A genetic algorithm variational approach to data assimilation and application to volcanic emissions

Variational data assimilation methods optimize the match between an observed and a predicted field. These methods normally require information on error variances of both the analysis and the observations, which are sometimes difficult to obtain for transport and dispersion problems. Here, the variational problem is set up as a minimization problem that directly minimizes the root mean squared error of the difference between the observations and the prediction. In the context of atmospheric transport and dispersion, the solution of this optimization problem requires a robust technique. A genetic algorithm (GA) is used here for that solution, forming the GA-Variational (GA-Var) technique. The philosophy and formulation of the technique is described here. An advantage of the technique includes that it does not require observation or analysis error covariances nor information about any variables that are not directly assimilated. It can be employed in the context of either a forward assimilation problem or used to retrieve unknown source or meteorological information by solving the inverse problem. The details of the method are reviewed. As an example application, GA-Var is demonstrated for predicting the plume from a volcanic eruption. First the technique is employed to retrieve the unknown emission rate and the steering winds of the volcanic plume. Then that information is assimilated into a forward prediction of its transport and dispersion. Concentration data are derived from satellite data to determine the observed ash concentrations. A case study is made of the March 2009 eruption of Mount Redoubt in Alaska. The GA-Var technique is able to determine a wind speed and direction that matches the observations well and a reasonable emission rate.