Using Observations to Improve Hurricane Initialization X. ZouDepartment of MeteorologyFlorida State UniversityFebruary 14, 2007

OutlineHurricane Observations...A 4D-Var ApproachNumerical ResultsHurricane Initialization.(Vortex bogusing schemes)(Potential applications)(Vortex bogusing and/or data assimilation)(Hurricane forecast impact)

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

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 constraintsBogus VortexCreation of a bogus vortexVortex Bogussing

Conditions for Bogus Vortex SpecificationThe structure of the vortex should be dynamically and thermodynamically consistentWind and mass fields in balanceCoherent moisture fieldSize and intensity of the real TC should be representedReal storms evolving in different environmental conditions possess unique size and intensity The bogus vortex is compatible with the resolution and physics of the prediction modelPrevent false spinup

Observations within and around hurricanes could be either insufficient or problematic

Radiosonde observations are not over oceans.Rain contamination with QuikSCAT surface windsCloud 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 forecastsWhy is a bogus vortex needed?

Specify a bogus vortex of a single variableHow is vortex bogussing done? Generate a dynamically and thermodynamically consistent initial vortex of all model variablesRankine vortex --- tangential windFujitas vortex --- sea-level pressureHollands vortex --- seal-level pressureTraditional method: Simplified dynamical constraints

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.

1) Specify an empirical surface pressure field with observed > pressure at the vortex center (pc) > pressure of the outermost closed isobar (pout at r=Rout) > 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 Rout

1) Specify an empirical surface pressure field with observed2) Derive vortex fields of other model variables3) Merge vortex fields with the gridded large-scale analysis

where

An Early Method Used at NCEP

Hurricane Gilbert (1988) at 1200 UTC 14 SeptemberPotential 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 corePrescribed bogus vortex: Strongest cyclonic winds close to the center A warm core with a large warm temperature anomaly in the middle and upper troposphereLarge-scale analysis:

Stronger wind Warmer temperature Deeper hurricane48-h forecast without bogus vortex48-h forecast with bogus vortexFigure 2 from Mathur (1991)Hurricane Gilbert (1988) at 1200 UTC 16 SeptemberThe 48-h forecast with bogus vortex is characterized byFigure 2 from Mathur (1991)

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

The task of GFDL vortex initialization is completed by adding(IC) = (GA) - (vortex in GA) + (specified bogus vortex)Environmental field hEhsv

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 equationMain procedures

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

Hurricane Observations..TOMS ozoneGPS RORadiances.Challenges and potential applications.Dropsonde.Radar data.QuikSCAT

..TOMS ozone tropopause heightGPS RO high-vertical-resolution profile ofRadiances hydrometeor, temperature.Information.Dropsonde atmospheric vertical profiles.Radar data high resolution radial wind and .QuikSCAT surface windatmospheric refractvityrefractivity

SSM/I obs. (18 km)18 km85V Tbs for Hurricane Bonnie at 00 UTC 24 Aug 1998Model simulated (30km)The maximum difference of Tb at 85GHz within Hurricane Bonnie >100 K.The difference of maximum Tb at 85GHz within Hurricane Bonnie >40 K.

RTM ImprovementsThe 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 N0 of the drop size distribution and the density of the hydrometeor are made more consistent with the values of these parameters in the explicit moisture schemes.

Reisner scheme 1Goddard schemeSchultz schemeSSM/ITb at 85 GHz for Hurricane Bonnie(8/25 00 UTC, 1998)Reisner scheme 2The maximum Tb difference < 20 K18 km6 km6 km6 km6 km

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

SLPGHT340KTOMS ozoneTropical depressionTropical stormHurricane category 36 Sept. 20018 Sept. 200110 Sept. 2001

Scatter plot for TOMS O3 and geopotential at 340 K (All data within 650-km radial distance for all 12 chosen hurricanes are included)

Case-dependent radial mean TOMS O3 versus GHT340K profilesRadial mean TOMS ozone (DU)Radial mean GHT340K (gpm)

Bonnie(1998)Aug.22-24,26Alberto(2000)Aug. 12,13Isaac(2000)Sept. 22-25,27Erin(2001)Sept. 6,8,10Felix(2001)Sept. 9-11Lili(2002)Sept. 26,27,29Isidore(2002)Sept. 19,20Fabian(2003)Aug. 30, Sept 1-3Isabel (2003)Sept. 6,9,11,12

Case-dependent radial mean TOMS O3 versus GHT340K with daily means subtracted from both fieldsRadial mean TOMS ozone (DU) Radial mean GHT340K (gpm)

A linear regression model for hurricane initialization using TOMS ozoneSTDE=176m (~1-2%)

Large-scale analysisTOMS ozoneHurricane Erin on September 10, 2001Geopotential field at 340Kwith O3 data incorporated

..TOMS ozone not directly linked to model variablesGPS RO too little data within a hurricaneRadiances large model/observation difference.Challenges.Dropsonde not available above flight levels and.Radar data too high resolution with limited coverage.QuikSCAT rain contaminationwithin extreme weathers

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

A 4D-Var Vortex Bogus SchemeSpecify a bogus SLP.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:

Fujitas Formula:Specification of a Bogus SLPpc --- Central SLPpout --- Pressure of the outermost closed isobarRout --- Radius of the outermost closed isobarR35kt --- Radius of the 35kt wind whereFour observedTPC parameters(linear regression model)

Fujitas SLP Radial Profiles

Sensitivity studies suggest:Linear regression model?Differences in the size of real hurricanes are appreciable.Hurricane track and intensity forecasts are sensitive tospecified size of initial vortex. ..Hurricane forecast model- derived R0, Rmax,R35kt, ..TPC Observed(known)Input to Fujitasformula

needed for vortex size specificationSize Specification for Initial Vortex17 cases:Felix (1995)-1Opal (1995)-1Fran (1996)-3Erika (1997)-1Bonnie (1998)-9Floyd (1999)-2

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

Hurricane Bonnie (1998)

Initializing Hurricane Bonnieat 12 UTC August 23, 1998

Hurricane Bonnie (1998)Hurricane initialization time: 12 UTC, 23 August 1998TPC observed parameters: Pc = 958 hPa, Rmax=25 km, Vmax=100kt, R34kt=255 km, Numerical Experiments:Linear regression model Model: MM5 at 18-km resolution

Large-scale analysisEHEF1EF2Radial profile of the bogus SLP 9589589581000Radial profiles

Wind increments at 850 mb after BDA with R0=34 kmuvWind Increments at 850 hPa after 4D-Var BDA

East-west cross sections of the difference between EF2 and analysis at 6-h interval30min Time 0 1West 420km East420kmPressure PerturbationTemperature4 hPa-40-18-4820K

East-west cross sections of the divergence increments after hurricane initialization0-30 min30-60 min

Adiabatic warmingWarmingUpper-level convergenceLow-level divergenceAt t0, hydrostatic balance dominates.Less denser air

WarmingUpper-level divergenceLow-level convergenceLatent heatAt tR, dynamic balance dominates.

East-west cross sections of the difference between EF2 and large-scale analysis of mixing ratio 30min 60min TimeWest 420km East420km0-30 min30-60 min 0 1

Central pressureMaximum wind speedTrackTrack error

Hurricane Alberto (12-14 Aug., 2000)

Assimilation of Satellite RadianceInitialization time: 1200 UTC 23 August 1998 (Hurricane Bonnie)Forecast model: COAMPSResolution: 30 km horizontal grid spacing, 30 vertical levelsExperiments: CNTRL Control forecast using COAPS analysisETB with SSM/I observations and a non-diagonal B ETBN with SSM/I observations and a diagonal B

Shown as a correlation matrix and a profile of standard deviationqc qi qr qs qgBackground Error CovarianceHeight (km)Height (km)Height (km)Height (km)Hydrometeor std. (g/kg))

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

B Matrix and Its ApproximationHeight (km)Height (km)Height (km)qr Full Matrixqr Largest Singular Value1 x 107 kg/kgThe general structure of the full B matrix is captured by the largest singular vector.

Inverse Background Covariance MatricesMultiplied by 1 x 10-5 kg/kgqc qi qr qs qg Height (km)Height (km)Height (km)Height (km)

Tb at 19 GHz (12 UTC, 23 August 1998)Obs..without Tb assim.with Tb assim.

SSM/ICNTRLTb at 85 GHz (12 UTC, 23 August 1998)Obs..without Tb assim.with Tb assim.

Initial condition of qr after Tb AssimilationETB non-diagonal BETBD diagonal Bqr cross sections (unit: g/kg)Difference (K)Height (m)

IntensityTrack24 h Forecast (initial time: 1200 UTC 08/23/98)

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 Tb at lower frequency 19 GHz, 37 GHz and 22 GHz (sensitive to liquid precipitation and water vapor) matched the observations much better than Tb at 85V (sensitive to precipitating ice concentrations). Some forecast improvement was seen in the minimum central SLP and Tbs after the assimilation of Tb. There are a lot of available hurricane observations whose applications to hurricane initialization represent a challenge and have great potential.

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.

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)