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 todata assimilation and adaptive observations is formulated and illustrated for an extended Kalman filter and for an OI/3DVar 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.

Contents

1. Introduction
2. Adaptive observations in the Lorenz 95 system - Methodology
3. Adaptive observations in the Lorenz 95 system - Results
4. Reduced rank prediction of forecast error variance reductions in an operational NWP context
5. Discussion
6. Conclusions
7. References