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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. Background The new probability-matching technique Performance of probabilistic rainfall forecast

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Xingqin fang and bill kuo ncar ucar

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

Outline

  • Background

  • The new probability-matching technique

  • Performance of probabilistic rainfall forecast

  • Performance of ensemble mean rainfall forecast

  • Summary


Xingqin fang and bill kuo ncar ucar

  • 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?


Xingqin fang and bill kuo ncar ucar

  • 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?


Xingqin fang and bill kuo ncar ucar

  • Probability Matching:

  • Match the probability between SM and the entire ensemble population

  • Ebert (2001), MWR


Xingqin fang and bill kuo ncar ucar

SM – Simple mean

PM – Probability matching


Xingqin fang and bill kuo ncar ucar

SM – Simple mean

PM – Probability matching


Xingqin fang and bill kuo ncar ucar

Observation

Analysis of observed rainfall from Central Weather Bureau


Xingqin fang and bill kuo ncar ucar

  • 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


Xingqin fang and bill kuo ncar ucar

  • 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


Xingqin fang and bill kuo ncar ucar

Serious topography-locked over-prediction

in 4-km ensembleover southern Taiwan

Fang et al. 2011


Xingqin fang and bill kuo ncar ucar

  • 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


Xingqin fang and bill kuo ncar ucar

  • 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


Xingqin fang and bill kuo ncar ucar

  • 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.


Xingqin fang and bill kuo ncar ucar

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.


Xingqin fang and bill kuo ncar ucar

Two loops of resampling around LREN mean track

For

time 18/8

For

member 6


Xingqin fang and bill kuo ncar ucar

Two loops of resamplings around LREN mean track

For

member: 13

For

time 18/8


Xingqin fang and bill kuo ncar ucar

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.


Xingqin fang and bill kuo ncar ucar

3-h rainfall RPS

Time

18/8-21/8

3-h rainfall OBS

3-h rainfall PM mean


Xingqin fang and bill kuo ncar ucar

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


Xingqin fang and bill kuo ncar ucar

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.


Xingqin fang and bill kuo ncar ucar

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


Xingqin fang and bill kuo ncar ucar

Better

Day 1

Day 2

Day 3

3 days

ETS in the HA


Xingqin fang and bill kuo ncar ucar

Better

Day 1

Day 2

Day 3

3 days

ETS in the VA


Xingqin fang and bill kuo ncar ucar

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


Xingqin fang and bill kuo ncar ucar

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


Summary

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.


Xingqin fang and bill kuo ncar ucar

  • 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.


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