Water Resources Research

Temperature dependence of the water retention curve for dry soils



[1] Water retention curves (WRCs) are equivalent to water adsorption isotherms that display the soil water content as a function of water activity in the pore space. The use of water activity implies that pure (unbound) water at the given temperature is considered to be a reference state. In this study we measured the temperature dependence of WRCs for nine European soils under dry conditions (i.e., water activity < 90% relative humidity (RH), matrix tension <−1.5 MPa). The results show a significant temperature dependence of the WRCs. The absolute value of the adsorption enthalpy of water, equation image, which reflects this temperature dependence, increased with decreasing water content and thus deviated from the condensation enthalpy of a pure (unbound) water phase, equation image. These results are explained by the following facts: under increasingly drier conditions the interactions between water molecules and the mineral surfaces become more and more dominant because the sorbed water film becomes very thin. These interactions between water and minerals are stronger than those between pure water molecules. The observed temperature dependence of WRCs varied only a little between the studied soils. Therefore, the average equation, equation image, derived from our experimental data may serve as a good approximation of equation image for soils in general and thus allow the temperature extrapolation of WRCs (in the dry region down to 30% RH) between 5°C and 40°C without the need for additional experimental information.

1. Introduction

[2] The transport and availability of water in dry soils is of high concern for desertification, irrigation farming, and other applications. Tuller and Or [2005] have shown that unsaturated soils cannot be represented by a hypothetical mixture consisting of pores that are completely filled with water and pores that are completely devoid of water. In dry soils (here defined as having a matrix pressure below the wilting point of −1.5 MPa) the water phase is mostly discontinuous [Salager et al., 2006; Tuller and Or, 2005]. At this state all mineral surfaces are still covered with several layers of water molecules because of the ability of mineral surfaces to form strong hydrogen H-bonds with water. This water layer is mobile enough to allow significant water flow in dry soils [Tuller and Or, 2005; Goss and Madliger, 2007]. In order to better understand water movement under such conditions the soil characteristic functions in dry soils need to be known. It has been shown, however, that neither the water retention curves (WRCs) nor functions for water conductivity that have been established for moist soils can be extrapolated into the dry region [Ross et al., 1991; Rossi and Nimmo, 1994].

[3] The impact of the temperature on the water retention curve under moist conditions has been shown by several researchers (e.g., see review by Bachmann and van der Ploeg [2002]). There are different reasons for this effect, such as variation of the surface tension and the contact angle [Bachmann et al., 2002], changes of quantity of solute [Nimmo and Miller, 1986], variation of trapped air bubbles [Hopmans and Dane, 1986], and isolated water packets [Liu and Dane, 1993]. Salager et al. [2010] give an equation to predict the temperature effect on water retention curves by considering the main effects. However, the various reasons for temperature dependence under moist conditions do not hold for the dry conditions studied here. Under dry conditions the pores are no longer filled with water, and the binding of the water is not caused by capillary forces but by adsorptive forces. Still, significant temperature dependence for the WRCs of a dry soil was reported by Goss and Madliger [2007] and Salager et al. [2006]. Here we set out to study this temperature effect on WRCs in dry soils more systematically.

2. Theory

[4] In general, the temperature effect on any adsorption equilibrium (including the adsorption of water on mineral surfaces) is quantified by the enthalpy of adsorption equation image. equation image is the heat that is absorbed when 1 mol of the compound is transferred from the surface into the gas phase. This equation image represents the interaction energy of the sorbate molecules with the sorbing surface and depends on the sorbate molecule (here water), the sorbing surface, and the temperature.

[5] Water retention curves are equivalent to water adsorption isotherms that display the soil water content as a function of the matrix pressure. The matrix pressure h is a measure of water activity in the soil and thus is directly related to 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]:

equation image

where R is the universal gas constant, T is the temperature in K, equation image is the density of water, MH2O is the molecular mass of water, and g is the constant of gravity. The equilibrium RH often is a more convenient scale to use than the matrix pressure h when dealing with dry soils. The wilting point (−1.5MPa), for example, corresponds to a RH of 98.9% at 20°C.

[6] At 90% RH, mineral surfaces in equilibrium are usually covered with 5–10 molecular layers of water. Even at fairly dry conditions, a complete coverage of water can still be found (e.g., 1–2 molecular layers at 30% RH) [Goss, 2004]. A study on the adsorption of organic molecules to moist mineral surfaces demonstrated that adsorption on mineral surfaces at RH above 90% RH is similar to adsorption at the pure water surface [Goss, 2004]. This goes along with the finding that equation image of water at RH >90% on a hydrated mineral surface agrees well with the enthalpy of condensation equation image of water [Goss and Madliger, 2007]. At lower RH, however, the absolute value of equation image is expected to increase with decreasing RH because of the increasing strength with which the water molecules are bound to the underlying mineral. The same effect has also been shown to influence water vapor diffusion through soils [Jabro, 2009]. Intuitively, under dry conditions, equation image for water may depend on the specific minerals and thus the type of soil considered. Therefore, it is important to examine the variability of equation image (thus temperature dependence of WRCs) across various soils.

[7] The influence of temperature on sorption equilibrium is described by the van't Hoff equation with enthalpy as the characteristic parameter:

equation image

where K is the adsorption coefficient (defined as mass of sorbate per mass of sorbent over the sorbate's partial pressure in the gas phase) at a given absolute temperature T. In order to derive equation image values from the WRCs at various temperatures one first has to transform the water activity scale (here RH) into a scale of absolute partial pressures of water vapor. This can be done by multiplying the relative humidity value with the saturation vapor pressure of water, ps, at the specific temperature

equation image

[8] Values of ps can be calculated from the following vapor pressure saturation curve according to Morton [1975]:

equation image

3. Materials and Methods

[9] The WRCs were measured by following the method described by Goss and Madliger [2007]. The disturbed soil was dried in an oven at 105°C for 24 h 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 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 20°C. Afterward, the soil was partially dried at ambient air, and the device was closed again for equilibration. The development of the actual RH in the closed system was continuously measured using a data logger (Hydrolog NT) until no further change in RH occurred, indicating that equilibrium was reached. The RH value at equilibrium was recorded together with the corresponding weight of the soil sample. The procedure was repeated down to a RH of around 30%. At each water content the soil water system was equilibrated and measured at 5°C, 20°C, 30°C, and 40°C. The different temperature states were achieved by transferring the experimental setup from a refrigerator (5°C) to ambient air (20°C) and finally into a drying oven (30°C–40°C). Temperature and RH were measured by the same probe.

[10] The measuring accuracy of the sensor is ±1% RH according to the manufacturer. This does not allow meaningful measurements above 98% RH, where the water adsorption curve is, in general, very steep. Temperature dependence of the WRCs was measured for nine soils with different textures (Table 1). In addition, literature data for a Haplic Acrisol from Tanzania with a high content of kaolinite are considered in the discussion in section 4 [Goss and Madliger, 2007]. Soils with a clay content below 13.0% were not included because for RH <100% such soils would contain so little water that even small changes in the absolute water content could result in unacceptable high errors in the measured sorption isotherms. In general, the water content in the soils was assumed to be constant at all four temperature states. The amount of water that would evaporate because of the temperature change was negligibly small and beneath the balance accuracy. The amount of water that was lost during the experiment because of a general small leak of the calibration device resulted in an error of 1% in the final water content and was also neglected.

Table 1. Texture Classes of the Different Soils
Soil NotationClay (%)Silt (%)Sand (%)

4. Results and Discussion

[11] Figure 1 shows the water retention curves of soil number 716 at different temperatures. The error bars are plotted for 5°C only. Note that in Figure 1 the soil water content is plotted against RH. RH is the water activity scale and thus uses pure water (i.e., 100% RH) at the given temperature as a reference. Hence, curves for different temperatures only deviate from each other if equation image of water on the soil differs from equation image of water into its own pure phase. In the region with RH >90% the curves for the different temperatures superpose each other. This is reasonable because the thick multilayer water film on minerals at >90% RH resembles pure water, and thus, the interaction energy of a water molecule adsorbing on such a multilayer water film is similar to adsorption on a pure water surface (i.e., condensation). With decreasing RH, however, the temperature dependence becomes more and more visible because of the additional interactions that water undergoes with the minerals when the adsorbed water film becomes thinner. These additional interactions grow stronger at lower RH because of the decreasing water film thickness on the mineral surface, i.e., the divergence of the curves measured at different temperature increases with decreasing water content. The results are similar to those of Salager et al. [2006], who showed temperature-dependant sorption isotherm data for a loamy sand.

Figure 1.

Water retention curves at 5°C, 20°C, 30°C and 40°C for soil number 716.

[12] In the first evaluation step we used the van't Hoff equation (equation (2)) to derive equation image for all soils from the water adsorption isotherms at 5°C and 20°C. The results are depicted in Figure 2 and show the expected features: (1) At RH close to 100% RH, equation image on all soils is identical to the equation image of water (also shown by Goss and Madliger [2007]). (2) With decreasing water activity and thus decreasing water content the absolute equation image values increase above that of equation image; this effect was also shown for lepidocrocite (equation image-FeOOH) by Majzlan et al. [2007]. (3) The equation image values for the different soils become more scattered because of their different mineral composition. Nevertheless, the observed scatter between different soils is quite small: the equation image values of the various soils below 50% RH (a value that is rarely exceeded even in dry soils) differ by a maximum of 1.7 kJ/mol from the average value. It is noteworthy that even a soil from Tanzania rich in kaolinite does not deviate from the other soils. This agrees with the finding of Likos and Lu [2002]. They estimated water adsorption isotherms for kaolinite-smectite mixtures without finding any trend in the heat of adsorption. Therefore, for practical purposes the average values calculated from the data in Figure 2 can represent all soils studied and may serve as a good approximation of the actual equation image values for other types of soils. What remains is a significant influence of the equilibrium RH (as a parameter that represents the thickness of the adsorbed water film) on equation image for all soils. For practical purposes it is desirable to describe the relationship between the average equation image of all soils and RH at equilibrium by a mathematical function. The best fit was obtained by the following logarithmic function:

equation image

for the temperature interval 5°C–20°C, where SD is the standard deviation. The experimental data for the two remaining temperature intervals were evaluated in the same way, giving the following results (see Figure 3):

equation image

for 20°C–30°C and

equation image

for 30°C–40°C.

Figure 2.

equation image calculated from sorption isothermes at 5°C and 20°C for different soils plotted against the average relative humidity.

Figure 3.

Fitted logarithmic function of equation image for the different temperature intervals against the average relative humidity. equation image of water at different temperatures were calculated from eq. 2 and 4 for 100%RH.

[13] The results show a small but statistically significant temperature dependence of equation image. At higher temperatures the absolute value of equation image is lower because of weaker intermolecular interactions. This was also recognizable for all soils. Similarly, a temperature dependence for equation image of pure water can be derived from the water vapor saturation curve by Morton [1975]. These temperature-dependent equation image values, which are plotted as diamonds in Figure 3, at 100% RH fit perfectly to the curves of equation image extrapolated to 100% RH. Note that the temperature dependence of equation image demonstrated here is significant but so small that for practical purposes it will be sufficient to work with an average for the temperature range between 5°C and 40°C and assume this value to be constant over this temperature range. An average equation image as a function of RH calculated from the temperature interval from 5°C to 40°C is given by the following logarithmic equation:

equation image

[14] Equation (6) summarizes the central results of this work and enables us to extrapolate WRCs measured at equilibrium RH <90% from one temperature to other ambient temperatures. For validation we checked how well the estimated average equation image from equation (6) is suited to extrapolating the measured water retention curve at 20°C to the curves that were measured at 5°C, 30°C, and 40°C. Figure 4 shows the extrapolated and measured water retention curves at 5°C, 30°C, and 40°C for soil number 716. The observed deviation is mostly due to our simplifying assumption that the dependence of equation image on the relative humidity is similar for all soils. Neglecting the temperature dependence of equation image has only a small influence on the results.

Figure 4.

Extrapolated and measured relative humidity data for soil nr. 716 at 5°C, 30°C and 40°C.

5. Conclusion

[15] The absolute value of equation image for water adsorption in dry soils (matrix tension of <−1.5 MPa) increases above the value of equation image with decreasing water content of the soil. This leads to an increasing temperature dependence of the WRC with increasing dryness. Our data indicate that the influence of the soil type on this temperature effect is small. Therefore, the average values of equation image determined here can serve as a good approximation for other soils without generating a substantial error and thus can allow a temperature correction for WRC data under dry conditions. In the auxiliary material we provide our raw data and an Excel spreadsheet that shows an example for a temperature extrapolation using these average equation image values, which can easily be adjusted by any user to own data. To describe water transport in dry soils, it is essential to know the hydraulic conductivity and the WRC. In a future paper we will discuss the prediction of the WRC in dry soils at a reference temperature. Then, on the basis of this study, the WRC (in the dry region down to 30% RH) can be extrapolated to a desired temperature between 5°C and 40°C.


[16] We thank the ETH Zürich, the Helmholtz Centre for Environmental Research in Halle, and Agro Paris for providing the soil samples and texture data and Satoshi Endo for careful review of the manuscript. This work was supported by Helmholtz Impulse and Networking Fund through Helmholtz Interdisciplinary Graduate School for Environmental Research (HIGRADE).