A Parameterization Scheme Accounting for Nonhydrostatic Effects on the Momentum Flux of Vertically Propagating Orographic Gravity Waves: Formulas and Preliminary Tests in the Model for Prediction Across Scales (MPAS)

Xin Xu aKey Laboratory of Mesoscale Severe Weather, Ministry of Education, Nanjing University, Nanjing, Jiangsu, China
bSchool of Atmospheric Sciences, Nanjing University, Nanjing, Jiangsu, China
cCMA Radar Meteorology Key Laboratory, Nanjing, Jiangsu, China

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Rongrong Zhang aKey Laboratory of Mesoscale Severe Weather, Ministry of Education, Nanjing University, Nanjing, Jiangsu, China
bSchool of Atmospheric Sciences, Nanjing University, Nanjing, Jiangsu, China

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Miguel A. C. Teixeira dDepartment of Meteorology, University of Reading, Reading, United Kingdom

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Annelize van Niekerk eEuropean Centre for Medium-Range Weather Forecasts, Reading, United Kingdom

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Ming Xue fCenter for Analysis and Prediction of Storms, University of Oklahoma, Norman, Oklahoma

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Yixiong Lu gCMA Earth System Modeling and Prediction Centre, Beijing, China

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Haile Xue gCMA Earth System Modeling and Prediction Centre, Beijing, China

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Runqiu Li aKey Laboratory of Mesoscale Severe Weather, Ministry of Education, Nanjing University, Nanjing, Jiangsu, China
bSchool of Atmospheric Sciences, Nanjing University, Nanjing, Jiangsu, China

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Yuan Wang aKey Laboratory of Mesoscale Severe Weather, Ministry of Education, Nanjing University, Nanjing, Jiangsu, China
bSchool of Atmospheric Sciences, Nanjing University, Nanjing, Jiangsu, China

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Abstract

The momentum transport by orographic gravity waves (OGWs) plays an important role in driving the large-scale circulation throughout the atmosphere and is subject to parameterization in numerical models. Current parameterization schemes, which were originally developed for coarse-resolution models, commonly assume that unresolved OGWs are hydrostatic. With the increase in the horizontal resolution of state-of-the-art numerical models, unresolved OGWs are of smaller horizontal scale and more influenced by nonhydrostatic effects (NHE), thus challenging use of the hydrostatic assumption. Based on the analytical formulas for nonhydrostatic OGWs derived in our recent study, the orographic gravity wave drag (OGWD) parameterization scheme in the Model for Prediction Across Scales is revised by accounting for NHE. Global simulations with 30-km horizontal resolution are conducted to investigate NHE on the momentum transport of OGWs and their impacts on the large-scale circulation in boreal winter. NHE are evident in regions of complex terrain such as the Tibetan Plateau, Rocky Mountains, southern Andes, and eastern Antarctica. The parameterized surface wave momentum flux can be either reduced or enhanced depending on the relative importance of NHE and model physics–dynamics interactions. The NHE corrections to the OGWD scheme significantly reduce the easterly biases in the polar stratosphere of the Northern Hemisphere, due to both weakened OGWD in the upper troposphere and lower stratosphere and suppressed upward propagation of resolved waves into the stratosphere. However, the revised OGWD scheme only has a weak influence on the large-scale circulation in the Southern Hemisphere during boreal winter.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xin Xu, xinxu@nju.edu.cn

Abstract

The momentum transport by orographic gravity waves (OGWs) plays an important role in driving the large-scale circulation throughout the atmosphere and is subject to parameterization in numerical models. Current parameterization schemes, which were originally developed for coarse-resolution models, commonly assume that unresolved OGWs are hydrostatic. With the increase in the horizontal resolution of state-of-the-art numerical models, unresolved OGWs are of smaller horizontal scale and more influenced by nonhydrostatic effects (NHE), thus challenging use of the hydrostatic assumption. Based on the analytical formulas for nonhydrostatic OGWs derived in our recent study, the orographic gravity wave drag (OGWD) parameterization scheme in the Model for Prediction Across Scales is revised by accounting for NHE. Global simulations with 30-km horizontal resolution are conducted to investigate NHE on the momentum transport of OGWs and their impacts on the large-scale circulation in boreal winter. NHE are evident in regions of complex terrain such as the Tibetan Plateau, Rocky Mountains, southern Andes, and eastern Antarctica. The parameterized surface wave momentum flux can be either reduced or enhanced depending on the relative importance of NHE and model physics–dynamics interactions. The NHE corrections to the OGWD scheme significantly reduce the easterly biases in the polar stratosphere of the Northern Hemisphere, due to both weakened OGWD in the upper troposphere and lower stratosphere and suppressed upward propagation of resolved waves into the stratosphere. However, the revised OGWD scheme only has a weak influence on the large-scale circulation in the Southern Hemisphere during boreal winter.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xin Xu, xinxu@nju.edu.cn
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  • Alexander, M. J., and Coauthors, 2010: Recent developments in gravity-wave effects in climate models and the global distribution of gravity-wave momentum flux from observations and models. Quart. J. Roy. Meteor. Soc., 136, 11031124, https://doi.org/10.1002/qj.637.

    • Search Google Scholar
    • Export Citation
  • Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. Academic Press, 489 pp.

  • Charney, J. G., and P. G. Drazin, 1961: Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J. Geophys. Res., 66, 83109, https://doi.org/10.1029/JZ066i001p00083.

    • Search Google Scholar
    • Export Citation
  • Chen, P., and W. A. Robinson, 1992: Propagation of planetary waves between the troposphere and stratosphere. J. Atmos. Sci., 49, 25332545, https://doi.org/10.1175/1520-0469(1992)049<2533:POPWBT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Choi, H.-J., and S.-Y. Hong, 2015: An updated subgrid orographic parameterization for global atmospheric forecast models. J. Geophys. Res. Atmos., 120, 12 44512 457, https://doi.org/10.1002/2015JD024230.

    • Search Google Scholar
    • Export Citation
  • Choi, H.-J., S.-J. Choi, M.-S. Koo, J.-E. Kim, Y. C. Kwon, and S.-Y. Hong, 2017: Effects of parameterized orographic drag on weather forecasting and simulated climatology over East Asia during boreal summer. J. Geophys. Res. Atmos., 122, 10 66910 678, https://doi.org/10.1002/2017JD026696.

    • Search Google Scholar
    • Export Citation
  • Cohen, N. Y., E. P. Gerber, and O. Bühler, 2013: Compensation between resolved and unresolved wave driving in the stratosphere: Implications for downward control. J. Atmos. Sci., 70, 37803798, https://doi.org/10.1175/JAS-D-12-0346.1.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and Coauthors, 2011: The ERA-interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Search Google Scholar
    • Export Citation
  • de la Cámara, A., F. Lott, V. Jewtoukoff, R. Plougonven, and A. Hertzog, 2016: On the gravity wave forcing during the southern stratospheric final warming in LMDZ. J. Atmos. Sci., 73, 32133226, https://doi.org/10.1175/JAS-D-15-0377.1.

    • Search Google Scholar
    • Export Citation
  • Edmon, H. J., Jr., B. J. Hoskins, and M. E. McIntyre, 1980: Eliassen-Palm cross sections for the troposphere. J. Atmos. Sci., 37, 26002616, https://doi.org/10.1175/1520-0469(1980)037<2600:EPCSFT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ehard, B., and Coauthors, 2017: Horizontal propagation of large-amplitude mountain waves in the vicinity of the polar night jet. J. Geophys. Res. Atmos., 122, 14231436, https://doi.org/10.1002/2016JD025621.

    • Search Google Scholar
    • Export Citation
  • Eichinger, R., H. Garny, P. Šácha, J. Danker, S. Dietmüller, and S. Oberländer-Hayn, 2020: Effects of missing gravity waves on stratospheric dynamics; Part 1: Climatology. Climate Dyn., 54, 31653183, https://doi.org/10.1007/s00382-020-05166-w.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., and M. J. Alexander, 2003: Gravity wave dynamics and effects in the middle atmosphere. Rev. Geophys., 41, 1003, https://doi.org/10.1029/2001RG000106.

    • Search Google Scholar
    • Export Citation
  • Garcia, R. R., A. K. Smith, D. E. Kinnison, A. de la Cámara, and D. J. Murphy, 2017: Modification of the gravity wave parameterization in the Whole Atmosphere Community Climate Model: Motivation and results. J. Atmos. Sci., 74, 275291, https://doi.org/10.1175/JAS-D-16-0104.1.

    • Search Google Scholar
    • Export Citation
  • Hájková, D., and P. Šácha, 2024: Parameterized orographic gravity wave drag and dynamical effects in CMIP6 models. Climate Dyn., 62, 22592284, https://doi.org/10.1007/s00382-023-07021-0.

    • Search Google Scholar
    • Export Citation
  • Hasha, A., O. Bühler, and J. Scinocca, 2008: Gravity wave refraction by three-dimensionally varying winds and the global transport of angular momentum. J. Atmos. Sci., 65, 28922906, https://doi.org/10.1175/2007JAS2561.1.

    • Search Google Scholar
    • Export Citation
  • Hu, D., Y. Guo, and Z. Guan, 2019: Recent weakening in the stratospheric planetary wave intensity in early winter. Geophys. Res. Lett., 46, 39533962, https://doi.org/10.1029/2019GL082113.

    • Search Google Scholar
    • Export Citation
  • Jiang, Q., A. Reinecke, and J. D. Doyle, 2014: Orographic wave drag over the Southern Ocean: A linear theory perspective. J. Atmos. Sci., 71, 42354252, https://doi.org/10.1175/JAS-D-14-0035.1.

    • Search Google Scholar
    • Export Citation
  • Kalisch, S., P. Preusse, M. Ern, S. D. Eckerman, and M. Riese, 2014: Differences in gravity wave drag between realistic oblique and assumed vertical propagation. J. Geophys. Res. Atmos., 119, 10 08110 099, https://doi.org/10.1002/2014JD021779.

    • Search Google Scholar
    • Export Citation
  • Kim, Y.-J., and A. Arakawa, 1995: Improvement of orographic gravity wave parameterization using a mesoscale gravity wave model. J. Atmos. Sci., 52, 18751902, https://doi.org/10.1175/1520-0469(1995)052<1875:IOOGWP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kim, Y.-J., and J. D. Doyle, 2005: Extension of an orographic-drag parameterization scheme to incorporate orographic anisotropy and flow blocking. Quart. J. Roy. Meteor. Soc., 131, 18931921, https://doi.org/10.1256/qj.04.160.

    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., and D. R. Durran, 1983: An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models. Mon. Wea. Rev., 111, 430444, https://doi.org/10.1175/1520-0493(1983)111<0430:AUBCPI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kruse, C. G., R. B. Smith, and S. D. Eckermann, 2016: The midlatitude lower-stratospheric mountain wave “valve layer.” J. Atmos. Sci., 73, 50815100, https://doi.org/10.1175/JAS-D-16-0173.1.

    • Search Google Scholar
    • Export Citation
  • Kruse, C. G., and Coauthors, 2022: Observed and modeled mountain waves from the surface to the mesosphere near the Drake Passage. J. Atmos. Sci., 79, 909932, https://doi.org/10.1175/JAS-D-21-0252.1.

    • Search Google Scholar
    • Export Citation
  • Li, R., X. Xu, X. Xu, T. G. Shepherd, and Y. Wang, 2023: Importance of orographic gravity waves over the Tibetan Plateau on the spring rainfall in East Asia. Sci. China Earth Sci., 66, 25942602, https://doi.org/10.1007/s11430-023-1204-6.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R. S., 1981: Turbulence and stress owing to gravity wave and tidal breakdown. J. Geophys. Res., 86, 97079714, https://doi.org/10.1029/JC086iC10p09707.

    • Search Google Scholar
    • Export Citation
  • Lott, F., and M. J. Miller, 1997: A new sub-grid orographic drag parameterization: Its formulation and testing. Quart. J. Roy. Meteor. Soc., 123, 101127, https://doi.org/10.1002/2014JD021779.

    • Search Google Scholar
    • Export Citation
  • Lu, Y., T. Wu, X. Xu, L. Zhang, and M. Chu, 2020: Improved simulation of the Antarctic stratospheric final warming by modifying the orographic gravity wave parameterization in the Beijing climate center atmospheric general circulation model. Atmosphere, 11, 576, https://doi.org/10.3390/atmos11060576.

    • Search Google Scholar
    • Export Citation
  • McFarlane, N. A., 1987: The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci., 44, 17751800, https://doi.org/10.1175/1520-0469(1987)044<1775:TEOOEG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • McLandress, C., T. G. Shepherd, S. Polavaparu, and S. R. Beagley, 2012: Is missing orographic gravity wave drag near 60°S the cause of the stratospheric zonal wind biases in chemistry–climate models? J. Atmos. Sci., 69, 802818, https://doi.org/10.1175/JAS-D-11-0159.1.

    • Search Google Scholar
    • Export Citation
  • Miranda, P. M. A., and I. N. James, 1992: Non-linear three-dimensional effects on gravity-wave drag: Splitting flow and breaking waves. Quart. J. Roy. Meteor. Soc., 118, 10571081, https://doi.org/10.1002/qj.49711850803.

    • Search Google Scholar
    • Export Citation
  • Palmer, T. N., G. J. Shutts, and R. Swinbank, 1986: Alleviation of systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parameterization. Quart. J. Roy. Meteor. Soc., 112, 10011039, https://doi.org/10.1002/qj.49711247406.

    • Search Google Scholar
    • Export Citation
  • Polichtchouk, I., A. van Niekerk, and N. Wedi, 2023: Resolved gravity waves in the extra-tropical stratosphere: Effect of horizontal resolution increase from O(10 km) to O(1 km). J. Atmos. Sci., 80, 473486, https://doi.org/10.1175/JAS-D-22-0138.1.

    • Search Google Scholar
    • Export Citation
  • Ribstein, B., and U. Achatz, 2016: The interaction between gravity waves and solar tides in a linear tidal model with a 4-D ray-tracing gravity-wave parameterization. J. Geophys. Res. Space Phys., 121, 89368950, https://doi.org/10.1002/2016JA022478.

    • Search Google Scholar
    • Export Citation
  • Šácha, P., A. Kuchar, R. Eichinger, P. Pisoft, C. Jacobi, and H. E. Rieder, 2021: Diverse dynamical response to orographic gravity wave drag hotspots—A zonal mean perspective. Geophys. Res. Lett., 48, e2021GL093305, https://doi.org/10.1029/2021GL093305.

    • Search Google Scholar
    • Export Citation
  • Sandu, I., P. Bechtold, A. Beljaars, A. Bozzo, F. Pithan, T. G. Shepherd, and A. Zadra, 2016: Impacts of parameterized orographic drag on the Northern Hemisphere winter circulation. J. Adv. Model. Earth Syst., 8, 196211, https://doi.org/10.1002/2015MS000564.

    • Search Google Scholar
    • Export Citation
  • Sandu, I., and Coauthors, 2019: Impacts of orography on large‐scale atmospheric circulation. npj Climate Atmos. Sci., 2, 10, https://doi.org/10.1038/s41612-019-0065-9.

    • Search Google Scholar
    • Export Citation
  • Sato, K., S. Tateno, S. Watanabe, and Y. Kawatani, 2012: Gravity wave characteristics in the Southern Hemisphere revealed by a high-resolution middle-atmosphere general circulation model. J. Atmos. Sci., 69, 13781396, https://doi.org/10.1175/JAS-D-11-0101.1.

    • Search Google Scholar
    • Export Citation
  • Scinocca, J. F., and N. A. McFarlane, 2000: The parametrization of drag induced by stratified flow over anisotropic orography. Quart. J. Roy. Meteor. Soc., 126, 23532393, https://doi.org/10.1002/qj.49712656802.

    • Search Google Scholar
    • Export Citation
  • Shepherd, T. G., 2014: Atmospheric circulation as a source of uncertainty in climate change projections. Nat. Geosci., 7, 703708, https://doi.org/10.1038/ngeo2253.

    • Search Google Scholar
    • Export Citation
  • Shutts, G., 1995: Gravity-wave drag parameterization over complex terrain: The effect of critical-level absorption in directional wind-shear. Quart. J. Roy. Meteor. Soc., 121, 10051021, https://doi.org/10.1002/qj.49712152504.

    • Search Google Scholar
    • Export Citation
  • Sigmond, M., and J. F. Scinocca, 2010: The influence of the basic state on the Northern Hemisphere circulation response to climate change. J. Climate, 23, 14341446, https://doi.org/10.1175/2009JCLI3167.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp., https://doi.org/10.5065/D68S4MVH.

  • Skamarock, W. C., J. B. Klemp, M. G. Duda, L. D. Fowler, S.-H. Park, and T. D. Ringler, 2012: A multiscale nonhydrostatic atmospheric model using centroidal Voronoi tesselations and C-grid staggering. Mon. Wea. Rev., 140, 30903105, https://doi.org/10.1175/MWR-D-11-00215.1.

    • Search Google Scholar
    • Export Citation
  • Song, I.-S., and H.-Y. Chun, 2008: A Lagrangian spectral parameterization of gravity wave drag induced by cumulus convection. J. Atmos. Sci., 65, 12041224, https://doi.org/10.1175/2007JAS2369.1.

    • Search Google Scholar
    • Export Citation
  • Teixeira, M. A. C., P. M. A. Miranda, and R. M. Cardoso, 2008: Asymptotic gravity wave drag expression for non-hydrostatic rotating flow over a ridge. Quart. J. Roy. Meteor. Soc., 134, 271276, https://doi.org/10.1002/qj.196.

    • Search Google Scholar
    • Export Citation
  • van Niekerk, A., and Coauthors, 2020: COnstraining ORographic Drag Effects (COORDE): A model comparison of resolved and parametrized orographic drag. J. Adv. Model. Earth Sys., 12, e2020MS002160, https://doi.org/10.1029/2020MS002160.

    • Search Google Scholar
    • Export Citation
  • van Niekerk, A., S. B. Vosper, and M. A. C. Teixeira, 2023: Accounting for the three-dimensional nature of mountain waves: Parametrizing partial critical level filtering. Quart. J. Roy. Meteor. Soc., 149, 515536, https://doi.org/10.1002/qj.4421.

    • Search Google Scholar
    • Export Citation
  • Webster, S., A. R. Brown, D. R. Cameron, and C. P. Jones, 2003: Improvements to the representation of orography in the Met Office unified model. Quart. J. Roy. Meteor. Soc., 129, 19892010, https://doi.org/10.1256/qj.02.133.

    • Search Google Scholar
    • Export Citation
  • White, R. H., J. M. Wallace, and D. S. Battisti, 2021: Revisiting the role of mountains in the Northern Hemisphere winter atmospheric circulation. J. Atmos. Sci., 78, 22212235, https://doi.org/10.1175/JAS-D-20-0300.1.

    • Search Google Scholar
    • Export Citation
  • Xu, X., J. Song, Y. Wang, and M. Xue, 2017a: Quantifying the effect of horizontal propagation of three-dimensional mountain waves on the wave momentum flux using Gaussian beam approximation. J. Atmos. Sci., 74, 17831798, https://doi.org/10.1175/JAS-D-16-0275.1.

    • Search Google Scholar
    • Export Citation
  • Xu, X., Y. Wang, M. Xue, and K. Zhu, 2017b: Impacts of horizontal propagation of orographic gravity waves on the wave drag in the stratosphere and lower mesosphere. J. Geophys. Res. Atmos., 122, 11 30111 312, https://doi.org/10.1002/2017JD027528.

    • Search Google Scholar
    • Export Citation
  • Xu, X., Y. Tang, Y. Wang, and M. Xue, 2018: Directional absorption of mountain waves and its influence on the wave momentum transport in the Northern Hemisphere. J. Geophys. Res. Atmos., 123, 26402654, https://doi.org/10.1002/2017JD027968.

    • Search Google Scholar
    • Export Citation
  • Xu, X., M. Xue, M. A. C. Teixeira, J. Tang, and Y. Wang, 2019: Parameterization of directional absorption of orographic gravity waves and its impact on the atmospheric general circulation simulated by the Weather Research and Forecasting Model. J. Atmos. Sci., 76, 34353453, https://doi.org/10.1175/JAS-D-18-0365.1.

    • Search Google Scholar
    • Export Citation
  • Xu, X., M. A. C. Teixeira, M. Xue, Y. Lu, and J. Tang, 2020: Impacts of wind profile shear and curvature on the parameterized orographic gravity wave stress in the weather research and forecasting model. Quart. J. Roy. Meteor. Soc., 146, 30863100, https://doi.org/10.1002/qj.3828.

    • Search Google Scholar
    • Export Citation
  • Xu, X., R. Li, M. A. C. Teixeira, and Y. Lu, 2021: On the momentum flux of vertically-propagating orographic gravity waves excited in nonhydrostatic flow over three-dimensional orography. J. Atmos. Sci., 78, 18071822, https://doi.org/10.1175/JAS-D-20-0370.1.

    • Search Google Scholar
    • Export Citation
  • Xue, M., and A. J. Thorpe, 1991: A mesoscale numerical model using the nonhydrostatic pressure-based sigma-coordinate equations: Model experiments with dry mountain flows. Mon. Wea. Rev., 119, 11681185, https://doi.org/10.1175/1520-0493(1991)119<1168:AMNMUT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zängl, G., 2003: Orographic gravity waves close to the nonhydrostatic limit of vertical propagation. J. Atmos. Sci., 60, 20452063, https://doi.org/10.1175/1520-0469(2003)060<2045:OGWCTT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhang, R., X. Xu, and Y. Wang, 2020: Impacts of subgrid orographic drag on the summer monsoon circulation and precipitation in East Asia. J. Geophys. Res. Atmos., 125, e2019JD032337, https://doi.org/10.1029/2019JD032337.

    • Search Google Scholar
    • Export Citation
  • Zhou, X., A. Beljaars, Y. Wang, B. Huang, C. Lin, Y. Chen, and H. Wu, 2017: Evaluation of WRF simulations with different selections of subgrid orographic drag over the Tibetan Plateau. J. Geophys. Res. Atmos., 122, 97599772, https://doi.org/10.1002/2017JD027212.

    • Search Google Scholar
    • Export Citation
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