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A B S T R A C T We discuss the computation of observation sensitivities and observation impact for incremental variational data assimilation (VDA), accounting for the inner and outer loops. To fully account for the outer loops, a second-order adjoint of the data assimilation system is required, which makes it impractical for an operational data assimilation system. However, some approximations can be made that allow useful results to be obtained with multiple outer loop iterations, indoi:10.1111/j.1600-0870.2008.00349.x fatcat:r6ofbdli4baijc4w3w3xmxqpxe