Lecture 4: Tropical Cyclone Track Prediction

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Lecture 4 Tropical Cyclone Track Prediction
Meteo 452/597C Fall 2002
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Some Historical Impacts of Tropical Cyclones
Kublia Khans attempted invasions of Japan
13th century
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Kublai Khans letter to the Japanese emperor,
August 1266
Under the authority of heaven, the emperor of
Greater Mongolia sends this letter to the King of
Japan
I think that, from ancient times, kings of
minor nations tried to communicate and maintain
friendly relations among them, if their borders
were close. Needless to say, my ancestors, by
order of the heaven, conquered vast western
territories. Countless people in far foreign
regions are afraid of us and eager to pay tribute
to us. When I became the Emperor, I withdrew my
troops from Korea, because the innocent people of
Korea had suffered so much for a long time of the
war, and returned their territories and
prisoners. Korean King and subjects Were so
thankful that they visited and paid tribute.
Although our (Mongolian and Korean) relationship
is officially that between lord and subject, our
friendship is more like between a father and son.
I suppose that your officials and subjects are
already aware of these facts. Korea is now our
Eastern Barbarian (subject).
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Kublai Khans letter to the Japanese emperor,
August 1266
Japan is very close to Korea and, since its
foundation, communicated to China at times.
However, you never sent a mission to ask
friendship with us since I became the Emperor. I
am afraid that your country is still ignorant
about us. Therefore, I specially send a mission
and let him carry my letter to declare my will. I
hope that, from now, we mutually communicate and
establish a friendship. A wise person usually
tries to make friends all over the world.
Otherwise how could there be a rule in a family?
I have no choice but to use force. Who does like
it? You, the King, think about it (the
consequences) and do it (as I, Khan, have
said). Japan refused to answer .the war
was unavoidable!
Translated by Michio Yanai and Jen Hwa Chu Spring
1975
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Some Historical Impacts of Tropical Cyclones
Kublia Khans attempted invasions of Japan
13th century
Columbus loses a ship 15th century Typhoons
sink U.S. ships in World War II 20th century
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Track Forecasting

• BASIC DYNAMICS
• GUIDANCE MODELS
• USE OF INITIAL MOTION, CLIMATOLOGY, AND
  PERSISTENCE
• CONTINUITY FROM PREVIOUS FORECAST
• SYNOPTIC FLOW EXAMPLES
• NON-METEOROLOGICAL FACTORS

Courtesy Richard Pasch, NHC/TPC forecaster
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Scale analysis of the vorticity equation
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Scale analysis of the inviscid vertical vorticity
equation
1010 1010 1011 1010 1011 and
the equation for the vertical component of
vorticity can be well approximated by
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Factors Affecting TC Motion

• Zero Order Conservation of relative vorticity
• Vortex Moves with environmental steering flow
• First Order - Conservation of absolute vorticity
• Vortex induces b-gyres and modifies motion
• General Model
• Vertical structure is important
• Interaction with orography, friction, convection,
  3D environmental winds

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Track Guidance Models

• Zero Order statistical or statistical /dynamical
  models
• CLIPER, NHC90/91/98
• First Order barotropic models
• BAM, LBAR, VICBAR
• General Models dynamical numerical models
• GFDL, AVN/MRF, NOGAPS, UKMET,
• ECMWF, ETA, NGM

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CLIPER (CLImatology and PERsistence)

• Statistical track model developed in 19721
• Required Input
• Current/12 h old speed/direction of motion
• Current latitude/longitude
• Julian Day, Storm maximum wind
• Average 24, 48, 72 h errors 210, 450, 650 km
• Used as benchmark for other models
• forecasts having errors greater than CLIPER are
  considered to have no skill.

1From historical storm track data for all storms
in the North Atlantic Ocean, Caribbean Sea and
Gulf of Mexico that persisted for at least five
days during the period 1931-1970
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CLIPER example Danielle 1998
72-HR FORECAST
48-HR FORECAST
36-HR FORECAST
24-HR FORECAST
12-HR FORECAST
INITIAL
CLIPER EXAMPLE HURRICANE DANIELLE, 1998
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NHC90 (Atlantic), NHC91 (East Pacific)

• Statistical/Dynamical track model
• Required Input
• CLIPER forecast tracks
• Analyzed and forecast deep layer mean heights
  (1000-100 mb) from NCEP or UKMET global model
• Input used as predictors for TC motion (along-
  cross-track components) in a multiple regression
• New version for Atlantic with vortex removal
  scheme (NHC98)

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Typical NHC90 predictor locations
Typical Predictor Locations for NHC90
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THE SIMPLIFIED STEERING (OR TRAJECTORY) MODEL,
BAM (BETA AND ADVECTION MODEL)
USES STEERING (TRAJECTORY) GIVEN BY
LAYER-AVERAGED WINDS FROM AVN MODEL (SMOOTHED
HORIZONTALLY TO T25 RESOLUTION), PLUS A
CORRECTION TERM TO SIMULATE THE SO-CALLED BETA
EFFECT b-EFFECT USE THREE DIFFERENT LAYER
AVERAGES SHALLOW (850-700 hPa) - BAMS MEDIUM
(850-400 hPa) - BAMM DEEP (850-200 hPa) -
BAMD
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Scale analysis of the inviscid vertical vorticity
equation
1010 1010 1011 1010 1011 and
the equation for the vertical component of
vorticity can be well approximated by
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The b-Drift or Vortex Propagation
The circulation of a tropical cyclone combined
with the north-south variation in the Coriolis
parameter induces vorticity asymmetries in the
storm known as the b-gyres Since vorticity and
velocity must change together, the b-gyres
produce a net flow across the storm center. This
additional contribution to the storm motion is
known as the b-drift or propagation Generally the
b-drift is towards the northwest at a few knots
the speed and actual direction is related to the
vortex size and strength
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Perturbation analysis of the simplified vorticity
equation
Express the derivatives and velocity in a
cylindrical coordinates reference frame
a natural coordinate system for a vortex
Also phrase each dependent variable in terms of
mean (vortex) and perturbation (environment) compo
nents
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Perturbation analysis of the simplified vorticity
equation
Only the mean tangential flow is non-zero in the
balanced vortex, so the secondary flow
is confined to the perturbations
Substituting for the perturbation expansions and
canceling any terms with squares in
the perturbations results in
creation of b-gyres
steering propagation due to the b-gyres
environmental modification of of b-gyres
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INDUCED STEERING
HIGHER VALUES OF EARTHS VORTICITY
H
?vgt0
?vlt0
L
N
LOWER VALUES OF EARTHS VORTICITY
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Environmental b-Drift

• In the real atmosphere, the background flow also
  has vorticity gradients associated with it these
  do not usually line up with the variation in
  Coriolis parameter
• need to consider the full effects of the cyclone
  vortex advection of the background (zENV f)
• The circulation of the tropical cyclone combined
  with the spatial variation in absolute vorticity
  induces vortex asymmetries similar to b-gyres
  refer to these as environmental-b-gyres

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Environmental b-Drift

• These environmental-b-gyres produce an
  additional contribution to the vortex motion that
  is related to the environmental flow, but is not
  pure steering
• As with the b-gyres the orientation of the
  asymmetries is determined by the direction of the
  absolute vorticity gradient since the
  environmental flow can have a wide range of
  structures, the direction of vortex propagation
  cannot be pre-determined, but must be evaluated
  for each case

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INDUCED STEERING environmental beta effect
HIGHER VALUES OF ENVIRONMENTAL VORTICITY
H
?ENVvSgt0
?ENVvSlt0
L
?zENV max
LOWER VALUES OF ENVIRONMENTAL VORTICITY
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LBAR (Limited-area BARotropic)

• Barotropic dynamics, i.e. 2-d motions
• Shallow water equations on Mercator projection
  solved using sine transforms
• Initialized with 850-200 mb average winds/heights
  from NCEP global model
• Sum of idealized vortex and current motion vector
  added to large-scale analysis
• Boundary conditions from global model

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Hurricane Erika (1997) LBAR