On the influence of coarse fragments on soil water retention

Transcription

1 WATER RESOURCES RESEARCH, VOL. 45, W07408, doi: /2008wr007402, 2009 On the influence of coarse fragments on soil water retention J. M. Baetens, 1 K. Verbist, 1,2 W. M. Cornelis, 1 D. Gabriels, 1 and G. Soto 2 Received 29 August 2008; revised 14 April 2009; accepted 30 April 2009; published 10 July [1] The classical determination of the soil water retention curve (SWRC) by measuring soil water content q at different matric potentials y using undisturbed soil samples is time consuming and expensive. Furthermore, undisturbed soil sampling can be an intricate task when coarse soil fragments (>2 mm) are present. The objective of this study was to test whether tension infiltrometry could be used to estimate the SWRC of stony soils and to investigate to what extent the coarse fragments affected the SWRC. Tension infiltrometer measurements were conducted at 44 sites with stony soils in arid Chile. Soil water retention curves obtained through inverse modeling were compared with laboratory-determined water retention (q, y) data pairs. Differences were found to be small, confirming the applicability of the inverse modeling method. Rock fragments had a significant indirect influence on water retention for matric potentials higher than 0.30 kpa, which could be attributed to their direct influence on pore size distribution. Citation: Baetens, J. M., K. Verbist, W. M. Cornelis, D. Gabriels, and G. Soto (2009), On the influence of coarse fragments on soil water retention, Water Resour. Res., 45, W07408, doi: /2008wr Introduction [2] Relationships between a soil s water content q and its energy, typically expressed in terms of pressure y, is determined by the soil s physical and chemical properties. Such soil water retention curves (SWRC) are a unique property for a given soil. For modeling purposes, the use of a continuous function describing the SWRC such as those proposed by Brooks and Corey [1964], van Genuchten [1980], and Kosugi [1994] is preferred. In comparing various analytical expressions to describe the SWRC between saturation and 1500 kpa, Cornelis et al. [2005] demonstrated that the van Genuchten [1980] and Kosugi [1994] models were superior to others. Although the former relationship often fails to describe the observed trend in matric potential beyond the residual water content [Cornelis et al., 2005], the model of van Genuchten [1980] remains widely used. [3] Typically, the parameters of the van Genuchten [1980] model are estimated by fitting the model against discrete (q, y) data pairs which can be obtained using a tension table [Romano et al., 2002] and a pressure plate extractor [Dane and Hopmans, 2002]. Unfortunately, these determinations are time and work consuming, stimulating researchers to find alternative methods to obtain the SWRC more rapidly. As such, pedotransfer functions are often proposed to estimate either the parameters of the model of van Genuchten [1980] [e.g., Vereecken et al., 1990; Wösten et al., 1999] or the soil water content at certain matric potentials [e.g., Gupta and Larson, 1979; Rawls and Brakensiek, 1982] using readily available soil properties. 1 Department of Soil Management and Soil Care, Ghent University, Ghent, Belgium. 2 Centro del Agua para Zonas Áridas y Semiáridas de América Latina y el Caribe, UNESCO, La Serena, Chile. Copyright 2009 by the American Geophysical Union /09/2008WR However, there exists a lot of uncertainty in applying PTFs to soil conditions different from those under which PTFs were derived [Cornelis et al., 2001; Lee, 2005]. Therefore, determination of hydraulic properties through measurements that can be executed relatively fast and with a limited amount of work, gain growing interest. Tension infiltrometry fulfills these criteria and is therefore well established for determining unsaturated hydraulic conductivity [Reynolds, 2006]. Also, flow effects associated with processes influencing the soil s macrostrucure such as soil cracking [Thony et al., 1991], macrostructure collapse [Messing and Jarvis, 1993], tillage [Sauer et al., 1990; Reynolds et al., 1995], soil crusts [Šimŭnek et al., 1998] and root growth [White et al., 1992] have been investigated by means of tension infiltrometry. [4] Traditionally, tension infiltrometer data are analyzed using procedures based on Wooding s [1968] analysis for unconfined steady state infiltration from a disk [Ankeny et al., 1999; Logsdon and Jaynes, 1993; Reynolds and Elrick, 1991; Smetten and Clothier, 1989]. Alternatively, tension infiltrometer data can be analyzed through inverse modeling of cumulative infiltration data yielding estimates of the van Genuchten [1980] parameters [Šimŭnek and van Genuchten, 1996]. In this way, the SWRC can be obtained without the necessity to measure (q, y) data pairs. Following the work of Šimŭnek et al. [1999], who demonstrated the usability of the inverse modeling technique using data from laboratory tension infiltrometer experiments, Ramos et al. [2006] showed the potential of the technique for determining water retention of coarse to medium textured soils in Portugal, on the basis of a limited set of field measurements. Especially in stony soils, this approach could be an alternative to determine soil hydraulic properties in comparison to the conventional method using undisturbed ring samples that are extremely difficult to obtain in such soils. Until present, however, this has not been tested yet. [5] Several researchers have addressed the influence of coarse soil fragments on water retention [e.g., Cousin et al., W of14

2 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W ; Fiès et al., 2002; Ravina and Magier, 1984; Sharma et al., 1993]. However, their conclusions are always based upon water retention measurements conducted on undisturbed or, more frequently, on constructed soil samples. For example, Fiès et al. [2002] used glass fragments to simulate rock fragments, and found that on average the volumetric water content at a fixed matric potential decreased as the percentage glass fragments increased. Cousin et al. [2003] focused on the water retention of a soil rich in calcareous rock fragments. They found that it is important to take water retention properties of calcareous rock fragments into account when evaluating the soil water balance. Sharma et al. [1993] and Ravina and Magier [1984] conducted water retention measurements on disturbed clay and coal containing samples, respectively. Ravina and Magier [1984] concluded that rock fragments mainly affected water retention at pressures higher than 9.81 kpa. Sharma et al. [1993] found that gravimetric water content at the same matric potential tended to increase as coal content increased which they ascribed to an attribution to soil water retention by the coal fragments. Nevertheless, the effect of rock fragments on the SWRC is still under debate, to which this paper contributes in the following aspects: (1) evaluating the effectiveness of the inverse modeling technique for soil water assessment and (2) gaining insight in the influence of coarse soil fragments on soil water retention by means of tension infiltrometry. 2. Materials and Methods 2.1. Field Site [6] All field measurements were conducted in a 65 ha experimental watershed near La Serena, Chile ( S, W on WGS 1984). The study area has an arid climate according to the UNEP index [Middleton and Thomas, 1997]. On the basis of data from 1990 to 2000, July is the coldest month with a mean monthly temperature of 12 C and January is the hottest month with a mean monthly temperature of 19 C. Precipitation is highly seasonal, concentrated in winter months and the mean annual precipitation is 113 mm. The topography is formed by a central valley enclosed by hillslopes where the altitude varies between 400 m at the watershed outlet and about 500 m at the highest ridge top. Slopes range from less than 1% in the riverbed to more than 30% at the steepest parts of the hillsides. Because of the arid conditions vegetation is sparse and dominated by shrubs, herbs and cacti [Miller, 1976; Casanova and Navarrete, 1992] Infiltrometer Measurements [7] Infiltration measurements were conducted at 44 sites located along three transects in the watershed, which were established from hill top to hill top (Figure 1). First, a ponded head infiltration measurement was conducted using a constant head single-ring infiltrometer with an inner diameter of 0.28 m. The soil enclosed by the infiltrometer was leveled by means of contact sand with a saturated hydraulic conductivity of ms 1. The Mariotte system of the Guelph permeameter (model 2800, Soilmoisture Equipment, Santa Barbara, California, United States) was used to maintain a constant head of 0.03 m. Readings of the cumulative infiltration were made manually every minute for at least 30 minutes or until the infiltration rate during three successive time intervals were constant. Ponded head infiltration data were analyzed using the method of Wu and Pan [1997] [see also Wu et al., 1999]. [8] After reaching steady state ponded head infiltration, the Guelph permeameter was removed and its reservoir was attached to a tension infiltrometer (Model 2825, Soilmoisture Equipment, Santa Barbara, California, United States). The tension infiltrometer, having a disk diameter of 0.20 m, was used to measure the unsaturated infiltration rate at three successive imposed pressure potentials: 0.3, 0.6 and 1.2 kpa (wet-to-dry sequence). As soon as air bubbles raised in the reservoir, cumulative infiltration at these potentials was recorded every minute and continued for at least 15 minutes or until the infiltration rate during three successive time intervals was constant. Although no correction was made for the variable contact sand layer thickness between different measurement sites, calculations using the approach formulated by Reynolds [2006] indicated that contact sand layer effects on hydraulic conductivities were limited, with mean errors of , and m s 1, respectively, for the successive applied pressure heads. A wet-to-dry sequence has been applied by several researchers [e.g., Ankeny et al., 1999; Logsdon and Jaynes, 1993; Mohanty et al., 1994], and was followed in this study in order to reduce antecedent negative head effect at low infiltration rates, and to make a meaningful comparison with soil water retention curves obtained for undisturbed soil samples using the sand box and pressure plate apparatus (see section 3.2), which yields a desorption curve. Indeed, by following a wet-to-dry sequence with the tension infiltrometer one obtains a drying curve of the SWRC which should be compared to the drying curve found using water retention measurements by means of the sand box and pressure plate apparatus. Nonetheless, it should be emphasized that the presented SWRC might suffer from pronounced hysteresis effects, especially in the low-suction range, which can be attributed to two main causes. First, the ink bottle effect can be quite pronounced because of the fairly large part of macropores in stony soils, which might be interconnected by narrow conducting channels, and second, entrapped air in blind pores, which could be abundant in these coarse soils, can reinforce the hysteresis effect due to the nonunifomity of the soil s pores. Yet, applying a ponded head measurement prior to the tension infiltrometer measurements will have eliminated most of the soil air by the rapidly advancing water front. [9] Tension infiltrometry can provide information about the pore size distribution using the relation proposed by Watson and Luxmoore [1986]. According to their relation, the maximum number of actively conducting (e.g., effective) pores per unit area, Z, is given by Z ¼ 8mK d r w gpr 4 m where m is the viscosity of water, g the acceleration due to gravity, r w the density of water, r m is the minimum pore radius in a particular class and K d is the difference in hydraulic conductivity between two consecutive tensions. The effective porosity e is given by e ¼ Zpr 2 m ð1þ ð2þ 2of14

3 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 Figure 1. The experimental watershed with indication of the established transects, the river bed, and the altitude of the measurement sites Laboratory Measurements [10] At each measurement site an undisturbed soil sample was taken by means of a steel 100-cm 3 Kopecky ring (height 5 cm, diameter 5.3 cm) which was driven into the soil using a dedicated ring holder (Eijkelkamp Agrisearch Equipment, Giesbeek, Netherlands) and a percussion-free hammer. The sample was taken at a distance not more than 0.20 m from the single-ring infiltrometer. Resampling was often necessary to obtain a sample which was as little disturbed as possible. Nevertheless, we observed that the soil structure of the samples could still be seriously modified because of occurring vibrations when the steel ring hit a coarse fragment. The soil water retention curve for these undisturbed soil samples was determined using the sand box apparatus (Eijkelkamp Agrisearch Equipment, Giesbeek, Netherlands) for matric potentials between 1 and 10 kpa, and with pressure chambers (Soilmoisture Equipment, Santa Barbara, California, United States) for matric potentials between 20 and 1500 kpa. The van Genuchten [1980] model was fit to the registered (q, y) data pairs with the iterative algorithm of Levenberg-Marquardt [Levenberg, 1944; Marquardt, 1963] by means of the mathematical software program MATLAB (version 7, The MathWorks Inc.), yielding the van Genuchten [1980] parameters. Parameter values reported by Carsel and Parrish [1988] were taken as initial estimates. Also disturbed soil samples were taken at every site, from which the <2 mm fraction was used to fill up Kopecky rings with an appropriate fine earth bulk density, determined for the corresponding site [see Verbist et al., 2009]. [11] At each measurement site, organic matter content, bulk density, rock fragment content, rock fragment size distribution, and finally soil texture, were determined. Organic matter content was measured by means of the Walkley and Black [1934] method. Bulk density was determined by means of the excavation method [Blake and Hartge, 1986]. In this method we used a noncompressible well sorted fine sand with a known bulk density of 1.56 ± 0.01 Mg m 3. As shown in Figure 2, bulk density varied between 1.2 and 1.7 Mg m 3 and organic matter content was for most sites constrained between 5.0 and 35.0 g kg 1. Volumetric rock fragment content R v and rock fragment size distribution were determined from sample volumes of approximately m 3. Rock fragment size distribu- 3of14

4 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 Figure 2. Variation in soil bulk density and organic matter content at the observation sites. tion was quantified in terms of mean weighted diameter (MWD) which we defined mathematically as MWD ¼ P Nf r i m i i¼1 P Nf m i i¼1 where N f is the number of fractions distinguished, m i is the mass of rock fragments retained with the ith sieve, and r i is the mesh size diameter of the ith sieve. Figure 3 shows the range of R v and MWD covered by this study. The former varied between 0.04 and 0.60 m 3 m 3 and the latter between and m. The correlation coefficient between both properties was only 0.06 indicating that an increase in rock fragment content was not necessarily the consequence of larger fragments present. Soil texture was determined by the pipette method [Gee and Or, 2002] after separating particles with a diameter larger than 50 mm by wet sieving (Figure 4). All measurement sites, except one with a sandy texture, and one with a sandy clay loam texture, were classified as loam or loamy sand according to the USDA texture triangle [Soil Survey Staff, 2003]. The sandy measurement site was located in the river bed along the third transect. Since not all infiltration measurements could be performed properly at this site because of its very high rock fragment content (R v 0.70 m 3 m 3 ), it was excluded from further analysis. Furthermore, the sandy clay loam site was classified under the loam sites Parameter Estimation [12] A widely used empirical model for describing the SWRC, was developed by van Genuchten [1980] and contained originally five parameters: ð3þ Figure 3. Volumetric rock fragment content and mean weighted diameter observed at the observation sites. have to be estimated. Estimates of the van Genuchten [1980] parameters can be used to evaluate the specific water The relative maximum of this function indicates the inflection point of the SWRC [Bohne, 2005]. van Genuchten [1980] also derived a theoretical model describing the K(y) relationship on the basis of equation (4) and the theoretical pore size distribution model of Mualem [1976]: 8h i 2 9 >< 1 ðay j jþ n 1 ð1 þ ðay j jþ n Þ m >= KðyÞ ¼ K s ½1 þ ðay j jþ n Š m 2 >: >; in which the parameter l is a pore size distribution parameter and K s is the soil s saturated hydraulic conductivity. Estimation of the parameters of equations (4) and (5) by inverse analysis of tension infiltrometer data requires ð5þ 1 m q ¼ q r þ ðq s q r Þ 1 þ ðay j jþ n ð4þ where a, and n and m are parameters respectively related to y 1 and the curve s slope at its inflection point. Often m = Figure 4. Variation in clay (0 2 mm), silt (2 50 mm), and 1 1 n is introduced, hence, only four independent parameters sand ( mm) content at the observation sites. 4of14

5 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 numerical solutions of the Richards [1931] equation adapted for radially symmetric ¼ 1 1 r w @r þ 1 r where r and z are respectively the radial and vertical coordinate, the latter being positive upward with z = 0 at the soil surface, and t denotes time. This equation is subject to the following initial and boundary conditions [Warrick, 1992]: qðr; z; tþ ¼ q i ðþor z yðr; z; tþ ¼ y i ðþat z t ¼ 0 yðr; z; tþ ¼ y 0 ðþwith t 0 < r < r 0 at z ¼ 0 1 r w g ð6þ ð7aþ z; tþ ¼ 1with r > r 0 at z ¼ 0 yðr; z; tþ ¼ y i at r 2 þ z 2 ¼1 ð7dþ where y i is the initial pressure potential, q i is the initial water content and y 0 is the imposed supply pressure potential. [13] We used DISC software [Šimŭnek and van Genuchten, 2000] to obtain the van Genuchten [1980] parameters through inverse modeling. This approach is based on the minimization of an objective function F, describing the discrepancies between the simulated and observed values, and is defined as [Šimŭnek and van Genuchten, 1996] ( ) X Fðv; q Ms Þ ¼ XMs Nj n j w ij q j * 2 ðt i Þ q j ðt i ; vþ j¼1 i¼1 where M s is the number of different sets of measurements used in the analysis, N j represents the number of measurements in a particular set, q* j (t i ) is the measurement at time t i for the jth measurement set, v is the vector of optimized parameters (q r, q s, a, n, l and K s ), q j (t i, v) represents the model predictions for the parameter vector v, and v j and w ij are the weights associated with a measurement set j or measurement i within set j, respectively. In our study, M s = n j = 1, because only one measurement set of cumulative infiltration data per sample location was used to estimate the van Genuchten [1980] parameters. [14] Minimization of equation (8) is performed using the Levenberg-Marquardt algorithm [Levenberg, 1944; Marquardt, 1963]. According to Šimŭnek and van Genuchten [1997] the inverse modeling approach yields a unique solution for the unknown parameters when cumulative infiltration data at multiple tensions are combined with measured values of the initial and final water contents. Ramos et al. [2006] found this method to be a reliable method for determining K(y) and y(q) curves. Furthermore, Verbist et al. [2009] have found good agreement between K(y) values for stony soils calculated by means of inverse modeling and methods based on work of Wooding [1968] for unconfined steady state infiltration from a circular pond. We used a fixed value of 0.5 for l, which has been found acceptable for many soils [Mualem, 1976], in order to limit ð8þ 5of14 the degrees of freedom, though Schaap and Leij [2000] stated that optimizing this parameter yields better estimates of the unsaturated hydraulic conductivity. Two variants of the inverse modeling technique were tested. In a first one, all five parameters (q r, q s, a, n, and K s ) were estimated through inverse modeling of tension infiltrometer data, whereas in the second, K s in equation (5) was set to the values calculated with the method of Wu and Pan [1997] using data from the ponded head experiment. Hence, in the second variant, the same number of parameters had to be estimated as when fitting the model of van Genuchten [1980] against laboratory-measured (q, y) data pairs. Also here, the van Genuchten [1980] parameter values reported by Carsel and Parrish [1988] were taken as initial estimates. Initial water content, being the moisture content at saturation, was set to 95% of the porosity which was calculated from the measured bulk density. Final water content, being the moisture content at y = 1.2 kpa, had to be derived from the SWRC fitted to laboratory-measured (q, y) data sets since bulk density had to be measured at the same locations after the infiltration measurements were finished Evaluation Methods [15] The performance of the inverse modeling technique could be assessed by calculating the discrepancies between measured and fitted cumulative infiltration by means of the mean error (ME p ), the root-mean-square error (RMSE p ) and the Pearson correlation coefficient (r p ). These indices are given by ME p ¼ 1 M X M i¼1 I fit i I obs i vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 1 X M RMSE p ¼ t Ii fit Ii obs 2 M i¼1 ð9þ ð10þ fit cov Ii ; Ii obs 2 r p ¼ varðii fit Þvar Ii obs ð11þ where M is the number of observations, I i corresponds to the ith data pair, and obs and fit denote observed and fitted cumulative infiltration, respectively. The subscript p was introduced to distinguish these indices from those used to compare the continuous functions obtained by fitting the model of van Genuchten [1980] against (q, y) data pairs measured in the laboratory, further referred to as ex situ SWRC (SWRC ex ) to the functions obtained through inverse modeling of tension infiltrometer data, further referred to as in situ SWRC (SWRC in ). SWRC in derived using measured K s values are denoted as SWRC in,4, while SWRC in obtained by setting K s a free parameter are denoted as SWRC in,5. [16] The comparison between SWRC ex and SWRC in was done by integrating both curves over the range of matric potentials covered by the laboratory soil water retention measurements conducted on the undisturbed soil samples. As such, possible irregular data points are smoothed and the outcome of the evaluation depends not only on the choice of

6 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 Table 1. Mean Error ME p, Root-Mean-Square Error RMSE p, and Pearson Correlation Coefficient r p Comparing the Observed and Modeled Cumulative Infiltration a Technique Mean ME p (m 3 ) Mean RMSE p (m 3 ) Mean r p SWRC in, SWRC in, a Values are means of 43 measurements. the matric potentials at which water content was measured [Cornelis et al., 2001]. To express the degree of agreement between both SWRC ex and SWRC in, we considered ME c, RMSE c and r c which were now defined as ME c ¼ 1 b a Z b a qy ð Þ i qy ð Þ e dy ð12þ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z u 1 b RMSE c ¼ t 2dy qy ð Þ b a i qy ð Þ e a ð13þ potentials of 0.3, 0.6 and 1.2 kpa indicate a very good fit between observed and modeled cumulative infiltration for both SWRC in,4 and SWRC in,5 (Table 1). Nevertheless, fitted cumulative infiltration was on average slightly higher than the observed values, as indicated by the positive sign of ME p. Indices were on average slightly, but not significantly, better when K s values had to be estimated which could be attributed to the extra degree of freedom introduced by setting K s a free parameter. The very good correlations between observed and modeled cumulative infiltration are in agreement with the findings of Ramos et al. [2006] and Šimŭnek et al. [1998, 1999] and is further confirmed in Figure 5, which illustrates the measured and modeled cumulative infiltration for a sandy loam and loam soil Comparison of the Water Retention Curves [18] Validation indices comparing SWRC in and SWRC ex are shown in Table 2, and indicate good agreement between SWRC in and SWRC ex. The mean correlation coefficients r c were always higher than 0.95, indicating that the shape of R b qy ð Þ i q i qy ð Þe q e dy a r c ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R b 2dy R qy ð Þ i q b 2dy i qy ð Þ e q e a a ð14þ where q(y) i and Rq(y) e are the in situ and ex situ functions, q i = 1 b b a a q(y) idy is R the mean water content of the SWRC in of soil i, q e = 1 b b a a q(y) edy is the mean water content of the SWRC ex and the subscript c indicates that these indices were used to compare SWRC ex and SWRC in. The integrals in equations (12) (14) were evaluated using equation (4) with the appropriate optimized parameter values. The ME c allows the evaluation of positive or negative bias, so its absolute value should be as small as possible. The RMSE c is a measure for the overall error, increasing with increasing overall error and always positive because of the square in its equation. The dimensionless Pearson correlation coefficient is a measure for the strength of the linear relationship between SWRC ex and SWRC in. The shape of these curves is more comparable as its value approaches 1, since then in situ and ex situ data pairs are more linearly located around the line of perfect agreement. The integration boundaries a and b were set to log(0.3 kpa) and log(1500 kpa), respectively, which is the range of matric potentials at which water contents for the SWRC ex were measured. By using logjyj, assigning too much weight too more negative matric potentials was avoided [Tietje and Hennings, 1993]. All statistical analysis was performed in S-Plus (version 7.0, Insightful Corporation), and the significance of the reported correlation coefficients was verified at p = 0.05 level of confidence. 3. Results and Discussion 3.1. Applicability of the Inverse Modeling Method Inverse Modeling Performance [17] Validation indices comparing observed and fitted cumulative infiltration at three consecutive supply pressure 6of14 Figure 5. Observed and fitted cumulative infiltration at consecutive supply pressure potentials of 0.3, 0.6, and 1.2 kpa for (a) sandy loam and (b) loam soil.

7 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 Table 2. Mean Error, Root-Mean-Square Error, and Pearson Correlation Coefficient r c Between the SWRC Determined Through Inverse Modeling and by Fitting Equation (4) Against Observed (q, y) Data Pairs a Textural Class Technique ME c Mean Absolute ME c Mean RMSE c Mean r c Loam SWRC in, (0.81) 1.06 (0.68) 2.40 (1.23) 0.97 (0.030) SWRC in, (0.03) 2.12 (0.03) 4.15 (0.07) 0.96 (0.001) Sandy loam SWRC in, (1.20) 1.06 (1.06) 2.71 (1.78) 0.97 (0.070) SWRC in, (0.02) 1.11 (0.01) 2.44 (0.01) 0.98 (0.001) a ME c is mean error, RMSE c is root-mean-square error, SWRC in is SWRC determined through inverse modeling, and SWRC ex is SRC determined by fitting equation (4) against observed data pairs. Standard deviation is given in parentheses. Units are 10 2 m 3 m 3. SWRC ex and SWRC in agreed very well. Furthermore, the mean absolute ME c was only once larger than 0.05 m 3 m 3 which suggests small discrepancies in modeled water content between the two methods. Volumetric water contents predicted with inverse modeling were on average lower, as indicated by the negative ME c. The large uncertainty on the estimation of the parameter a, sometimes encountered for SWRC ex of loam soils can probably explain the lower the correlation indices found for these soils (Table 2). Further, it has to be mentioned that no significant correlations were found between any of the indices reported in Table 2 and rock fragment content, suggesting that rock fragment content did not have a significant influence on the applicability of the inverse modeling method. Mean validation indices reported in Table 2 were better than most of the indices found by Cornelis et al. [2001] when comparing the predictive quality of PTFs in estimating the SWRC. This suggests that SWRC in are more reliable than the ones determined by means of PTFs. [19] Figure 6 depicts some typical SWRC in,5 and SWRC ex for both textural classes covered in our study. As illustrated by Figure 6, especially q s showed high similarity among the two techniques. This could be expected since the lowest applied pressure potential ( 0.29 kpa) with the tension infiltrometer was taken close to saturation. [20] Figure 6 further shows that the linear part of the curves, where 10 kpa < y < 1 kpa, agreed mostly well, especially for sandy loam soils. Deviation between curves at lower matric potentials, which was most pronounced for loams soils, was probably due to lacking tension infiltrometer measurements at the dry end of the SWRC. This deviation came also forward when comparing optimized Figure 6. Soil water retention curves obtained through numerical inversion of tension infiltrometer data (SWRC in,5 ) and by fitting of equation (4) against observed (q, y) data determined in the laboratory (SWRC ex ) for (a, b, c) three loam and (d, e, f) three sandy loam soils. 7of14

8 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 Figure 7. Measured saturated hydraulic conductivity versus estimated hydraulic conductivity obtained through inverse modeling. q r values obtained by both techniques, and might have resulted from wide uncertainty bands sometimes observed for q r of the SWRC in. As such, the lower confidence limit of q r was sometimes slightly negative. Also, Šimŭnek et al. [1999] reported that numerical optimization could yield unrealistic values for q r. Similar observations with respect to q r and q s were made by Ramos et al. [2006] and Šimŭnek et al. [1999]. The former authors further found good agreement between both methods in terms of n and a, determining the curve s slope. This was however not observed in our study. Poor agreement between model estimates for these parameters was probably partly caused by the large uncertainty sometimes encountered on the estimation of a and n when fitting the model of van Genuchten [1980] against observed (q, y) data pairs. In addition, it was observed that the soil structure within the soil cores was to some extent damaged during soil sampling and transport. The flat SWRC in,5 for loam samples indicates that these soils had a sandy soil-like pore structure, with a large number of large pores that empty as soon as matric potential becomes slightly negative. We suppose that this structure originated from the presence of coarse fragment related pore space which was to some extent destructed during soil sampling and transport, explaining the steeper linear part mostly observed for SWRC ex (Figures 6a and 6b). [21] Comparing the estimated and measured K s values gave a further indication of the applicability of the inverse modeling technique. The scatterplot of measured versus estimated K s values reveals a rather good agreement between both, which is further stated by a significant correlation coefficient of 0.62 and a mean absolute difference of ms 1 (Figure 7). [22] Our findings suggest that inverse modeling of tension infiltrometer data provides an interesting alternative to obtain the soil s water retention curve with a limited amount of efforts. One only needs to measure cumulative infiltration at different tensions and determine the initial and final water content gravimetrically [Šimŭnek and van Genuchten, 1997]. As such, undisturbed soil sampling, which is in particular cumbersome in stony soils, is avoided and disturbance of soil structure is reduced to a minimum. In 8of14 addition, we found that inclusion of measured K s values in the inverse modeling process did not significantly improve the inverse modeling performance, and that K s estimated from the inverse modeling technique agreed rather well with independently obtained K s values Influence of Rock Fragments on Water Retention Patterns Observed [23] In Figure 8, soil water content obtained from SWRC in,5 is plotted versus volumetric rock fragment content R v at nine matric potentials. It can be seen that the negative relation between R v and the amount of soil water retained became weaker as matric potential decreased. This indicates that rock fragments altered especially pores which can conduct soil water near saturation what coincides with the observations of Ravina and Magier [1984] and Fiès et al. [2002], who reported that pores originating from the presence of glass fragments can contribute to water retention until the matric potential is reached at which these pores empty. [24] Although correlation coefficients were less pronounced, the same findings can be drawn from Figure 9, representing scatterplots of laboratory-measured soil water content at various matric potentials versus R v. Lower correlation coefficients were most probably caused by disturbance of the soil s structure during soil sampling and transport. Furthermore, one has to keep in mind that only a part of the soil s pore structure, probably smaller than the representative elementary volume, was sampled with the steel Kopecky rings. Figures 8 and 9 suggest that the amount of water retained by the bulk soil dropped as more coarse fragments were present per unit volume and this behavior was more notable as matric potential approached saturation. Only a very weak (<0.15) correlation coefficient was found between MWD and soil water content, suggesting that in the MWD range covered by this study water retention was not influenced by the size of the rock fragments. [25] Plotting the specific water capacity (@q/@y) as a function of the matric potential gives a better insight in the range of matric potentials where rock fragments substantially influenced water retention. Figure 10 as a function of y for different classes of R v illustrating that the influence of R v on specific water capacity dropped beyond a pressure potential of approximately 30 kpa. This range of influence is approximately three times wider than the value reported by Ravina and Magier [1984], but their conclusions were drawn upon measurements conducted on disturbed soil samples. Figure 10 further illustrates clearly that the maximum of the curves corresponding to rock fragment containing samples was higher than the maximum reached by the curve determined for the disturbed samples cleared from rock fragments. This indicates that a decrease in soil water content as the matric potential became slightly negative was much higher in samples containing rock fragments. In contrast with the results of Ravina and Magier [1984] the increase in maximum as rock fragment content increased was not consistent over the R v range covered in this study. [26] Mean soil water retention curves for samples grouped by volumetric rock fragment content are depicted in Figure 11. It is clearly shown that q tended to decrease as R v increased which agrees with the findings of Fiès et al.

9 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 Figure 8. Soil water content modeled through inverse modeling versus volumetric rock fragment content R v at different matric potentials. Significant correlation coefficients are indicated with an asterisk. [2002]. Mean q r and q s were always, except for the group with a R v between 0.15 and 0.20 m 3 m 3, lower at sites containing rock fragments, although only q s correlated significantly to R v with r = When the other [van Genuchten, 1980] parameters are considered only a correlated significantly to R v (r = 0.48). Since a equals approximately the inverse of the pressure potential at the inflection point has its maximum value it indicates that the pressure potential at the inflection point tended to decrease as rock fragment content increased, which was 9of14 confirmed by the visual observation of the SWRC with increasing stone fragment content (Figure 11). This also comes forward in slightly right-skewed peaks of curves originating from sites containing rock fragments compared to the peak of the curve determined for disturbed samples cleared from rock fragments (Figure 10) Focus on Pore Size Distribution [27] The maximum number of effective pores, Z, was calculated according to equation (1) for three pairs of consecutive pressure potentials, y =0kPaandy = 0.29 kpa,

10 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 Figure 9. Soil water content measured in the laboratory versus volumetric rock fragment content R v at different matric potentials. Significant correlation coefficients are indicated with an asterisk. y = 0.29 kpa and y = 0.59 kpa and finally, y = 0.59 kpa and y = 1.18 kpa. The variable r m in equation (1) was set to the radius obtained from the expression of Young-Laplace in which y was set to the most negative pressure potential of each pair consecutive potentials. In this way, it was possible to obtain Z, and subsequently e for pores with diameters larger than 1 mm (class 1), diameters constrained between 1 and 0.5 mm (class 2) and diameters constrained between 0.5 and 0.25 mm (class 3). Figure 12 clearly illustrates the positive relationship between the volumetric rock fragment content and the estimated maximum number of pores. As pore radii became smaller, the relationship became less pronounced, although it remained significant. On the other hand the correlation coefficient between Z 10 of 14 and the silt fraction increased to 0.34 for class 3. This indicates that rock fragments had certainly a positive influence on pore volume formed by pores with diameters larger than 0.25 mm, beyond which the actual number of pores seemed to become more dependent on soil texture. Conducting tension infiltrometer measurements at lower pressure heads than covered in this study, should give confirmation about the range of pore radii influenced by rock fragments. 4. Summary [28] Using tension infiltrometer data collected at 44 sites located along three transects in arid Chile we tried to gain

11 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 Figure 10. Mean specific water capacity versus matric potential y as a function of volumetric rock fragment content R v. insight in the influence of coarse soil fragments, in terms of their dimension and abundance, on water retention. Soil water retention curves were constructed through inverse modeling of tension infiltrometer data. Obtaining these data is easy, relatively quickly and can happen without disturbing the soil s structure which is critically if one wants to study effects of coarse fragments on water retention. The inverse modeling method performed very well compared to the classical method on soil cores. Concerning rock fragments three major conclusions can be drawn from this study. First, we found that rock fragment content lowered soil water retention but this relationship became weaker as matric potential became more negative. Influence became negligible when matric potential dropped beyond 30 kpa. Second, we observed that the coarse fragment content was positively related to the estimated number of pores with diameters between 1 and 0.25 mm. However, this relationship became weaker as pore diameter narrowed. Third, no influence of rock fragment dimensions on water retention was observed in this study. Future research should focus on finding a quantitative relationship between rock fragment content and water content at different matric potentials on the basis of tension infiltrometer measurements applied at larger number of matric potentials. Furthermore, we suggest Figure 11. Mean soil water retention curves for samples grouped by volumetric rock fragment content. 11 of 14

12 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 Figure 12. Actual number of pores Z a with diameters larger than 1 mm (class 1), diameters between 1 and 0.5 mm (class 2), and diameters between 0.5 and 0.25 mm (class 3) versus volumetric rock fragment content R v. Significant correlation coefficients are indicated with an asterisk. the construction of PTFs incorporating rock fragment content as a predictor for estimating (q, y) data couples of the soil water retention curve. Notation g acceleration due to gravity, m/s 2. K d difference in hydraulic conductivity between two consecutive tensions, m/s. K s saturated hydraulic conductivity, m/s. l pore size distribution parameter in the van Genuchten [1980] model, dimensionless. m shape parameter in the van Genuchten [1980] model, dimensionless. m i mass of rock fragments retained with the ith sieve, g. ME c mean error comparing SWRC in and SWRC ex, m 3 /m of 14 ME p mean error comparing observed and fitted cumulative infiltration, m 3. MWD mean weighted diameter, m. n shape parameter in the van Genuchten [1980] model, dimensionless. N f number of rock fragment size fractions distinguished through dry sieving, dimensionless. r radial coordinate, m. r i mesh size diameter of the ith sieve used for dry sieving, m. r m minimum pore radius, m. RMSE c root-mean-square error comparing SWRC in and SWRC ex,m 3 /m 3. RMSE p root-mean-square error comparing observed and fitted cumulative and infiltration, m 3. R v volumetric rock fragment content, m 3 /m 3. z vertical coordinate, m. Z maximum number of effective pores per unit area, 1/m 2.

13 W07408 BAETENS ET AL.: COARSE FRAGMENTS AND SOIL WATER RETENTION W07408 a shape parameter in the van Genuchten [1980] model, kpa 1. e effective porosity, m 3 /m 3. m viscosity of water, g/m 3. q volumetric soil water content, m 3 /m 3. q i initial soil water content, m 3 /m 3. q r residual soil water content in the van Genuchten [1980] model, m 3 /m 3. q s saturated soil water content in the van Genuchten [1980] model, m 3 /m 3. r c Pearson correlation coefficient comparing SWRC in and SWRC ex, dimensionless. r p Pearson correlation coefficient comparing observed and fitted cumulative and infiltration, dimensionless. r w density of water, Mg/m 3. y matric potential, kpa. y 0 imposed pressure potential, kpa. initial pressure potential, kpa. y i [29] Acknowledgments. This research was funded by the Flemish Government, Department Sciences and Innovation/Foreign Policy. The authors wish to thank Thérèse Buyens and Jan Restiaen for their assistance in analysis and data reporting. 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