Recent developments in data assimilation for atmosphere and ocean Adaptive observations, the Hessian metric and singular vectors

Techniques for planning adaptive observations that are based on tangent-linear models and their adjoints are discussed. The emphasis is on the validation of techniques that predict the statistically expected impact of additional non-routine observations on the forecast error. The concepts are illustrated using the Lorenz-95 system, which is a low-dimensional system that has similar error growth characteristics as operational NWP systems. The objective of a consistent approach to data assimilation and adaptive observations is formulated and illustrated for an extended Kalman filter and for an OI/3D-Var system. A reduced rank technique is introduced. It predicts forecast error variance in a singular vector subspace. The reduced rank predictions of forecast error variance are evaluated for both assimilation systems. Furthermore, a few examples are given of possible applications of the reduced rank estimate in the context of an operational variational assimilation scheme.