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Numerical Buoyancy-Wave Model for Wave Stress and Drag Simulations in the Atmosphere

Published online by Cambridge University Press:  03 June 2015

M. Zirk ,
R. Rõõm ,
A. Männik ,
A. Luhamaa ,
M. Kaasik  and
S. Traud
M. Zirk*
Affiliation:
Institute of Physics, Tartu University, Tartu 50090, Estonia
R. Rõõm*
Affiliation:
Institute of Physics, Tartu University, Tartu 50090, Estonia
A. Männik*
Affiliation:
Institute of Physics, Tartu University, Tartu 50090, Estonia
A. Luhamaa*
Affiliation:
Institute of Physics, Tartu University, Tartu 50090, Estonia
M. Kaasik*
Affiliation:
Institute of Physics, Tartu University, Tartu 50090, Estonia
S. Traud*
Affiliation:
Institute of Physics, Tartu University, Tartu 50090, Estonia
*
Corresponding author.Email:Marko.Zirk@ut.ee
Email:rein.room@ut.ee
Email:Aarne.Mannik@ut.ee
Email:Andres.Luhamaa@ut.ee
Email:Marko.Kaasik@ut.ee
Email:Sebastian.Traud@ut.ee
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Abstract

Orographic drag formation is investigated using a numerical wave model (NWM), based on the pressure-coordinate dynamics of non-hydrostatic HIRLAM. The surface drag, wave stress (vertical flux of horizontal momentum), and wave drag are split to the longitudinal and transverse components and presented as Fourier sums of their spectral amplitudes weighted with the power spectrum of relative orographic height. The NWM is accomplished, enabling a spectral investigation of the buoyancy wave stress, and drag generation by orography and is then applied to a cold front, characterised by low static stability of the upper troposphere, large vertical and directional wind variations, and intensive trapped wave generation downstream of obstacles. Resonances are discovered in the stress and drag spectra in the form of high narrow peaks. The stress conservation problem is revisited. Longitudinal stress conserves in unidirectional flow, 2D orography conditions, but becomes convergent for rotating wind or 3D orography. Even in the convergent case the vertical momentum flux from the troposphere to stratosphere remains substantial. The transverse stress never conserves. Disappearing at the surface and on the top, it realises the main momentum exchange between lower an upper parts of the troposphere. Existence of stationary stratospheric quasi-turbulence (SQT) is established above wind minimum in the stratosphere.

Keywords

92.60.Kc92.70.Bc92.60.hh02.30.Nw47.11.Kb47.27.erFourier spectrumorographic buoyancy wavessurface dragwave dragwave stressmomentum fluxwave equationnumerical wave modelling
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 1 , January 2014 , pp. 206 - 245
Copyright
Copyright © Global Science Press Limited 2014

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References

[1] Palmer, T. N., Shutts, G. J. and Swinbank, R., Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parameterization, Q. J. R. Meteorol. Soc., 112 (1986), 1001–1039.CrossRefGoogle Scholar
[2] McFarlane, N. A., The Effect of Orographically Excited Gravity Wave Drag on the General Circulation of the Lower Stratosphere and Troposphere, J. Atmos. Sci., 44 (1987), 1775–1800.Google Scholar
[3] Baines, P. G. and Palmer, T. N., Rationale for a new physically based parametrization of sub-grid scale orographic effects, ECMWF Tech. Memo, 169 (1990), ECMWF, Shinfield Park, Reading, Berkshire, U.K. Google Scholar
[4] Kirtman, B., Vernekar, A., DeWitt, D. and Zhou, J., Impact of orographic gravity wave drag on extended-range forecasts with the COLA-GCM, Atmósfera, 6 (1993), 3–23.Google Scholar
[5] Kim, Y. J., Eckermann, S. D. and Chun, H. Y., An Overview of the Past, Present and Future of Gravity-Wave Drag Parameterization for Numerical Climate and Weather Prediction Models, Atmosphere-Ocean, 41 (2003), 65–98.Google Scholar
[6] Rontu, L., A study on parametrization of orography-related momentum fluxes in a synoptic-scale NWP model, Tellus A, 58 (2006), 69–81.Google Scholar
[7] Chun, H-Y., Choi, H-J. and Song, I-S., Effects of Nonlinearity on Convectively Forced Internal Gravity Waves: Application to a Gravity Wave Drag Parameterization, J. Atmos. Sci., 65 (2008), 557–575.Google Scholar
[8] Richter, J. H., Sassi, F. and Garcia, R. R., Toward a Physically Based Gravity Wave Source Parameterization in a General Circulation Model, J. Atmos. Sci., 67 (2010), 136–156.Google Scholar
[9] Zhu, X., Yee, J.-H., Swartz, W. H., Talaat, E. R. and Coy, L.,A Spectral Parameterization of Drag, Eddy Diffusion, and Wave Heating for a Three-Dimensional Flow Induced by Breaking Gravity Waves, Atmos, J. Sci., 67 (2010), 2520–2536.Google Scholar
[10] Alexander, M. J., Geller, M., Mc, C.Landress, Polavarapu, S., Preusse, P., Sassi, F., Sato, K., Eckermann, S., Ern, M., Hertzog, A., Kawatani, Y., Pulido, M., Shaw, T. A., Sigmond, M., Vincent, R. and Watanabe, S., Recent developments in gravity-wave effects in climate models and the global distribution of gravity-wave momentum flux from observations and models, Q. J. R. Meteorol. Soc., 136 (2010), 1103–1124.Google Scholar
[11] Choi, H-J. and Chun, H-Y., Momentum Flux Spectrum of Convective Gravity Waves. Part I: An Update of a Parameterization Using Mesoscale Simulations, J. Atmos. Sci., 68 (2011), 739–759.CrossRefGoogle Scholar
[12] Sawyer, J. S., The introduction of the effects of topography into methods of numerical forecasting, Q. J. R. Meteorol. Soc., 85 (1959), 31–43.Google Scholar
[13] Smith, R. B., The Influence of Mountains on the Atmosphere, Advances in Geophysics, 21 (1979), 87–230.Google Scholar
[14] Smith, R. B., Linear theory of stratified hydrostatic flow past an isolated mountain, Tellus, 32 (1980), 348–364.Google Scholar
[15] Phillips, D. S., Analytical Surface Pressure and Drag for Linear Hydrostatic Flow over Three-Dimensional Elliptical Mountains, J. Atmos. Sci., 41 (1984), 1073–1084.2.0.CO;2>CrossRefGoogle Scholar
[16] Eliassen, A. and Palm, E., On the transfer of energy in stationary mountain waves, Geofysiske Publikasjoner, 22 (1961), 1–23.Google Scholar
[17] Charney, J. G. and Drazin, P. G., Propagation of Planetary-Scale Disturbances from the Lower into the Upper Atmosphere, J. Geophys. Res., 66 (1961), 83–109 Google Scholar
[18] Andrews, D. G. and McIntyre, M. E., Planetary Waves in Horizontal and Vertical Shear: The Generalized Eliassen-Palm Relation and the Mean Zonal Acceleration, J. Atmos. Sci., 33 (1976), 2031–2048.Google Scholar
[19] Bretherton, F. P., Momentum transport by gravity waves, Q. J. R. Meteorol. Soc., 95 (1969), 213–243.Google Scholar
[20] Peltier, W. R. and Clark, T. L., The Evolution and Stability of Finite-Amplitude Mountain Waves. Part II: Surface Wave Drag and Severe Downslope Windstorms, J. Atmos. Sci., 36 (1979), 1498–1529.Google Scholar
[21] Durran, D. R. and Klemp, J. B., The Effects of Moisture on Trapped Mountain Lee Waves, J. Atmos. Sci., 39 (1982), 2490–2506.Google Scholar
[22] Durran, D. R. and Klemp, J. B., A Compressible Model for the Simulation of Moist Mountain Waves, Mon. Weather Rev., 111 (1983), 2341–2361.Google Scholar
[23] Pierrehumbert, R. T., An essay on the parameterization of orographic gravity-wave drag, in Seminar/Workshop 1986: observation, theory, and modelling of orographic effects, 251–282. ECMWF, Shinfield Park, Reading, U.K., 1987.Google Scholar
[24] Kim, Y.-J. and Arakawa, A., Improvement of Orographic Gravity Wave Parameterization Using a Mesoscale Gravity Wave Model, J. Atmos. Sci., 52 (1995), 1875–1902.Google Scholar
[25] Durran, D. R., Do Breaking Mountain Waves Decelerate the Local Mean Flow?, J. Atmos. Sci., 52 (1995), 4010–4032.2.0.CO;2>CrossRefGoogle Scholar
[26] Welch, W. T., Smolarkiewicz, P., Rotunno, R. and Boville, B. A., The Large-Scale Effects of Flow over Periodic Mesoscale Topography, J. Atmos. Sci., 58 (2001), 1477–1492.2.0.CO;2>CrossRefGoogle Scholar
[27] Broad, A. S., Momentum flux due to trapped lee waves forced by mountains, Meteo-rol, Q. J. R. Soc., 128 (2002), 2167–2173.Google Scholar
[28] Doyle, J. D. and Reynolds, C. A., Implications of Regime Transitions for Mountain-Wave-Breaking Predictability, Mon. Weather Rev., 136 (2008), 5211–5223.Google Scholar
[29] Lindeman, J., Boybeyi, Z., Broutman, D., Ma, Jun, Eckermann, S. D. and Rottman, J. W., Mesoscale Model Initialization of the Fourier Method for Mountain Waves, J. Atmos. Sci., 65 (2008), 2749–2756.Google Scholar
[30] Klemp, J. B. and Lilly, D. R., The Dynamics of Wave-Induced Downslope Winds, J. Atmos. Sci., 32 (1975), 320–339.Google Scholar
[31] Grisogono, B., Dissipation of Wave Drag in the Atmospheric Boundary Layer, J. Atmos. Sci., 51 (1994), 1237–1243.Google Scholar
[32] Leutbecher, M., Surface Pressure Drag for Hydrostatic Two-Layer Flow over Axisymmetric Mountains, J. Atmos. Sci., 58 (2001), 797–807.Google Scholar
[33] Holton, J. R., Beres, J. H. and Zhou, X., On the Vertical Scale of Gravity Waves Excited by Localized Thermal Forcing, J. Atmos. Sci., 59 (2002), 2019–2023.Google Scholar
[34] Beres, J. H., Gravity Wave Generation by a Three-Dimensional Thermal Forcing, J. Atmos. Sci., 61 (2004), 1805–1815.Google Scholar
[35] Teixeira, M. A. C. and Miranda, P. M. A., The Effect of Wind Shear and Curvature on the Gravity Wave Drag Produced by a Ridge, J. Atmos. Sci., 61 (2004), 2638–2643.Google Scholar
[36] Teixeira, M. A. C. and Miranda, P. M. A., A linear model of gravity wave drag for hydrostatic sheared flow over elliptical mountains, Q. J. R. Meteorol. Soc., 132 (2006), 2439–2458.Google Scholar
[37] Teixeira, M. A. C. and Miranda, P. M. A., On the Momentum Fluxes Associated with Mountain Waves in Directionally Sheared Flows, J. Atmos. Sci., 66 (2009), 3419–3433.Google Scholar
[38] Teixeira, M. A. C., Miranda, P. M. A. and Argaín, J. L., Mountain Waves in Two-Layer Sheared Flows: Critical-Level Effects, Wave Reflection, and Drag Enhancement, J. Atmos. Sci., 65 (2008), 1912–1926.CrossRefGoogle Scholar
[39] Rõõm, R. and Zirk, M., An Efficient Solution Method for the Buoyancy Wave Equation at Variable Wind and Temperature, Mon. Weather Rev., 135 (2007), 3633–3641.Google Scholar
[40] Miller, M. J., On the use of pressure as vertical co-ordinate in modelling convection, Q. J. R. Meteorol. Soc., 100 (1974), 155–162.Google Scholar
[41] Miller, M. J. and Pearce, R. P., A three-dimensional primitive equation model of cumulonimbus convection, Meteorol, Q. J. R. Soc., 100 (1974), 133–154.Google Scholar
[42] Rõõm, R., Männik, A. and Luhamaa, A., Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme, Tellus A, 59 (2007), 650–660.Google Scholar
[43] Rõõm, R., Männik, A. and Luhamaa, A., Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: Numerical testing, Tellus A, 59 (2007), 661–673.Google Scholar
[44] Rõõm, R. and Männik, A., Responses of Different Nonhydrostatic, Pressure-Coordinate Models to Orographic Forcing, J. Atmos. Sci., 56 (1999), 2553–2570.Google Scholar
[45] Rõõm, R., Nonhydrostatic adiabatic kernel for HIRLAM. Part I: Fundamentals of nonhy-drostatic dynamics in pressure-related coordinates, HIRLAM Technical Report, 48 (2001), Available at http://hirlam.org/publications/TechReports/TR48.pdf. Google Scholar
[46] Smith, R. B., A Theory of Lee Cyclogenesis, J. Atmos. Sci., 41 (1984), 1159–1168.Google Scholar
[47] Lott, F., Alleviation of Stationary Biases in a GCM through a Mountain Drag Parameterization Scheme and a Simple Representation of Mountain Lift Forces, Mon. Weather Rev., 127 (1999), 788–801.Google Scholar
[48] Scorer, R. S., Theory of waves in the lee of mountains, Meteorol, Q. J. R. Soc., 75 (1949), 41–66.Google Scholar
[49] Broad, A. S., Linear theory of momentum fluxes in 3-D flows with turning of the mean wind with height, Meteorol, Q. J. R. Soc., 121 (1995), 1891–1902.Google Scholar
[50] Durran, D. R., Numerical Methods for Wave Equations in Geophysical Fluid Dynamics, Springer (1998), 465 p.Google Scholar
[51] Smith, R. B., Further Development of a Theory of Lee Cyclogenesis, J. Atmos. Sci., 43 (1986), 1582–1602.2.0.CO;2>CrossRefGoogle Scholar
[52] P., Undén, Rontu, L., Järvinen, H., Lynch, P., Calvo, J., Cats, G., Cuxart, J., Eerola, K., Fortelius, C., Garcia-Moya, J. A., Jones, C., Lenderlink, G., McDonald, A., McGrath, R., Navascues, B., Nielsen, N. W., Ødegaard, V., Rodriguez, E., Rummukainen, M., Rõõm, R., Sattler, K., Sass, B. H., Savijärvi, H., Schreur, B. W., Sigg, R., The, H. and Tijm, A., HIRLAM-5 Scientific Documentation, December 2002. Swedish Meteorological and Hydrological Institute, Norrköping, Sweden. 20021.Google Scholar
[53] Nance, L. B. and Durran, D. R., A Modeling Study of Nonstationary Trapped Mountain Lee Waves. Part I: Mean-Flow Variability, J. Atmos. Sci., 54 (1997), 2275–2291.Google Scholar
[54] Nance, L. B. and Durran, D. R., A Modeling Study of Nonstationary Trapped Mountain Lee Waves. Part II: Nonlinearity, J. Atmos. Sci., 55 (1998), 1429–1445.Google Scholar
[55] Vosper, S. B., Sheridan, P. F. and Brown, A. R., Flow separation and rotor formation beneath two-dimensional trapped lee waves, Meteorol, Q. J. R. Soc., 132 (2006), 2415–2438.Google Scholar
[56] Jiang, Q., Doyle, J. D. and Smith, R. B., Interaction between Trapped Waves and Boundary Layers, J. Atmos. Sci., 63 (2006), 617–633.CrossRefGoogle Scholar
[57] Grubišic, V. and Stiperski, I., Lee-Wave Resonances over Double Bell-Shaped Obstacles, J. Atmos. Sci., 66 (2009), 1205–1228.Google Scholar
[58] Jiang, Q., Smith, R. B. and Doyle, J. D., Impact of the Atmospheric Boundary Layer on Mountain Waves, J. Atmos. Sci., 65 (2008), 592–608.Google Scholar
[59] Stiperski, I. and Grubiŝic, V., Trapped Lee Wave Interference in the Presence of Surface Friction, J. Atmos. Sci., 68 (2011), 918–939.Google Scholar