Sensitivity analysis applied to a variational data assimilation of a simulated pollution transport problem

Abstract

SummaryUnderstanding the impact of the changes in pollutant emission from a foreign region onto a target region is a key factor for taking appropriate mitigating actions. This requires a sensitivity analysis of a response function (defined on the target region) with respect to the source(s) of pollutant(s). The basic and straightforward approach to sensitivity analysis consists of multiple simulations of the pollution transport model with variations of the parameters that define the source of the pollutant. A more systematic approach uses the adjoint of the pollution transport model derived from applying the principle of variations. Both approaches assume that the transport velocity and the initial distribution of the pollutant are known. However, when observations of both the velocity and concentration fields are available, the transport velocity and the initial distribution of the pollutant are given by the solution of a data assimilation problem. As a consequence, the sensitivity analysis should be carried out on the optimality system of the data assimilation problem, and not on the direct model alone. This leads to a sensitivity analysis that involves the second‐order adjoint model, which is presented in the present work. It is especially shown theoretically and with numerical experiments that the sensitivity on the optimality system includes important terms that are ignored by the sensitivity on the direct model. The latter shows only the direct effects of the variation of the source on the response function while the first shows the indirect effects in addition to the direct effects. Copyright © 2016 John Wiley & Sons, Ltd.