Inverse Modeling Water Contents of Semiarid Soils Using Multi-Objective Parameter Optimization to Obtain the Compromise Solution.

Soil moisture is a critical component in the active restoration of semiarid rangelands, where the near-surface microclimate controls seed germination dynamics. The Simultaneous Heat and Water (SHAW) model was optimized using the multi-objective, parameters estimation algorithm AMALGAM. Three objective functions (OF) were constructed to minimize the root mean square error of surficial (OF₁, 2- and 5-cm), near-surface (OF₂, 10- and 20-cm), and soil profile (OF₃, 0-60cm) moisture data obtained from the Orchard Field Test Site in southwestern Idaho. The site is semi-arid (293 mm, mean annual precipitation) sagebrush rangeland undergoing intense invasion by cheatgrass.  Data used were taken under a bare soil treatment (no transpiration was simulated). Four optimizations were conducted, each with an increasing level of vertical heterogeneity, including a one-layer to a four-layer (L₁ to L₄) soil profile with horizons identified at textural breaks. Sensitivity analysis results indicate that air entry (Ψ_e) had the only consistent response for all three OF. Other water retention parameters (pore-size distribution, b, and saturated water content, [θ_s]) were sensitive but inconsistent across the different OF. Saturated conductivity (K_s) was insensitive for all OF. The multi-objective framework generates a population of equally viable Pareto solutions. In all cases, the Pareto extreme values for OF_1-3 were 0.034, 0.023 and 0.008 m³ m^-3, respectively, under L₁. However, the estimated Pareto front showed that L₁ and L₂ were poorly sampled in the OF space, likely due to the high correlation between OF₂ and OF₃. Considerable tradeoffs between OFs also existed. With increasing heterogeneity (and more parameters), lower OF were obtained but ultimately the variance increased significantly with depth. The Euclidean compromise solution (the single Pareto solution closest to the origin) between all three normalized OF produced a particularly ‘good’ parameter set with values within physically realistic bounds. For cases where observed surficial measurement data are noisy, as in this case, a compromise solution is a promising means to statistically obtain a solution across multiple sensors and OF.