A study on the optimization of the deployment of targeted observations using adjoint‐based methods

A new adjoint‐based method to find the optimal deployment of targeted observations, called Kalman Filter Sensitivity (KFS), is introduced. The major advantage of this adjoint‐based method is that it allows direct computation of the reduction of the forecast‐score error variance that would result from future deployment of targeted observations. This method is applied in a very simple one‐dimensional context, and is then compared to other adjoint‐based products, such as classical gradients and gradients with respect to observations. The major conclusion is that the deployment of targeted observation is strongly constrained by the aspect ratio between the length‐scale of the sensitivity area and the length‐scale of the analysis‐error covariance matrix. This very simple example also clearly illustrates that the reduction of forecast‐error variance is stronger for assimilation schemes which have a smaller characteristic length‐scale. Finally, the KFS technique is applied in a diagnostic way (i.e. once the observations are done) to four FASTEX cases. For these cases, the reduction of the forecasterror variance is in agreement with the efficiency of targeted observations as previously studied. A preliminary step towards an operational use has been performed on FASTEX IOP18, and results seem to validate the KFS approach of targeting.