Prediction of water retention curves for dry soils from an established pedotransfer function: Evaluation of the Webb model

Transcription

1 WATER RESOURCES RESEARCH, VOL. 48, W06603, doi: /2011wr011049, 2012 Prediction of water retention curves for dry soils from an established pedotransfer function: Evaluation of the Webb model M. Schneider 1 and K.-U. Goss 1,2 Received 17 June 2011; revised 27 April 2012; accepted 29 April 2012; published 12 June [1] The van Genuchten curve, and its prediction by various pedotransfer functions, has long been an established method to describe the water retention curve (WRC) in soils, but it cannot be used to describe water retention under conditions dryer then the wilting point. Water retention under dry conditions follows a log linear function, which does not agree with the extrapolated van Genuchten curve. As a remedy Webb (2000) proposed an approach that predicts this linear function for the dry range with a smooth transition to the van Genuchten curve that has been fitted to experimental data for the moist range. In this work we present the prediction of water retention curves for 31 soils under dry conditions using the approach presented by Webb. In addition to the larger number of soils that we use for evaluation we deviate from the original Webb approach in two ways: (a) we use predicted (Rosetta) rather than fitted van Genuchten curves and (b) we use a corrected endpoint at zero water content. The outcome reveals good results for the prediction of water retention curves for the dry region and provides a smooth transition between the moist and the dry region of the water retention curve. Occasional inferior performance for some data is likely due to uncertainties in the texture data or in the choice of the right bulk density rather than due to conceptual shortcomings of the Webb approach. This work shows that the WRC for the whole humidity range, from oven dryness to full saturation, can be described by two functions with a smooth transition whose parameters can all be predicted by Rosetta without the need of experimental information. Citation: Schneider, M., and K.-U. Goss (2012), Prediction of water retention curves for dry soils from an established pedotransfer function: Evaluation of the Webb model, Water Resour. Res., 48, W06603, doi: /2011wr Introduction [2] Water retention curves (WRCs) provide the water potential as a function of the water content in the soil. They describe the water holding capacity and are essential for modeling the water flow in the vadose zone. For dry conditions though neither the WRCs of soils nor their hydraulic functions are well established yet [Tuller and Or, 2001; Lebeau and Konrad, 2010; Zhang, 2011]. Under dry conditions the WRC is also needed to predict the sorption of organic vapors to the mineral surfaces in the soil [Goss, 2004; Garcia, 2010]. [3] To describe the water retention curve under dry conditions (log 10 ð ½cmŠÞ > 4:2) Campbell and Shiozawa [1992] proposed a linear relationship between the logarithm of the water potential and the degree of water saturation. This log linear function can be predicted from the clay fraction of the soil [Campbell et al., 1993; Resurreccion et al., 2011; Schneider and Goss, 2012]. Under moist conditions 1 Helmholtz Centre for Environmental Research, Leipzig, Germany. 2 Institute of Chemistry, University of Halle Wittenberg, Halle, Germany. Corresponding author: M. Schneider, Helmholtz Centre for Environmental Research, Permoserstraße 15, D-04318, Leipzig, Germany. (martina. schneider@ufz.de) American Geophysical Union. All Rights Reserved /12/2011WR (log 10 ð ½cmŠÞ < 4:2) water retention is typically described by the van Genuchten curve [van Genuchten, 1980]. For modeling purposes it is highly desirable to describe the WRC for the complete moisture regime with a function that exhibits a smooth transition between the dry and the moist region, i.e., the two different functions for the dry and moist regions should have the same first derivative at the connecting point. [4] Different models have been presented that connect the established WRC models for the humid region with the log linear description under dry conditions proposed by Campbell and Shiozawa [1992] [e.g., Rossi and Nimmo, 1994; Fayer and Simmons, 1995; Khlosi et al., 2006; Webb, 2000]. These models are designed to show a smooth transition between the dry and the moist region. But there are only few experimental data sets for the dry range on which these approaches were evaluated. Khlosi et al. [2008] have used data sets for 137 soils to test eight different models that predict the WRC from oven dryness to water saturation with a single function. However the presented results do not reveal the specific performance on the dry range of the WRC and it is not clear how many experimental data sets for dry conditions have been used in this evaluation. Lu et al. [2008] tested the Fayer and Simmons [1995], Khlosi et al. [2006], and the Webb [2000] model on a data set of eight soils containing measurements for the whole humidity range and documented good results for all models with the Webb model being slightly superior. W of5

2 [5] All these literature works have in common that they are based on fitting some existing data of the WRC in order to then predict the WRC on the whole humidity range. Here we are interested in evaluating a method that does not require any experimental data for calibration but that is simply based on an existing, well established pedotransfer function for the moist range of the WRC in combination with a fixed endpoint of the dry end of the WRC. [6] The approach we use here is based on the work of Webb [2000]. Webb extends the WRC from the moist range to the dry range as a continuous transition without the need for fitting any experimental data. This approach can be applied to the van Genuchten model as well as to the Brooks- Corey equation. The idea behind the Webb approach is to define a so called matching point that connects the van Genuchten [1980] or Brooks and Corey [1966] function with the log linear function of the dry range that has been proposed by Campbell and Shiozawa [1992]. The matching point is chosen such that its tangent goes directly through the endpoint log 10 ð Þ wc¼0 at zero water content at the dry end of the WRC. The matching point based on the van Genuchten curve can be calculated by the following equation [Webb, 2000]: 1 log 10 ð Þ wc¼0 ¼ log 10 ðs 1=m le 1Þ 1=n Sl 1 1 þ log 10 ðeþ Sl S lr nm 1 S 1=m le ; (1) S le ¼ ðs l S lr Þ ðs ls S lr Þ ; (2) where log 10 ð Þ wc¼0 is the water potential at a water content zero, S lr is the liquid residual saturation, S ls is the liquid saturation, and m and n are the van Genuchten parameters. The liquid saturation at the matching point Sl can be calculated by a few iteration steps. Thus the tangent (first derivative of the van Genuchten curve) at the matching point represents the Campbell function for the dry part of the WRC and at the same time provides a smooth transition to the van Genuchten or the Brooks-Corey function. With this approach Webb [2000] was able to fit data from saturation to oven dryness for six soils measured by Campbell and Shiozawa [1992]. Lu et al. [2008] confirmed this approach with water retention data for eight other soils. In both cases, Webb [2000] and Lu et al. [2008] used a van Genuchten model that had been fitted to existing experimental data from the WRC in the moist range. However, it should also be possible to predict the van Genuchten curve from existing pedotransfer functions and then use the Webb approach to further predict the dry part of the WRC. Thus the WRC for the complete humidity range would be estimated from texture data. This is what we want to evaluate here, based on a data set for the dry region that is larger (additional 18 soils) and more diverse than what has previously been used for evaluating the original Webb approach. [7] Like others [Ross et al., 1991, Campbell and Shiozawa, 1992], Webb [2000] used an endpoint of log 10 ð ½cmŠÞ wc¼0 ¼ 7:0 at zero water content for his approach. He points out that every optional endpoint can be used according to the experimental conditions. We have shown in previous work that an endpoint of log 10 ð ½cmŠÞ wc¼0 ¼ 7:0 is not realistic because it corresponds to a relative humidity of 9% at 20 C in the lab in which the soil is oven dried. We presented a revised endpoint of log 10 ð ½cmŠÞ wc¼0 ¼ 6:8 (average corresponding to 30% to 70% RH at 20 C) that can be derived theoretically from the Kelvin equation [Or and Wraight, 2000] and that was further supported by our experimental data [Schneider and Goss, 2012]. 2. Materials and Method [8] Water retention data for the dry region (log 10 ð ½cmŠÞ > 4:2) from the following sources were used: data from Campbell and Shiozawa [1992] measured with a water activity meter, Lu et al. [2008] using a dew point potential meter, and Schneider and Goss [2012] using a relative humidity sensor. Sokolowska et al. [2002] measured the water vapor adsorption data using a vacuum microbalance technique. In general measurements of the water retention data in the dry region are done using disturbed soil. All measurements were performed at room temperature. Note that, if needed, a temperature correction should be done separately for the moist and the dry region because the temperature dependence is caused by different mechanisms [Schneider and Goss, 2011]. [9] The program Rosetta, version 1.2 [Schaap et al., 2001] was downloaded from the US Salinity Laboratory webpage and used to predict the van Genuchten parameters from the texture data (Rosetta model SSC). [10] In dry soils the WRC is actually expected to be independent from the pore structure because the water is retained only by adsorption to the mineral surfaces and not by the pore filling/draining processes. Therefore, the WRC in the dry range should be independent of the actual bulk density during the experiment. However, in order to transform the gravimetric water content (typically reported for the dry part of the WRC) into the volumetric water content (typically reported for the humid region) a value for the bulk density had to be chosen. The bulk density was not known for most of our soils. Therefore we estimated the bulk density bd from the saturated water content S given by Rosetta and a particle density pd of 2.65 g cm 3 (compare soil bulk density calculator on pedosphere.com based on Saxton et al. [1986]): bd ¼ð1 s Þ pd : (3) [11] Note that the saturated water content value is typically lower than the porosity (mainly because of entrapped air). This can result in an overestimation of the bulk density. In addition, the bulk density in undisturbed, natural soils can depend also on the organic content, the age of the soil, and, of course, anthropogenic influences. These influences can have a strong impact on the water retention curve under humid conditions but are not considered by the program. 3. Results and Discussion [12] Table S1 (Supplemental Material) lists the achieved root mean square errors (rmse) for the prediction of the dry region of the WRC plotted in a log linear diagram. 1 A graphical illustration of the results for the 18 soils measured 1 Auxiliary materials are available in the HTML. doi: / 2011WR of5

3 Figure 1. Predicted van Genuchten curve by Rosetta, measured WRC data within the dry region, and our prediction of the log linear function using the Webb model for the soils measured by Schneider and Goss [2012]. 3of5

4 Figure 1. by Schneider and Goss [2012] is given in Figure 1. The graphs depict a good agreement of the prediction with the experimental data for most of the soils. In fact, the results presented here are almost as good as a pedotransfer function that had been calibrated on just these experimental data for predicting the log linear function under dry conditions only, and not the complete WRC [Schneider and Goss, 2012]. For soils with low clay content (Kreinitz and RV 6) the approach presented here provides even better predictions. [13] Note that we found the results to be quite sensitive to the bulk densities that were used (see Figure 4 in Supplemental Material). Simply working with an average value of 1.35 g cm 3 for the bulk density of all soils gives results that are inferior to those presented here with bulk densities predicted from the texture. The consideration of the uncertainty intervals for the soil hydraulic parameters predicted by Rosetta did only show a neglectable influence on the final results. The prediction of the WRC for the soils measured by Campbell and Shiozawa [1992] and Lu et al. [2008] are presented and discussed within the supporting information. Overall they did not give as good results but were still within an acceptable range. It is remarkable that for most of the soils (except soils with very low clay content, e.g., Kreinitz and L-soil) the water content at the matching point is very close to the predicted water content at pf 4.2 received from the predicted van Genuchten curve. [14] Schneider and Goss [2012] showed that soils containing mostly kaolinite as the dominant clay mineral cannot be described well by the log linear function proposed by Campbell and Shiozawa [1992]. Therefore in these cases the Webb approach cannot be applied either. (continued) 4. Conclusion [15] For water contents above log 10 ð ½cmŠÞ ¼ 4:2 the van Genuchten approach and its prediction by various pedotransfer functions has long been established. Water adsorption at water contents below the log 10 ð ½cmŠÞ ¼ 4:2 is best described by a log linear relationship as first proposed by Campbell and Shiozawa [1992]. Here we demonstrate that the Webb approach based on predicted van Genuchten parameters (Rosetta) and based on a revised endpoint at the dry end of the WRC works quite well for predicting the linear function of the WRC in the dry region. We assume that the occasionally inferior performance for the data by Campbell and Shiozawa [1992] and Lu et al. [2008] is more likely due to uncertainties in the texture data rather than due to conceptual shortcomings. Lu et al. [2008] and Webb [2000] obtained a very good prediction of the dry WRC for eight soils when the van Genuchten parameters were derived from the experimental data rather than estimated from Rosetta. Therefore if the bulk density or additional data of the WRC within the moist region are known, they should be included into the prediction of the van Genuchten parameters to improve the results. But still the prediction from texture data alone works quiet well. [16] The Webb approach [Webb, 2000] has the advantage of yielding a steady function with a continuous first derivative for the whole WRC. The matching point works as a flexible intersection point with the van Genuchten curve which can be derived from the required gradient of the log linear function. This feature makes the approach first choice for any water transport models. If only the water retention curve for the dry region needs to be known, 4of5

5 without a connection to the humid part of the WRC, then the simpler approach of using a specific PTF based on the clay content might be more convenient [Ressureccion, 2011; Schneider and Goss, 2012]. [17] Acknowledgments. This work was kindly supported by Helmholtz Impulse and Networking Fund through Helmholtz Interdisciplinary Graduate School for Environmental Research (HIGRADE). Special thanks to Trevor Brown for a careful review of the manuscript. References Brooks, R. H., and A. T. Corey (1966), Properties of porous media affecting fluid flow, J. Irrig. Drain. Eng., 92, Campbell, G. S., and S. Shiozawa (1992), Prediction of hydraulic properties of soils using particle-size distribution and bulk density data, paper presented at International Workshop on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils, Univ. of Calif., Riverside. Campbell, G. S., J. D. Jungbauer, S. Shiozawa, and R. D. Hungerford (1993), A one-parameter equation for water sorption isotherms of soils, Soil Sci., 156, Fayer, M. J., and C. S. Simmons (1995), Modified soil water retention function for all matric suctions, Water Resour. Res., 31(5), Garcia, L. (2010), Volatilisation de l ammoniac et des pesticides au champ Analyse et modélisation de l influence des propriétés et des conditions physiques de la surface à l aide du modèle Volt Air, Ph.D. thesis, p. 26, Pierre and Marie Curie Univ., Paris, France. Goss, K.-U. (2004), The air/surface adsorption equilibrium of organic compounds under ambient conditions, Crit. Rev. Environ. Sci. Technol., 34, , doi: / Khlosi, M., M. W. Cornelis, D. Gabriels, and S. Sin (2006), Simple modification to describe the soil water retention curve between saturation and oven dryness, Water Resour. Res., 47, W06522, doi: /2010wr Khlosi, M., M. W. Cornelis, A. Douaik, M. Th. van Genuchten, and D. Gabriels (2008), Performance evaluation of models that describe the soil water retention curve between saturation and oven dryness, Vadose Zone J., 7, 87 96, doi: /vzj Lebeau, M., and J.-M. Konrad (2010), A new capillary and thin film flow model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 46, W12554, doi: /2010wr Lu, S., T. Ren, Y. Gong, and R. Horton (2008), Evaluation of three models that describe soil water retention curves from saturation to oven dryness, Soil Sci. Soc. Am. J., 72, , doi: /sssaj n. Or, D., and M. Wraight (2000), Soil water content and water potential relationship, in Handbook of Soil Science, edited by M. E. Summer, pp , CRC Press, Boca Raton, FL. Resurreccion, A. C., P. Moldrup, M. Tuller, T. P. A. Ferr, 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, W06522, doi: /2010wr Ross, P. J., J. Williams, and K. L. Bristow (1991), Equation for extending water-retention curves to dryness, Soil Sci. Soc. Am. J., 55, Rossi, C., and J. R. Nimmo (1994), Modeling of soil-water retention from saturation to oven dryness, Water Resour. Res., 30, Saxton, K. E., W. J. Rawls, J. S. Romberger, and R. I. Papendick (1986), Estimating generalized soil-water characteristics from texture, Soil Sci. Soc. Am. J., 50, Schaap, M. G., F. J. Leij, and M. T. van Genuchten (2001), ROSETTA: A computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions, J. Hydrol., 251, Schneider, M., and K.-U. Goss (2011), Temperature dependence of the water retention curve for dry soils, Water Resour. Res., 47, W03506, doi: /2010wr Schneider, M., and K.-U. Goss (2012), Prediction of the water adsorption isotherm in air dry soils, Geoderma, 170, 64 69, doi: /j.geoderma Sokolowska, Z., M. Borowko, J. Reszko-Zygmunt, and S. Sokolowski (2002), Adsorption of nitrogen and water vapor by alluvial soils, Geoderma, 107, Tuller, M., and D. Or (2001), Hydraulic conductivity of variably saturated porous media: Film and corner flow in angular pore space, Water Res. Res., 37(5), van Genuchten, M. Th. (1980), A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, Webb, S. W. D. (2000), A simple extension of two-phase characteristic curves to include the dry region, Water Resour. Res., 36(6), , doi: /2000wr Zhang, F. Z. (2011), Soil water retention and relative permeability for conditions from oven-dry to full saturation, Vadose Zone J., 10, , doi: /vzj of5