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By: Andrew Lee

Kaplan and Demaria 2003 Paper

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.

Data Statistical Hurricane Intensity Prediction Scheme (SHIPS)

database

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.

Predictors

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, respectively.

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 variances * = 95%, **=99%,

***=99.9%

RI systems tend to be

located farther south and west than Non-RI systems RI systems have a more westerly component of motion

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, POT, and RHLO 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

Goals 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 thresholds

Methodology 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 first: 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

restricted Few North of 300N Concentrated in central

Atlantic between 100N and 200N and 200 and 600W

RI Predictor Data RI systems have high

PER, OHC, D200, RHLO, PX30, and SDBT RI systems have low SHRD and SDB

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 thresholds Predictors can be treated as independent of each other

RII Skill Calculation First, compute the Brier Score (BS) Convert Rs and Rd values to RI probabilities (0 to 1) by linearly interpolating 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

Conclusions Revised RII index made for Atlantic and North Pacific

Basins 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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Kaplan and Demaria 2003 Paper

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.

Data Statistical Hurricane Intensity Prediction Scheme (SHIPS)

database

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.

Predictors

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, respectively.

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 variances * = 95%, **=99%,

***=99.9%

RI systems tend to be

located farther south and west than Non-RI systems RI systems have a more westerly component of motion

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, POT, and RHLO 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

Goals 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 thresholds

Methodology 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 first: 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

restricted Few North of 300N Concentrated in central

Atlantic between 100N and 200N and 200 and 600W

RI Predictor Data RI systems have high

PER, OHC, D200, RHLO, PX30, and SDBT RI systems have low SHRD and SDB

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 thresholds Predictors can be treated as independent of each other

RII Skill Calculation First, compute the Brier Score (BS) Convert Rs and Rd values to RI probabilities (0 to 1) by linearly interpolating 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

Conclusions Revised RII index made for Atlantic and North Pacific

Basins 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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