Simulating soil moisture dynamics in coarse-textured alluvial soils under high evaporative demand and infrequent rainfall challenges both characterization and numerical methods. For this study, three geomorphically young disturbed soils in the central Mojave Desert were characterized using direct, indirect, and inverse parameter estimation methods for numerical simulations using HYDRUS. Observations of soil water content (θ) and matric head (h) were used to formulate our multiobjective framework optimized using the AMALGAM algorithm. Both the direct and indirect parameterization methods reproduced θ but proved inadequate for h data. Sensitivity analysis found the parameters related to the dry end of the soil hydraulic function—including residual water content (θr) and pore-size distribution (n)—most sensitive but often conflicting between the two criteria while soil temperature was effectively simulated but insensitive. At the sites, a large dynamic range of h (1–400 m) was accompanied by a relatively small range of θ (0.04–0.10 m3 m−3), limiting our ability to resolve the wet-end of the hydraulic functions. Direct parameterization from infiltrometer data and indirect pedotransfer functions had good agreement with θ but largely underestimated h. Pareto analysis determined the trade-off between fitting both criteria and revealed model structure inadequacies as well as bifurcations into parameter populations, favoring either θ or h error minimization. The Pareto solutions compensated for the underestimation of h by forcing the α and n parameters to uncharacteristically low values for such coarse textures. This compensation kept the water capacity sufficiently high at lower θ to maintain conductivity toward the surface. These results are likely a consequence of either the disturbed soil system or hysteresis between measurements of θ and h.