1. Downscaling ensembles using forecast analogs Jeff Whitaker and Tom Hamill tom.hamill@noaa.gov jeffrey.s.whitaker@noaa.gov

2. CDC MRF Reforecast Data Set Definition: a data set of retrospective numerical forecasts using the same model to generate real-time forecasts Model: T62L28 MRF, circa 1998 ( http://www.cdc.noaa.gov/people/jeffrey.s.whitaker/refcst for details). Initial States: NCEP Reanalysis plus 7 +/- bred modes (Toth and Kalnay 1993). Duration: 15 days runs every day at 00Z from 19781101 to now. ( http://www.cdc.noaa.gov/people/jeffrey.s.whitaker/refcst/week2 ). Data: Selected fields (winds, hgt, temp on 5 press levels, precip, t2m, u10m, v10m, pwat, prmsl, rh700, heating). NCEP/NCAR reanalysis verifying fields included ( Web form to download at http://www.cdc.noaa.gov/reforecast ).

3. Applications Predictability studies Diagnosis of model error Statistical correction of real-time forecasts –6-10 day and week 2 CPC temp and precip tercile probabilities  (now operational) Uses logistic regression at stations (Hamill et al, 2004, MWR, p. 1434)

4. HSS scores 9/10/03- 9/9/04 Week 2 Temp: Official: 14.74 CDC: 16.80 Precip: Official: 10.27 CDC: 8.09

5. But these forecasts are very coarse resolution… Finer-scale detail is desirable, especially for precip. How can we take large-scale NWP/GCM output and “downscale” it to provide skillful higher-resolution forecasts? How to correct for ‘regime-dependant’ errors?

6. Analog technique: (pioneered by van den Dool, Toth, von Storch, others) Step 1: make today’s forecast Step 3: extract observed weather Observed Wx, 3/1/83 Observed Wx, 2/12/95 Observed Wx, 1/16/98 Forecast Analog 3, 3/1/83 Forecast analog 1, 2/12/95 Forecast analog 2, 1/16/98 TODAY’S ENS MEAN PRECIP FORECAST BMA? Step 2: find dates of old analogs

7. Local analogs are patched together Initial implementation very simple: Single forecast field (precip). L2 norm (rms) using ens. mean fcst. Analog ensemble members receive equal weight. 50 analog members - NARR.

8. Example: 4-6 day analog forecasts, valid 29-31 Dec 1996)

9. Skill of Analog Forecasts

11. 3 days

12. Skill of Analog Forecasts

13. Application - Tercile Forecasts Prob of above normal for 2nd N days of forecast ( N =1 to 6). All JFMs 1979-20035 (no analogs within +/- 45 days of verifying analysis used). NARR precip over entire CONUS. day 2 days 3-4 days 4-6 days 5-8 days 6-10

14. Analog Forecast Skill - Upper Tercile

21. Analog Size Analog Search Region (75 analogs) Finding analogs for each member: 5 analogs per member, skill is degraded (BSS = 0.183). Forecast variable, analog weighting? Free parameters (WCoast, 4-6 day upper decile) # of Analogs255075100 BSS0.20500.21790.21850.2168 Grid Points41636 BSS0.19670.21850.2165

22. Conclusions Forecast analogs (using ensemble mean) hold great promise. – preserves covariances. – non-parameteric. – corrects for regime-dependant errors. – produces 3-day lead time improvement in PQPF skill relative to operational system run at twice the resolution.