Estimating future changes in daily precipitation distribution from GCM simulations 11 th International Meeting on Statistical Climatology Edinburgh, July 2010 Jonathan Eden* and Martin Widmann School of Geography, Earth and Environmental Sciences, University of Birmingham, UK. School of Geography, Earth and Environmental Sciences, University of Birmingham, UK.Acknowledgements: Xiaoming Cai and Chris Kidd (University of Birmingham) David Grawe (Universität Hamburg, Germany) Sebastian Rast (Max-Planck-Institut fuer Meteorologie, Hamburg, Germany)

Simulating daily precipitation Introduction – Method and Setup – Results – Summary Changes in extremes; relative to (IPCC AR4, adapted from Tebaldi et al. (2006).

Performing a nudged simulation Simulated precipitation Parameterisations ERA-40 reanalysis Large-scale circulation reflects temporal variability in observed record. Simulated precipitation able to capture temporal variability. Large-scale circulation ECHAM5 GCM simulation ( ) T63 L31 - Prognostic variables nudged towards corresponding ERA-40 fields. Krishnamurti et al. (1991); Kaas et al. (2000); Eden et al. (submitted) Introduction – Method and Setup – Results – Summary

MOS downscaling correction Parameterisations Large-scale circulation Observed precipitation Downscaling Robust MOS downscaling models. ECHAM5 GCM simulation ( ) T63 L31 Simulated precipitation able to capture temporal variability. Simulated precipitation Large-scale circulation reflects temporal variability in observed record. Introduction – Method and Setup – Results – Summary

Skill of simulated precipitation – monthly means - Correlations of simulated and observed monthly mean precipitation for all months of the year ( ). - Normal simulation exhibits weak correlation; ~zero - Nudged simulation able to represent interannual variability; clear to see where model performance is high. - MOS downscaling correction all show good, though spatially varying, skill and outperform traditional perfect prog approaches. Eden et al. (submitted, J. Clim) Introduction – Method and Setup – Results – Summary

Daily precipitation: Comparison with observations Introduction – Method and Setup – Results – Summary NORM – E-OBS NUDG – E-OBS European RMSE in simulation of daily precipitation at different quantiles ( ).

Long-term extreme daily precipitation ( ) Introduction – Method and Setup – Results – Summary DJF JJA

Downscaling 1: Quantile mapping Introduction – Method and Setup – Results – Summary - Leave-one-out cross validation used to estimate observations using independent fitting period. - Corrections for each year ( ) derived from distributions of observed and simulated precipitation across all other years. - Each empirical distribution fitted with two-parameter gamma distribution. Example CDF correction derivation

Downscaling 1: Quantile mapping Introduction – Method and Setup – Results – Summary - Correlation between land-only E-OBS and ‘correction’ (using cross-validation); DJF precipitation, Method shows good skill in much of western and southern Europe.

Two approaches to linking a predictand time series (in this case daily precipitation) to a two-dimensional time-dependent predictor field: -one-dimensional singular value decomposition (SVD) (also known as maximum covariance analysis). -one-dimensional canonical correlation analysis (CCA) (or equivalently PC multiple linear regression). - See Widmann (2005) for details on methods. - Predictor variable is ECHAM5 simulated precipitation. - Size of spatial domain is constant. - Only for British Isles at present. Introduction – Method and Setup – Results – Summary Downscaling 2: Non-local MOS using SVD and CCA

Introduction – Method and Setup – Results – Summary SVD CCA (5PCs) Correlation between observed and corrected daily winter (DJF) precipitation ( ).

Towards a correction of future projections Introduction – Method and Setup – Results – Summary Percentage change in 90 th percentile DJF precipitation; relative to ECHAM5 A1B scenarioDownscaled correction - Downscaled correction based on quantile mapping. - Correction can be considered skillful where overall model skill is high.

Summary and outlook Quantification of the GCM precipitation skill given a simulated large-scale circulation extends to skill of daily precipitation simulated Both local (quantile mapping) and non-local (SVD and CCA) downscaling corrections have been developed. Quantile mapping shows good skill, but potential of non-local methods is unclear. FUTURE: -Focus on precipitation extremes; potential for estimating changes in extreme value distribution. -Identical analysis for other GCMs and for other regions where high-quality observational data is available. Introduction – Method and Setup – Results – Summary

Thank you

Downscaling 1: Heaviest precipitation events (DJF) Introduction – Method and Setup – Results – Summary Difference in corrected and observed 90 th percentile of DJF precipitation on wet days. - Corrected precipitation is generally skillful. - Largest errors apparent in mountainous regions of central Europe. Correlation of average precipitation on 5 wettest days (DJF; ). - Average of precipitation of 5 wettest days