Incorporating spatially heterogeneous infiltration capacity into hydrologic models with applications for simulating post-wildfire debris flow initiation

Soils in post-wildfire environments are often characterized by a low infiltration capacity with a high degree of spatial heterogeneity relative to unburned areas. Debris flows are frequently initiated by run-off in recently burned steeplands, making it critical to develop and test methods for incorporating spatial variability in infiltration capacity into hydrologic models. We use Monte Carlo simulations of run-off generation over a soil with a spatially heterogenous saturated hydraulic conductivity (K_s) to derive an expression for an aerially averaged saturated hydraulic conductivity (K_e^*) that depends on the rainfall rate, the statistical properties of K_s, and the spatial correlation length scale associated with K_s. The proposed method for determining K_e^* is tested by simulating run-off on synthetic topography over a wide range of spatial scales. Results provide a simplified expression for an effective saturated hydraulic conductivity that can be used to relate a distribution of small-scale K_s measurements to infiltration and run-off generation over larger spatial scales. Finally, we use a hydrologic model based on K_e^* to simulate run-off and debris flow initiation at a recently burned catchment in the Santa Ana Mountains, CA, USA, and compare results to those obtained using an infiltration model based on the Soil Conservation Service Curve Number.