A stochastic germ-grain model to estimate wildfire induced debris flow risks in a changing climate

Debris flows following wildfire can wash sediment and ash into streams and reservoirs, contaminating water supplies for cities and towns. The fire behavior and erosion processes preceding these contamination events are frequently modeled separately. However climate change may alter both the size and frequency of fires, as well as the intensity and frequency of post-fire erosive storm events. What are the water quality risks associated with these possible simultaneous changes to both the fire and erosive rainfall regimes? When assessing changes in risk due to climate change we argue that the most important property of the system is the "volume" of the intersection in space and time of burnt areas and debris-flow generating storms. The modeling focus should therefore be directed at quantifying changes in the overlap (in space and time) between fire and debris-flow generating storm events, rather than at the geophysical processes that drive them individually. In this presentation we propose the use of a germ-grain based coverage process model to quantify the size of this intersection as a function of the regional fire regime and the local rainfall properties. In this new model we consider fires and debris-flow generating storms as independent stochastic processes with properties of spatial extent, temporal duration, and frequency of occurrence. The approach is illustrated in Figure 1, where we have superimposed random realizations of fires (large discs) and erosive storm processes (small discs) in space (horizontal axis) and time (vertical axis). The volume of intersection of the two processes, shown by the overlap of the large and small discs, gives a measure of hazard of debris flows, and we can quantify how the magnitude of this hazard changes in response to changing fire and rainfall regimes. We use fire history and climatology data to parameterize the germ-grain model for historic conditions in the South East of Australia to illustrate how the model parameters can be obtained from readily available data.