Editorial Type:
Article
Article Type:
Research Article

Sensitivity of Tropical Cyclone Simulations to Parametric Uncertainties in Air–Sea Fluxes and Implications for Parameter Estimation

Benjamin W. Green Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

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Fuqing Zhang Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

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Print Publication:
01 Jun 2014
DOI:
https://doi.org/10.1175/MWR-D-13-00208.1
Page(s):
2290–2308
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Abstract

Tropical cyclones (TCs) are strongly influenced by fluxes of momentum and moist enthalpy across the air–sea interface. These fluxes cannot be resolved explicitly by current-generation numerical weather prediction models, and therefore must be accounted for via empirical parameterizations of surface exchange coefficients (CD for momentum and Ck for moist enthalpy). The resultant model uncertainty is examined through hundreds of convection-permitting Weather Research and Forecasting Model (WRF) simulations of Hurricane Katrina (2005) by varying four key parameters found in commonly used parameterizations of the exchange coefficient formulas. Two of these parameters effectively act as multiplicative factors for the exchange coefficients over all wind speeds (one each for CD and Ck); the other two parameters control the behavior of CD at very high wind speeds (i.e., above 33 m s−1). It is found that both the intensity and the structure of TCs are highly dependent upon the two multiplicative parameters. The multiplicative parameter for CD has a considerably larger impact than the one for Ck on the relationship between maximum 10-m wind speed and minimum sea level pressure: CD alters TC structure, with higher values shifting the radius of maximum winds inward and strengthening the low-level inflow; Ck only affects structure by uniformly strengthening/weakening the primary and secondary circulations. The TC exhibits the greatest sensitivities to the two multiplicative parameters after a few hours of model integration, suggesting that these parameters could be estimated by assimilating near-surface observations. The other two parameters are likely more difficult to estimate because the TC is only marginally sensitive to them in small areas of high wind speed.

Corresponding author address: Dr. Fuqing Zhang, Dept. of Meteorology, The Pennsylvania State University, 503 Walker Bldg., University Park, PA 16802. E-mail: fzhang@psu.edu

Abstract

Tropical cyclones (TCs) are strongly influenced by fluxes of momentum and moist enthalpy across the air–sea interface. These fluxes cannot be resolved explicitly by current-generation numerical weather prediction models, and therefore must be accounted for via empirical parameterizations of surface exchange coefficients (CD for momentum and Ck for moist enthalpy). The resultant model uncertainty is examined through hundreds of convection-permitting Weather Research and Forecasting Model (WRF) simulations of Hurricane Katrina (2005) by varying four key parameters found in commonly used parameterizations of the exchange coefficient formulas. Two of these parameters effectively act as multiplicative factors for the exchange coefficients over all wind speeds (one each for CD and Ck); the other two parameters control the behavior of CD at very high wind speeds (i.e., above 33 m s−1). It is found that both the intensity and the structure of TCs are highly dependent upon the two multiplicative parameters. The multiplicative parameter for CD has a considerably larger impact than the one for Ck on the relationship between maximum 10-m wind speed and minimum sea level pressure: CD alters TC structure, with higher values shifting the radius of maximum winds inward and strengthening the low-level inflow; Ck only affects structure by uniformly strengthening/weakening the primary and secondary circulations. The TC exhibits the greatest sensitivities to the two multiplicative parameters after a few hours of model integration, suggesting that these parameters could be estimated by assimilating near-surface observations. The other two parameters are likely more difficult to estimate because the TC is only marginally sensitive to them in small areas of high wind speed.

Corresponding author address: Dr. Fuqing Zhang, Dept. of Meteorology, The Pennsylvania State University, 503 Walker Bldg., University Park, PA 16802. E-mail: fzhang@psu.edu
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  • Aksoy, A., F. Zhang, and J. W. Nielsen-Gammon, 2006a: Ensemble-based simultaneous state and parameter estimation in a two-dimensional sea-breeze model. Mon. Wea. Rev., 134, 2951–2970, doi:10.1175/MWR3224.1.

    • Search Google Scholar
    • Export Citation

  • Aksoy, A., F. Zhang, and J. W. Nielsen-Gammon, 2006b: Ensemble-based simultaneous state and parameter estimation with MM5. Geophys. Res. Lett., 33, L12801, doi:10.1029/2006GL026186.

    • Search Google Scholar
    • Export Citation

  • Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 2884–2903, doi:10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Bao, J.-W., S. A. Michelson, and J. M. Wilczak, 2002: Sensitivity of numerical simulations to parameterizations of roughness for surface heat fluxes at high winds over the sea. Mon. Wea. Rev., 130, 1926–1932, doi:10.1175/1520-0493(2002)130<1926:SONSTP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Bao, J.-W., S. G. Gopalakrishnan, S. A. Michelson, F. D. Marks, and M. T. Montgomery, 2012: Impact of physics representations in the HWRFX model on simulated hurricane structure and wind–pressure relationships. Mon. Wea. Rev., 140, 3278–3299, doi:10.1175/MWR-D-11-00332.1.

    • Search Google Scholar
    • Export Citation

  • Black, P. G., and Coauthors, 2007: Air–sea exchange in hurricanes: Synthesis of observations from the Coupled Boundary Layer Air–Sea Transfer Experiment. Bull. Amer. Meteor. Soc., 88, 357–374, doi:10.1175/BAMS-88-3-357.

    • Search Google Scholar
    • Export Citation

  • Bleck, R., 2002: An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates. Ocean Modell., 4, 55–88, doi:10.1016/S1463-5003(01)00012-9.

    • Search Google Scholar
    • Export Citation

  • Braun, S. A., and W.-K. Tao, 2000: Sensitivity of high-resolution simulations of Hurricane Bob (1991) to planetary boundary layer parameterizations. Mon. Wea. Rev., 128, 3941–3961, doi:10.1175/1520-0493(2000)129<3941:SOHRSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Brutsaert, W., 1975: A theory for local evaporation (or heat transfer) from rough and smooth surfaces at ground level. Water Resour. Res., 11, 543–550, doi:10.1029/WR011i004p00543.

    • Search Google Scholar
    • Export Citation

  • Bryan, G. H., 2012: Effects of surface exchange coefficients and turbulence length scales on the intensity and structure of numerically simulated hurricanes. Mon. Wea. Rev., 140, 1125–1143, doi:10.1175/MWR-D-11-00231.1.

    • Search Google Scholar
    • Export Citation

  • Charnock, H., 1955: Wind stress on a water surface. Quart. J. Roy. Meteor. Soc., 81, 639–640, doi:10.1002/qj.49708135027.

  • DelSole, T., and X. Yang, 2010: State and parameter estimation in stochastic dynamical models. Physica D, 239, 1781–1788, doi:10.1016/j.physd.2010.06.001.

    • Search Google Scholar
    • Export Citation

  • Donelan, M. A., B. K. Haus, N. Reul, W. J. Plant, M. Stiassnie, H. C. Graber, O. B. Brown, and E. S. Saltzman, 2004: On the limiting aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett., 31, L18306, doi:10.1029/2004GL019460.

    • Search Google Scholar
    • Export Citation

  • Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 3077–3107, doi:10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Dyson, F., 2004: A meeting with Enrico Fermi. Nature, 427, 297, doi:10.1038/427297a.

  • Emanuel, K. A., 1986: An air-sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585–604, doi:10.1175/1520-0469(1986)043<0585:AASITF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Emanuel, K. A., 1995a: The behavior of a simple hurricane model using a convective scheme based on subcloud-layer entropy equilibrium. J. Atmos. Sci., 52, 3960–3968, doi:10.1175/1520-0469(1995)052<3960:TBOASH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Emanuel, K. A., 1995b: Sensitivity of tropical cyclones to surface exchange coefficients and a revised steady-state model incorporating eye dynamics. J. Atmos. Sci., 52, 3969–3976, doi:10.1175/1520-0469(1995)052<3969:SOTCTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • French, J. R., W. M. Drennan, J. A. Zhang, and P. G. Black, 2007: Turbulent fluxes in the hurricane boundary layer. Part I: Momentum flux. J. Atmos. Sci., 64, 1089–1102, doi:10.1175/JAS3887.1.

    • Search Google Scholar
    • Export Citation

  • Garratt, J. R., 1992: The Atmospheric Boundary Layer.Cambridge University Press, 316 pp.

  • Gray, W. M., 1968: Global view of the origin of tropical disturbances and storms. Mon. Wea. Rev., 96, 669–700, doi:10.1175/1520-0493(1968)096<0669:GVOTOO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Green, B. W., and F. Zhang, 2013: Impacts of air–sea flux parameterizations on the intensity and structure of tropical cyclones. Mon. Wea. Rev., 141, 2308–2324, doi:10.1175/MWR-D-12-00274.1.

    • Search Google Scholar
    • Export Citation

  • Grell, G. A., and D. Devenyi, 2002: A generalized approach to parameterizing convection combining ensemble and data assimilation techniques. Geophys. Res. Lett., 29, 1693, doi:10.1029/2002GL015311.

    • Search Google Scholar
    • Export Citation

  • Holthuijsen, L. H., M. D. Powell, and J. D. Pietrzak, 2012: Wind and waves in extreme hurricanes. J. Geophys. Res., 117, C09003, doi:10.1029/2012JC007983.

    • Search Google Scholar
    • Export Citation

  • Hong, S.-Y., and J.-O. J. Lim, 2006: The WRF single-moment microphysics scheme (WSM6). J. Korean Meteor. Soc., 42, 129–151.

  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 2318–2341, doi:10.1175/MWR3199.1.

    • Search Google Scholar
    • Export Citation

  • Hu, X.-M., F. Zhang, and J. W. Nielsen-Gammon, 2010: Ensemble-based simultaneous state and parameter estimation for treatment of mesoscale model error: A real-data study. Geophys. Res. Lett., 37, L08802, doi:10.1029/2010GL043017.

    • Search Google Scholar
    • Export Citation

  • Ito, K., Y. Ishikawa, and T. Awaji, 2010: Specifying air-sea exchange coefficients in the high-wind regime of a mature tropical cyclone by an adjoint data assimilation method. SOLA, 6, 13–16, doi:10.2151/sola.2010-004.

    • Search Google Scholar
    • Export Citation

  • Ito, K., T. Kawabata, T. Kato, Y. Honda, Y. Ishikawa, and T. Awaji, 2013: Simultaneous optimization of air-sea exchange coefficients and initial conditions near a tropical cyclone using JNoVA. J. Meteor. Soc. Japan, 91, 337–353, doi:10.2151/jmsj.2013-307.

    • Search Google Scholar
    • Export Citation

  • Jarosz, E., D. A. Mitchell, D. W. Wang, and W. J. Teague, 2007: Bottom-up determination of air-sea momentum exchange under a major tropical cyclone. Science, 315, 1707–1709, doi:10.1126/science.1136466.

    • Search Google Scholar
    • Export Citation

  • Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability.Cambridge University Press, 341 pp.

  • Kara, A. B., P. A. Rochford, and H. E. Hurlburt, 2002: Air-sea flux estimates and the 1997-1998 ENSO event. Bound.-Layer Meteor., 103, 439–458, doi:10.1023/A:1014945408605.

    • Search Google Scholar
    • Export Citation

  • Knabb, R. D., J. R. Rhome, and D. P. Brown, 2006: Tropical cyclone report: Hurricane Katrina 23–30 August 2005. NOAA, 43 pp. [Available online at http://www.nhc.noaa.gov/pdf/TCR-AL122005_Katrina.pdf.]

  • Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, 16 663–16 682, doi:10.1029/97JD00237.

    • Search Google Scholar
    • Export Citation

  • Nielsen-Gammon, J. W., X.-M. Hu, F. Zhang, and J. E. Pleim, 2010: Evaluation of planetary boundary layer scheme sensitivities for the purpose of parameter estimation. Mon. Wea. Rev., 138, 3400–3417, doi:10.1175/2010MWR3292.1.

    • Search Google Scholar
    • Export Citation

  • Ooyama, K., 1969: Numerical simulation of the life cycle of tropical cyclones. J. Atmos. Sci., 26, 3–40, doi:10.1175/1520-0469(1969)026<0003:NSOTLC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Peng, S., Y. Li, and L. Xie, 2013: Adjusting the wind stress drag coefficient in storm surge forecasting using an adjoint technique. J. Atmos. Oceanic Technol., 30, 590–608, doi:10.1175/JTECH-D-12-00034.1.

    • Search Google Scholar
    • Export Citation

  • Pollard, R. T., P. B. Rhines, and R. O. R. Y. Thompson, 1972: The deepening of the wind-mixed layer. Geophys. Fluid Dyn., 4, 381–404, doi:10.1080/03091927208236105.

    • Search Google Scholar
    • Export Citation

  • Powell, M. D., P. J. Vickery, and T. A. Reinhold, 2003: Reduced drag coefficient for high wind speeds in tropical cyclones. Nature, 422, 279–283, doi:10.1038/nature01481.

    • Search Google Scholar
    • Export Citation

  • Rappaport, E. N., and Coauthors, 2009: Advances and challenges at the National Hurricane Center. Wea. Forecasting, 24, 395–419, doi:10.1175/2008WAF2222128.1.

    • Search Google Scholar
    • Export Citation

  • Rosenthal, S. L., 1971: The response of a tropical cyclone model to variations in boundary layer parameters, initial conditions, lateral boundary conditions, and domain size. Mon. Wea. Rev., 99, 767–777, doi:10.1175/1520-0493(1971)099<0767:TROATC>2.3.CO;2.

    • Search Google Scholar
    • Export Citation

  • Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, and S. Tarantola, 2008: Global Sensitivity Analysis: The Primer.Wiley Publishing, 304 pp.

  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp. [Available online at http://www.mmm.ucar.edu/wrf/users/docs/arw_v3_bw.pdf.]

  • Smith, R. K., M. T. Montgomery, and G. L. Thomsen, 2013: Sensitivity of tropical-cyclone models to the surface drag coefficient in different boundary-layer schemes. Quart. J. Roy. Meteor. Soc., doi:10.1002/qj.2057, in press.

    • Search Google Scholar
    • Export Citation

  • Sraj, I., and Coauthors, 2013: Bayesian inference of drag parameters using Fanapi AXBT data. Mon. Wea. Rev., 141, 2347–2367, doi:10.1175/MWR-D-12-00228.1.

    • Search Google Scholar
    • Export Citation

  • Vickery, P. J., D. Wadhera, M. D. Powell, and Y. Chen, 2009: A hurricane boundary layer and wind field model for use in engineering applications. J. Appl. Meteor. Climatol., 48, 381–405, doi:10.1175/2008JAMC1841.1.

    • Search Google Scholar
    • Export Citation

  • Weng, Y., and F. Zhang, 2012: Assimilating airborne Doppler radar observations with an ensemble Kalman filter for convection-permitting hurricane initialization and prediction: Katrina (2005). Mon. Wea. Rev., 140, 841–859, doi:10.1175/2011MWR3602.1.

    • Search Google Scholar
    • Export Citation

  • Zhang, F., Y. Weng, J. A. Sippel, Z. Meng, and C. H. Bishop, 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 137, 2105–2125, doi:10.1175/2009MWR2645.1.

    • Search Google Scholar
    • Export Citation

  • Zhang, J. A., P. G. Black, J. R. French, and W. M. Drennan, 2008: First direct measurements of enthalpy flux in the hurricane boundary layer: The CBLAST results. Geophys. Res. Lett., 35, L14813, doi:10.1029/2008GL034374.

    • Search Google Scholar
    • Export Citation

  • Zupanski, D., and M. Zupanski, 2006: Model error estimation employing an ensemble data assimilation approach. Mon. Wea. Rev., 134, 1337–1354, doi:10.1175/MWR3125.1.

    • Search Google Scholar
    • Export Citation
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