Effects of soil heterogeneity on steady state soil water pressure head under a surface line source

There are numerous analytical solutions available for flow in unsaturated homogeneous porous media. In this paper, the stream tube model for one‐dimensional water movement is extended to two‐dimensional (2‐D) water movement from a line source as the stream plane model. As well, new solutions are derived to predict the mean and variance of pressure head of water movement under a surface line source in heterogeneous soil using the perturbation method with first‐order approximation (PM1) and with second‐order approximation (PM2). A variance expression was also developed based on the spectral relationship presented by Yeh et al. [1985a]. The new solutions were tested using the 2‐D stream plane model with parameters A = ln(α) and Y = ln(KS) and measurements from field experiments. Results show that the mean of steady state pressure head below the line source is not only a function of the mean parameter values but also a function of the variances of A and Y and the linear cross‐correlation coefficient (ρ) between A and Y. The PM2 model can predict the mean pressure head accurately in heterogeneous soils at any level of correlation between A and Y, except when both the soil variability and ρ are high. The pressure head variance estimation based on the PM1 model predicts the measured variance well only when both the soil variability and ρ are low. The field experimental results show that both the PM1 and the spectral models give reasonable predictions of the pressure head variance. Both the measured and predicted values of the variance of pressure head using the two models increase with the depth of soil. Both models show that the variance of pressure head decreases as the source strength increases, but on average, the pressure head variance was underestimated by both models.