Circumventing storage limitations in variational data assimilation studies

The aim of data assimilation is to infer the state of a system from a geophysical model and possibly incomplete or nonuniformly distributed spatiotemporal observational data. Used extensively in engineering control theory applications, data assimilation has relatively recently been introduced into meteorological forecasting, natural-resource recovery modeling, and climate dynamics. Variations data assimilation is a promising assimilation technique in which it is assumed that the state of the system is an extrema of a carefully chosen objective function. Provided that an adjoint model is available, the required model gradients can be computed by integrating the model forward and its adjoint backward. the gradients are then used to extremize the cost function with a suitable iterative or conjugate gradient solver. The problem addressed in this study is the explosive growth in both on-line computer memory and remote storage requirements of large-scale assimilation studies. This imposes a severe physical limitation on the size of assimilation studies, even on the largest computers. By using a recursive strategy, a schedule can be constructed that enables the forward/adjoint model runs to be performed in such a way that storage requirements can be traded for longer computational times. This generally applicable strategy enables data assimilation studies on significantly larger domains that would otherwise be possible given particular hardware constraints. The authors show that this tradeoff is indeed viable and that when the schedule is optimized, the storage and computational times grow at most logarithmically