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Multi-model ensemble post-processing and the replicate Earth paradigm (Manuscript available on-line in Climate Dynamics) Multi-model ensemble post-processing and the replicate Earth paradigm (Manuscript available on-line in Climate Dynamics) Craig H. Bishop Naval Research Laboratory, Monterey Gab Abramowitz Climate Change Research Centre, UNSW

Slartibartfast and the replicate Earth ensemble • Imagine a very large number of Earth Slartibartfast and the replicate Earth ensemble • Imagine a very large number of Earth replicates that experienced the same orbital / solar / GHG forcing • Each Earth has a slightly different atmosphere / ocean state but all are consistent with observations Slartibartfast: Magrathean planet designer Hitchhikers guide to the Galaxy (D. Adams) • Behaviour across replicate Earths defines the PDF • Clim. Ensemble forecasts can be viewed as attempts to create replicate Earths conditioned on the observations used for model development and initialization

Properties of replicate Earth Ensemble 1. Mean of distribution of replicate Earths is the Properties of replicate Earth Ensemble 1. Mean of distribution of replicate Earths is the linear combination of Earths that minimises distance from our Earth’s observations. 2. Time average of variance of replicate Earths equals mean square error of climate forecast based on mean of the replicate Earths. Multi-model ensembles do not look like replicate Earths

Replicate System Ensemble Transformation Ensemble created by sampling with frequency is like a replicate Replicate System Ensemble Transformation Ensemble created by sampling with frequency is like a replicate Earth ensemble in that (a) its sample mean is the minimum error variance estimate, and (b) its variance equals the error variance of the sample mean.

Forecast Test • Take an ensemble of K CMIP 5 climate forecasts initialized in Forecast Test • Take an ensemble of K CMIP 5 climate forecasts initialized in the late 1800 s and subject to prescribed future Green house gas forcing scenarios. • Replace real 20 th century observations by pseudoobservations from one of the models and then use these to derive the ensemble transformation weights. • Apply the derived transformation to the 21 st century ensemble and measure the performance of this transformed ensemble. • Repeat the experiment using a different model as the pseudo. Earth

Distribution of forecast Improvements are relative to ensemble mean improvements Forecast improvements are significant! Distribution of forecast Improvements are relative to ensemble mean improvements Forecast improvements are significant!

Application of method to climate forecasts • Derive transformation weights using real 20 th Application of method to climate forecasts • Derive transformation weights using real 20 th century observations • Use weights to make a forecast of the CPD under a variety of predicted Green house gas forcing scenarios.

Apply to 4 distinct forcing scenarios Apply to 4 distinct forcing scenarios

Transformation significantly affects regional variation of predicted warming Transformation significantly affects regional variation of predicted warming

Conclusions • The degree of model independence between the members of an ensemble influences Conclusions • The degree of model independence between the members of an ensemble influences the skill of a multi-model mean. • Earth replicate ensemble an observationally plausible PD. Nevertheless, it provides: – A framework for understanding role of chaos in climate prediction, – properties that ensemble post-processing schemes should aim to emulate • The replicate system post-processing method led to a marked reduction in RMSE of prediction in both hindcast and forecast mode. • Application of technique to CMIP 5 ensembles results in CPD predictions that relative to the unprocessed ensemble have: 1. less variance 2. more warming north of 45 North for all scenarios except the RCP 85 scenario 3. less warming otherwise – particularly for the RCP 85 scenario