Download - 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 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