Xingqin Fang and Bill Kuo NCAR/UCAR

1. Prediction of Extreme Rainfall of Typhoon Morakot (2009) with the WRF model:Part II: Ensemble Forecast with a New Probability Matching Scheme Xingqin Fang and Bill Kuo NCAR/UCAR

2. Outline • Background • The new probability-matching technique • Performance of probabilistic rainfall forecast • Performance of ensemble mean rainfall forecast • Summary

3. 1. Background --- Valuable QPF by ensemble? • The quantitative precipitation forecast (QPF) of the topography-enhanced typhoon heavy rainfall over Taiwan is challenging. • Ensemble forecast is necessary due to various uncertainties. • Low-resolution ensemble (LREN): computationally cheap, smooth large scales, but systematic under-prediction. • High-resolution ensemble (HREN): computationally expensive, more small scales, generally reasonable rainfall amount, but serious topography-locked over-prediction along the south tip of Central Mountain Range (CMR). • Ensemble tends to have too large track spread after landfall. • Question: • How to extract valuable QPF from ensemble at affordable cost? • Ensemble mean? Probability matching?

4. 1. Background --- Valuable ensemble mean rainfall? • The simple ensemble mean (SM) tends to smear the rainfall and reduce the maximum; excessive track spread also makes SM failing to capture realistic rainfall pattern. • The probability-matched ensemble mean (PM), which has the same spatial pattern as SM and the same frequency distribution as the entire ensemble, is often used to reproduce more realistic rainfall amount. • However, poor pattern representativeness of SM and poor frequency distribution representativeness of ensemble would impact PM’s performance. • For the topography-enhanced typhoon heavy rainfall over Taiwan, serious issues in high-resolution ensemble definitely impact PM’s performance and produce poor QPF guidance. • Question: How to get valuable ensemble mean rainfall?

5. Probability Matching: • Match the probability between SM and the entire ensemble population • Ebert (2001), MWR

6. SM – Simple mean PM – Probability matching

7. SM – Simple mean PM – Probability matching

8. Observation Analysis of observed rainfall from Central Weather Bureau

9. Rainfall forecast situations in 36-km ensemble • Systematic negative bias in rainfall amount. • Smooth pattern, no topography-locked over-prediction • Typical PM helps to increase maximum value based on SM rainfall distribution and the maximum of individual ensemble member. LREN_PM OBS SM OBS LREN_PM 3-h rainfall at 18/8-21/8 72-h rainfall ending at 00/9

10. Rainfall forecast situations in 4-km ensemble • Generally reasonable heavy rain amount. • Serious topography-locked over-prediction over Southern Taiwan. • Typical PM exaggerates the over-prediction bias. HREN_PM OBS VA HA 72-h rainfall ending at 00/9

11. Serious topography-locked over-prediction in 4-km ensembleover southern Taiwan Fang et al. 2011

12. 2. A new probability-matching technique • Suppose we have two real ensembles: • LREN---Large-sample-size low-resolution ensemble, i.e., 32-member 36-km • HREN---Small-sample-size high-resolution ensemble, i.e., 8-member 4-km • Basic hypotheses: • LREN mean can produce reasonable storm track. • Good relationship between track and rainfall. • Basic idea: • Based on LREN mean track, blend rainfall realizations in different resolutions (ignoring timing) to reconstruct a new “bogus” rainfall ensemble NEWEN: • Resample size, i.e., 16-member • On an arbitrary high-resolution grid, i.e., 2-km, by interpolation

13. Basic hypothesis: • --- LREN has similar or better track • Large scale circulation controls track. • 36-km is capable for track forecast. • 4-km on the contrary might suffer from model deficiencies and small sample size • Sampling error reduced by larger sample size of LREN. LREN: 32-member 36-km HREN: 8-membe 4-km

14. 2. A new probability-matching technique • Main features: • Basically, a probability-matching process needs an “ensemble” and a “pattern”. • The new technique is aiming to improve the “ensemble” and the “pattern” before probability matching by : • Using resampled HREN realizations as “ensemble”. • Performing “pattern” adjustment with LREN member: • Performing bias-correction for “ensemble” • remove top 1% (2.5%) before (after) landfall.

15. 2. A new probability-matching technique Two loops: Time loop: 3-h rainfall ensemble time series will be reconstructed if the matching process is run at 3-h interval. Member loop: at each time point, the new probability-matching technique is used repeatedly to build up “members” for NEWEN, with each “member” resembling one “ensemble mean”. Note: The new probability-matching technique is utilized to build up an “ensemble time series”, rather than an “ensemble mean” as done in a typical probability-matching technique.

16. Two loops of resampling around LREN mean track For time 18/8 For member 6

17. Two loops of resamplings around LREN mean track For member: 13 For time 18/8

18. 3. Performance of probabilistic rainfall forecast ---LREN, HREN, and NEWEN1 Better Time 18/8-21/8 Time evolution of 3-h rainfall RPS averaged over the land area in the HA by LREN, HREN, and NEWEN1.

19. 3-h rainfall RPS Time 18/8-21/8 3-h rainfall OBS 3-h rainfall PM mean

20. Importance of resampling, pattern adjustment, and bias-correction RPS comparison of 5 NEWEN variants • Both bias-correction and pattern adjustment are useful remedies. • Relative importance varies with time. • Resampling is a valuable technique when typhoon centers diverse. NEWEN2: no pattern adjustment NEWEN3: no bias-correction NEWEN4: no pattern adjustmentnor bias-correction NEWEN5: no probability-matching Better

21. 4. Performance of ensemble mean rainfall forecast Question: How to get valuable ensemble mean rainfall? Based on the 3-h rainfall time series of LREN, HREN, and NEWEN1, 9 kinds of“ensemble mean accumulated rainfall” can be defined: LSM, SM of the accumulated rainfall of LREN; HSM, SM of the accumulated rainfall of HREN; NSM, SM of the accumulated rainfall of NEWEN1; LPMa, accumulation of 3-h rainfall LPM; HPMa, accumulation of 3-h rainfall HPM; NPMa, accumulation of 3-h rainfall NPM; LPMb, PM of the accumulated rainfall of LREN; HPMb, PM ofthe accumulated rainfall of HREN; NPMb, PM of the accumulated rainfall of NEWEN1.

22. Rainfall ME (F–O) of various definitions of ensemble mean Accumulation of 3-h rainfall PM mean (PMa) PM mean of accumulated rainfall ensemble (PMb) Simple mean (SM) Day 1 Day 2 Day 3 3 days L H N L H N L H N

23. Better Day 1 Day 2 Day 3 3 days ETS in the HA

24. Better Day 1 Day 2 Day 3 3 days ETS in the VA

25. Better • NEW > H_4km > L_36km New probability matching technique • PMa > PMb >= SM H_4km L_36km ETS of 72-h rainfall in the VA

26. Inspiring QPF of Typhoon Morakot (2009) by the new probability-matching technique QPF by NEWEN 32-member 36-km ensemble 8-member 4-km ensemble OBS LPMa HPMa NPMa The ensemble mean accumulated 72-h rainfall (PMa) ending at 0000 UTC 9 August

27. Summary • A new probability matching scheme is developed for ensemble prediction of typhoon rainfall: • Make use of (i) large-sample-size low-resolution (36-km) ensemble, and (ii) small-sample-size high-resolution (4-km) ensemble • Three key elements: • Reconstruction of a rainfall ensemble (ignoring timing) from both ensembles • Adjusting rainfall patterns • Perform bias correction • The new probability matching scheme is shown to be effective in producing improved rainfall forecast.

28. While the scheme shows promises, it is not optimized, and it is only being tested for one case. • Many further improvement is possible through testing and tuning on a large number of cases. • We seek possible collaboration on this effort.