiment Takele B. Zeleke and Bing C. Si Department of Soil Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada Received 10 June 2004; revised 8 November 2004; accepted 7 December 2004; published 23 February [1] Soil hydraulic parameters have high spatial variability. A large number of measurements are needed to characterize these parameters in a field. Therefore there is a need to develop quicker and cheaper methods to determine soil hydraulic parameters. The objective of this study was to examine the uniqueness of the K fs (field saturated hydraulic conductivity) and a (inverse macroscopic capillary length scale) parameters obtained through inverting the falling head infiltration model. Five simulated scenarios were imposed on the cumulative infiltration data [L(t)] during the inverse procedure. The uniqueness of the K fs and a estimates under each scenario was studied. In situ infiltration data were used to verify the scenario that provided unique parameter estimates. It appears that the falling head infiltration model can be used to simultaneously estimate the K fs and a parameters when estimates (or published values) of the a parameter for the site are available. Citation: Zeleke, T. B., and B. C. Si (2005), Parameter estimation using the falling head infiltration model: Simulation and field experiment, Water Resour. Res., 41,, doi: /2004wr Introduction [2] Reliable parameter estimates of hydraulic properties are a prerequisite for characterization of water flow and chemical transport through soil profiles. Field scale determination of these parameters is expensive and time consuming because of the numerous point measurements required. Additionally, soil hydraulic properties have strong spatial variability [Hillel, 1998]; hence the reliability of field scale estimates is dependent on a large numbers of spatial replications. It is desirable to develop methods and analytical approaches that enable repeated determination of soil hydraulic parameters with minimal input of time and other resources. [3] Determination of field saturated hydraulic conductivity, K fs, and the associated inverse capillary length scale, a, is usually based on constant head methods that rely on attainment of a steady state flow rate [Elrick et al., 1995; Odell et al., 1998]. Attainment of a steady state flow rate for most agricultural soils requires several hours, making it costly and time-consuming. Studies have shown that shorttime transient flow measurements can also be used to estimate these parameters [Odell et al., 1998; Elrick et al., 1995; Bagarello et al., 2004; Zeleke et al., 2004]. None of these methods can be used to estimate both K fs and a parameters from a single infiltration event. Therefore either one parameter must be measured independently or steady state flow measurements need to be taken under two or more ponded heads [Elrick et al., 1995, 1989]. While these methods are well established, no studies have reported problems involved with estimating both parameters from a single run of transient infiltration experiment using the inverse method approach. [4] The objective of this study was to identify the uniqueness of the K fs and a parameters estimated through Copyright 2005 by the American Geophysical Union /05/2004WR inverting the Green and Ampt [1911] expression for falling head infiltration derived by Philip [1992]. To the best of our knowledge this is the first document reporting the performance of this method for simultaneous estimation of the two parameters under different simulated scenarios and in situ verification of the promising ones. 2. Theory 2.1. Falling Head Model for Ring Infiltrometer [5] A simple, but useful, model that describes the steplike infiltration of water in soil during ponded infiltration was developed by Green and Ampt [1911]. The assumptions used in the derivation of the model include the following: (1) Vertical flow of water is governed by Darcy s law; (2) piston flow creates a sharp wetting front in the initially uniformly dry soil profile; (3) the suction head at the wetting front remains constant, regardless of time and position; (4) behind the wetting front, the soil is uniformly wet and the hydraulic conductivity is constant; and (5) the soil is homogeneous and rigid. For vertical and constant head infiltration into initially dry and uniform soil, the infiltration rate [i(t)] is described by this model as it ðþ¼ di dt ¼ K D þ C þ zt ðþ fs zt ðþ where K fs [L T 1 ] is the mean hydraulic conductivity of the wetted part of the soil profile (assumed to equal the field saturated hydraulic conductivity), z(t) [L] is the timedependent depth of the wetting front, C [L] is the effective suction head for the wetting at the wetting front, I is the cumulative infiltration [L], and D [L] is the depth of ponded water on the surface at initial time t =0. [6] By applying the Green and Ampt [1911] conceptual model to various initial and boundary conditions, Philip [1969, 1992] developed solutions with more physical ð1þ 1of7

2 ZELEKE AND SI: HYDRAULIC PARAMETER ESTIMATION FALLING HEAD METHOD meaning. The recent version of this model that pertains to uniform initial and variable boundary conditions under falling head ponded infiltration condition is described as follows. For a uniform initial water content q i [L 3 L 3 ], field saturated water content qs [L 3 L 3 ], wetting front depth z(t) [L], and effective suction head at the wetting front C [L], the total potential difference (Dh) between the pond floor and the wetting front at any time t > 0 is given by [Philip, 1992] Dh ¼ zt ðþþcþ½d ðq s q i Þzt ðþš ð2þ Rearranging the right-hand side of equation (2) leads to Dh ¼ zt ðþ1 ½ ðq s q i ÞŠþC þ D ð3þ Applying Darcy s law the hydraulic head gradient in the wetted region becomes Dh zt ðþ ¼ 1 ð q s q i Þþ C þ D zt ðþ Infiltration rate, i(t) at any time t >0,is it ðþ¼ðq s q i Þ dz dt ¼ K fs 1 ðq s q i Integrating equation (5) yields [Philip, 1992] ½1 ðq s q i Þ q s q i ŠK fs t ¼ zt ðþ C þ D 1 ðq s q i Þ ln 1 þ 1 q ½ ð s q i ÞŠzt ðþ C þ D Þþ C þ D zt ðþ [7] Equation (6) is solved simultaneously for the K fs [L T 1 ] and C [L] from infiltration data recorded as a series of measurements of the depth of water in the ring [L(t)], the initial water content (q i ), the final water content (q s ), and the initial depth of ponding (D) using nonlinear regression techniques. Also, at any time t (t > 0), and for the depth of water in the pond at any time t, L(t), the cumulative infiltration, I(t) [L], is obtained from It ðþ¼ðq s q i Þzt ðþ¼d Lt where D = L(0). [8] For the rectangular hydraulic conductivity functions (Figure 1) such as the conceptual model of Green and Ampt [1911], the matrix flux potential, f m [L 2 T 1 ] is related to C and the field saturated hydraulic conductivity, K fs [Elrick et al., 2002]: Also f m is related to a as f m ¼ K fs C f m ¼ K fs a ð4þ ð5þ ð6þ ð7þ ð8aþ ð8bþ [9] The relationships described in equations (8a) and (8b) show that C is the inverse of the soil inverse macroscopic Figure 1. Schematic diagram showing the relationship between the Green and Ampt suction at wetting front, C, and the matrix flux potential, f m, for Gardner (the curve) and Green and Ampt hydraulic conductivity functions. capillary length parameter, a [L 1 ], given by Elrick and Reynolds [1992]. Substituting ( 1/a) for C, L(t) forz(t) using the relationship in equation (7) and shortening the expression (q s q i )todq, equation (6) can be written as ð1 DqÞ D Lt K fs t ¼ ðþ Da þ 1 Dq Dq að1 DqÞ 1 Dq ln 1 þ ð Þ ð D Lt ðþþa DqðDa þ 1Þ Given the estimate of the difference between the mean initial and final water content of the soil and infiltration data recorded as a series of measurements of the depth of water in the ring, equation (9) may be numerically inverted to obtain estimates of the soil hydraulic parameters a and K fs Formulation of the Forward and the Inverse Problems [10] During field infiltration experiments, researchers take a series of measurements of the depth of water in the ring, L, and the corresponding time, t. These measured variables will then be used to determine the hydraulic parameters K fs and a. Thus the forward problem becomes predicting either L as a function of t, L(t, K fs, a) ort as a function of L, t(l, K fs, a), for given K fs and a values. Although L(t, K fs, a) makes more sense physically, the resulting function is complicated because of the logarithmic component. However, t (L, K fs, a) can serve exactly the same purpose without yielding a complicated relationship. Thus the forward problem relating the measured variables (L and t) and the parameters to be estimated can be defined on the basis of equation (9) as D L Dq Da þ 1 t L; K fs ; a ¼ ð1 DqÞK fs ð1 DqÞ 2 ak fs 1 Dq ln 1 þ ð ÞðD LÞa DqðDa þ 1Þ ð9þ ð10þ [11] The inverse problem was formulated to estimate the best fit parameters (K fs and a) through nonlinear optimiza- 2of7

3 ZELEKE AND SI: HYDRAULIC PARAMETER ESTIMATION FALLING HEAD METHOD tion of objective functions that express the discrepancy between observed and predicted infiltration time. Since measurement errors are uncorrelated (i.e., errors involved in reading L(t) are independent of each other) and assumed to be normally distributed, a simpler form of the maximum likelihood estimator (i.e., the weighted least squares method) can be used to define the objective function in this particular case. This objective function (OBJ) is expressed as [Simunek and Hopmans, 2002] 1 X n s 2 t* L; K fs ; a tkfs ; a ð11þ where s 2 is the variance of the measurement errors in t(l), n is number of t(l) data pairs, t* (L, K fs, a) are the measured times, and t(l, K fs, a) are the times predicted by the model (equation (10)). Usually s 2 is unknown and could be treated as unknown parameter in minimizing equation (10). However, this will introduce more uncertainty in the inverse problem, which is not recommended [Si and Kachanoski, 2000]. Therefore s 2 is selected empirically from other sources of information or experience (the Bayesian philosophy). 3. Materials and Methods 3.1. Inverse Simulation for Uniqueness Analyses [12] A solution of the inverse problem is attained by minimization of equation (11). Hence a pair of K fs and a values that provide the minimum of the objective function is considered to be the best estimate. In the ideal case, the minimum value of the objective function should be zero [i.e., OBJ(K fs, a) = 0]. However, given measurement and model errors, this minimum value is different from zero and found for multiple pairs of K fs and a values, i.e., nonuniqueness. In other words, the solution is said to be nonunique whenever the objective function is nonconvex, i.e., has multiple local minima, or the global minimum occurs for a range of parameter values [Si and Kachanoski, 2000; Simunek and Hopmans, 2002]. [13] To investigate the question of nonuniqueness we simulated L(t) data at a depth interval of DL = 0.24 cm from L = 0 to 12 cm using equation (10) for a uniform silt loam soil with q i = 0.20, q s = 0.42 and with a field average a and K fs values of 12 m 1 and m s 1 (=1 cm h 1 ), respectively. The response surface of the objective function (of the simulated data) was studied on the K fs -a plane for uniqueness of parameter estimates. To this end, values of K fs and a have been generated around the assumed true values (a*=12m 1 and K fs * = m s 1 ) and the corresponding OBJ values were plotted against these simulated K fs and a values. Five different cases were studied and compared to one another Case I: Simulation With Error Free Data (S) [14] In the first case (S) the objective function to be minimized was X n tl i ; K fs *; a* tkfs ; a ð12þ where L i, K fs, and a are the numerically generated values (50 values of K fs and a, which results in a total of n = 2500 entries in the objective function). These generated data are error-free, in the sense that they are identical to the predicted data. Thus this case is used only to demonstrate the response surface in the case of unique parameter estimates. [15] In practice, however, measurements of soil water properties are subject to error [Si and Kachanoski, 2000]. The main measurement error in the ring infiltrometer experiment comes mainly from reading error, especially in low-permeability soils Case II: Simulation With Random Measurement Error (SE) [16] The second case incorporated a random and normally distributed measurement error (N(0, s)) in L readings. To this end, a 10% error (i.e., 1 mm reading error per 1 cm depth) was added to L readings. The objective function to be minimized in this case becomes ð13þ This allowed evaluation of the inverse solution using data that reproduce the actual field conditions Case III: Inclusion of Steady State Information (SESS) [17] In the third case the objective function was reformulated by including information on a quasi-steady state flux from Reynolds and Elrick [1990]: þ 1 s 2 q s K fs *; a* qs K fs ; a ð14þ q where q s [L T 1 ] is a quasi-steady state infiltration rate estimated as [Reynolds and Elrick, 1990] D q s K fs ; a ¼ Kfs 1 þ C 1 d þ C 2 a þ 1 aðc 1 d þ C 2 aþ ð15þ where a is the radius of the ring, d is the depth of insertion of the cylinder, and C 1 and C 2 are constants (C 1 = 0.316p and C 2 = 0.184p). Note that the D for the constant head experiment is much smaller than that of the falling head and is maintained throughout the experiment. This case was designed to improve the uniqueness of parameter estimates despite measurement errors by including steady state information in the optimization procedure Case IV: Inclusion of Sorptivity Information (SESP) [18] The fourth case was designed to improve the uniqueness of parameter estimates using sorptivity information. To this end, the analytical relationship describing sorptivity at a constant ponding head, H [White and Sully, 1987], was included in the objective function as þ 1 s 2 S H K fs *; a* SH K fs ; a ð16þ SH 3of7

4 ZELEKE AND SI: HYDRAULIC PARAMETER ESTIMATION FALLING HEAD METHOD Table 1. Soil Physical Properties at the Surface 0 15 cm of the Laura Site Selected Soil Properties (0 15 cm Depth) Mean Values a (n > 5) Soil texture, % Clay 14 (1.60) Silt 62 (4.83) Sand 24 (4.10) Bulk density, Mg m (0.11) Organic carbon content, g kg (0.07) Macroporosity, b % (3.55) a Values in parentheses represent standard error. b Macroporosity stands for pores with >1 mm effective diameter. where S H [L T 1/2 ] is the soil sorptivity at a constant ponding depth, H, and described as S H K fs ; a ¼ 1:818Kfs Dq H þ 1 0:5 ð17þ a Case V: Inclusion of Prior Information About the A Parameter (SEPI) [19] The last case was to improve the uniqueness of parameter estimates by including prior information about the a parameter. The objective function was redefined so that the a parameter is constrained (penalized) to lie within a closer range of prior estimates of its value. In other words, it means confining the estimation procedure to a certain range of values of the parameters by imposing bounds on the estimates. The definition of the objective function in this case becomes þ 1 ða* aþ 2 ð18þ s 2 a 3.2. Field Verification [20] Among the different simulated cases (S, SE, SESS, SESP, and SEPI), the case that resulted in a unique parameter estimate (i.e., under the presence of measurement errors) was selected and evaluated on in situ infiltration data from Laura, Saskatchewan. The K fs and a parameters estimated using this case (FH) were compared to estimates made by two commonly used methods: constant head double ring infiltrometer (CH) and tension disk infiltrometer (TI). [21] The soil at Laura ( N latitude and W longitude) is a Dark Brown Chernozemic (Typic Ustolls subgroup) developed on a loamy glaciolacustrine parent material. The site has been under a crop-fallow rotation dominated by wheat (Triticum aestivum L.) with some barley (Hordeum vulgare L.). The long-term average precipitation at the site is 321 mm yr 1. Selected soil and climatic properties of the site are summarized in Table 1. [22] In the summer of 2003, infiltration measurements were conducted using double-ring and tension disc infiltrometers. The double-ring infiltrometer [Bouwer, 1986] used in this experiment consisted of metal cylinders, measuring 25 cm in height. The diameters of the inner and outer rings were 20 and 30 cm, respectively. The rings were manually driven to a depth of 5 cm into the soil at each measurement point. Equal water depth was maintained in both cylinders and the infiltration rate was measured from the inner ring. In cases where maintaining a constant depth of water was required, water was added after every 1 cm depth fall and the corresponding time was recorded. To obtain sufficient readings, 12 cm of water was used as an initial depth of ponding for falling head experiments, whereas for constant head infiltration 5 cm of water was used. Initial and final soil water content of the soil within the inside ring was determined from a vertically installed 10 cm TDR probe. [23] The double-rings (with a vertical TDR probe and data logger) were installed at three randomly selected measurement points within a 6 m radius area. Falling head measurements were conducted for 1 2 hours depending on the infiltration rates. As soon as the water in the ring was reduced to less than 0.5 cm in depth, another 5 cm was added and the experiment resumed, measuring the constant head infiltration. The constant head infiltration lasted for 30 to 60 min until a steady state was achieved, and the K fs and a values were determined using equation (15). The choice to start with the falling head method was dictated by the fact that the falling head model is defined for an initially uniformly dry soil, and hence the infiltration process cannot start with constant head infiltration and then shift to falling head infiltration. [24] The tension disk infiltrometer (Soil Measurement Systems, Tucson, Arizona) used was the type described by Perroux and White [1988] and Ankeny et al. [1988]. The unit used in this experiment has a 20 cm disk diameter, 2.5 cm internal diameter bubble tower, and 5 cm internal diameter water reservoir. The tension disk infiltrometer measurement was also conducted in three replicates. The measurement points were located within the 6 m radius area of the double ring infiltrometer site. To improve hydraulic contact between the soil and the disk, a thin (<3 mm) layer of fine sand was applied to the soil surface at each measurement location. The sand used for this purpose had an air entry value slightly higher than 3 kpa pressure head and saturated hydraulic conductivity of ms 1. Infiltration measurements were run at six water tensions: 22, 17, 13, 10, 6, and 3 cm starting with the 22 cm tension. The measurement at each tension was run until a steady state rate was achieved. Saturated hydraulic conductivity, K s [L T 1 ], and inverse macroscopic capillary length scale, a [L 1 ], were determined using Wooding s [1968] steady state solution Statistical Analyses [25] Simulation of the different scenarios and analyses of the corresponding objective functions were performed using programs written in Mathcad 2000 Professional [MathSoft Engineering and Education, Inc., 2002]. Parameter estimations for the field data (nonlinear least squares fittings) were performed using the Gauss-Newton method as implemented in the SAS program (SAS 2 Statistical Software Version 8, SAS Institute, Cary, North Carolina). Parameter uncertainty statistics (such as confidence intervals and correlation between parameters) were obtained from SAS outputs. Each parameter and the corresponding statistics were obtained independently for the three measurement stations and then 4of7

5 ZELEKE AND SI: HYDRAULIC PARAMETER ESTIMATION FALLING HEAD METHOD Figure 2. Contours of the objective function for (a) error-free cumulative infiltration data and (b) for cumulative infiltration data with random normally distributed measurement error. the geometric mean value of the three values was used as estimate for the whole site. 4. Results and Discussion 4.1. Uniqueness of Parameter Estimates: Simulation [26] Response surfaces of the objective function, OBJ, under the different scenarios are shown in Figures 2 through 4. The response surface of the objective function on the K fs a plane for the error-free data (case I) is shown in Figure 2a. For this case, the objective function has a single well-defined minimum at the true parameter values (i.e., a =12m 1 and K fs = ms 1 ). The OBJ(K fs, a) value at this point was 0.00, expected for errorfree data. Thus case I of this study shows the type of the response surface to be expected when the estimated parameters are unique. [27] Addition of a 10% measurement error (case II), which is a practical scenario for field infiltration measurements with ring infiltrometers, changed the response surface of the objective function (Figure 2b). The minimum of the OBJ function, which was about 0.33, was observed for a wide range of a values, suggesting nonunique solutions. Therefore, with measurement error of 10% or more, the inverse solution does not provide a unique a estimate and prediction could be very erroneous. [28] In an effort to improve the uniqueness of parameter estimates from infiltration data with measurement errors, steady state and sorptivity information (equations (14) and (16)) were included in the objective function (i.e., cases III and IV). The response surfaces of the objective functions under these two cases are shown in Figures 3a and 3b. The minima of the OBJ functions for cases III and IV were 0.43 and 0.39, respectively. These minimum values were Figure 3. Contours of the objective function for (a) cumulative infiltration data with random measurement error and steady state information and (b) cumulative infiltration data with random measurement error and sorptivity information. 5of7

6 ZELEKE AND SI: HYDRAULIC PARAMETER ESTIMATION FALLING HEAD METHOD Figure 4. Contours of the objective function for cumulative infiltration data with random measurement error and prior information about the a parameter. obtained for a wide range of a values (10 to 14 m 1 ). Therefore inclusion of both steady state and sorptivity information did not result in unique a estimates. In other words, the minimum of the OBJ function has occurred at a wide range of a values, indicating nonuniqueness. [29] The effect of including prior information about one of the parameters to be estimated was the other case evaluated in this study (case V). Since the a parameter is more likely to be nonunique (Figures 3a and 3b), including prior information about this parameter was considered (Figure 4). A value of 10 m 1, obtained using the tension disk infiltrometer method, was used [Waduwawatte and Si, 2004]. In this case, a single well-defined minimum of the OBJ function, which was 0.04, was observed at the true parameter values (i.e., a = 12 m 1 and K fs = ms 1 ). Therefore including prior values of a resulted in unique parameter estimates. Given the low sensitivity of the model to a and the high natural variability of this parameter, the values obtained from cases III and IV may still be good enough for most practical applications. However, in the presence of a prior estimate of the parameter, case V is the best choice since it provides a unique estimate a in addition to reducing the time and effort spent on determination of steady state and sorptivity parameters Field Experiment: Comparative Evaluation [30] The estimated K fs values and the associated confidence intervals using the three different methods (FH, CH, and TI) are summarized in Table 2. The K fs estimate was highest for the FH method and lowest for the CH method, with values of and m s 1, respectively. The K fs estimated by the TI method ( ms 1 ) lies in between these values. The differences observed between the three methods were not statistically significant at 0.05 probability level. Furthermore, relative to the high spatial variability involved in the field determination of this parameter, the observed differences were negligible, and hence the three methods were comparable for K fs determination. [31] The estimated a values along with their confidence intervals for the three methods are summarized in Table 3. The a estimate was highest for FH method and lowest for TI method, with values of 24.3 and 10 m 1, respectively. The estimate from TI method is very close to what has been documented [Elrick and Reynolds, 1992] for most structured soils (i.e., 12 m 1 ). The estimate from the other two methods lies between the above range (12 m 1 ) and that documented for coarse sands and highly structured soils (36 m 1 ). However, there were no statistically significant differences among the three methods. Furthermore, the falling head model usually cannot produce accurate estimates of a because the model s sensitivity to this parameter tends to be low. As pointed out by Elrick et al. [1995], falling head infiltration is sensitive to a only when the capillary component of infiltration is substantial relative to the gravity and pressure components of infiltration (such as may occur in dry, fine-textured, structureless materials). [32] Comparing the two parameters, the accuracy and identifiability of K fs is more guaranteed than that of the a parameter. Analysis of the field falling head transient infiltration data without prior information about the parameters showed that the error involved in estimating the a parameter was higher than that of the K fs. This observation was in agreement with the simulation experiment where a wider range of the a values satisfied the same objective function values (Figures 2 through 4). Sensitivity study for early time falling head infiltration by Elrick et al. [1995] also showed that the falling head solution is uniformly sensitive to changes in K fs, whereas the sensitivity for changes in a was generally low and limited to lowpermeability soils. Addition of prior information about the a parameter is therefore desirable in order to simultaneously estimate both parameters from a single falling head infiltration experiment. Table 2. Field Saturated Hydraulic Conductivity (K fs ) at the Laura Site Method Estimate a Standard Error 95% Confidence Limits Lower Upper Falling head Constant head Tension disk infiltrometers a Estimates are times 10 6 ms 1. Table 3. The a Parameter Estimates at the Laura Site a Method Estimate b Standard Error 95% Confidence Limits Lower Upper Falling head Constant head Tension disk infiltrometers a The a parameter is the inverse macroscopic length scale. b Unit of the estimates is m 1. 6of7

7 ZELEKE AND SI: HYDRAULIC PARAMETER ESTIMATION FALLING HEAD METHOD [33] The proposed method requires that the soil is a uniform initial soil water content and the initial and final soil water content be known. Otherwise, there will be more unknowns in equation (9) and more uncertainty in the estimated parameters will be caused. Given the current soil water content measurement technologies such as TDR, the initial and final soil water content are easy to measure and it is reasonable to assume that initial and final soil water content are known. [34] Nonlinear models such as the falling head infiltration model may converge into several solutions (i.e., local minima). Some of these solutions are not the true parameter values. The success of obtaining the true solutions depends mainly on the use of appropriate initial guess values that will constrain the solution into a physically meaningful range. This study clearly demonstrated that in the presence of such physically meaningful initial guess value, the falling head infiltration model can be successfully used to determine two parameters simultaneously. It should also be noted that the priori value may not necessarily be closer to the final value, as long as it is in a physically meaningful range for the given soil. 5. Summary and Conclusion [35] The uniqueness of parameters (K fs and a) estimated using the falling head infiltration model that includes gravity [Philip, 1992] was evaluated under five different simulated cases. The cases include inversion of falling head transient infiltration data under (1) zero measurement error; (2) a 10% random and normally distributed measurement error; (3) the presence of steady state infiltration rate estimates; (4) the presence of sorptivity estimates; and (5) the presence of prior estimates of the a parameter. Response surface analysis was employed to study the uniqueness of the estimates. The result showed that, under the presence of measurement error, unique estimates of K fs and a are obtained only when prior information about the a parameter is included. Under this condition, the falling head method was comparable to the constant head and tension disk infiltrometer methods for estimating the K fs and a parameters. This implies that with a reasonable estimate of the a parameter, or when prior estimate for the site is available, the falling head method can be used for estimating K fs and a parameters. The study results look sufficiently promising to warrant extensive field testing on a range of soil types and conditions. Since the method requires only a single infiltration run, transient data, and easily available materials, it could be a better option for replicated measurement of the parameters, which is deemed necessary by the high spatial variability. References Ankeny, M. D., T. C. 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C. J. Grevers, B. C. Si, A. R. Mermut, and S. Beyene (2004), Effect of residue incorporation on physical properties of the surface soil in the south central rift valley of Ethiopia, Soil Tillage Res., 77, B. C. Si and T. B. Zeleke, Department of Soil Science, University of Saskatchewan, 51 Campus Drive, Saskatoon, Saskatchewan, Canada S7N 5A8. (bing.si@usask.ca) 7of7