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

Outline November Background 2.The new probability-matching technique 3.Performance of probabilistic rainfall forecast 4.Performance of ensemble mean rainfall forecast 5.Summary

3 November 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 November 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 PMs performance. For the topography-enhanced typhoon heavy rainfall over Taiwan, serious issues in high-resolution ensemble definitely impact PMs 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

SM – Simple mean PM – Probability matching

SM – Simple mean PM – Probability matching

Observation Analysis of observed rainfall from Central Weather Bureau

9 November 2012 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 72-h rainfall ending at 00/9 3-h rainfall at 18/8-21/8 LREN_PM OBS SM

10 November 2012 HREN_PM 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. OBS 72-h rainfall ending at 00/9 VA HA

11 November 2012 Fang et al Serious topography-locked over-prediction in 4-km ensemble over southern Taiwan

12 November 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 November 2012 LREN: 32-member 36-km 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. 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. November 2012

15 November A new probability-matching technique Two loops: 1) Time loop: 3-h rainfall ensemble time series will be reconstructed if the matching process is run at 3-h interval. 2) 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 November 2012 For time 18/8 For time 18/8 For member 6 For member 6 Two loops of resampling around LREN mean track

17 November 2012 For member: 13 For member: 13 For time 18/8 For time 18/8 Two loops of resamplings around LREN mean track

18 November 2012 Time evolution of 3-h rainfall RPS averaged over the land area in the HA by LREN, HREN, and NEWEN1. Better 3. Performance of probabilistic rainfall forecast ---LREN, HREN, and NEWEN1 Time 18/8-21/8 Time 18/8-21/8

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

20 November 2012 RPS comparison of 5 NEWEN variants Better NEWEN2: no pattern adjustment NEWEN3: no bias-correction NEWEN4: no pattern adjustment nor bias-correction NEWEN5: no probability-matching Importance of resampling, pattern adjustment, and bias-correction Both bias-correction and pattern adjustment are useful remedies. Relative importance varies with time. Resampling is a valuable technique when typhoon centers diverse.

21 November 2012 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: 1)LSM, SM of the accumulated rainfall of LREN; 2)HSM, SM of the accumulated rainfall of HREN; 3)NSM, SM of the accumulated rainfall of NEWEN1; 4)LPMa, accumulation of 3-h rainfall LPM; 5)HPMa, accumulation of 3-h rainfall HPM; 6)NPMa, accumulation of 3-h rainfall NPM; 7)LPMb, PM of the accumulated rainfall of LREN; 8)HPMb, PM of the accumulated rainfall of HREN; 9)NPMb, PM of the accumulated rainfall of NEWEN1. 4. Performance of ensemble mean rainfall forecast

22 November 2012 Rainfall ME (F–O) of various definitions of ensemble mean Simple mean (SM) Accumulation of 3-h rainfall PM mean (PMa) PM mean of accumulated rainfall ensemble (PMb) Day 1 Day 2 Day 3 3 days L H N

23 November 2012 ETS in the HA Day 1Day 2 Day 33 days Better

24 November 2012 ETS in the VA Day 1Day 2 Day 33 days Better

25 November 2012 NEW > H_4km > L_36km Better L_36km H_4km ETS of 72-h rainfall in the VA New probability matching technique PMa > PMb >= SM

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

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. MONTH 2012 Monthly Report27

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. MONTH 2012 Monthly Report28