Variational chemical data assimilation with approximate adjoints

Data assimilation obtains improved estimates of the state of a physical system by combining imperfect model results with sparse and noisy observations of reality. In the four-dimensional variational (4D-Var) framework, data assimilation is formulated as an optimization problem, which is solved using gradient-based optimization methods. The 4D-Var gradient is obtained by forcing the adjoint model with observation increments. The construction of the adjoint model requires considerable development effort. Moreover, the computation time associated with the adjoint model is significant (typically, a multiple of the time needed to run the forward model). In this paper we investigate the use of approximate gradients in variational data assimilation. The approximate gradients need to be sufficiently accurate to ensure that the numerical optimization algorithm makes progress toward the maximum likelihood solution. The approximate gradients are obtained through simplified adjoint models; this decreases the adjoint development effort, and reduces the CPU time and the storage requirements associated with the computation of the 4D-Var gradient. The resulting approach, named quasi-4D-Var (Q4D-Var), is illustrated on a global chemical data assimilation problem using satellite observations and the GEOS-Chem chemical transport model. (C) 2011 Elsevier Ltd. All rights reserved.