Polynomial Chaos Quadrature-based Minimum Variance Approach for Source Parameters Estimation

We present a polynomial chaos based minimum variance formulation to solve inverse problems. The utility of the proposed approach is evaluated by considering the ash transport problem arising due to volcanic eruption. Volcanic ash advisory centers generally makes use of mathematical models for column eruption and advection and diffusion of ash cloud in atmosphere. These models require input data on source conditions such as vent radius, vent velocity and distribution of ash-particle size. The inputs are usually not well constrained, and estimates of the uncertainty in the inputs is needed to make accurate predictions of cloud motion. The recent eruption of Eyjafjallajökull, Iceland in April 2010 is considered as test example. For validation, the puff advection and diffusion model is used to hindcast the motion of the ash cloud through time concentrating on the period 14-16 April 2010. Variability in the height and loading of the eruption is introduced through the volcano column model bent. Output uncertainty due to uncertain input parameters is determined with a polynomial chaos quadrature (PCQ)-based sampling of the multidimensional puff input vector space. Furthermore, the posterior distribution for input parameters is obtained by assimilating satellite imagery data with PCQ predictions using a minimum variance approach.