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Published online 28 September 2007
Published in Soil Sci Soc Am J 71:1667-1675 (2007)
DOI: 10.2136/sssaj2006.0227
© 2007 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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SOIL PHYSICS

Assessing the Size Dependency of Measured Hydraulic Conductivity Using Double-Ring Infiltrometers and Numerical Simulation

Jianbin Lai and Li Ren*

Department of Soil and Water Sciences, China Agricultural Univ., Key Lab. of Plant–Soil Interactions, MOE, Beijing 100094, China

* Corresponding author (renl{at}mx.cei.gov.cn).


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Saturated hydraulic conductivity measurements are important for understanding and modeling hydrologic processes at the field scale. Few systematic studies have been conducted on how the size of double-ring infiltrometers affects the measured hydraulic conductivity. To determine this size effect, we measured saturated hydraulic conductivity at seven sites using four different sizes of double-ring infiltrometers. Inner-ring diameters, di, were 20, 40, 80, and 120 cm. Detailed numerical investigations were also conducted to explain how the inner-ring size of a double-ring infiltrometer influences the measured hydraulic conductivity in a heterogeneous soil. Field and simulation results both demonstrated that the variability in measured hydraulic conductivity was greater for smaller inner rings (e.g., di <40 cm), and gradually decreased as the ring size increased. Our study indicates that where soil spatial variability is high, infiltrometers having a large inner ring (in general, di >80 cm) are essential for reliable measurement.


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Soil physical and hydrologic simulation models utilize a set of soil hydraulic parameters that are specific to the location being simulated, and the computed water balance is quite sensitive to the parameters (Mmolawa and Or, 2003; van Dam and Feddes, 2000; Govindaraju et al., 1992). Among these soil hydraulic parameters, saturated hydraulic conductivity and its related measurements are reported to have the highest variability (Biggar and Nielsen, 1976). Stockton and Warrick (1971) demonstrated that variability in saturated hydraulic conductivity relates to both the soil depth and location in the field, as well as measurement errors. This warrants developing both accurate techniques for measuring soil hydraulic properties and tools for describing the spatial variability of these properties (Ciollaro and Romano, 1995).

When double-ring infiltrometers are used to determine saturated hydraulic conductivity, it is commonly assumed that the soil is homogeneous within the measured area. Hydraulic conductivity can change by more than an order of magnitude within a short distance, however, due to soil spatial variability and heterogeneity. This suggests that double-ring infiltrometers, widely used for determining the saturated hydraulic conductivity, may give size-dependent results. Several investigators have studied the size dependency of hydraulic conductivity measurements in porous media (Dirk et al., 1999; Rovey and Cherkauer, 1995; Guimera et al., 1995). One common conclusion of these studies is that, in heterogeneous media, measured hydraulic conductivity increases with increasing measurement size, and then becomes constant above a certain measurement size. Such variation was not observed in homogeneous media, however. Sharma et al. (1980) performed 26 tests using double-ring infiltrometers with ring diameters of 45.7 and 76.2 cm for inner and outer rings, respectively, on a 9.6-ha watershed in Oklahoma. Their measured infiltration rates spanned two orders of magnitude. Shouse et al. (1994) studied steady-state infiltration rates with three infiltrometer sizes within a field plot, and observed that the mean infiltration rate for a 4- by 4-m plot area increased with increasing measurement size. Haws et al. (2004) conducted a set of experiments using three concentric, square infiltrometers (20 by 20, 60 by 60, and 100 by 100 cm) to characterize the spatial variability of steady-state infiltration rate Is as affected by measurement size at the hillslope and landscape scales. The overall mean as well as individual measurements of Is values for a 100- by 100-cm infiltrometer were greater than the values obtained by the smaller infiltrometers.

Other scientists (Sisson and Wierenga, 1981; Clothier and White, 1981) further observed that the underlying statistical distribution of steady-state infiltration rates changed with the measurement scale. The mean infiltration rate increased, and the variance decreased, with increasing measurement scale. Later, Bachu and Cuthiell (1990) used numerical simulations to study the effects of core-scale heterogeneity on steady-state flow, and the dependence of the effective hydraulic conductivity on the heterogeneity fraction. Their results showed that the effective hydraulic conductivities depended both on the intrinsic structure of the medium, and on the flow process. More recent work by Zhang (1997) resulted in a parametric relationship based on numerical simulation. In his work, a series of disk infiltration simulations was conducted with different disk radii, using a fractal model for the soil. The simulation results showed that the calculated values of hydraulic conductivity change with both location and sampling size (soil contact area of the disk infiltrometer), and increase with disk radius.

Double-ring infiltrometers are widely used for in situ determination of soil hydraulic conductivity (Ashraf et al., 1997; Ben-Hur and Assouline, 2002; Bouwer, 1986; Dirk et al., 1999). Marshall and Stirk (1950) showed that infiltration rates measured using single rings decreased as the ring diameter increased. Swartzendruber and Olson (1961a, 1961b) conducted a series of double-ring infiltration experiments with different sizes of outer rings to determine the buffer effect for a sandy soil. They found that buffering brings the actual infiltration velocity close to the one-dimensional infiltration rate, and the measurement error due to lateral flow becomes negligible as the diameter of the outer ring increases to 1.2 m. Wu et al. (1997) showed that when the outer-ring diameter was increased to 120 cm (inner-ring diameter kept at 20 cm), the measured infiltration rates were 20 to 33% greater than the one-dimensional infiltration rates for their three test soils. As ring size increased, measurement error due to lateral flow decreased, and consequently the measured infiltration rates better approximated the one-dimensional vertical flow rates. More recently, Wuest (2005) showed that the influence of a large infiltrometer is not only limited to a larger sample volume. It might be attributed to the effect of the lateral matrix flow forming a bulb below the bottom of the cylinder. Another factor is that water flow was somehow blocked by the cylinder wall.

Studies investigating the size dependency of ring infiltrometer measurements have mainly focused on lateral flow, and little attention has been devoted to size dependency caused by soil heterogeneity. Hydraulic conductivity measured in a heterogeneous soil is strongly linked to the representativeness of the measured volume. This representativeness involves both the representative elementary volume and the correlation scale of the hydraulic conductivity (Ciollaro and Romano, 1995). The objectives of this study were (i) to evaluate the effect of measurement size on the soil hydraulic conductivity, and (ii) to find the smallest diameter double-ring infiltrometer needed to cover a representative area for reliable soil hydraulic conductivity measurements in the semiarid region of China.


   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Measurement of Saturated Hydraulic Conductivity
Several mathematical expressions are used to describe infiltration into soils. Among the physically based expressions (e.g., Green and Ampt, 1911; Philip, 1957), Philip's two-term equation is the most attractive both for ease of computation and because time can be expressed as an explicit function of cumulative infiltration (Sharma et al., 1980). Philip (1957) showed that cumulative infiltration I under water-ponded conditions is approximated at time t by

Formula 1[1]
where I is cumulative infiltration [L], S is sorptivity [L/T0.5], and A is a constant [L/T]. As time progresses, the first term becomes negligible and the importance of A, which represents the main part of the gravitational influence, increases (Koorevaar et al., 1983). The A term can be taken as the saturated hydraulic conductivity of the wetted zone (Kw) after a long period of infiltration (Bouwer, 1986). This equation was applied to the data collected in the present study. By fitting Eq. [1] to the cumulative infiltration data, we obtained Kw of the wetted zone for each infiltration test.

The available literature shows that the probability of overestimating vertical infiltration decreases as the ring size increases (Wu et al., 1997; Swartzendruber and Olson, 1961a, 1961b). Swartzendruber and Olson (1961a, 1961b) introduced the buffer index b = (ro – ri)/ro, where ro and ri are outer-ring and inner-ring radii, respectively. They found that, for ro = 30 cm and b ≥ 0.33, the velocity ratio (the ratio of the average infiltration velocity to the one-dimensional flow velocity) never exceeded ±25% error. Further, for ro = 61 cm, the velocity ratio was unity within ±25% regardless of b. In the present study, four infiltrometers, designated S1 through S4, having outer-ring diameters of 70, 70, 100, and 140 cm were used (Fig. 1 ). The corresponding buffer indices are b = 0.71, 0.43, 0.20, and 0.14 (Table 1 ), respectively. All of our velocity ratios were therefore expected to fall within Swartzendruber and Olson's (1961a, 1961b) ±25% error limits, assuming similar soil variability. This assumption is reasonable considering the similar clay content of the soils used in the two studies.


Figure 1
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  		Fig. 1. Four sets of double-ring infiltrometers with different diameters (only inner rings with nested rings are shown here).

 

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  		Table 1. Basic parameters of the four double-ring infiltrometers, S1 through S4.

 
The outer-ring sizes we used should be large enough to mask the lateral flow contribution to total infiltration, particularly with our initial soil moisture. When the test soils had a relatively high initial water content, field measurements showed little difference between buffered and unbuffered infiltration velocities (Burgy and Luthin, 1956; Schiff, 1953). In this study, the average initial volumetric water content along the profile was 0.23, >50% of the saturated water content. This relatively high initial water content weakens the capillary effect, thereby decreasing the lateral flow contribution to total infiltration. Since the lateral flow contribution to total infiltration was relatively small in this study, and its difference among different size infiltrometers is negligible, we did not take these differences into account in the calculation procedure for hydraulic conductivities.

Field Experiment
The field experiment was conducted in a long-term tillage plot within the Minqin oasis in the lower reaches of the Shiyang River (38°54' N, 103°03' E) in Gansu province, northwest China. Seven sites within the 100- by 100-m experimental plot, about 30 to 40 m away from each other, were randomly selected. Soil dry bulk density and saturated water content at each site were measured with the oven-dry method, using a sample size of 100 cm3. Soil particle-size distribution was measured using the pipette method (Gee and Bauder, 1986). Measured soil physical properties for each site are listed in Table 2 .


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  		Table 2. Soil physical properties of the seven test sites.

 
At each site, one measurement was taken with each of the four double-ring infiltrometers (Fig. 1), each in close proximity to the others. The water level in the inner ring was maintained using a Mariotte tube, while the water level in the outer ring was adjusted manually to match that in the inner ring (Fig. 2 ). Water was carefully added to the outer ring every few seconds, so water level fluctuations were kept within 0.5 cm and had negligible impact on the infiltration inside the inner ring. A polyvinyl chloride pipe was used as a Mariotte tube to supply water to the inner ring. The flux in the inner ring was measured using a calibrated sight tube attached to the side of the Mariotte tube (Fig. 2). The Mariotte tube was 180 cm high, with a 14-cm inner diameter for the 20- and 40-cm-diameter infiltrometers, and a 20-cm inner diameter for the 80- and 120-cm infiltrometers. The Mariotte tubes were graduated from 0 to 160 cm in 0.1-cm subdivisions, which were easily read and accurately measured.


Figure 2
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  		Fig. 2. Cross-section sketch of the double-ring infiltrometer.

 
For each inner ring, one more cylinder with a base was nested and fixed in the ring by four pins. This nested cylinder was about 20 cm in height, and its diameter was 3 cm less than that of the inner ring. The cylinder was held several centimeters above the soil surface, so it did not affect the infiltration process. When the inner ring was filled with water, the nested cylinder was surrounded by water but had no water inside. The nested cylinder had two functions: (i) it mainly reduced the upper free water area in the inner ring, resulting in improved measurement accuracy; and (ii) it minimized surface evaporative losses, especially for long-term infiltration.

The measurement procedure was the same for each of the seven sites. For each infiltrometer, the two concentric rings were driven at least 5 cm into the soil surface without removing the crop stubble or otherwise preparing the surface. Rings were gently driven in with a rubber hammer and a special driving cap, always ensuring that the upper rim of the ring remained horizontal to avoid producing cracks between ring and soil during insertion. To minimize the risk of altering the soil surface at the beginning of the infiltration process, water was carefully poured on the soil surface confined by the ring to a depth of approximately 5 cm just before switching on the Mariotte tube. Both the inner and outer rings were filled with water at the same time. The Mariotte tube supplied water automatically, and a constant 5-cm water head was maintained at the soil surface (Fig. 3 ). The rate of fall of the water level in the Mariotte tube was monitored and recorded at 15-s intervals during the initial stage of infiltration, and the time interval was gradually increased to 5 min as infiltration proceeded. Steady state was reached after an average infiltration time of 90 min at each site. The criterion we used for attaining steady-state infiltration was that 5-min infiltration volumes remained constant for a 30-min period.


Figure 3
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  		Fig. 3. Photograph of field experiment setup for the double-ring infiltrometer with an inner-ring diameter of 40 cm.

 
Numerical Experiments
A series of numerical experiments was conducted to investigate how the inner-ring size of a double-ring infiltrometer influences the accuracy of the measured saturated hydraulic conductivity in heterogeneous soil. The two-dimensional model HYDRUS-2D (Simunek et al., 1999) was used to simulate infiltration under a double-ring infiltrometer. All simulations were performed using axisymmetric domains of 120 cm in depth, with six different radii: 5, 10, 20, 40, 60, and 100 cm. The hydraulic conductivity field in a simulation domain was assumed to be isotropic. Nodes were equally spaced 1 cm apart in both the vertical (z) and radial (x) directions. The hydraulic conductivities we measured in the field were effective values of the domain inside the inner ring; in nature, this domain is heterogeneous. In the simulations, we included soil heterogeneity by treating Kw as a realization of a stationary, second-order, spatially random distributed field with correlation length L and standard deviation SD. The scaling factor fields were generated with a stochastic field generator embedded in HYDRUS-2D (Simunek et al., 1999). Then the stochastic Kw fields for each infiltrometer were obtained by multiplying the scaling factor at each node by the measured input hydraulic conductivity value. Six correlation lengths (L = 0, 10, 20, 50, 100, and 200 cm) and six standard deviation values (SD = 0, 0.1, 0.25, 0.5, 0.75, and 1.0) of the random field of log(Kw) were used for the various realizations of hydraulic conductivity fields. We performed 10 realizations for each combination of (L,SD) treatments and infiltrometer diameters (10, 20, 40, 80, 120, and 200 cm). Because only a single realization is needed when SD = 0, this gave a total of 1806 realizations.

The van Genuchten (1980) hydraulic function was used in the simulations with m = 1 – 1/n. Parameters of the van Genuchten {theta}(h) and K(h) relationships were obtained from soil sampled at Site 7 in the field: Kw = 3.167 x 10–6 m s–1, residual volumetric soil water content {theta}r = 0.057, saturated volumetric soil water content {theta}s = 0.452, n = 1.63, and {alpha} = 0.0059 m–1. The initial soil volumetric water content, {theta}i = 0.23, was from field measurement. The simulated infiltration duration was 2 h. Boundary conditions were free drainage at the bottom of the domain and a constant water head (h = 5 cm) at the surface, reproducing the infiltration conditions. A no-flux boundary condition was imposed on the lateral borders of the simulation domain, since the lateral flow contribution to total infiltration should be negligible in our field experiment, as discussed above. Numerical modeling also demonstrated that the flow fields in our simulation were essentially two dimensional rather than one dimensional.

Numerical Model Validation
Experimental data from the fourth site were selected to calibrate the HYDRUS-2D model. First, each pair of (L,SD) parameters was applied to generate random Kw fields for simulation domains 20 and 80 cm in diameter, and infiltration was simulated within all these domains. Then by comparing the simulated cumulative flux with the field-measured data from infiltrometers 20 and 80 cm in diameter, we chose that (L,SD) parameter pair whose simulated fluxes best fit the measured data (Fig. 4a ). In our case, the parameters L = 20 cm and SD = 0.25 were selected. Figure 5 shows the random field of scaling factors generated by HYDRUS-2D using L = 20 cm and SD = 0.25. Areas in red have a large hydraulic conductivity, while blue indicates a smaller value. The ratio of the maximum to the minimum Kw is 283.2 (i.e., 4.588:0.0162). Infiltration with infiltrometers 40 and 120 cm in diameter were then simulated with the same random field (Fig. 4b). The simulated flux nicely approximated the infiltration curve for both infiltrometers. These results demonstrate that HYDRUS-2D can adequately simulate the infiltration processes operative in our field study.


Figure 4
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  		Fig. 4. The cumulative infiltration (Is) curves of (a) measured and simulated infiltration at Site 4 under double-ring infiltrometers for inner-ring diameters (di) of 20 and 80 cm, and (b) measured and predicted infiltration at Site 4 under double-ring infiltrometers for di of 40 and 120 cm.

 

Figure 5
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  		Fig. 5. Scaling factor distribution field of the saturated hydraulic conductivity of the wetted field, Kw(x,y) (HYDRUS-2D generated with correlation length L = 20 cm, SD = 0.25). Note: the hydraulic conductivity at each node was obtained through multiplying the scaling factor at the corresponding node by the reference hydraulic conductivity value, which we have input into the hydraulic parameter module.

 

   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Field Experiment
Sites 1, 3, and 5 showed different behaviors than Sites 2, 4, 6, and 7, so results are presented separately for these two groups. Hydraulic conductivity (Kw) at Sites 1, 3, and 5 (Fig. 6a ) increased as the inner-ring diameter (di) increased. This result is consistent with the results of Rovey and Cherkauer (1995), Zhang (1997), and Dirk et al. (1999), who reported that hydraulic conductivity increased with the scale of measurement in heterogeneous media. When the rings were small (di < 40 cm), there was a notable increase in hydraulic conductivities with increasing ring diameter, but increases beyond di = 40 cm for Sites 1 and 3, and di = 80 cm for Site 5, gave negligible changes.


Figure 6
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  		Fig. 6. Variation in saturated hydraulic conductivity of the wetted field (Kw) with inner-ring diameter for (a) Sites 1, 3, and 5, and (b) Sites 2, 4, 6, and 7.

 
At the other four sites (2, 4, 6, and 7), in contrast, measured hydraulic conductivities sharply decreased as inner-ring diameters increased from 20 to 40 cm (Fig. 6b). Sites 2 and 4 showed an overall decrease in Kw, while Sites 6 and 7 showed an overall increase, as di increased from 20 to 120 cm. With one exception (Site 7), the greatest change in Kw occurred between di = 20 and 40 cm.

If we treat the individual sites as replicates (reasonable given their similar textures [Table 1]), we see that the mean hydraulic conductivity does not change significantly across the full range of inner-ring diameters (Fig. 7 ). This supports our earlier assertion that lateral flow would not cause significant differences between ring sizes in our experimental setup. The range and standard deviation of the measurements, however, decreased appreciably with increasing di. As mentioned above, several researchers (Rovey and Cherkauer, 1995; Zhang, 1997; Dirk et al., 1999) concluded that the measurement-scale effect was due to the heterogeneity of the soil. Our results support their conclusion. As the ring size increases, the representativeness of the area covered by the infiltrometer also increases, so the measured hydraulic conductivity becomes more representative and stable.


Figure 7
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  		Fig. 7. Variation in saturated hydraulic conductivity of the wetted field (Kw) with inner-ring diameter for all sites.

 
Numerical Modeling
Detailed infiltration simulations were performed using various random hydraulic conductivity fields. One set of maps of the scaling factor fields (L = 20 cm and SD = 0.25) for different diameters is shown in Fig. 8 . The corresponding simulated velocity vector fields at a specific infiltration time (90 min) are presented in Fig. 9 , with the direction of the arrows indicating flow direction, and the length and color of the arrows indicating flow rate. The maps show that water flow from the inner ring was not strictly vertical; rather, there was horizontal flow in some parts of the simulation domain even though the model had no flux across the lateral boundaries. Additionally, the flow rates show great variation even within a given depth. When we simulate infiltration into a homogeneous soil, we get one-dimensional flow—strictly vertical arrows of approximately equal lengths (not shown). In addition, comparing the velocity vector distribution map (Fig. 9) with the map of the saturated hydraulic conductivity scaling factor field (Fig. 8), we could find that the water flow has slowed down in the region with low hydraulic conductivity, while the region with higher hydraulic conductivity has a higher flow rate. Moreover, as indicated by the water potential distribution map (Fig. 10 ), the wetting front was unstable and there is more flow through locations with higher hydraulic conductivity than through lower. These comparisons show that infiltration into heterogeneous media is essentially different from the one-dimensional flow in homogeneous media, despite there being no flux across the lateral boundaries.


Figure 8
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  		Fig. 8. Representative maps of scaling factor fields (correlation length L = 20 cm, SD = 0.25) for different diameters: (a) 10 cm, (b) 20 cm, (c) 40 cm, (d) 80 cm, (e) 120 cm, and (f) 200 cm.

 

Figure 9
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  		Fig. 9. Representative velocity vector maps under infiltrometers of different diameters: (a) 10 cm, (b) 20 cm, (c) 40 cm, (d) 80 cm, (e) 120 cm, and (f) 200 cm.

 

Figure 10
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  		Fig. 10. The soil water potential distribution map under the infiltrometer with a diameter of 80 cm at the infiltration time of 90 min. Only part of the simulation domain (50 cm in vertical) is shown here.

 
For a randomly distributed Kw field with some spatial structure, measuring a larger volume of soil is equivalent to pooling smaller samples (Parkin and Robinson, 1992). Therefore, both the large and small rings are sampling the same population and will center on the same mean. Because Kw is lognormally distributed, however, the Kw distribution measured with a larger ring should be more normal than that measured with a smaller ring. Descriptive statistics on the overall hydraulic conductivities show the tendency toward normality with increased ring size (Table 3 ). The standard deviation, range, and skewness decreased as the ring size increased, while the mean decreased less and the median Kw value varied hardly at all. An exception is for di = 40 cm and further research is needed. Meanwhile, the asymptote significance of the Kolmogorov–Smirnov tests was <0.05, so the distribution of the data for all the ring sizes was significantly different from the normal (Gaussian). All six rings produced distributions with means much greater than medians and large, positive skewness. The Q–Q plot of log(Kw) (Fig. 11 ) shows that the calculated Kw values from the infiltrometers of all six diameters were approximately lognormally distributed, except for some points with small values. These results are consistent with the findings of Sisson and Wierenga (1981), who found that infiltration rates were lognormally distributed for all ring sizes.


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  		Table 3. Statistics of the simulated soil hydraulic conductivities.{dagger}

 

Figure 11
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  		Fig. 11. The Q–Q plot of the log-transformed saturated hydraulic conductivity of the wetted field (Kw).

 
Figure 12 shows the distribution of simulated Kw across all realizations and treatments. The Kw values scatter across a large range for small ring size, and the range gradually decreases with increasing ring diameter. The interquartile range also decreases with increasing ring size. The median Kw value does not change appreciably across the full range of ring diameters.


Figure 12
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  		Fig. 12. Distribution of the simulated log-transformed saturated hydraulic conductivity of the wetted field (Kw) under different ring diameters.

 
As the SD of the log(Kw) field increased, the range of simulated hydraulic conductivities also increased (Fig. 13 ). If the SD is small, the Kw values always show less variation, no matter the size of the infiltrometer. In other words, if the soil spatial variability is low, infiltrometers of any size will get similar hydraulic conductivities. The greatest scatter in calculated hydraulic conductivities was observed for small rings and large standard deviations. Large rings showed little scatter regardless of the standard deviation; likewise, media with a small standard deviation showed little scatter regardless of ring size. The Kw values simulated for a homogeneous hydraulic conductivity field (SD = 0) were essentially constant across all ring diameters (Fig. 13a). This is consistent with the observation of Dirk et al. (1999) that, in homogeneous media, hydraulic conductivity does not change with the measurement scale.


Figure 13
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  		Fig. 13. The relationship between simulated saturated hydraulic conductivity of the wetted field (Kw) and ring diameter with standard deviations (a) 0.1, (b) 0.25, (c) 0.5, (d) 0.75, and (e) 1.0.

 
The effect of L was similar to that of SD (Fig. 14 ). Even a small ring is likely to sample the full range of Kw values if the correlation length is small, but a larger ring is needed to integrate across a greater correlation length. Whether L was large or small, the calculated Kw values were scattered in a broad range for small ring sizes (e.g., di < 40 cm), then converged to a relatively small range for larger rings.


Figure 14
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  		Fig. 14. The relationship between simulated saturated hydraulic conductivity of the wetted field (Kw) and ring diameter with correlation lengths (a) 0 cm, (b) 10 cm, (c) 20 cm, (d) 50 cm, (e) 100 cm, and (f) 200 cm.

 
Due to soil heterogeneity, the soil hydraulic conductivity that we measured with the double-ring infiltrometers was actually the effective value of the soil that happened to be under the infiltrometer. The numerical simulations reveal the basic cause of the scale effect on measuring soil hydraulic conductivity with a double-ring infiltrometer. When the soil heterogeneity is great (larger L or SD), larger rings are needed for a reliable measurement. Our simulations indicate that, for the heterogeneity encountered in our field study, infiltrometers with di ≥ 80 cm are needed to ensure a reasonably stable and representative measurement.


   CONCLUSIONS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
Soil hydraulic conductivities were measured using four sizes of double-ring infiltrometers at seven randomly selected sites within a research field. Infiltrometer sizes, buffer indices, and initial soil moisture were selected to reduce the impact of lateral flow, which has been suggested as a cause of size-dependent infiltrometer measurements. Size dependency of the measurements was seen at all seven sites.

Numerical modeling revealed the cause of the size effect on soil hydraulic conductivity measurements. If the correlation length or standard deviation of hydraulic conductivity is small, then the hydraulic conductivity has less size dependency. Conversely, as the correlation length and standard deviation of the hydraulic conductivity field increase, the measured values become more size dependent. Increasing the ring diameter is helpful in improving the representativeness of soil hydraulic conductivity measurements. For the soils tested in this study, a large ring (in general di > 80 cm) is required to reliably quantify the soil hydraulic conductivity. Given these results, the infiltrometer sizes that have generally been used on these soils (20–50 cm) are far from optimal.

In summary, as the size of a double-ring infiltrometer increases, the representativeness of the area covered also increases, and the measured hydraulic conductivity becomes more stable with respect to the heterogeneity of the soil. Large-diameter infiltrometers (in most cases, with di ≥ 80 cm) also minimize the effects of lateral divergence due to capillary gradients. As a conclusion, large-diameter infiltrometers produce more stable values than small-diameter ones, so they represent an efficient method for improving measurement representativeness.


   ACKNOWLEDGMENTS
 
This research was funded by Grant no.50339030 key research project and Grant no. 50479012 research project from National Natural Science Foundation of China. It was also sponsored by the Program for Changjiang Scholars and Innovative Research Team in University (IRT0412), Ministry of Education, China. We are very grateful to Dr. Robert P. Ewing for providing insightful suggestions and helping us go over the manuscript. We also would like to express our heartfelt thanks to Dr. Jirka Simunek, who helped us upgrade the HYDRUS-2D model. In addition, the authors acknowledge the associate editor and the anonymous reviewers for their constructive comments.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
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Received for publication June 15, 2006.


   REFERENCES
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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The SCI Journals Agronomy Journal Crop Science
Journal of Natural Resources
and Life Sciences Education		 Vadose Zone Journal
Journal of Plant Registrations Journal of
Environmental Quality		 The Plant Genome