Estimating ensemble size requirements of AGCM simulations

This study investigates the statistical methods for determining the minimum sample size necessary for an ensemble set generated with an atmospheric general circulation model. Due to the limits imposed by computational cost, an improved and a priori estimation of ensemble size is highly desirable. In this context, the methodology shown here is an important step for defining the number of integrations required in a numerical experiment. We show that the global distribution of ensemble size has a spatial and seasonal dependence. In addition, the ensemble size is dependent on the variable being analyzed and the geographic region of interest. For example, we show that a relatively large number of integrations are required to simulate the seasonal mean air temperature at 925hPa and the sea-level pressure at mid to high latitudes. The seasonal mean precipitation, however, can be well represented with relatively few integrations at high latitudes, but it requires a large ensemble size at the tropics, particularly over the monsoon regions. These latitudinal differences in the number of integrations are associated with the internal variability in the model. Furthermore, differences among the variable fields partly arise due to the distinct shapes of the associated property distributions. Both Gaussian and nonparametric statistics are considered here. The Wilcoxon Rank Sum test reveals that the air temperature, sea-level pressure and precipitation do not follow a Gaussian distribution in some regions of the globe. Thus, we suggest the nonparametric approach be used whenever the normal assumption is violated or cannot be assessed. This study is based on the determination of the sampling size of ensemble simulations using the statistical Gaussian method of Wehner (2000). We extend this previous by considering a nonparametric approach.