Improving Tropical Cyclone Intensity Forecasting with Theoretically-Based

Statistical ModelsCo-PI’s:

Wayne Schubert1

Mark DeMaria2

Buck Sampson3

Jim Cummings4

Team Members:John Knaff2

Brian McNoldy5

Kate Musgrave6

Chris Slocum1

Rick Taft1

Scott Fulton7

Andrea Schumacher6

Jim Peak3

1 Colorado State University, Department of Atmospheric Science, Fort Collins, CO2 NOAA/NESDIS, Regional and Mesoscale Meteorology Branch, Fort Collins, CO3 Department of the Navy, Naval Research Laboratory, Monterey, CA4 Department of the Navy, Naval Research Laboratory, Stennis Space Center, MS5 University of Miami, RSMAS, Miami, FL6 Colorado State University/CIRA, Fort Collins, CO7 Clarkson University, Department of Mathematics, Potsdam, NY

NOPP Review 1 March 2012 Miami, FL

NOPP Review 1 March 2012 Miami, FL

Project Overview

Part I: • Theoretical study of the inner core of tropical cyclones

• Observational study of upper ocean response to tropical cyclones

• Application of results from Parts I and II to intensity forecast models

Part II:

Part III:

Part I:Theoretical Study of the Inner Core of Tropical

CyclonesImpact of Vortex Structure on Tropical Cyclone Response to

Diabatic Heating

Introduction• Several studies have examined TCs using

Eliassen's balanced vortex model (1952)

• Vigh and Schubert (2009) investigated effects of diabatic heating inside and outside the radius of maximum wind (RMW) on intensification

• Their use of Rankine wind profiles limited the vorticity to within the RMW... we're expanding to include the effect of vorticity “skirts” on the efficiency of heating to intensify vortices

Eliassen’s Balanced Vortex Model• Governing equations:

• To focus on role of inertial stability, neglect baroclinic terms

• Assume static stability is constant:

• Assume inertial stability is function of r only:

Geopotential Tendency Equation• Instead of eliminating and

solving for the secondary circulation, eliminate and to get the GTE

• GTE is a 2nd order elliptic PDE

• Use separation of variables

• Choose appropriate BC’s

• Assume the following vertical structure:

Resulting Radial Structure Problem• 2nd order ODE

• Have developed code in Mathematica and Fortran to solve this problem

• Rossby length:

• Other radial structure functions can then be recovered

• For example:

Initial Profiles for Idealized RunsRMW Skirt Edge

RMW Skirt Edge

Hea

ting

Insi

de R

MW

Hea

ting

Acr

oss

RM

WH

eating Inside Skirt

Heating O

utside Skirt

Results for Idealized RunsRMW Skirt Edge

RMW

Skirt Edge

Hea

ting

Insi

de R

MW

Hea

ting

Acr

oss

RM

WH

eating Inside Skirt

Heating O

utside Skirt

Mathematica to Fortran

Converting from Mathematica to Fortran allows for a wider variety of profile specifications and for greater portability and automation

Mathematica example:Heating inside RMW

Fortran example:Heating inside RMW

Testing GTE with HWRF

• The GTE model is being tested with HWRF model fields:

• as initial conditions

• as baselines for result comparisons

• HWRF model fields allow for regular assessment and serve as a bridge to incorporating observed heating and wind profiles

Case Studies

Hurricane Igor 2010

Hurricane Katia 2011

Igor: 10 Sep 2010 1200 UTC, 90hr fcst‘In

itial

’ Tim

e14

Sep

201

0 06

00

UTC

T +

12 h

r

T +

6 hr

T +

24 h

r

Katia: 03 Sep 2010 1200 UTC, 36hr fcst‘In

itial

’ Tim

e05

Sep

201

0 00

00

UTC

T +

12 h

r

T +

6 hr

T +

24 h

r

Differences in Vortex Profiles

• Caution must be used in trying to carry instantaneous tendencies out to longer times

• Some discrepancies at longer lead-times can also be attributed to the DH profile changing over time

Kinetic Energy vs. Max. Wind

• KE200 vs Vmax • When heating is inside or

across the RMW, Vmax

increases more than the

kinetic energy

(right side of curve)

• When heating is outside the

RMW, KE increases more

than Vmax

(left side of curve)(from Maclay et al. 2008: 1244 AL & EP recon cases)

Tropical Cyclone LifecycleLifec

ycle

base

d on

result

s of

Ooya

ma

1969

KE

1000

vs.

Vm

ax

TC Lifecycle: Wilma 2005

10/17

10/1810/19

10/20

10/2110/22

10/23

Part IAccomplishments & Future Work

Mathematica code for solving idealized problems

Analysis of Geopotential Tendency Equation for a range of idealized parameters

Fortran code for solving more realistic problems

Apply to HWRF model output as a diagnostic tool (in coordination with HFIP diagnostic team)

Apply to real data derived from microwave imagery

Part II:Observational Study of

Upper Ocean Response to Tropical Cyclones

Assessing Upper Oceanic Response to Tropical Cyclone

Passage

NOPP Review 2012

NO

PP R

evie

w 2

012

• Makes use of six years of the NCODA-based ocean heat content files developed in Year-1

• Composite analyses are used to investigate the type, magnitude, and persistence of the upper ocean’s response to TC passage

• Complete findings submitted for publication:Knaff, J. A., M. DeMaria, C. R. Sampson, J. E. Peak, J. Cummings, and W. Schubert, 2012: Upper Oceanic Energy Response to Tropical Cyclone Passage. In revision Journal of Climate.

Response to TC Passage

1. 12 different fields including OHC26C, OHC20C, T100, Td, where d is depth of the mixed layer defined by temperature and density gradients and maximum stability

2. Seven-years of data

3. Processing moved to operations at FNMOC

4. Methods and dataset has been documented and submitted for publication:

Peak, J. E., C. R. Sampson, J. Cummings, J. A. Knaff, M. DeMaria, and W. Schubert, 2012: An upper ocean thermal field metrics dataset. Submitted to Geophysical Research Letters.

NCODA Ocean Heat Content FilesN

OPP

Rev

iew

201

2

Composite Analyses• Ocean variables and their climatologies are interpolated to

the points associated with global six-hourly TC tracks at 10 separate lead and lag times

• Six-years of data were used

• Examine the temporal changes of the upper ocean prior to and following TC passage Account for the seasonal cycle Composite the responses as a function of initial ocean

conditions, latitude, translation speed, a simplified kinetic energy based on wind radii, and intensity

• Use the composites to develop simple parameterizations of upper ocean responses to TC passage as a function of routinely measured TC metrics

NO

PP R

evie

w 2

012

Data and ClimatologiesSept. 15, 2005 Sept. 15 Climatologies

NO

PP R

evie

w 2

012

NO

PP R

evie

w 2

012

Example: OHC26C 10-day Response

NO

PP R

evie

w 2

012

Example: OHC26C Persistence

NO

PP R

evie

w 2

012

Summary of Findings• An average sized hurricane results in

~ 0.6 C cooling 12 kJ/cm^2 decrease of OHC26C ~0.5 C cooling of the upper 100m of the ocean

• SST cooling persists on the order of 30 days• The upper ocean response persists on the order of 60

days• TC size helps determine the response and existing

information seems adequate• SST cooling can be estimated from KE and latitude• OHC and T100 changes can be estimated by KE, initial

conditions and translation speed

NO

PP R

evie

w 2

012

Future Plans• Use upper ocean metric fields:

Real-time LGEM, SHIPS and RII in the Western North Pacific

For re-examination of potential intensity Assessment of different metrics in SHIPS/LGEM

framework. (i.e., Do other measures of oceanic heat content provide superior information to statistical-dynamic forecasts of intensity change?)

A reanalysis of ocean data going further back in time is being done under different funding at NRL Stennis

Part III:Application of Results from Parts I and II to Intensity

Forecast Models

NOPP Review 1 March 2012 Miami, FL

Intensity Forecast Models

• NHC Statistical Intensity Models:– SHIFOR: No-skill baseline with climatology and persistence input

• Max wind at t=0, -12 hr, lat/lon at t=0, -12 hr, Julian Day

– SHIPS: Linear regression model with additional input from GFS forecast fields, SST analyses, GOES data and satellite altimetry

– LGEM: Generalization of SHIPS that relaxes linear assumption• SPICE (experimental): Ensemble of SHIPS and LGEM with input from GFS,

HWRF and GFDL

– Rapid Intensification Index: Subset of SHIPS input to estimate probability of RI

• Dynamical Models: – HWRF and GFDL

– Coupled ocean-atmosphere 3-D prediction systems

Atlantic Intensity Model Errors2007-2011

NOPP Statistical Model Tasks

• Develop SHIPS, LGEM and Rapid Intensification Index for Western Pacific– If successful, transition to JTWC operations

• Improve statistical intensity models – New parameters from NCODA

• SST cooling algorithm

– Input from balance model solutions for cases with aircraft and satellite data

West Pacific Accomplishments

• SHIPS database developed for WPAC – 2000-2011 cases– GFS analyses– NCODA sea surface temperatures and oceanic heat

content (OHC)• Satellite altimetry OHC before 2005

– Geostationary satellite infrared imagery

• SHIPS and LGEM fitted to WPAC database• Coordination with NRL on implementation in the

ATCF for 2012 season– Planned for May 2012 along with Atlantic and East

Pacific versions for NHC

Preliminary SHIPS/LGEM Hind-cast Errors with Real Time Track Forecast Input

(2008-2010 WPAC Sample)

Mean Absolute Error

Skill Relative to ST5D

The Rapid Intensification Index

• SHIPS and LGEM fit to basin-wide statistics using least squares approaches

• Outliers (rapid intensity changes) not captured well

• Kaplan, DeMaria, Knaff (2003, 2010) developed method for identification of RI cases– Subset of SHIPS parameters most related to RI– Discriminate analysis approach estimates probability of RI

• WPAC implementation of SHIPS/LGEM will include the rapid intensification index

Example of RII from 2011 Season(Hurricane Adrian in the East Pacific)

• LGEM forecasted 24 hr intensity increase of 19 kt (35 to 54 kt)

• BUT: the RII suggested increases could be much larger

• Observed 24 hr increase was 35 kt

Next Steps for Part III

• Implement West Pacific SHIPS/LGEM/RII on the ATCF for JTWC

• Continue statistical model improvements for West Pacific, East Pacific and Atlantic– Test new ocean parameters from NCODA– Test balance model solutions using input from

aircraft and satellite on

Checklist from B. Sampson for West Pacific LGEM, SHIPS and RII in ATCF

1. Obtain 6-h GFS grib files real-time

2. Develop reader for IR imagery

3. Generate 2004-2011 IR imagery dataset for testing

4. Produce NWP model input files (PACK files)

5. Implement LGEM, SHIPS and RII code in objective aid run

• Expected by May 15, 2012

Example Aircraft/Satellite Dataset

Flight level winds from Air Force ReserveC-130 and heating rate from AMSU precipitation product

Radial profiles of tangentialwind and heating rate (input to balance model)

Upcoming Conference Talks30th Conference on Hurricanes and Tropical Meteorology

(15-20 April 2012, Ponte Vedra Beach, FL)

• DeMaria, M., J. A. Knaff, A. B. Schumacher, and J. Kaplan, 2012: Improving Tropical Cyclone Rapid Intensity Change Forecasts.

– Wed. 18 April 2012 at 9:30 am, Session 8B (Tropical Cyclone Intensity Change II)

• Knaff, J. A., M. DeMaria, C. R. Sampson, J. E. Peak, J. Cummings, and W. Schubert, 2012:  The Upper Ocean's Thermal Response to Tropical Cyclones.

– Fri. 20 April 2012 at 2:45 pm,  Session 16D (Ocean Observations & Air-Sea Interaction)

• Peak, J. E., C. R. Sampson, J. Cummings, J. A. Knaff, M. DeMaria, and W. H. Schubert, 2012: An Upper Ocean Thermal Field Metrics Dataset.

– Fri. 20 April 2012 at 2:15 pm, Session 16D (Ocean Observations & Air-Sea Interaction)

• Slocum, C. J., 2012: Determining Tropical Cyclone Intensity Change through Balanced Vortex Model Applications.

– Wed.18 April 2012 at 10 am, Session 8B (Tropical Cyclone Intensity Change II)

Upcoming Papers• Knaff, J. A., M. DeMaria, C. R. Sampson, J. E. Peak, J.

Cummings, and W. H. Schubert, 2012: Upper oceanic energy response to tropical cyclone passage. Submitted to J. Climate.

• Musgrave, K. D., R. K. Taft, J. L. Vigh, B. D. McNoldy, and W. H. Schubert, 2012: Time evolution of the intensity and size of tropical cyclones.  J. Adv. Model. Earth Syst., in press.

• Peak, J. E., C. R. Sampson, J. Cummings, J. A. Knaff, M. DeMaria, and W. H. Schubert, 2012: An upper ocean thermal field metrics dataset. Submitted to Geophys. Res. Lett.