Model error Treatment in Data Assimilation and the initialization of long-term predictions
The prediction problem in geophysical fluid dynamics typically relies on two complementary elements: the model and the data. The mathematical model, and its discretized version, embodies our knowledge about the laws governing the system evolution, while the data are samples of the system's state. They give complementary information on the same object. The sequence of operations that merges model and data to obtain a possibly improved estimate of the flow's state is usually known as data assimilation.
Data assimilation in geophysics, particularly in numerical weather prediction, has experienced a long and fruitful stream of research in the last decades. As a result the overall accuracy of the Earth's system estimate and prediction, particularly the atmosphere, has improved dramatically. Despite this trend of improvement, the treatment of model error in data assimilation procedures is still, in most instances, done following simple assumptions such as the absence of time correlation. The lack of attention on model error is in part justified by the fact that on the time scale of numerical weather prediction, where most of the geophysical data assimilation advancements have occurred, its influence is reasonably considered small as compared to the initial condition error that grows in view of the chaotic nature of the dynamics. Nevertheless, the improvement in data assimilation techniques and observational networks on the one hand, and the recent grow of interest in seasonal-to-decadal prediction on the other, has placed model error, and its treatment in data assimilation, as a main concern and a key priority.
In the present contribution we describe a new approach in which the deterministic evolution of the model error is described based on a short-time approximation suitable for realistic applications and used to estimate the model error contribution in the state estimate. We have distinguished two situations: first assuming that model error originates only from a misspecification of the parameters, and second from the presence of unresolved scales. The approach has been applied in the context of sequential and variational methods, for state and parameter estimation. Results using different model dynamics are presented.
The second part of the talk discusses the problem of initializing seasonal-to-decadal predictions and presents two proposals for advanced formulations. Nowadays, initialization techniques fall into two main categories, namely Full Field Initialization (FFI) and Anomaly Initialization (AI) where the aim is to forecast future anomalies by assimilating observed anomalies on an estimate of the model climate, and the model drift is partly reduced.
The large variety of experimental setups, models and observational networks adopted worldwide make difficult to draw firm conclusions on the respective advantages and drawbacks of FFI and AI, or identifying distinctive lines for improvement. We studied FFI and AI using a low order climate model and compared them in experiments in which either the full system or the atmosphere and ocean independently was initialized. Two advanced formulations, LSI and EPU, are discussed. Using LSI the initialization makes use of model statistics to propagate information from observation locations to the entire model domain. EPU is an online drift correction method in which the drift caused by the parametric error is estimated and removed during the forecast run.