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Published online 23 May 2006
Published in Soil Sci Soc Am J 70:1071-1081 (2006)
DOI: 10.2136/sssaj2005.0177
© 2006 Soil Science Society of America
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Soil Physics

Geostatistical Tools for Characterizing the Spatial Variability of Soil Water Repellency Parameters in a Laurel Forest Watershed

C. M. Regaladoa,* and A. Ritterb

a Instituto Canario de Investigaciones Agrarias (ICIA), Dep. Suelos y Riegos, Apdo. 60 La Laguna, 38200 Tenerife, Spain
b Dep. Ingeniería, Producción y Economía Agrarias, ICIA and Univ. de La Laguna Ctra. Geneto, 2 La Laguna, 38200 S/C Tenerife, Spain

* Corresponding author (cregalad{at}icia.es)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Soil water repellency is recognized to be a widespread phenomenon which may affect a wide range of spatially dependent hydrological processes that take place in the vadose zone such as infiltration, preferential flow, and soil water distribution. Despite this, the spatial structure of soil repellency has received almost no attention in the past. The objective of this study is to investigate the spatial variability of water repellency in the top horizon of a laurel forest watershed. Water repellency was measured with the molarity of an ethanol droplet (MED) test, from saturation to oven-dry, in 140 soil samples taken in a nested structure that encompasses both short (centimeter scale) and long (meter scale) distances. Geostatistical tools such as correlograms and kriging were used to quantify the spatial structure of soil organic matter (SOM) content and the parameters that characterize the water repellency curve. Both showed characteristic spatial trends, and, in general, spatial correlation followed a spherical, exponential, or gaussian model. All parameters investigated exhibit scale dependence, in particular, variability of SOM and the area below the repellency curve point toward a self-similar fractal scaling. Cross-correlation of some of the repellency parameters and SOM was not random but showed spatial structure.

Abbreviations: IGF, indicative goodness of fit • MED, molarity of an ethanol droplet • QQ, quantile–quantile • SOM, soil organic matter


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
NOWADAYS IT IS ACCEPTED that soil water repellency is more widespread than was initially expected (Wallis and Horne, 1992). All soil processes where water is involved are believed to be affected by water repellency, such as the soil water characteristic curve (DiCarlo et al., 1999; Bauters et al., 2000), infiltration (Wallis et al., 1990; van Dam et al., 1996), soil available water (Scott and Van Wyk, 1990), preferential flow (Jaminson, 1945; Ma'shum and Farmer, 1985; Wallis and Horne, 1992), and soil surface erosion (Shakesby et al., 1994). Most of such soil physical and hydrological properties show some kind of spatial dependence (see Table 9.2 in Mulla and McBratney, 2002), which has been quantified by means of scaling techniques (Regalado, 2004, and the references therein) and geostatistical tools (Goovaerts, 1998; Nielsen and Wendroth, 2003). It is thus expected that if soil water repellency is spatially correlated, so will the physical and hydrological processes that depend on this; therefore, the need exists to investigate its spatial structure. However, the spatial distribution of water repellency has not been rigorously studied, despite the fact that it is well known that, for example, SOM affects soil hydrophobicity (Bond and Harris, 1964; Dekker, 1998; Moral, 1999) and that SOM exhibits spatial variation (Mulla and McBratney, 2002, and the references therein; García-Sinovas et al., 2003). Additionally, we would expect a reinforcing of SOM content with water repellency, since water repellency enhances soil aggregate stability against dispersion, hence increasing stability of SOM against microbial decomposition (Piccolo and Mbagwu, 1999). The consequences of this feedback process on the spatial distribution of repellency and SOM are unknown. Additionally, knowing the spatial structure of water repellency can render useful a priori information needed in other studies, such as how should the sampling domain be, how far apart should measurements be taken, is water repellency scale invariant, or how spatial interpolation may be performed (e.g., for mapping in geographic information systems; Nielsen and Wendroth, 2003).

Several authors previously reported spatial variability of soil water repellency. Ritsema and Dekker (1994) were probably the first ones that attempted to quantify the spatial variability of soil water repellency, although as early as the 1960s Osborn et al. (1964) had already reported patchiness of hydrophobicity. Uneven spatial distribution of water repellency has been confirmed later on in many other studies (Brock and DeBano, 1990, p. 206–209; Scott and Van Wyk, 1990; Imeson et al., 1992). Dekker et al. (2001) found highly spatial variability of water repellency in a dune sand, but Doerr et al. (1998) found low spatial variability of in situ surface soil hydrophobicity for a burnt and unburnt forested land. None of these studies have, however, analyzed the spatial structure of water repellency using geostatistical tools. Of the very few exceptions we may mention, that of Hallett et al. (2004), who found a distinct spatial structure at scales below 50 mm for ethanol sorptivity, but not so for water sorptivity and water repellency, measured with a miniaturized infiltrometer. And also that of Moral (1999), who investigated the semivariograms of actual water repellency in terms of water drop penetration time and percentage of ethanol in the sandy soils of Doñana National Park, and found almost no spatial structure in most plots. Thus, in very few cases and little success, the spatial correlation of soil water repellency has been rigorously quantified. This analysis is further complicated because water repellency varies nonlinearly with soil water content (cf. Fig. 2 in Regalado and Ritter, 2005). Neither the work of Hallett et al. (2004) nor Moral (1999) took into account the dynamic behavior of soil wettability in the spatial analysis. In general, soils are wettable close to saturation, becoming water repellent up to a maximum as water content decreases. After this maximum water repellency diminishes monotonically with decreasing water content, or raises again to a second local maximum (de Jonge et al., 1999; Goebel et al., 2004). The origin of this nonlinear behavior is not understood, although some hypotheses have been proposed (Roberts and Carbon, 1971; Jex et al., 1985; Wallis et al., 1990; Doerr and Thomas, 2000; Doerr et al., 2002; Goebel et al., 2004). Regalado and Ritter (2005) found useful correlations between some of the parameters that describe such a repellency curve. This is the case of the integrated area below the repellency curve and the soil water content at minimum repellency. Consequently, they designed an efficient strategy for describing the repellency curve based on a combination of parameter interdependence and a minimum number of determinations.

The current study was performed in a mature laurel forest (locally known as laurisilva) watershed where we had previously observed evidences of soil water repellency. Many methods have been proposed to quantify the degree of soil water repellency (Wallis and Horne, 1992; Letey et al., 2000). We measured water repellency with the MED) test (Roy and McGill, 2002). Main advantages of the MED test are its simplicity and rapidity, especially for severely repellent soils (as in our case) where other methods, such as the water drop penetration time test, may take hours to conclude (Wallis and Horne, 1992). The main disadvantage of the MED is that it is unsuitable for low repellent soils, but this did not represent a major drawback in our case since most samples were at least moderately hydrophobic. The test was performed in 140 soil samples collected in a nested structure that encompasses both short (microscale, centimeters) and long (macroscale, meters) distances. The MED test measurements were performed from saturation to oven-dry in decreasing steps of soil water content.

The main objective of this study is thus to investigate the spatial structure and scale dependence of SOM and parameters that characterize the soil repellency vs. water content curve. Geostatistical tools such as correlograms and kriging are used to analyze spatial correlations. Spatial cross-correlation of some of these hydrophobicity parameters and SOM is also investigated.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Area of Study and Sampling design
The area of study (Fig. 1a ), located in the Garajonay National Park (Spain) is described in Regalado and Ritter (2005). Samples came from a systematic sampling scheme consisting on a regular rectangular grid (100 by 75 m) with 56 intersection points, and four additional randomly placed short range grids of 21 intersection points each (Fig. 1b and 1c). The sampling strategy selected permitted us to characterize both large- and short-range variability without having to resort to an intensive sampling campaign. It is worth noting here that each extra sampling point implies at least 10 extra MED determinations. A regular coarse grid fulfills the requirements of systematic sampling necessary for accurate kriging interpolation; this coarse grid is supplemented with the cluster nested grids for accurate estimation of spatial structure at short separation distances. Sampling points were localized by GPS, with an error of ±2 m. Euclidean (x, y) relative positions within the watershed were used for the spatial analysis. In total, 140 samples (n = 56 + 4 x 21) collected at a soil depth of 0 to 0.03 m, after removing the top layer of decaying tree leaves. These were used for water repellency and SOM determinations with the MED test and the Walkey-Black method (Schnitzer, 1986), respectively. Soil samples were placed in plastic bags and kept at field moisture for transportation to the laboratory. The sampling campaign was carried during the summer of 2000.


Figure 1
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  		Fig. 1. Watershed selected for soil sampling. (a) 3-D view; (b) rectangular grid (100 by 75 m); (c) grid at centimeter scale in the four points marked with squares in (b).

 
Water Repellency Determinations
The degree of repellency can be expressed by the contact angle, {alpha}. This was determined with the MED test (Roy and McGill, 2002), which was performed in decreasing soil moisture steps as described in Regalado and Ritter (2005). The {alpha} varies nonmonotonically with soil water content ({theta}g) according to Fig. 2 . This {alpha}–{theta}g curve can be described with a combination of the following parameters (which constitute the data set used in this study): the increasing (s+) and decreasing (s–) repellency slopes, the trapezoidal integrated area below the curve (S), the maximum contact angle measured ({alpha}max), the water content at {alpha}max ({theta}g-max), the contact angle in the dry soil ({alpha}105°C) or potential repellency, the lowest {theta}g at which {alpha} is negligible ({theta}g-min), and the difference between maximum and potential repellency, {alpha}err (i.e., {alpha}err = {alpha}max – {alpha}105°C).


Figure 2
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  		Fig. 2. Example of repellency curve, indicating the parameters selected for its study.

 
Geostatistical Analysis
Geostatistics is the name proposed for a method of spatial analysis that makes predictions from a sample data whose relative spatial locations are known. The two most common measures of spatial dependence in geostatistics are variograms and correlograms. These characterize how a variance or autocorrelation quantity varies with the separation distance (lag), h, and possibly direction. In geostatistics it is often required that the expectation of a random measurement made at a location is constant. This hypothesis is known as the stationarity assumption. As acknowledged by Cressie and Horton (1987), most authors proceed to apply geostatistical techniques without previously checking that their data are consistent with such a stationarity assumption, thus making their spatial analysis invalid. By plotting the sample mean and sample median across rows and down columns, one may detect possible nonstationarity trends in the mean (Cressie and Horton, 1987). Additionally, skewness of the data can mask some of its spatial structure, and makes variograms less reliable (Webster and Oliver, 1990); thus, we worked with normalized stationary data after applying a suitable transformation. On the other hand, possible proportional effects of local means of parameters vs. their local variance (Journel and Huijbregts, 1978, p. 186–189) should be checked. Here, this was performed by means of scatterplots obtained from a moving window technique (Goovaerts, 1997, p. 82–83) with Geostats 3-Plot98 4.60 [1999; BRAE (Nuclear Safety Institute), Moscow] using 10 overlapping 150- by 300-m windows with no less than seven data values each. Both variograms and correlograms give us a numerical estimation of how our sampled data vary, as we get further apart from neighbor points. The main difference between the two are that correlograms, and not so variograms, standardize for both local means and local variations. In general, variograms and correlograms are characterized by a nugget or purely random effect, that accounts for both microvariance (i.e., spatial variation occurring at distance closer than the sampling spacing) and measurement error, and a spatially correlated or structured part, which is modeled by two parameters: the sill and the range. The sill is the variance or autocorrelation value at which the variogram or correlogram reaches a plateau; the range is the distance (lag) at which the sill is reached. Some authors have noticed, however, that the dichotomy between random and deterministic features is generally an arbitrary/subjective division (Chiles and Delfiner, 1999, p. 233–234).

Data pairs of separation distance vs. estimated variation (or autocorrelation) conform the so-called experimental variogram (or correlogram), and models (linear, spherical, exponential, gaussian, power, etc.) can be fitted to these to obtain numerical values for the nugget, sill, and range. The three most common models, the spherical, the exponential, and the gaussian, have the following mathematical expressions:

Formula 1[1]

Formula 2[2]

Formula 3[3]
where {gamma}(h) is a variogram and {rho}(h) a correlation measure, C is the so-called scale (= sill – nugget), and a is the range. Both correlogram and variogram are related via the variance, {sigma}2. Notice that the exponential model does not have a true range (as occurs with the spherical model). Instead, the effective or practical range is the distance at which {gamma}(h) is 95% of the sill. The gaussian model has an asymptotic sill and the range is thus defined similar to the exponential model.

Experimental nonergodic correlograms and variograms were computed with Variowin (Pannatier, 1996) and fitted to models described in Eq. [1], [2], and [3]. The quality of the fitted models is given by the indicative goodness of fit (IGF) criterium (Pannatier, 1996). Fitted variograms were then used for interpolating values at unsampled locations by kriging (see Nielsen and Wendroth, 2003, for a detailed explanation). Data cross-correlation was investigated by means of cross-correlography. The above models were fitted to the experimental cross-correlograms using a global optimization algorithm (Ritter et al., 2004, and the references therein).


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Statistical Data Quality
Mean comparison tests and quantile–quantile (QQ) plots were performed to check for the absence of bias in the data due to preferential sampling in the nested design. Means were significantly equal for the gridded (Fig. 1b) and the clustered (Fig. 1c) data. Additionally, QQ plots showed that clustered and gridded data follow the same distribution (results not shown).

Both normality and stationarity of the data were checked. Highly skewed data distribution can mask spatial structure, so normality was assessed by means of Box-Cox normality plots and the data normalized accordingly (Regalado and Ritter, 2005). The parameters {theta}g-max, SOM, and S were found to be closely normal; {theta}g-min, s+ and s– were highly skewed, log-normally distributed; and {alpha}err improved normality after a square root transformation (cf. Table 2 in Regalado and Ritter, 2005). Additionally, normalization of the data is not necessary for kriging per se, but it minimizes chance of numerical instability in solving the kriging matrices.

Stationarity in the mean was checked by plotting the sample mean and sample median across rows and down columns. There appears to be no trend in the rows or columns direction, thus stationarity in the mean is assumed (results not shown). Stationarity in the variance was assessed by comparing the median vs. the squared interquartile range (a measure of data spreading, independent of symmetry) for different data transformations (Cressie and Horton, 1987). No significant improvement was observed between the untransformed data and the square root and log transformations, so stationarity in the variance was also assumed (results not shown).

Proportionality effects, that is, possible trends in local mean vs. variance of repellency parameters and SOM, are summarized in Fig. 3 . No clear relation between average repellency parameter values and local variability are observed, thus the so-called proportional effect or spatial heteroscedasticity may be discarded. However, SOM suggests a possible proportional effect, given that only one point on the graph indicates otherwise (and this is underrepresented since it only includes seven data values).


Figure 3
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  		Fig. 3. Plots of local variances vs. local means computed from 150 by 300 m moving overlapping windows for the water repellency parameters and SOM.

 
Correlograms
Spatial correlation was analyzed by means of correlograms. No clear anisotropy structure was observed, so omnidirectional correlograms, with uniform lag class distance intervals of 64 m, were computed (Fig. 4 ). In general, at large scale, either an exponential or spherical model fit the data. The maximum repellency ({alpha}max) exhibits a pure nugget effect (results not shown). Fitted correlogram parameters provide a quantitative expression of spatial structure. The sill, that is, the autocorrelation of the repellency parameters at large lag distance, is in all cases around unity as a consequence of normalization. The range of water repellency parameters, that is, the distance beyond which no spatial autocorrelation is observed, is always >210 m, with {theta}g-max having the greatest range (338 m). By contrast, a lower range (147 m) is observed for SOM content. This has implications for sampling design. Flatman and Yfantis (1984) suggested a value of 1/4 to 1/2 of the range, as the optimal lag distance for sampling. The range values obtained indicate a large spatial dependence, as compared with other soil properties (c.f. Table 9.2 in Mulla and McBratney, 2002).


Figure 4
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  		Fig. 4. Experimental and fitted omnidirectional correlograms at meter scale.

 
Scale Dependence
We also investigated the spatial structure of soil water repellency parameters at small (centimeter) scale. Figure 5 shows the omnidirectional correlograms fitted for one of the short-scale grids depicted in Fig. 1c. Some of the soil water repellency parameters ({alpha}105°C and {theta}g-max) and the SOM follow the same correlogram trends at both short and large scale (cf. Fig. 4 and 5). The spatial structure of the other parameters ({alpha}err, {theta}g-min, s+, |s–|, and S) is better fitted to a gaussian model. Although supported by a lower number of pair comparisons, small-scale correlogram models exhibit a better fit (lower IGF) than their corresponding models at larger scale (cf. Fig. 4 and 5). At small scales, 0.88 ≤ range ≤ 1.58 m and 1.16 ≤ sill ≤ 1.34. Such range values are within those found, for example, for the soil saturated hydraulic conductivity (c.f. Table 9.2 in Mulla and McBratney, 2002). The above results indicate that the correlogram range is dependent on the scale investigated, and that the repellency parameters measured may be viewed as the sum of a microscopic (nugget), short-scale (centimeter), and long-scale (meter) spatial component. Furthermore, we cannot discard that under the nugget or microvariance component a millimeter-scale spatial structure also exists, as previous studies indicate (Hallett et al., 2004), and also that above the scale measured a kilometer-scale is also feasible. The observed relation between correlation range and scale of observation has been reported repeatedly in the literature. For example, Gelhar (1993, p. 292–294) discusses that the estimated correlation range is typically 10% of the overall experimental scale. Such scale-dependent relations are indicative of common underlying physical processes that operate at different spatial scales (Goovaerts, 1998).


Figure 5
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  		Fig. 5. Experimental and fitted omnidirectional correlograms at centimeter scale.

 
We also explored the possibility of a fractal scaling. Fractal omnidirectional semivariograms (i.e., a plot of log |h| vs. log semivariance) were computed for the water repellency parameters and SOM. The implication of the fractal scaling is that we can determine the variance of a particular soil property at one scale based on the variance at any other scale; that is, such property is said to be self-similar. In general the fractal hypothesis was difficult to assert for almost all repellency parameters, apart from S and SOM (Fig. 6 ). In these last two cases, although the middle separation distances from 2.5 to 40 m are not well represented, the fractal scaling may hold (linear relationship). The Hausdorff-Besicovitch fractal dimension D = 2 – m/2 is thus defined, where m is the slope of the log-log semivariogram, and renders DS = 1.907 and DSOM = 1.893, respectively.


Figure 6
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  		Fig. 6. Fractal omnidirectional semivariograms for S and SOM.

 
Kriging
One way to integrate the above information is that of using kriging as an interpolator to obtain values of the measured data at unsampled locations. Kriging equations can be derived employing either covariances, correlograms, or variograms. In our case we have used variograms to linearly estimate such interpolated values. Figure 7 shows the kriging maps for the water repellency parameters and SOM. Several results may be obtained from the resulting kriging maps. Parameter values and SOM content do not follow the same spatial 2-D trend. Except for s+ and {alpha}105°C, parameter minima for {alpha}err, {theta}g-max, {theta}g-min, |s–|, S, and SOM are placed in the lower corner of the watershed. The s+ and {alpha}105°C minima are located in the middle part. Hence, within this watershed region, the overall repellency status is less prominent (lower S); soil water repellency increases slower until reaching its maximum, as water content diminishes, and it is triggered at lower soil moisture content (lower {theta}g-min). Neglecting possible hysteresis effects, the opposite would be also true and, as soil moisture increases, full wettability is recovered at slower rate and lower {theta}g-min in this area. The parameter {alpha}105°C or potential repellency is often used as an indicator of soil water repellency. Notice that conclusions about the spatial distribution of soil water repellency would be quite different if one uses S (as a measure of the overall water repellency) instead of the potential repellency for characterizing spatial repellency patterns within the watershed (cf. first and penultimate contour map in Fig. 7). Furthermore, since potential repellency refers to a soil moisture status difficult to reach in field conditions, its applicability for the interpretation of the 2-D spatial distribution of repellency is rather limited.


Figure 7
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  		Fig. 7. Kriging maps for the water repellency parameters and SOM.

 
Soil organic matter shows a more homogeneous distribution than the repellency parameters, and this is a consequence of the sharper increase in variability at short lag distances (Fig. 5). In many instances in the literature, the SOM has been referred to as being responsible for soil water repellency. If this is the case here, it is made clear that this effect is further amplified in space, since the overall repellency status of the soil (represented by the above-defined parameters) shows higher spatial heterogeneity than the SOM. Finally, from a kriging map comparison, it is evident that {theta}g-min and S follow similar spatial patterns, and this is further explored next.

Cross-Correlation
Spatial cross-correlation between the soil properties studied was investigated by means of cross-correlography. Table 1 summarizes the cross-correlogram models obtained when fitted to the experimental water repellency parameters and SOM data. In general, spherical and exponential models described the cross correlations. The goodness of fit, given by the coefficient of efficiency (Nash and Sutcliffe, 1970), varied between 0.70 and 0.93. The range of water repellency parameters is generally above 200 m, except for {theta}g-max vs. {alpha}err, s+ vs. {alpha}err, and S vs. |s–|. In fact, the latter shows the smallest cross-correlation range, a = 72 m. By contrast, SOM shows a lower cross-correlation range (below 130 m) except for S vs. SOM (a = 217 m). In Table 1, some soil repellency parameters have positive and others negative scale, C. When C is positive this would mean that correlation between the two attributes compared increases with separation distance. Additionally, in all cases we found that nugget and scale have opposite signs, and hence a change in sign of the cross correlogram values occurs (results not shown). This indicates a change in the correlation between soil repellency attributes as a function of the spatial scale (short or long separation distance), also observed in previous studies (Goovaerts, 1998, and the references therein).


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  		Table 1. Cross-correlation matrix for the repellency parameters and SOM. Models Sph(a, C) and Exp(a, C) refer to Eq. [1] and [2], respectively. Numbers in parentheses correspond to cross-correlation range (a) and scale (C).

 
In addition, some of the parameters showed no cross-correlation if their spatial component is not taken into account (cf. Table 4 in Regalado and Ritter, 2005). These are highlighted in Table 1 with a cross. Thus, it is worth noting that for some of the soil properties studied, cross-correlation may only be detected if their spatial structure is considered.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
Geostatistical tools were successfully applied to analyze the spatial structure of both SOM and water repellency parameters in the top horizon of a laurel forest watershed in the Garajonay National Park. These parameters, which describe the repellency vs. water content curve, were obtained with the MED test in decreasing steps of water content (from saturation to oven-dry). Computed correlograms showed a spatial structure for all parameters and the SOM at both centimeter and meter scales. Spatial structure was quantified with either a spherical, exponential, or a gaussian model fitted to the correlograms. Results indicated a large range for the repellency parameters. By contrast, SOM presented a sharper increase in variability at short lag distances. Furthermore, the correlogram range was a function of measurement scale, and for SOM and the area below the repellency curve a fractal scaling may be suggested, indicating a possibility of scale self-similarity. On the basis of the models fitting, the variability of the water repellency parameters and SOM within the watershed was computed using kriging. Differences in the 2-D spatial trend of the soil properties studied were found. The kriging maps indicated a similar spatial pattern within the watershed for S and the water content for minimum repellency. The SOM showed a more homogeneous distribution than the repellency parameters as a consequence of the sharper increase in variability at short lag distances. Cross-correlations were also observed among most of the repellency parameters and SOM.


   ACKNOWLEDGMENTS
 
This work was financed with funds of the INIA-Programa Nacional de Recursos y Tecnologías Agroalimentarias (Project RTA2005-228). The authors would like to thank A. R. Socorro (ICIA) for her help in the laboratory analysis, and A. Fernández and L. A. Gómez (Garajonay National Park) for their support.

Received for publication June 7, 2005.


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





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