Dr. Ralph Peterson, Dr. Bill Bua, Dr. Wassila Thiaw

1. Use of the National Centers for Environmental Prediction (NCEP) Ensemble Prediction System in the Weather Forecast Process Dr. Ralph Peterson, Dr. Bill Bua, Dr. Wassila Thiaw

2. Talk Outline • Review of rationale for general ensemble prediction system design and products • The NCEP ensemble prediction system (EPS) • Examples of ensemble output • Training resources • Summary and references

3. What is an ensemble? • A group of forecasts with the same valid time • Before ensemble prediction systems were developed, what kind of ensembles were available? • One model from different initial times • Different models from the same initial time • Some combination of these • So …. • If you’ve used the GFS, UKMET, and ECMWF in the forecast process at the same time, you’ve used a form of ensemble prediction!

4. Ensemble Prediction Systems (EPSs) • Atmospheric behaviors that have been a problem for deterministic forecasts, are used to create EPSs • Forecast sensitivity to initial conditions (chaotic behavior) • Forecast sensitivity to imperfect model formulations • Why not use these characteristics intelligently to come up with a range of plausible forecast outcomes? • Recognizes limitations of atmospheric science, and uses our understanding of the atmosphere to best advantage • Considers range of values for weather elements rather than a single expected value • Allows for determination of probability of extreme/severe events

5. Ensemble Prediction Systems (con’d) • How to “take advantage” of known atmospheric behavior in EPSs? • EPS methods typically include either or both of: • Different or “perturbed” initial conditions (ICs) • Method for “perturbation” chosen such that the perturbed ICs cover as much of the IC uncertainty as possible • Good IC uncertainty coverage with perturbations will lead to good (but not perfect) coverage of possible forecast outcomes. • Example: NCEP GFS-based EPS • “Perturb the NWP models”: Multiple models or same model with different model configurations (e.g. different parameterization schemes for convection, radiation, other physics) • Example: New North American Ensemble Forecast System (NAEFS) will combine two IC perturbation ensembles using different NWP models

6. NCEP Medium Range EPS configuration

7. Ensemble Transform Bred Vector (ETBV) Rescaling P1 forecast P2 forecast ANL P3 forecast P4 forecast …… t=t0 t=t0+2Δt t=t0+Δt • P1, P2, P3, P4 are independent (orthogonal) perturbation vectors • No positive and negative “bred pairs” any more • To centralize all perturbed vectors, sum of all vectors are equal to zero (want to have the control initial condition be at the center of the perturbations) • Scaling down by applying mask (scaling factor based on expected error size in initial conditions, which varies from place to place) • The direction of vectors will be tuned by ET to give the best ensemble forecast spread, while staying in the region of plausible initial states (dashed oval)

8. The NCEP EPS Cycle • How the cycling works • 14 initial random perturbations run for 6 hours • At 6 hours, take the 14 differences from each model run, “orthogonalize” them (ie. make them statistically independent of each other) and force differences to add to zero • Apply differences to “control” initial condition (from operational GFS but truncated to T126, 28 levels from T382, 64 levels) • Run forecast members to 384 hours, output forecast data every 6 hours

9. Why do we need to summarizeensemble data? • EPS presents a challenge in post-processing • Graphic shows a 500-hPa height forecast at 10 decameter intervals • Each ensemble member has a different color • Which member is which, and where are the atmospheric features important to the weather in any particular area? • This information must be simplified to be made useful in the forecast process.

10. The Ensemble Mean and Spread Diagram • Characteristics of mean • Arithmetic average of values from all ensemble members • The ensemble mean performs better on average than operational model on which it is based. Why? • Because predictable features remain intact, less predictable features are smoothed out • Characteristics of spread • Standard deviation of the ensemble members • Allows assessment of uncertainty, since more spread means more uncertainty

11. “Spaghetti” Plots Spaghetti Plot of 5500-m and 5670-m 500-hPa Heights, Initial Conditions Valid 12z 25 October 2006 • Plots at most two or three contours for ease of readability (here the 5500-m and 5670-m lines), each member in a different color • Operational GFS and ensemble mean are also shown • Gives qualitative picture of distribution of 500-hPa heights near chosen contour • Circled area shows uncertainty in initial position of shortwave trough south of Capetown.

12. Probability of Exceedance • Helps determine the probability of extreme events • Gives probability of exceeding meaningful threshold • Calculation represents count of what % of ensemble members exceed the threshold of interest • Adjustment may be made for systematic model bias (not done here, though) • Example here is for winds exceeding 30-kt at 10-m • Useful for shipping interests

13. Systematic Error Correction Past Forecasts/Verifications bias • Bias correction • Shifting the current ensemble mean forecast based on past ensemble mean forecast bias • Bias usually weighted toward more recent forecasts • To correct bias • Shift current forecast by amount of past forecast bias (in this case, a cold bias) • NOTE: Not dealing here with spread adjustments Past forecasts Past verifications Current Forecast Past bias Bias-corrected forecast Current forecast Past verifications

14. NCEP EPS Systematic Error Correction • Deals with errors in the GFS model, on which the NCEP EPS is based. • Random error cannot be adjusted for in ensemble forecasts. • Systematic error can be corrected by comparing past forecasts with verifications and applying the result to the ensemble forecasts. • Comparison period at NCEP is set to 50 days, with heaviest weight given to most recent verifications • The most recent flow regime model biases will be most heavily taken into account in bias correction. • If the flow regime has recently changed or is predicted to soon change, this may result in bias adjustment errors.

15. Bias Correction Method & Application • Bias Assessment: adaptive (Kalman Filter type) algorithm decaying averaging mean error = (1-w) * prior t.m.e + w * (f – a) • For separated cycles, each lead time and individual grid point, t.m.e = time mean error, w = weighting 6.6% • Test different decaying weights. • 0.25%, 0.5%, 1%, 2%, 5% and • 10%, respectively • Decide to use 2% (~ 50 days) • decaying accumulation bias • estimation 3.3% 1.6% Toth, Z., and Y. Zhu, 2001 • Bias Correction: application to NCEP operational ensemble 15 members

16. Africa Desk Ensemble Web Page • Ensemble products (at 12 hour intervals from 00 hr to 144 hrs): • Spaghetti plots • 500mb height (5500 and 5670, 5700 and 5870-m contours) • 10-m winds (20-kt and 30-kt contours) • 6-hr accumulated precipitation (50-mm contour) • Probability of exceedance • 10-m wind exceeding 20- and 30-kt • 6-hr accumulated precipitation exceeding 10- and 50-mm • Earlier ensemble forecasts can be obtained from links for other forecast runs.

17. Example Graphics from Web Page Spaghetti plot of 20-kt 10-m winds Spaghetti plot of 5700 and 5870-m 500-hPa heights

18. Training on Ensemble Forecasting • On UCAR/COMET web site (http://meted.ucar.edu, click on NWP (forecasting)) • Module: Ensemble Forecasting Explained(http://meted.ucar.edu/nwp/pcu1/ensemble/) • “Webcast”: Introduction to Ensemble Forecasting (http://meted.ucar.edu/nwp/pcu1/ensemble_webcast) • Case studies (not from Africa, unfortunately): http://meted.ucar.edu/nwp/pcu3/cases

19. http://meted.ucar.edu/nwp/pcu1/ensemble/

20. http://meted.ucar.edu/nwp/pcu1/ensemble_webcast/

21. Case Studies Using Ensemble Forecasts: http://meted.ucar.edu/nwp/pcu3/cases/

22. Training from NCEP: Ensemble Prediction Systems http://www.hpc.ncep.noaa.gov/ensembletraining/

23. Intro to Ensemble Prediction via ECWMF

24. Summary • Ensemble prediction systems (EPSs) reflect: • Our current understanding of the atmosphere as a chaotic system and • Our current limitations in NWP modeling • The NCEP EPS uses initial condition uncertainty to produce its forecasts • EPS data must be “condensed” using statistical methods, including • Plotting only some contour values (spaghetti plots) • Using the mean and “spread” (standard deviation) of the forecasts for EPS output • Developing probability distributions and probability of exceedance products for important weather thresholds • Bias correction can improve EPS forecasts • Graphical forecasts for southern Africa are available through the NCEP Climate Prediction Center web page • Training is available on the intelligent use of ensembles from a number of sources, including UCAR/COMET, NCEP and the ECMWF.

25. (Not exhaustive) Reference List • Gleick, J., 1987. Chaos. Penguin Books, 352 pp. • Tennant, W., Z. Toth and K.Rae 2006: Application of the NCEP Ensemble Prediction System to Medium-range Forecasting in South Africa: New Products, Benefits and Challenges. Wea. Forecasting, in press.  • Toth, Z., and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer. Meteor. Soc.,74, 2317–2330. • Toth, Z., E. Kalnay, S. M. Tracton, R. Wobus, and J. Irwin, 1997: A synoptic evaluation of the NCEP ensemble. Wea. Forecasting, 12, 140-153. • Toth, Z., Y. Zhu, and T. Marchok, 2001: On the ability of ensembles to distinguish between forecasts with small and large uncertainty. Wea. Forecasting, 16, 436-477. • Tracton, M. S., and E. Kalnay, 1993: Operational Ensemble Prediction at the National Meteorological Center: Practical Aspects. Wea. Forecasting, 8, 379-398.