Introduction of KMA statistic model and ensemble system
Korea Meteorological AdministrationNumerical Weather Prediction DivisionJoo-Hyung Son
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Statistical models
PPM (Perfect Prognostic Method) Daily Max/Min and midnight temperature Probability of Precipitation
MOS (Model Output Statistics) Digital Forecast
KF(Kalman Filtering)/DLM(Dynamic Linear Model) Daily Max/Min Temperature 3 hourly temperature Daily Max/Min Temperature of 10 days
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MA RDAPS KF
PPM
Max/Min Temp
Max/Min TempPoP
GDAPS
DLM
DLM Max/Min Temp
3hr Temp
Statistical models
PPM
KF
RDLM
GDLM
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PPM for Max/Min Temp
Predictant 00 UTC : +1(00UTC, Max/Min) 12UTC : +1(Max), +2(00UTC, Min)
Forecast regions 70 sites in Korea
Model development May 1, 1988 – Feb 28, 1992 (4 years) Regional reanalysis of JMA Climate data of 70 weather sites
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PPM Model structure for Max/Min Temp
Temp (t) = A + B*obs(0) + {Ci*model predictori(t)}A, B, Ci (i=1,2,…,n): fixed coefficients
Forecast equation
1000, 850, 700,500,400,300hPa Wind speed, direction, Temperature
Dewpoint temp, Height et al. from RDAPS
Observation, climate
PredictantMax/Min and 00LST temperature
of 70 sights
predictor
Forecast eqs for each season, sights
predictor
predictant
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PPM Predictors• select a group of predictors which explain predictant(temperature) well from 44 predictors <method: forward-backward selection>
• the number of the predictors of each seasonal and regional forecast equations are ranged from 5 to 10
Main predictors for +12hr Max temp Main predictors for +24hr Max temp
Spring Summer Fall Winter Spring Summer Fall Winter
T850, CLMT,OBS, VOR8PCWT
OBS,CTOPVOR8RH50,PCWT
T85, CLMT,OBS,TTD8,VORS
T85,CLMT,OBS,TTDB,VOR8
T85,CLMT,PCWT,VOR8,OBS
OBS,VORS,T85,
CTOP,RH70
T85,CLMT,TTD8,PCWT, VOR8
T85,CLMT,VOR8,TTD8,70Q4
Main predictors for +12hr Min temp Main predictors for +24hr Min temp
Spring Summer Fall Winter Spring Summer Fall Winter
CLMT,OBS,T85,KYID,TTD8
OBS,T85,
CLMT,VOR8,TTD8
CLMT,OBS,TTD8,VOR8,T85
T85,OBS,TTD8,TAD8,VOR8
CLMT,T85,KYID,TTD8,S70
OBS,T85,
CLMT,VOR8,PCWT
CLMT,TTD8,PCWT,T85,OBS
T85,OBS,TTD8,VOR8,TAD8
※ OBS: observation, CLMT: climate, PCWT: virtual prediction, VOR: vorticity, TAD: temperature advection, KYID: KY index
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PPM Model structure for PoP
1000, 850, 700,500,400,300hPa Wind speed, direction, Temperature
Dewpoint temp, Height et al. from RDAPS
Observation, climate
PredictantPoP of 18 regions
predictor
Forecast eqs for Each region according
to warm and cold season
predictor
predictant
Temp (t) = A + B*obs(0) + {Ci*modeli(t)}A, B, Ci (i=1,2,…,n): fixed coefficients
Forecast equation
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PPM Predictors• PoP
the number of sites observed precipitation in the region
Total number of sites in the region• 18 regions : 24 region by cluster analysis (Moon(1990)) + forecast experiment
※18 regions for forecast of PoP
• the forecast equations are developed according to the warm(April-September) and cold(October-March) season and each regions.
principle predictors for PoP
Warm season
DWL, VR850, QA700, VV700, S850, RH500
Cold season
DWL, VV850, RH850, VR850, S850, 7Q4
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KF for Max/Min Temp
Predictant 00 UTC : +1(Min/Max), +2(Min) 12 UTC : +1(Max), +2(Min/Max)
Forecast regions 40 in Korea, 32 in North Korea, China, Japan
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Kalman Filter algorithm
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1 equationsystemwG
equationnobservatiovFY
tttt
tttt
KF for Max/Min Temp
vt~N(0,Vt): observation noise
wt~N(0,Wt) : process noise
1Ft = RDAPS Latest Obs temp
Gt = 1
V0 = 2
4/365 0 0 W0= 0 1/365 0 0 0 1/365
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DLM(Dynamic Linear Model)
DLM Improved Kalman Filter algorithm Weights(regression coefficient) are modified according to the
prior condition with time.
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DLM
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1 equationsystemwG
equationnobservatiovFY
tttt
tttt
vt~N(0,Vt) wt~N(0,Wt
)
Use the updating algorithm to estimate Wt with time Find appropriate Wt increasing discount
factor(0<delta<1) from 0.01 to 1 with interval 0.01 the discount factor is selected when RMSE between
observation and forecast is the lowest
DLM(Dynamic Linear Model)
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RDLM(Regional DLM) 3hourly forecast up to 48hr RDAPS 38 sites
GDLM(Global DLM) Max/Min temp for 10 days GDAPS 38 sites
DLM(Dynamic Linear Model)
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Ensemble Prediction System
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KMA Ensemble Prediction System
GBEPS 1.1.1~ GBEPS 1.2.1
GBEPS 2.1.1~ GBEPS 2.3.1
GBEPS 2.3.1.1~ GBEPS 2.3.1.2
Operation period 2001.3.1 2003.10.31∼ From 2003.11.1 From 2005.2.
Data assimilation 2dOI → 3dOI 3dOI → 3dVar 3dVar
Model GDAPS T106L21 GDAPS T106L30 GDAPS T106L30
Vertical resolution 21 levels 30 levels 30 levels
Perturbation method
BreedingBreeding → Breeding +
Factor RotationBreeding → Breeding +
Factor Rotation
Target area (BV) Global Northern Hemisphere Northern Hemisphere
Lead time 10 days 8 days 8 days
Ensemble members 17 (16 members + 1 control) 17 members
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AnalysisAnalysisDD
AnalysisD+Perturbation Pert. run
Control run
normalization
AnalysisAnalysisD+1D+1
Breeding
Schematic diagramSchematic diagram
The global spectral model T106L30 with the slightly different initial conditions run 17 times.
Both perturbed analysis and control analysis are projected to 24hours with the model, and departures from the control analysis at +24hours are scaled down to the norm of initial perturbations
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D day D day + 12hr D+1 day D+1 day +12hr
AnalysisAnalysisDD
AnalysisD+Perturbation
Pert. ru
n
Control run Rotation
normalization
AnalysisAnalysisD+1D+1 Rotation
Breeding + Rotation
Schematic diagramSchematic diagram
17members could be similar each other because they are generated from the identical model, so this is to make different perturbation among the members manually.
In the new system, the factor rotation was added every alternative step.
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2005. 6. 11
old(cray-before) NEW (cray-frot)
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2005. 6. 11
old(cray-before) NEW (cray-frot)
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EPS products (http://190.1.20.56)
mean and spread spaghetti stamp map categorical PoP probability of Surface Max Wind time series of probability
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Mean and Spread
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Spaghetti
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Spaghetti ( with ensemble spread)
5640m
5520m
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Stamp map
• display the global model, mean and standard deviation and spaghetti as well as each member.
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12-hour precipitation > given thresholds : 1, 5, 10mm for winter season: 1, 10, 50mm for other seasons The probability
These probability maps are used for the early warning guidance of severe weather.
100)(
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totalmember
categorymemberP
Categorical PoP
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Categorical PoP
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Surface maximum wind > 10m/s, 14m/s The probability
These probability maps are used for the
early warning guidance of severe weather.
100)(
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totalmember
categorymemberP
Probability of Surface Max Wind
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Probability of Surface Max Wind
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Time series of Probability
Precipitation
Sfc Max Wind
Precipitation 12hr accumul >= 1mm 12hr accumul >= 10mm 12hr accumul >= 50mm
Surface Max Wind sfc wind >= 10m/s sfc wind >= 14m/s
Principle cities Seoul, Daegu, Daejeon Busan et al.
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EPSgramLargest value
Upper quartile
Lower quartile
Median
Smallest value
Interpretationof boxplots
Imageof PDF
Time series of primary cities
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Ensemble Plumes
Time series of 8-day foTime series of 8-day forecast at citiesrecast at cities
The dispersion of meThe dispersion of members with forecast evmbers with forecast ev
olutionolution
Variable : Pmsl, 500H, Variable : Pmsl, 500H, 850 T850 T
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Hwangsa (yellow sand) trajectoryHwangsa (yellow sand) trajectory
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Typhoon Strike Probability Map by Typhoon Strike Probability Map by EPSEPS
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Thank you
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Factor analysis
Factor analysis Factor analysis is a statistical technique to explain
the most of the variability among a number of observable random variables in terms of a smaller number of unobservable random variables called factors
Factor rotation Factor rotation is to find a parameterization in which
each variable has only a small number of large loadings. That is, each variable is affected by a small number of factors, preferably only one. This can often make it easier to interpret what the factors represent.