A New Two-Stage Approach to predicting the soil water characteristic from saturation to oven-dryness

Accepted Manuscript A New Two-Stage Approach to Predicting the Soil Water Characteristic from Saturation to Oven-Dryness Dan Karup Jensen, Markus Tuller, Lis W. de Jonge, Emmanuel Arthur, Per Moldrup PII: DOI: Reference:

S0022-1694(14)01029-4 http://dx.doi.org/10.1016/j.jhydrol.2014.12.018 HYDROL 20114

To appear in:

Journal of Hydrology

Received Date: Revised Date: Accepted Date:

23 July 2014 10 December 2014 11 December 2014

Please cite this article as: Jensen, D.K., Tuller, M., de Jonge, L.W., Arthur, E., Moldrup, P., A New Two-Stage Approach to Predicting the Soil Water Characteristic from Saturation to Oven-Dryness, Journal of Hydrology (2014), doi: http://dx.doi.org/10.1016/j.jhydrol.2014.12.018

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A New Two-Stage Approach to Predicting the Soil Water Characteristic from Saturation to OvenDryness Dan Karup Jensen1*, Markus Tuller2, Lis W. de Jonge1, Emmanuel Arthur1, and Per Moldrup3.

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Department of Agroecology, Faculty of Science and Technology, Aarhus University, Blichers Allé 20, P.O.

Box 50, DK-8830 Tjele, Denmark 2

Department of Soil, Water and Environmental Science, The University of Arizona, 1177 E. 4th Street,

Tucson, AZ 85721-0038, USA 3

Department of Civil Engineering, Aalborg University, Sofiendalsvej 11, DK-9200 Aalborg SV, Denmark

*Corresponding author: D. K. Jensen ([email protected])

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Abstract The present study proposes a new two-step approach to prediction of the continuous soil water characteristic (SWC) from saturation to oven-dryness from a limited number of measured textural data, organic matter content and dry bulk density. The approach combines dry- and wet-region functions to obtain the entire SWC by means of parameterizing a previously developed continuous equation. The dry region function relates gravimetric soil fractions to adsorptive forces and the corresponding water adsorbed to soil particles. The wet region function converts the volumetric particle size fractions to pore size fractions and utilizes the capillary rise equation to predict water content and matric potential pairs. Twenty-one Arizona source soils with clay and organic carbon contents ranging from 0.01 to 0.52 kg kg-1 and 0 to 0.07 kg kg-1, respectively, were used for the model development. The SWCs were measured with Tempe cells, a WP4-T Dewpoint Potentiameter, and a water vapor sorption analyzer (VSA). The model was subsequently tested for eight soils from various agricultural fields in Denmark with clay contents ranging from 0.05 to 0.41 kg kg-1. Test results clearly revealed that the proposed model can adequately predict the SWC based on limited soil data. The advantage of the new model is that it considers both capillary and adsorptive contributions to obtain the SWC from saturation to oven-dryness. Keywords: capillarity; adsorption; unsaturated soil; water retention; soil moisture

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1. Introduction The soil water characteristic (SWC) relates the water content and the matric potential of a soil. The SWC is key for studying various soil water related processes such as water availability for plants, evapotranspiration, and modeling of water and gas flow in partially saturated soils. The SWC is highly non-linear and can be directly measured in the laboratory or field, or be predicted from soil properties with pedotransfer functions. Measurements of the SWC across a wide range of matric potentials are laborious due to long equilibration times, thus rendered impractical for many applications. Numerous empirical parametric models have consequently been proposed with the Brooks and Corey (1964) and the van Genuchten (1980) equations being the most commonly applied in soil and porous media research. Soil water characteristic measurements are primarily conducted for matric potentials above -1500 kPa or below pF 4.2 (where pF is the common logarithm of the absolute matric potential in cm) due to reduced accuracy and longer equilibration times at low matric potentials (Bittelli and Flury, 2009). The longer equilibration time is a consequence of adsorptive surface forces governing the dry region of the SWC, which are stronger than the capillary forces that dominate the wet region of the SWC (Tuller et al., 1999). Measurements of the SWC under dry conditions may, however, now be achieved faster and with higher accuracy using the well-established, dew point technique, which enables measurement of the vapor pressure of soil air in equilibrium with the matric potential (Gee et al., 1992). This method has been used to measure the dry-end SWC for six soils with textures ranging from sandy to silty clay (Campbell and Shiozawa, 1992), where a linear relationship between the water content and the logarithm of the matric potential above pF 4 was established. This classical dataset has been used in several other studies (e.g. Fayer and Simmons, 1995; Khlosi et al., 2006; Webb, 2000), who all used a linear approach to describe the soil water characteristic. These models were later evaluated by Lu et al. (2008), who also measured the dry-end SWC for eight soils by

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means of the chilled mirror dewpoint technique. The fairly rapid and accurate methods available for measuring the energy state and water content under dry conditions have resulted in several recent studies presenting new dry-end SWC data and establishing that intimate relationships exist between the dry-end SWC and clay content (Arthur et al., 2014a; Chen et al., 2014; Schneider and Goss, 2012a; Wuddivira et al., 2012; Wäldchen et al., 2012), and soil specific surface area (Arthur et al., 2013; Leão and Tuller, 2014; Resurreccion et al., 2011). The availability of such relationships in the dry SWC range provides the basis for the development of a model that can predict the water content associated to different matric potentials in the dry region. Because there has been a general lack of measured dry-end SWC data there is a lack of models to predict the entire SWC from saturation to oven-dryness, for all textural soil classes. Most existing SWC models can be applied with varying success for wet conditions, depending on texture, and they usually have restricted applicability in the dry region (Khlosi et al., 2008). Suggestions have consequentially been made to obtain the SWC by parameterizing the van Genuchten (1980) model and extending it linearly throughout the dry region to oven-dryness (e.g. Schneider and Goss, 2012b; Webb, 2000). Recent studies have shown that there is a relationship between the pore size distribution, which is linked to the SWC, and the volumetric soil size fractions including organic matter (Moldrup et al., 2007; Naveed et al., 2012). However, these studies only analyzed sandy and loamy soils and did not include the dry region of the SWC and further noted that more research on the topic would be necessary. The objective of the presented study was to develop a robust model that predicts the entire SWC from saturation to oven-dryness for all soil textural classes based on texture, organic matter content, and bulk density. The model parameters were determined based on 21 differently textured soils and the model thereafter validated for data of eight independently measured soils. The

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proposed new approach uses a combination of volumetric and gravimetric texture size fractions to predict the wet and dry regions of the SWC, respectively. The model predicts 10 matric potential and water content pairs that are subsequently used to parameterize a previously developed continuous equation that captures the SWC from saturation to oven-dryness.

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2. Model development The forces governing the retention of water within the soil matrix are capillary and adsorptive surfaces forces. While the adsorptive surfaces forces govern the dry region, the capillary forces dominate the wet region (Or and Tuller, 1999; Tuller et al., 1999). Common measurements of the SWC are usually conducted at matric potentials below pF 4.2 (>-1500 kPa) (Lu et al., 2008), and this study therefore used pF 4.2 to separate the dry and wet region. Since the dry and wet regions are dominated by different forces, two models capturing the wet- and dry-ends of the SWC are proposed to predict equilibrium matric potential-volumetric water content pairs that are subsequently used to parameterize a continues SWC equation. 2.1 Dry-region model A linear relationship between pF and the water content between pF 4 and pF 7 where pF 7 is ovendryness, was introduced by Campbell and Shiozawa (1992) based on six soils with clay contents ranging from 0.05-0.47 kg kg-1. Later it was recommended that pF 6.9 should be applied instead of pF 7 as the matric potential for oven-dry conditions (Arthur et al., 2013; Groenevelt and Grant, 2004). The water content in the dry SWC range is governed by adsorptive forces, and hence controlled by the specific surface area. The specific surface area is primarily governed by the quantity of fines (clay, organic matter and silt). Due to the relation between fines and adsorption, studies have related the gravimetric water content at a specific relative humidity (RH) to the clay content for a wide range of soil types and clay minerals (Arthur et al., 2014a; Chen et al., 2014; Wuddivira et al., 2012; Wäldchen et al., 2012). Organic matter significantly contributes to water adsorption, particularly in soils with low clay contents that are not considered hydrophobic (Arthur et al., 2014a). It was also shown that the weighting factor for organic matter (OM) is twice that of the clay content for soils with water contents at pF 4.2 based on measured data of 41 soils (Hansen,

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1976). The large surface areas of clay and OM are expected to have the largest influence on water adsorption, but silt can likewise have a significant effect on water adsorption, especially for soils with high silt and low clay contents. If linearity between pF and water content can be assumed, it is possible to develop a model to predict the water content in the dry region by using a single reference point. In this study pF 6 (~50% RH) was used as a reference point, and assuming a weighting factor of 2 for OM, a regression model for the volumetric water content (cm3 cm-3) at pF 6 (θpF6) can be proposed as:

θ pF 6 = A(CL + 2 OM + B S)ρ b

(1)

where CL, S, and OM are the clay, silt and organic matter contents (kg kg-1), respectively, ρb is the dry bulk density (g cm3), and A and B are free model parameters, where A has units of cm3 g-1. The best-fit model parameters A and B are determined and evaluated in the results and discussion section based on measured data. We propose a new linear dry-region model for θ(ψ) when θpF6 is known or obtained from Eq. (1), by adopting the linearity concept for the dry region with the matric potential at oven-dryness assumed at pF 6.9:

θ (−ψ ) =

θ pF 6 (6.9 − log 10 (−ψ )) 6.9 − 6

(2)

where ψ is the matric potential (cm H2O) and θ is the volumetric water content (cm3 cm-3). The value of 6.9 is the pF at oven-dryness, and 6 is the pF value of the known or predicted water content. 2.2 Wet-region model

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The wet region soil water retention is primarily governed by capillary forces that are described by the well-known Young-Laplace equation. In simple terms, the Young-Laplace equation can be approximated to be a relation between the matric potential and the pore size (Hillel, 1980): −ψ =

3000 d

(3)

where d is the pore diameter (µm) and ψ is capillary rise equivalent to the matric potential (cm). In such system the pore diameter is linked to the particle size, with the coarse particles generating the biggest pores and the fine particles generating the smallest pores. Since Eq. (3) is controlled by capillarity, and Tuller et al. (1999) showed that for loamy soils the adsorptive forces dominate capillary forces at pF 3, Eq.(3) was not applied for potentials higher than pF 3 to alleviate prediction errors. The mean pore diameter was found to be approximately 30% of the mean particle diameter, based on experimental data of sandy and loamy soils (Hamamoto et al., 2011; Sakaki et al., 2014). The proposed model in this subsection was thus derived based on Eq. (3) with d = 0.3D, where D is the mean particle diameter. As an example, a soil matrix exhibiting a matric potential of -20 cm H2O (pF 1.3) will, in equilibrium, have drained the pores ≥ 150 µm, or what corresponds to pore fractions formed by the particles ≥ 500 µm (coarse sand). Assuming Eq. (3) is valid for a soil matrix and d = 0.3D, the pores generated by different soil particle size fractions can be separated into different groups. For example, the pores generated by coarse sand (CS), fine sand (FS), silt (S) and clay and organic matter (CL+OM), will then be completely drained at pF 1.3, pF 2.3, pF 3.7, and somewhere above pF 3.7, respectively. One avenue to estimate the pore volume for each soil-size fraction is to assume that each fraction generates a volume of pores corresponding to the relative mass of its particles.

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Separating the particles into n fractions, the water content of a soil matrix can be calculated as (Arya et al., 1999): j =i

θ i = φ SW

∑w

j

i =1,2,…,n

(4)

j =1

where θi is the water content (cm3 cm-3), φ is the total porosity (cm3 cm-3), S W is the ratio of saturated water content to the porosity of the entire sample, wj is the relative mass of the fraction j (kg kg-1), and j starts with the biggest particles. The initial idea behind Eq. (4) originated from observations indicating that the particle size distribution (PSD) and the SWC exhibit a similar shape (Arya and Paris, 1981). A common method for obtaining a pore-size distribution is then to assume the grains as uniformly-sized spheres and to relate the particle diameters of each fraction to poresize fractions, assuming that the SWC is the pore-size distribution derived from the capillary rise equation (Arya and Paris, 1981; Mohammadi and Vanclooster, 2011; Naveed et al., 2012). In a fully-mixed soil matrix, however, the soil particles intermix, whereby smaller particles become embedded between larger particles, reducing the pore diameters generated by the bigger particles and thereby increasing the pore volume generated by the fines. This follows Mohammadi and Vanclooster (2011), who used Eq. (4) to estimate the water content and linked it to matric potential that was derived based on the assumption that the matrix consists of uniformly-sized spherical particles. They underestimated the water content for several soils at matric potentials above pF 2.5, where the pores generated from the sandy particles were expected to have drained, and thereby overestimated the pore volume generated by sand and vice versa for the fines. Based on previous studies that have shown a strong correlation between volumetric soil size fractions and the volume of the pore sizes (Moldrup et al., 2007; Naveed et al., 2012), we assumed a relationship between the pores generated by each volume soil-size fraction and the

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relative volumetric soil-size fraction and thereby emphasized the effect of OM due to the fact that OM has a lower bulk density. We additionally assumed that the squared summation of the relative volumetric particle size fractions accounts for the mixing of small and large particles. The effective summation of the water content (volumetric pore space) for each soil size fraction in a soil matrix can thus be calculated as:

 j =i  θi = θ s  ∑ V j   j =1 

2

i =1,2,…,n

(5)

where θi is the summed water content (cm3 cm-3) or pore space generated from each volume soil fraction, θs is the saturated water content (cm3 cm-3), substituting ‘ φ S W’, and Vj is the relative volume of fraction j (cm3 cm-3). j starts with the volume fraction range consisting of the biggest particles to the nth volume of a fraction (n consisting of the smallest particle), since the largest particles are expected to generate the largest pores but lowest volume. A more convenient expression of Eq. (5) is:

 j =i  θ (ψ ) = θ s - θ s  ∑ V j (ψ )   j =1 

2

i=1,2,…,n

(6)

where ψ separates the volume of solid fractions by pore size and potential capillary rise, given by Eq. (3). It is only possible to couple Eq. (6) with Eq. (3) at potentials below pF 3, since adsorptive forces become dominant at drier conditions (Or and Tuller, 1999), which may result in prediction errors. Application of Eq. (6) requires knowledge of the PSD and narrow particle-size ranges between each fraction in order to assume linearity between the water content and two particle-size fractions, as suggested by Arya and Paris (1981). Since description of the PSD in such detail is

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rather uncommon, texture and OM were separated into the four particle-size groups mentioned earlier: CS, FS, S, and CL+OM. Due to the lack of linearity between the volume size fractions and the water content, Eq. (6) can then be only used to predict two matric potential and water content pairs (at V j = VCS and V j = VFS ), and because Eq. (6) is only applicable for pF ≤ 3, with the smallest pores generated from silt having a capillary potential of pF 3.7. An expanded version of Eq. (6) is given as:

θ (ψ ) = θ s (1 - (VCS + VFS β1 + VS β 2 )α )

(7)

where β1 and β2 are parameters determining whether the pores of the FS and S fractions are filled, partially filled or completely drained (-). The β1 and β2 parameters range from 0 to 1 as a function of the capillary rise equation with d =0.3D, where β1 equals 1 at pF 2.3 and β2 equals 1 at pF 3.7 (outside the capillarity-dominated domain). The α parameter is the squared volume fraction, where α is VCS at pF <1.3, VCS + VFS at pF 1.3–2.3 and VCS + VFS + VS at pF 2.3–3, determined based on Eq. (3). No β-values were assigned to the coarse sand fraction, since associated pores drain at potentials of less than pF 1.3, which lies within the domain primarily governed by soil structure that commonly yields over-prediction of the water content. A better prediction near saturation can be obtained by fitting a SWC equation to SWC data points. The concept behind Eq. (7) is depicted in Fig. 1, where the volumetric water content is expressed as a function of particle diameters based on Eq. (3). Fig. 1 conceptualizes and uses Eq. (7) to obtain three SWC data pairs, where CS, FS, and S are expected to be drained. The point where silt is expected to be drained is, however, outside the applicability of Eq. (7). To establish further SWC data points below pF 3, Eq. (7) was fitted to measured SWC and textural data to obtain the best possible fit by varying β-values between 0 and 1 from a dataset that encompasses different soil textures. 2.3 Obtaining a continuous soil-water characteristic curve

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The preceding section presented the first step of the proposed approach where matric potential and water content pairs were predicted based on dry bulk density, OM content, and mineral particle size fractions. Numerous empirical parametric models have been proposed in literature for the continuous SWC, with Brooks and Corey (1964) (BC) and van Genuchten (1980) (vG) being the most widely applied in soil science. The BC has problems for saturation degrees close to the airentry pressure, and in some instances, both the BC and the vG models have difficulties to represent the dry-end of the SWC (Fayer and Simmons, 1995). The BC and vG models were therefore modified and extended to the dry region by adopting a linear contribution of water adsorption (Fayer and Simmons, 1995). The modified BC and vG models are only applicable as long as the water content does not reach saturation, since the saturated water content is not included in the models, and the estimated saturated water content may significantly deviate from total porosity. The Campbell and Shiozawa (1992) model was similarly used in a three-step method to obtain the entire SWC by parameterizing the original vG-model and subsequently using the obtained vG-parameters to determine the matching point between the Campbell and Shiozawa (1992) and the vG-model (Webb, 2000). This method is very convenient if only vG-parameters are available. It is, however, a complicated method if measured SWC-data are available or predicted, since it requires several steps to obtain the curve. Fredlund and Xing (1994) presented a parametric SWC model (Eq. (8)), which is a modification of the vG model. The equation has three parameters and is applicable over the entire matric potential range:

θ = C (ψ )

C (ψ ) =

θs

[ln (e + (ψ / a ) )] n

m

ln (1 +ψ max /ψ r ) +1 ln (1 +ψ /ψ r )

(8)

(9)

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where ψ is the matric potential (kPa), θ s is the saturated volumetric water content (cm3 cm-3), ψ r is the matric potential corresponding to residual water content (kPa), ψ max is the matric potential at zero water content (kPa), and a, n and m are fitting parameters. The residual water content is assumed to be at the transition point where the water content decreases linearly with the logarithm of the absolute matric potential value (pF). According to Fredlund and Xing (1994) the matric potential at residual water content lies between -1500 and -3000 kPa, which approximately corresponds to what is known as the permanent wilting point for plants (-1500 kPa ~ pF 4.2). This model is applicable for sandy to clayey soils over the entire matric potential range (Fredlund and Xing, 1994). In this study, Eq. (8) is therefore used to obtain a continuous, smooth curve from saturation to oven-dryness, where ψ r = −1500 kPa. The model is hereafter denoted as FX-model. The parameter a is related to the air-entry value and n is related to the slope of the curve. The matric potential at zero water content was set to ψ max = −10 5.9 kPa, as stated earlier.

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3. Materials and Methods

Twenty one source soils from the University of Arizona Soil and Environmental Science Department, and eight soils from four different agricultural fields in Denmark, were used to demonstrate the applicability of the proposed two-stage SWC modeling approach. The clay mineralogy, determined by means of x-ray diffraction, of the 21 Arizona soils indicated mixed clay mineralogy (kaolinite, mica/illite, smectite, and/or vermiculite and chlorite and biotite), while the eight Danish soils consisted primarily of mica/illite and traces of smectite. The soils from Arizona were used for model testing and development, and the Danish soils were used for model validation. 3.1. Texture and organic matter Particle size distributions (Table 1) for the Arizona soils were determined with a combination of wet-sieving and pipette methods (Gee and Or, 2002). For the Danish soils the particle size distributions were measured with a combination of wet-sieving and hydrometer methods (Gee and Or, 2002). The organic carbon (OC) content was measured with an ELTRA Analyzer (Verder Scientific, Germany) coupled with an infrared CO2 detector. Prior to the analysis, the inorganic carbon was removed with hydrochloric acid (HCl). The organic matter content (Table 1) was estimated as OC/0.6 (Romano and Santini, 1997). The Arizona soils are denoted AZ, and the Danish soils L, A, S and J for Lerbjerg, Aarup, Saeby and Jyndevad, respectively. . 3.2. Soil water characteristic in the dry region Dry-region water retention data were determined with either a WP4-T Dewpoint Potentiameter or a Vapor Sorption Analyzer (VSA) (Decagon Devices Inc., Pullman WA). The WP4-T and the VSA measure the relative humidity (RH) in soil air that is considered to be in equilibrium with the soil water phase with a chilled-mirror dew point technique, and convert RH into matric potential with

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the well-known Kelvin equation assuming negligible osmotic potential. The Arizona soils were all measured with the WP4-T that is capable of measuring matric potentials between -1 MPa and -300 MPa (pF 4 to pF 6.5). To determine the gravimetric water content, the samples were oven-dried at 105˚C. Several weeks prior to the measurements, subsamples of the AZ soils were brought to different predetermined moisture levels and stored in a refrigerator at 4 oC to ensure equilibrium. The soils were all measured in triplicate at 25 ˚C. The VSA measures the potential between ~-10 and -450 MPa. Air-dried soil samples were used for the VSA measurements. For a detailed description of the VSA measurements readers are referred to (Arthur et al., 2014b; Arthur et al., 2014c) 3.3. Soil water characteristic in the wet region Several studies have shown that the porosity of the soil is intimately linked to texture (Cosby et al., 1984; Or et al., 2012). In Cosby et al. (1984), the saturated water content of a soil was found to be correlated with the sand content (R2=0.77) based on 1448 American soils. The equation for this correlation (θs= -0.126*Sand% + 48.9) was used to calculate a target dry bulk (packing) density for the AZ soils. The soils were air-dried, crushed, passed through a 2-mm sieve, and packed into 70 cm3 Tempe cells on top of a saturated, 1-bar ceramic plate. The Tempe cells (Soil moisture Equipment Corp., Santa Barbara, CA, USA) were connected to a pressure manifold with a high resolution pressure/vacuum regulator and a high-precision digital pressure/vacuum gauge. Samples were slowly saturated from the bottom using a constant head reservoir to minimize potential air entrapment. The saturated samples were sequentially drained at matric potentials corresponding to superatmospheric pressures of 0.5, 1.5, 3.0, 5.0, 10.0, 15.0, 50.0 and 80.0 kPa and the water content was determined after each drainage step after the samples reached equilibrium. For further details interested readers are referred to Tuller and Or (2004). Each soil was measured in triplicate at 25 ˚C.

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The Danish soils (except Jyndevad, which was undisturbed) were air-dried, crushed, sieved and packed into 100-cm3 cores. The SWC for all the Danish soils was measured using sandboxes controlled by water columns between 0 and -10 kPa, and with a pressure plate apparatus between -10 kPa and -100 kPa (Tuller and Or, 2004). The bulk density for all the Danish soils is also given in Table 1. The obtained saturated water content was not measured for the Danish soils and the soils were assumed fully saturated. The porosity was calculated using a particle density of 2.65 g cm-3. 3.4. Statistical Analysis

To evaluate the performance of the proposed models, the root mean square error (RMSE) and mean error (ME) (bias) were calculated as: RMSE =

ME =

1 n (θ p − θ m )2 ∑ n i =1

1 n ∑ (θ p − θ m ) n i =1

(10)

(11)

where θp and θm are predicted and measured water content, respectively, and n is the number of data points (number of soils multiplied with the number of pressure steps). Positive ME denotes model over-prediction and negative ME denotes model under-prediction.

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4. Results and Discussion

The measured SWC data for the Arizona soils is presented in Fig. 2 grouped by clay content, where Fig. 2a depicts soils with the lowest clay contents and Fig. 2d soils with the highest clay contents. No measurements were conducted between pF 3 and pF 4. In the wet region (below pF 3), the curves are non-linear, and above pF 4 the water contents follow a nearly linear slope (see Fig. 3a for magnification of the dry region), which confirms previous findings in Campbell and Shiozawa (1992). Fig. 3a shows the effects of clay content on water adsorption. Clay is, however, not the only contributor, as seen from Fig. 3a, where the soil with 23% clay (72% silt) has higher water content in the dry region than the soil with 27% clay (21% silt). Grouped by silt content, the water content at pF 6 was plotted against clay content for the AZ soils (Fig. 3b). This reveals potential prediction errors when the contributions of the silt fraction and the OM content to water adsorption are ignored. There was a strong correlation between the water content and clay content (R2=0.87), but the regression line divides the soils into two groups. Soils containing a larger amount of silt (> 20%) are mainly located above the line, whereas soils with lower silt contents (< 20%) all fall below the line. Additionally, the soil furthest away from the regression line contained 0.50 kg silt kg-1 soil and the largest amount of OM (0.067 kg kg-1), indicating a significant influence of OM on water adsorption. However, the high silt content suggests that OM cannot be considered as the sole reason for the discrepancy. In Fig. 4a, Eq. (1) is fitted to measured AZ soil data to obtain the highest R2 by changing the silt model parameter ‘B’ in steps of 0.05 up to 1. The parameter A was then changed stepwise to achieve the highest R2 between measured and predicted water content at pF 6. The best fit was determined for B ≈ 0.15 and A ≈ 0.08 (Fig. 4a), resulting in a stronger correlation (R2=0.95) between water content

and clay, silt, and sand (Fig. 4b). It is noteworthy that the consideration of silt may lead to over-

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prediction of the water content if the silt fraction primarily consists of large silt particles (20-50 µm). In Fig. 5, the wet region model (Eq. (7)) is tested by deriving β-values between 0 and 1 from the AZ soil data to obtain the best possible fit between measured and predicted data. The obtained β-values are listed in Table 2, where five β-values were chosen based on measured data. Eq. (7) performed considerably well with an average RMSE of 0.022 and ME of 0.003 over the entire wet region. No clear trend was observed with regard to any over- or under-prediction of water content across soil textures. Since the Arizona soils exhibited a wide range of different textures and were applicable for the wet-region model, we recommend using the obtained β-values given in Table 2 as general parameters to predict the wet region SWC for any soil. The high accuracy presented in Fig. 5 suggests that squaring the volume-size distribution including organic matter gives a good estimate for the pore-size distribution of the soil matrix. To obtain the continuous SWC we recommend parameterizing the FX model (Eq. (8)) based on the reference points predicted by the wet- and dry-region models (Eqs. (1-2) and (7)). The wet-region model predicts five SWC reference points (pF 1.7, 2, 2.2, 2.7 and 3). Between pF 3 and pF 5 the SWC transitions from the capillarity dominated to the adsorption dominated region, with capillarity becoming negligible at pF 5 (Tuller and Or, 2005). Hence, we recommend to only consider reference points obtained from the dry region between oven-dryness and pF 5 as input for the FX model. We used five reference points in the dry region, namely 20%, 50%, 70%, 80% and 90% RH (at pF 6.3, 6.0, 5.7, 5,5 and 5.2, respectively), giving a total of 10 reference points. This concept of predicting the continuous SWC from saturation to oven-dryness is presented in Fig. 6a for soil AZ 20, where the measured and predicted SWC data are depicted together with the FX model. Experimental SWC data for four of the AZ soils with clay contents ranging from 0.02 to 0.50 kg kg-1, and the corresponding SWC predicted based on the FX model combining the wet- and 18

dry-region models, is shown in Fig. 6b. As evidenced in Fig. 6b, the FX model proved applicable for the entire soil textural range using the predicted data points. It is therefore recommended to use the obtained SWC based on the FX model fitted to the predicted reference data points to obtain a continuous and smooth SWC. A continuous SWC function is required for all numerical modeling tasks aimed at estimating moisture dynamics and flow processes in soils. The SWC curve, for instance, may be used to determine the unsaturated hydraulic conductivity as shown in Fredlund et al. (1994), who used a function to predict the unsaturated permeability from the SWC curve from Fredlund and Xing (1994). Hence, we recommend applying a combination of Eqs. (1-2), (7) and (8) to obtain the SWC curve, which is hereafter, denoted the ‘New Two-Stage Approach’. 4.1. Test of the proposed New Two-Stage Approach The New Two-Stage Approach was tested for eight Danish soils with clay contents ranging from 0.05 to 0.41 kg kg-1. The model performance for the SWC is presented in Fig. 7a and in Fig. 7b for the dry and wet regions, respectively. The eight soils were separated by sampling location instead of texture, since no tendency for prediction discrepancy was observed due to the content of fines. For the wet region, there was a tendency for the water contents of the Aarup and Saeby soils to be overpredicted, as observed from Fig. 7b. This could be an indication of different clay mineralogy and organic matter quality. Similarly, Fig. 7a supports the theory that the difference in clay and OM quality could be the cause of over-prediction by inducing change in water capacity, since the model generally over-predicted for both Aarup soils and for one of the Saeby soils in the dry region. Additionally, soil S5 had a relatively high silt content (33%), which may also be the reason for the over-prediction since the silt particles can be coarse silt (20-50 µm) and therefore have a low specific surface area. The contribution of silt was not further analyzed in this study, but a minor tendency to over-predict can generally be observed when estimating the water content for the dry region. It is therefore recommended to further analyze the contribution of each of the fines fractions

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using larger datasets. The general performance accuracy of the New Two-Stage Approach is very reasonable with a RMSE of 0.04 for the wet region and 0.01 for the dry region. The New TwoStage Approach performed equally well for the undisturbed Jyndevad soil as for the disturbed soils. However, the input parameters for the wet region model do not account for structural effects due to aggregation or formation of worm and root channels. Thus, prediction of the water content and matric potential close to saturation may be prone to some uncertainty. Because only one of the investigated soils (S1) exhibited a porosity above 0.5 the wet region model should be used with caution for high porosity soils. Fig. 8a presents the stepwise method for obtaining the entire SWC for the A2 soil, where the FX model is fitted to the predicted SWC reference points from the wet and dry regions, similarly to Fig. 6a. The predicted SWCs for four of the Danish soils with different clay contents (0.05, 0.11, 0.22, 0.37 kg kg-1) are compared to measured data in Fig. 8b. The optimized FX model parameters for measured as well as predicted data points based on Eqs. (1-2) and (7) are presented in Table 3. As argued above, the New Two-Stage Approach performed considerably well for the entire matric potential range and across different soil textures. 4.2. Model limitations To begin with, water adsorption on solid surfaces is clearly affected by the amount of clay and OM. On the other hand, the contribution of the silt fraction to water adsorption in the dry region is highly dependent on whether it is coarse (20–50 µm) or fine silt (2-20 µm). The impact of the different silt fractions on water adsorption was not investigated and could be a potential source of prediction error for the dry region. However, as this research clearly shows, the influence of silt on water adsorption cannot be neglected. The effect of different clay mineralogy on the water retention was not analyzed in this study, but the AZ soils used for model development exhibit mixed mineralogy (kaolinite, 20

mica/illite, smectite, vermiculite and chlorite and biotite) with traces of carbonates, amphiboles and hydroxides, which suggests that the model can be used for soils with different types of clay minerals. The applicability of the model for soils dominated by one type of clay (e.g. 1:1 kaolinite, or 2:1 expandable clays) was not evaluated and provides an avenue for further research. Furthermore, the relative squared volume fraction was used to estimate the volumetric pore-size fraction (Eq. (6)). This squared function is likely dependent on soil structure (i.e. void ratio and bulk density). Therefore, the applicability of the model for highly structured soil is likely to be limited, particularly close to saturation. The model was not evaluated for matric potentials lower than pF 1.7, but the predictions are likely less accurate for undisturbed soils due to the effect of soil structure as discussed above. The New Two-Stage Approach was developed and evaluated for soils exhibiting a wide range of textures (1-52% clay) and OM contents (0-7%), but since peat soils or soils with high amounts of expansive clays were not considered, the model should be used with caution. The same holds for soils with pronounced hysteretic water retention behavior. 5. Conclusions

The objective of the presented study was to develop and evaluate a novel two-stage approach to predict the soil water characteristic across the entire matric potential range from saturation to ovendryness to be applicable to all soil textural classes. The proposed new approach combines a dry and a wet region model to obtain 10 data points from particle volume fractions and OM content that are subsequently applied to parameterize the SWC model proposed by Fredlund and Xing (1994). The dry- and wet-region expressions convert a limited number of measured textural data, together with organic matter and bulk density, into volumetric water content, and the respective adsorptive and capillary forces. Based on evaluating the approach for 29 soils from Arizona and Denmark, the

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model performed reasonably well over the entire matric potential range. From the results it is also evident that not only clay and organic matter affect water adsorption, but also silt content plays a vital role. The findings suggest that silt may be a potential source for prediction inaccuracy due to the wide broad silt fraction (2 µm - 50 µm) of the soils considered for this study. Research on structured soils and on the impact of silt content on water adsorption is ongoing. Acknowledgements

The authors gratefully acknowledge the technical assistance provided by M. Koppelgaard and M. S. Meding. The study was supported by the international project Soil Infrastructure, Interfaces, and Translocation Processes in Inner Space (Soil-it-is) funded by the Danish Research Council for Technology and Production Sciences (http://www.agrsci.dk/soil-it-is/) and by the Danish Pesticide Leaching Assessment Programme (http://www.pesticidvarsling.dk).

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Resurreccion, A.C., Moldrup, P., Tuller, M., Ferre, T.P.A., Kawamoto, K., Komatsu, T., De Jonge, L.W., 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: W06522. Romano, N., Santini, A., 1997. Effectiveness of using pedo-transfer functions to quantify the spatial variability of soil water retention characteristics. J Hydrol, 202(1): 137-157. Sakaki, T., Komatsu, M., Takahashi, M., 2014. Rules-of-Thumb for Predicting Air-Entry Value of Disturbed Sands from Particle Size. Soil Sci. Soc. Am. J., 78(2): 454-464. Schneider, M., Goss, K.U., 2012a. Prediction of the water sorption isotherm in air dry soils. Geoderma, 170: 64-69. Schneider, M., Goss, K.U., 2012b. Prediction of water retention curves for dry soils from an established pedotransfer function: Evaluation of the Webb model. Water Resour Res, 48. Tuller, M., Or, D., 2004. Water retention and characteristic curve. . In: Hillel, D. (Ed.), Encyclopedia of Soils in the Environment, vol. 4. Elsevier Ltd., Oxford: 278–289. Tuller, M., Or, D., 2005. Water films and scaling of soil characteristic curves at low water contents. Water Resour Res, 41(9): 10.1029/2005wr004142. Tuller, M., Or, D., Dudley, L.M., 1999. Adsorption and capillary condensation in porous media: Liquid retention and interfacial configurations in angular pores. Water Resour Res, 35(7): 1949-1964. van Genuchten, M.T., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J, 44(5): 892-898. Webb, S.W., 2000. A simple extension of two-phase characteristic curves to include the dry region. Water Resour Res, 36(6): 1425-1430.

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Wuddivira, M.N., Robinson, D.A., Lebron, I., Brechet, L., Atwell, M., De Caires, S., Oatham, M., Jones, S.B., Abdu, H., Verma, A.K., Tuller, M., 2012. Estimation of soil clay content from hygroscopic water content measurements. Soil Sci Soc Am J, 76(5): 1529-1535. Wäldchen, J., Schoning, I., Mund, M., Schrumpf, M., Bock, S., Herold, N., Totsche, K.U., Schulze, E.D., 2012. Estimation of clay content from easily measurable water content of air-dried soil. J Plant Nutr Soil Sc, 175(3): 367-376.

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Figure Captions Figure 1. Sketch depicting the proposed concept for converting volumetric particle size fractions to SWC data pairs by calculating the volume and diameters of the pores generated by each fraction (Eqs. (3) and (7)). DCS, DFS , and DS, are the smallest particle diameters of coarse sand (500 µm), fine sand (50 µm) and silt (2 µm), respectively. Figure 2. Measured soil water characteristic data for investigated Arizona soils grouped by clay content. Percentage in bracket is clay content. Figure 3. (a) Measured dry-region soil water characteristic data for selected Arizona soils exhibiting a linear relationship between the water content and pF in the dry region. Percentage in bracket is clay content. (b) Water content at pF 6 (dotted line from Fig. 3a) as a function of clay content for the Arizona soils grouped by silt content. The soil with the greatest deviation from the regression line exhibits high OM (0.07 kg kg-1 ) and silt contents (0.50 kg kg-1). Figure 4. (a) Coefficient of determination (R2) and parameter A plotted as a function of parameter B (Eq. (1)). The ‘B’ parameter is varied in steps of 0.05 between 0-1, and the A value is varied accordingly to obtain the highest R2 for each step. (b) Relation between water content at pF 6 as a function of the best fit of measured data for the Arizona soils to Eq. (1). Figure 5. Comparison of measured and predicted water contents based on the wet region model for the Arizona soils. Figure 6. (a) Proposed SWC modeling concept. The dry- and wet-region models (Eq. (1-2) and Eq. (7)) are used to predict reference points, and the FX model (Eq. (8)) is parameterized to obtain the continuous curve based on the predicted reference points for soil AZ20. (b) Measured and predicted soil water characteristic for four AZ soils with different clay contents. The FX model is fitted to predicted SWC data points as illustrated in Fig. 6a (the predicted data points are not shown in Fig. 6b, where only the measured points are presented). Percentage in bracket is clay content.

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Figure 7. Comparison of measured and predicted water contents based on the New Two-Stage Approach. (a) Comparison for matric potentials of pF 5 and pF 6, respectively. (b) Comparison for matric potentials of pF 2, pF 2.7, and pF 3. Figure 8. (a) Concept of the New Two-Stage Approach, where the FX model (Eq. (8)) is fitted to single SWC points predicted with the dry- and wet-region models (Equations (1-2) and (7)) for soil A2. (b) Predicted soil-water characteristic curves from saturation to oven-dryness for four of the Danish soils, applying the New Two-Stage Approach. J1, L1, L3 and L5 are measured data points. Percentage in bracket is clay content.

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Table 1. Properties of the soils considered in this study Soil ID

Bulk density

Organic matter

Clay

g cm-3

Silt

Fine sand

Coarse sand

kg kg −1

AZ1 AZ2 AZ3 AZ4 AZ5 AZ6 AZ7 AZ8 AZ9 AZ10 AZ11 AZ12 AZ13 AZ14 AZ15 AZ16 AZ17 AZ18 AZ19 AZ20 AZ21 L1

1.65 1.64 1.59 1.58 1.61 1.60 1.56 1.50 1.51 1.39 1.40 1.51 1.57 1.49 1.48 1.40 1.40 1.40 1.43 1.51 1.57 1.45

0.00 0.000 0.015 0.009 0.008 0.009 0.008 0.008 0.026 0.067 0.013 0.011 0.005 0.004 0.007 0.013 0.018 0.019 0.015 0.008 0.009 0.024

0.024 0.006 0.052 0.087 0.054 0.084 0.137 0.093 0.205 0.230 0.165 0.211 0.194 0.264 0.268 0.227 0.287 0.496 0.514 0.300 0.093 0.114

0.069 0.031 0.137 0.174 0.141 0.243 0.155 0.318 0.254 0.498 0.453 0.397 0.144 0.154 0.214 0.724 0.444 0.395 0.184 0.206 0.197 0.090

0.350 0.962 0.447 0.446 0.792 0.597 0.478 0.505 0.404 0.205 0.356 0.340 0.483 0.344 0.372 0.036 0.231 0.091 0.208 0.281 0.416 0.663

0.557 0.001 0.349 0.282 0.006 0.066 0.220 0.074 0.111 0.000 0.010 0.041 0.173 0.234 0.139 0.000 0.020 0.000 0.057 0.203 0.285 0.109

L3 L5 A2 A9

1.46 1.43 1.40 1.36

0.027 0.030 0.021 0.034

0.224 0.373 0.111 0.223

0.098 0.129 0.180 0.375

0.524 0.384 0.443 0.266

0.126 0.084 0.244 0.103

S1 S5 J1

1.27 1.45 1.53

0.029 0.014 0.033

0.114 0.411 0.046

0.294 0.329 0.044

0.493 0.207 0.653

0.071 0.039 0.224

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Table 2: Input parameters for Eq. (7). The β-values were optimized to obtain the best fit between measured and predicted soil water characteristic data. pF

β1

β2

α

1.7

0.3

0

VCS+VFS

2

0.6

0

VCS+VFS

2.2

0.9

0

VCS+VFS

2.7

1

0.2

VCS+VFS+ VFS

3

1

0.4

VCS+VFS+ VFS

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Table 3: Fredlund and Xing (1994) model parameters for measured and predicted data points. Soil ID AZ1 AZ2 AZ3 AZ4 AZ5 AZ6 AZ7 AZ8 AZ9 AZ10 AZ11 AZ12 AZ13 AZ14 AZ15 AZ16 AZ17 AZ18 AZ19 AZ20 AZ21 L1 L3 L5 A2 A9 S1 S5 J1

Measured a n 2.34 1.24 8.92 4.57 0.92 2.63 1.40 4.61 3.62 5.08 2.67 10.27 2.20 4.03 1.30 10.30 1.30 10.69 2.04 29.18 2.00 15.59 2.95 17.18 1.93 4.69 1.15 4.26 1.92 5.65 1.98 34.51 1.42 18.08 1.44 36.97 0.82 7.71 1.18 8.09 0.91 4.17 1.50 5.83 0.78 7.16 0.97 33.25 1.25 5.37 1.07 12.90 1.93 8.78 1.39 23.52 1.96 0.61

m 0.96 0.71 1.11 0.87 0.62 0.59 0.56 0.88 0.60 0.36 0.61 0.40 0.49 0.53 0.42 0.43 0.54 0.34 0.41 0.46 1.06 0.88 0.87 0.56 1.01 0.87 0.74 0.61 1.36

Predicted a n 1.10 1.86 1.79 11.58 0.99 3.10 1.13 3.49 2.08 5.74 1.44 6.91 1.33 3.31 1.27 9.77 0.90 10.29 1.18 69.47 1.30 22.54 1.30 16.15 1.53 3.24 0.94 2.79 0.99 5.93 1.74 63.15 1.25 32.80 1.43 62.67 0.73 31.28 0.84 5.03 1.06 3.86 3.91 1.61 4.44 0.79 20.23 0.57 5.00 0.85 28.75 0.93 13.80 0.97 43.87 0.99 2.81 1.99

m 1.61 4.00 1.15 0.90 0.89 0.85 0.68 0.89 0.71 0.75 0.73 0.57 0.50 0.52 0.53 0.58 0.54 0.28 0.35 0.49 0.91 0.69 0.72 0.72 1.00 0.78 1.01 0.52 0.71

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Research Highlights •

We present a new approach to predict the entire SWC using limited data

•

The approach considers capillarity and adsorptive contributions to obtain the SWC

•

We obtained accurate prediction of SWC regardless of soil texture

•

Clay, silt and organic matter contribute significantly to water adsorption

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