1. WCRP Extremes Workshop - 27-29 Sept 2010 Detecting human influence on extreme daily temperature at regional scales Photo: F. Zwiers (Long-tailed Jaeger) Francis Zwiers 1, Xuebin Zhang 2, Yang Feng 2 1 Pacific Climate Impacts Consortium, University of Victoria, Victoria, Canada 2 Climate Research Division, Environment Canada, Toronto, Canada

2. Outline WCRP Extremes Workshop - 27-29 Sept 2010 Introduction Changes in the mean state An analog for extremes Example application Discussion Photo: F. Zwiers

3. Introduction The causes of changes in mean temperatures have been robustly attributed on global and regional scales The literature on the causes of changes in extreme temperature is still developing Principal study was by Christidis et al (2005) –Warmest night  ANT influence robustly detected –Coldest day, coldest night  ANT less robustly detected –Warmest day  ANT not detected Recent work strengthens these results, extends to all four extreme temp indices and to regions WCRP Extremes Workshop - 27-29 Sept 2010

4. Evaluate amplitude estimates Observations 1946-56 Model 1986-96 Total least squares regression in reduced dimension space Filtering and projection onto reduced dimension space Evaluate goodness of fit Weaver and Zwiers, 2000 WCRP Extremes Workshop - 27-29 Sept 2010

5. Have a Gaussian setup Space-time observations vector (decadal means) Space-time signal matrix (one column per signal) Vector of scaling factors Covariance structure WCRP Extremes Workshop - 27-29 Sept 2010 From a statistical perspective

6. Ultimate small sample problem Fingerprints to look for are from models. Error covariance structure also from models (eg., control runs) Do generalized linear regression (optimize signal-to- noise ratio) Take some aspects of signal uncertainty into account using either a total least squares or errors-in-variables approach WCRP Extremes Workshop - 27-29 Sept 2010 A few features Photo: F. Zwiers

7. Space-time vector of annual extremes Space-time signal matrix (one column per signal) Vector of scaling factors Vector of scale parameters Vector of shape parameters Note that these are vectors WCRP Extremes Workshop - 27-29 Sept 2010 An extremes analogue

8. Photo: F. Zwiers Photo: F. Zwiers (Arctic Tern) Amount of high quality, gridded daily data is limited Assume that the location parameter varies with time and space (e.g., due to external forcing) Assume that scale and shape parameters constant in time Unable to explicitly represent spatial or temporal dependence Unable to reduce dimension so as to include only scales where variability of extremes is well simulated WCRP Extremes Workshop - 27-29 Sept 2010 A few features / limitations

9. Typically have ensembles of 20 th century simulations from a given model –M ensemble members  M annual extremes per year Assume that signal changes slowly –If roughly constant within decades  10M annual extremes per decade Fit GEV to these decadal samples at grid boxes Retain the decadal fields of location parameter estimates as signal Average across multiple models to reduce signal uncertainty Currently consider only one signal at a time (either ALL or ANT) How do we get the signal? WCRP Extremes Workshop - 27-29 Sept 2010

10. Observed annual temperature extremes TNn (annual minimum daily minimum temperature) TNx (annual maximum daily minimum temperature) TXn (annual minimum daily maximum temperature) TXx (annual maximum daily maximum temperature) –HadEX, compiled by Alexander et al. 2006 –Dataset covers 1946-2000; we analyze 1961-2000 Simulated annual temperature extremes –ANT – 7 models, 25 simulations –ALL – 3 models, 11 simulations What extremes do we consider?

11. Observations from HadEX, Alexander et al., 2006 Express signal in decade j at gridbox k as Note that same scaling factor β is used everywhere Obtain mle for β by profile likelihood technique WCRP Extremes Workshop - 27-29 Sept 2010 How do we fit the GEV to obs?

12. From internal variability –Block bootstrap on observations using 5-year blocks –For a given signal, resample residuals, re-estimate β Includes ENSO timescale Does not include lower frequency timescales Do not resample in space, so variability in re-estimated β’s reflects effects of spatial dependence Signal uncertainty due to model simulated internal variability –Block bootstrap on model output Compare with approximate confidence intervals from profile likelihood Check goodness of fit WCRP Extremes Workshop - 27-29 Sept 2010 How do we assess uncertainty?

13. Results: Global TNn TXn TNx TXx Coldest night Coldest day Warmest night Warmest day WCRP Extremes Workshop - 27-29 Sept 2010

14. Results: Regional WCRP Extremes Workshop - 27-29 Sept 2010

15. TNn TXn TNx TXx Coldest night Coldest day Warmest night Warmest day Implied change in waiting times (1990’s vs 1960’s)

16. Spatial smoothing of signal, scale, shape Attempt to separate two signals Unable to optimize Need better approach for taking signal uncertainty into account – what is the parallel to TLS/EIV? Should be able to calculate FAR directly Potentially a constraint on future extremes WCRP Extremes Workshop - 27-29 Sept 2010 Refinements / Discussion

17. WCRP Extremes Workshop - 27-29 Sept 2010 Photo: F. Zwiers The End Photo: F. Zwiers