MPO 674 Lecture 9

2/10/15

Hypotheses

1. Singular Vector structures are dependent on the barotropic instability condition in the initial vortex.

2. The spreading in TC track forecasts is due to instabilities in the storm and its environment.

Singular Vectors

Solve “analysis error covariance optimals” via

Result: perturbation structures that grow, in a linear sense, to maximize total energy within a verification region around the tropical cyclone.

Compute here for barotropic version of Spectral Element Ocean Model (SEOM, Iskandarani 2008), with initial vortices on f- and beta-planes.

Yamaguchi et al. (2011, JAS)

Transient growth, upshear

tilt vanishes.

SVs capture

barotropic instability,

faster growth.

f-plane

Necessary condition for barotropic instability NOT

satisfied

Necessary condition for barotropic instability satisfied

Yamaguchi et al. (2011, JAS)

beta-plane: Sinlaku Yamaguchi et al. (2011, JAS)

beta-plane: Sinlaku Yamaguchi et al. (2011, JAS)

Results 1H: SV structures are dependent on the barotropic

instability condition in the initial vortex.

• f-plane: initial vortices don’t meet barotropic instability condition:– SVs tilted against shear, grow via Orr mechanism– Leading singular value increases with Vmax, decreases with RMW– Locations of SVs move outward with RMW

• f-plane: initial vortices meet barotropic instability condition:– SVs initially tilted against shear, period of transient growth– SV then locks into normal mode structure, grows exponentially

• Beta-plane:– All 1st and 2nd SVs have a wavenumber 1 structure at topt

– Some dependence on resolution

Hypotheses

1. Singular Vector structures are dependent on the barotropic instability condition in the initial vortex.

2. The spreading in TC track forecasts is due to instabilities in the storm and its environment.

Ensemble prediction systems

NCEP: use Ensemble Transform to initialize ensemble.ECMWF: use Singular Vectors to initialize ensemble.

What mechanisms cause the spreading of the ensemble members?

ECMWF NCEP

0 h

Background steering

Asymmetric propagation

Yamaguchi and Majumdar (2010, MWR)

12 h

Baroclinic instability centered

on the vortex

Perturbation draws eddy available potential energy

from mean flow

Theory Shading: StreamfunctionContour: Temperature

Ensemble perturbation

Yamaguchi and Majumdar (2010, MWR)

0 h

12 h

6 h

18 h

Eddy APE is converted into

EKE wind perturbation grows where

radial heat flux is positive

WindRadial heat flux

Yamaguchi and Majumdar (2010, MWR)

Results 2

H: The spreading in TC track forecasts is due to instabilities in the storm and its environment.

• Growth of advection flow perturbations for Sinlaku is larger in ECMWF than NCEP.

• Perturbation growth in ECMWF ensemble associated with – 1) baroclinic energy conversion in a vortex, – 2) baroclinic energy conversion in midlatitude waves,– 3) barotropic energy conversion in a vortex.