Linking the Anomaly Initialization Approach to the Mapping Paradigm: A Proof-of-Concept Study

Seasonal-to-decadal predictions are initialized using observations of the present climatic state in full field initialization (FFI). Such model integrations undergo a drift toward the model attractor due to model deficiencies that incur a bias in the model. The anomaly initialization (AI) approach reduces the drift by adding an estimate of the bias onto the observations at the expense of a larger initial error. In this study FFI is associated with the fidelity paradigm, and AI is associated with an instance of the mapping paradigm, in which the initial conditions are mapped onto the imperfect model attractor by adding a fixed error term; the mapped state on the model attractor should correspond to the nature state. Two diagnosis tools assess how well AI conforms to its own paradigm under various circumstances of model error: the degree of approximation of the model attractor is measured by calculating the overlap of the AI initial conditions PDF with the model PDF; and the sensitivity to random error in the initial conditions reveals how well the selected initial conditions on the model attractor correspond to the nature states. As a useful reference, the initial conditions of FFI are subjected to the same analysis. Conducting hindcast experiments using a hierarchy of low-order coupled climate models, it is shown that the initial conditions generated using AI approximate the model attractor only under certain conditions: differences in higher-than-first-order moments between the model and nature PDFs must be negligible. Where such conditions fail, FFI is likely to perform better.

Full-field and anomaly initialization using a low-order climate model: a comparison and proposals for advanced formulations

Initialization techniques for seasonal-to-decadal climate predictions fall into two main categories; namely full-field initialization (FFI) and anomaly initialization (AI). In the FFI case the initial model state is replaced by the best possible available estimate of the real state. By doing so the initial error is efficiently reduced but, due to the unavoidable presence of model deficiencies, once the model is let free to run a prediction, its trajectory drifts away from the observations no matter how small the initial error is. This problem is partly overcome with AI where the aim is to forecast future anomalies by assimilating observed anomalies on an estimate of the model climate. The large variety of experimental setups, models and observational networks adopted worldwide make it difficult to draw firm conclusions on the respective advantages and drawbacks of FFI and AI, or to identify distinctive lines for improvement. The lack of a unified mathematical framework adds an additional difficulty toward the design of adequate initialization strategies that fit the desired forecast horizon, observational network and model at hand. Here we compare FFI and AI using a low-order climate model of nine ordinary differential equations and use the notation and concepts of data assimilation theory to highlight their error scaling properties. This analysis suggests better performances using FFI when a good observational network is available and reveals the direct relation of its skill with the observational accuracy. The skill of AI appears, however, mostly related to the model quality and clear increases of skill can only be expected in coincidence with model upgrades. We have compared FFI and AI in experiments in which either the full system or the atmosphere and ocean were independently initialized. In the former case FFI shows better and longer-lasting improvements, with skillful predictions until month 30. In the initialization of single compartments, the best performance is obtained when the stabler component of the model (the ocean) is initialized, but with FFI it is possible to have some predictive skill even when the most unstable compartment (the extratropical atmosphere) is observed. Two advanced formulations, least-square initialization (LSI) and exploring parameter uncertainty (EPU), are introduced. Using LSI the initialization makes use of model statistics to propagate information from observation locations to the entire model domain. Numerical results show that LSI improves the performance of FFI in all the situations when only a portion of the system's state is observed. EPU is an online drift correction method in which the drift caused by the parametric error is estimated using a short-time evolution law and is then removed during the forecast run. Its implementation in conjunction with FFI allows us to improve the prediction skill within the first forecast year. Finally, the application of these results in the context of realistic climate models is discussed.