Spatial Analysis to Quantify Numerical Model Bias and Dependence: How Many Climate Models Are There?

A limited number of complex numerical models that simulate the Earth's atmosphere, ocean, and land processes are the primary tool to study how climate may change over the next century due to anthropogenic emissions of greenhouse gases. A standard assumption is that these climate models are random samples from a distribution of possible models centered around the true climate. This implies that agreement with observations and the predictive skill of climate models will improve as more models are added to an average of the models. In this article we present a statistical methodology to quantify whether climate models are indeed unbiased and whether and where model biases are correlated across models. We consider the stimulated mean state and the simulated trend over the period 1970-1999 for Northern Hemisphere summer and winter temperature. The key to the statistical analysis is a spatial model for the bias of each climate model and the use of kernel smoothing to estimate the correlations of biases across different climate models. The spatial model is particularly important to determine statistical significance of the estimated correlation under the hypothesis of independent climate models. Our results suggest that most of the climate model bias patterns are indeed correlated. In particular, climate models developed by the same institution have highly correlated biases. Also, somewhat surprisingly, we find evidence that the model skills for simulating the mean climate and simulating the warming trends are not strongly related.