In the present study, we modified the one-layer water balance model developed for low-latitude arid regions by Yamaguchi and Shinoda (2002) to represent the extra-tropical characteristics (such as seen in Mongolia) of winter soil freezing and spring snowmelt. This model, which is well known as the ‘bucket model’, was widely used for general circulation models (Manabe, 1969) and this has also been used for an operational monitoring of soil moisture in many regions of the world (e.g. Marengo et al., 1996; Huang et al., 1996; Yamaguchi and Shinoda, 2002; Shinoda and Yamaguchi, 2003; Yeung, 2005). We applied this water balance model to the 20-year (1986–2005) soil moisture observations of the top 50-cm soil layer for 26 Mongolian stations. The model calculates absolute plant available soil moisture content using only daily precipitation (P) and air temperature (T) data with a limited number of measured soil parameters, as expressed by the following equations:
where W, the plant-available soil moisture, is expressed as the actual soil moisture minus the moisture content at the wilting point (mm) that exists from the surface to 50-cm depth; t is time (days); Pr is daily rainfall (mm); and M is the melt of the snow (expressed as snow water equivalent, mm) that is accumulated when air temperature is equal to or below 0 °C. If air temperature is above 0 °C, the accumulated snow melts. E is the evapotranspiration (mm) and R is the combination of surface runoff and deep drainage (mm). In the model, the Pr is considered to occur when the air temperature is above 0 °C. The soil is assumed to have one layer with field capacity Wfc. For this model, if W > Wfc, the excess is assumed to be R (Equation (2)). In arid regions, such as Mongolia, these two factors are generally negligible as described by Yamanaka et al. (2007). Moreover, a negligible small amount of deep percolation was commonly found within natural vegetation areas of various arid regions where the annual precipitation was less than 300 mm (Scanlon et al., 1997). In Mongolia, the annual precipitation is approximately 200 mm that is almost exactly matched by the annual evapotranspiration (Robock et al., 2000). Most of the precipitated water on the grassland quickly returns to the atmosphere from the upper layers of the soil via evapotranspiration and the fact that precipitated water never infiltrates to depths below 20 cm (Yamanaka et al., 2007). Thus, we consider that, although the treatment of surface runoff and deep drainage in our model is simplified, this would not cause a serious error in the soil moisture estimation. The evapotranspiration (E) varies with W such that:
where τ is interpreted as a ‘residence time’ or ‘turnover period’ that signifies the time required for a volume of water equal to the annual mean of exchangeable soil moisture to be depleted by evapotranspiration. W* is a moisture storage capacity of the 0–50 cm layer soil (mm). The actual value of τ is a function of soil properties, including Wwp, Wfc, and the potential evapotranspiration rate (PET) with higher PET values resulting in lower residence times. In addition, the parameters of Wwp and Wfc used in this study were measured in the grass-covered field, thus including some information of not only soil properties but also of the root system (implicitly). Yamanaka et al. (2007) showed that the value of τ ranges from 20 to 26 days, suggesting that the precipitated water on the grassland in Mongolia quickly returns to the atmosphere via evapotranspiration. Following Serafini and Sud (1987), we calculated the value of τ such that:
In the above equation, α accounts for variations in vegetation type and Minths and Serafini (1984) determined it on the basis of the experimental relationship between the actual and potential evapotranspiration. Serafani and Sud (1987) suggested that α should be adjusted to account for the variations in vegetation type; α = 16–20 may be suitable for a forest, and α = 2 may be appropriate for a desert. However, Mintz and Serafini (1984), and Serafani and Sud (1987) suggested using α = 6.81 for most vegetation types everywhere in the world. Thus, an α value of 6.81 was used in this study. The PET depends mainly on the net radiative heating on the surface. However, long-term measurements or sufficiently accurate calculations of the net radiation at the surface are inadequate or absent over large areas of Mongolia. With this background, we estimate PET from the observed air temperature and duration of sunlight using the Thornthwaite method (1948). The PET was calculated on a daily basis with the Thornthwaite (1948) formula as modified by Mintz and Walker (1993):
where T is the daily mean air temperature ( °C), Tm is the monthly mean air temperature ( °C), h is the length of daylight (hours), and I is the annual heat index (sum of the 12 monthly heat indices i). Worldwide, this method has been used to calculate soil moisture indexes (Palmer, 1965, 1968) and derive global soil moisture fields (Mintz and Serafini, 1984). The wide use of this method is due to the simplicity of the calculation, using only surface air temperature. Yamaguchi and Shinoda (2002) examined the applicability of this method to the semi-arid Sahel region, demonstrating that the Thornthwaite PET coincided fairly well with the Penman PET during May–October when the daily air temperature was below 26.5 °C. However, the Thornthwaite PET reached the maximum during March–May and October–November, which is the nature of this formula when the air temperature is above 26.5 °C (Yamaguchi and Shinoda, 2002). In Mongolia, the air temperature was generally below 26.5 °C all year around (Figure 6), making the Thornthwaite method a reliable choice in this country. The effectiveness of this model was validated by comparison with the 20-year soil moisture observations in Section 3.3.