By: Andrew Lee
Kaplan and Demaria 2003
Findings of Previous Studies
 Ocean’s impact on tropical cyclone (TC) intensity:
 Upwelling and vertical mixing of the cool ocean due to
the vortex can have a negative feedback
 On the other hand, eddies can contribute to rapid
intensification (RI)
 Inner core processes: concentric eyewall cycles
 Collapse of inner eyewall results in weakening
 Contraction of outer eyewall can strengthen a TC
 Vertical Shear
 Low vertical shear results in RI
Findings of Previous Studies Continued
 Interaction of a TC with an upper-level trough
 Studies are conflicting on this matter
 Other important factors
 Deep layer of warm water
 Time of Day
 Eye diameter
 And many others
Goal of the Study
 Determine if RI mechanisms proposed in previous
studies can be confirmed for a large dataset
 Compare characteristics of RI and non-RI storms
 Develop a method for estimating the probability of RI
 Serves as a rapid intensity index (RII)
Rapid Intensification (RI) definition)
 95th percentile of over-water 24-hour intensity
changes of Atlantic basin tropical cyclones that
developed from 1989 to 2000
 Maximum sustained surface wind speed increase of 15.4
m/s (30 kt) over a 24-h period.
 Statistical Hurricane Intensity Prediction Scheme (SHIPS)
 Contains synoptic information every 12 hours
 the NHC Hurricane Database (HURDAT) file used to
analyze data
 6-hour estimates of various variables
All Atlantic basin TCs from 1989 to 2000
Variables measured starting at t=0 hours
Non-developing depression information in NHC B Decks
If TC is over land for ≤1 hour, it is an over-water system.
163 TCs (tropical depressions, tropical storms, and
hurricanes) for a total of 2621 cases.
Maximum Potential Intensity(MPI)
 MPI = min[X, 85]
 X = A + B(exp)[C(SST-SST0)]
 A = 34.2 m/s
 B = 55.8 m/s
 C=0.1813 0C-1
 SST0 = 300C
Frequency Distribution
 Tropical storms had
more changes exceeding
3 m/s than hurricanes or
tropical depressions
 Tropical storms are
further from their MPI
and are better organized
initially, so they can
intensify faster.
Distribution of Intensity Change
 Sample size: 50 TCs, 159
RI cases
 4.4%, 7.4%, and 5.4% of
the tropical depression,
tropical storm, and
hurricane samples
underwent RI,
Systems that featured RI
 60% of systems were
hurricane strength
 83% reached major
hurricane intensity
 All category 4 and 5
hurricanes underwent RI
at least once
 31% of all Atlantic TCs
and 38% of all named
storms underwent RI
Seasonality and Location of RI
 RI occurs mostly south
of 300N
 Fewer RI cases in eastern
Caribbean and eastern
Gulf of Mexico.
 Most RI during August
and September.
Large-Scale Conditions
 Statistical significance
determined by 2-sided t
test that assumes unequal
 * = 95%, **=99%,
 RI systems tend to be
located farther south and
west than Non-RI systems
 RI systems have a more
westerly component of
Large-Scale Conditions Continued
 RI systems have high SST, RHLO, and POT
 No statistical significance between VMX, JDAY, and SPD for RI
and non-RI
Most statistically significant differences for SST, RHLO, POT,
SHR, and U200.
RI have low SHR and REFC, situated in a 200-hPa flow
Impact of troughs on TC depends on environment
RI cases have low VMX
RI occurs most frequently from 10 to 15 degrees N, and generally
decreases with increasing LAT
RI tend to commence east of 400W and from 800 to 1000W
Slow storm speed negatively impacts TC intensity.
92% of RI cases have SSTs about 270C
RI cases have high POT, RHLO and relative humidity
RI cases have low SHR and REFC
Estimating Probability of RI
 Only done for statistical significance of 95% or greater
 RI threshold = RI sample mean
 RI probability = number of RI cases satisfying RI
threshold / number of cases in entire sample that
satisfy the threshold.
 Various sets of predictors combined into 5 predictors
(at 99.9% statistically significant): DVMX, SHR, SST,
 The resulting data on next slide:
Predictor Probability Data
Key Findings from Study
 Definition of RI proposed for Atlantic TCs
 The RI cases tended to occur farther south and west than
the non-RI cases.
 The RI cases were farther from their maximum potential
intensity and developed in regions of warmer water and
higher lower-tropospheric relative humidity than the nonRI cases.
 Probability of RI prediction involved 5 factors: previous 12h intensity change, sea surface temperature, low-level
relative humidity, vertical shear, and the difference
between the current intensity and the maximum potential
TC intensity
Future Work
 Add additional predictors:
 Upper-ocean heat content
 Geostationary Operational Environmental Satellite
(GOES) infrared satellite imagery
 Use More sophisticated statistical methods
Kaplan 2010 Paper
 Develop a revised rapid intensity index (RII)
 Both for Atlantic and eastern North Pacific basin
 Create versions of RII for 2 other RI thresholds: 25 and
35 kt (Kaplan 2003’s was 30 kt)
 Verify the revised RII using basin samples for all 3
 Mostly same procedures and data as in the Kaplan
2003 paper.
 Subtropical cases are included.
 4 new predictors added:
Methodology Differences from 2003
 SHRD is evaluated after the storm vortex is removed
 POT is determined using an adjusted inner-core SST
computed using an algorithm derived exclusively for
the Atlantic basin.
 Large-scale predictors are averaged along the storm
track from t=0 to t=24 h as opposed to being evaluated
at t=0 hours
 Cases used for the study had to pass through screening
 POT must be as large as the RI threshold
Methodology Differences Continued
 Cases where the values of any of the 8 predictors are
outside the range of RI predictor magnitudes of the RI
cases in the development sample aren’t used
RI distribution
 Tracks for 35-kt are more
 Few North of 300N
 Concentrated in central
Atlantic between 100N
and 200N and 200 and
RI Predictor Data
 RI systems have high
PX30, and SDBT
 RI systems have low
Scaled Version of RII
 Kaplan 2003 paper couldn’t account for the degree to which
conditions were favorable or unfavorable.
 Each predictor is assigned a scaled value between 0 (least
conductive) and 1 (most conductive) for RI (Sp)
 Sum all the scaled values (RS)
 RS = 0 if any of the Sp = 0
 Place RS values into 4 quartiles
 Lowest RS in the first quartile
 Equal number of RI cases in each quartile
 Probability is calculated by dividing number of RI cases by
total number of cases in each quartile.
Linear Discriminant version of RI
 Accounts for relative importance of each predictor
 RS = 0 samples excluded
 Each weight, Wn, is multiplied by the corresponding
Sp, then add everything (Rd)
 The Rd’s are put into quartiles and the probabilities
calculated in the same way as the scaled version
RI Predictor Weight Results
 Kinematic predictors
(D200 and SHRD) have
at least twice the weight
of thermodynamic
predictors (POT, RHLO,
and OHC) for all
 Predictors can be treated
as independent of each
RII Skill Calculation
 First, compute the Brier Score (BS)
 Convert Rs and Rd values to RI probabilities (0 to 1) by linearly
 Subtract from 0 if RI is not observed
 Subtract from 1 when RI is observed
 Square that number
 Compute the Brier Skill Score (BSS):
 BSS = [1-(BSM/BSC)] x 100
 BSM= BS of RII forecast
 BSC= BS of climatological forecast
 100%= prefect skill
RI Skill Data
Probabilistic Verification
 Cross validation method
 Storms from each of the individual years that composed
the 12-year developmental sample are excluded
 RII is rederived for each RI threshold using only cases
from the remaining 11-year sample
 That RII is run on the cases from the excluded year
 Repeat the procedure for each of the individual years in
the 12 year sample and tabulate results
Probabilistic Verification Data
Deterministic Verification
 Choose a single probability threshold
 The value of the discriminant function that matches the
climatological probability of false detection (POFD)
 POFD = climatological probability of RI/ (1 +
climatological probability of RI for each RI threshold)
 Repeat the calculation of POFD for each quartile and
each threshold
Probability Thresholds
 Revised RII index made for Atlantic and North Pacific
 Separate RII index made for 25kt and 35 kt
 Probability of detection (POD) for the RII ranged from
15% to 59% (53% to 73%) while the false alarm ratio
(FAR) ranged from 71% to 85% (53% to 79%) in the
Atlantic (eastern North Pacific) basins, respectively.
So, generally pretty good.
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