Empirical model for predicting erosion on slope covered by unconsolidated tephra

Volcanic eruption is known as multi-hazards to the surrounding environment and society causing the formation of lahar as the frequent hazards that shortly occurred due to airborne tephra after an eruption. Erosion triggered by rainfall on unconsolidated tephra material, such as volcanic ash, is the primary lahar initiation mechanism. The time and scale of lahars vary based on eruptions and watershed conditions. The variability of the erosion process is driven by a set of local factors including the grain size and spatial distribution of volcanic ash thickness, slope, and rainfall intensity. Laboratory simulation experiments were conducted in a 3.00 m long, 0.75 m wide, and 0.50 m deep flume to study the relationship of volcanic ash erosion rate to three driven parameters, namely slope, rainfall intensity, and volcanic ash thickness. Three slope gradients were selected to represent gentle (14.1%), mild (26.8%), and steep (46.6%) slopes. Meanwhile, the rainfall intensity ranged from 0.65 to 1.85 mm.min^-1, and the variations of volcanic ash layer thickness were 1.00 cm; 2.50 cm; and 5.00 cm. The erosion rate model was generated from a dimensional analysis accommodating slope, rainfall intensity, flow discharge, and the ratio of critical and applied boundary shear stress as independent variables. The variable coefficients were obtained by parameter optimization of experiment data through nonlinear regression analysis. The erosion rate model performance was tested using the Nash-Sutcliffe model Efficiency (NSE), Index of Agreement (IOA), and Root Mean Square Error (RMSE). The performance of the volcanic ash erosion rate model was proven to be satisfactory with the NSE>0.75, IOA>0.95, and RMSE values ranging from 0.005 to 0.009. This model has proven applicable better for volcanic ash erosion than other erosion models which are sandy soil material-based experiments because of the specific characteristics of volcanic material itself. The volcanic ash erosion model in this study can be implemented to predict the sediment yield of tephra as part of volcanic disaster mitigation.