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) Numerical Weather Prediction Division KMA n n Daily Max/Min and midnight temperature Probability of Precipitation MOS (Model Output Statistics) n Digital Forecast KF(Kalman Filtering)/DLM(Dynamic Linear Model) n n n Daily Max/Min Temperature 3 hourly temperature Daily Max/Min Temperature of 10 days

Statistical models Numerical Weather Prediction Division KMA PPM RDAPS KF DLM GDAPS DLM PPM KF RDLM GDLM Max/Min Temp Po. P Max/Min Temp 3 hr Temp Max/Min Temp

PPM for Max/Min Temp Predictant Numerical Weather Prediction Division KMA n n 00 UTC : +1(00 UTC, Max/Min) 12 UTC : +1(Max), +2(00 UTC, Min) Forecast regions n 70 sites in Korea Model development n n n May 1, 1988 – Feb 28, 1992 (4 years) Regional reanalysis of JMA Climate data of 70 weather sites

PPM Model structure for Max/Min Temp Forecast equation Temp (t) = A + B*obs(0) + {Ci*model predictori(t)} Numerical Weather Prediction Division KMA A, B, Ci (i=1, 2, …, n): fixed coefficients predictor 1000, 850, 700, 500, 400, 300 h. Pa Wind speed, direction, Temperature Dewpoint temp, Height et al. from RDAPS Observation, climate predictor Forecast eqs for each season, sights predictant Max/Min and 00 LST temperature of 70 sights Predictant

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 Numerical Weather Prediction Division KMA forecast equations are ranged from 5 to 10 Main predictors for +12 hr Max temp Main predictors for +24 hr Max temp Spring Summer Fall Winter T 850, CLMT, OBS, VOR 8 PCWT OBS, CTOP VOR 8 RH 50, PCWT T 85, CLMT, OBS, TTD 8, VORS T 85, CLMT, OBS, TTDB, VOR 8 T 85, CLMT, PCWT, VOR 8, OBS, VORS, T 85, CTOP, RH 70 T 85, CLMT, TTD 8, PCWT, VOR 8 T 85, CLMT, VOR 8, TTD 8, 70 Q 4 Main predictors for +12 hr Min temp Main predictors for +24 hr Min temp Spring Summer Fall Winter CLMT, OBS, T 85, KYID, TTD 8 OBS, T 85, CLMT, VOR 8, TTD 8 CLMT, OBS, TTD 8, VOR 8, T 85, OBS, TTD 8, TAD 8, VOR 8 CLMT, T 85, KYID, TTD 8, S 70 OBS, T 85, CLMT, VOR 8, PCWT CLMT, TTD 8, PCWT, T 85, OBS, TTD 8, VOR 8, TAD 8 ※ OBS: observation, CLMT: climate, PCWT: virtual prediction, VOR: vorticity, TAD: temperature advection, KYID: KY index

PPM Model structure for Po. P Forecast equation Temp (t) = A + B*obs(0) + {Ci*modeli(t)} Numerical Weather Prediction Division KMA A, B, Ci (i=1, 2, …, n): fixed coefficients predictor 1000, 850, 700, 500, 400, 300 h. Pa Wind speed, direction, Temperature Dewpoint temp, Height et al. from RDAPS Observation, climate predictor Forecast eqs for Each region according to warm and cold season predictant Po. P of 18 regions Predictant

PPM Predictors • Po. P Numerical Weather Prediction Division KMA 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. principle predictors for Po. P Warm season DWL, VR 850, QA 700, VV 700, S 850, RH 500 Cold season DWL, VV 850, RH 850, VR 850, S 850, 7 Q 4 ※ 18 regions forecast of Po. P

Numerical Weather Prediction Division KMA

KF for Max/Min Temp Predictant Numerical Weather Prediction Division KMA n n 00 UTC : +1(Min/Max), +2(Min) 12 UTC : +1(Max), +2(Min/Max) Forecast regions n n 40 in Korea, 32 in North Korea, China, Japan

KF for Max/Min Temp Kalman Filter algorithm vt~N(0, Vt): observation noise Numerical Weather Prediction Division KMA wt~N(0, Wt) : process noise Gt = 1 V 0 = 2 4/365 0 0 W 0= 0 1/365 0 0 1/365 1 Ft = RDAPS Latest Obs temp

Numerical Weather Prediction Division KMA

Numerical Weather Prediction Division KMA DLM(Dynamic Linear Model) DLM § Improved Kalman Filter algorithm § Weights(regression coefficient) are modified according to the prior condition with time.

DLM(Dynamic Linear Model) Numerical Weather Prediction Division KMA DLM 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) RDLM(Regional DLM) Numerical Weather Prediction Division KMA n n n 3 hourly forecast up to 48 hr RDAPS 38 sites GDLM(Global DLM) n n n Max/Min temp for 10 days GDAPS 38 sites

Numerical Weather Prediction Division KMA

Ensemble Prediction System

Numerical Weather Prediction Division KMA Ensemble Prediction System GBEPS 1. 1. 1 ~ GBEPS 1. 2. 1 GBEPS 2. 1. 1 ~ GBEPS 2. 3. 1. 2 Operation period 2001. 3. 1∼ 2003. 10. 31 From 2003. 11. 1 From 2005. 2. Data assimilation 2 d. OI → 3 d. Var Model GDAPS T 106 L 21 GDAPS T 106 L 30 Vertical resolution 21 levels 30 levels Perturbation method Breeding → Breeding + Factor Rotation Target area (BV) Global Northern Hemisphere Lead time 10 days 8 days Ensemble members 17 (16 members + 1 control) 17 members

Schematic diagram Breeding Analysis. D+Perturbation un Pert. r Numerical Weather Prediction Division KMA normalization Control run Analysis. D+1 The global spectral model T 106 L 30 with the slightly different initial conditions run 17 times. Both perturbed analysis and control analysis are projected to 24 hours with the model, and departures from the control analysis at +24 hours are scaled down to the norm of initial perturbations

Schematic diagram Breeding + Rotation D day Analysis D+Perturbation Numerical Weather Prediction Division KMA t. er r un D day + 12 hr D+1 day +12 hr P normalization Analysis. D Control run Rotation Analysis. D+1 Rotation 17 members 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.

2005. 6. 11 Numerical Weather Prediction Division KMA old(cray-before) NEW (cray-frot)

Numerical Weather Prediction Division KMA EPS products § § § (http: //190. 1. 20. 56) mean and spread spaghetti stamp map categorical Po. P probability of Surface Max Wind time series of probability

Numerical Weather Prediction Division KMA Mean and Spread

Numerical Weather Prediction Division KMA Spaghetti

Numerical Weather Prediction Division KMA Spaghetti ( with ensemble spread) 5520 m 5640 m

Stamp map Numerical Weather Prediction Division KMA • display the global model, mean and standard deviation and spaghetti as well as each member.

Categorical Po. P Numerical Weather Prediction Division KMA 12 -hour precipitation > given thresholds : 1, 5, 10 mm for winter season : 1, 10, 50 mm for other seasons The probability These probability maps are used for the early warning guidance of severe weather.

Numerical Weather Prediction Division KMA Categorical Po. P

Numerical Weather Prediction Division KMA Probability of Surface Max Wind Surface maximum wind > 10 m/s, 14 m/s The probability These probability maps are used for the early warning guidance of severe weather.

Numerical Weather Prediction Division KMA Probability of Surface Max Wind

Numerical Weather Prediction Division KMA Time series of Probability l Precipitation 12 hr accumul >= 1 mm 12 hr accumul >= 10 mm 12 hr accumul >= 50 mm Precipitation l Surface Max Wind sfc wind >= 10 m/s sfc wind >= 14 m/s l Principle cities Seoul, Daegu, Daejeon Busan et al. Sfc Max Wind

Time series of primary cities Largest value EPSgram Numerical Weather Prediction Division KMA Upper quartile Median Lower quartile Smallest value Interpretation of boxplots Image of PDF

Numerical Weather Prediction Division KMA Ensemble Plumes Time series of 8 -day forecast at cities The dispersion of members with forecast evolution Variable : Pmsl, 500 H, 850 T

Numerical Weather Prediction Division KMA Hwangsa (yellow sand) trajectory

Numerical Weather Prediction Division KMA Typhoon Strike Probability Map by EPS

Numerical Weather Prediction Division KMA Thank you

Numerical Weather Prediction Division KMA 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 one. This can often make it easier to interpret what the factors represent.