Downscaling ensembles using forecast analogs

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

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

10. Skill of Analog Forecasts

11. Skill of Analog Forecasts 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

15. Analog Forecast Skill - Upper Tercile

16. Analog Forecast Skill - Upper Tercile

17. Analog Forecast Skill - Upper Tercile

18. Analog Forecast Skill - Upper Tercile

19. Analog Forecast Skill - Upper Tercile

20. Analog Forecast Skill - Upper Tercile

21. Free parameters(WCoast, 4-6 day upper decile) • 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?

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.