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Division S-1—Soil Physics

Spatial Variability and Measurement Scale of Infiltration Rate on an Agricultural Landscape

^a School of Civil Engineering, Purdue Univ., West Lafayette, IN 47907-2051
^b Dep. of Agronomy, Purdue Univ., West Lafayette, IN 47907
^c Dep. of Natural Resources and Environmental Sciences, Univ. of Illinois, Urbana, IL 61801
^d Currently at Dep. of Geography and Environmental Engineering, Johns Hopkins Univ., Baltimore, MD 21218-2686
^e Currently at National Lab of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil & Water Conservation, Chinese Academy of Sciences, Yangling, Shaanxi 712100, China

^* Corresponding author (pscr{at}purdue.edu).

	ABSTRACT

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

 
Determining representative infiltration rate parameters for use in modeling field-scale flow and transport processes is difficult because of the spatial variability of soil properties. To determine how steady-state infiltration rate variability is affected by support scale, steady-state infiltration rates (I_s) were measured at three spatial scales (local, hillslope, and landscape) along a 710-m transect on a swell–swale landscape in Indiana. Spatial variability at the local scale was studied using measurements in a 1 x 1 m² array of 100 ring infiltrometers (7.2-cm diam.) for three soils at three horizons each. Studies were conducted at the hillslope and landscape scales using three nested infiltrometers of sizes 20 x 20, 60 x 60, and 100 x 100 cm². Geostatistical analyses show a decrease in the sample variance of the I_s values and an increase in spatial correlation of I_s with depth. They also suggest that an area >10, 7.2-cm diam. rings (i.e., approximately >400 cm²) is needed to provide a representative measurement area (RMA; i.e., area needed to filter out smaller-scale heterogeneities) at the local scale. Hillslope- and landscape-scale tests indicate that I_s measurements with infiltrometers require an infiltrometer with a support area greater than the local-scale RMA to show the spatial correlation of the larger scales. In addition, these infiltrometer measurements may not provide appropriate effective I_s estimates at these greater scales unless they are averaged over a domain that extends across the landscape's range of variability, estimated from the computed semivariograms to be 120 to 200 m for this study.

Abbreviations: I_s, steady-state infiltration rate • RMA, representative measurement area

	INTRODUCTION

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

 
WATER RETENTION and flow dynamics in agricultural soils are primary drivers of crop growth, nutrient cycling, and contaminant transport. In particular, infiltration is a dominant process controlling the soil–water status for plants and the vadose zone transport of pesticides and nutrients. The I_s is dictated by such factors as soil properties, initial and boundary conditions at the soil surface, landscape features, and agricultural management—all of which can be spatially and temporally heterogeneous (Heard et al., 1988; Wu et al., 1995; Logsdon and Jaynes, 1996; Paz-Gonzalez et al., 2000). The observed I_s, like most environmental processes, can manifest spatial patterns across a continuum of measurement scales (Cushman, 1984; Atkinson and Tate, 2000) as a complex function of time and space (Wilding and Drees, 1983; Logsdon and Jaynes, 1996). The importance of accurate quantification of representative hydraulic parameters for use in predictive modeling has been increasingly recognized with the growing need to forecast water-related processes, such as runoff, soil erosion, and solute transport, at different spatial scales. It is thus imperative to understand how to interpret measurements of soil hydraulic properties made at different spatial scales and to know which measured values are appropriate for simulating water and solute fluxes at various spatial scales.

Measurements of soil properties are most representative of a given scale when the scale of spatial measurement is the same size as, or exceeds, the scale of spatial variation (Atkinson and Tate, 2000). The characterization of the spatial variability and scale-dependence of I_s, as well as other soil properties, is commonly performed using geostatistical approaches (Sisson and Wierenga, 1981; Vieira et al., 1981; Cressie and Horton, 1987; Lauren et al., 1988; Gupta et al., 1994; Shouse et al., 1994; Hoosbeek and Bouma, 1998; Goovaerts, 1999; Goovaerts, 2001). In this study, geostatistical techniques were used to address the subject of spatial variability and the effect of sample support on the measurement of the steady-state I_s for typical agricultural soils within an agricultural landscape of undulating hills (swells) and drainage ways (swales). The swell–swale landscape, typical to central Indiana and other areas of the midwestern USA, includes heterogeneous macropore networks at the local-scale and continuously changing soil layering and taxonomic units at larger scales. These two kinds of variability complicate the concept of a RMA (i.e., the measurement support area required to filter out smaller-scale heterogeneities) such that the appropriate two-dimensional measurement support must be specifically defined for the scale of interest (Dagan, 1986; Lauren et al., 1988; Lischeid et al., 1998; Wagenet, 1998).

To evaluate the relationship between scale of interest and measurement support, the geostatistical relationships of measured I_s values were assessed from measurements taken at the local scale (interior to a 1 x 1 m² area), hillslope scale (along a 90-m transect), and landscape scale (along a 710-m transect) with the specific objectives of: (i) determining how I_s variability is affected by support scale; and (ii) estimating appropriate RMA support areas for I_s measurements.

	MATERIALS AND METHODS

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

 
Site and Soils
The site is located in a hay field at the Animal Science Research Center, Purdue University, about 16 km northwest of West Lafayette, IN. A transitional region from hardwood forest to prairie vegetation surrounds the site, and the general topography gently declines to the southwest. All measurements focus along a straight north–south transect (Fig. 1) offset 10 m west of a fence separating the hayland from a row crop field. This transect is representative of the typical till-plain toposequence, consisting of depressional areas (swales or drainage ways), convex areas (swells) and intermediate hillslope elements. The profile topography (Fig. 1) has maximum elevation difference of 2.7 m with slopes ranging from 0 to 3.6% (average slope of 1%). The hillslopes on the 710-m transect have an average length of about 100 m, or a wavelength of about 200 m in the north-south direction. Pedon descriptions, made in pits excavated near the transect, identified three major soils classified as Drummer silty clay (fine-silty, mixed, superactive, mesic Typic Endoaquoll) in the depressions, Brenton silt loam (fine-silty, mixed, superactive, mesic Aquic Argiudoll) on the swells, and Dana silt loam (fine-silty, mixed, superactive, mesic Oxyaquic Argiudoll) on the lower summits. Other minor soil inclusions along the transect were Parr silt loam (fine-silty, mixed, active, mesic Oxyaquic Argiudoll) on the higher summits, Pella silty clay loam (fine-silty mixed, superactive, mesic Typic Endaquoll) and Chalmers silty clay loam (fine-silty, mixed, superactive, mesic Typic Endoquoll) in the depressions, and Raub silt loam (fine-silty, mixed, superactive, mesic Aquic Argiudoll) on the footslopes.

View larger version (16K): [in this window] [in a new window]   Fig. 1. Elevation profile of the study transect, showing the location of the pedon description sites and the position of the hillslope transect (labeled H.T.). Note the exaggeration of the vertical scale.

Each local-scale infiltration measurement was conducted at a location near the site where the pedon description was made for that respective soil. Experimental procedures for each of the three soil horizons were identical. To prepare the infiltration measurement surface, hay vegetation and surface crust (about 2 cm) over an area about 1.5 x 1.5 m² were removed, and a 1 x 1 m² infiltrometer was then forced into the soil to a depth of 5 cm. Then, the area was cleaned with a vacuum cleaner to remove loose soil from the surface. Water was ponded on the surface to an 8-cm depth and was maintained for 1 h, after which the falling head during a subsequent 30-min period was read using a point gauge. Subsequent to the first series of falling head measurements, water was again added to the 8-cm depth, and the head drop over an additional 30-min interval was measured. The measured infiltration rate in the last 30-min period had approached an asymptotic value, which was recorded as the steady-state rate, I_s.

After the initial 1 x 1 m² infiltration measurement was completed at one horizon, the 1 x 1 m² infiltrometer was left in place. On the following day, the test area was divided into one hundred 10 x 10 cm² cells. At the center of each cell, an 11 cm long and 7.2 cm diameter ring was inserted to a depth of 3 cm. Water was then added to the volume of the 1 x 1 m² infiltrometer outside the rings. The water level was slowly raised until it spilled over the top of, and into, the rings. During filling, the seepage under the rings was examined. Few rings had visible seepage, which was readily controlled by gently pushing the ring slightly deeper. The entire infiltrometer area was saturated for 1.5 h and then the water head drop versus time was recorded for 30-min intervals for each ring. Since it was difficult to simultaneously measure infiltration rates in 100 rings, the measurements were completed over 2 d by dividing the 100 rings into two sections. Procedures for saturation and measurement were the same for both sections.

At the end of the second day of ring infiltration measurements, a dye tracer was added to the rings and the square infiltrometer, and the dye solution was allowed to drain for at least 24 h. Soil was then excavated to the middle of the test horizon and both stained and non-stained macropores were visually examined (Liu, 1995). Soil was then excavated to the top of the next horizon, and all procedures for surface preparation and infiltration measurement were repeated.

Hillslope- and Landscape-Scale Studies
The purpose of the hillslope-scale and landscape-scale studies was to investigate the manifestation of spatial variability across a single hillslope versus a series of swell–swale topographic features. Experimental procedures for the hillslope- and landscape-scale experiments were similar; except, a lag distance of 2 m was used for the hillslope scale and a 10-m lag was used for the landscape scale. The hillslope transect was 90 m long (between 300 and 390 m) and consisted of 46 points, while the landscape transect measured the full 710-m transect distance and included 72 locations (see Fig. 1). Three concentric, square infiltrometers of three sizes (20 x 20, 60 x 60, and 100 x 100 cm²) were used at each location to characterize the spatial variability of infiltration rate as affected by measurement scale. Surface preparation, installation of infiltrometers, mode of water supply, and saturation method were the same as for the local-scale study. Infiltration rates for the 60 x 60 and 100 x 100 cm² infiltrometers were calculated as a weighted mean of the I_s measured in the inner concentric infiltrometer(s) (Swartzendruber and Olson, 1961).

Geostatistical Analysis
Spatial variation of steady-state infiltration rate was described using semivariograms, assuming stationarity among similar lag increments (i.e., intrinsic stationarity; Goovaerts, 1997, p. 71; Chilès and Delfiner, 1999, p. 17) and horizontal isotropy. Semivariogram values at each lag separation, (h), were computed as:

[1]

where N(h) is the number of pairs separated by a lag distance of h, and Z(u_i) is the value of I_s at the location u_i.

The interpretation of the range of a semivariogram can be obscured by extreme data values and a proportionality effect (i.e., sample variance increases with the local mean; Goovaerts, 1997, p. 82; Chilès and Delfiner, 1999, p. 108). To account for the positive skewness in the measured data, semivariograms were computed using the log_e–transformed (Ln-transformed) data. As an aid in interpreting the Ln-transformed semivariograms, the trend of the computed semivariogram values was modeled using one of the semivariogram functions listed in Table 1. The model selected to represent the semivariogram values was chosen based on a qualitative interpretation of which function best represented the overall behavior of the computed data, and then the model parameters (nugget, range, sill) were calibrated based on a minimization of a weighted sum of the squared deviations between the modeled and computed values.

View this table: [in this window] [in a new window]   Table 1. Semivariogram models used in this study where a = range (slope–1 for linear model), Co = nugget, Co + C1 = sill, h = lag distance, = semivariance.

[2]

and the general relative semivariogram is:

[3]

where m_–h and m_+h are the mean of the Z(u) and Z(u + h) values, respectively.

All semivariograms and madograms in the study were computed using the 2001 WinGsLib software package (Statios LLC), which provides a graphical user interface to the GSLIB geostatistical code developed by Deutsch and Journel (1992). The semivariograms, madograms, and general relative semivariograms were only computed for the lag distances up to one-half of the transect length because values for lag distances greater than one-half of the transect neglect the central portion of the transect data, thus leading to biased semivariogram values for the greater lag distance (Isaaks and Srivastava, 1978; Russo and Jury, 1987; Goovaerts, 1997). The minimum lag pairs for the local-scale, hillslope-scale and landscape-scale studies were 100, 24, and 36, respectively. Because semivariograms and madograms were generally similar, only the Ln-transformed semivariogram plots are given in the results. However, relevant comparisons of the general relative semivariograms and madograms with the Ln-transformed semivariograms are cited in the discussion.

	RESULTS AND DISCUSSION

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

 
Local-Scale Study
The statistical parameters for the infiltration tests conducted over the three soils at the three horizons along with observed soil morphological features are given in Table 2. Steady-state infiltration rate values were lognormally distributed for all soil types and at all depths. The mean I_s value measured in the ring infiltrometers is generally lower than the corresponding 1 x 1 m² measurement (Table 2). Discrepancies between the two measurements are expected because of the difference in the total infiltration areas (0.41 vs. 1 m²) and general experimental errors. The lower mean I_s in the ring infiltration measurements also agrees with the findings of Shouse et al. (1994), whose work suggests that the smaller mean I_s values for the ring measurements versus the corresponding 1 x 1 m² measurement could result from the walls of the infiltrometers blocking non-vertically oriented macropores near the wall edges from conducting water. Since the surface/area ratio is less for the ring infiltrometers, this experimental artifact would be greater for the ring infiltrometer measurements.

Though the mean I_s values show no apparent pattern with depth, the sample variance in I_s values (i.e., dispersion variance among the samples) slightly decreases with depth, except for the surface horizon of the Drummer soil. In addition, the Ln-tranformed semivariogram analyses of the local-scale ring infiltrometer measurements (Fig. 2 , Table 3) show a trend of increasing spatial correlation with deeper horizon. Except for the Dana soil, which exhibits a slight linear trend in the semivariogram, the upper horizons of the soils show no spatial patterns (i.e., pure nugget). The semivariograms for the middle horizon (Btg1, BA, and Bt1 for Drummer, Brenton, and Dana, respectively) appear to be linear with no apparent sill over the range of lag distances modeled, which may reflect a non-stationary spatial mean (Isaaks and Srivastava, 1978; Goovaerts, 1997). The lower horizons for the Drummer and Brenton soils show the most spatial structure, with semivariograms that are clearly convex upward and reach sill values at ranges of about 34 cm. Though the semivariograms for the lower horizons of the Dana soil do not portray this same correlation behavior, the lower horizons of Dana do have a much smaller dispersion variance (as suggested by the lower sill values) than the upper horizon. The decrease in dispersion variance and increase in spatial correlation with depth may be the result of agricultural management practices, such as periodic tillage and mixing of the surface soils, destroying the spatial structure of the upper soils—an impact that would decrease with depth (Mohanty and Kanwar, 1994; Tsegaye and Hill, 1998; Mohanty and Mousli, 2000). In addition, recent studies report that clay fracture abundance, aperture size, and drainage network connectivity tend to naturally decrease with depth (O'Hare et al., 2000; Jorgensen et al., 2002; Deurer et al., 2003). Because macropore networks are the primary heterogeneity at the local scale, a decreased macropore density at the lower depths might also result in the decreased variance and increased spatial correlation in the lower horizons.

View larger version (26K): [in this window] [in a new window]   Fig. 2. Semivariograms (Ln-transformed) for local-scale infiltration measurement data for Drummer (top), Brenton (middle), and Dana (bottom) soils at their three respective horizons.

The sample variances of the nine sets of local-scale (ring) infiltration measurements are further analyzed in Fig. 3 . Sets of adjacent ring measurements were combined to represent a composite measurement at a larger support area. For instance, first 100 one-ring measurements were grouped, then 50 two-ring measurements, then 25 four-ring measurements and so on. In this grouping, no overlapping windows of sets were used so that the mean value of all the sets remained constant. The sample variances of the grouped sets were then plotted against support area (sum of the area of the grouped rings) on a log-log scale. The variance decreases rapidly with increasing support area (Fig. 3), and well over 90% of the total variance among samples is eliminated as the support area becomes greater than about 10 to 20 rings (approximately 400–800 cm²).

View larger version (16K): [in this window] [in a new window]   Fig. 3. Sample variance vs. total measurement support area for the local-scale study.

[4]

where V_n is the variance among n grouped samples with a total support area of A_n, V_o is the variance among the individual samples of area A_o, and b is an empirical "index of heterogeneity." For domains with no spatial correlation, the value of b is expected to be 1, and for a perfectly homogeneous field, b approaches zero. Applying this relationship to the local-scale infiltration measurements, and performing a least-squares regression, generated b-values with "goodness-of-fit" (r²) parameters as reported in Table 4. The b values are generally high, showing the lack of spatial correlation (note that b values >1, while theoretically not possible were also reported by Zhang et al., 1994). The b values averaged by soil type show the Dana soil to be slightly more spatially homogeneous (b = 0.91 for Dana vs. b = 0.97 for Drummer and 1.00 for Brenton). The b values averaged by horizon for the three soils decrease with the depth (b = 1.07 for upper, 0.99 for middle, and 0.82 for lower horizons). This finding is in accord with the slight decrease in the sample variance with increasing depth, as reported in Table 2.

View larger version (39K): [in this window] [in a new window]   Fig. 4. Cumulative probability plots (actual and Ln-transformed) for the hillslope and landscape transect infiltration measurements.

View larger version (34K): [in this window] [in a new window]   Fig. 5. Semivariograms (Ln-transformed) for (top) hillslope-scale and (bottom) landscape-scale infiltration measurement data.

It is possible that the oscillations in the semivariogram, which appear periodic with a half-wavelength of about 15 m, are due to variations in the soil series. The field soil survey indicates that soil series change roughly every 10 to 20 m. However, this linkage between change in soil series and semivariogram period is somewhat indefinite since soil series delineations are approximate at best and do not necessarily correspond to abrupt changes in soil type. Also, since the measurements in the 100 x 100 cm² infiltrometer do not as clearly manifest the periodic trend in the I_s semivariogram, much of the fluctuations may be due more from small-scale variability than larger scale changes in the soil series. The periodicity in the general relative semivariogram (data not shown) is much less than in the Ln-transformed variogram (Fig. 5), indicating that the heteroscedasticity (i.e., proportionality effect) is also likely responsible for some of the apparent oscillations (Goovaerts, 1997, p. 82–85).

The semivariogram, madogram, and general relative semivariogram trends for the three sets of infiltrometer measurements further argue against considering the hillslope as a separate scale. The semivariograms reach no sill value, and for the 20 x 20 cm² infiltrometer the maximum Ln-tranformed semivariogram value is much greater than the total sample variance of the Ln-transformed data (Fig. 5 and Table 5). These observations are evidence of a non-stationary data set (Isaaks and Srivastava, 1978; Goovaerts, 1997). As the hillslope is a transition between the swells and swales, it is reasonable that the hillslope itself is a non-stationary subunit that does not incorporate the full range of variability of a larger spatial scale. Consequently, the statistics (mean and sample variance) of local-scale measurements made only along the hillslope transect could be expected to give biased estimates of effective larger-scale parameters.

Landscape-Scale Study
Summary statistics of the landscape-scale I_s measurements (Table 5) are similar in many ways to the hillslope-scale tests. The 100 x 100 cm² infiltration rate is generally greater than the rates for the smaller infiltration sizes (greater than both for 54 out of the 72 tests and smaller than both for only three measurements), again indicative of possible lateral flow and/or the reduction effect (Shouse et al., 1994).

The models for the Ln-transformed semivariograms of the 100 x 100 and 60 x 60 cm² infiltrometer I_s data (Fig. 5 and Table 7) are similar in range, sill, and nugget. The I_s semivariogram for the 20 x 20 cm² infiltrometer data resembles the basic shape of the other semivariograms (spherical, range = 170 m), but the nugget, 0.65, is much greater than the nugget of the larger infiltrometer sizes. The plotted semivariogram points of the 20 x 20 cm² infiltrometer are also more scattered than the other two semivariograms. The larger nugget and greater scatter further imply that the 20 x 20 cm² infiltrometer does not fully support a local-scale RMA, with underlying local-scale heterogeneity masking the spatial structure of the larger scale.

Unlike the hillslope measurements, the distributions of the landscape-scale I_s measurements are more distinctly lognormal (Fig. 4 and Table 6). The semivariograms (and madograms and general relative semivariograms) at the landscape scale also reach more of a distinct sill value at a range of about 200 m. Thus, the 710-m transect better incorporates the full scope of variance at the landscape scale and is arguably more spatially stationary than is the 90-m transect that encompasses only one hillslope. The 200-m range of the semivariograms and madograms roughly corresponds to the average diameter of the swells found in the landscape profile (Fig. 1). This coincidence of the range with the landscape topography may also explain the small drop in the semivariogram values at the larger lag distances since similar landscape features would be expected to exhibit greater correlation in hydraulic properties.

The concurrence between semivariogram range and swell diameter also illustrates the need to include the upland swells, transitional hillslopes, and lowland depression areas (swales) to effectively represent the landscape scale. The inclusion of the different landscape features in the landscape transect may also explain the more distinct lognormal distribution of the measured I_s values as compared with the more normally distributed values of the hillslope transect. Because the landscape transect measurements do incorporate a full range of landscape-scale features, the mean and variance estimates of infiltration tests conducted on the landscape transect would give a more unbiased estimate of an equivalent landscape-scale conductivity than would those conducted on the shorter hillslope transect.

	CONCLUSIONS

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

 
Consideration of scale effects on spatial variability is essential in measuring and modeling soil hydraulic properties. The agricultural soils in the midwestern USA show a large variability in I_s at scales that are smaller than those that represent a suitable average of the effects of macropores and other structural anomalies. Additional variability is manifest at larger scales arising from features such as landscape position, soil type, and the spatial and temporal history of agricultural management.

This study shows that variance of I_s measurements at the local scale is dramatically reduced (>90%) with support areas of 400–800 cm². At the local scale, spatial correlation increases with depth and total variance tends to decrease with depth—a phenomenon attributed to agricultural practices that disturb the upper soil horizon and from the natural decrease in macropore size and abundance (Mohanty and Kanwar, 1994; Tsegaye and Hill, 1998; Sobieraj et al., 2004). Along a transect, local-scale measurements are most applicable to landscape-scale domains when they are measured using a sufficient support to integrate the smaller scale variability and also include measurements made at enough locations and covering a sufficient length to reveal the spatial correlation structure of the entire domain.

To model at the landscape scale using effective parameters, local-scale I_s measurements must integrate the full-range of landscape variance. Thus, when using deterministic (i.e., effective parameter) approaches to model water flow into and through these soils, the soil hydraulic properties used in the model should be selected from a measurement that integrates across the range of variability at the scale of interest. Based on semivariogram analysis of the infiltrometer measurement at the landscape scale, a transect distance of at least 200 m, or long enough to integrate over the landscape's swale–swell pattern, is needed to estimate an effective conductivity or infiltration rate.

	NOTES

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

 
Contribution of the Indiana Agricultural Research Programs, Purdue Journal Paper 17,205.

Received for publication September 16, 2003.

	REFERENCES

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

 

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