Introduction of kma statistic model and ensemble system
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Introduction of KMA statistic model and ensemble system. Korea Meteorological Administration Numerical Weather Prediction Division Joo-Hyung Son. PPM (Perfect Prognostic Method) Daily Max/Min and midnight temperature Probability of Precipitation MOS (Model Output Statistics)

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Introduction of kma statistic model and ensemble system

Introduction of KMA statistic model and ensemble system

Korea Meteorological Administration

Numerical Weather Prediction Division

Joo-Hyung Son


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

Statistical models


Introduction of kma statistic model and ensemble system

Statistical models

Max/Min Temp

PoP

PPM

PPM

RDAPS

KF

Max/Min Temp

KF

DLM

3hr Temp

RDLM

GDAPS

Max/Min Temp

DLM

GDLM


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

PPM for Max/Min Temp


Introduction of kma statistic model and ensemble system

PPM Model structure for Max/Min Temp

Forecast equation

Temp (t) = A + B*obs(0) + {Ci*model predictori(t)}

A, B, Ci (i=1,2,…,n): fixed coefficients

predictor

predictor

1000, 850, 700,500,400,300hPa

Wind speed, direction, Temperature

Dewpoint temp,

Height et al. from RDAPS

Observation, climate

Forecast eqs for

each season, sights

predictant

Max/Min and 00LST temperature

of 70 sights

Predictant


Introduction of kma statistic model and ensemble system

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

  • OBS: observation, CLMT: climate, PCWT: virtual prediction, VOR: vorticity, TAD: temperature advection, KYID: KY index


Introduction of kma statistic model and ensemble system

PPM Model structure for PoP

Forecast equation

Temp (t) = A + B*obs(0) + {Ci*modeli(t)}

A, B, Ci (i=1,2,…,n): fixed coefficients

predictor

predictor

1000, 850, 700,500,400,300hPa

Wind speed, direction, Temperature

Dewpoint temp,

Height et al. from RDAPS

Observation, climate

Forecast eqs for

Each region according

to warm and cold season

predictant

PoP of 18 regions

Predictant


Introduction of kma statistic model and ensemble system

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

  • the forecast equations are developed according to the warm(April-September) and cold(October-March) season and each regions.

  • 18 regions for forecast of PoP


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

KF for Max/Min Temp


Kf for max min temp1

Kalman Filter algorithm

KF for Max/Min Temp

vt~N(0,Vt): observation noise

wt~N(0,Wt) : process noise

Gt = 1

V0 = 2

4/365 0 0

W0= 0 1/365 0

0 0 1/365

1

Ft = RDAPS

Latest Obs temp


Introduction of kma statistic model and ensemble system

DLM(Dynamic Linear Model)

  • DLM

    • Improved Kalman Filter algorithm

    • Weights(regression coefficient) are modified according to the prior condition with time.


Introduction of kma statistic model and ensemble system

DLM

DLM(Dynamic Linear Model)

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


Introduction of kma statistic model and ensemble system

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)


Ensemble prediction system

Ensemble Prediction System


Kma ensemble prediction system

KMA Ensemble Prediction System


Introduction of kma statistic model and ensemble system

Breeding

Pert. run

AnalysisD+Perturbation

normalization

Control run

AnalysisD

AnalysisD+1

Schematic 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


Introduction of kma statistic model and ensemble system

Breeding + Rotation

AnalysisD+Perturbation

Pert. run

normalization

Control run

AnalysisD+1

AnalysisD

Rotation

Rotation

Schematic diagram

D+1 day

D day

D day + 12hr

D+1 day +12hr

  • 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.


Introduction of kma statistic model and ensemble system

2005. 6. 11

old(cray-before)

NEW (cray-frot)


Introduction of kma statistic model and ensemble system

2005. 6. 11

old(cray-before)

NEW (cray-frot)


Eps products http 190 1 20 56

  • mean and spread

  • spaghetti

  • stamp map

  • categorical PoP

  • probability of Surface Max Wind

  • time series of probability

EPS products (http://190.1.20.56)


Introduction of kma statistic model and ensemble system

Mean and Spread


Introduction of kma statistic model and ensemble system

Spaghetti


Introduction of kma statistic model and ensemble system

Spaghetti ( with ensemble spread)

5520m

5640m


Stamp map

Stamp map

• display the global model, mean and standard deviation and spaghetti as well as each member.


Categorical pop

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.

Categorical PoP


Categorical pop1

Categorical PoP


Probability of surface max wind

Surface maximum wind > 10m/s, 14m/s

The probability

These probability maps are used for the early warning guidance of severe weather.

Probability of Surface Max Wind


Probability of surface max wind1

Probability of Surface Max Wind


Time series of probability

Precipitation

Sfc Max Wind

Time series of Probability

  • 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.


Epsgram

Largest value

Upper quartile

Median

Lower quartile

Smallest value

Interpretation

of boxplots

Image

of PDF

Time series of primary cities

EPSgram


Introduction of kma statistic model and ensemble system

Ensemble Plumes

Time series of 8-day forecast at cities

The dispersion of members with forecast evolution

Variable : Pmsl, 500H, 850 T


Introduction of kma statistic model and ensemble system

Hwangsa (yellow sand) trajectory


Introduction of kma statistic model and ensemble system

Typhoon Strike Probability Map by EPS


Introduction of kma statistic model and ensemble system

Thank you


Introduction of kma statistic model and ensemble system

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.


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