Effect of random perturbations on adaptive observation techniques

An observation sensitivity (OS) method to identify targeted observations is implemented in the context of four-dimensional variational (4D-Var) data assimilation. This methodology is compared with the well-established adjoint sensitivity (AS) method using a nonlinear Burgers equation as a test model. Automatic differentiation software is used to implement the first-order adjoint model (ADM) to calculate the gradient of the cost function required in the 4D-Var minimization algorithm and in the AS computations and the second-order ADM to obtain information on the Hessian matrix of the 4D-Var cost that is necessary in the OS computations. Numerical results indicate that the observation-targeting is particularly successful in reducing the forecast error for moderate Reynolds numbers. The potential benefits of the OS targeting approach over the AS are investigated. The effect of random perturbations on the performance of these adaptive observation techniques is also analyzed.