Variational chemical data assimilation with approximate adjoints

6 Data assimilation obtains improved estimates of the state of a physical system by com7 bining imperfect model results with sparse and noisy observations of reality. In the four 8 dimensional variational (4D-Var) framework data assimilation is formulated as an opti9 mization problem, which is solved using gradient based optimization methods.The 4D10 Var gradient is obtained by forcing the adjoint model with observation increments. The 11 construction of the adjoint model requires considerable development effort. Moreover, 12 the compute time associated with the adjoint model is significant (typically, a multiple 13 of the time needed to run the forward model). 14 In this paper we investigate the use of approximate gradients in variational data assim15 ilation. The approximate gradients need to be sufficiently accurate to ensure that the 16 numerical optimization algorithm makes progress toward the maximum likelihood so17 lution. The approximate gradients are obtained through simplified adjoint models; this 18 decreases the adjoint development effort, and reduces the CPU time and the storage 19 requirements associated with the computation of the 4D-Var gradient. 20 Preprint submitted to Computers & Geosciences June 30, 2011 The resulting approach, named quasi 4D-Var (Q4D-Var), is illustrated on a global chemi21 cal data assimilation problem using satellite observations and the GEOS-Chem chemical 22 transport model. 23