Forced response and internal variability in ensembles of climate simulations: identification and analysis using linear dynamical mode decomposition

Estimating climate response to observed and projected increases in atmospheric greenhouse gases usually requires averaging among multiple independent simulations of computationally expensive global climate models to filter out the internal climate variability. Studies have shown that advanced pattern recognition methods allow one to obtain accurate estimates of the forced climate signal from just a handful of such climate realizations. The accuracy of these methods for a fixed ensemble size, however, decreases with an increasing magnitude of the low-frequency, decadal and longer internal climate variability. Here we generalize a previously developed Bayesian methodology of Linear Dynamical Mode (LDM) decomposition for spatially extended time series to enable joint identification and analysis of forced signal and internal variability in ensembles of climate simulations, a methodology dubbed here an ensemble LDM, or ELDM. The new ELDM method is shown to outperform its pattern-recognition competitors by more accurately isolating the forced signal in small ensembles of both toy- and state-of-the-art climate-model simulations. It is able to do so by explicitly recognizing a non-random structure of the internal variability, identified by the ELDM algorithm alongside the optimal forced-signal estimate, which allows one to study possible dynamical connections between the two types of variability. The optimal ELDM filtering provides a unique opportunity for objective intercomparison of decadal and longer climate variability across different global climate models—a task that proved difficult due to uncertainties associated with the noisy character and limited length of historical climate simulations combined with parameter uncertainties of alternative signal-detection methods.