Relationship between specific surface area and the dry end of the water retention curve for soils with varying clay and organic carbon contents

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1 WATER RESOURCES RESEARCH, VOL. 47,, doi: /2010wr010229, 2011 Relationship between specific surface area and the dry end of the water retention curve for soils with varying clay and organic carbon contents Augustus C. Resurreccion, 1 Per Moldrup, 2 Markus Tuller, 3 T. P. A. Ferré, 4 Ken Kawamoto, 5,6 Toshiko Komatsu, 5,6 and Lis Wollesen de Jonge 7 Received 17 November 2010; revised 8 April 2011; accepted 18 April 2011; published 23 June [1] Accurate description of the soil water retention curve (SWRC) at low water contents is important for simulating water dynamics and biochemical vadose zone processes in arid environments. Soil water retention data corresponding to matric potentials of less than 10 MPa, where adsorptive forces dominate over capillary forces, have also been used to estimate soil specific surface area (SA). In the present study, the dry end of the SWRC was measured with a chilled mirror dew point psychrometer for 41 Danish soils covering a wide range of clay (CL) and organic carbon (OC) contents. The 41 soils were classified into four groups on the basis of the Dexter number (n = CL/OC), and the Tuller Or (TO) general scaling model describing water film thickness at a given matric potential (< 10 MPa) was evaluated. The SA estimated from the dry end of the SWRC (SA_SWRC) was in good agreement with the SA measured with ethylene glycol monoethyl ether (SA_EGME) only for organic soils with n > 10. A strong correlation between the ratio of the two surface area estimates and the Dexter number was observed and applied as an additional scaling function in the TO model to rescale the soil water retention curve at low water contents. However, the TO model still overestimated water film thickness at potentials approaching ovendry condition (about 800 MPa). The semi log linear Campbell Shiozawa Rossi Nimmo (CSRN) model showed better fits for all investigated soils from 10 to 800 MPa and yielded high correlations with CL and SA. It is therefore recommended to apply the empirical CSRN model for predicting the dry part of the water retention curve ( 10 to 800 MPa) from measured soil texture or surface area. Further research should aim to modify the more physically based TO model to obtain better descriptions of the SWRC in the very dry range ( 300 to 800 MPa). Citation: Resurreccion, A. C., P. Moldrup, M. Tuller, T. P. A. Ferré, K. Kawamoto, T. Komatsu, and L. W. de Jonge (2011), Relationship between specific surface area and the dry end of the water retention curve for soils with varying clay and organic carbon contents, Water Resour. Res., 47,, doi: /2010wr Introduction [2] A soil water retention curve (SWRC) model that can accurately describe the soil water content and associated energy state under dry conditions is crucially important for 1 Institute of Civil Engineering, University of the Philippines Diliman, Quezon City, Philippines. 2 Department of Biotechnology, Chemistry and Environmental Engineering, Environmental Engineering Section, Aalborg University, Aalborg, Denmark. 3 Department of Soil, Water and Environmental Science, University of Arizona, Tucson, Arizona, USA. 4 Department of Hydrology and Water Resources, University of Arizona, Tucson, Arizona, USA. 5 Graduate School of Science and Engineering, Saitama University, Saitama, Japan. 6 Institute of Environmental Science and Technology, Saitama University, Saitama, Japan. 7 Department of Agroecology and Environment, Aarhus University, Tjele, Denmark. Copyright 2011 by the American Geophysical Union /11/2010WR simulating water transport and biochemical processes for both arid climatic conditions and for the top few centimeters of a soil profile during prolonged droughts. An accurate description of the soil moisture status under dry conditions also improves simulations of water vapor transport, which aids the prediction of pesticide volatilization [Chen et al., 2000; Chen and Rolston, 2000] and is important for remediation of volatile organic chemicals by means of vapor extraction [Batterman et al., 1995; Yoon et al., 2003; Qin et al., 2010]. [3] Several empirical SWRC models, such as the widely used Brooks and Corey [1964], Campbell [1974], and van Genuchten [1980] relationships, are available to describe soil water retention at intermediate soil wetness. Although these models capture the measured soil water retention reasonably well down to 1.5 MPa, they commonly fail to describe measured soil water retention at lower matric potentials [Nimmo, 1991; Ross et al., 1991; Silva and Grifoll, 2007]. Similarly, the residual soil water content, when treated as a fitting parameter in the van Genuchten 1of12

2 [1980] SWRC model, can have physically unrealistic values [Groenevelt and Grant, 2004]. [4] Only a very limited number of measurement series covering the dry range of SWRC have been published in the literature. Measurements are scarce because of the very long equilibration times (often exceeding 4 weeks) for soil samples drained to matric potentials below 1.5 MPa in a pressure plate apparatus [Campbell, 1988; Bittelli and Flury, 2009; Davis et al., 2009]. However, measurement of very low soil water matric potentials can now be achieved easily by means of the rapid and convenient chilled mirror dew point technique [Gee et al., 1992]. Campbell and Shiozawa [1992] used this method to obtain the highly cited SWRC data sets for six soils from Washington state with textures ranging from sand to silty clay. Lu et al. [2008] also used the dew point technique to obtain the soil water retention data for eight Chinese soils. These data sets were then used to evaluate the soil water retention models proposed by Fayer and Simmons [1995], Webb [2000], and Khlosi et al. [2006] that describe the soil water retention curves from saturation to oven dryness. Likewise, Davis et al. [2009] used the dew point technique to measure hysteresis of soil water retention at low water contents for sand and silt loam for both hydrophilic and hydrophobic conditions. These data sets demonstrate the value of measurements made with the dew point technique, but, more data are needed to test SWRC models at dry conditions. [5] Or and Tuller [1999] showed that for a wide range of soil textures the capillary contributions to SWRC become negligible for matric potentials lower than 10 MPa. On the basis of this finding, Tuller and Or [2005] set this as a threshold matric potential to define the boundary between the dry adsorptive region and the wet capillary region of the SWRC. Adsorption isotherms that are based on the Campbell and Shiozawa [1992] semi logarithmic function were formulated to extend the applicability of a SWRC model to cover near ovendry conditions [Campbell et al., 1993; Rossi and Nimmo, 1994; Fayer and Simmons, 1995; Webb, 2000; Khlosi et al., 2006]. [6] The specific surface area (SA) is an important soil parameter, which influences numerous physical and chemical processes. The surface area as determined by means of the ethylene glycol monoethyl ether method (SA_EGME) has been correlated with clay content, cation exchange capacity (CEC), soil water retention at 1.5 MPa, and hydraulic conductivity [Petersen et al., 1996]. Several studies show that the amount and status of adsorbed soil water are intimately correlated to SA and clay content [Grismer, 1987; Campbell and Shiozawa, 1992; Petersen et al., 1996]. The amount of adsorbed soil water is related to SA since water coats soil particles as a thin film of water. This insight is the basis for incorporating direct relations to soil specific surface area for extension of SWRC functions to low water contents [Or and Tuller, 1999; Silva and Grifoll, 2007]. [7] Tuller and Or [2005] proposed a general scaling relationship for the soil water retention at the dry end that relates the soil water potential to water film thickness and SA. This scaling relationship described the dry SWRC of the Campbell and Shiozawa [1992] soils reasonably well. The SA determined from the dry end of the SWRC using the Tuller and Or [2005] model was also in good agreement with the SA_EGME. However, this model still needs to be verified for a larger number of SWRC data sets across all soil textures, including soils with different organic carbon contents. [8] For this study, we measured the water pressure under dry conditions with a WP4T Dewpoint Potentiameter (Decagon Devices, Inc., Pullman, Washington) and the SA by means of the ethylene glycol monoethyl ether (EGME) method for 41 Danish soils with clay contents ranging from 2.9 to 27.6% (on mass basis) and organic carbon contents ranging from 0.1 to 2.2%. We also developed an empirical scaling function to modify the Tuller and Or [2005] model for these soils. As an alternative to the Tuller and Or [2005] model, we propose a linear relation between the logarithm of the soil water matric potential and volumetric soil water content adopted from Campbell and Shiozawa [1992] and Rossi and Nimmo [1994]. We show that the parameters in this soil water retention relationship can be related to clay content, organic carbon content, or surface area. [9] The specific objectives of this study were (1) to evaluate and modify, where applicable, the Tuller and Or [2005] general scaling relationship based on the SWRC of 41 soils from the Danish Soil Library and (2) to compare the ability of the physically based Tuller and Or [2005] model and an empirical linear model derived from Campbell and Shiozawa [1992] and Rossi and Nimmo [1994] for predicting the SWRC at low water contents. 2. Materials and Methods 2.1. Soil Physical Parameters and Water Retention Data [10] A total of 41 soils (soil numbers 54 67; Table 1) from the Danish Soil Library [Lamm, 1971; Hansen, 1976] were used for this study. These soils are not necessarily predominant in Denmark, but they represent most soils of agricultural significance. The soils were initially air dried and passed through a 2.0 mm sieve. Soil texture was determined by a combination of mechanical sieving and the hydrometer method [Gee and Or, 2002]. Total organic carbon (OC) was determined on a Leco (St. Joseph, Michigan) Carbon Analyzer coupled to an infrared CO 2 detector. [11] Air dried subsamples of 10 g were prepared and a small amount of water was added. The soil samples were mixed, sealed in small airtight plastic bags, and left to equilibrate for four weeks. For water contents below air dry, samples were placed in a dessicator for different lengths of time. Following the equilibration/desiccation period, the matric potential was measured with a chilled mirror WP4 T Dewpoint Potentiameter (Decagon Devices, Inc., Pullman, Washington) [Scanlon et al., 2002]. The water content was determined gravimetrically at each measured matric potential condition. Hysteresis effects emanating from differences in sample preparation (wetting and dessicator drying) were considered to be insignificant at the dry end of the SWRC [Tuller and Or, 2004]. [12] The SA of 29 soils were taken from Petersen et al. [1996], and those of the remaining 12 soils were measured in this study. All SA values were determined using the EGME method [Heilman et al., 1965; Petersen et al., 1996; Pennell, 2002]. Surface area of organic soil materials measured by EGME was found to be similar to SA measured by CO 2 [de Jonge et al., 2000]. Cihacek and Bremner [1979] investigated the effect of removing organic matter on the results of surface area measured by means of the EGME 2of12

3 Table 1. Physical Properties of the 41 Soils Considered for This Study a Soil Location Soil Number Soil Depth (cm) Bulk Density (Mg m 3 ) Sand Fraction mm (kg kg 1 ) Silt Fraction mm (kg kg 1 ) Clay Fraction <0.002 mm (kg kg 1 ) Texture Organic Carbon (kg kg 1 ) Dexter n b Askov 54A sandy loam B sandy loam C sandy loam Hojer 55A sandy loam B sandy loam C sand Jyndevad 56A sand C sand D sand E sand Roskilde 57A sandy loam B sandy loam C sandy loam D sandy clay loam Ronhave 58A sandy loam B sandy loam C sandy loam Aarslev 60A sandy loam B sandy loam Blangstedgaard 61A sandy loam B sandy loam C sandy loam Borris 62A sand B sand C sand Lundgaard 63A sand B sand C sand Silstrup 64A sandy loam B sandy loam C sandy loam Studsgaard 65A loamy sand B loamy sand C sand Tylstrup 66A sand B sand C loamy sand D sand Odum 67A sandy loam B sandy loam C sandy loam a Data are from Hansen [1976]. b Here n = clay fraction/organic carbon. method, and found no difference on the overall SA results for samples with and without pretreatment. Further, de Jonge et al. [2000] found that the microporous structure of more rigid soil organic materials was not strongly affected by EGME penetration. On these bases, soils were not pretreated to remove organic matter and were not also saturated with Ca Soil Water Retention Models Tuller and Or Model [13] Following Tuller and Or [2005], the SWRC was divided into a wet capillary region and a dry adsorptive region separated at a matric potential of 10 MPa. In the dry adsorptive region, water exists as thin liquid films with thickness, h (m), defined in terms of the gravimetric water content m, (kg kg 1 ), density of water r w (kg m 3 ), and SA (m 2 kg 1 )[Tuller and Or, 2005] as h ¼ m w SA : ð1þ Disregarding contributions of capillary condensation at relatively low matric potentials (< 10 MPa), and considering only van der Waals forces on planar surfaces (with negligible steric interactions across adjacent surfaces), Tuller and Or [2005] adopted the expression from Iwamatsu and Horii [1996] to describe the thickness h of an adsorbed water film (< m) as a function of matric potential head, y (m H 2 O), sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h ¼ 3 A svl ; ð2þ 6 w gy where A svl (J) is the Hamaker constant (for solid vapor interactions) through the intervening liquid, and g (m s 2 )is the acceleration due to gravity. [14] This SWRC model, equation (2), contains two parameters, namely the specific surface area (SA) and the Hamaker constant (A svl ). The Hamaker constant represents interactions between macro objects such as mineral surfaces and liquid due to short range (<100 A ) van der Waals forces [Ackler et al., 1996; Bergström, 1997]. Tuller and Or 3of12

4 [2005] defined J as an effective Hamaker constant that accounts for combined effects of heterogeneous surface properties, geometry, and electrostatic and van der Waals forces. Tuller and Or [2005] noted that this value lies within the typical values between 10 and J reported in the literature. Combining equations (1) and (2), the Tuller and Or (TO) model becomes s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! m ¼ w SA 3 A svl : ð3þ 6 w gy The TO model, equation (2), using the effective Hamaker constant of J, fitted the dry soil water retention data reasonably well when tested against the six Campbell and Shiozawa [1992] SWRC data sets [Tuller and Or, 2005]. In our study, the TO model was tested against the soil water retention data sets for the 41 Danish soils. In addition, equation (3) was used to estimate the SA by freely fitting SA to the dry end of the SWRC using nonlinear regression analysis [Wraith and Or, 1998]. This SA estimated using the dry end of the soil water retention curve is denoted by SA_SWRC Campbell Shiozawa Rossi Nimmo Model [15] Campbell and Shiozawa [1992] introduced a simple linear relationship between gravimetric water content and the logarithm of matric potential at values between 10,000 and 100 m H 2 O (between 100 MPa and 1 MPa). Rossi and Nimmo [1994] used seven SWRC data sets, including the six Campbell and Shiozawa [1992] soils and one soil from Schofield [1935], to develop the three parameter sum SWRC model to cover the entire soil water retention range from saturated condition to zero water content at ovendry condition. In the dry SWRC region of the Rossi and Nimmo [1994] model, the volumetric soil water content is proportional to the logarithm of matric potential intersecting the matric potential axis at a finite value at which the water content assumes a zero value. This finite value of the matric potential that corresponds to ovendry condition depends on the temperature, pressure, and humidity during ovendrying. Groenevelt and Grant [2004] showed that the matric potential at zero water content has a value of mof H 2 O (approximately 800 MPa), which serves as the universal reference matric potential value for measurements of soil water content. This value has been used by Resurreccion et al. [2008] as the matric potential at ovendry condition. [16] On the basis of the studies of Campbell and Shiozawa [1992], Rossi and Nimmo [1994], and Groenevelt and Grant [2004], a semi log linear model relating matric potential y (m H 2 O) to volumetric soil water content (m 3 m 3 ) is proposed. This relationship is, hereafter, called the Campbell Shiozawa Rossi Nimmo (CSRN) model:! log y y ref ¼ ð SLÞ ; ð4þ where y ref (m H 2 O) is the reference soil water matric potential which is set at mh 2 O, and SL is the dimensionless slope of the linear model. Several published soil water retention models at low water contents such as the one recently tested by Lu et al. [2008] are based on the semi log linear relationship of Campbell and Shiozawa [1992], i.e., equation (4), anchored at a finite matric potential (approximately at 10 5 m H 2 O) of zero water content representing oven dryness [e.g., Ross et al., 1991; Fayer and Simmons, 1995; Webb, 2000; Khlosi et al., 2006]. In this study, we considered the CSRN. 3. Results and Discussion 3.1. Dexter n Soil Groups [17] Dexter et al. [2008] presented an index to classify soils on the basis of the amount of clay associated with organic carbon. This index, denoted here as Dexter n, is the ratio of the clay fraction (CL) and organic carbon (OC) content (i.e., n = CL/OC). The Dexter n is an effective index to group soils on the basis of the amount of complexed clay that controls soil physical processes such as water retention, water repellency, and soil self organization [Dexter et al., 2008; de Jonge et al., 2009]. [18] A threshold value of n = 10 was proposed to mark clay saturation for both low OC arable and high OC pasture soils [Dexter et al., 2008; de Jonge et al., 2009]. For n < 10, all clay particles are already complexed with OC so that free OC becomes available. For n > 10, noncomplexed clay is still available to bind with free OC. The recent study of Liu et al. [2010] on adsorption of butachlor onto organically rich soils and size fractions has suggested this formation of organoclay complexes. They found that at very low OC content, mineral colloids could enhance sorption because of highly exposed mineral surfaces, while at high OC contents colloid (clay) minerals may weaken the sorption of butachlor because of strong association and coating of organic matter by minerals. It is likely that organic matter partially covers the available clay surfaces when forming organomineral complexes, hereby reducing the effective surface area measured using the EGME method. [19] The Dexter n, although a purely empirical index, is useful for grouping soils on the basis of clay to organic carbon content ratio. The soil data represent a large interval of Dexter n, covering almost 2 orders of magnitude from 1.8 to 167 (Table 1). Our soils were divided into four groups (groups I IV) on the basis of the Dexter n values (Figure 1a), where high OC soils (n 10; groups I and II) are differentiated from low OC soils (n > 10; groups III and IV). The high OC soils were further subdivided into group I (n < 4) and group II (4 < n < 10) and the low OC soils were further subdivided into group III (10 < n < 50) and group IV (n > 50). The number of soils in groups I through IV are 8, 10, 13, and 10; respectively. Eleven soils with very low OC (OC kg kg 1 ), which are comparable in OC with the six pretreated Campbell and Shiozawa [1992] soils, were used as a platform to assess the performance of the TO model. These 11 soils are shown with red symbols for ease of identification. [20] The 41 soils are mostly illite dominated soils from a narrow geographical and climatic area and does not include substantial amounts of high surface, expandable clay minerals. This allows a stricter test of models with regard to the effects of organic carbon coverage on the relation of surface area and dry end of soil water retention curve. [21] The surface area measured by means of the EGME method (SA_EGME) was observed to increase with increasing clay content that can be fitted by a second order polynomial (Figure 1b). This is in agreement with the findings of Petersen et al. [1996] for the 29 soils that are common 4of12

5 Figure 1. (a) Dexter plot of organic carbon content against clay fraction (CL) for 41 Danish soils. The 41 Danish soils are grouped into four Dexter classes. (b) Variation of surface area measured by ethylene glycol monoethyl ether (EGME) (SA_EGME, m 2 kg 2 ) with clay fraction. Also included are the best fit linear and second degree polynomial regression curves. Red symbols represent soils with organic carbon of less than or equal to kg kg 1, placed below the horizontal dashed line in Figure 1a. The symbols given here are used throughout the paper. with this study. Or and Wraith [1999] showed that the magnitude of SA_EGME is highly dependent on the types of clay minerals present in the soil. However, the differences in SA_EGME values across the four Dexter groups in this study cannot be attributed to differences in clay mineralogy because most of the 41 soils contain illite as the predominant clay mineral [Hansen, 1976; Petersen et al., 1996]. Rather, the observed differences in SA are mainly due to the different proportions of clay and OC as represented by the Dexter n. This is shown in Figure 1b as separation of groups I and II, which generally have smaller surface than groups III and IV with generally larger surface areas. This is in agreement with Dexter et al. [2008], who showed that different pedotransfer functions are required to relate soil parameters such as surface area with total clay fraction for different Dexter classes. Figure 2. Plot of matric potential (MPa) against water film thickness (10 9 m) for eight Danish soils with different Dexter n values. The short dashed,solid,andlong dashed lines are plotted using equation (2) with a Hamaker constant, A svl,of , , and J, respectively. 5of12

6 Table 2. Surface Area Measured Using the Ethylene Glycol Monoethyl Ether Method (SA_EGME), Surface Area Estimated From the Soil Water Retention Data (SA_SWRC), Fitted Hamaker Constant (A svl ), and the Campbell Shiozawa Rossi Nimmo (CSRN) Model Slope (SL) Soil Location Soil SA_EGME SA_SWRC a Number (m 2 kg 1 ) (m 2 kg 1 ) Hamaker Constant A svl b (10 20 J) Slope SL c Askov 54A 23,800 32, B 35,500 40, C 94,000 64, Hojer 55A 30,630 47, B 33,950 46, C 6,900 14, Jyndevad 56A 7,400 21, C 8,400 37, D 15,100 31, E 8,300 6, Roskilde 57A 18,900 35, B 50,100 42, C 69,900 59, D 111,300 87, Ronhave 58A 52,700 41, B 50,600 36, C 71,800 40, Aarslev 60A 28,500 24, B 48,700 35, Blangstedgaard 61A 30,040 42, B 43,360 49, C 51,380 52, Borris 62A 7,800 19, B 11,800 11, C 12,000 9, Lundgaard 63A 4,970 16, B 4,260 12, C 3,890 9, Silstrup 64A 24,900 46, B 89,800 63, C 90,300 57, Studsgaard 65A 12,870 30, B 11,130 24, C 8,710 12, Tylstrup 66A 5,300 19, B 12,100 23, C 19,500 21, D 10,700 8, Odum 67A 23,900 28, B 42,700 27, C 53,600 32, a Fitted values surface area using equation (3) with Hamaker constant equal to A svl = J. b Fitted values of Hamaker constant using equation (3) with surface area equal to the values measured with EGME. c Fitted values of CSRN Slope SL using equation (4) Tuller and Or Scaling Soil Water Retention Model [22] The Tuller and Or [2005] model was applied to eight selected soils representing different Dexter n values (Figure 2). Using the SA_EGME for calculating h in equation (2) and an effective Hamaker constant, A svl,of J, the TO model (solid lines in Figure 2) captured well the soil water retention data for low OC groups III and IV soils (Figure 2, soil numbers 57D, 62B, 66C, and 57B). However, as illustrated for the low OC soil 67B (n = 48.44) in Figure 2b, the TO model requires A svl to be close to J in order to match measured soil water retention data reasonably well. Thus, the TO model describes soil water retention data for group III and IV soils well, where the apparent A svl is between J and J (Figure 2, short dashed and long dashed lines, respectively). [23] For group I and II soils (i.e., for n < 10 such as 57A in Figure 2c, and for n < 4 such as 66A in Figure 2d), the TO model deviates markedly from measured soil water retention data. Most of the measured soil water retention data points are located at the far right of the TO model predictions, even when a lower boundary value of J was used for A svl. This indicates that the SA needs to be different from SA_EGME in order for the TO model to describe the dry soil water retention with A svl kept constant at J, especially for group I and II soils. This SA value that may be different from SA_EGME in order for the TO model (equation (3)) to describe well the dry end of SWRC is the SA_SWRC. Table 2 gives the SA_EGME and SA_SWRC for the 41 soils investigated in this study. [24] Figure 3a shows the plot of soil water retention for all of the soils examined in this study. Here SA_EGME was used in equation (1) to evaluate water film thickness, h, from measured gravimetric soil water content, m. Also shown are the TO model curves with Hamaker constants of J (short dashed line), J (solid line), and J (long dashed line). As previously illustrated in Figure 2 and now in Figure 3a, the measured soil water retention for highly organic group I soils (n < 4) cannot be predicted well with the TO model. Measured soil water retention data are located above, outside the region bounded by the TO model curves. For the low organic group III and IV soils (n > 10), there were smaller differences between the observed water film thickness and those predicted by the TO model. [25] The TO model worked reasonably well for the 11 low organic soils (OC < kg kg 1, mostly group IV soils; Figure 3b), which is in agreement with the findings of Tuller and Or [2005] for the seven soils pretreated to remove organic matter. The soil water retention data points of the 11 low organic soils are located slightly to the left of the TO model with A svl of J, while the seven pretreated soils from Tuller and Or [2005] are located slightly to the right of the TO model, except for one pretreated soil. [26] For each of the 41 soils examined, an effective Hamaker constant was determined by fitting the TO model, equation (3), to dry soil water retention data, with the SA value set to SA_EGME. Figure 4 and Table 2 show the variation of the estimated Hamaker constant with Dexter index. For most low organic group III and IV soils, A svl is within the range to J, reported by Tuller and Or [2005]. However, for high organic group I and II soils, the estimated effective A svl is much lower than J, around 2 orders of magnitude below the typical range of A svl values reported in literature. The fitted A svl decreases with increasing Dexter n (Figure 4). [27] Both the specific surface area and Hamaker constant are affected by the presence of clay complexed with OC, as represented by the Dexter n. As evident from Figures 2 4, either the surface area or the Hamaker constant needs to be adjusted for the universal scaling relationship of Tuller and Or [2005] to be able to describe the dry soil water retention for soils with different clay and organic carbon contents. Since the fitting of the Hamaker constant, A svl, to the TO model may result in values outside the typical range of reported values, we, at present, propose that a scaling factor 6of12

7 Figure 3. Plot of matric potential (MPa) against water film thickness (10 9 m) for (a) 41 Danish soils and (b) 11 Danish soils with low organic carbon (red symbols) and Tuller and Or [2005] data (blue symbols). The short dashed, solid, and long dashed lines are plotted using equation (2) with a Hamaker constant, A svl,of , , and J, respectively. The vertical line indicates a monolayer water film thickness. should be used in the TO model with the A svl value fixed at J to modify the value of SA_EGME and to predict the soil water retention curve at low water contents across textural classes. [28] Figure 5a depicts a scatterplot of SA_SWRC obtained from the TO model with A svl = J, against SA_EGME. Deviations from the 1:1 line were observed for group I soils (n < 4) with high organic carbon contents, resulting in generally higher values of SA_SWRC than SA_EGME. A higher value for SA_SWRC than SA_EGME was required to capture the soil water retention data of group I soils. For group II and III soils (4 < n < 50) and the Tuller and Or [2005] soils (except for one pretreated soil), the TO model yielded SA_SWRC values that were remarkably close to SA_EGME values (i.e., data points are within the vicinity of the 1:1 line). For very low organic soils (OC < kg kg 1 ), the SA_SWRC values are estimated to be 75 percent of the SA_EGME values, on average, as shown in Figure 5a. Thus, the SA_EGME significantly differs from SA_SWRC for either very low or, especially, for very high OC soils. [29] To further quantify the difference between SA_SWRC and SA_EGME, the ratio of SA_SWRC to SA_EGME (i.e., SA Ratio = SA_SWRC/SA_EGME) was Figure 4. Plot of fitted Hamaker constants (10 20 J) against Dexter n values. The surface area measured with EGME was used as SA in equation (3) to the dry soil water retention data at y < 10 MPa. The horizontal dashed line is for a value of the Hamaker constant of J. 7of12

8 Figure 5. (a) Plot of estimated surface area using soil water retention data (SA_SWRC) against surface area measured by EGME (SA_EGME) for the 41 Danish soils and seven soils from Tuller and Or [2005] (blue symbols). A best fit line was fitted only to the 11 soils with low organic carbon (red symbols). (b) Plot of the ratio SA_SWRC/SA_EGME against Dexter n. correlated with the Dexter n (Figure 5b). The 0.75 slope of the best fit line for the 11 low OC soils in Figure 5a is the horizontal dashed line in Figure 5b at an SA Ratio of Within the range of Dexter n for the 41 soils considered in this study, the SA Ratio showed a very strong correlation with Dexter n given as a power function: 3.3. Campbell Shiozawa Rossi Nimmo Soil Water Retention Model at Low Water Contents [31] At low water contents, the soil water retention for all of the studied soils followed a semi log linear y() trend that is best captured by the CSRN soil water retention model SA Ratio ¼ 5:25n 0:84 þ 0:65 r 2 ¼ 0:80: ð5þ Equation (5) was used as an additional scaling function to convert the value of measured SA_EGME (measured SA) to SA_SWRC (estimated SA). This SA_SWRC is the specific surface area value to be used in the TO universal scaling soil water retention model, equation (2), at low water contents. [30] Figure 6 is a rescaled SWRC plot of Figure 3 after applying the additional scaling function (equation (5)) to the soil water retention data of the 41 Danish soils. The soil water retention data are now better described by the TO model, especially for the group I soils where almost all soil water retention data points are now contained within the TO model curves bounded within the typical range of A svl between J and J. However, the water film thickness at a soil water matric potential of less than 300 MPa was slightly lower than predicted by the TO model (see data points above the horizontal line in Figure 6). There is an apparent increase in deviation of water film thickness from the TO model line as the value of the matric potential decreases, approaching 800 MPa (i.e., near m H 2 O) at ovendry conditions. Both calculated h values using equation (1) and using the TO model (equation (2)) at matric potentials below 300 MPa are smaller than one molecular layer of water, indicating that not all surfaces are covered with water. Figure 6. Plot of matric potential (MPa) against water film thickness (10 9 m) for 41 Danish soils. The SA_EGME was adjusted using the best fit curve obtained in Figure 5b (equation (5)) and used as SA in calculating the water film thickness h in equation (1). The short dashed, solid, and long dashed lines are plotted using equation (2) with a Hamaker constant, A svl,of , , and J, respectively. The vertical line indicates a monolayer water film thickness. 8of12

9 Figure 7. Plot of slope of the Campbell Shiozawa Rossi Nimmo (CSRN) model (SL) against (a) clay fraction and (b) surface area measured using EGME. SL is the calculated slope of best fit line of logarithm of matric potential (y) versus volumetric soil water content () for the soil water retention data (y < 10 MPa). (equation (4)). The best fit line intersects the matric potential axis at approximately 800 MPa, which corresponds to the matric potential at ovendry conditions [Groenevelt and Grant, 2004]. Silva and Grifoll [2007] pointed out the challenges of defining a finite matric potential value for completely dry conditions (i.e., no water molecules adsorbed on particle surfaces). However, the practicality of having a reference finite matric potential value at ovendry conditions eases the modeling of soil water retention at low water contents because soil water contents are usually measured with reference to ovendry condition. In addition, the observed soil water retention data for our 41 soils showed that water content approached zero at the matric potential of 800 MPa. [32] The soil water retention data suggest that the empirical semi log linear CSRN soil water retention model, equation (4), can be used to capture the behavior of the dry SWRC and overcome the difficulty of approaching an apparent finite matric potential at ovendry condition. For all 41 Danish soils and the six Campbell and Shiozawa [1992] soils, the CSRN model fitted the behavior of the dry SWRC reasonably well (linear best fit lines not shown). The slope of the best fit line (i.e., SL in equation (4)) was determined for all 41 Danish soils and for the six soils from Campbell and Shiozawa [1992]. The slope SL values were plotted against clay fraction (CL) and SA_EGME (see Figures 7a and 7b). [33] Empirical correlation between SL and CL, or between SL and SA_EGME was determined from the SWRC data of the 41 Danish soils. The highly organic group I soils (n < 4) were excluded when determining the empirical relations between SL and CL and between SL and SA_EGME (Figures 7a and 7b). These group I soils that behave quite differently from all other soils may serve as independent data sets for evaluating the CSRN model (see Figures 8b and 8c). As expected, there is a decrease in slope SL with increasing CL (Figure 7a) since soils with high clay content generally retain more water. The empirical relation between SL (dimensionless) and CL (kg kg 1 ) is given as SL ¼ 10:75 CL 0:80 r 2 ¼ 0:94: ð6þ Similarly, SL decreases with the increasing SA_EGME following the empirical relation SA EGME 0:66 SL ¼ 604 r 2 ¼ 0:71; ð7þ 1000 where SA_EGME is in m 2 kg 1. There is a similarity in the trend for the correlations between SL and the clay fraction in Figure 7a and SL and SA_EGME in Figure 7b since SA_EGME is highly correlated with the clay fraction (as illustrated in Figure 1b). [34] Similar to equations (6) and (7), both SA_EGME and Dexter n can be used concurrently to improve the estimate of slope SL. The slope SL can be estimated on the basis of the strong correlation between the slope SL and SA_SWRC (not shown). The empirical relation describing the variation of SL with SA_SWRC is given as SA SWRC 0:96 SL ¼ 1631 r 2 ¼ 0:98; ð8þ 1000 where SA_SWRC is in m 2 kg 1. All soils were included to obtain the regression line in equation (8). The strong correlation was expected because both SL and SA_SWRC were derived by fitting the CSRN and TO models to the same dry soil water retention data. Equation (8) is combined with equation (5) to determine the slope SL from the values of SA_EGME and Dexter n. From equation (5), the SA Ratio can be calculated at the given Dexter n. This is required to compute SA_SWRC from SA_EGME (i.e., 9of12

10 Figure 8. Plot of matric potential (MPa) against gravimetric water content (kg kg 1 )forfourdanish soils with different Dexter n values. The solid lines are from the Tuller and Or [2005] model (TO), equation (3), using measured SA_EGME (red) and SA_SWRC estimated from soil water retention (black). The dashed lines are from the semi log linear y() soil water retention model (Campbell Shiozawa Rossi Nimmo (CSRN) model; equation (4)). The slope SL values were estimated from the clay fraction (black) using equation (6) or from SA_EGME and Dexter n (red) using equations (5) and (8). SA_SWRC = SA Ratio SA_EGME). Once SA_SWRC is determined, the value for SL used in the CSRN model can be calculated using equation (8). [35] If either CL or SA_EGME is known, the soil water retention curve at low water contents can be produced using the CSRN model with slope SL determined from the correlations given in equation (6) or equation (7) as illustrated in Figures 7a and 7b. On the other hand, using both SA_EGME and Dexter n, a better estimate of the slope SL can also be calculated from a combination of the correlation equations from equations (5) and (8). Also, with a knowledge of the slope SL of the CSRN model fitted to the soil water retention at low water contents, the clay content and SA_EGME can be solved inversely from the correlation equations, equations (6) and (7), respectively, or from the combination of equations, equations (5) and (8). [36] Figure 8 shows the difference between the CSRN and TO models for four selected soils representing different Dexter n values (group I to IV soils). As illustrated in Figure 2 and now in Figure 8, the TO universal scaling model performed better when SA_SWRC was used instead of SA_EGME. However, an overestimation is apparent for matric potentials below 300 MPa, approaching ovendry conditions (approximately 800 MPa). In contrast to the physically based TO model, the empirical CSRN model with the slope SL calculated from CL performed reasonably well, as evident from an independent test conducted for a group I soil (Figure 8a). The CSRN model with SL obtained from equations (5) and (8) using the SA_EGME and Dexter n values gave reasonably accurate descriptions of soil water retention for all 41 soils from 10 to 800 MPa. 4. Conclusions [37] In this study, we showed that the amount of complexed clay as represented by the Dexter et al. [2008] index had a significant impact on the estimation of surface area from soil water retention when using the Tuller and Or [2005] model. The TO model gave good predictions of soil water retention for low OC soils, but failed to scale soil water retention curves for soils with very high OC contents. An empirical rescaling parameter was derived to consider 10 of 12

11 different Dexter n values. This parameter can be used as a corrective scaling factor to calculate the surface area to be used as a parameter of the TO universal scaling relationship [Tuller and Or, 2005]. A linear Campbell Shiozawa Rossi Nimmo soil water retention model with the sole parameter obtained from the clay fraction, organic carbon content (or as combined Dexter n) and surface area measured by EGME provided a better fit to the soil water retention data for the soils considered in this study. The application of the empirical CSRN model is recommended for the prediction of the dry part of the water retention curve ( 10 to 800 MPa) from measured clay to organic carbon content ratio or surface area and, prospectively, to modify the physically based TO model to obtain better descriptions of the soil water matric potential under dry conditions. [38] Acknowledgments. 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