Multi-model ensemble post-processing and the replicate Earth paradigm

(Manuscript available on-line in Climate Dynamics)

Craig H. BishopNaval Research Laboratory, Monterey

Gab AbramowitzClimate Change Research Centre, UNSW

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

• Behaviour across replicate Earths defines the PDF

• ClimEnsemble forecasts can be viewed as attempts to create replicate Earths conditioned on the observations used for model development and initialization

Slartibartfast: Magrathean planet designerHitchhikers guide to the Galaxy (D. Adams)

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

1

Transform original models to new models using

where , and are all constants chosen so that positive

weights for which 1 can be found for which

(1

i i

i e i e

e

K

i ii

x x

x x x x

w w

e1

2 2

e e e1

) is the minimum error variance estimate, and

(2) is the variance of the obs about

K

i ii

K

i ii

w x

w x y

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.

ix iw

Forecast Test• Take an ensemble of K CMIP5 climate forecasts initialized in

the late 1800s and subject to prescribed future Green house gas forcing scenarios.

• Replace real 20th century observations by pseudo-observations from one of the models and then use these to derive the ensemble transformation weights.

• Apply the derived transformation to the 21st century ensemble and measure the performance of this transformed ensemble.

• Repeat the experiment using a different model as the pseudo-Earth

Distribution of forecast improvementsImprovements are relative to ensemble mean

Forecast improvements are significant!

Application of method to climate forecasts

• Derive transformation weights using real 20th 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

Transformation significantly affects regional variation of predicted warming

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 CMIP5 ensembles results in CPD predictions that relative to the unprocessed ensemble have:

1. less variance2. more warming north of 45 North for all scenarios except the RCP85 scenario3. less warming otherwise – particularly for the RCP85 scenario