Prediction of the water sorption isotherm in air dry soils

Prediction of the water sorption isotherm in air dry soils

Geoderma 170 (2012) 64–69 Contents lists available at SciVerse ScienceDirect Geoderma journal homepage: Prediction...

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Geoderma 170 (2012) 64–69

Contents lists available at SciVerse ScienceDirect

Geoderma journal homepage:

Prediction of the water sorption isotherm in air dry soils Martina Schneider a,⁎, Kai-Uwe Goss a, b,⁎ a b

Helmholtz Centre for Environmental Research, Permoserstraße 15, D-04318 Leipzig, Germany Institute of Chemistry, University of Halle Wittenberg, Kurt Mothes Straße 2, D-06120, Halle, Germany

a r t i c l e

i n f o

Article history: Received 3 March 2011 Received in revised form 26 September 2011 Accepted 10 October 2011 Available online 24 December 2011

a b s t r a c t Within this work we present a revised pedotransfer function (PTF) that predicts water sorption isotherms for dry soils based on the clay content of the soils. When the water sorption isotherm is plotted as a water retention curve (log water potential plotted against the water content) it typically results in a log linear function as described by Campbell and Shiozawa (1992). The linear function is defined by its slope and a fixed endpoint at zero water content. The reciprocal of the slope shows a strong correlation with the clay fraction. For the calibration of a PTF we measured water sorption data for 18 soils with clay contents from 2% to 61%. The final predictions of the water sorption isotherms from the clay mass fraction were very good if the clay content was higher than 7%. The use of a revised theoretical endpoint at the dry end of the WRC did improve the prediction as compared to the endpoint that has been used in the literature before. In addition Literature data for 22 soils and 3 pure clay minerals were used for validation. The good performance of the PTF only occurred if the clay fraction was dominated by 2:1 clay minerals. The water retention isotherm of soils rich in the 1:1 clay mineral kaolinite could not be predicted by this approach; the actual water content was strongly overpredicted and the water retention curve did not follow a log linear relationship. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The water sorption isotherm presents the water content of the soil plotted against the equilibrium relative humidity in the pore space. Knowledge of this water sorption isotherm is essential for various tasks like predicting the sorption of organic vapors to mineral surfaces or for a better understanding of the water balance in dry soils. In dry soils (here defined as having a water content below the permanent wilting point PWP) most pores are drained (Tuller and Or, 2005) but all mineral surfaces are still covered with several layers of water molecules due to the ability of mineral surfaces to form strong hydrogen bonds with water. Water sorption isotherms are equivalent to the water retention curves (WRC) that display the soil water content as a function of the log water potential, log(− Ψ). The water potential, Ψ in cm water column, is a measure of water activity in the soil and directly related to the relative humidity rh (water activity) in the surrounding air, if equilibrium is achieved. This relationship is given by the Kelvin equation (Or and Wraight, 2000). Ψ¼

rh R·T·ln 100 M H2O ·g


⁎ Corresponding authors: Tel.: + 49 3412351411. E-mail addresses: [email protected] (M. Schneider), [email protected] (K.-U. Goss). 0016-7061/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.geoderma.2011.10.008

where R is the universal gas constant, T is the temperature in K, ρH2O is the density of water, MH2O is the molecular mass of water, g is the constant of gravity, and rh is relative humidity in %. Several empirical functions for the water retention curve (WRC) have been developed for soils that have a lower water potential then the permanent wilting point (PWP) of log(− Ψ[cm]) = 4.2 (equivalent to 98.9% relative humidity in the pore space). One of the most common models for humid conditions is the van Genuchten approach (van Genuchten, 1980). This approach assumes that for water contents below the PWP the water potential decreases to minus infinity while the water content tends towards the so-called residual water content, θR, which is a fitting parameter. Cornelis et al. (2005) give a good overview about the different definitions of θR. However, from a physical point of view it makes no sense to define a dry endpoint of the WRC at infinite water potential (see Results and discussion for a more detailed discussion) and indeed the van Genuchten model is not able to describe the WRC in the dry region beyond the wilting point (Ross et al., 1991; Rossi and Nimmo, 1994). Campbell and Shiozawa (1992) proposed a linear relationship between the logarithm of the water potential and the degree of water saturation as a general function for describing the water retention curve under dry conditions. This linear function is defined by its two intersection points (end points) with the x-axis (water content) and the y-axis (log water potential). In order to parameterize this linear function a water potential of log(− Ψ) = 7.0 has been used by various researchers as the endpoint at the intersection with the y-axis to fit the water retention curves beyond the PWP (Fayer and Simmons,

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1995; Rossi and Nimmo, 1994; Webb, 2000). Based on this fixed endpoint Campbell et al. (1993) presented a correlation between the remaining endpoint on the x-axis and the clay content of the soil. Thus, this approach aims to predict the WRC in the dry region simply based on the clay content of soils. Such a relationship is indeed very plausible. Under dry conditions all mineral surfaces are still covered with several molecular layers of water. The sorption capacity results from the binding strength and the number of sorption sites. Likos and Lu (2002) and Schneider and Goss (2011) showed that the binding strength for water (i.e. the enthalpy of sorption of water) in dry soils has little dependence on the type of the mineral surface. For the number of sorption sites, however, a strong correlation with the specific surface area can be expected. The specific surface area is dominated by the clay content in most soils. Therefore a relationship between the WRC in the dry region and the clay content can be expected. The empirical correlation between clay content and water retention by Campbell and Shiozawa was derived from experimental data for only 8 soils covering a clay content range from 5% to 45% (7 soils with clay fraction less then 35%) and excluding one outlier. Given the practical importance of such a pedotransfer function we set out to calibrate and validate a revised pedotransfer function based on a more diverse set of soils and pure clay minerals. To this end we measured water sorption isotherms for 18 soils (clay content between 2% and 61%). The resulting pedotransfer function was then validated with literature data for 25 more soils including pure clays. Note that Resurreccion et al. (2011) recently presented a pedotransfer function derived from a data set including 33 soils from the Danish



Fig. 1. Water content versus relative humidity in the soil pore space at equilibrium (1a, water sorption isotherm) and the logarithmic water potential log (− Ψ) against the water content (1b, water retention curve) for the soils RV 9,6 S, 716 and 732. The clay contents of the soil in % are set in brackets.


Fig. 2. Texture triangle for the soils measured in this study and soils from the literature used for validation.

soil library with clay content up to only 27.6%. This work was only published after submission of this paper. 2. Materials and methods The water sorption isotherms were measured with the same method as described by Goss and Madliger (2007). Around 4 g of the air-dry, disturbed soil was dried in an oven at 105 °C for 24 hours and cooled down in a desiccator with silica-gel. The dry soil was weighed and filled into the calibration device (ER-15, Rotronic) of the relative humidity sensor that was used for measuring water activity (sensor Hydro Clip S, a capacitive sensor by Rotronic containing a hygroscopic polymer). Then the soil was wetted by spraying water using a small aerosol can to yield a water content equivalent to more than 99% rh. Subsequently the calibration device containing the sensor and the soil was closed and equilibrated for around 3 days at room temperature. Afterwards the soil was dried by exposing it to ambient air, the device was closed again for equilibration and the corresponding rh was continuously measured using a data logger (Hydrolog NT) until no further change occurred indicating that equilibrium was reached. This relative humidity value was recorded together with the corresponding weight of the soil sample. The procedure was repeated step-wise down to a relative humidity of around 30% (if the rh in the lab was higher then 30%, the samples

Fig. 3. Linear relationship between the inverse of the slope of the log linear function (1/SL) and the clay fraction of the 18 soils used for calibration of the pedotransfer function.


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Fig. 4. Water adsorption isotherm data for soils measured in this study and their prediction from the clay fraction by the PTF.

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were dried additionally in a desiccator with silica gel). We tested different soil types with different soil textures. In order to account for small changes in room temperature we applied the temperature correction described in a previous paper (Schneider and Goss, 2011) to normalize all data to 20 °C. Afterwards the rh data were transformed via Eq. (1) to obtain matrix potential data. The water sorption isotherms were only measured under drying conditions because no hysteresis was expected based on previous experimental work. A large dataset of measurements of organic vapor sorption on the sorbed water films on various minerals had not shown any discrepancy depending on whether the specific humidity (ranging from 30% to 90%) had been achieved by either drying or wetting (Goss, 2004). It is important to note that the experimentally determined water content at the wetter end of the WRC (rh larger then 90% rh) may start to depend on the bulk density and pore structure of the soil sample and thus data for disturbed soils as presented here may not be a good representation of the more humid part of the curve of undisturbed field soils (Goss and Madliger, 2007). We measured the water sorption isotherms for 18 soils with different soil textures and clay contents from 2% up to 61% (texture triangle see Figure 2). If the source area of the soil is known, it is named after its origin place. In addition we measured a pure kaolinite from Fluka and 4 soils with clay contents from 48% to 76% where the mineral composition of the clay fraction was dominated by kaolinite. The measuring accuracy of the sensor is ±1% rh according to the manufacturer and the final error in the gravimetrical water content accounted 1%. This does not allow meaningful measurements above 98% rh where the water retention curve is very steep. Water retention data for the dry region (log(− Ψ[cm]) > 4.2) from the following additional sources were used: data from Campbell and Shiozawa (1992) measured with a water activity meter, Lu et al. (2008) and Montes et al. (2003) using a dew point potential meter, Sokolowska et al. (2002) measuring the water vapor adsorption data using a vacuum microbalance technique. 3. Results and discussion Fig. 1 shows as an example water sorption isotherms and the corresponding water retention curves for four soils with different clay contents. While Fig. 1b may be more informative in terms of soil physics, Fig. 1a is preferred if the sorption of organic vapors in dry soils is considered (Goss, 2004). The empirical linear relationship between the water content wc and the base-ten logarithm of the negative water potential log(−Ψ) as proposed by Campbell and Shiozawa (1992) fits most of the data well (see supporting information for all plots). Soils with a high content of kaolinite, however, deviate systematically from this linear function and were excluded from the further model calibration (for detailed discussion see below). For the remaining 18 soils we characterized the fitted log linear equations by their slope SL and their endpoint log(− Ψ)wc = 0 at zero water content on the log water potential axis. logð−ΨÞ ¼ SL ×wc þ logð−ΨÞwc¼0


soils dried at 105 °C. These water molecules, however, are bound so tightly that they are not important for practical purposes in soil science. Drying a soil at 105 °C does correspond to a finite value of water activity on the water potential axes as already noted by Ross et al. (1991). This finite value can actually be calculated from the operational conditions. In a laboratory with a room temperature between 20 °C and 25 °C, a relative humidity between 30% and 70% is equivalent to a water vapor pressure between 701 Pa and 2214 Pa (water vapor pressure was calculated by Morton, (1975)). The conditions in the oven at 105 °C can thus be estimated via the Kelvin equation (Eq. (1)) to correspond to a relative humidity between 0.6 and 1.8% based on a saturation vapor pressure of 121883 Pa for water at 105 °C. It follows that the soil samples are equilibrated with a water potential log log(− Ψ)wc = 0 of 6.85 to 6.75 when dried in the oven at 105 °C. This revision of the theoretical endpoint from 7.0 (value so far being used in the literature) to 6.8 (average value derived here) agrees with our experimental results. The individual values of the endpoints log(− Ψ)wc = 0 that are received for every soil from a linear regression have an average value of 6.8 with a standard deviation of 0.15 (supporting information table 1). In the final evaluation we therefore forced all our fitted curves through the reasonable mean value for typical lab conditions of log(− Ψ)wc = 0 = 6.8. Fitting the log linear functions through the endpoint of log(− Ψ)wc = 0 = 7.0 for comparison resulted in a worse correlation for 13 of 18 soils (see supporting information). It is noteworthy that the theoretical endpoint of log(− Ψ)wc = 0 = 7.0 would correspond to a relative humidity of 9% in the laboratory air at 20 °C. This is not realistic under any circumstances and we therefore propose that our conditions of 30%–70%rh in the laboratory air and a resulting endpoint at log(− Ψ)wc = 0 = 6.8 should generally be valid for soils dried at 105 °C. After having fixed the endpoint at zero water content log (− Ψ)wc = 0 in Eq. (2) at the theoretically derived value of log (− Ψ)wc = 0 = 6.8 the slope SL remains the only variable that defines the log linear relationship of the WRC in the dry region. This slope becomes shallower with increasing clay content of the soils (see also Figure 1b). The inverse of the slope, 1/SL, shows a very strong linear correlation with the clay content (Figure 3) and can therefore be used for creating a pedotransfer function (PTF). The PTF for the slope, SL, was calibrated using the data of 18 soils measured in this study. The data set was obtained with one consistent experimental method and it covers a wide range of clay contents. The resulting PTF is:

SL ¼

1 −0:109·½clayfraction−0:003



Campbell and Shiozawa (1992) had used a second endpoint (at almost water saturated conditions) instead of the slope to define their fitted regressions. This is not very intuitive because it involves an extrapolation far beyond the dry range to which this equation is limited. Note that we express water activity by the base-ten logarithm of the negative water potential value in cm water column and not as the natural logarithm of the negative water potential in [J/kg], as done by Campbell and Shiozawa (1992). In the following we start with a revision of the endpoint at the dry end of the WRC: On the water content axes the “zero” water content in reality corresponds to a measurable amount of water that is left in

Fig. 5. Fitted slopes of the log linear function for the water retention data of 22 soils and 3 pure clays from the literature and the slope predicted from the pedotransfer function.


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Fig. 6. Water adsorption isotherm for a pure bentonite with different interlayer cations (Montes et al., 2003) and the prediction with the PTF for 100% clay.

The clay content of a soil is the dominant factor in determining water sorption in the dry region of the WRC. All other influences are represented by the intercept which has only a small value here. The root mean square error (rmse) between the experimental data points of the log linear relationship and those predicted by the PTF are reported in the supporting information. The predictions for the resulting water sorption isotherms for the soils measured in this study are presented in Fig. 4 and show good results for the soils with higher clay contents. For the soils Kreinitz and RV 6 the pedotransfer function underestimates the water sorption isotherm. These two soils have clay contents below 7%. For these low clay contents the clay surface appears to be not the dominant sorption site anymore; a high organic carbon content could influence the water sorption and the intercept of the PTF does not cover these influences

precisely. Resurreccion et al. (2011) showed in their regression that soils with a ratio of clay to organic carbon less then 4 had to be excluded from the calibration. The two studies mainly show the same results for the pedotransfer function. Although our data set is smaller than the one from Resurreccion et al. (2011) it is more diverse and also contains soils with higher clay contents. The literature data for water sorption isotherms from Sokolowska et al. (2002), Montes et al. (2003) and Likos and Lu (2002) and the water retention curve data by Lu et al. (2008), none of which had been used for calibration of the PTF, were used for validation purposes. We transformed the water activity data into log water potential data, plotted them and received the slope SL by forcing the linear regression through the endpoint at log(− Ψ)wc = 0 = 6.8. The PTF for the slope SL agrees well with the estimated slopes for the different soils from Poland and China (see Figure 5, predicted water sorption isotherm data for the soils are presented in supporting information). As already observed for the calibration data set the predictions for soils with lower clay content do not fit the data as well. On the other hand the slope for the WRC of a pure smectite and a pure bentonite (Figure 5) can be predicted very well by the PTF. Montes et al. (2003) showed that the water sorption curve of a pure bentonite is also influenced by the dominating interlayer cations. The best agreement between our PTF and the data from Montes et al. (2003) for pure clay is achieved for bentonite containing Ca 2 + and Na + cations (see Figure 6). This is plausible because Ca 2 + and Na + are the most common cations in natural soil solutions (Scheffer and Schachtschabel, 1989, pg.224) and the PTF was calibrated with data from natural soils. The soils used for calibration of the PTF are all from Europe and are dominated by 2:1 clay minerals. In addition to literature data for a pure kaolinite (1:1 clay mineral), we also measured the WRC for a pure kaolinite from Fluka (Sigmar Aldrich). The two independent measurements agree with each other very well but the prediction of the WRC for a 100% clay largely overestimates the water retention

Fig. 7. Water retention curve for pure kaolinite (measured by Likos and Lu (2002) and ourselves), soils with a high percentage of kaolinite in the clay fraction and their prediction by the pedotransfer function according to the clay content.

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capacity of kaolinite (see Figure 7a). This is plausible because 2:1 clay minerals are able to swell and thus possess sorption sites in the inner layers that are not present in kaolinite. Fig. 7b–c shows the WRC for different kaolinite soils also measured in this study that were not included into the calibration of the pedotransfer function. The prediction of the log linear function from the pedo transfer function according to the clay content does not agree well with the data. The pure kaolinite shows the maximum deviation. The deviation of all other soils is lower due to the natural composition of the clay minerals (mixtures of different minerals). In addition, the data are not well described using a log linear function. Therefore we conclude that the PTF presented here is only valid for soils containing 2:1 clay minerals as the dominant clay type. This limitation had not become clear in the work of Campbell and Shiozawa (1992) and Resurreccion et al. (2011). The possibility to calibrate a pedotransfer function especially for kaolinite soils seams to be impractical because natural soils will typically contain a mixture of 1:2 and 1:1 clay types and even a small amount of 1:2 type minerals are able to substantially influence the water sorption in kaolinite soils (see different deviations for different soils in Figure 7). Also the threshold for the influence of organic carbon might be even lower for soils rich in kaolinite. In this context it is interesting to note that Likos and Lu (2002) were able to predict the water sortion isotherm of kaolinite and smectite mixtures from the weighted contributions of the different minerals assuming additive behavior. However a quantitative evaluation of the mineral composition of a soil highly exceeds the costs of directly measuring a water sorption isotherm. 4. Conclusion Experimental water sorption isotherm data from 42 soils and pure bentonite and smectite minerals were described well by a log linear relationship of the transformed water activity data. The fixed endpoint of this log linear relationship at log(− Ψ)wc = 0 = 6.8 agrees better with the experimental values than the value of log(− Ψ)wc = 0 = 7.0 that has been favored in the literature. Based on a more diverse data set than had been used by Campbell and Shiozawa (1992) and Resurreccion et al. (2011) we were able to present a revised pedotransfer function that predicts the experimental water sorption isotherm data for most of the soils based on their clay content. This PTF appears to hold for soils with more than 7% clay and with a clay fraction that consists mostly of 2:1 clays. Soils that contain mostly kaolinite as the dominant clay mineral cannot be described by the log linear function proposed by Campbell and Shiozawa (1992) and sorb substantially less water than predicted by our PTF. Acknowledgements We thank the ETH Zürich, the Helmholtz Centre for Environmental Research in Halle, the University of Halle, the Technical University


Berlin and Agro Paris for providing the soil samples and related texture data and Michael Madliger, Hans-Jörg Vogel and Trevor Brown for advice on the manuscript. This work was kindly supported by Helmholtz Impulse and Networking Fund through Helmholtz Interdisciplinary Graduate School for Environmental Research (HIGRADE). Appendix A. Supporting information Supplementary data to this article can be found online at doi:10. 1016/j.geoderma.2011.10.008. References Campbell, G.S., Shiozawa, S., 1992. Prediction of Hydraulic Properties of Soils Using Particle Size Distribution and Bulk Density Data, International Workshop on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils. University of California Press, Berkely. Campbell, G.S., Jungbauer, J.D., Shiozawa, S., Hungerford, R.D., 1993. A one-parameter equation for water sorption isotherms of soils. Soil Science 156, 302–305. Cornelis, W.M., Khlosi, M., Hartmann, R., Van Meirvenne, M., De Vos, B., 2005. Comparison of unimodal analytical expressions for the soil–water retention curve. Soil Science Society of America Journal 69 (6), 1902–1911. Fayer, M.J., Simmons, C.S., 1995. Modified soil–water retention functions for all matric suctions. Water Resources Research 31, 1233–1238. Goss, K.-U., 2004. The air/surface adsorption equilibrium of organic compounds under ambient conditions. Critical Reviews in Environmental Science and Technology 34, 339–389. Goss, K.-U., Madliger, M., 2007. Estimation of water transport based on in situ measurements of relative humidity and temperature in a dry tanzanian soil. Water Resources Research 43 doi:10.1029/2006WR005197. Likos, W., Lu, N., 2002. Water vapor sorption behavior of smectite–kaolinite mixtures. Clays and Clay Minerals 50, 553–561. Lu, S., Ren, T., Gong, Y., Horton, R., 2008. Evaluation of three models that describe soil water retention curves from saturation to oven dryness. Soil Science Society of America Journal 72, 1542–1546 doi:10.2136/sssaj2007.0307N. Montes, H.G., Duplay, J., Martinez, L., Geraud, Y., Rousset-Tournier, B., 2003. Influence of interlayer cations on the water sorption and swelling-shrinkage of mx80 bentonite. Applied Clay Science 23, 309–321. Morton, F.I., 1975. Estimating evaporation and transpiration from climatological observations. Journal of Applied Meteorology 14 (4), 488–497. Or, D., Wraight, M., 2000. Soil water content and water potential relationship. Handbook of Soil Science, pp. 53–85. 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 Resources Research 47 doi:10.1029/2010WR010229. Ross, P.J., Williams, J., Bristow, K.L., 1991. Equation for extending water-retention curves to dryness. Soil Science Society of America Journal 55, 923–927. Rossi, C., Nimmo, J.R., 1994. Modeling of soil–water retention from saturation to oven dryness. Water Resources Research 30, 701–708. Scheffer, F., Schachtschabel, P., 1989. Lehrbuch der Bodenkunde. Schneider, M., Goss, K.-U., 2011. The temperature dependence of the water retention curve for dry soils. Water Resources Research 47 doi:10.1029/2010WR009687. Sokolowska, Z., Borowko, M., Reszko-Zygmunt, J., Sokolowski, S., 2002. Adsorption of nitrogen and water vapor by alluvial soils. Geoderma 107, 33–54. Tuller, M., Or, D., 2005. Water films and scaling of soil characteristic curves at low water contents. Water Resources Research 41 doi:10.1029/2005WR004142. van Genuchten, M.T., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44, 892–898. Webb, S., 2000. A simple extension of two-phase characteristic curves to include the dry region. Water Resources Research 36, 1425–1430 doi:10.1029/2000WR900057.