Abstract
Statistical emulators are a key tool for rapidly producing probabilistic hazard analysis of geophysical processes. Given output data computed for a relatively small number of parameter inputs, an emulator interpolates the data, providing the expected value of the output at untried inputs and an estimate of error at that point. In this work, we propose to fit Gaussian Process emulators to the output from a volcanic ash transport model, Ash3d. Our goal is to predict the simulated volcanic ash thickness from Ash3d at a location of interest using the emulator. Our approach is motivated by two challenges to fitting emulators—characterizing the input wind field and interactions between that wind field and variable grain sizes. We resolve these challenges by using physical knowledge on tephra dispersal. We propose new physically motivated variables as inputs and use normalized output as the response for fitting the emulator. Subsetting based on the initial conditions is also critical in our emulator construction. Simulation studies characterize the accuracy and efficiency of our emulator construction and also reveal its current limitations. Our work represents the first emulator construction for volcanic ash transport models with considerations of the simulated physical process.
Highlights
Statistical emulators are a powerful tool used in uncertainty analysis and statistical inversion
By exploring the relationship between the inputs and output from the simulation data, we find that this is related to three main factors: (i) simulations could have the same dominant grain size under two physically distinct scenarios: with or without wind; (ii) dominant grain size calculated from the semi-analytical solution (equation (2.7)) and determined from Ash3d simulation could be different even with the same initial conditions; and (iii) we neglect the wind speed above the source height in calculating values of lj, λj and τj
The simulated physical process is controlled by the advection–diffusion equation solved by the simulator Ash3d
Summary
Statistical emulators are a powerful tool used in uncertainty analysis and statistical inversion. Say from a moderate number of large numerical simulations that solve a system of differential equations, statistical emulators rapidly provide an approximation of the simulation output at untested input initial conditions, and give an estimate of the possible variability in that approximation [1]. Emulators-based hazard analysis for forecasting or reconstructing an eruption that combines models and data will be explored in future work. As it is still unclear what the best way is to properly and effectively construct statistical emulators for volcanic ash transport models, we think that it is necessary to begin with relatively simple scenarios. We present them here hoping that they could potentially help future studies inherit contributions from the present work, and build up and improve the current emulator construction or avoid pitfalls noted in this work, and propose alternative, better solutions
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