Uncertainty components estimates in transient climate projections. Bias of moment-based estimators in the single time and time series approaches.

In most climate impact studies, model uncertainty in projections is estimatedas the empirical variance of the climate responses for the different modelingchains. These estimates are however biased. We explore the importance ofthe bias for a simple but classical configuration where uncertainties in projectionsare composed of two sources: model uncertainty and internal climatevariability. We derive exact formulation of the bias. It is positive, i.e. theempirical variance tends to overestimate the true model uncertainty variance.It can be especially high when a single time ANOVA is used for the analysis.In the most critical configurations, when the number of members availablefor each modeling chain is small (≤ 3) and when internal variability explainsmost of total uncertainty variance (75% or more), the overestimation is higherthan 100% of the true model uncertainty variance. The bias is considerablysmaller with a time series ANOVA approach, owing to the multiple time stepsaccounted for. The longer the transient time period used for the analysis,the smaller the bias. When a quasi-ergodic ANOVA approach is applied todecadal data for the whole 1980-2100 period, the bias is up to 2.5 to 20 timessmaller than that obtained with a single time approach, depending on the projectionlead time. Whatever the approach, the bias is likely to be not negligiblefor a large number of climate impact studies resulting in a likely large overestimationof the contribution of model uncertainty to total variance. In manycases, classical empirical estimators of model uncertainty should be thus biascorrected