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 themapping paradigm, in which the initial conditions aremapped onto the imperfectmodel attractor by adding a fixed error term; the mapped state on themodel 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 themodel 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.