Downscaling Downscaling precipitation extremesprecipitation extremes

Rob Wilby* & Chris Dawson†

* Climate Change Unit, Environment Agency† Department of Computer Science, Loughborough

MotivationMotivation

“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 extremesA 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 Experimental development of SDSM multi-site functionality and extremesmulti-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.

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MSLP QSUR

Variations in predictor strengthVariations 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.

Predictor variable means for the largest 100 daily precipitation amounts across SEE

DJF JJARankPredictor Mean Predictor Mean

1 FSURSE 1.79 SSURSE 1.582 VSURSE 1.69 S850SE 1.513 DSURSE 1.59 S500SE 1.484 F850SE 1.58 S850SW 1.425 FSURSW 1.53 SSURSW 1.416 VSURSW 1.44 S500SW 1.337 DSURSW 1.42 TSURSE 1.158 F850SW 1.42 TSURSW 1.269 H850SW 1.35 ZSURSE 0.9010 MSLPSW 1.31 V500SE 0.78Bold denotes significant at p<0.05

Compositing daily extremes in SEECompositing daily extremes in SEE

Predictor variable means for the largest 100 daily precipitation amounts across NWE

DJF JJARankPredictor Mean Predictor Mean

1 RSURWA 0.98 S500WA 1.672 TSURWA 0.86 SSURWA 1.613 R850WA 0.83 S850WA 1.564 TSURIR 0.81 SSURIR 1.455 R850IR 0.81 S850IR 1.416 RSURIR 0.69 S500IR 1.307 S850WA 0.67 TSURWA 1.128 SSURIR 0.67 TSURIR 1.069 SSURWA 0.66 ZSURIR 0.9910 H850IR 0.60 Z850IR 0.86Bold denotes significant at p<0.05

Compositing daily extremes in NWECompositing daily extremes in NWE

Conditional re-sampling methodConditional 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 rt are available in SDSM, including exponential, fourth root, and inverse normal (version 2.3 only).

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Illustration of the inverse normal transformation

Inverse normal transformationInverse normal transformation

Conditional variables, including nonzero precipitation amounts rt are simulated by

ε+β=rt z

where Z is a K1 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 variablesConditional variables

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Precipitation total (tenths mm)

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Downscaled (red) daily precipitation totals using NCEP predictors for 1976-1990 compared with observations (blue).

Example results for Kew Gardens, LondonExample 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 modellingMulti-site modelling

Predictor Description EE(n=12)

SB(n=12)

Q500 †*

H500 †*

VWND *

VORT *

MSLPRSUR *

QSUR †

F500 *

UWND †

U500U850V850 †

V500H850Z850F850D850

Specific humidity at 500 hPa500 hPa geopotential heightNear surface southerly windNear surface vorticityMean sea level pressureNear surface relative humidityNear surface specific humidityWind strength at 500 hPaNear surface westerly windWesterly wind at 500 hPaWesterly wind at 850 hPaSoutherly wind at 850 hPaSoutherly wind at 500 hPa850 hPa geopotential heightVorticity at 850 hPaWind strength at 850 hPaDivergence at 850 hPa

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127975915332011010

Frequency of predictor variable selection Frequency of predictor variable selection for individual stationsfor individual stations

† included in EE area model; * included in SB area model

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NN-day annual max winter precipitation in EE-day annual max winter precipitation in EE

Solid lines represent observations; other symbols are model syntheses (triangles = VAR; squares = RND; circles = DET model).

Solid lines represent observations; other symbols are model syntheses (triangles = VAR; squares = RND; circles = DET model).

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NN-day annual max winter precipitation in SB-day annual max winter precipitation in SB

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Solid lines represent observations; other symbols are model syntheses (triangles = VAR; squares = RND; circles = DET model).

Annual maximum winter precipitation Annual maximum winter precipitation (20- and 60-day totals) at selected stations(20- and 60-day totals) at selected stations

Pairwise correlations of station daily precipitation series 1961-1990

Inter-station correlations for all pairs of Inter-station correlations for all pairs of stations in EE and SBstations in EE and SB

VAR

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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 Correlation decay lengths for all pairs of stations in EEfor all pairs of stations in EE

Concluding remarksConcluding 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