Ensemble Prediction with Perturbed Initial and Lateral Boundary

Conditions over Complex TerrainJinhua Jiang, Darko Koracin, Ramesh Vellore

Desert Research Institute, Reno, NevadaDesert Research Institute, Reno, Nevada

Weather Impacts Decision Aids (WIDA) Workshop, 2012, Reno, NV

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Outline

Introduction

WRF Model

Perturbed Initial conditions (ICs)

Perturbed lateral boundary conditions (LBCs)

ICs’ ensemble

LBCs’ ensemble

Conclusion & discussion

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Introduction

Where is the uncertainty of NWP from?

A Initial-boundary value problem

Model frame/structure （ Grid structure, model discretization）Physical parameterizations

Domain size, grid resolution

Model topography, SST, soil moisture…

“KNOW WHAT YOU KNOW,KNOW WHAT YOU DO NOT KNOW.”“ “知之为知之，不知为不知

Ref: Lorenz, 1982, Atmospheric predictability experiments with a large numerical model. Tellus (1982), 34, 505-513.

Lagged Ensemble

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WRF Model

Flow Chart

WRFWRF

Arakawa-C grid; Terrain-following hydrostatic-

pressure vertical coordinate (η); Flux-form Euler Equations; Discretization: Runge-Kutta

scheme, (Wicker & Skamarock(2002) time splitting for acoustic integration;

Gravity wave/Vertical velocity: Rayleigh Damping layer.

Ref: Skamarock, W. C., J. B. Klemp, J. Dudhia, et al. 2008, A Description of the Advanced Research WRF Version 3. NCAR Technical Note. NCAR/TN-475+STR.

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Model set-up

The two-nested domains

• Time period: 12-27 Dec. 2008;• Vertical level: 37;• ICs/LBCs: GFS data;

0-180hr, 0.5° x 0.5° ;180-384 hrs , 2.5 x 2.5.

• PBL: Mellor-Yamada-Janjic;• Radiation: RRTM LW scheme,

Goddard SW scheme;• Land surface: Unified Noah LSM;• Microphysics:

Morrison 2-moment scheme;

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Perturbed Initial Conditions

)3(** RpUUURpUx hvp

Where, Uh stands for horizontal correlations, Uv for vertical covariances, and Up for multivariate covariances.

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Background error

Cross-section1

Cross-section2

Cross-section2

Cross-section1

Mod

el le

vels

Mod

el le

vels

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Perturbed Initial Conditions (continued)

Perturbation of temperature (left) and pressure (right).

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Perturbed Lateral Boundary Conditions

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Perturbed Lateral Boundary Conditions (Cntnd)

a b

700hpa T 0.4239 0.3867

500hpa T 0.4829 0.4485300hpa T 0.2755 0.1563

700hpa GHT 0.4061 0.4263

500hpa GHT 0.4922 0.5428

300hpa GHT 0.4683 0.4887

700hpa U 0.3737 0.3345

500hpa U 0.3725 0.3475

300hpa U 0.275 0.2244

700hpa V 0.3104 0.2631

500hpa V 0.4092 0.3882

300hpa V 0.1904 0.1407

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Perturbed Lateral Boundary Conditions (Cntnd)

Error curve

Error curve(left) & Ration of error growth(right).

Error growth ratio of temperature at 500hpa from the physical ensemble RMSEs data(Koracin & Vellore, et. al.)

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Perturbed Lateral Boundary Conditions (Cntnd)

Perturbed pressure at 10-m model level

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ICs’ ensemble (50 members)

Pert. ICs onlyfor D01, interpolate ICs from D01 for D02

Domain1 Domain1

Domain2 Domain2

Temperature (right) and Geopotential height (left) of domain 1 and domain 2 at 500hPa at OAK, CA, from ICs’ ensemble (only D01 perturbed).

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“Spaghetti” plots of the 238 K (blue lines) and 258 K (green lines) air temperature from domain 2 for forecast times of 2, 5, 10 and 15 days.

Domain 2

Pert. ICs only for D01

2nd day5th day

10th day 15th day

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Pert. ICs only for D02

Domain2 Domain2

ICs’ ensemble (50 members)

Difference: LBCs for domain 2

(size: 3708 km X 3708 km)

Temperature (right) and Geopotential height (left) of domain 2 at 500hPa at OAK, CA, from ICs’ ensemble (only D02 perturbed).

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Pert. ICs only for D02ICs’ ensemble (50 members)

Domain 2

With same LBCs the perturbation in ICs fades.

2nd day5th day

10th day 15th day

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LBCs’ ensemble (50 members)LBCs’ perturbation only for domain 2

Temperature (right) and Geopotential height (left) of domain 2 at 500hPa at Oakland and Reno, CA, from LBCs’ ensemble (only D02’s LBCs perturbed).

Caught the second front passage.

Oakland

Reno

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LBCs’ ensemble (50 members)LBCs’ perturbation only for domain 2

2nd day5th day

10th day 15th day

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Talagrand diagram (500hPa)

More obs. fall between ensemble members, less out the range.

LBCs’ ensemble (50 members)

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Talagrand diagram (700hPa)

More obs. fall between ensemble members, less out the range.

LBCs’ ensemble (50 members)

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RMSE vs. spread

ICs Ens: spread 1.5/2 times smaller than RMSE

LBCs Ens: spread is equivalent with RMSE.

700mb 850mb 925mb

300mb 500mb

LBCs’ ensemble (50 members)

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Conclusion & discussion

For the limited-area ensemble, e.g. a domain size ~ 4000kmX4000km:

Error in out-domain/lateral boundary conditions is important.

Small error in initial conditions fades after two days;

Perturbation in lateral boundary conditions play a main role later on.

More issues to be addressed:

?Different domain size,

?Multi-models (different grid structure, discretization)

?Model SST/Soil moisture & temperature/Topography

?Physical parameterizations

?Ensemble member size…

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Thanks for your attention.

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