A New Method to Estimate the Maximum Sensitivity in Climate Simulation: Nonlinear Ensemble Parameter Perturbation

Model parameters can introduce significant uncertainties in climate simulations. Sensitivity analysis provides a way to quantify such uncertainties. Existing sensitivity analysis, however, cannot estimate the maximum sensitivity in climate simulations due to parameter uncertainties. In this study, we propose a new concept of nonlinear ensemble parameter perturbation (NEPP) to estimate the maximum effect of parameter uncertainties on the simulation of Earth's climate. The NEPP is obtained by solving a maximization problem which is defined by the maximum variation of a unique ensemble of short-term predictions with large enough members and whose gradient is estimated by an ensemble-based approach. This method is applied to investigate the maximum variation of the climate of Lorenz-63 model and a sophisticated climate model, respectively, caused by uncertain parameters. It is found that the NEPP method is capable of estimating the maximum sensitivity in climate simulations due to parameter uncertainties. The results also illustrate that there is a high relevance between short-term prediction sensitivities and long-term climatic sensitivities. Apart from being independent of the initial conditions, the NEPP belongs to the most unstable mode of parameter perturbation for the model climate. Furthermore, the NEPP depends only weakly on, although related to, the time scales of short-term predictions.