1. Using Observations to Improve Hurricane Initialization X. Zou Department of Meteorology Florida State University February 14, 2007

2. Outline Hurricane Observations... A 4D-Var Approach Numerical Results Hurricane Initialization. (Vortex bogusing schemes) (Potential applications) (Vortex bogusing and/or data assimilation) (Hurricane forecast impact)

3. Hurricane Initialization Using Bogus Vortex.. How is vortex bogussing done? What is the forecast impact? Why is bogus vortex needed?.

4. An artificial initial vortex which is conceptually correct and is specified based on a few available observational parameters, an empirical structure of a model variable and dynamic and thermodynamic constraints Bogus Vortex Creation of a bogus vortex Vortex Bogussing

5. Conditions for Bogus Vortex Specification 1.The structure of the vortex should be dynamically and thermodynamically consistent Wind and mass fields in balance Coherent moisture field 2.Size and intensity of the real TC should be represented Real storms evolving in different environmental conditions possess unique size and intensity 3.The bogus vortex is compatible with the resolution and physics of the prediction model Prevent false spinup

6.  Observations within and around hurricanes could be either insufficient or problematic Radiosonde observations are not over oceans. Rain contamination with QuikSCAT surface winds Cloud contamination with satellite radiances  Initial vortices in model initial conditions are often too weak and misplaced  Having an initial vortex at correct location with realistic intensities and structures is important for hurricane track and intensity forecasts Why is a bogus vortex needed?

7.  Specify a bogus vortex of a single variable How is vortex bogussing done?  Generate a dynamically and thermodynamically consistent initial vortex of all model variables Rankine vortex --- tangential wind Fujita’s vortex --- sea-level pressure Holland’s vortex --- seal-level pressure Traditional method: Simplified dynamical constraints

8. An Early Method Used at NCEP Mukut B. Mathur. 1991: The National Meteorological Center's Quasi-Lagrangian Model for Hurricane Prediction. Monthly Weather Review, 119, 1419-1447.

9. 1) Specify an empirical surface pressure field with observed > pressure at the vortex center (p c ) > pressure of the outermost closed isobar (p out at r=R out ) > pressure of the hurricane environment 2) Derive vortex fields of other model variables > surface wind speed using the gradient wind relation (GWR) >3D wind speed from surface wind using empirical vertical structure functions >3D geopotential from 3D wind speed using GWR >3D wind vector from geopotential using GWR with variable f >virtual temperature from geopotential using the hydrostatic eq. >relative humidity (RH) by a linear interpolation assuming a saturated vortex center and a lower value of RH at R out

10. 1) Specify an empirical surface pressure field with observed 2) Derive vortex fields of other model variables 3) Merge vortex fields with the gridded large-scale analysis where An Early Method Used at NCEP

11. Hurricane Gilbert (1988) at 1200 UTC 14 September Figure 1 from Mathur (1991) NCEP analysis Prescribed bogus vortex Potential temperature (solid line, unit: K) Normal component of wind velocity (dashed line, unit: m/s)  The maximum wind is located far from the center (>300 km)  Little evidence of a warm core Prescribed bogus vortex: Strongest cyclonic winds close to the center A warm core with a large warm temperature anomaly in the middle and upper troposphere Large-scale analysis:

12.  Stronger wind  Warmer temperature  Deeper hurricane 48-h forecast without bogus vortex 48-h forecast with bogus vortex Figure 2 from Mathur (1991) Hurricane Gilbert (1988) at 1200 UTC 16 September The 48-h forecast with bogus vortex is characterized by Figure 2 from Mathur (1991)

13. Yoshio Kurihara, Morris A. Bender and Rebecca J. Ross, 1993: An Initialization Scheme of Hurricane Models by Vortex Specification. Monthly Weather Review, 121, 2030- 2045. Morris A. Bender, Rebecca J. Ross, Robert E. Tuleya and Yoshio Kurihara. 1993: Improvements in Tropical Cyclone Track and Intensity Forecasts Using the GFDL Initialization System. Monthly Weather Review, 121, 2046-2061. A GFDL Method

14. The task of GFDL vortex initialization is completed by adding (IC) = (GA) - (vortex in GA) + (specified bogus vortex) Environmental field h E h sv

15.  Obtain the environmental fields by removing often poorly analyzed tropical cyclone vortex from the large-scale analysis  Specify a symmetric vortex tangential wind field  Generate a symmetric vortex of all variables using an axisymmetric hurricane prediction model, with a nudging term imposing the specified tangential wind field  Obtain an asymmetric component of wind from integrating a simplified barotropic vorticity equation initialized by the symmetric tangential wind (Capture the asymmetric structure of TCs due to the planetary vorticity advection by the symmetric flow within the vortex)  Readjust mass fields to a state of balance to the asymmetric wind using divergence equation Main procedures

16. Improved Hurricane Track Forecast (include seven cases of Atlanta storms) Figure 6 from Kurihara et al. (1993)

17. Hurricane Observations.. TOMS ozone GPS RO Radiances. Challenges and potential applications. Dropsonde. Radar data. QuikSCAT

18. .. TOMS ozone tropopause height GPS RO high-vertical-resolution profile of Radiances hydrometeor, temperature. Information. Dropsonde atmospheric vertical profiles. Radar data high resolution radial wind and. QuikSCAT surface wind atmospheric refractvity refractivity

19. SSM/I obs. (18 km) 18 km 85V T b s for Hurricane Bonnie at 00 UTC 24 Aug 1998 Model simulated (30km) The maximum difference of T b at 85GHz within Hurricane Bonnie >100 K. The difference of maximum T b at 85GHz within Hurricane Bonnie >40 K.

20. RTM Improvements The RTM includes effects of absorption, emission, scatter, and multi-scattering (Liu, 1998). In the original version, the ice particles and air had been assumed a homogeneous mixture with the dielectric constant of the ice particle and the volume of the mixture considered as a solid sphere with the mass of the ice particle. In the modified version, the Maxwell-Garnett mixing formula is used for the calculation of the dielectric constant for ice particles. In the modified version, the values of the intercept parameter N 0 of the drop size distribution and the density ρ of the hydrometeor are made more consistent with the values of these parameters in the explicit moisture schemes.        

21. Reisner scheme 1 Goddard schemeSchultz scheme SSM/I T b at 85 GHz for Hurricane Bonnie (8/25 00 UTC, 1998) Reisner scheme 2 The maximum T b difference < 20 K 18 km 6 km

22. Hurricane Erin observed by TOMS ozone on 15UTC 12 September 2001

23. SLP GHT340KTOMS ozone Tropical depression Tropical storm Hurricane category 3 6 Sept. 2001 8 Sept. 2001 10 Sept. 2001

24. Scatter plot for TOMS O 3 and geopotential at 340 K (All data within 650-km radial distance for all 12 chosen hurricanes are included)

25. Case-dependent radial mean TOMS O 3 versus GHT340K profiles Radial mean TOMS ozone (DU) Radial mean GHT340K (gpm) Bonnie(1998)Aug.22-24,26 Alberto(2000)Aug. 12,13 Isaac(2000)Sept. 22-25,27 Erin(2001)Sept. 6,8,10 Felix(2001)Sept. 9-11 Lili(2002)Sept. 26,27,29 Isidore(2002)Sept. 19,20 Fabian(2003) Aug. 30, Sept 1-3 Isabel (2003)Sept. 6,9,11,12

26. Case-dependent radial mean TOMS O 3 versus GHT340K with daily means subtracted from both fields Radial mean TOMS ozone (DU) Radial mean GHT340K (gpm)

27. A linear regression model for hurricane initialization using TOMS ozone STDE=176m (~1-2%)

28. Large-scale analysis TOMS ozone Hurricane Erin on September 10, 2001 Geopotential field at 340K with O 3 data incorporated

29. .. TOMS ozone not directly linked to model variables GPS RO too little data within a hurricane Radiances large model/observation difference. Challenges. Dropsonde not available above flight levels and. Radar data too high resolution with limited coverage. QuikSCAT rain contamination within extreme weathers

30. A 4D-Var Approach for Bogusing Vortex and/or Data assimilation  Indirect remote-sensing observations can be assimilated simultaneously while generating bogus vortex Advantages:..  The best dynamic and thermodynamic constraint --- hurricane forecast model --- is imposed within bogus vortex.  Diabatic effect is included

31. A 4D-Var Vortex Bogus Scheme 1.Specify a bogus SLP. 2.Generate fields of all model variables describing an initial vortex by fitting a hurricane forecast model to the bogus SLP. Key features: (i) A bogus SLP field can be specified based on TPC (tropical prediction center) observed parameters. (ii) A 4D-Var assimilation window as short as 15-30 minutes is sufficient for this vortex initialization. Procedures:

32. Fujita’s Formula: Specification of a Bogus SLP p c --- Central SLP p out --- Pressure of the outermost closed isobar R out --- Radius of the outermost closed isobar R 35kt --- Radius of the 35kt wind where Four observed TPC parameters (linear regression model)

33. Fujita’s SLP Radial Profiles

34. Sensitivity studies suggest: Linear regression model? Differences in the size of real hurricanes are appreciable. Hurricane track and intensity forecasts are sensitive to specified size of initial vortex... Hurricane forecast model- derived R 0, R max,R 35kt, ….. TPC Observed (known) Input to Fujita’s formula

35. A TPC parameter needed for vortex size specification Size Specification for Initial Vortex 17 cases: Felix (1995)-1 Opal (1995)-1 Fran (1996)-3 Erika (1997)-1 Bonnie (1998)-9 Floyd (1999)-2

36. Numerical Results: Impact on Hurricane Forecast 1.Applying a 4D-Var vortex bogusing to the prediction of Hurricane Bonnie (1998) and Hurricane Alberto (2000) 2.Assimilation of microwave radiance for the prediction of Hurricane Bonnie (1998)

38. Initializing Hurricane Bonnie at 12 UTC August 23, 1998

39. Hurricane Bonnie (1998) Hurricane initialization time: 12 UTC, 23 August 1998 TPC observed parameters: P c = 958 hPa, R max =25 km, V max =100kt, R 34kt =255 km, EHHolland EF1FujitaR 0 = 25 km=R max EF2FujitaR 0 = 93 km Numerical Experiments: Linear regression model Model: MM5 at 18-km resolution

40. Large-scale analysis EHEF1EF2 Radial profile of the bogus SLP 958 1000 Radial profiles

41. Wind increments at 850 mb after BDA with R0=34 km u’v’ Wind Increments at 850 hPa after 4D-Var BDA

42. East-west cross sections of the difference between EF2 and analysis at 6-h interval 30min Time  0 1 West 420km East 420km Pressure Perturbation Temperature 4 hPa -40-18 -4 8 20K

43. East-west cross sections of the divergence increments after hurricane initialization 0-30 min 30-60 min

44. Adiabatic warming Warming Upper-level convergence Low-level divergence At t 0, hydrostatic balance dominates. - pp Bogusing Less denser air

45. Warming Upper-level divergence Low Low-level convergence Latent heat At t R, dynamic balance dominates.

46. East-west cross sections of the difference between EF2 and large-scale analysis of mixing ratio 30min 60min Time West 420km East 420km 0-30 min 30-60 min  0 1

47. Central pressureMaximum wind speed TrackTrack error

48. Hurricane Alberto (12-14 Aug., 2000)

49. Assimilation of Satellite Radiance Initialization time: 1200 UTC 23 August 1998 (Hurricane Bonnie) Forecast model: COAMPS Resolution: 30 km horizontal grid spacing, 30 vertical levels Experiments: CNTRL – Control forecast using COAPS analysis ETB – with SSM/I observations and a non-diagonal B ETBN – with SSM/I observations and a diagonal B

50. Shown as a correlation matrix and a profile of standard deviation qcqc qiqi qrqr qsqs qgqg Background Error Covariance Height (km) Hydrometeor std. (g/kg))

51. Singular Values of B Most variances are accounted for by the first few singular vectors for hydrometeor variables.

52. B Matrix and Its Approximation Height (km) q r Full Matrixq r Largest Singular Value 1 x 10 7 kg/kg The general structure of the full B matrix is captured by the largest singular vector.

53. Inverse Background Covariance Matrices Multiplied by 1 x 10 -5 kg/kg qcqc qiqi qrqr qsqs qgqg Height (km)

54. T b at 19 GHz (12 UTC, 23 August 1998) SSM/IETBCNTRL Obs.. without T b assim. with T b assim.

55. SSM/I ETB CNTRL T b at 85 GHz (12 UTC, 23 August 1998) Obs.. without T b assim.with T b assim.

56. Initial condition of q r after T b Assimilation ETB – non-diagonal BETBD – diagonal B q r cross sections (unit: g/kg) Difference (K) Height (m)

57. IntensityTrack 24 h Forecast (initial time: 1200 UTC 08/23/98)

58. Conclusions  The 4D-Var approach is an effective method for hurricane initialization, which allows forecast model constraint and hurricane observations be incorporated simultaneously.  Model simulated T b at lower frequency 19 GHz, 37 GHz and 22 GHz (sensitive to liquid precipitation and water vapor) matched the observations much better than T b at 85V (sensitive to precipitating ice concentrations).  Some forecast improvement was seen in the minimum central SLP and T b s after the assimilation of T b.  There are a lot of available hurricane observations whose applications to hurricane initialization represent a challenge and have great potential.

59. 4D-Var hurricane initialization: Zou, X., and Q. Xiao, 2000: Studies on the initialization and simulation of a mature hurricane using a variational bogus data assimilation scheme. J. Atm. Sci., 57, 836- 860. Park, K., and X. Zou, 2004: Toward developing an objective 4D-Var BDA scheme fo hurricane initialization based on TPC observed parameters. Mon. Wea. Rev., 132, 2054-2069.

60. Assimilation of satellite observations: Zou, X., Q. Xiao, Alan E. Lipton, and George D. Modica, 2001: A numerical study of the effect of GOES sounder cloud-cleared brightness temperatures on the prediction of hurricane Felix. J. Appl. Meteor., 40, 34-55. Amerault, C. and X. Zou, 2003: Preliminary steps in assimilating SSM/I brightness temperatures in a hurricane prediction scheme. J. Atmos. Oceanic Technol., 20, 1154-1169. Zou, X. and Y.-H. Wu, 2005: On the relationship between TOMS ozone and hurricanes. J. Geoph. Res., 110, No. D6, D06109 (paper no. 10.1029/2004JD005019). Wu, Y.-H. and X. Zou, 2007: Impact of TOMS ozone on hurricane track prediction. (to be submitted)