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.
The relationship between atmospheric boundary layer (ABL) depth uncertainty and uncertainty in atmospheric transport and dispersion (ATD) simulations is investigated by examining profiles of predicted concentrations of a contaminant. Because ensembles are an important method for quantifying uncertainty in ATD simulations, this work focuses on the utilization and analysis of ensemble members' ABL structures for ATD simulations. A 12-member physics ensemble of meteorological model simulations drives a 12-member explicit ensemble of ATD simulations. The relationship between ABL depth and plume depth is investigated using ensemble members, which vary both the relevant model physics and the numerical methods used to diagnose ABL depth. New analysis methods are used to analyze ensemble output within an ABL-depth relative framework. Uncertainty due to ABL depth calculation methodology is investigated via a four-member mini-ensemble. When subjected to a continuous tracer release, concentration variability among the ensemble members is largest near the ABL top during the daytime, apparently because of uncertainty in ABL depth. This persists to the second day of the simulation for the 4-member diagnosis mini-ensemble, which varies only the ABL depth, but for the 12-member physics ensemble the concentration variability is large throughout the daytime ABL. This suggests that the increased within-ABL concentration variability on the second day is due to larger differences among the ensemble members' predicted meteorological conditions rather than being solely due to differences in the ABL depth diagnosis methods. This work demonstrates new analysis methods for the relationship between ABL depth and plume depth within an ensemble framework and provides motivation for directly including ABL depth uncertainty from a meteorological model into an ATD model.
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