1. MPO 674 Lecture 9 2/10/15

6. 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.

7. 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.

8. Yamaguchi et al. (2011, JAS)

9. 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)

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

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

12. 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: – 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 1 st and 2 nd SVs have a wavenumber 1 structure at t opt – Some dependence on resolution

13. 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.

14. 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?

15. ECMWF NCEP 0 h Background steering Asymmetric propagation Yamaguchi and Majumdar (2010, MWR) 12 h

16. Baroclinic instability centered on the vortex Perturbation draws eddy available potential energy from mean flow Theory Shading: Streamfunction Contour: Temperature Ensemble perturbation Yamaguchi and Majumdar (2010, MWR)

17. 0 h 12 h 6 h 18 h Eddy APE is converted into EKE  wind perturbation grows where radial heat flux is positive Wind Radial heat flux Yamaguchi and Majumdar (2010, MWR)

18. 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.