1. A BAYESIAN ENSEMBLE METHOD FOR CLIMATE CHANGE PROJECTION
Sven Kotlarski
ETH Zurich
Buser C., Künsch H.R., Lüthi D., Wild M. and Schär C. (2009): Estimating Uncertainties in Predicting Climate Distributions: A Bayesian Ensemble Method. Submitted to Climate Dynamics.
Weber A. (2008): Probabilistic Predictions of the Future Seasonal Precipitation and Temperature in the Alps. Master Thesis at ETH Zurich.

2. OVERVIEW
Bayesian approach to combine projections of different GCM/RCM combinations into an ensemble projection
Extension of Tebaldi et al. (2005)
Method explicitly accounts for (temporally varying) model biases
Output: PDF for future seasonal mean 2m temperature (DJF, JJA) averaged over European Alps
Bivariate extension (precipitation)
Model data: PRUDENCE RCMs (CTRL and SCEN)
5 models (CHRM, CLM, HIRHAM, RCAO, ARPEGE)
Observations: CRU
OVERVIEW
METHOD
RESULTS
extension wrt Tebaldi 2005: change in interannual variations in addition to shift in mean, RCM instead of GCM

3. σi = σ0 · bi (bias of variability)
BASICS
RCM i (detrended) N(μi,σi2)
Obs (detrended) N(μ0,σ02) T f
Bias:
μi = μ0 + βi (bias of mean)
σi = σ0 · bi (bias of variability)
apply βi and bi to scenario PDF
OVERVIEW
METHOD
RESULTS
assumption: model results represent "true" climate up to an additive and multiplicative bias
allow for small bias changes Δβi with ΣiΔβi2 small
obtained by chosing an appropriate prior distribution of bias changes Δβi
similar method for bi
implicit weighting! T f

4. IS BIAS INDEPENDENT OF CLIMATIC STATE?
Observations
(quantiles: ordered and detrended model output)
CTRL (dito)
Winter temperatures (yearly)
OVERVIEW
METHOD
RESULTS
Models systematically too cold or too warm
Bias ≈ constant
Summer temperatures (yearly)
CTRL (dito)
Observations
(quantiles: ordered and detrended model output)
Bias ≠ constant
Overestimation of temperature variability

5. TWO APPROACHES TO COPE WITH BIAS
Assume that relation between model and observations is essentially constant (extrapolation of bias)
OVERVIEW
METHOD
RESULTS
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Assume that bias is essentially constant (temperature shift correctly reproduced)

6. +5.4°C +3.4°C RESULTS: SUMMER observations (CTRL) individual RCMs
OVERVIEW
METHOD
RESULTS
+5.4°C
+3.4°C
individual RCMs
multi model projection
( )
observations (CTRL)

7. only small difference in expected temperature change
RESULTS: WINTER
OVERVIEW
METHOD
RESULTS
only small difference in expected temperature change
(reason: models approx. reproduce interannual variability of winter temperature in CTRL climate)

8. BIVARIATE EXTENSION: TEMPERATURE + PRECIP
(Weber, 2008)
OVERVIEW
METHOD
RESULTS
THANK YOU!
CTRL climate
SCEN climate
RCMs
Summer drying, wetter conditions in winter
Temperature shift larger in summer than in winter