Track Forecasting of Track Forecasting of 2001 Atlantic Tropical 2001 Atlantic Tropical Cyclones Using a Kilo-Cyclones Using a Kilo-

Member EnsembleMember Ensemble

8:30 AM April 30, 20028:30 AM April 30, 2002

Jonathan VighJonathan VighMaster’s StudentMaster’s Student

Colorado State UniversityColorado State UniversityDepartment of Atmospheric ScienceDepartment of Atmospheric Science

AcknowledgmentsAcknowledgments

Wayne Schubert, graduate advisorWayne Schubert, graduate advisor Mark DeMariaMark DeMaria Scott FultonScott Fulton Rick TaftRick Taft FundingFunding

– Significant Opportunities in Atmospheric Significant Opportunities in Atmospheric Research and Science (SOARS) Program, Research and Science (SOARS) Program, fellowshipfellowship

– American Meteorological Society, American Meteorological Society, fellowshipfellowship

What causes track error?What causes track error?

Inaccurate spatial and temporal sampling -Inaccurate spatial and temporal sampling -> analysis uncertainty> analysis uncertainty

Incomplete representation of physical Incomplete representation of physical processesprocesses

Discretization and truncation errorDiscretization and truncation error Atmosphere’s inherent chaotic nature Atmosphere’s inherent chaotic nature

– InstabilityInstability– Nonlinear interactions between various spatial Nonlinear interactions between various spatial

scalesscales

(Leslie et al., 1998)(Leslie et al., 1998)

What is an ensemble?What is an ensemble?

A collection deterministic realizations A collection deterministic realizations obtained by varying:obtained by varying:– Model (numerics, resolution, or physics)Model (numerics, resolution, or physics)– Perturbing model parametersPerturbing model parameters– Initial analysis fields Initial analysis fields

Time of analysisTime of analysis Generation method (adjoint or 4DVAR Generation method (adjoint or 4DVAR

methods)methods) Stochastic or bred perturbationsStochastic or bred perturbations

Benefits of an ensembleBenefits of an ensemble

With many realizations over properly With many realizations over properly perturbed initial conditions, the subspace perturbed initial conditions, the subspace of dynamical pathways can be sampledof dynamical pathways can be sampled

Ensemble mean is generally more Ensemble mean is generally more accurate than a single deterministic accurate than a single deterministic forecast (Leith, 1974)forecast (Leith, 1974)

Ensemble allows estimation of higher Ensemble allows estimation of higher moment statistics of the forecastmoment statistics of the forecast– Forecast uncertaintyForecast uncertainty– Bifurcation of dynamical pathwaysBifurcation of dynamical pathways– Probability density functionsProbability density functions

MBAR: Multigrid Barotropic MBAR: Multigrid Barotropic ModelModel

Modified barotropic vorticity equationModified barotropic vorticity equation Finite difference, multigrid methods (Fulton, Finite difference, multigrid methods (Fulton,

2001)2001) 3 Nested grids on a square 6000 km domain3 Nested grids on a square 6000 km domain

hh11 = 125 km, h = 125 km, h22 = 63 km, h = 63 km, h33 = 31 km = 31 km Efficient and accurate multigrid methods Efficient and accurate multigrid methods

makes a kilo-scale operational model makes a kilo-scale operational model feasiblefeasible– Accuracy comparable to LBAR in only 1/38 of the Accuracy comparable to LBAR in only 1/38 of the

computing timecomputing time– Each 120-hr track forecast takes ~2.5 secondsEach 120-hr track forecast takes ~2.5 seconds– A 1980 member ensemble takes approximately A 1980 member ensemble takes approximately

1.3 hours on a 1 GHz Intel PC1.3 hours on a 1 GHz Intel PC

Perturbations in initial and Perturbations in initial and background fieldsbackground fields

Operational MRF ensemblesOperational MRF ensembles 5 independent breeding cycles are 5 independent breeding cycles are

used in the analysis cycle to estimate used in the analysis cycle to estimate subspace of fastest growing analysis subspace of fastest growing analysis errors (Toth and Kalnay, 1997)errors (Toth and Kalnay, 1997)

Adding and subtracting these vectors Adding and subtracting these vectors from the analysis yields 10 + control from the analysis yields 10 + control initial and background fields for MBARinitial and background fields for MBAR

00Z at 2 degree resolution 00Z at 2 degree resolution

Perturbations to vertical Perturbations to vertical averagingaveraging

Four deep layer vertical averages of Four deep layer vertical averages of wind field simulate uncertainties in wind field simulate uncertainties in steering layer depthsteering layer depth

Pressure weighted averages of Pressure weighted averages of following layers (mb):following layers (mb):– Shallow Shallow (850 - 700)(850 - 700)– Medium Medium (850 – 350)(850 – 350)– Deep Deep (850 – 200) (850 – 200) – EntireEntire (1000 – 100)(1000 – 100)

Perturbations to vertical Perturbations to vertical decomposition of vertical decomposition of vertical

modesmodes In 2D barotropic vorticity models, ultra-In 2D barotropic vorticity models, ultra-

long Rossby waves experience excessive long Rossby waves experience excessive retrogression (Wiin-Nielsen, 1959)retrogression (Wiin-Nielsen, 1959)

Inclusion of inverse Rossby radius in the Inclusion of inverse Rossby radius in the prognostic equation can fix thisprognostic equation can fix this

Uncertainties in the vertical decomposition Uncertainties in the vertical decomposition of the tropical atmosphere are handled by of the tropical atmosphere are handled by perturbing equivalent phase speedperturbing equivalent phase speed– 50 ms50 ms-1-1

– 150 ms150 ms-1-1

– 300 ms300 ms-1-1

Perturbations to vortex Perturbations to vortex size/strength size/strength

Simulates uncertainties in the size Simulates uncertainties in the size and strength of the vortexand strength of the vortex– Weak or small TS (vmax = 15 msWeak or small TS (vmax = 15 ms-1-1))– Weak or medium sized hurricane (wmax Weak or medium sized hurricane (wmax

= 35 ms= 35 ms-1-1))– Strong or large hurricane (vmax = 50 Strong or large hurricane (vmax = 50

msms-1-1)) For a barotropic model, the size of For a barotropic model, the size of

the outer circulation is important the outer circulation is important factor in the track forecastfactor in the track forecast

Perturbations to storm motion Perturbations to storm motion vectorvector

Simulates uncertainties in the initial storm Simulates uncertainties in the initial storm location and directionlocation and direction

Motion vector added to wind field of bogus Motion vector added to wind field of bogus vortex with exponentially decaying vortex with exponentially decaying blending radiusblending radius– No motion perturbationNo motion perturbation– Fast and to rightFast and to right– Slow and to rightSlow and to right– Fast and to leftFast and to left– Slow and to left Slow and to left

Cross-multiplication across the Cross-multiplication across the five perturbation classesfive perturbation classes

11 initial and background fields 11 initial and background fields (180)(180) 4 deep layer averages 4 deep layer averages (495)(495) 3 vertical decompositions 3 vertical decompositions (660)(660) 3 vortex sizes/strengths 3 vortex sizes/strengths (660)(660) 5 motion vectors 5 motion vectors (396)(396)

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1980 ensemble members1980 ensemble members

26 sub-ensembles26 sub-ensembles

So what does the kilo-So what does the kilo-ensemble look like?ensemble look like?

ChantalChantal DeanDean ErinErin IrisIris MichelleMichelle OlgaOlga

ChantalChantalAugust 17 and 18August 17 and 18

Well handled by the ensembleWell handled by the ensemble A fairly weak storm embedded in A fairly weak storm embedded in

trade flowtrade flow For first several days of forecast, a For first several days of forecast, a

tight envelope, indicating high tight envelope, indicating high confidenceconfidence

DeanDeanAugust 23August 23

Example of the challenges of Example of the challenges of recurvature off the East Coastrecurvature off the East Coast

Total ensemble mean lagged behind Total ensemble mean lagged behind actual pathactual path

Ensemble ‘swarm’ stretched out in Ensemble ‘swarm’ stretched out in the direction of recurvaturethe direction of recurvature

ErinErinSeptember 3September 3

A storm which weakened to a tropical A storm which weakened to a tropical depression, then later strengthened depression, then later strengthened to a strong hurricaneto a strong hurricane

Ensemble mean successfully Ensemble mean successfully predicted path, although significant predicted path, although significant cross-track spread developedcross-track spread developed

IrisIrisOctober 5October 5

Another example of a tight envelope Another example of a tight envelope early on, suggesting high forecast early on, suggesting high forecast confidenceconfidence

Ensemble spreads out at end, but Ensemble spreads out at end, but actual track still contained in actual track still contained in envelopeenvelope

A minority of members experience A minority of members experience recurvaturerecurvature

MichelleMichelle

Storm tracked along edge and then Storm tracked along edge and then outside of envelope – an example of outside of envelope – an example of the ensemble’s failure to accurately the ensemble’s failure to accurately span all dynamical pathwaysspan all dynamical pathways

An example of rapid growth in An example of rapid growth in ensemble spread with time, ensemble spread with time, suggesting low confidence in suggesting low confidence in ensemble mean forecastensemble mean forecast

Ensemble mean caught in middle of Ensemble mean caught in middle of bifurcation -> large errorsbifurcation -> large errors

OlgaOlga

Forecasts for 11/24/02 inaccurately Forecasts for 11/24/02 inaccurately predict recurvature – large spread predict recurvature – large spread developsdevelops

Forecasts for 11/25/02 catch onto the Forecasts for 11/25/02 catch onto the correct path. Large spread but correct path. Large spread but ensemble means are accurateensemble means are accurate

Forecasts for 11/26/02 show an Forecasts for 11/26/02 show an example of one sub-ensemble example of one sub-ensemble correctly picking the storm pathcorrectly picking the storm path

Average error of sub-ensembles based on vertical averaging

0

100

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0 12 24 36 48 60 72 84 96 108 120

Forecast period (hrs)

Av

era

ge

tra

ck e

rro

r (n

m) CLP5

A5K0

ZTOT

SLY4

SLY5

SLY6

SLY7

Average track error for sub-ensembles over ceqv

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0 12 24 36 48 60 72 84 96 108 120

Average track error (nm)

Fo

reca

st p

eri

od

(h

rs)

CLP5

A5K0

ZTOT

SGM1 (50 m/s)

SGM2 (100 m/s)

SGM3 (300 m/s)

Average track error of sub-ensembles based on vortex size/strength

0

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0 12 24 36 48 60 72 84 96 108 120

Forecast period (hrs)

Av

era

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rro

r (n

m)

CLP5

A5K0

ZTOT

SVM1 (15 m/s)

SVM2 (30 m/s)

SVM3 (50 m/s)

Average xbias of sub-ensembles based on vertical averaging

-350

-300

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-150

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-50

0

50

0 12 24 36 48 60 72 84 96 108 120

Forecast period (hrs)

Av

era

ge

xb

ias

(nm

) CLP5

A5K0

ZTOT

SLY4

SLY5

SLY6

SLY7

Average xbias over sub-ensembles based on ceqv

-200

-150

-100

-50

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1 2 3 4 5 6 7 8 9 10 11

Forecast period (hrs)

Av

era

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ias

(nm

) CLP5

A5K0

ZTOT

SGM1 (50 m/s)

SGM2 (100 m/s)

SGM3 (300 m/s)

Average ybias over sub-ensembles based on ceqv

-200

-150

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-50

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0 12 24 36 48 60 72 84 96 108 120

Forecast period (hrs)

Av

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(nm

) CLP5

A5K0

ZTOT

SGM1 (50 m/s)

SGM2 (100 m/s)

SGM3 (300 m/s)

Average ybais of sub-ensembles based on vertical averaging

-80

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1 2 3 4 5 6 7 8 9 10 11

Forecast period (nm)

Av

era

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yb

ias

(nm

) CLP5

A5K0

ZTOT

SLY4

SLY5

SLY6

SLY7

Average xbias over sub-ensembles based on vortex size/strength

-450

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-150

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-50

0

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0 12 24 36 48 60 72 84 96 108 120

Forecast period (hrs)

Av

era

ge

xb

ias

(nm

) CLP5

A5K0

ZTOT

SVM1 (15 m/s)

SVM2 (30 m/s)

SVM3 (50 m/s)

Average ybas of sub-ensembles based on vortex size/strength

-200

-150

-100

-50

0

50

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0 12 24 36 48 60 72 84 96 108 120

Forecast period (hrs)

Av

era

ge

yb

ias

(nm

) CLP5

A5K0

ZTOT

SVM1 (15 m/s)

SVM2 (30 m/s)

SVM3 (50 m/s)

0

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12 24 36 48 60 72 84 96 108 120

To

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(nm

)

Forecast time (hrs)

Average spread across perturbation class

SBF

SGM

SLY

SMV

SVM

ZTOT

ConclusionsConclusions

Swarm diagrams can lead to useful Swarm diagrams can lead to useful estimates of forecast confidenceestimates of forecast confidence

Ensembles are useful for spotting Ensembles are useful for spotting bifurcations in possible future tracksbifurcations in possible future tracks

The ensemble mean isn’t more accurate The ensemble mean isn’t more accurate than control than control

But great utility of ensembles is the But great utility of ensembles is the estimation of higher moments, such as estimation of higher moments, such as forecast spread -> estimates of forecast forecast spread -> estimates of forecast reliability reliability

Future WorkFuture Work Tune ensemble perturbation classes to reduce Tune ensemble perturbation classes to reduce

bias of ensemble meanbias of ensemble mean Tune ensemble spread to be the ‘right’ sizeTune ensemble spread to be the ‘right’ size Calculate probability density functions of storm Calculate probability density functions of storm

location from ensemble outputlocation from ensemble output Use fuzzy logic/adaptive weighting/neural Use fuzzy logic/adaptive weighting/neural

network to select more accurate custom sub-network to select more accurate custom sub-ensemblesensembles

Automate for operational use, web outputAutomate for operational use, web output Create ensemble toolbox for forecasters allowing Create ensemble toolbox for forecasters allowing

effect of perturbations in parameters on the effect of perturbations in parameters on the forecast track to be easily seen and quantifiedforecast track to be easily seen and quantified

ReferencesReferences Fulton, S. R., 2001: An adaptive multigrid Fulton, S. R., 2001: An adaptive multigrid

barotropic cyclone track model. barotropic cyclone track model. Mon. Wea. Rev.Mon. Wea. Rev.,, 129129, 138-151., 138-151.

Leith, C. E., 1974: Theoretical skill of Monte Carlo Leith, C. E., 1974: Theoretical skill of Monte Carlo forecasts. forecasts. Mon. Wea. Rev.Mon. Wea. Rev.,, 102 102, 409-418., 409-418.

Leslie, L. M., Abbey, R. F., and Holland, G. J., Leslie, L. M., Abbey, R. F., and Holland, G. J., 1995: Tropical Cyclone Track Predictability. 1995: Tropical Cyclone Track Predictability. Meteorol. Atmos. Phys.Meteorol. Atmos. Phys., , 6565, 223-231., 223-231.

Toth, Z., and E. Kalnay, 1997: Ensemble Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. forecasting at NCEP and the breeding method. Mon. Wea. Rev.Mon. Wea. Rev., , 125125, 3207-3310., 3207-3310.

Wiin-Nielsen, A., 1959: On barotropic and Wiin-Nielsen, A., 1959: On barotropic and baroclinic models, with special emphasis on ultra baroclinic models, with special emphasis on ultra long waves. long waves. Mon. Wea. Rev.Mon. Wea. Rev., , 8787, No. 5, 171-183., No. 5, 171-183.