Forecasting of Atlantic Tropical Cyclones Using a Kilo-Member Ensemble

1. Forecasting of Atlantic Tropical Cyclones Using a Kilo-Member Ensemble M.S. Defense Jonathan Vigh

2. Acknowledgements • Graduate Adviser: Dr. Wayne Schubert • Master’s Committee • Dr. Mark DeMaria • Dr. William Gray • Dr. Gerald Taylor • Dr. Scott Fulton (MUDBAR) • Schubert Research Group • Data Sources: NCEP and TPC/NHC • Mary Haley and NCL Developers • Funding: • Fellowship Support from Significant Opportunities in Atmospheric Research and Science Program (UCAR/NSF) and the American Meteorological Society • NSF Grant ATM-0087072, NSF Grant ATM-0332197, NASA/CAMEX Grant NAG5-11010, and NOAA Grant NA17RJ1228

3. Outline • The Big Picture • Background • The MUDBAR Model • Design of a Kilo-Member Ensemble • Postprocessing and Verification • Results • Case Studies • Conclusions

5. Why study track? • Major improvements in official track errors • 72-h Official Track Forecast Errors • -1.9% per year from 1970-1998 • -3.5% per year from 1994-1998 • Societal vulnerability increasing faster (e.g. Mitch, evacuation times) • Even with accurate forecasts of intensity, wind field, rain – all for naught if the track is wrong

6. It’s Chaos Out There! • The idea behind a forecast • Perfect models and perfect initializations • The nefarious atmosphere • Error saturation and predictability limits • Much of the track errors come from the major forecast errors of storms that follow erratic tracks • Would be good to know in advance before large errors occur

9. Ensemble Background • Definition: Any set of forecasts that verify at the same time. • Idea is to simulate the sources of uncertainty present in the forecast problem • Uncertainty in the initial state • Uncertainty in the model • Theory dictates that the mean forecast of a well-perturbed ensemble should perform better than any comparable single deterministic forecast

11. Types of Ensembles • Monte Carlo simulations • Lagged-average Forecasting • Multimodel Consensus (Poor Man’s Ensemble) • Dynamically constrained methods: • Breeding of Growing Modes • Singular Vector Decomposition

12. Questions and the thesis: • Can a well-perturbed ensemble mean give a better forecast than any single realization? • How many ensemble members are necessary to give the “right” answer? • Is there a relationship between ensemble spread and forecast error? • Can this relationship be used to provide meaningful forecasts of forecast skill? • How accurately does the ensemble envelope of all track possibilities encompass the actual observed track?

13. The MUDBAR Model • The nondivergent modified barotropic equation model (MUDBAR) of Scott Fulton • Data enter the model through the initial condition (specify q) and the time-dependent boundary conditions (specify ψ on boundary, q on inflow)

14. Model Setup (Vigh et al. 2003) • 6000-km square domain • Optimized 3 grid configuration, 32 x 32 grid points • Mesh spacing: 194, 97, and 48 km • Each 120-h forecast takes 1.4 s on a 1 GHz PC (entire ensemble runs in ~1 h) • Is able to reproduce the accuracy of the shallow water LBAR model

15. Bogussing Procedure • The vortex profile of DeMaria (1987); Chan and Williams (1987): • This bogus vortex is blended with the GFS initial wind field at the operationally-estimated storm position with the appropriate motion vector:

16. Ensemble Design • Simple parameter-based perturbation methodology (fixed) • Number and magnitudes of perturbations in each class chosen based on sensitivity experiments • Five perturbations classes: • 11 environmental perturbations (NCEP GFS ensemble) • 1 control forecast • 10 perturbed forecasts • 4 perturbations to the depth of the layer-mean averaging of the wind • very deep layer mean (1000 hPa – 100 hPa) • standard deep layer mean (850 hPa – 200 hPa) • Moderate depth layer mean (850 hPa – 350 hPa) • Shallow depth layer mean (850 hPa – 500 hPa)

17. Ensemble Design, cont’d • 3 perturbations to the model’s equivalent phase speed • 300 m/s appropriate for Subtropical Highs • 150 m/s middle of the road • 50 m/s appropriate for convective systems • 3 perturbations to the bogus vortex size (Vm) • Vm = 15 m/s small vortex • Vm = 30 m/s medium-size vortex • Vm = 50 m/s large vortex • 5 perturbations to the storm motion vector • All perturbations are cross multiplied to get an ensemble of: • 11 x 4 x 3 x 3 x 5 = 1980 members! The Kilo-Ensemble

20. Postprocessing • 1980 individual member forecasts – what to do now? • Total ensemble mean (ZTOT), spread • 20% cutoff used • Subensemble means (for each perturbation), spread • Calculation of spatial strike probabilities • Value of probabilistic forecasting: • Probabilities don’t hedge • The high tomorrow will be 73 . . . • Capture the entire essence of the ensemble forecast

27. Verification • Murphy (1993) talks about 3 types of ‘goodness’ for forecasts • Consistency • Quality • Value • Job of verification is to measure goodness • Measures-oriented methods • Distribution-oriented methods

28. Verification Procedures • 293 cases from roughly 50 storms from the 2001-2003 Atlantic Hurricane Seasons • Only tropical and subtropical cases included • All seasonal statistics are homogeneous • Statistics calculated for the total ensemble mean and subensemble mean track forecasts: • Mean track error • x-bias • y-bias • Skill relative to CLIPER • Frequency of superior performance

37. Other measures of ensemble performance • Reliability of the ensemble envelope • The outer envelope (0%) contained the retained the verification 80% of the time at 72-h, and 66% at 120-h • Reliability of the spatial probabilities • Spread vs. error relationship • Large spread -> large error • Small spread -> small error