PNNL

Abstract

We consider the problem of estimating the ensemble sizes required to characterize the forced component and the internal variability of a range of extreme metrics. While we exploit existing large ensembles contributed to the CLIVAR Large Ensemble Project, our perspective is that of a modeling center that wants to estimate such sizes on the basis of an existing small ensemble (we use five members here). We therefore ask if such small-size ensemble is sufficient to estimate the population variance in a way accurate enough to apply a well established formula that can estimate the expected error as a function of n (the larger ensemble size). We find that indeed we can estimate errors in the estimation of the forced component for temperature and precipitation extreme metrics as a function of n on the basis of the estimates of the population variance based on five members. For a range of spatial and temporal scales, forcing levels and at least the two models considered here as our proof of concept, CESM1-CAM5 and CanESM2, it appears that an ensemble size of 20 or 25 members provides estimates of the forced component for the extreme metrics considered, within small absolute and percentage errors, and additional members after those add only marginal precision to the estimate, also when extreme value analysis is used. Consistently with this findings, when we ask about the ensemble size required to estimate the ensemble variance (a measure of internal variability) along the length of the simulation, and -- importantly -- about the ensemble size required to detect significant changes in such variance along the simulation with increased external forcings, we find that 5 to 10 ensemble members provide a statistically equivalent representation of this same variance when calculated on the basis of the full large ensemble size (up to 50 members in our study). While we recognize that there will always exists applications and metric definitions that will require larger statistical power and therefore ensemble sizes, our results suggests that for a wide range of analysis targets and scales an effective estimate of both forced component and internal variability can be achieved with sizes below 30 members, inviting consideration of the possibility of exploring additional sources of uncertainty, like physics parameter settings, when designing ensemble simulations.