Numerical investigation of streamtube approach to model flow in heterogeneous unsaturated sandy soils

Abstract

The streamtube approximation has been commonly used for upscaling of flow and transport in spatially heterogeneous unsaturated soils. This study investigates the prediction ability of streamtube approach to model flow in heterogeneous unsaturated sandy soils under a rainfall event at a plot scale. Towards this aim, a numerical model for solving 3-D Richards’s equation was developed and verified for 1-D and 3-D cases. Turning band method was used to generate the random field of soil hydraulic parameters. The 3-D soil field heterogeneity was represented by considering variation in both van Genuchten parameter (α) and Ks. For streamtube models, two cases of heterogeneity were investigated: i) variability in Ks only, and ii) variability in both Ks and α. Both the parameters were assumed to follow a log-normal distribution. For different boundary conditions at the soil surface and varying soil heterogeneity, the average Darcy's flux and mean field-scale soil moisture obtained using streamtube approach were compared with 3-D numerical solutions. The results identify that for high recharge rate at the soil surface, streamtube model is a good approximation of the 3-D heterogeneous soil field, and the average difference in mean soil moisture obtained from 3-D model and streamtube based 1-D model was below 10% when variability in both Ks and α was considered for all timesteps. The inclusion of variability in α leads to improvement in prediction capability of streamtube model. Further, regression equations were developed that can be utilized to predict the mean field soil moisture for heterogeneous 3-D sandy soil fields given the mean field soil moisture obtained from streamtube approach for both the cases. The regressions equations follow exponential model for case-1 and linear model for case-2 with R2 values 0.80 and 0.99, respectively. The developed equations can be reliably used to predict mean field soil moisture for heterogeneous sandy soil fields.