Forecasting wetting and drying of post-wildfire soils in response to precipitation: A time series optimization approach

Abstract:

Volumetric water content (VWC) in soils is critical for forecasting thresholds for runoff-driven erosion caused by rainfall. Even though theoretical relations (e.g., Richards equation) have been developed to quantify VWC in unsaturated granular soils, site-specific field conditions and hysteresis of suction and VWC in soil preclude their direct use. Although attempts have previously been made to forecast VWC using various time-series models (e.g., autoregressive integrated moving average or ARIMA), these approaches lack hydrologic foundations and perform poorly when used to forecast VWC over time periods longer than 24 hours.

In this work, we extend an existing Antecedent Water Index (AWI) based model to express VWC as a function of time and rainfall. AWI models typically overfit data and cannot be used for forecast VWC over long time periods. We developed a new model to overcome this limitation, which accumulates rainfall over a time window and fits a diverse range of wetting and drying curves. Hydraulic redistribution parameters in this model bear resemblance to hydrologic processes driven by gravity and suction. This model reasonably forecasts VWC using only initial VWC values and rainfall forecasts.

Experimental VWC data were collected from steep gradient post-wildfire sites in southern California. Rapid landscape change was observed in response to small to moderate rain storms. We formulated a mean-squared error minimization problem over the model parameters and optimized using genetic algorithms. We found that our model fits VWC data for 3 distinct soil textures, each occurring at 3 different depths below the ground surface (5 cm, 15 cm, and 30 cm). Our model successfully forecasts VWC trends, such as drying and wetting rate. To a certain extent, our model achieves spatial and seasonal generalizability. Our accumulative rainfall model is also applicable to continuous predictions, where VWC values are repeatedly used to predict future ones within a 12-hr time frame.