A Modeling Study of a Trapped Lee-Wave Event over the Pyrénées

Mireia Udina Departament d’Astronomia i Meteorologia, Universitat de Barcelona, Barcelona, Spain

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Maria Rosa Soler Departament d’Astronomia i Meteorologia, Universitat de Barcelona, Barcelona, Spain

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Ona Sol Weathernews, Soest, Netherlands

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Abstract

A trapped lee-wave mountain event in the southern part of the Pyrénées area is analyzed using the Weather Research and Forecasting (WRF) Model. Model experiments are designed to address the WRF predictability of such an event and to explore the influence of the model parameters in resolving the mountain waves. The results show that the model is able to capture a trapped lee-wave event using the 1-km horizontal grid model outputs. Different initial conditions, the vertical grid resolution, and the resolved topography lead to changes in the wave field distribution and the wave amplitude meaning that an ensemble of different model settings may be able to quantify the uncertainty of the numerical solutions. However, the model experiments do not significantly change the wavelength of the generated mountain waves, which is shorter in the three-dimensional real simulations than the one derived from satellite imagery. Comparison with observational data from the surface stations and a wind profiler upstream of the mountain range shows that the model underestimates the horizontal wind speed and this can be the reason for the underestimation of the wavelength. In addition, the valley circulations and the formation of a rotor near the surface are explored. The formation of a low-level rotor in the model is intermittent and brief, and it interacts with other flows coming from multiple directions. The first strong wave updraft is located over the valley aligned with the highest mountain peaks and strong vorticity is captured from the surface up to the first wave crest.

Corresponding author address: Mireia Udina, Dept. d’Astronomia i Meteorologia, C/Marti i Franques, 1, Universitat de Barcelona, 08028 Barcelona, Spain. E-mail: mudina@am.ub.es

Abstract

A trapped lee-wave mountain event in the southern part of the Pyrénées area is analyzed using the Weather Research and Forecasting (WRF) Model. Model experiments are designed to address the WRF predictability of such an event and to explore the influence of the model parameters in resolving the mountain waves. The results show that the model is able to capture a trapped lee-wave event using the 1-km horizontal grid model outputs. Different initial conditions, the vertical grid resolution, and the resolved topography lead to changes in the wave field distribution and the wave amplitude meaning that an ensemble of different model settings may be able to quantify the uncertainty of the numerical solutions. However, the model experiments do not significantly change the wavelength of the generated mountain waves, which is shorter in the three-dimensional real simulations than the one derived from satellite imagery. Comparison with observational data from the surface stations and a wind profiler upstream of the mountain range shows that the model underestimates the horizontal wind speed and this can be the reason for the underestimation of the wavelength. In addition, the valley circulations and the formation of a rotor near the surface are explored. The formation of a low-level rotor in the model is intermittent and brief, and it interacts with other flows coming from multiple directions. The first strong wave updraft is located over the valley aligned with the highest mountain peaks and strong vorticity is captured from the surface up to the first wave crest.

Corresponding author address: Mireia Udina, Dept. d’Astronomia i Meteorologia, C/Marti i Franques, 1, Universitat de Barcelona, 08028 Barcelona, Spain. E-mail: mudina@am.ub.es
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  • Ágústsson, H., H. Ólafsson, M. Jonassen, and Ó. Rögnvaldsson, 2014: The impact of assimilating data from a remotely piloted aircraft on simulations of weak-wind orographic flow. Tellus, 66A, 25421, doi:10.3402/tellusa.v66.25421.

    • Search Google Scholar
    • Export Citation
  • Bougeault, P., A. Jansa Clar, B. Benech, B. Carissimo, J. Pelon, and E. Richard, 1990: Momentum budget over the Pyrénées: The PYREX Experiment. Bull. Amer. Meteor. Soc., 71, 806818, doi:10.1175/1520-0477(1990)071<0806:MBOTPT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bougeault, P., B. Benech, P. Bessemoulin, B. Carissimo, A. J. Clar, J. Pelon, M. Petitdidier, and E. Richard, 1997: PYREX: A summary of findings. Bull. Amer. Meteor. Soc., 78, 637650, doi:10.1175/1520-0477(1997)078<0637:PASOF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bougeault, P., and Coauthors, 2001: The MAP Special Observing Period. Bull. Amer. Meteor. Soc., 82, 433462, doi:10.1175/1520-0477(2001)082<0433:TMSOP>2.3.CO;2.

    • Search Google Scholar
    • Export Citation
  • Broad, A. S., 1996: High-resolution numerical-model integrations to validate gravity-wave-drag parametrization schemes: A case-study. Quart. J. Roy. Meteor. Soc., 122, 16251653, doi:10.1002/qj.49712253508.

    • Search Google Scholar
    • Export Citation
  • Caccia, J., B. Benech, and V. Klaus, 1997: Space–time description of nonstationary trapped lee waves using ST radars, aircraft, and constant volume balloons during the PYREX Experiment. J. Atmos. Sci., 54, 18211833, doi:10.1175/1520-0469(1997)054<1821:STDONT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Chen, F., and J. Dudhia, 2001: Coupling an advanced land surface–hydrology model with the Penn State–NCAR MM5 modeling system. Part I: Model implementation and sensitivity. Mon. Wea. Rev., 129, 569585, doi:10.1175/1520-0493(2001)129<0569:CAALSH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Clark, T. L., W. D. Hall, R. M. Kerr, D. Middleton, L. Radke, F. M. Ralph, P. J. Neiman, and D. Levinson, 2000: Origins of aircraft-damaging clear-air turbulence during the 9 December 1992 Colorado downslope windstorm: Numerical simulations and comparison with observations. J. Atmos. Sci., 57, 11051131, doi:10.1175/1520-0469(2000)057<1105:OOADCA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Cohn, S. A., V. Grubišic, and W. O. Brown, 2011: Wind profiler observations of mountain waves and rotors during T-REX. J. Appl. Meteor. Climatol., 50, 826843, doi:10.1175/2010JAMC2611.1.

    • Search Google Scholar
    • Export Citation
  • Cox, K. W., 1986: Analysis of the Pyrenees lee wave event of 23 March 1982. Mon. Wea. Rev., 114, 11461166, doi:10.1175/1520-0493(1986)114<1146:AOTPLW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Darby, L. S., and G. S. Poulos, 2006: The evolution of lee-wave-rotor activity in the lee of Pike’s Peak under the influence of a cold frontal passage: Implications for aircraft safety. Mon. Wea. Rev., 134, 28572876, doi:10.1175/MWR3208.1.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and D. R. Durran, 2002: The dynamics of mountain-wave-induced rotors. J. Atmos. Sci., 59, 186201, doi:10.1175/1520-0469(2002)059<0186:TDOMWI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and R. B. Smith, 2003: Mountain waves over the Hohe Tauern: Influence of upstream diabatic effects. Quart. J. Roy. Meteor. Soc., 129, 799823, doi:10.1256/qj.01.205.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and D. R. Durran, 2007: Rotor and subrotor dynamics in the lee of three-dimensional terrain. J. Atmos. Sci., 64, 42024221, doi:10.1175/2007JAS2352.1.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and Coauthors, 2000: An intercomparison of model-predicted wave breaking for the 11 January 1972 Boulder windstorm. Mon. Wea. Rev., 128, 901914, doi:10.1175/1520-0493(2000)128<0901:AIOMPW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., M. A. Shapiro, Q. Jiang, and D. L. Bartels, 2005: Large-amplitude mountain wave breaking over Greenland. J. Atmos. Sci., 62, 31063126, doi:10.1175/JAS3528.1.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., V. Grubišic, W. O. Brown, S. F. De Wekker, A. Dörnbrack, Q. Jiang, S. D. Mayor, and M. Weissmann, 2009: Observations and numerical simulations of subrotor vortices during T-REX. J. Atmos. Sci., 66, 12291249, doi:10.1175/2008JAS2933.1.

    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and Coauthors, 2011: An intercomparison of T-REX mountain-wave simulations and implications for mesoscale predictability. Mon. Wea. Rev., 139, 28112831, doi:10.1175/MWR-D-10-05042.1.

    • 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, 30773107, doi:10.1175/1520-0469(1989)046<3077:NSOCOD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Feltz, W., K. Bedka, J. Otkin, T. Greenwald, and S. Ackerman, 2009: Understanding satellite-observed mountain-wave signatures using high-resolution numerical model data. Wea. Forecasting, 24, 7686, doi:10.1175/2008WAF2222127.1.

    • Search Google Scholar
    • Export Citation
  • Fritts, D. C., and Coauthors, 2015: The Deep Propagating Gravity Wave Experiment (DEEPWAVE): An airborne and ground-based exploration of gravity wave propagation and effects from their sources throughout the lower and middle atmosphere. Bull. Amer. Meteor. Soc., 97, 425453, doi:10.1175/BAMS-D-14-00269.1.

    • Search Google Scholar
    • Export Citation
  • Georgelin, M., and F. Lott, 2001: On the transfer of momentum by trapped lee waves: Case of the IOP 3 of PYREX. J. Atmos. Sci., 58, 35633580, doi:10.1175/1520-0469(2001)058<3563:OTTOMB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gossard, E. E., and W. H. Hooke, 1975: Waves in the Atmosphere: Atmospheric Infrasound and Gravity Waves: Their Generation and Propagation. Developments in Atmospheric Science, Vol. 2, Elsevier, 472 pp.

  • Grubišic, V., and B. J. Billings, 2007: The intense lee-wave rotor event of Sierra Rotors IOP 8. J. Atmos. Sci., 64, 41784201, doi:10.1175/2006JAS2008.1.

    • Search Google Scholar
    • Export Citation
  • Grubišic, V., and I. Stiperski, 2009: Lee-wave resonances over double bell-shaped obstacles. J. Atmos. Sci., 66, 12051228, doi:10.1175/2008JAS2885.1.

    • Search Google Scholar
    • Export Citation
  • Grubišic, V., and Coauthors, 2008: The Terrain-Induced Rotor Experiment: A field campaign overview including observational highlights. Bull. Amer. Meteor. Soc., 89, 15131533, doi:10.1175/2008BAMS2487.1.

    • Search Google Scholar
    • Export Citation
  • Hertenstein, R. F., and J. P. Kuettner, 2005: Rotor types associated with steep lee topography: Influence of the wind profile. Tellus, 57A, 117135, doi:10.1111/j.1600-0870.2005.00099.x.

    • Search Google Scholar
    • Export Citation
  • Hoinka, K. P., 1984: Observations of a mountain-wave event over the Pyrenees. Tellus, 36A, 369383, doi:10.1111/j.1600-0870.1984.tb00255.x; Corrigendum, 38, 93–94.

    • Search Google Scholar
    • Export Citation
  • Janjić, Z. I., 1990: The step-mountain coordinate: Physical package. Mon. Wea. Rev., 118, 14291443, doi:10.1175/1520-0493(1990)118<1429:TSMCPP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Janjić, Z. I., 1996: The surface layer parameterization in the NCEP Eta Model. Preprints, 11th Conf. on Numerical Weather Prediction, Norfolk, VA, Amer. Meteor. Soc., 354–355.

  • Janjić, Z. I., 2002: Nonsingular implementation of the Mellor–Yamada level 2.5 scheme in the NCEP Meso model. NCEP Office Note 437, 61 pp. [Available online at http://www.emc.ncep.noaa.gov/officenotes/newernotes/on437.pdf.]

  • Jiang, Q., J. D. Doyle, and R. B. Smith, 2006: Interaction between trapped waves and boundary layers. J. Atmos. Sci., 63, 617633, doi:10.1175/JAS3640.1.

    • Search Google Scholar
    • Export Citation
  • Jiménez, P. A., and J. Dudhia, 2012: Improving the representation of resolved and unresolved topographic effects on surface wind in the WRF model. J. Appl. Meteor. Climatol., 51, 300316, doi:10.1175/JAMC-D-11-084.1.

    • Search Google Scholar
    • Export Citation
  • Jiménez, P. A., J. Dudhia, J. F. González-Rouco, J. Navarro, J. P. Montávez, and E. García-Bustamante, 2012: A revised scheme for the WRF surface layer formulation. Mon. Wea. Rev., 140, 898918, doi:10.1175/MWR-D-11-00056.1.

    • Search Google Scholar
    • Export Citation
  • Kain, J. S., 2004: The Kain–Fritsch convective parameterization: An update. J. Appl. Meteor., 43, 170181, doi:10.1175/1520-0450(2004)043<0170:TKCPAU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kirkwood, S., M. Mihalikova, T. Rao, and K. Satheesan, 2010: Turbulence associated with mountain waves over northern Scandinavia—A case study using the ESRAD VHF radar and the WRF mesoscale model. Atmos. Chem. Phys., 10, 35833599, doi:10.5194/acp-10-3583-2010.

    • Search Google Scholar
    • Export Citation
  • Klemp, J., and D. Lilly, 1975: The dynamics of wave-induced downslope winds. J. Atmos. Sci., 32, 320339, doi:10.1175/1520-0469(1975)032<0320:TDOWID>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kühnlein, C., A. Dörnbrack, and M. Weissmann, 2013: High-resolution Doppler lidar observations of transient downslope flows and rotors. Mon. Wea. Rev., 141, 32573272, doi:10.1175/MWR-D-12-00260.1.

    • Search Google Scholar
    • Export Citation
  • Lilly, D. K., 1978: A severe downslope windstorm and aircraft turbulence event induced by a mountain wave. J. Atmos. Sci., 35, 5977, doi:10.1175/1520-0469(1978)035<0059:ASDWAA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mahalov, A., M. Moustaoui, and V. Grubišić, 2011: A numerical study of mountain waves in the upper troposphere and lower stratosphere. Atmos. Chem. Phys., 11, 51235139, doi:10.5194/acp-11-5123-2011.

    • Search Google Scholar
    • Export Citation
  • Masson, V., and P. Bougeault, 1996: Numerical simulation of a low-level wind created by complex orography: A cierzo case study. Mon. Wea. Rev., 124, 701715, doi:10.1175/1520-0493(1996)124<0701:NSOALL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • 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 66316 682, doi:10.1029/97JD00237.

    • Search Google Scholar
    • Export Citation
  • Mobbs, S., and Coauthors, 2005: Observations of downslope winds and rotors in the Falkland Islands. Quart. J. Roy. Meteor. Soc., 131, 329351, doi:10.1256/qj.04.51.

    • Search Google Scholar
    • Export Citation
  • Nakanishi, M., and H. Niino, 2006: An improved Mellor–Yamada level-3 model: Its numerical stability and application to a regional prediction of advection fog. Bound.-Layer Meteor., 119, 397407, doi:10.1007/s10546-005-9030-8.

    • Search Google Scholar
    • Export Citation
  • Nance, L. B., and D. R. Durran, 1997: A modeling study of nonstationary trapped mountain lee waves. Part I: Mean-flow variability. J. Atmos. Sci., 54, 22752291, doi:10.1175/1520-0469(1997)054<2275:AMSONT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • NCAR, 2013: NCEP FNL operational model global tropospheric analyses, continuing from July 1999. Computational and Information Systems Laboratory, accessed 11 March 2016. [Available online at http://rda.ucar.edu/datasets/ds083.2/.]

  • Olafsson, H., and P. Bougeault, 1996: Nonlinear flow past an elliptic mountain ridge. J. Atmos. Sci., 53, 24652489, doi:10.1175/1520-0469(1996)053<2465:NFPAEM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Otkin, J. A., and T. J. Greenwald, 2008: Comparison of WRF model-simulated and MODIS-derived cloud data. Mon. Wea. Rev., 136, 19571970, doi:10.1175/2007MWR2293.1.

    • Search Google Scholar
    • Export Citation
  • Plougonven, R., A. Hertzog, and H. Teitelbaum, 2008: Observations and simulations of a large-amplitude mountain wave breaking over the Antarctic Peninsula. J. Geophys. Res., 113, D16113, doi:10.1029/2007JD009739.

    • Search Google Scholar
    • Export Citation
  • Ralph, F. M., P. J. Neiman, T. L. Keller, D. Levinson, and L. Fedor, 1997: Observations, simulations, and analysis of nonstationary trapped lee waves. J. Atmos. Sci., 54, 13081333, doi:10.1175/1520-0469(1997)054<1308:OSAAON>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ray, P. S., 1986: Mesoscale Meteorology and Forecasting. Amer. Meteor. Soc., 793 pp.

  • Scorer, R., 1949: Theory of waves in the lee of mountains. Quart. J. Roy. Meteor. Soc., 75, 4156, doi:10.1002/qj.49707532308.

  • Sheridan, P., and S. Vosper, 2012: High-resolution simulations of lee waves and downslope winds over the Sierra Nevada during T-REX IOP 6. J. Appl. Meteor. Climatol., 51, 13331352, doi:10.1175/JAMC-D-11-0207.1.

    • Search Google Scholar
    • Export Citation
  • Sheridan, P., V. Horlacher, G. G. Rooney, P. Hignett, S. D. Mobbs, and S. B. Vosper, 2007: Influence of lee waves on the near-surface flow downwind of the Pennines. Quart. J. Roy. Meteor. Soc., 133, 13531369, doi:10.1002/qj.110.

    • Search Google Scholar
    • Export Citation
  • Shin, H. H., and S.-Y. Hong, 2011: Intercomparison of planetary boundary-layer parametrizations in the WRF model for a single day from CASES-99. Bound.-Layer Meteor., 139, 261281, doi:10.1007/s10546-010-9583-z.

    • 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., doi:10.5065/D68S4MVH.

  • Smith, C. M., and E. D. Skyllingstad, 2009: Investigation of upstream boundary layer influence on mountain wave breaking and lee wave rotors using a large-eddy simulation. J. Atmos. Sci., 66, 31473164, doi:10.1175/2009JAS2949.1.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., 1979: The influence of mountains on the atmosphere. Advances in Geophysics, Vol. 21, Academic Press, 87–230, doi:10.1016/S0065-2687(08)60262-9.

  • Smith, R. B., 1989: Hydrostatic airflow over mountains. Advances in Geophysics, Vol. 31, Academic Press, 1–41, doi:10.1016/S0065-2687(08)60052-7.

  • Smith, R. B., 2007: Interacting mountain waves and boundary layers. J. Atmos. Sci., 64, 594607, doi:10.1175/JAS3836.1.

  • Smith, R. B., Q. Jiang, and J. D. Doyle, 2006: A theory of gravity wave absorption by a boundary layer. J. Atmos. Sci., 63, 774781, doi:10.1175/JAS3631.1.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., J. D. Doyle, Q. Jiang, and S. A. Smith, 2007: Alpine gravity waves: Lessons from MAP regarding mountain wave generation and breaking. Quart. J. Roy. Meteor. Soc., 133, 917936, doi:10.1002/qj.103.

    • Search Google Scholar
    • Export Citation
  • Spiga, A., H. Teitelbaum, and V. Zeitlin, 2008: Identification of the sources of inertia-gravity waves in the Andes Cordillera region. Ann. Geophys., 26, 25512568, doi:10.5194/angeo-26-2551-2008.

    • Search Google Scholar
    • Export Citation
  • Stiperski, I., and V. Grubišic, 2011: Trapped lee wave interference in the presence of surface friction. J. Atmos. Sci., 68, 918936, doi:10.1175/2010JAS3495.1.

    • Search Google Scholar
    • Export Citation
  • Sun, J., L. Mahrt, C. Nappo, and D. H. Lenschow, 2015: Wind and temperature oscillations generated by wave–turbulence interactions in the stably stratified boundary layer. J. Atmos. Sci., 72, 14841503, doi:10.1175/JAS-D-14-0129.1.

    • Search Google Scholar
    • Export Citation
  • Telišman Prtenjak, M., and D. Belušić, 2009: Formation of reversed lee flow over the north-eastern Adriatic during bora. Geofizika, 26, 145155.

    • Search Google Scholar
    • Export Citation
  • Thompson, G., R. M. Rasmussen, and K. Manning, 2004: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part I: Description and sensitivity analysis. Mon. Wea. Rev., 132, 519542, doi:10.1175/1520-0493(2004)132<0519:EFOWPU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Udina, M., M. R. Soler, S. Viana, and C. Yage, 2013: Model simulation of gravity waves triggered by a density current. Quart. J. Roy. Meteor. Soc., 139, 701714, doi:10.1002/qj.2004.

    • Search Google Scholar
    • Export Citation
  • Valkonen, T., T. Vihma, S. Kirkwood, and M. M. Johansson, 2010: Fine-scale model simulation of gravity waves generated by Basen nunatak in Antarctica. Tellus, 62A, 319332, doi:10.1111/j.1600-0870.2010.00443.x.

    • Search Google Scholar
    • Export Citation
  • Vosper, S., 2004: Inversion effects on mountain lee waves. Quart. J. Roy. Meteor. Soc., 130, 17231748, doi:10.1256/qj.03.63.

  • Vosper, S., P. Sheridan, and A. Brown, 2006: Flow separation and rotor formation beneath two-dimensional trapped lee waves. Quart. J. Roy. Meteor. Soc., 132, 24152438, doi:10.1256/qj.05.174.

    • Search Google Scholar
    • Export Citation
  • Wurtele, M., R. Sharman, and A. Datta, 1996: Atmospheric lee waves. Annu. Rev. Fluid Mech., 28, 429476, doi:10.1146/annurev.fl.28.010196.002241.

    • Search Google Scholar
    • Export Citation
  • Zhang, D., and R. A. Anthes, 1982: A high-resolution model of the planetary boundary layer- sensitivity tests and comparisons with SESAME-79 data. J. Appl. Meteor., 21, 15941609, doi:10.1175/1520-0450(1982)021<1594:AHRMOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zink, F., and R. Vincent, 2001: Wavelet analysis of stratosphere gravity wave packets over Macquarie Island: 1. Wave parameters. J. Geophys. Res., 106, 10 27510 288, doi:10.1029/2000JD900847.

    • Search Google Scholar
    • Export Citation
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