Prediction of Typhoon Torrential Rainfall over Taiwan using a Modified Probability Matching

Technique

Ying-Hwa Kuo and Xingqin Fang UCAR

Outline

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1. Background

2. The new probability-matching technique

3. Performance of probabilistic rainfall forecast

4. Performance of ensemble mean rainfall forecast

5. Summary

Topographical Influence of the Central Mountain Range on Typhoons

• Central Mountain Range: – Occupies 2/3 of the island of

Taiwan; – More than 200 peaks with

elevation exceeding 3000 m.

• Central Mountain Range: – Influences typhoon tracks – Enhances and modulates typhoon

rainfall

• Interaction of typhoons with Central Mountain Ranges causes: – Heavy rainfall, severe flooding,

and debris flows – Loss of human lives – Significant damage to agriculture,

industry, and properties

From August 6 to 10, 2009, extraordinary rainfall was brought over Taiwan by Typhoon Morakot, breaking 50 year’s precipitation record, causing a loss of more than 700 people and estimated property damage exceeding US$5.5 billion

Observed Rainfall of Typhoon Morakot (2009)

Typhoon Morakot (2009) Max. 24-h gauge 1504 mm Max. 96-h gauge 2874mm

at Chiayi County (windward slope of CMR)

Accumulated rainfall: (a) 96-h on August 6-10 (b) 24-h on August 8-9

* Objective analysis ~450 automatic stations

24-h rain world record 1825 mm

(a) (b)

The spatial distribution of the simulated 96-h accumulated rainfall on August 6-10 over Taiwan

(unit: mm) by 32-member, 4-km ensembles (a) with and (b) without CMR.

OBS

(a) With Taiwan topography • Intensive rainfall areas (>819.2 mm) well captured • Extremes (>2500 mm) captured, with displacements • Peak 3276 mm

(b) Without Taiwan topography • Homogeneous rainfall distribution • No obvious local rainfall enhancement • Peak 615 mm, less than 25%

The Impact of Central Mountain Range on Typhoon Rainfall Distribution

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QPF for Typhoon Rainfall

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.

Challenges:

How to extract valuable QPF from ensemble at affordable cost?

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Probability Matching QPF

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.

Challenge: How to obtain accurate QPF from ensemble forecast?

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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

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QPF from 36-km Ensemble: PM vs. SM • 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

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HREN_PM

QPF from 4-km Ensemble: PM • 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

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Fang et al. 2011

Serious topography-locked

over-prediction in 4-km ensemble

over southern Taiwan

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A New Probability-Matching Technique Two 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 synthetic rainfall ensemble NEWEN:

Resample size, i.e., 16-member

On an arbitrary high-resolution grid, i.e., 2-km, by interpolation

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LREN: 32-member 36-km Basic hypothesis: Reasonably good track prediction can be provided by a low-resolution ensemble

• 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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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.

 

RHRESAMPLED im,ip( )

 

RPattern ip( ) =WL *RLSELECTED ip( ) +WH *RHRESAMPLED ip( )

 

RHRESAMPLED im,ip( )

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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.

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For time 18/8

For member 6

Two loops of resampling around LREN mean track

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For member: 13

For time 18/8

Two loops of resamplings around LREN mean track

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Time evolution of 3-h rainfall RPS (rank probability score) averaged over the land area in the HA by LREN, HREN, and NEWEN1 (which is the control of NEWEN).

Better

RPS ip, it( ) =1

K -1FCDFk ip, it( ) -OCDFk ip, it( )( )

2

k=1

K

å

Performance of probabilistic rainfall forecast ---LREN, HREN, and NEWEN1

Time 18/8-21/8

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3-h rainfall RPS

3-h rainfall PM mean

3-h rainfall OBS

Time 18/8-21/8

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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.

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Question: How to obtain QPF of longer time period?

Three approaches:

SM: Simple Mean

PMa: Accumulation of 3-h PM

PMb: PM of accumulated rainfall

These can be constructed based on the 3-h rainfall time series:

LREN: Low-resolution ensemble

HREN: high-resolution ensemble

NEWEN1: New synthetic rainfall ensemble constructed

from LREN and HREN

QPF for Accumulated Rainfall over Longer Period

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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

30 ETS in the HA

Day 1 Day 2

Day 3 3 days

Better

31 ETS in the VA

Day 1 Day 2

Day 3 3 days

Better

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• 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

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32-member

36-km ensemble

QPF by

NEWEN OBS

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

LPMa HPMa NPMa

QPF of Typhoon Jangmi (2008)

by the new probability-matching technique

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!

!

Fig. 22. The accumulated 72-h rainfall ending at 1200 UTC 29 September 2008

(unit: mm, color shaded in levels as indicated in the color bar) as the simulated

ensemble mean derived by (a) LPMa, (b) HPMa, and (c) NPMa, and (d) as observed

for Typhoon Jangmi.

The accumulated 72-h rainfall ending at 1200 UTC 29 September 2008 as the simulated ensemble mean derived from (a) LPMa, (b) HPMa, and (c) NPMa, and (d) as the observed for Typhoon Jangmi.

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.

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Fang, X. and Y.-H. Kuo: Improving ensemble-based quantitative prediction forecast for topography-enhanced typhoon heavy rainfall over Taiwan with a modified probability-matching technique. Mon. Wea. Rev., 141, 3908-3932.