forecasting of atlantic tropical cyclones using a kilo-member ensemble m.s. defense jonathan vigh
TRANSCRIPT
Forecasting of Atlantic Tropical Cyclones Using
a Kilo-Member Ensemble
M.S. Defense
Jonathan Vigh
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
Outline
The Big Picture Background The MUDBAR Model Design of a Kilo-Member Ensemble Postprocessing and Verification Results Case Studies Conclusions
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
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
Predictability Limits for a Barotropic Model
(Leslie et al. 1998)
(nm) 0 24 48 72
Inherent 21 52 80 118
Practical 46 90 138 208
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
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
dt
d (prog)
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?
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)
eqvcf
a
qm
m
xm
yx
qm
t
q
0
0
)(
,
0),(
),(
222
coscoscos2
2
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
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:
b
mmm
mvor r
r
rr
rVrVv 1
1exp)(
km 1000 ,exp)(
)()1(2
0
bb
cenvoranal
rr
rrw
vvwvwv
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)
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
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
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
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
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
Conclusions
Ensemble mean forecast did not outperform the control forecast
Ensemble strike probabilities seem within the realm of reality (reliability plot)
Weak relationship between spread and error peaks at 60-h -> can estimate forecast skill
Validity of barotropic model decreases at around 84-h, just as the benefits of the GFS environmental perturbations start to kick in
Questions:
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?
Possible reasons for performance degradation
Reasons for poor ensemble performance: Barotropic dynamics are too simple Artificial edge biases Poor design – fixed perturbations not too good Spurious binary interactions between bogus
vortex and GFS-analyzed vortex
Future Work
Immediate future work (before Miami) Verify the strike probabilities using the Brier and
the ROC scores Calculate a 26-member ensemble from just the 26
perturbations (without cross multiplication) Derive and verify cluster analysis forecasts Determine extent and effect of the binary
interactions
Future Work (cont’d)
Select an optimal subensemble for the particular forecast situation (error recycling)
Redesign the ensemble to use relative perturbations
Compare to other ensembles for track forecasting (GFS, GUNA, ECMWS, etc.)
Questions