Low-rank approximations for computing observation impact in 4D-Var data assimilation

We present an efficient computational framework to quantify the impact of individual observations in four dimensional variational data assimilation. The proposed methodology uses first and second order adjoint sensitivity analysis, together with matrix-free algorithms to obtain low-rank approximations of observation impact matrix. We illustrate the application of this methodology to important applications such as data pruning and the identification of faulty sensors for a two dimensional shallow water test system.