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A Statistical DownScaling Model (SDSM) Primer Dr Rob Wilby King’s College London Presentation outline • A brief reminder • The Statistical DownScaling Model (SDSM) • Overview of software structure and data archive • Main functions of SDSM • A few cautionary remarks What impacts modellers need…... Point 1m 10km 50km 300km What climate modellers supply…... Statistical DownScaling Model Precipitation occurrence An nth order, two state process governs daily precipitation occurrence, with serially independent precipitation amounts on wet days π t = xβ + ε where t is the conditional probability of a wet day, X 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 random noise. Precipitation occurrence (cont.) The binary event of precipitation, Pt or no precipitation is determined by Pt = { 1, if utt 0, otherwise where ut denotes uniform independent random forcing for the occurrence process (probability density f[u] =1, 0 u 1). Notes: • Autocorrelation is incorporated implicitly by predictors • Separate equations may be specified for each month Conditional variables Conditional variables, including nonzero precipitation amounts rt are simulated by rt = zβ + ε 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 variables (cont.) Many conditional variables (such as nonzero precipitation amounts and sunshine hours) are strongly skewed to the right. Therefore, a range of transformations for rt are available in SDSM, including exponential, fourth root, and inverse normal (version 2.3 only). Illustration of the inverse normal transformation Cumulative probability ly Au gu Se st pt em be r O ct ob er N ov em be D r ec em be r Validation of SDSM (red) wet-day occurrence (%) 1976-1990 compared with observations (blue). Q95 Q05 Q50 40000 20000 0 01/01/76 0.4 0.2 0 10 100 1000 Validation of SDSM (red) daily precipitation totals 1976-1990 compared with observations (blue). Precipitation anomaly (%) CuSum (tenths mm) 60000 0.6 100.00 Observed 80000 0.8 Precipitation total (tenths mm) 120000 100000 1 1 Ju Ju ne ay M Ap r il 60 55 50 45 40 35 30 25 20 Ja nu ar y Fe br ua ry M ar ch Wet-days (%) Examples of SDSM performance (at Kew) 50.00 0.00 -50.00 -100.00 01/01/79 01/01/82 01/01/85 01/01/88 01/01/91 Validation of SDSM (violet, red, orange) cumulative precipitation totals (tenths mm) 1976-1990 compared with observations (blue). 1960 1980 2000 2020 2040 2060 2080 2100 20-day winter maximum precipitation anomalies (%) for the Eastern England grid-box of HadCM3 (grey) and for SDSM (red) under the A2 emission scenario. Structure and data archive Select predictand Quality control Station data Scatter plot Select predictors Screen variables NCEP data (Un)conditional process? Set model structure Transform variables Calibrate model Station and NCEP data NCEP predictors Downscale predictand GCM predictors Generate scenario Weather generator Model output Analyse results Compare results Chart results Impact assessment SDSM climate scenario generation SDSM file extensions and definitions Extension Explanation *.DAT Observed daily predictor and predictand files employed by the Calibrate and Weather Generator operations (input). *.PAR Meta–data and model parameter file produced by the Calibrate operation (output) and used by the Weather Generator and Generate Scenario operations (input). *.SIM Meta–data produced by the Weather Generator and Generate Scenario operations (output). *.OUT Daily predictand variable file produced by the Weather Generator and Generate Scenario operations (output). *.TXT Summary statistics produced by the Analyse operations (output). The HadCM3 cells used in the UKSDSM predictor set SC NIa SB NEb IR WA EE SWc SE aNI Scotland Northern Ireland Scottish Boarders Northeast England Ireland Wales Eastern England Southwest England Southern England = (SB+IR)/2 bNE = (SB+EE)/2 cSW = (WA+SE)/2 Daily variables held in the UKSDSM data archive Daily variable Code Precipitation prec Maximum temperature tmax Minimum temperature tmin Mean temperature temp Mean sea level pressure mslp 500 hPa geopotential height p500 850 hPa geopotential height p850 Near surface relative humidity rhum Relative humidity at 500 hPa height r500 Relative humidity at 850 hPa height r850 Near surface specific humidity shum Geostrophic airflow velocity **_f Vorticity **_z Zonal velocity component **_u Meridional velocity component **_v Wind direction **th Divergence **zh NCEP 1961–2000 × × × × × × × × × × × × × × HadCM2 GG 1961–2099 HadCM3 SRES 1961–2099 × × × × × × × × × × × × × × × × × × × × × × × × × × Generic nomenclature Each file in the archive complies with a generic nomenclature of the form [source] [variable] [grid box] . dat The source is denoted by characters 1–4, the variable name by characters 5–8, and the grid box code by characters 9– 10. All files have the extension *.dat. For example nceprhumee.dat indicates that the source is NCEP [ncep], the variable is near surface relative humidity [rhum], and the grid box is Eastern England [ee]. Relationship to UKCIP02 scenarios SDSM HadCM3H 1961-1990 2071-2100 Statistical downscaling 1961-2100 SRES (A2,B2) HadCM3 UKCIP02 HadCM3H 1961-1990 2071-2100 HadRM3 1961-1990 2071-2100 Pattern scaling 1990-2100 Baseline climatology 25 variables station 5km grid daily 1961-2100 monthly 2020s, 2050s, 2080s Main functions SDSM functions • • • • • • • Quality control and data transformation Selection of predictor variables Model calibration Weather generation (observed predictors) Statistical analyses of model output Graphing model output Scenario generation (climate model predictors) Example bar chart Example line chart Example scenario output Cautionary remarks Please remember • SDSM provides a parsimonious technique of scenario construction that complements other methods • SDSM should not be used uncritically as a “black box” (evaluate all relationships using independent data) • Local knowledge is an invaluable source of information when determining sensible combinations of predictors • Daily precipitation amount at individual stations is the most problematic variable to downscale • The plausibility of all SDSM scenarios depends on the realism of the climate model forcing • Try to apply multiple forcing scenarios (via different GCMs, ensemble members, time–slices, emission pathways, etc.) http://www.sdsm.org.uk/ http://www.cics.uvic.ca/scenarios/sdsm/select.cgi Further reading ** Conway, D., Wilby, R.L. and Jones, P.D. 1996. Precipitation and air flow indices over the British Isles. Climate Research, 7, 169–183. Hay, L.E., Wilby, R.L. and Leavesley, G.H. 2000. A comparison of delta change and downscaled GCM scenarios for three mountainous basins in the United States. Journal of the American Water Resources Association, 36, 387–397. Wilby, R.L. 1998. Statistical downscaling of daily precipitation using daily airflow and seasonal teleconnection indices. Climate Research, 10, 163–178. Wilby, R.L. 1997. Nonstationarity in daily precipitation series: implications for GCM downscaling using atmospheric circulation indices. International Journal of Climatology, 17, 439–454. Wilby, R.L. and Wigley, T.M.L. 2000. Precipitation predictors for downscaling: observed and General Circulation Model relationships. International Journal of Climatology, 20, 641–661. Wilby, R.L. and Wigley, T.M.L. 1997. Downscaling General Circulation Model output: a review of methods and limitations. Progress in Physical Geography, 21, 530–548. Wilby, R.L., Conway, D. and Jones, P.D. 2002. Prospects for downscaling seasonal precipitation variability using conditioned weather generator parameters. Hydrological Processes, in press. Wilby, R.L., Dawson, C.W. and Barrow, E.M. 2002. SDSM – a decision support tool for the assessment of regional climate change impacts. Environmental and Modelling Software, 17, 145–157. Wilby, R.L., Hay, L.E., Gutowski, W.J., Arritt, R.W., Tackle, E.S., Leavesley, G.H. and Clark, M. 2000. Hydrological responses to dynamically and statistically downscaled General Circulation Model output. Geophysical Research Letters, 27, 1199–1202. Wilby, R.L., Hassan, H. and Hanaki, K. 1998. Statistical downscaling of hydrometeorological variables using General Circulation Model output. Journal of Hydrology, 205, 1–19. Wilby, R.L., Wigley, T.M.L., Conway, D., Jones, P.D., Hewitson, B.C., Main, J. and Wilks, D.S. 1998. Statistical downscaling of General Circulation Model output: a comparison of methods. Water Resources Research, 34, 2995– 3008. Wilks, D.S. and Wilby, R.L. 1999. The weather generation game: a review of stochastic weather models. Progress in Physical Geography, 23, 329-357.