Séminaire
Data Assimilation (DA) - Numerical Prediction (NP) systems are designed to monitor the behavior of natural systems. We interpret such systems as shadowing with observations. In this presentation, a general and minimalistic approach is proposed to model the behavior of the coupled Nature - Observing - Data Assimilation - Prediction (NODAP) system. In a General Error Behavior (GEB) model, we decomposes the difference between the natural and simulated systems (i.e., error variance characterized by a wide spectrum of amplification factors) into just two components (one fast amplifying, and another decaying).
In case of successful shadowing, the distance in the amplifying subspace between the natural and simulated systems is found to reflect an equilibrium between information gained in the DA step from observing the natural system, and information lost in the NP step of the DA-NP subsystem due to the chaotic expansion of errors. The region that supports successful long term shadowing is quantitatively studied in the parameter space of observational information accessed by DA, chaotic error growth, the analysis ratio between the assumed observational and background forecast error variances, and the amount of noise added in the DA step.
A Statistical Analysis and Forecast Error (SAFE) estimation method, independent of DA-NP assumptions or methods is described to diagnose the quality of shadowing (i.e., analysis error variance) in coupled NODAP systems. A method for the Prediction of Impacts from Changes in Observing Systems (PICOS) will also be presented and demonstrated. Other potential applications of the general error behavior model include targeted observations and ensemble forecasting.
muller@lmd.ens.fr