Soil Science Society of America Journal 63:1599-1608 (1999)
© 1999 Soil Science Society of America
DIVISION S-1-SOIL PHYSICS
Integrated Assessment of Space, Time, and Management-Related Variability of Soil Hydraulic Properties
H.M. van Esa,
C.B. Ogdena,
R.L. Hillb,
R.R. Schindelbecka and
T. Tsegayec
a Dep. of Soil, Crop and Atmospheric Sci., Cornell Univ., Ithaca, NY 14853-1901 USA
b Dep. of Natural Resources Sciences and Landscape Architecture, Univ. of Maryland, College Park, MD 20742-5821 USA
c Dep. of Plant, Soil, and Animal Sciences, Alabama A&M Univ., Normal, AL 35762 USA
hmv1{at}cornell.edu
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ABSTRACT
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Soil hydraulic properties have numerous sources of variability related to spatial, temporal, and management-related processes. Soil type is considered to be the dominant source of variability, and parameterization is typically based on soil survey databases. This study evaluated the relative significance of other sources of variability: spatial and temporal at multiple scales, and management-related factors. Identical field experiments were conducted for 3 yr at two sites in New York on clay loam and silt loam soils, and at two sites in Maryland on silt loam and sandy loam soils, all involving replicated plots with plow-till and no-till treatments. Infiltrability was determined from 2054 measurements using permeameters, and Campbell's a and b parameters were determined based on water-retention data from 875 soil cores. Variance component analysis showed that differences among the sites were the most important source of variability for a (coefficient of variation, CV = 44%) and b (CV = 23%). Tillage practices were the most important source of variability for infiltrability (CV = 10%). For all properties, temporal variability was more significant than field-scale spatial variability. Temporal and tillage effects were more significant for the medium- and fine-textured soils, and correlated to initial soil water conditions. The parameterization of soil hydraulic properties solely based on soil type may not be appropriate for agricultural lands since soil-management factors are more significant. For infiltrability, temporal factors also need to be explicitly recognized. Sampling procedures should give adequate recognition to soil-management and temporal processes as significant sources of variability to avoid biased results.
Abbreviations: VCE, variance component estimate
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INTRODUCTION
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KNOWLEDGE of soil hydraulic properties is essential to effectively apply many research and management tools related to agronomic and environmental decision making. In particular, computer-based models that simulate soil hydrologic processes and their impacts on crop growth and contaminant transport depend on accurate characterization of soil hydraulic properties (Addiscott and Wagenet, 1985). The lack of such information is often considered to be a major obstacle to using these tools (van Genuchten et al., 1992).
It is generally recognized that soil hydraulic properties are affected by numerous sources of variability, mostly associated with spatial, temporal, and management-related factors. Their importance may be considered from two different perspectives: (i) the relative magnitude of these sources of variability on soil hydraulic properties themselves, and (ii) the impact of such variation in soil hydraulic properties on the simulated processes, which are often highly nonlinear. The latter issue of the functional sensitivity has been studied by Boesten (1991), Kickert (1984), Persicani (1996), and Holden et al. (1996) and results varied, depending on the processes and boundary conditions that were simulated.
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Sources of Variability
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In the absence of direct field measurements, soil hydraulic properties are often estimated based on soil type, typically represented by a soil taxonomic class. These estimates may be based on measurements from typical pedons or are derived from extensive soil survey data bases (e.g., Wösten et al., 1985). Pedotransfer functions (Bouma and van Lanen, 1987; Wösten and van Genuchten, 1988) may also be applied to functionally relate soil hydraulic properties and model parameters to easily measured soil properties such as texture, structure, bulk density, and organic matter content, typically derived from standard soil survey databases. The accuracy of such procedures generally varies (Wösten et al., 1990).
Within-soil type spatial variability in soil hydraulic properties has also been extensively evaluated, although mostly as it relates to single fields. Soil hydraulic properties were generally found to be variable and spatially correlated (e.g., Nielsen et al., 1973; Vieira et al., 1981; Russo and Bresler, 1981a; van Es et al., 1991a). Several researchers (e.g., Amoozegar-Fard et al., 1982; Russo and Bresler, 1981b) have suggested that within-field variability is sufficiently significant that it warrants the use of stochastic modeling approaches that incorporate a description of uncertainty rather than the use of field averages. Anderson et al. (1987), however, found the gain from a stochastic over field-average approach to predicting water stress from variable soil hydraulic properties to be marginal for a loamy sand soil.
Several studies demonstrated the significance of temporal variation in soil hydraulic properties (e.g., Starr, 1990) and found that tillage is a significant interacting factor. Mapa et al. (1986) determined that water retention and hydraulic conductivity were greatly increased as a result of tillage, but soil settling and recompaction occurred with subsequent wetting and drying cycles. Model simulations of soil water movement based on parameterized hydraulic properties showed significantly higher water contents in tilled compared with untilled soil. Larson and Pierce (1994) suggested a greater emphasis on the temporal aspects of soil properties as part of the dynamic assessment of soil quality, similar to that used in the manufacturing industries.
Soil management is another important source of variability for soil hydraulic properties (Mapa et al., 1986; van Es, 1993), although it is generally not incorporated into simulation efforts. Most agrichemicals are applied to agricultural fields that have been recently tilled, and therefore have a physical status different from those described in most standard databases. Moreover, tillage has a profound impact on the spatial distribution of water and solute flow processes, especially as it relates to preferential flow (Andreini and Steenhuis, 1990; van Es et al., 1991b). Rawls and Brakensiek (1983) parameterized the effects of tillage on soil water retention for different soil textural classes.
In general, variability among soil types is assumed to be the most important source of variability for soil hydraulic properties, and is therefore usually accounted for in sampling and parameterization efforts. The relative significance of other temporal, spatial, and management-induced sources is not well known, nor are they typically explicitly accounted for in modeling efforts. Knowledge of their significance is nevertheless important for the development of both efficient sampling protocols and proper parameterization scenarios.
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Sampling Protocols
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Observations on soil hydraulic properties may be taken in space, time, or both, and may involve various scales of sampling. In the majority of cases in the literature, observations were made for one or more management units, typically a field, with multiple observations in space based on random or systematic sampling patterns. The optimum number of samples may be determined by the classical equation (Eq. [1]):
 | (1) |
where ta is the value of Student's t distribution for a given confidence level 
, 
2 is the population variance, and x - µ denotes the desired precision around the mean value. For spatially correlated data, n may be reduced as the variance for nearby locations is lower (Webster and Burgess, 1984).
The variance is typically defined for a specific spatial domain (e.g., a field), although the soil hydraulic properties may also vary within time or may be affected by management practices. Failure to recognize the significance of these sources of variability may lead to incorrect interpretations. For example, if a soil property exhibits temporal variability, a single sampling, even if it includes many observations in space, poorly represents the average behavior of this property since it is not replicated in time. Similar issues exist when inferences are made for large spatial domains from samples collected from a small domain, e.g., a representative pedon at a type location as is used in soil survey.
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Parameterization
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Variation in soil properties may be expressed in terms of deterministic or stochastic parameters, or both. Various levels of sophistication may be considered in the parameterization of soil hydraulic properties:
1. Traditionally, variation among soil types is deterministically characterized by assigning different capacity parameter values. It is thereby assumed that parameter values Yi are identical (a constant cv) within soil types v, without uncertainty, and may differ only among soil types (Eq. [2]):
 | (2) |
The assignment of parameter values may be based on the mean value of field observations from study sites, or indirectly from database information or pedotransfer functions for similar soil types. Spatial, temporal, or other sources of variability are not considered to be important.
2. In the typical stochastic approach, the hydraulic parameters of a soil type are described through a mean value and an uncertainty statistic, either a variance or a semivariogram function. In such cases, the underlying hypothesis is that the spatial and temporal domain contain sources of variability that cannot be deterministically parameterized, but can be characterized through a single variance statistic or function. The property is now considered to be a random, or regionalized, variable (Yi) with the same expected value over the (spatial or temporal) domain (Eq. [3]):
 | (3) |
and a constant variance (Eq. [4]):
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In the geostatistical approach, the variance is a function of distance between observations, 
(h), and is generally assumed identical within the same soil type (Eq. [5]):
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3. Increasingly sophisticated approaches may deterministically and/or stochastically characterize spatial, temporal, or management effects. For example, the temporal variation of a parameter value may be modeled through a function (e.g., reflecting tillage disturbance and subsequent settling under management system m; compare with Mapa et al., 1986) while the spatial component is stochastically characterized in Eq. [6] and [7]:
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and
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A key question related to the characterization of soil hydraulic properties is whether spatial, temporal, or management-related sources of variability should be accounted for by deterministic or stochastic parameter values. In the latter case, it is implied that the spatial or temporal domain is first- and second-order (quasi)stationary (Cressie, 1991) and the process is adequately characterized by a mean value and an uncertainty statistic.
The objectives of this study were (i) to evaluate the relative magnitude of tillage-induced variability, and spatial and temporal variability at different scales for soil hydraulic properties, and (ii) to provide guidance for appropriate sampling and parameterization methods related to the characterization of soil hydraulic properties.
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Materials and methods
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Near-identical field experiments were conducted at four sites of 
0.5 to 1 ha during the 1992, 1993, and 1994 growing seasons. Two sites were located in New York: (i) at the Musgrave Research Farm near Aurora, NY (42°45' N, 76°35' W) with a glacial till-derived Honeoye-Lima silt loam soil (Glossoboric Hapludalf, fine-loamy, mixed, mesic), and (ii) at the Willsboro Research Farm near Willsboro, NY (44°21' N, 73°20' W) with a glacio-lacustrine Kingsbury clay loam (Aeric Ochraqualf, fine, illitic, frigid). Both soils were artificially drained. The two other sites were located in Maryland: (i) at the University of Maryland Southern Maryland Research and Extension Center in the Coastal Plain region near Upper Marlboro, MD (38°51' N, 76°46' W) on a Monmouth fine sandy loam (Typic Hapludult, very-fine, illitic, mesic), and (ii) at the University of Maryland Wye Research and Education Center in the Coastal Plain region near Wye Mills, MD (38°54' N, 76°8' W) on a Mattapex silt loam soil (Aquic Hapludult, fine-silty, mixed, mesic). Neither Maryland site had artificial drainage. Plow-till and no-till soil-management systems under maize production were established at all sites using spatially balanced complete block designs (van Es and van Es, 1993) with four replications (six at the Honeoye-Lima silt loam site). Times of tillage and planting are outlined in Table 1
. Controlled traffic patterns were used at all sites.
In 1992 and 1993, infiltration measurements were made and undisturbed soil samples were collected seven or eight times during the growing season (Table 2)
. In 1994, observations were made twice at the New York sites and three times at the Maryland sites. In all cases, infiltration measurements and soil samplings were accomplished within 2 d. Infiltration methods were consistent among all locations using 152-mm diameter steel rings inserted into the soil to a depth of 76 mm. Simulated rainfall was used to mimic natural soil wetting and prevent possible artificial slaking and air entrapment associated with instantaneous ponding. Small drippers (Ogden et al., 1997) were placed on the rings at a height of 120 mm above the surface to wet the soil at a dripping rate of 76 mm h-1. Several layers of cheesecloth were placed on the soil surface of recently-plowed soil to prevent excessive impact of drops. After ponding or 1800 s, whichever occurred earlier, the rainfall simulators were replaced with Marriot-type permeameters that maintained a 0.10-m constant hydraulic head within the infiltration ring (Fig. 1)
. Field-saturated infiltrability was determined from water intake rates during the period 1440 to 1800 s after ponding. In each tillage plot, four infiltration measurements were made simultaneously within an 1-m2 arrangement with two measurements each in the row and nontrafficked interrow positions. Among all sites, years, dates, replicates, tillage treatments, and plots, 2054 infiltration measurements were used in the analysis.
Field-saturated infiltrability, ifs, was determined according to Reynolds and Elrick (1990), assuming one-dimensional water flow in the infiltration ring and divergent three-dimensional flow below the ring (Eq. [8]):
 | (8) |
where G is a dimensionless shape parameter determined from numerical solutions of Richards' equation (0.552 for this infiltrometer setup, as determined by Reynolds and Elrick, 1990), Q is the steady intake rate (flux) of water, H is the hydraulic head of water in the ring, a is the radius of the infiltration ring, and * is a parameter related to soil hydraulic conductivity functions, assumed to be equal to 12, as suggested by Elrick et al. (1989).
For each plot, an undisturbed soil core was collected on each sampling date from each row and nontrafficked interrow position in close proximity (<2 m) to the infiltration sites. Undisturbed soil cores, with a 76-mm height and 76-mm i.d. (102-mm i.d. for the Honeoye-Lima site), were collected from the 51- to 127-mm depth interval. These were weighed to determine water content and were stored refrigerated at 1 to 3°C until laboratory analysis was done for the soil water-retention curve. Soil cores were slowly saturated for 1 wk. The volume fraction of pores >0.79 mm was determined by allowing free drainage of the cores for 4 h on a saturated cheesecloth. Water retention at seven soil water potentials ranging from -1 to -102 kPa were obtained using tension-table (Topp and Zebchuk, 1979; Maryland sites only for -1 to -7.4 kPa potentials) and pressure-chamber methods (Klute, 1986; using fritted glass funnels for the Maryland sites and nylon-filter membrane chambers for the New York sites). Soil cores were subsequently oven-dried (after subsampling at the Maryland sites) to determine the water-retention curve and volumetric soil water content at the time of sampling.
Water-retention data were summarized using Campbell's (1974) equation (Eq. [9]):
 | (9) |
where h is the pressure potential, 
is the volumetric water content, s is the saturated volumetric water content, and a and b are fitting parameters. The RETFIT procedure of the LEACHM model (Hutson and Wagenet, 1992) was used to obtain the a and b parameters. Water-retention parameters of 875 soil cores were used in the statistical analysis.
Statistical Analyses
Values for ifs, a, and b represent the soil hydraulic properties from these experiments. Statistical analyses were performed using the SAS software package Version 6.1 (SAS Institute, Cary, NC). Standard univariate analyses showed that b values were normally distributed, while ifs and a values were highly skewed to the left. Infiltrability data therefore were transformed to ln(ifs) and a values were transformed to ln|a| (the norm value was used to allow a logarithmic transform of a negative value), which were used in all further analyses.
Analysis of variance of the experiments was conducting using the GLM procedure in SAS. The relative magnitude of variability from Site, Year within Site, Week, Replicate within Site, Tillage, and Position relative to the row were determined through variance component analyses using the VARCOMP procedure of SAS. Variance component estimates (VCE) for each variability source s (tillage, site, year, etc.) were computed under the assumption that all effects were random. VCEs were normalized using Eq. [10]:
 | (10) |
where CVs is the coefficient of variation, and 
is the arithmetic mean value of the variable over all variability sources. CVs values were subsequently ranked to facilitate evaluating their relative significance. These analyses were repeated for each individual site using the arithmetic mean value for each site in Eq. [10]. Lognormal(ifs), ln|a|, and b were also correlated with each other and with the initial volumetric soil water content (i).
The semivariance (h) (Eq. [5]) for three distance classes, 1, 2 to 8, and 50000 to 700000 m was determined for ln(ifs) using the variance components for duplicate measurements within each position, replicates of treatments within a field, and multiple sites, respectively to evaluate the structure of spatial variability. (h) estimates were computed by cumulating the variance components with increasing distance class; these estimates represent an averaged semivariance over years, weeks, tillage, and position. They thereby exclude the confounding effects of interactions.
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Results
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Mean values for ln(ifs) (Table 3)
indicate that the lowest infiltrability (-12.14 m s-1) was associated with the coarse-textured Monmouth sandy loam, which appeared to be the result of poor soil structure and surface sealing. The two silt loam sites in this study (Mattapex in Maryland and Honeoye-Lima in New York) showed different mean ln(ifs) values of -11.41 and -10.08 m s-1, respectively, indicating that soil hydraulic properties may vary considerably within the same soil textural class. Higher infiltrability for the finer-textured New York sites was unexpected, but may in part be explained by differences in soil structure from the previous alfalfa (Medicago sativa L.) crop.
Campbell's a parameter is often interpreted as the air-entry value. Lognormal|a| generally decreased from coarse- to medium- to fine-textured soils (Table 3), contrary to expectations. This reflects the effect of good soil structure, especially at the Kingsbury clay loam, which had 3- to 10-mm aggregates in the years following alfalfa (Karunatilake, 1996). Campbell's b parameter values were generally highest for the Mattapex silt loam and Kingsbury clay loam sites (15.18 and 15.13, respectively), and lowest for the Monmouth sandy loam and Honeoye-Lima silt loam sites (10.79 and 9.12, respectively). Higher b values generally imply a more gradual release of soil water with decreasing water potential, which in this case also appears to vary greatly among and within soil texture classes (Table 3). They do not show a consistent pattern from coarse- to fine-textured soils, which may be the result of varying soil structure. Differences in average soil water conditions at the time of measurement/sampling among the sites reflect variability in water-retention capacity and weather patterns. The Maryland sites generally showed lower variability in initial soil water content than the New York sites (Table 3).
Variance Component Analysis
The design of these experiments recognized three scales of spatial variability: Site (mostly representing soil type differences), Replicate (field-scale variability), and Position relative to the plant row (pedon-scale variability, also strongly affected by field management); and two scales of temporal variability: Year and Week. Year effects were analyzed within Sites, recognizing that each research farm was subject to different weather conditions. Similarly, dates of measurement, represented by Weeks, were analyzed as nested within Sites and Years. Tillage is a source of variability that was measured across all spatial and time scales, except Position. In addition to these main effects, the experimental design allows numerous interactions to be evaluated. Multi-way interactions are generally of little interest here because they are difficult to parameterize. Therefore, only two-way interactions with high variance components were considered in this study, and other interactions were pooled into the Error term. The statistical analysis does not account for errors in the data themselves. These include the lack of fit associated with the regression procedure used for deriving Campbell's a and b parameters, errors associated with the G and * parameters used for estimating ln(ifs), and possible other inaccuracies with measurement and data-management methods.
An analysis of variance of the data set of all sites combined showed that the main effects Site, Year (except for b), Replicate, Position, Week, and Tillage were significant for all three soil hydraulic parameters (results not shown). Since analyses of variance procedures merely evaluate the significance of the sources of variability (which depends in part on the experimental design), a variance component analysis was used to assess the relative magnitude of these variability sources (Table 4)
.
Site effects were a large source of variability for the water-retention parameters ln|a| and b (CVs of 44.0 and 23.0. respectively), which appears to corroborate the accepted notion that soil hydraulic properties are best parameterized based on soil type. Unexpectedly, infiltrability was little affected by Site effects (CV = 5.8, rank = 4), but more strongly influenced by Tillage and Week effects (CVs of 10.0 and 7.6, respectively). This suggests that inherent soil properties (e.g., soil texture) are less important to infiltration behavior than soil management and within-season temporal changes. The Error term, which incorporates all higher levels of interaction, is an important source of variability for all three parameters. Also, temporal variability within years (Week) was in all cases a greater sources of variability than spatial sources within sites, i.e., Replicate and Position. Combined over all sites, the latter sources were generally not important. CVs associated with two-way interactions of Tillage with spatial and temporal factors were generally lower than the main effects, but were of notable magnitude. Tillage response was generally not consistent over all sites and varied temporally within growing seasons, as evidenced by high Site x Till and Week x Till interaction terms.
Analysis by Site
A separate variance component analysis for each site provides greater insight into the significance of spatial, temporal, and tillage-induced variability for each soil type. CV values for ln(ifs) (Table 5)
show that the Error term was generally the largest source of variability, indicating that multi-way interactions and random effects are very significant. Tillage effects appeared to be very important and relatively consistent among soil types in that ln(ifs) for plow-till was higher than for no-till (Fig. 2)
. Temporal changes in ln(ifs), however, appeared to vary among soil types. The New York soils generally showed a dramatic increase in infiltrability from the first (before tillage) to the second measurement date (after tillage and planting) in each year under the plow-till treatment. This reflects the dramatic change in soil pore size and continuity as a result of tillage-induced soil disturbance. The Maryland soils did not show any ostensible change in ln(ifs) between the first and second measurement dates as a result of tillage, which may in part be the result of a cropping history different from the New York sites. Temporal changes in ln(ifs) were most dramatic for the Kingsbury clay loam (Fig. 2), for which orders of magnitude changes were measured within a growing season. This is explained by the effects of soil shrinkage under dry soil conditions. The infiltration measurement period used in this study (1 h) was shorter than the time required for dry, cracked soil to re-swell, and the in situ pore geometry was therefore affected by initial soil water conditions.
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Fig. 2 Field-saturated infiltrability for four soil types under plow-till and no-till management in 1992–1994. Each line point is a mean of 12 (Maryland sites) or 16 (New York sites) observations
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The Honeoye-Lima silt loam showed different seasonal variability for ln(ifs) from 1992 to 1993 because of varying weather conditions (Fig. 2), as also reflected by the high CV for Year effects (Table 5). The 1992 growing season received more than 200 mm in July, which prevented the soil from excessive drying during the remainder of the growing season, while pronounced drying periods in 1993 created more temporally variable infiltration patterns. The Maryland soils also experienced considerable temporal variation (Table 5), primarily through Year x Tillage interactions, and Week effects for the Monmouth sandy loam. In general, temporal variation in infiltrability through main effects or two-way interactions at the Year and Week scales appeared to be more significant than spatial variation at the Replicate and Position scale.
For ln|a|, the pooled Error term was the largest source of variability for all soil types (Table 6)
. Tillage effects were strongly present for the New York soils, but were of minor significance for the Maryland soils (only through the Position x Tillage interaction, Fig. 3)
. Temporal sources of variability through main effects and interactions involving Year and Week generally were large, while spatial effects appeared to be minor.
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Fig. 3 Campbell's a parameter for four soil types under plow-till and no-till management in 1992 to 1994. Each line point is a mean of six (Maryland sites) or eight (New York sites) observations
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The pooled Error term was also generally the largest source of variability for the b parameter, except for the Mattapex silt loam (Table 7)
. Tillage effects were generally large, either as main effect or through the interactions at different time scales (Year x Till and Week x Till for the Kingsbury Clay loam and the Mattapex silt loam, respectively), as is also evident in Fig. 4
. Similar to ln|a|, spatial sources of variability were generally of lower magnitude than the temporal sources for all four sites.
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Fig. 4 Campbell's b parameter for four soil types under plow-till and no-till management in 1992–1994. Each line point is a mean of six (Maryland sites) or eight (New York sites) observations
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Spatial Structure of Infiltration
Ln(ifs) shows the same semivariance (2.7 m2 s-2, Fig. 5)
for measurements at the 1-m distance (duplicate measurements within each position in a plot) and measurements at the 20- to 80-m distance (plot replicates). Ln(ifs) therefore does not show any spatial correlation at the field scale. The semivariance for observations at the 50000- to 700000-m distance (sites) is higher (4.1 m2 s-2) than those for the shorter distances, representing an increase in variability due to the effects of varying soil types and cropping history. It is noteworthy that 66% of the variability in infiltrability among four widely varying and widely spaced soil types, and 100% of the variability within single fields is measured within an area of about 1 m2.
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Fig. 5 Semivariance of ln(ifs) for different distance ranges, representing duplicate measurements at a 1-m distance, treatment replicates at 20- to 80-m distance, and sites at 50000- to 700000-m distance
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Correlations
In the analysis across all sites, ln(ifs) was significantly negatively correlated with b, indicating that, as predicted, higher infiltrability is generally associated with soils that exhibit more rapid water release (Table 8)
. High ln(ifs) and low b values were not necessarily associated with coarser-textured soils (Table 3), presumably due to structure effects. Lognormal(ifs) was not strongly correlated with ln|a|, as would have been predicted. All parameters were significantly correlated to i. Infiltrability increased with dryer soil, presumably due to soil shrinkage. Campbell's parameters generally decreased with dryer soil, either from soil cracking or less artificial compaction during sampling.
In the by-site analysis, ln(ifs) was significantly negatively correlated to b for all four sites, indicating that, as would be predicted, higher infiltrability is associated with soils that exhibit more rapid water release (Table 8), except in the case of the Kingsbury Clay loam. Although a strong relationship between the air-entry value and ln(ifs) may be expected, it appeared not to be significant for these sites, except in the case of the Kingsbury clay loam. For three of the four sites, ln(ifs) exhibited a negative correlation with initial water content (Table 8). Infiltrability for such soils is a time-transient property, not only due to sorptivity but also as a result of the time required for cracked soils to wet up and swell. This is apparently an important factor for some soils when considering 1-h infiltration and runoff events.
Unlike ln(ifs), a and b are derived from a measurement procedure that involves an extended wetting and saturation period, thereby presumably removing the effects of initial water contents. Nevertheless, ln|a| exhibited positive correlations with i at two sites and b showed significant correlations with i , especially for the Maryland sites (Table 8). This raises the question whether soil pore geometries change throughout the season as soils wet and dry, or whether the measured pore-size distributions are artificially impacted by the sampling procedures in that the sample integrity may be affected by water conditions at the time of sampling.
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Discussion
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The analysis of this large data set on soil hydraulic properties of agricultural lands revealed that Sites were the greatest sources of variability for water-retention parameters. However, using static soil characteristics as the primary basis for assigning water-retention parameter values (e.g., from soil survey data and pedotransfer functions) should be done with adequate consideration of all relevant properties, as parameter averages varied considerably within the same textural class (Mattapex silt loam in Maryland and Honeoye-Lima silt loam in New York, Table 3). The different pedogenetic history is taxonomically recognized by the fact that these soil types are distinguished at the order level (Ultisols vs. Alfisols). Varying cropping history for these sites did not allow for an explicit quantitative evaluation of the soil type effects. For infiltrability, Site differences were of less significance.
Tillage was the dominant source of variability for infiltrability and a secondary source of variability for the slope of the retention curve. It had an insignificant effect on the air-entry value. Other sources of variability were also important and when combined, exceeded the magnitude of the Site variation.
Tillage effects were generally consistent and more favorable for the plow-till compared with the no-till soil. The significance of tillage effects warrants the explicit parameterization, as was attempted by Rawls and Brakensiek (1983), although the high variance components for interactions of Tillage with temporal sources of variability (Year and Week) suggest that a simple deterministic parameterization may not be appropriate, at least not for all soil types.
Temporal processes also appear to be a large source of variability, although the relative significance varied among soil types. Within Sites, it was generally a greater source of variability than spatial sources (Replicate and Position). Significant correlations of the soil hydraulic parameters with initial soil water contents suggest that much of this temporal variability may be explained by antecedent soil wetness conditions. It is noted that no measurements were made during the winter when frozen or fully-saturated conditions affect soil hydraulic properties, especially infiltration rates, and thereby increase the significance of temporal variability.
These results have important implications to the design of sampling protocols and parameterization methods. Soil management strongly impacts soil hydraulic properties and needs to be explicitly dealt with in designing sampling protocols. Temporal variability is also very significant, especially for medium- to fine-textured soils (Fig. 2, 3, and 4). The common practice of single-time sampling may result in inaccurate estimation of these properties. For individual field sites, sampling in time appears to be as critical as sampling in space, although an optimum sampling effort should include both. Also, observations made at different times may lead to inappropriate conclusions if the data are used to infer temporal changes, e.g., soil quality improvement or degradation. For example, measurements of infiltrability taken on the Kingsbury clay soil in May 1992 and September 1993 (Fig. 2) would suggest a dramatic improvement in soil quality, while in fact it represented mostly the effects of temporal variability within growing seasons.
Since the optimum number of samples n for each variability source is proportional to the variance 2 (Eq. [1]), the relative sampling effort expended in time or space at any scale should be commensurate with the magnitude of the variance for that source of variability (Eq. [11]):
 | (11) |
where s1, s2, ..., and t1, t2, ... denote different scales in space and time, respectively, depending on the desired spatial or temporal generalization of the study. In reality, the cost of sampling varies in time and space and among scales, and economic optimization should therefore also include a cost function. Also, the Error term, reflecting random variability including many spatial, temporal, and management-related interactions, was always an important source of variability (Table 5), emphasizing the need for replicated sampling at any scale in space and time.
Studies aiming at characterizing temporal and spatial trends need to explicitly consider the potential confounding effects from spatial and temporal variability. Studies that measure soil hydraulic properties over a spatial domain during an extended time period, for example, by moving across a land area for several weeks or months, may be temporally confounded and include biases. Also, the practice commonly used in soil surveys to assess soil properties from a typifying pedon, that is, a small area sampled at one time under a given management practice, appears to provide limited relevant information.
Parameterization efforts similarly need to account for the true stochastic nature of the soil properties. Assuming that most variability is the result of soil type differences (compare Eq. [1]) appears inappropriate. For water retention and infiltration, parameter assignment by soil type and a stochastic component (as shown in Eq. [3], [4], and [5]) is a minor improvement if it includes spatial, temporal, and management components. For appropriate parameterization of water retention and infiltration behavior, management and temporal effects may need to be explicitly incorporated, while other factors may be handled stochastically.
In conclusion, sampling, parameterization, and modeling efforts related to soil hydraulic properties need to recognize the relative magnitude of the various spatial, temporal, and management-related sources of variability. In this study, effects of Sites (soil types) were prominent. Temporal and management effects appear to be similarly important, indicating that explicit recognition of these sources of variability is essential to avoiding misrepresentation of soil hydraulic properties.
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ACKNOWLEDGMENTS
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We acknowledge the following individuals for their assistance in field preparation, data collection, and analysis: Koos Jonker, Roel van der Veen, Wim Werkman, Udaya Karunatilake, Norm Wade, David Wilson, and Robert Lucey.
Received for publication January 4, 1999.
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REFERENCES
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ABSTRACT
INTRODUCTION
