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 KuoNCAR/UCAR

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Outline

November 2012

1. Background

2. The new probability-matching technique

3. Performance of probabilistic rainfall forecast

4. Performance of ensemble mean rainfall forecast

5. Summary

3November 2012

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?

4November 2012

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?

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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

9November 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

10November 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

VAHA

11November 2012

Fang et al. 2011

Serious topography-locked

over-predictionin 4-km ensemble

over southern Taiwan

12November 2012

2. A new probability-matching techniqueSuppose 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

13November 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

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2. A new probability-matching techniqueMain 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

15November 2012

2. A new probability-matching techniqueTwo 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.

16November 2012

Fortime 18/8

Formember 6

Two loops of resampling around LREN mean track

17November 2012

Formember: 13

Fortime 18/8

Two loops of resamplings around LREN mean track

18November 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

Time18/8-21/8

19November 2012

3-h rainfall RPS

3-h rainfall PM mean

3-h rainfall OBS

Time18/8-21/8

20November 2012

RPS comparison of 5 NEWEN variants

BetterNEWEN2: no pattern adjustmentNEWEN3: no bias-correctionNEWEN4: 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.

21November 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

22November 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 L H N L H N

23November 2012ETS in the HA

Day 1 Day 2

Day 3 3 days

Better

24November 2012ETS in the VA

Day 1 Day 2

Day 3 3 days

Better

25November 2012

• NEW > H_4km > L_36kmBetter

L_36km

H_4km

ETS of 72-h rainfall in the VA

New probability matching technique • PMa > PMb >= SM

26November 2012

32-member36-km ensemble

QPF byNEWEN

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-member4-km ensemble

LPMa HPMa NPMa

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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 Report

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• 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 Report