Linear Inverse Modeling for Coupled Atmosphere-Ocean Ensemble Climate Prediction

Paleoclimate data assimilation (PDA) experiments reconstruct climate fields by objectively blending information from climate models and proxy observations. Due to high computational cost and relatively low forecast skill, most reconstruction experiments omit the prediction step, where a forecast is made from the previously reconstructed state to the next time proxy data is available. In order to enable this critical aspect of PDA, we propose an efficient method of generating forecast ensembles of coupled climate fields using a linear inverse model (LIM). We describe the general calibration of a LIM on multiple fields using a two-step empirical orthogonal function field compression to efficiently represent the state. We find that a LIM calibrated on global climate model (GCM) data yields skillful forecasts, including for out-of-sample tests on data from a different GCM. The deterministic forecast skill tests for scalar indices show that the LIM outperforms damped persistence at leads up to 3years and has skill up to 10years for global average sea surface temperature. Analysis of 1-year forecasts reveals that the LIM captures dynamic climate features with local and remote predictability related to teleconnections. The forecast ensemble characteristics of the LIM, which in part determine the weighting of information for PDA experiments, show that the LIM generally produces ensemble forecast errors that are 10% to 70% larger than ensemble variance for 1-year forecasts on data representative of the last millennium. These results show that the LIM produces ensembles with reasonable calibration but also that LIMs for PDA may require some variance tuning to work optimally for data assimilation experiments. Plain Language Summary Climate models are complex codes that are expensive to run, which limits their applicability to a wide range of problems. For example, reconstructing the climate history of Earth before the widespread availability of instrumental measurements involves blending proxy information (e.g., tree rings and ice cores) with climate model data. Typically, because long climate model simulations are expensive, most studies do not perform this blending process using a forecast from the climate model, so information from the proxies is not transferred between reconstructed years. Here, we propose a lightweight statistical approximation to the climate models. This simplified linear inverse model (LIM) captures the predictable aspects of the climate models, along with uncertainty, at a drastically lower cost. We show quantitatively that a LIM approximates well many important features of the climate system, outperforms a basic persistence forecast model, and produces reasonable measures of forecast uncertainty.