The saturated hydraulic conductivity (K s ) of a porous medium is a critically

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1 Soil Physics Buffer Index Effects on Hydraulic Conductivity Measurements Using Numerical Simulations of Double-Ring Infiltration Jianbin Lai Yi Luo* Yucheng Station Key Lab. of Ecosystem Network Observation and Modeling Institute of Geographic Sciences and Natural Resources Research Chinese Academy of Sciences 11A Datun Rd. Anwai Chaoyang District Beijing , China Li Ren Dep. of Soil and Water Sciences Key Lab. of Plant Soil Interactions Ministry of Education China Agricultural Univ. Beijing , China The double-ring infiltrometer is widely used to measure soil saturated hydraulic conductivity in the field. Both the inner ring size and outer ring size (two factors in the buffer index) of an infiltrometer affect the measurements of saturated hydraulic conductivity. Few systematic studies have been conducted to investigate the combined effects of the inner and outer ring sizes of a double-ring infiltrometer on the measurements of field saturated hydraulic conductivity. A total of 7224 numerical simulations were conducted to investigate the optimum combination of inner and outer ring sizes for reliable saturated hydraulic conductivity measurements by using 24 infiltrometers with six inner ring diameters (10, 20, 40, 80, 120, and 200 cm) and, for each ring diameter, four buffer indices (b = 0.2, 0.33, 0.5, and 0.71). Results demonstrated that the inner ring size is a more important factor to be considered than the buffer index itself (or the outer ring size) in practice, and a larger inner ring diameter assembled with an outer ring (in most cases, with diameter 80 cm and b 0.33) is recommended to obtain reliable in situ measurement of soil field saturated hydraulic conductivity. The saturated hydraulic conductivity (K s ) of a porous medium is a critically important parameter for all activities connected with soil water flow (Iwanek, 2008). Many agroecological or hydrologic models describing and simulating water movement and solute transport in soils require K s (Feddes et al., 1988; Poulsen et al., 1998). Thus, K s measurements are essential for understanding and modeling hydrologic processes. Ciollaro and Romano (1995) suggested that using cost-effective and accurate methods to determine soil hydraulic properties may be extremely important for detecting correlations between adjacent measurements, especially in a fairly homogeneous soil like that considered in their study. Stockton and Warrick (1971) demonstrated that variability in K s is a function of both soil depth and location in the field, as well as experimental errors in measuring K s. This requires the development of accurate techniques for measuring the K s and tools for describing its spatial variability (Ciollaro and Romano, 1995). Many laboratory and in situ methods have been developed and modified with time for the determination of K s (Reynolds and Elrick, 1987; Poulsen et al., 2003; Bagarello et al., 2004; Hayashi and Quinton, 2004; Johnson et al., 2005). Nevertheless, the results of K s determination can be influenced for many reasons e.g., sample size, flow geometry, and variability of the soil physical and hydrologic characteristics (Si and Kachanoski, 2000; Reynolds et al., 2000; Iwanek, 2008). Double-ring infiltrometers are widely used to determine the soil K s in the field (Bouwer, 1986; Ashraf et al., 1997; Dirk et al., 1999; Ben-Hur and Assouline, 2002; Iwanek, 2008). In an earlier study, Marshall and Stirk (1950) concluded that infiltration rates measured with single rings decreased as the ring diameter increased. The double-ring method was designed with an outer buffer area to minimize lateral flow from the inner ring, thereby obtaining a more accurate measurement in Soil Sci. Soc. Am. J. 74:2010 Published online 2 Aug doi: /sssaj Received 8 Dec *Corresponding author (luoyi.cas@gmail.com). Soil Science Society of America, 5585 Guilford Rd., Madison WI USA All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher. SSSAJ: Volume 74: Number 5 September October

2 Fig. 1. Framework of the combinations and treatments of all the simulations; b is the buffer index, d i is the inner ring diameter, SD is standard deviation, and L is the correlation length. the inner ring. By introducing a buffer index b = (d o d i )/d o, where d o is the outer ring diameter and d i is the inner ring diameter, Swartzendruber and Olson (1961a,b) conducted a series of double-ring infiltration experiments with different sizes of outer rings and a constant inner ring radius of cm to determine the buffer effects for a sandy soil. They found that the measurement error due to lateral flow becomes negligible as the diameter of the outer ring increases to 1.2 m, and concluded that buffering brings the actual infiltration velocity close to the one-dimensional infiltration rate. Later, the study of Wu et al. (1997) showed that, for their three test soils, the measured infiltration rates were 20 to 33% greater than the one-dimensional infiltration rates when the outer ring diameter was increased to 1.2 m (inner ring diameter kept at 0.2 m). Measurement error due to lateral flow decreased as the outer ring size increased, and consequently the measured infiltration rates better approximated the one-dimensional vertical flow rates. More recently, Wuest (2005) investigated the influence of sample volume and shape on estimates of saturated flow in a cylinder infiltrometer and demonstrated that the mean infiltration rate increased as the diameter increased, while the standard deviation and range also increased with increasing diameter. Then Wuest (2005) concluded that these phenomena might be attributed to deep insertion of the cylinder and high antecedent soil moisture. In a previous study of Lai and Ren (2007), both field experiments and numerical simulations were conducted to investigate the dependency of the measured hydraulic conductivity on the inner ring size of the double-ring infiltrometer. They concluded that the variability of the measured hydraulic conductivity was greater for smaller inner rings and gradually decreased as the inner ring size increased. Their study focused on the effects of inner ring size on the soil saturated hydraulic conductivity measurement, however, and the difference in the error due to lateral flow among different size infiltrometers was neglected. Given all this, previous studies have focused on either the buffer effect (outer ring size) or inner ring size effect on the measurement of soil hydraulic conductivity. Few systematic studies have been conducted to reveal the combination effect of inner and outer ring sizes of a double-ring infiltrometer on the hydraulic conductivity measurement. It s very time consuming and costly to conduct lots of field experiments but limited field experiments can hardly reveal the influence mechanism in soil hydraulic conductivity measurement using a double-ring infiltrometer, especially for various heterogeneous soils. The previous study of Lai and Ren (2007) and other research (Skaggs et al., 2004; Lazarovitch et al., 2005) has shown the robustness of the numerical model in imitating and reproducing the infiltration process in the field. Therefore, we adopted numerical simulation to perform a series of numerical experiments in this study. This study investigated the combined effects of inner ring size and outer ring size (i.e., two factors of the buffer index) on the soil K s measurement in order to find the optimum buffer size for the double-ring infiltrometer to obtain reliable soil hydraulic conductivity measurements. The estimated wetted field saturated soil hydraulic conductivities (K w ) with a smaller standard deviation (SD) have been taken as reliable or stable measurements in this study because the true value cannot be measured or simulated exactly in reality. Materials and Methods The framework of this study was as follows (Fig. 1), while detailed descriptions of the numerical and field experiments are presented separately below. Four buffer indices (b = 0.2, 0.33, 0.5, and 0.71) and six inner ring sizes (d i = 10, 20, 40, 80, 120, and 200 cm) were used in the geometry domain setting of the numerical simulation. This gave a total of 24 infiltrometers of different sizes. For each infiltrometer size, by adopting six correlation lengths (L = 0, 10, 20, 50, 100, and 200 cm) and six standard deviations (SD = 0, 0.1, 0.25, 0.5, 0.75, and 1.0), 31 stochastic fields of K s were randomly generated in the simulation domain. Ten simulations were performed for each of the 30 stochastic fields because only a single simulation was needed for the completely random field (L = 0 with SD = 0). Therefore, all in all, 7224 simulations were conducted to find the optimum inner and outer ring sizes for a double-ring infiltrometer. In addition, before the numerical simulation, 16 sets of field experiments of double-ring infiltration with various inner ring sizes and buffer indices were conducted to validate the numerical simulation. Numerical Experiments The HYDRUS-2D code (Šimůnek et al., 1999) allows the user to simulate a wide range of boundary conditions and irrigation regimes (Roberts et al., 2009), and it has been previously used to successfully simulate the water flow of drip irrigation (Skaggs et al., 2004; Lazarovitch et al., 2005) and, recently, infiltration under a double-ring infiltrometer (Lai 6 SSSAJ: Volume 74: Number 4 July August 2010

3 Fig. 2. The HYDRUS-2D/3D simulation domain and boundary conditions. and Ren, 2007). The HYDRUS software package (Šimůnek et al., 2007) was used in our study. Axisymmetric domains were assumed to contain the wet volumes of the double-ring infiltrometer tests. Infiltration processes within the domains were simulated by the HYDRUS software package. The depth of the domains for all simulations was designated as 160 cm below the ground; however, lengths in the radial direction of the domains varied among the simulations corresponding to the dimensions of the double-ring infiltrometers (Fig. 2). The surface of each simulation domain included three subareas: the inner ring area, the outer ring area, and the extended area. To imitate field infiltration conditions, the extended area was always kept 50 cm away from the outer ring in the radial direction so that soil water could flow freely from the outer ring area to and within a semi-infinite domain (i.e., the extended area). A finite-element mesh was generated using the MESHGEN subroutine embedded in the HYDRUS software package (Šimůnek et al., 2007). Both a constant and a variable mesh size discrete scheme were designed to test their impacts on the simulation results. For the homogeneous case, a mesh size of 1 cm was used for the whole domain. For the variable case, the mesh size was 1 cm from the top of the simulation domain downward to the depth of 40 cm and then gradually increased to 5 cm from the depth of 40 cm to the lower border. It was finally found that the impact of the mesh sizes on the simulation results was negligible (not shown) and the variable-size scheme used much less computation time than the constant-size scheme. With consideration of the limitation of the number of finite elements in the HYDRUS software (n max = 100,000) and the computation efficiency of >7000 simulations, the variable-size scheme was adopted in this study. The initial condition of the simulation domain was given in form of the soil water pressure head. According to the variation in soil moisture, which was measured in the field along the profile, the top pressure head and bottom pressure head were set to be 160 and 0 cm, respectively, and the soil water pressure head was linearly distributed with depth. A constant water head (h = 5 cm) was imposed at the surface of both the inner and outer ring areas. A no-flux boundary was assumed for the extended area. A constant water head (h = 0 cm) was assumed for the lower boundary. No lateral flow was considered for the vertical boundary of the simulated domain (Fig. 2). Besides, two vertical inner boundaries were set to imitate the cylinder wall of the infiltrometer, and a no-flux boundary was imposed on these two parts. Both of the vertical inner boundaries were 5 cm high as per the field experiment setting. The van Genuchten Mualem soil hydraulic properties model (Mualem, 1976; van Genuchten, 1980) was selected for the numerical simulations with m = 1 1/n. The soil hydraulic parameters utilized in the model were determined via Rosetta Lite (Schaap et al., 2001), which is embedded in the HYDRUS software package (Šimůnek et al., 2007), by inputting the particle-size distribution and bulk density of the topsoil in the field; the values that entered into the model were: residual volumetric water content θ r = 0.046; saturated volumetric water content θ s = 0.419; shape parameters n = and α = 0.65 m 1 ; and K s = m s 1 (K s was set as a reference value for the hydraulic conductivity fields, see below). The hydraulic conductivity field in a simulation domain was assumed to be isotropic. We included soil heterogeneity in the simulations by treating K s as the realization of a spatially randomly distributed field with a specified SD and L. The scaling factor fields were generated via a stochastic field generator within HYDRUS. Then, by multiplying the scaling factor at each node by the input reference value of the hydraulic conductivity, the stochastic K s fields for each simulation were obtained. Six SD values (0, 0.1, 0.25, 0.5, 0.75, and 1.0) and six L values (0, 10, 20, 50, 100, and 200 cm) of a random field of log(k s ) were used for the various simulations of hydraulic conductivity fields. Ten simulations were performed for each combination of (L, SD) treatments and infiltrometers. Because only a single simulation is needed when SD = 0, this gave a total of 7224 simulations (i.e., 6 inner ring sizes 4 buffer indices 301) (Fig. 1). Numerical simulation of the double-ring infiltration process was then performed with respect to each of the K s field realizations, and for each realization, one single simulation has been done. Considering the soil variability and time requirement to reach a relative steady-state infiltration, the infiltration duration was 2 h for simulations for all the infiltrometers. The initial, minimum, and maximum time steps were 10, 1, and 60 s, respectively. The HYDRUS software package calculates both the volumetric water flux and its cumulative values across the upper borders along the inner and outer rings. Consequently, the cumulative cross-border water volume data at every minute (i.e., the cumulative infiltration data) were used to fit an infiltration equation to estimate the K w. In this study, Philip s two-term SSSAJ: Volume 74: Number 4 July August

4 Table 1. Basic parameters of the double-ring infiltrometers in the field experiment for inner ring diameter (di) of 20, 40, 80, and 120 cm. b di = 20 cm Outer ring diameter (do) di = 40 cm di = 80 cm di = 120 cm cm Buffer index b = (do di)/do. equation (Philip, 1957) was adopted, and the Kw for each numerical infiltration test was obtained by fitting the cumulative infiltration data to the equation (see also Lai and Ren, 2007): I = St At [1] where I is the cumulative infiltration (L), S is called sorptivity(l T 0.5), and A is a constant (L T 1). The A term approaches the Kw after a relatively long period of infiltration (Bouwer, 1986). Field Experiments for Validation of the Numerical Simulation The HYDRUS software package has been previously used successfully to simulate infiltration under a double-ring infiltrometer (Lai and Ren, 2007), but the geometry (e.g., upper border) of the simulated do- mains and the flow field in this study were more complex than those in the previous study. Therefore, it was necessary to conduct a set of field experiments to validate the numerical simulation. To represent and imitate the field experiment in the numerical simulations, most simulation parameters, such as the domain geometry, the soil hydraulic parameters, the initial and boundary conditions, and the simulated infiltration duration came from field measurements. The field experiments were performed at the Yucheng Comprehensive Experimental Station (37 10 N, E) of the Chinese Academy of Sciences, which is located in the northwest of Shandong province, China. Four inner ring sizes of double-ring infiltrometers were used, and for each inner ring size, four outer ring sizes were used. Consequently, 16 infiltrometers were used in the experiment (Table 1; Fig. 3). For each infiltrometer, one test was performed. The test sites were randomly arranged, and all the infiltration tests were conducted within a 10- by 10-m block in a tillage field. Soil profiles were investigated within the block in situ and the particle size distribution and bulk density were determined by the hydrometer method (Gee and Bauder, 1979) and the core method (Blake and Hartge, 1986), respectively (Table 2). The infiltration measurement procedures were the same as described by Lai and Ren (2007) but double-ring infiltrometers with different size buffer indices for the various inner ring sizes were tested. For the infiltration tests, two concentric rings were carefully inserted 5 cm into the ground to minimize disturbance to the soil Fig. 3. Four sets of double-ring infiltrometers (inner ring diameter di = 80 cm) for field experiments with different buffer indices: (a) b = 0.71, (b) b = 0.5, (c) b = 0.33, and (d) b = SSSAJ: Volume 74: Number 4 July August 2010

5 surface. The water level in the inner ring was stabilized using a Mariotte tube, and that in outer ring was maintained manually and carefully to match the outer level with the inner level. The water level difference was kept within 0.5 cm so that any water head impact on the infiltration inside both the inner and outer rings could be considered negligible. It took about 60 min for smaller rings and about 90 min for larger rings to reach a steady-state infiltration. Results and Discussion Validation of the Numerical Simulation To validate the HYDRUS software package in the performance of double-ring infiltration under specific initial and boundary conditions, the simulated infiltration processes of two different infiltrometers (d i = 20 cm with b = 0.71, and d i = 80 cm with b = 0.33) were adopted to compare with the field measurements (Fig. 4). The measured data under each infiltrometer and the corresponding scatter range of 301 simulated curves under conditions of various hydraulic conductivity fields are presented in Fig. 4. The result demonstrated that the simulated cumulative flux scattered in a relatively wide range, and the field-measured data fell completely in that range. Thus, it indicates that the numerical simulation can adequately reproduce the field experimental conditions, and our field experiments can be taken as the realizations among the numerous treatments of numerical simulation. One set of maps of simulated velocity vector fields at three specific infiltration times (5, 50, and 100 min) and the corresponding water potential distribution maps are presented in Fig. 5. Both of the sets of maps vividly demonstrate the complexity of the simulation domain in this study. The color and length of the arrows in the maps of the velocity vector field indicating the flow rate, and the direction of the arrows indicate the flow direction. The maps show that the buffering area (i.e., the outer ring) played a notable role in guaranteeing a one-dimensional vertical flow in the inner ring, as the influence of lateral flow was lessened through the buffering area. In spite of the buffer effect Table 2. Basic soil properties along a soil profile at the test site in the field experiment. Depth Sand Silt Clay Texture Bulk density Initial soil moisture cm % Mg m 3 m m silt silt silt silt silt silt silt silt of the outer ring, the water flow in the inner ring was not strictly vertical or one dimensional; rather, horizontal flow existed in some part of the simulation domain. Moreover, these maps also showed that water flow occurred always within the simulation domain for the entire infiltration duration, at least for most cases. The field experiments showed that the mean of the K w decreased continuously when b increased from 0.2 to 0.5 (Fig. 6a), whereas there was a notable increase of the mean when b increased from 0.5 to High values of the mean at b = 0.71 might be attributed to the effect of the small inner rings (e.g., d i = 20 and 40 cm), which resulted in unstable measurements of K w (Lai and Ren, 2007). Moreover, the overall trend of the SD of K w was unstable as b increased from 0.2 to 0.71 (Fig. 6a). Similarly, the mean of the measured K w showed no consistent trend with increasing inner ring diameter (Fig. 6b). The SD of K w at d i = 20 cm was smaller than at d i = 40 cm, and it then showed a decreasing trend as the inner ring diameter increased from 40 to 120 cm (Fig. 6b). Just as stated in Nimmo et al. (2009), smaller rings are clearly more vulnerable to the various edge effects related to radial spreading, blockage of horizontal flow paths, and other phenomena. The previous study of Lai and Ren (2007) suggested that a numerical model can be a potentially powerful tool for revealing the combination effect of the inner and outer ring sizes of a double-ring infiltrometer on the K w measurement by simulat- Fig. 4. The measured vs. simulated cumulative infiltration curves under infiltrometers with (a) inner ring diameter d i = 20 cm, buffer index b = 0.71; and (b) d i = 80 cm, b = (Shading indicates the scatter range of the corresponding 301 simulated curves under conditions of various hydraulic conductivity fields.) SSSAJ: Volume 74: Number 4 July August

6 Fig. 5. Representative velocity vector (v) maps (left) and soil water potential (h) maps (right) at three infiltration times of 5 (upper), 50 (middle), and 100 min (lower) under an infiltrometer with inner ring diameter di = 80 cm. Only part of the simulation domain (110 cm vertically) is shown here; r is radius and z is depth. 6 SSSAJ: Volume 74: Number 4 July August 2010

7 ing plenty of infiltration tests under various soil conditions rather than a few field experiments. Effects of the Buffer Index on Distribution of Wetted Field Hydraulic Conductivity The SD of the stochastic field of log(k s ) appeared to have more impact on the scatter range of the simulated K w than that of buffer index. The range of K w increased as the SD of the log(k s ) field increased (Fig. 7). The greatest scatter in K w was observed for large SD. If the SD was small, the K w always showed less variation, no matter what the buffer index was. Compared with the SD, the buffer indices showed little, if any, influence on the variation range of the K w. In other words, for a heterogeneous and structured soil, the stability of the measured saturated hydraulic conductivity can hardly be increased solely by increasing the buffer index. The effect of the correlation length (L) of the stochastic field of log(k s ) was similar to that of SD (Fig. 8). The K w values were scattered in a relatively small range when L = 0 cm, and then sharply extended to a broader range as the L increased. The variation range of the K w did not change appreciably across the full range of L, except for within a completely random medium (L = 0 cm). Furthermore, the buffer index showed almost no influence on the variation range of the K w. Descriptive statistics for the overall simulated K w are listed in Table 3. There was a notable decrease in the mean, median, and SD as the buffer index increased for all inner ring sizes. As mentioned above, several researchers (Swartzendruber and Olson, 1961a,b; Wu et al., 1997) concluded that the measurement error due to lateral flow decreased as the outer ring size (i.e., the buffer index) increased, and consequently the measured infiltration rates better approximated the one-dimensional vertical flow rates. We got similar results. In addition, the skewness varied hardly at all. An exception was for b = 0.33 and further research is needed. Furthermore, the asymptote significance of the Kolmogorov Smirnov tests was <0.05, so the distribution of the data for all the buffer Fig. 6. Variation in the measured saturated hydraulic conductivity of the wetted field (K w ) with (a) buffer index b, and (b) inner ring diameter d i. indices was significantly different from the normal (Gaussian). All four buffer indices produced distributions with means much greater than medians and large, positive skewness. The Q Q plot of log(k w ) showed that the K w values from the infiltrometers of all four buffer indices were approximately lognormally distributed, except for some points with small or extremely large values (Fig. 9). Furthermore, comparing the four Q Q plots of the different buffer indices with each other, there was little difference in the distribution pattern of the simulated K w. Different from the inner ring size effect (i.e., the overall hydraulic conductivities show a tendency toward normality with Fig. 7. The relationship between the simulated saturated hydraulic conductivity of the wetted field (K w ) and the buffer index with various correlation lengths (L) and standard deviations of (a) 0.1, (b) 0.25, (c) 0.5, (d) 0.75, and (e) 1.0. SSSAJ: Volume 74: Number 4 July August

8 Fig. 8. The relationship between the simulated saturated hydraulic conductivity of the wetted field (K w ) and the buffer index with various standard deviations (SD) and correlation lengths (a) 0 cm, (b) 10 cm, (c) 20 cm, (d) 50 cm, (e) 100 cm, and (f) 200 cm. increased inner ring size), which was reported in Lai and Ren (2007), the buffer index shows little influences on the distribution of the simulated K w. All the simulated K w values across all treatments were clustered by the buffer index and are presented in Fig. 10. The median and quartile of the simulated K w values decreased notably as the inner ring diameter increased, even though the buffer index was the same. Compared with the K w value at d i = 10 cm, it decreased by 85.4, 87.9, 87.5, and 80.9% for b = 0.2, 0.33, 0.5, and 0.71, respectively, as d i increased to 200 cm. Moreover, when the buffer index was small (e.g., b = 0.2), the median and quartile of the simulated K w continuously decreased as the inner ring diameter increased. But as the buffer index increased to 0.33 or Table 3. Statistics of the simulated soil hydraulic conductivities. greater, the decreasing trend of the median and quartile of the simulated K w slowed with increasing inner ring diameter and then reached a stable level. When d i increased from 80 to 200 cm, the K w decreased by 38.9% for b = 0.2 but only by 17.6% for b = At b = 0.71, the median and quartile of K w under the infiltrometer with d i = 80 cm were comparable with those under infiltrometers with larger inner ring sizes. In other words, infiltrometers with too large inner ring sizes are unnecessary in practice. The data shown in Fig. 11 are the same as those in Fig. 10, but rearranged and clustered by the inner ring diameter. There was a continual decrease in the K w with increase in both the buffer index and the inner ring diameter. As mentioned above, several researchers (Swartzendruber and Olson, 1961a,b; Wu et al., 1997) concluded that the measurement error due to lateral flow decreased as the outer ring size (buffer index) increased, and consequently the measured infiltration rates better approximated the one-dimensional vertical flow rates; we got similar results. Moreover, when the inner ring diameter was large (e.g., d i 120 cm), the differences in the quartile and median between the buffer indices become indistinctive. Compared with the K w value of d i = 200 cm at b = 0.71, it increased by 67.7% when b decreased from 0.71 to 0.2; but it increased by 424.2% when inner ring diameter d i decreased from 200 to 10 cm. Comparing the median of the simulated K w under various inner ring diameters and buffer indices (Fig. 12), it was noticed that the medians decreased abruptly and got close to each other as the inner ring diameter increased. The average of median of K w at d i = 10 cm was cm min 1, and then continually decreased to cm min 1 at d i = 200 cm. The decreasing rate was 36.7 and 4.9% as d i increased from 10 to 20 cm and from 120 Buffer index Mean Min. Max. Median SE SD Skewness Asymptote significance cm min n = 1806 for each buffer index. Asymptote significance of the Kolmogorov Smirnov test; the test distribution was normal. 6 SSSAJ: Volume 74: Number 4 July August 2010

9 to 200 cm, respectively. The SD of the median of K w at d i = 10 cm was 0.08 cm min 1, which then continually decreased to cm min 1 at d i = 200 cm. The median values of K w became comparable (SD < cm min 1 ) with each other as the inner ring diameter increased beyond 80 cm. Therefore, the inner ring size plays a more important role than the buffer index in getting a stable measurement of the soil saturated hydraulic conductivity. The soil hydraulic conductivities that were measured with the double-ring infiltrometers were actually the approximate and effective values of the soil that happened to be under the infiltrometer; both the soil heterogeneity and lateral flow appreciably affect the accuracy of the measured soil hydraulic conductivity. The numerical simulations revealed the combined effects of inner ring size and buffer index on the measurement of soil hydraulic conductivity with a double-ring infiltrometer. When the soil heterogeneity is great (larger L or SD), there is a limited effect on increasing the stability of K w measurement solely by increasing the buffer index. It s more effective to increase the inner ring size than the outer ring s in getting a more stable and reliable measurement of K w. In other words, a larger inner ring assembled with an outer ring (with a specific buffer index) is necessary for a reliable measurement. As revealed in our simulation results, for the condition encountered in our field study, infiltrometers with d i 80 cm and b 0.33 are suggested to ensure a reasonably stable and representative measurement. Fig. 9. The Q Q plot of the simulated log-transformed saturated hydraulic conductivity of the wetted field (K w ) for all the buffer indices b. Conclusions A large number of numerical simulations were conducted to illustrate the combined effects of the inner ring and outer ring sizes (or buffer index) of the double-ring infiltrometer on soil hydraulic con- Fig. 10. Distribution of the simulated log-transformed saturated hydraulic conductivity of the wetted field (K w ) with different buffer indices b with inner ring diameters (d i ) from 10 to 200 cm. SSSAJ: Volume 74: Number 4 July August

10 Fig. 11. Distribution of the simulated log-transformed saturated hydraulic conductivity of the wetted field (K w ) with different inner ring diameters and buffer indices from 0.20 to ductivity measurements. A total of 7224 wetted field hydraulic conductivities (K w ) were simulated using six inner ring sizes of double-ring infiltrometers and, for each ring size, four buffer indices. Both the inner ring size and buffer index have significant influence on the accuracy of the measurement of K w. Moreover, compared with the buffer index, the inner ring size plays a more important role in obtaining a reasonably stable and representative measurement by double-ring infiltrometer. Given a specific heterogeneous soil, for the infiltrometers with a small inner ring, the simulated K w values were highly variable and unstable although their stability can be slightly improved by increasing the buffer index. For infiltrometers with a larger inner ring, the simulated K w became more stable and the difference in the effect Fig. 12. Comparison of measured and simulated saturated hydraulic conductivity of the wetted field (K w ) for different inner ring diameters and buffer indices b. of various buffer indices became negligible. A large inner ring with a large buffer index, however, will no doubt result in high cost and more time-consuming, low-efficiency measurements. Therefore, the infiltrometer with a larger inner ring assembled with an outer ring (in practice, with d i 80 cm and b 0.33) represents an efficient method for improving measurement accuracy and representativeness. Acknowledgments This research was funded by the Natural Sciences Foundation of China (no ), the National 863 Program (no. 2007AA10Z223), and the National Basic Research Program (2005CB121103). It was also partially financed by the Open- Fund Project of the Key Laboratory of Ecological Network Observation and Modeling, Chinese Academy of Sciences (Grant no. LENOM07YC-04).. References Ashraf, M.S., B. Izadi, and B. King Transport of bromide under intermittent and continuous ponding conditions. J. Environ. Qual. 26: Bagarello, V., M. Iovino, and D. Elrick A simplified falling-head technique for rapid determination of field-saturated hydraulic conductivity. Soil Sci. Soc. Am. J. 68: Ben-Hur, M., and S. Assouline Tillage effects on water and salt distribution in a Vertisol during effluent irrigation and rainfall. Agron. J. 94: Blake, G.R., and K.H. Hartge Bulk density. p In A. Klute (ed.) Methods of soil analysis. Part 1. 2nd ed. Agron. Monogr. 9. ASA and SSSA, Madison, WI. Bouwer, H Intake rate: Cylinder infiltrometer. p In A. Klute (ed.) Methods of soil analysis. Part 1. 2nd ed. Agron. Monogr. 9. ASA and SSSA, Madison, WI. Ciollaro, G., and N. Romano Spatial variability of the hydraulic properties of a volcanic soil. Geoderma 65: Dirk, S.M., D.A. Carlson, D.S. Cherkauer, and P. Malik Scale dependency of hydraulic conductivity in heterogeneous media. Ground Water 37: Feddes, R.A., P. Kabat, P.J.T. van Bakel, J.J.B. Bronswijk, and J. Halbertsma Modelling soil water dynamics in the unsaturated zone: State of the art. J. Hydrol. 100: Gee, G.W., and J.W. Bauder Particle size analysis by hydrometer: A simplified method for routine textural analysis and a sensitivity test of measurement parameters. Soil Sci. Soc. Am. J. 43: Hayashi, M., and W.L. Quinton A constant-head well permeameter method for measuring field-saturated hydraulic conductivity above an impermeable layer. Can. J. Soil Sci. 84: Iwanek, M A method for measuring saturated hydraulic conductivity in anisotropic soils. Soil Sci. Soc. Am. J. 72: Johnson, D.O., F.J. Arriage, and B. Lowery Automation of a falling head permeameter for rapid determination of hydraulic conductivity of multiple samples. Soil Sci. Soc. Am. J. 69: Lai, J., and L. Ren Assessing the size dependency of measured hydraulic conductivity using double-ring infiltrometers and numerical simulation. Soil Sci. Soc. Am. J. 71: Lazarovitch, N., J. Šimůnek, and U. Shani System-dependent boundary condition for water flow from subsurface source. Soil Sci. Soc. Am. J. 69: Marshall, T.J., and G.B. Stirk The effect of lateral movement of water in soil on infiltration measurements. Aust. J. Agric. Res. 1: Mualem, Y A new model for predicting the hydraulic conductivity of 6 SSSAJ: Volume 74: Number 4 July August 2010

11 unsaturated porous media. Water Resour. Res. 12: Nimmo, J.R., K.M. Schmidt, K.S. Perkins, and J.D. Stock Rapid measurement of field-saturated hydraulic conductivity for areal characterization. Vadose Zone J. 8: Philip, J.R The theory of infiltration: 1. The infiltration equation and its solution. Soil Sci. 83: Poulsen, T.G., P. Moldrup, and O.H. Jacobsen One-parameter models for unsaturated hydraulic conductivity. Soil Sci. 163: Poulsen, T.G., P. Moldrup, O. Wendroth, and D.R. Nielsen Estimating saturated hydraulic conductivity and air permeability from soil physical properties using state space analysis. Soil Sci. 168: Reynolds, W.D., B.T. Bowman, R.R. Brunke, C.F. Drury, and C.S. Tan Comparison of tension infiltrometer, pressure infiltrometer, and soil core estimates of saturated hydraulic conductivity. Soil Sci. Soc. Am. J. 64: Reynolds, W.D., and D.E. Elrick In situ measurement of field-saturated hydraulic conductivity, sorptivity and the α-parameter using the Guelph permeameter. Soil Sci. 140: Roberts, T., N. Lazarovitch, A.W. Warrick, and T.L. Thompson Modeling salt accumulation with subsurface drip irrigation using HYDRUS-2D. Soil Sci. Soc. Am. J. 73: Schaap, M.G., F.J. Leij, and M.Th. van Genuchten Rosetta: A computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions. J. Hydrol. 251: Si, B.C., and R.G. Kachanoski Estimating soil hydraulic properties during constant flux infiltration: Inverse procedures. Soil Sci. Soc. Am. J. 64: Šimůnek, J., M. Šejna, and M.Th. van Genuchten HYDUS-2D software for simulating water flow and solute transport in two-dimensional variably saturated media. Version 2.0. Int. Ground Water Model. Ctr., Colorado School of Mines, Golden. Šimůnek, J., M. Šejna, and M.Th. van Genuchten The HYDRUS software package for simulating two- and three-dimensional movement of water, heat, and multiple solutes in variably-saturated media: User manual. Version 1.0. PC Progress, Prague, Czech Republic. Skaggs, T.H., T.J. Trout, J. Šimůnek, and P.J. Shouse Comparison of HYDRUS-2D simulations of drip irrigation with experimental observations. J. Irrig. Drain. Eng. 130: Stockton, J.G., and A.W. Warrick Spatial variability of unsaturated hydraulic conductivity. Soil Sci. Soc. Am. Proc. 35: Swartzendruber, D., and T.C. Olson. 1961a. Model study of the double ring infiltrometer as affected by depth of wetting and particle size. Soil Sci. 92: Swartzendruber, D., and T.C. Olson. 1961b. Sandy-model study of buffer effects in the double ring infiltrometer. Soil Sci. Soc. Am. Proc. 25:5 8. van Genuchten, M.Th A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44: Wu, L., L. Pan, M. Roberson, and P.J. Shouse Numerical evaluation of ringinfiltrometers under various soil conditions. Soil Sci. 162: Wuest, S.B Bias in ponded infiltration estimates due to sample volume and shape. Vadose Zone J. 4: SSSAJ: Volume 74: Number 4 July August