Topography noise and resolution effects on lava flow forecasting

The two main parameters that are required to forecast lava flows, are the eruption effusion rates and the pre-eruption topography. We seek here to understand how topography spatiotemporal resolution, and vertical errors affect lava flow forecasts. We develop a basic fluid mechanical flow model that combined with theory allows us to derive errors in down-slope flow advance, volume, and effusion rate. We find that topographic noise acts to retard and widen flows. We show that relative noise greater than ~10\% of the flow thickness significantly degrades advance and the retrieval of effusion rate and viscosity estimates. The effusion rate uncertainty scales with the vertical topographic error, spatial sampling, and the time sampling frequency. This work provides a basis for understanding the impacts that repeat topography data sampling and precision have on forecasting lava flow advance rate and coverage for volcano science and eruption hazard response.