How Predictable Is Tropical Cyclone Intensity Change?

1. How Predictable Is Tropical Cyclone Intensity Change? Mark DeMaria NOAA/NESDIS/RAMMB NCAR Collaborative Tropical Cyclone Meeting 16 January 2008

2. NHC Official Intensity Forecast Errors2001-2006 Atlantic Sample

3. Hurricane Intensity Research Working Group (HIRWG) Forecast Goal • From Oct 2007 Final Report • “Reduce the error in 48-hour intensity forecasts for hurricane strength storms by at least 10 kt within the next 5 years” Linear extrapolation HIRWG goal reached in 2107

4. NOAA Hurricane Forecast Improvement Program (HFIP) Forecast Goals • Increase Probability of Detection (POD) of rapid intensity change (30 kt or more in 24 hr) to 90% at 24 hr and 60% at 120 hr • Reduce False Alarm Ratio (FAR) of rapid intensity change to 10% at 24 hr and 30% at 120 hr

5. Hit Rate, False Alarm Rate and False Alarm Ratiofor a Yes/No Event Forecast Yes No Yes Observed No h = # of Yes forecasts that verified (hits) c = # of No forecasts that verified (correct non-events) f = # of Yes forecasts that did not verify (false alarms) m = # of No forecasts where event occurred (missed) hit rate or POD = h/(h+m) false alarm rate = f/(f+c) false alarm ratio = f/(f+h)

6. POD and FAR of GFDL Model (2003-2006)

7. Estimation of Tropical Cyclone Intensity Predictability • Use statistical-dynamical Logistic Growth Equation Model (LGEM) • Assume perfect track forecast • Assume large-scale environment forecasts as good as current analyses • Limit of statistical models • LGEM fitted to “perfect” large-scale input for large sample of cases • Limit of dynamical models • LGEM growth rate tuned to individual storms

8. Logistic Growth Equation (LGE) Model dV/dt = V - (V/Vmpi)nV (A) (B) Term A: Growth term, related to shear, structure, etc Term B: Upper limit on growth as storm approaches its maximum potential intensity (Vmpi) LGEM Parameters: (t) Growth rate  MPI relaxation rate Vmpi(t)MPI n “Steepness” parameter LGE replaced by Kaplan and DeMaria inland wind decay model over land

9. Analytic LGE Solutions for Constant , , n, Vmpi Vs = Steady State V = Vmpi(/)1/n Let U = V/Vs and T = t dU/dT = U(1-Un) U(t) = Uo{enT/[1 + (enT-1)(Uo)n]}1/n n=3 n=3 U U T   0   0

10. Sensitivity to n parameter

11. LGEM Parameter Estimation • Vmpi from • DeMaria and Kaplan (1994) • empirical formula f(SST), SST from Reynold’s analysis • Adjusted Bister and Emanuel (1998) • f(SST,Ps,T,q), Reynold’s SST and GFS sounding • Find parameters n,, to minimize model error • LGEM model is dynamical system, so data assimilation techniques can be used • Adjoint model provides method for parameter estimation

12. Application of Adjoint LGE Model • Discretized forward model: V0 = Vobs(t=0) V+1 = V + [V -(V /Vmpi)nV ]t, =1,2,…T • Error Function: E = ½ (V -Vobs )2 • Add forward model equations as constraints: J = E + {V+1 - V - [V -(V /Vmpi)nV ]t} • Set dJ/dV = to give adjoint model for  T = - (VT-VobsT),  = +1{-(n+1)(V/Vmpi)n]t} - (V-Vobs), =T-1,T-2,… • Calculate gradient of J wrt to unknown parameters dJ/d = - t  V-1 dJ/dn = t (V-1/Vmpi-1)nV-1 dJ/d = t  (V-1/Vmpi-1)nln(V-1/Vmpi-1)nV-1 • Use gradient descent algorithm to find optimal parameters

13. 2-Parameter Estimation of :Dynamic and Thermodynamic Terms • Vertical shear of horizontal wind (S) • S = 200-850 hPa vertical wind shear • Potential to support convection (C) • 0 to 15 km average vertical velocity from entraining plume model • Ps,T,q from GFS analyses • Similar to CAPE, but with entrainment, liquid water weight and ice phase included

14. Plume Model Sensitivity to Mid-level Moisture Mean tropical sounding for SAL/no-SAL cases from Jason Dunion

15.  as function of S,C •  = a0 + a1S + a2C + a3CS • Estimate n, , a0,a1,a2,a3 byfit of LGEM to NHC best track maximum winds • 2001-2006 Atlantic sample (2465 forecast cases) • Adjoint model technique for gradient calculation • Steepest descent algorithm • Converged in ~1000 iterations, MAE=11 kt • Each iteration required 2465 forward and adjoint model runs • Required 3 minutes on Linux workstation • n=2.6 -1= 39 hr

17. Statistical Model Predictability Limit X HIRWG Goal 6-28% improvements possible at 1-5 days

18. Dynamical Model Predictability • Statistical model assumes all storms respond in the same way to environmental forcing • Properly initialized dynamical model should include effect of storm structure on response • Represent storm to storm variation by fitting  to each 5 day forecast •  = a0 + a1S + a2C + a3CS • Find optimal values of a0,a1,a2,a3 for each forecast • Use “global fit” values for ,n

19. Test Case: Fit 15 Day Frances Forecast

20. Fitted LGEM Frances Forecast

21. Dynamical Model Predictability Estimate X HIRWG Goal

22. Summary • LGE model used to estimate TC intensity forecast predictability • Assuming all storms respond the same to environmental forcing • Error limit ~15 kt • Assuming storm specific response to environmental forcing • Error limit ~5 kt • SST, vertical shear, vertical stability exert strong control on TC intensity change

23. Entraining Parcel Model • Lagrangian parcel model with Ooyama (1990) thermodynamic formulation • Prognostic variables • vertical velocity • entropy mixing ratio • total condensate mixing ratio • total parcel mass • Single condensate: acts like liquid above 0oC and ice below 0oC • Entrainment included through specified entrainment rate • Buoyancy affected by condensate weight • Simple precipitation parameterization • Requires atmospheric T, RH sounding as input • Mean sounding from Atlantic hurricane season for testing • (J. Dunion 2007) • Soundings from NCEP GFS model for prediction