Downscaling precipitation extremes Rob Wilby* & Chris Dawson * Climate Change Unit, Environment Agency Department of Computer Science, Loughborough

Motivation One of the most important – and yet least well-understood – consequences of future changes in climate may be alterations in regional hydrologic cycles and subsequent changes in the quantity and quality of regional water resources. Gleick (1987: 137)

A hierarchy of precipitation extremes Sub-daily - flash floods, urban drainage and water quality Daily - riverine flooding and tidal surges Multi-day - extensive floodplain inundation Single-season - surface water dominated systems Multi-season - groundwater dominated resource zones Annual - strategic water supply

Why consider multi-site/ multi-day precipitation totals….? ….winter 2000/01! ….recent trends

Experimental development of SDSM multi-site functionality and extremes Two approaches to daily precipitation extremes: –Compositing predictors associated with the largest daily precipitation totals across SEE and NWE. –A conditional re-sampling method for multi-site, multi-day precipitation downscaling. Demonstrated using multiple stations in Eastern England (EE) and the Scottish Borders (SB). Concluding remarks.

Variations in predictor strength Correlation between daily wet–day amounts at Eskdalemuir (55º 19 N, 3º 12 W) and mean sea level pressure (MSLP), and near surface specific humidity (QSUR) over NWE, 1961–1990.

Compositing daily extremes in SEE

Compositing daily extremes in NWE

Conditional re-sampling method Inverse normal transformation of area-average wet-day amounts across EE and SB. Obtain coefficients and standard error of model residuals from linear regression of transformed amounts versus regional predictor variables. Downscale area-average amounts and map to nearest neighbour wet-day amount/date in training set. Resample single site amounts contributing to the area average on the chosen date(s).

Many conditional variables (such as nonzero precipitation amounts and sunshine hours) are highly skewed. Therefore, a range of transformations for r t are available in SDSM, including exponential, fourth root, and inverse normal (version 2.3 only). Illustration of the inverse normal transformation Inverse normal transformation

Conditional variables, including nonzero precipitation amounts r t are simulated by where Z is a K 1 vector of standard Gaussian (i.e., normally distributed, with zero mean and unit variance) explanatory variables, is the coefficient matrix, and is an error term which is modelled stochastically (by assuming zero mean and variance equal to model standard error). Conditional variables

Downscaled (red) daily precipitation totals using NCEP predictors for compared with observations (blue). Example results for Kew Gardens, London

The location of the climate model grid boxes and stations used to evaluate the muliti-site downscaling of precipitation extremes using SDSM. Multi-site modelling

Frequency of predictor variable selection for individual stations included in EE area model; * included in SB area model

N -day annual max winter precipitation in EE Solid lines represent observations; other symbols are model syntheses (triangles = VAR ; squares = RND ; circles = DET model).

N -day annual max winter precipitation in SB

Solid lines represent observations; other symbols are model syntheses (triangles = VAR ; squares = RND ; circles = DET model). Annual maximum winter precipitation (20- and 60-day totals) at selected stations

Pairwise correlations of station daily precipitation series Inter-station correlations for all pairs of stations in EE and SB EE SB

Solid lines represent exponential decay functions fitted to the observations (filled circles); open symbols are model syntheses (triangles = VAR ; squares = RND ; circles = DET model). Correlation decay lengths for all pairs of stations in EE

Concluding remarks Compositing could isolate key predictors for extremes Regional and seasonal dependency of predictor set Practical advantages of re-sampling via area-averages Fully deterministic re-sampling was least successful How best to stratify data for re-sampling? More work needed on spatial aspects of extremes