Abstract
Using scaling methods, a single solution of Richards' equation (RE) will suffice for numerous specific cases of water flow in unsaturated soils. In this study, a new method is developed to scale RE for the soil water redistribution process. Two similarity conditions are required: similarity in the shape of the soil water content profiles as well as of the water flux density curves. An advantage of this method is that it is not restricted to a specific soil hydraulic model - hence, all such models can be applied to RE. To evaluate the proposed method, various soil textures and initial conditions were considered. After the RE was solved numerically using the HYDRUS-1D model, the solutions were scaled. The scaled soil water content profiles were nearly invariant for medium- and fine-textured soils when the soil profile was not deeply wetted. The textural range of the soils in which the similarity conditions are held decreases as the initial conditions deal with a deeply wetted profile. Thus, the scaling performance was poor in such a condition. This limitation was more pronounced in the coarse-textured soils. Based on the scaling method, a procedure is suggested by which the solution of RE for a specific case can be used to approximate solutions for many other cases. Such a procedure reduces complicated numerical calculations and provides additional opportunities for solving the highly nonlinear RE as in the case of unsaturated water flow in soils.
Highlights
A reason for the undesirable deviations in the three sandy soils is that the soil water content profiles (SWCP) in these soils with the imposed initial conditions are not similar in shape to those of the other soils
It seems that the main reason for the deviations is that, regarding the Nielsen-similarity condition, these soils are not similar to the other soils
We studied the similarity condition in three soils of sand, loam, and clay textures under the conditions corresponding to Figure 2
Summary
Scaling methods based on the "similar media" concept (Miller and Miller, 1956) were developed to cope with the spatial variability of soils (Warrick et al, 1977; Sharma et al, 1980; Ahuja and Williams, 1991; Kosugi and Hopmans, 1998; Tuli et al, 2001; Kozak and Ahuja, 2005; Roth, 2008; Sadeghi et al, 2010). Vereecken et al (2007) comprehensively reviewed the scaling methods developed during the past years.Scaling has proven its success as a tool for numerical analyses. A single solution of Richards' equation (RE) will suffice for numerous specific cases of unsaturated water flow. These methods considerably reduce the calculations required for heterogeneous soils (Warrick and Hussen, 1993). These methods allow a linear transformation of RE variables to achieve invariant solutions for a set of similar soils. This similarity may be defined based on microscopic-scale geometry (Miller and Miller 1956), shape of soil hydraulic functions (Simmons et al, 1979), or a linear variability concept (Vogel et al, 1991)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have