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)(

)((%)

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.