Rainfall nowcasting using Burgers equation GyuWon Lee, Soorok Ryu - PowerPoint PPT Presentation

Rainfall nowcasting using Burgers’ equation GyuWon Lee, Soorok Ryu Kyungpook National University, Daegu, Korea(ROK)

R ADAR - BASED NOWCASTING 1. Motion fields of precip. Ex) MAPLE (Variational Echo Tracking: VET) Constant-vector forward scheme 3. Verification 2. Advect precip. fields: (compare fcst w/ obs) Semi-Lagrangian backward Predicted field Observed field - Growth/decay (scale of predictability) - Non-stationary motion fields Germann and Zawadzki (2002)

M ETHODOLOGY Lagrangian extrapolation (advection) OR Conservation equation We solved this simple advection equation(AE) directly : Type 1 Add diffusion term for spatial filtering (smoothing): advection diffusion equation (ADE) : Type 2

M ETHODOLOGY However, above two equations assume that the motion vector field is stationary in time (constant motion vectors for entire forecast time) Introduce Burgers’ equation: to allow non-stationarity of motion vectors. The s controls the degree of the smoothness.

M ETHODOLOGY Semi-Lagrangian extrapolation (S-L): Ty Type 1 pe 1: advection equation(AE) Ty Type 2 pe 2: advection diffusion equation(ADE) Ty Type 3 pe 3: advection equation(AE) + Burgers’ equation + Ty Type 4 pe 4: advection diffusion equation(ADE) + Burgers’ equation +

M ETHODOLOGY

D ATA 1. 1. Cas ases es - 6 events, 2.5 min CAPPI composite from 3 radars - 15 min nowcasting up to 3h 2. 2. Com omput putation on dom domai ain - Southeast area in South Korea - 312 km x 312 km at 0.25 km resolution (1248 x 1248 pixels) - Motion vectors : 10 km resolution - Verification domain: 250 km x 250 km (red box)

S KILL SCORES , ERROR STATISTICS  2D Contingency table  Categorical scores Verification score Formula Forecast Probability of a/(a+c) Obs R>=R th R <R th detection (POD) R >=R th Hit (a) Miss (c) False alarm ratio b/(a+b) (FAR) R< R th False Correct alarm (b) negative (d) Critical success a/(a+b+c) index (CSI) Equitable threat (a-w)/(a+b+c-w), score (ETS) w=(a+b)(a+c)/(a+b+c+d)

MAPLE VS . AE + D IFFUSION 0300 LST 30 June 2012 MAPLE Type 1 Advection eq

NON - STATIONARY MOTION VECTORS VET w/ OBS initial Burgers’ Vectors equation w/ Burgers’ eq.

MAPLE VS . AE + NON - STATIONARY +D IFFUSION MAPLE 3 Type 3 s=0.2

MAPLE VS . AE + NON - STATIONARY +D IFFUSION MAPLE

MAPLE VS . AE + NON - STATIONARY +D IFFUSION Skill scores R th = 0.1mm/h Type 4 MAPLE

MAPLE VS . AE + NON - STATIONARY +D IFFUSION Average skill scores: 6 events “Type 3, 4”

MAPLE VS . AE + NON - STATIONARY +D IFFUSION Average skill scores: 6 events • Lifetime : Type 4( >3h) > Type 3 (around 3h) > Type 2 (2.5h) > MAPLE (2h) = Type 1

MAPLE VS . AE + NON - STATIONARY +D IFFUSION Sensitivity to diffusion Type pe 2: 2: dif iffusion Type pe 4 4: dif iffusion+ n+Bur urgers rs’ e ’ eq. Ave Average ge correlati tion Ave Average ge CSI

NON - STATIONARY MOTION VECTORS 0 0

NON - STATIONARY MOTION VECTORS Non-stationarity? 2 3 2 2 3 3 2 2 3 3 Type 3, 4 (inclusion of Burgers’ equation) outperform

NON - STATIONARY MOTION VECTORS Type 2, 4 (inclusion of diffusion equation) perform better

S UMMARY  Introd oduc uced ed nowc wcas asti ting ng based o ed on advec ecti tion ( on (diffus fusion) on) equat ation w with B Burgers’ e equ quation  Perfor formanc ance: e: MAPLE LE ~ ~ Adv dvec ecti tion e on eq. < Adv dvec ecti tion e on eq. + Burger gers e eq. (S (S-L ~ ~ Ty Type1 < < Ty Type2 < < Ty Type 3 3 < < Ty Type 4 4)  Use o of diffusion t term rm and n non-stati tationar onary moti tion on v vector tor improv oves es f forec ecas asti ting ng s skill s scor ores es  When nons nsta tati tionar onarity ty of motion on f fiel elds ds i is s strong, ong, t the pre recipitation f fore recasts u using B Burg urgers rs’ e equa uation (Ty (Type pe3, Type 4 4) show s ow signi gnifi ficant ant i impr prov ovem ement ent. .