Estimation of Volcanic Ash Emissions Using Trajectory-Based 4D-Var Data Assimilation

Volcanic ash forecasting is a crucial tool in hazard assessment and operational volcano monitoring. Emission parameters such as plume height, total emission mass, and vertical distribution of the emission plume rate are essential and important in the implementation of volcanic ash models. Therefore, estimation of emission parameters using available observations through data assimilation could help to increase the accuracy of forecasts and provide reliable advisory information. This paper focuses on the use of satellite total-ash-column data in 4D-Var based assimilations. Experiments show that it is very difficult to estimate the vertical distribution of effective volcanic ash injection rates from satellite-observed ash columns using a standard 4D-Var assimilation approach. This paper addresses the ill-posed nature of the assimilation problem from the perspective of a spurious relationship. To reduce the influence of a spurious relationship created by a radiate observation operator, an adjoint-free trajectory-based 4D-Var assimilation method is proposed, which is more accurate to estimate the vertical profile of volcanic ash from volcanic eruptions. The method seeks the optimal vertical distribution of emission rates of a reformulated cost function that computes the total difference between simulated and observed ash columns. A 3D simplified aerosol transport model and synthetic satellite observations are used to compare the results of both the standard method and the new method.