Detecting human influence on extreme daily temperature at regional scales

1. WCRP Extremes Workshop - 27-29 Sept 2010 Detecting human influence on extreme daily temperature at regional scales Francis Zwiers1, Xuebin Zhang2, Yang Feng2 1Pacific Climate Impacts Consortium, University of Victoria, Victoria, Canada 2Climate Research Division, Environment Canada, Toronto, Canada Photo: F. Zwiers (Long-tailed Jaeger)

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

3. WCRP Extremes Workshop - 27-29 Sept 2010 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

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

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

6. WCRP Extremes Workshop - 27-29 Sept 2010 A few features • 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 Photo: F. Zwiers

7. WCRP Extremes Workshop - 27-29 Sept 2010 An extremes analogue 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

8. WCRP Extremes Workshop - 27-29 Sept 2010 A few features / limitations • 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 Photo: F. Zwiers Photo: F. Zwiers (Arctic Tern)

9. WCRP Extremes Workshop - 27-29 Sept 2010 How do we get the signal? • Typically have ensembles of 20th 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)

10. What extremes do we consider? • 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

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

12. WCRP Extremes Workshop - 27-29 Sept 2010 How do we assess uncertainty? • 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

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

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

15. WCRP Extremes Workshop - 27-29 Sept 2010 Implied change in waiting times (1990’s vs 1960’s) TNn TXn TNx TXx Coldest night Coldest day Warmest night Warmest day

16. WCRP Extremes Workshop - 27-29 Sept 2010 Refinements / Discussion • 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

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