Program in Applied Mathematical and Computational Sciences
The University of Iowa
14 MLH Iowa City, IA 52242
Joint work with Gregory R. Carmichael, Department of Chemical and Biochemical Engineering, The University of Iowa, Iowa City, IA 52242, firstname.lastname@example.org.
The 4D-Var data assimilation in air quality modeling finds an initial state of the system that minimizes the errors between model predictions and observations of the chemical species over the interval of assimilation. Some of the problems to consider are the high memory storage and CPU time requirements, the estimation of the model errors and the sparse distribution of data. In this paper we show that in the 4D-Var context a coupled numerical treatment of the transport-chemistry processes has great benefits on the qualitative and quantitative aspects of the assimilation. The forward model uses a 2-stage Rosenbrock method with approximate Jacobian (W-method). The advantage over operator splitting is that the stiff transients in the chemical system are eliminated, which allows for large step sizes and reduces the storage requirements of the forward integration. Implementation of the adjoint code is done by combining automatic differentiation tools (ADIFOR, TAMC) with symbolic processing (KPP), which leads to exact computation of the gradients and allows flexibility for the chemical model. Numerical results and a qualitative analysis are presented for a 1-D air pollution model.