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)
Necessary condition for
barotropic instability NOT
satisfied
Transient
growth,
upshear
tilt
vanishes.
f-plane
Necessary condition for
barotropic instability satisfied
SVs
capture
barotropic
instability,
faster
growth.
Yamaguchi et al. (2011, JAS)
beta-plane: Sinlaku
Yamaguchi et al. (2011, JAS)
beta-plane: Sinlaku
Yamaguchi et al. (2011, JAS)
Results 1
H: SV structures are dependent on the barotropic
instability condition in the initial vortex.
•
f-plane: initial vortices don’t meet barotropic instability condition:
–
–
–
•
f-plane: initial vortices 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
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
Background
steering
0h
Asymmetric
propagation
12 h
Yamaguchi and Majumdar (2010, MWR)
Theory
Ensemble perturbation
Shading: Streamfunction
Contour: Temperature
Baroclinic
instability
centered
on the
vortex
Perturbation draws eddy
available potential energy
from mean flow
Yamaguchi and Majumdar (2010, MWR)
Radial heat flux
Wind
0h
6h
12 h
Eddy APE is
converted into
EKE  wind
perturbation
grows where
radial heat
flux is positive
18 h
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.