Optimal metric and control variables for improved forecast

associated with the tropical cyclones

Kosuke Ito Department of Atmospheric Sciences, National Taiwan University

Seminar at the Weather-Chaos group meeting Maryland University, Maryland

2012/02/27

About me •  2008, M.S., Kyoto Univ. (Prof. Shigeo Yoden) •  2011, Ph.D., Kyoto Univ.

(Prof. Toshiyuki Awaji, Prof. Yoichi Ishikawa) •  Currently… Postdoc, National Taiwan Univ. 　 (Prof. Chun-Chieh Wu) •  Research interests:

Tropical cyclones Mesoscale data assimilation Sensitivity analysis

Typhoon Morakot (2009年8号) Max. total rainfall > 3000mm

2011年12号 (Typhoon Talas) Max. total rainfall > 2000mm

Fatalities: 789

Fatalities and missing: 92 Severely injured: 27

0

100

200

300

400

500

1960 1970 1980 1990 2000年

人 (Fire and Disaster Management Agency, Japan)

Mostly by Typhoon Talas & Roki

Data Assimilation: Model, Metric and Control Variables

Ø Intensity →Internal dynamics and thermodynamics

Ø Track →Large-scale flow

100E 120E 140E 160E

50N

40N

30N

20N

180

Midlatitude Trough

Subtropical high 10N

Wind field at 500 hPa (TC Conson(2004))

(Digital Typhoon Archive) (Emanuel, 2004)

Temperature anomaly field: Hurricane Fran (1999)

18 km June 8 June 9

June 10

June 11

June 12

Outline of the talk 1.  Track: Incremental Typhoon-position-

Oriented Sensitivity Analysis Employing TC position as a metric [Ito and Wu, 2012, submitted to JAS]

2.  Intensity: Data Assimilation Optimization of air-sea exchange coefficients as control variables [Ito et al., 2010, SOLA; Ito et al., 2011, JAS; Ito et al., 2012, submitted to QJRMS]

Track: Incremental Typhoon-position-Oriented

Sensitivity Analysis

Sensitivity analysis

Aircraft surveillance

Better track prediction

Targeted (Adaptive) observations

[Yamaguchi et al., 2009]

Observations only in the “sensitive” areas work to improve the track forecast.

ALL Dropsonde

Dropsondes in “sensitive” area

Besttracks

No Data assimilation or dropsondes “nonsensitive” area à TC disapears.

THOPEX/T-PARAC: Dropsonde observations à 15-20 % improvement in track forecast

•  MultiM: “Error” from multimodel-mean TC center　

(Weissmann et al., 2011)

Existing Targeted Observation Guidances (Sensitivity Analysis Methodology)

•  Singular vector method (SV) [Peng & Reynolds 2006; Buizza et al. 2007; Yamaguchi et al., 2009; Kim et al., 2011]

•  Ensemble transform Kalman filter technique (ETKF) [Majumdar et al., 2006]

•  Adjoint-derived sensitivity steering vector (ADSSV) [Wu et al., 2007; Wu et al., 2009a; Chen et al., 2011]

•  Deep layer mean wind variances (DLM) [Aberson et al., 2003]

Intercomparison: Targeted observation guidances [Majumdar et al., 2006; Reynolds et al., 2007; Wu et al., 2009b]

(Wu et al., 2009b)

ECMWF SV NOGAPS SV JMA SV

ETKF ADSSV NCEP DLM

Fundamental Problems in existing methods 1.  “Ad hoc” determination of a metric (Variable

and relevant region) related to TC motion Dry/Moist total energy (SV, ETKF)? Background steering flow (ADSSV)? Vertical weighing? Horizontal scales?

SV-based sentivity Evolved perturbation

(Kim et al., 2011)

Fundamental Problems in existing methods

Black: Evaluated by adjoint model Gray: Evaluated by nonlinear model

Changes of background flow (48hr) in three experiments

(Chen et al., 2011) (JMA HP)

2. Nonlinear development of initial perturbation SV & ADSSV assume a linear perturbation development.

Not suitable: Long-term prediction & Large spread case Ensemble track forecast

with large spread

We take TC position (e.g., Lat or Lon) as a metric Ensemble-based Sensitivity [Torn & Hakim, 2008; Aonashi & Eito, 2011] Sensitivity λ is defined as a slope of regression line. Large λ: change in a physical variable è LARGE TC displacement

Ensemble-based Sensitivity [Torn & Hakim, 2008; Aonashi & Eito, 2011] Metric j = Typhoon position (e.g., Lat or Lon)

Initial pertubation δx (n degree-of-freedom)

Metric δj Index of ensmeble members

Definition of sensitivity λ

m>n

m<n

Sensitivity λ defined as a slope →If the slope is large, a typhoon position is very sensitive to the physical variable.

Advantage and Disadvantage l  Objectivity: TC position itself employed as a metric l  Broad Applicability: No Assumption on the linearity

×Numerical cost: Number of ensemble members can not be far smaller than the degree-of-freedom of δx.

Ø Incremental approach: The perturbation field δx is defined in the reduced- dimension with a larger grid spacing.

“Incremental Typhoon-position-Oriented Sensitivity Analysis” (ITO-SAn)

To resolve this problem

Application to typhoon Shanshan(2006) Domain 1: ⊿x=⊿y=54km Domain 2: ⊿x=⊿y=18km

Circles: JMA besttrack data : Ensemble-mean TC position

Time Scheduling ◆ 00Z Sep 14: Spin-up by using EnKF system (28 members) for one day starting from the NCEP final analysis ◆ 00Z Sep 15: Add Gaussian noise and perform 2-day ensemble forecast (800 members) to conduct the sensitivity analysis Hereafter, we refer “00Z Sep 15” to as “initial time.”

Ensemble prediction system ◆WRF EnKF and ensemble prediction system developed by Guo-Yuan (Wu et al., 2010) →TC position is adjusted by EnKF

Generation of perturbations ◆Perturbed variables: (u,v) ◆Horizontal grid spacing: 540km ◆Verical levels: 5 levels ◆Gaussian noise independently in each grid and interpolated ◆Number of members: 800

Synoptic features around TC Shanshan

GPH and (u, v)

@500 hPa Initial time 00Z 15 Sep

00Z 16 Sep 00Z 17 Sep

subtropical high

mid latitude trough

Sensitivity of TC center latitude with respect to ζ (vorticity field) in the middle troposphere

t=12h @ σ=0.51 t=24h @ σ=0.51 t=48h @ σ=0.51

99.9% significance

90% significance

+⊿ζ yields Northward displacement

+⊿ζ yields Southward displacement

•  12 hour: Dipole pattern •  24-48 hour: swirling pattern centered at initial TC position

Sensitivity field of LAT with respect to ζ t=12h @ σ=0.29 t=24h @ σ=0.29 t=48h @ σ=0.29

t=12h @ σ=0.51 t=24h @ σ=0.51 t=48h @ σ=0.51

t=12h @ σ=0.85 t=24h @ σ=0.85 t=48h @ σ=0.85

99.9% significance

90% significance

Sensitivity with respect to the vorticity field

t=12h @ σ=0.51 t=24h @ σ=0.51 t=48h @ σ=0.51

t=12h @ σ=0.51 t=24h @ σ=0.51 t=48h @ σ=0.51

Sensitivity with respect to the divergence field

Verification experiments t=48h @ σ=0.51 t=48h @ σ=0.85

・Three verification experiments: The positive vorticity anomaly is introduced 　 at the initial time (t=0 h). ・We expect northward displacement after 48 hr in E500 and E850, southward in WEST.

E500 E850 WEST WEST

Results of verification experiments

Ensemble-mean differences in direction and magnitude relative to the control run are consistent with those expected.

Results of verification experiments

Sensitivity analysis with decreasing number of members →Smaller m yields less reliable sensitivity field.

m=800 m=400

m=200 m=100

Summary (Part I) •  Most of existing sensitivity analysis methods on

a tropical cyclone (TC) motion require an ”ad hoc” metric and the assumption of the linear time evolution of perturbations.

•  We proposed the new methodology (ITO-SAn), in which TC position is directly taken as a metric, to resolve these problems and applied to TC Shanshan (2006) as a first step.

•  This method is shown to be powerful indicator relevant to the TC motion in terms of the disaster prevention and research purpose.

Intensity: Data Assimilation Optimization of air-sea exchange coefficients

through a variational data assimilation method

Social impact: Tropical cyclone (TC) intensity

（Yamada et al., 2010）

Current End of 21st century

Maximum wind speed[m s-1]

Ø Financial cost relates to maximum wind speed through a power law (Nordhaus, 2010; Nishijima et al., 2010)

Ø Growing concerns about enhanced TC intensity due to global warming (e.g., Emanuel, 2005)

TC forecast skill in the recent 20 years

1990 2008

24-hr forecast 24-hr forecast

48-hr forecast 48-hr forecast 72-hr forecast 72-hr forecast 96-hr forecast

120-hr forecast 96-hr forecast

120-hr forecast

2008 1990

Ø Track: Errors halved in this 20 years Ø Intensity: No significant improvement

(National Hurricane Center website)

Max. wind speed in equilibrium (Emanuel, 1986)

eye eyewall

■ CE: Water vapor exchange coefficient ■ CD: Drag coefficient (Determining the magnitude of friction)

～ E

CE Water vapor exchange CD

Drag coefficient

CD

CE

No Direct Obs.

No Direct Obs.

Attempts to evaluate CD & CE

Ø  Direct eddy correlation measurements CBLAST, ITOP àIn spite of the vital effort, reliable direct observations are not available over 30 m/s (Black et al., 2007).

Ø  Profiling method (Powell et al., 2003) Ø  Numerical modeling (Moon et al., 2004; Kihara & Hirakuchi, 2009) Ø Theoretical estimate (Makin, 2005) Ø  Laboratory experiment (Donelan et al., 2004) è Large discrepancies among different methodologies

Schematic illustration in the physical coordinate: 4D-VAR method

(For simplicity, consider an advection-diffusion eqs.)

Optimized

Mesoscale data assimilation (MDA) as initial value and parameter value problem

Sensitivity of Max Wind to water vapor

Radius from TC center [km] 0 20 40 60 0

2 4

6 8

10

time = － min

•  You may think MDA is an initial value problem. •  Characteristic timescale for

Synoptic scale phenomena: ～1/f Vortex with high Rossby number ～1/(f+ζ)

See Ito et al. (2011) for details in physical interpretation.

Eyewall

Schematic illustration in the phase space Cost function (J)

★

★

★

JMin. ★

Initial variable (X-T)

ü  Smagorinsky Scheme

ü  Axisymmetric Non-hydrostatic Model [Rotunno and Emanuel, 1987]

ü Warm-rain ü  Tenv, qenv: Conditionally Unstable

ü  1-dimensional Mixed Layer Model

[Schade & Emanuel 1999]

ü  Coupling: Same as in Emanuel (2004)

ü ⊿r:3.75 km, ⊿z:313 m, time step:2 s ü  Vortexinit: Vmax=12 m/s ü  SSTenv: 30℃(day 0) à 27℃(day 10) ü  Translation speed of TC: 6 m/s

Model Setup

Oceanic Model

Tenv

比湿

z (k

m)

20 0

z (k

m)

qenv

Specific Humidity [g/kg]

Simple Coupled Model Description Temperature [K]

Atmospheric Model

Idealized perfect model experiment with an axisymmetric TC model (Rotunno and Emanuel, 1987)

•  Relatively simple but in a good agreement with real TC •  Maximum wind speed at the base of

Wind field (Shading: Tangential Wind)

Primary Heating in the eyewall region

Adiabatic Heating Profile

time Now (t=0) (t=-T)

Initial time of DA xi+1=M(xi,C)

Obs. x-T

X

x-T TRUE xi+1=M(xi,C ) TRUE

DA period

WRONG xi+1=M(xi,C )

x-T ASM

ASM

Idealized DA system: Identical Twin Experiment ■ Since we do not know the true state of the real atmosphere,

feasibility of DA method is not easily attested in a real case. ■ We assume the model results with the prescribed CD & CE as

artificial “True” field, and add Gaussian noise to generate “obs.” ■ It assures whether updated results xASM approach to xTRUE.

Idealized DA system: Identical Twin Experiment

■ Components of Identical Twin Experiment

NoAsm run with “wrong” CD, CE and initial state

Asm_NoCoef Initial state alone is adjusted by DA

Asm_Coef CD, CE, initial state are adjusted by DA

True run with “true” CD, CE and initial state

Obs. True field + Gaussian noise (We assume the

datasets are sampled as in multiple aircraft missions.)

Ø DA is successful if (Asm_Coef) ～ (True)

Experimental Setup

Adjoint eqs. Same as forward eqs. except that processes associated with sound wave and microphysics are not included.

Assim. window 4 days (Day 6.0 - Day 10.0)

Obs. variable Horizontal wind velocity, water vapor mixing ratio, and mixed layer momentum

Obs. Quantity Every grid within r<100 km, z<5 km (every 12 hour)

Settings of CD & CE [For True] CD: Powell et al.(2003), CE: Arbitrary [For NoAsm] CD, CE: Large & Pond (1981) (V≦30m/s)

Bg. err. cov. mat. B

Prescribed: Variance in time of True runà Magnitudes 2D-Fourier analysis of perturbed True runs à Scales

Obs. err. cov. mat. O

Prescribed: Diagonal matrix. Magnitudes are 1/20 of diagonal components of B.

Dropsonde obs. project by NOAA/HRD (Montgomery et al., 2006)

0 60 r(km) 0

4

Run with “wrong” CD and CE

updated CD and CE

“true” CD and CE

≒

Dropsonde obs.

Adjoint-based DA method

Result 1: Adjusted CD and CE

Ø RMSE from “True” case 　“NoAsm”: 8.9 m/s 　“Asm_NoCoef” 7.9 m/s 　“Asm_Coef” 2.1 m/s Ø TC intensity largely

controlled by CD and CE.

Obs.

Maximum Tangential Wind Speed Vθ at the surface

Result 2: Improved inner-core dynamics

Errors in wind and temperature (T) fields NoAsm Asm_NoCoef Asm_Coef

Erros in Wind Fields

Errors in T and heating

⊿θ<-4K

⊿θ<-2K

⊿θ<-2K ⊿θ<-4K

⊿θ<-2K

Weaker Condensation

Weaker Vmax

Weaker Vmax

Erros in Wind Fields Erros in Wind Fields

Errors in T and heating

Weaker Condensation

Errors in T and heating

Summary (Part II) •  Tropical cyclone (TC) intensity largely relies

on CD & CE, while they are quite uncertain. •  We have proposed an optimization of them

through a variational data assimilation (VDA) method which fully utilizes available observations away from sea surfaces.

•  VDA experiments exhibit significant improvements in TC intensity, inner-core structure and track.

•  In a mathematically strict sense, an information criterion is a better indictor of prediction skill. It will be a future topic.

Thank you.