Improving Tropical Cyclone Intensity Forecasting with Theoretically-Based Statistical Models Co-PI’s: Wayne Schubert 1 Mark DeMaria 2 Buck Sampson 3 Jim Cummings 4 Team Members: John Knaff 2 Brian McNoldy 5 Kate Musgrave 6 Chris Slocum 1 Rick Taft 1 Scott Fulton 7 Andrea Schumacher 6 Jim Peak 3 1 Colorado State University, Department of Atmospheric Science, Fort Collins, CO 2 NOAA/NESDIS, Regional and Mesoscale Meteorology Branch, Fort Collins, CO 3 Department of the Navy, Naval Research Laboratory, Monterey, CA 4 Department of the Navy, Naval Research Laboratory, Stennis Space Center, MS 5 University of Miami, RSMAS, Miami, FL 6 Colorado State University/CIRA, Fort Collins, CO 7 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 Cyclones Impact 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 2 nd order elliptic PDE Use separation of variables Choose appropriate BC’s Assume the following vertical structure:

Resulting Radial Structure Problem 2 nd 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:

Vortex Profiles Vortex profiles based on Gaussian vortex, con- trolled by V max and RMW V max =30m/s,RMW=30km Heating profiles based on warm-ring structure, with 4 shape parameters RMW V max r 1 r 2 r 3 r 4

Initial Profiles for Idealized Runs RMW Skirt Edge RMW Skirt Edge Heating Inside RMW Heating Across RMW Heating Inside Skirt Heating Outside Skirt

Results for Idealized Runs RMW Skirt Edge RMW Skirt Edge Heating Inside RMW Heating Across RMW Heating Inside Skirt Heating Outside Skirt

Results: Tangential Wind Tendencies The response determined by the interaction of the heating with vortex profile –Heating inside RMW produces most intense response and contracts RMW –Heating across RMW intensifies vortex, increases RMW –Heating inside Skirt intensifies vortex slightly, increases RMW –Heating outside Skirt inefficient, but could possibly form secondary wind maximum RMW

Results: Tangential Wind Tendencies The response determined by the interaction of the heating with vortex profile –Heating inside RMW produces most intense response and contracts RMW –Heating across RMW intensifies vortex, increases RMW –Heating inside Skirt intensifies vortex slightly, increases RMW –Heating outside Skirt inefficient, but could possibly form secondary wind maximum RMW

Results: Tangential Wind Tendencies The response determined by the interaction of the heating with vortex profile –Heating inside RMW produces most intense response and contracts RMW –Heating across RMW intensifies vortex, increases RMW –Heating inside Skirt intensifies vortex slightly, increases RMW –Heating outside Skirt inefficient, but could possibly form secondary wind maximum Skirt Edge

Results: Tangential Wind Tendencies The response determined by the interaction of the heating with vortex profile –Heating inside RMW produces most intense response and contracts RMW –Heating across RMW intensifies vortex, increases RMW –Heating inside Skirt intensifies vortex slightly, increases RMW –Heating outside Skirt inefficient, but could possibly form secondary wind maximum Skirt Edge

Sample Model Profiles - HWRF 96h fcst for Igor from early in life - Strong heating located inside vorticity skirt, and across RMW - GTE suggests storm should intensify and expand based on these profiles… - V max increased by 20kt, RMW increased by 9km, and R34 increased by 15% in next 12h!

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 UTC, 90hr fcst ‘Initial’ Time 14 Sep UTC T + 12 hr T + 6 hr T + 24 hr

Katia: 03 Sep UTC, 36hr fcst ‘Initial’ Time 05 Sep UTC T + 12 hr T + 6 hr T + 24 hr

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 KE 200 vs V max When heating is inside or across the RMW, V max increases more than the kinetic energy (right side of curve) When heating is outside the RMW, KE increases more than V max (left side of curve) (from Maclay et al. 2008: 1244 AL & EP recon cases)

Tropical Cyclone Lifecycle Lifecycle based on results of Ooyama 1969 KE 1000 vs. V max

TC Lifecycle: Wilma /17 10/18 10/19 10/20 10/21 10/22 10/23

Part I Accomplishments & 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

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 Files NOPP Review 2012

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 NOPP Review 2012

Data and Climatologies Sept. 15, 2005Sept. 15 Climatologies NOPP Review 2012

Example: OHC26C 10-day Response

NOPP Review 2012 Example: OHC26C Persistence

NOPP Review 2012 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

NOPP Review 2012 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 Errors

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 – 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 ( 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 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 Reserve C-130 and heating rate from AMSU precipitation product Radial profiles of tangential wind and heating rate (input to balance model)

Upcoming Conference Talks 30 th 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.