Boundary-Layer Meteorology

, Volume 166, Issue 2, pp 301–325 | Cite as

An Efficient Non-iterative Bulk Parametrization of Surface Fluxes for Stable Atmospheric Conditions Over Polar Sea-Ice

  • Vladimir M. GryanikEmail author
  • Christof Lüpkes
Research Article


In climate and weather prediction models the near-surface turbulent fluxes of heat and momentum and related transfer coefficients are usually parametrized on the basis of Monin–Obukhov similarity theory (MOST). To avoid iteration, required for the numerical solution of the MOST equations, many models apply parametrizations of the transfer coefficients based on an approach relating these coefficients to the bulk Richardson number \(Ri_{b}\). However, the parametrizations that are presently used in most climate models are valid only for weaker stability and larger surface roughnesses than those documented during the Surface Heat Budget of the Arctic Ocean campaign (SHEBA). The latter delivered a well-accepted set of turbulence data in the stable surface layer over polar sea-ice. Using stability functions based on the SHEBA data, we solve the MOST equations applying a new semi-analytic approach that results in transfer coefficients as a function of \(Ri_{b}\) and roughness lengths for momentum and heat. It is shown that the new coefficients reproduce the coefficients obtained by the numerical iterative method with a good accuracy in the most relevant range of stability and roughness lengths. For small \(Ri_{b}\), the new bulk transfer coefficients are similar to the traditional coefficients, but for large \(Ri_{b}\) they are much smaller than currently used coefficients. Finally, a possible adjustment of the latter and the implementation of the new proposed parametrizations in models are discussed.


Polar boundary layer SHEBA campaign Stability functions Transfer coefficients 



We thank Dr. Dmitry Sein, Dr. Dmitry Chechin and Dr. Felix Pithan for helpful comments and suggestions. We are grateful for constructive comments of Dr. Andrey Grachev and three other anonymous reviewers, especially concerning questions to the universality of the G2007 functions and the developed parametrization. We acknowledge also the support by the SFB/TR172 ArctiC Amplification: Climate Relevant Atmospheric and SurfaCe Processes, and Feedback Mechanisms (AC)\(^3\) funded by the Deutsche Forschungsgemeinschaft (DFG). Funding was also obtained by the German Federal Ministry of Education and Research (BMBF) for the project EXOSYSTEM ERA-NET (Research Grant 01DJ16016).


  1. Andreas EL, Horst TW, Grachev AA, Persson POG, Fairall CW, Guest PS, Jordan RE (2010a) Parametrizing turbulent exchange over summer sea ice and the marginal ice zone. Q J R Meteorol Soc 138:927–943CrossRefGoogle Scholar
  2. Andreas EL, Persson POG, Jordan RE, Horst TW, Guest PS, Grachev AA, Fairall CW (2010b) Parameterizing turbulent exchange over sea ice in winter. J Hydrometeorol 11:87–104CrossRefGoogle Scholar
  3. Basu S, Lacster A (2017) A cautionary note on the use of Monin-Obukhov similarity theory in very high-resolution large-eddy simulations. Boundary-Layer Meteorol 163:351–355CrossRefGoogle Scholar
  4. Beljaars ACM, Holtslag AAM (1991) Parameterization over land surfaces for atmospheric models. J Appl Meteorol 30:327–341CrossRefGoogle Scholar
  5. Businger JA, Wyngard JC, Izumi Y, Bradley EF (1971) Flux-profile relationships in the atmospheric surface layer. J Atmos Sci 28:181–189CrossRefGoogle Scholar
  6. Byun DW (1990) On the analytical solutions of flux-profile relationships for the atmospheric surface layer. J Appl Meteorol 29:652–657CrossRefGoogle Scholar
  7. Castellani G, Lüpkes C, Hendricks S, Gerdes R (2014) Variability of Arctic sea-ice topography and its impact on the atmospheric surface drag. J Geophys Res Oceans 119:6743–6762. doi: 10.1002/2013JC009712 CrossRefGoogle Scholar
  8. Cheng Y, Brutsaert W (2005) Flux-profile relationships for wind speed and temperature in the stable atmospheric boundary layer. Boundary-Layer Meteorol 114:519–538CrossRefGoogle Scholar
  9. Cuxart J, Holtslag AAM, Beare RJ, Bazile E, Beljaars A, Cheng A, Conangla L, Ek M, Freedman F, Hamedi R, Kerstein A, Kitagawa H, Lenderink G, Lewellen D, Mailhot J, Mauritsen T, Perov V, Schayes G, Steeneveld G-J, Svensson G, Taylor P, Weng W, Wunsch S, Xu K-M (2006) Single-column model intercomparison for a stably stratified atmospheric boundary layer. Boundary-Layer Meteorol 118:273–303. doi: 10.1007/s10546-005-3780-1 CrossRefGoogle Scholar
  10. Deardorff JW (1968) Dependence of air-sea transfer coefficients on bulk stability. J Geophys Res 73:2549–2557CrossRefGoogle Scholar
  11. Doms G, Förstner Heise E, Herzog H-J, Mironov D, Raschendorfer M, Reinhardt T, Ritter B, Schrodin R, Schulz J-P, Vogel G (2011) A description of the nonhydrostatic regional COSMO model. Part II physical parameterization, Deutscher Wetterdienst, Offenbach, p 154Google Scholar
  12. Dvornikov AY, Martyanov SD, Ryabchenko VA, Eremina TR, Isaev AV, Sein DV (2017) Assessment of extreme hydrological conditions in the Bothnian Bay, Baltic Sea, and the impact of the nuclear power plant Hanhikivi-1 on the local thermal regime. Earth Syst Dyn. 8:265–282. doi: 10.5194/esd-8-265-2017 CrossRefGoogle Scholar
  13. Dyer AJ (1974) A review of flux-profile relationship. Boundary-Layer Meteorol 7:363–372CrossRefGoogle Scholar
  14. Fairall CW, Markson R (1987) Mesoscale variations in surface stress, heat fluxes, and drag coefficient in the marginal ice zone during the 1983 Marginal Ice Zone Experiment. J Geophys Res 92:6921–6932CrossRefGoogle Scholar
  15. Foken T (2006) 50 years of the Monin-Obukhov similarity theory. Boundary-Layer Meteorol 119:431–447CrossRefGoogle Scholar
  16. Garratt JR (1992) The atmospheric boundary layer. Cambridge University Press, Cambridge, 316ppGoogle Scholar
  17. Giorgetta MA, Roeckner E, Mauritsen T, Stevens B, Bader J, Crueger T, Esch M, Rast S, Kornblueh L, Schmidt H, Kinne S, Möbis B, Krismer T (2012) The atmospheric general circulation model ECHAM6. Model description, MPI, Hamburg,156 ppGoogle Scholar
  18. Grachev AA, Fairall CW (1997) Dependence of the Monin-Obukhov stability parameter on the bulk Richardson number over the ocean. J Appl Meteorol 36:406–414CrossRefGoogle Scholar
  19. Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2007) SHEBA flux-profile relationships in the stable atmospheric boundary layer. Boundary-Layer Meteorol 124:315–333. doi: 10.1007/s10546-007-9177-6 CrossRefGoogle Scholar
  20. Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2013) The critical Richardson number and limits of applicability of local similarity theory in the stable boundary layer. Boundary-Layer Meteorol 147:51–82CrossRefGoogle Scholar
  21. Grachev AA, Andreas EL, Fairall CW, Guest PS, Persson POG (2015) Similarity theory based on the Dougherty-Ozmidov length scale. Q J R Meteorol Soc 141:1845–1856. doi: 10.1002/qj.2488 CrossRefGoogle Scholar
  22. Gromke C, Manes C, Walter B, Lehning M, Guala M (2011) Aerodynamic roughness length of fresh snow. Boundary-Layer Meteorol 141:21–34. doi: 10.1007/s10546-011-9623-3 CrossRefGoogle Scholar
  23. Guilloteau E (1998) Optimized computation of transfer coefficients in surface layer with different momentum and heat roughness length. Boundary-Layer Meteorol 87:147–160CrossRefGoogle Scholar
  24. Hartmann J, Kottmeier C, Wamser C, Augstein E (1994) Aircraft measured atmospheric momentum, heat and radiation fluxes over Arctic sea ice. In: Johannessen OM, Muench RD, Overland JE (eds) The polar oceans and their role in shaping the global environment. American Geophysical Union, Washington, DC, pp 443–454Google Scholar
  25. Holtslag AAM, De Bruin HAR (1988) Applied modeling of the nighttime surface energy balance over land. Boundary-Layer Meteorol 37:689–704Google Scholar
  26. Jiménez PA, Dudhia J, González-Rouco JF, Navarro J, Montávez JP, García-Bustamante E (2012) A revised scheme for the WRF surface layer formulation. Mon Weather Rev 140:898–918CrossRefGoogle Scholar
  27. Launiainen J (1995) Derivation of the relationship between the Obukhov stability parameter and the bulk Richardson number for flux profile studies. Boundary-Layer Meteorol 76:165–179CrossRefGoogle Scholar
  28. Li Y, Gao Z, Lenschow DH, Chen F (2010) An improved approach for parameterizing surface-layer turbulent transfer coefficients in numerical models. Boundary-Layer Meteorol 137:153–165. doi: 10.1007/s10546-010-9523-y CrossRefGoogle Scholar
  29. Li Y, Gao Z, Li D, Wang L, Wang H (2014) An improved non-iterative surface layer flux scheme for atmospheric stable stratification conditions. Geosci Model Dev 7:515–529. doi: 10.5194/gmd-7-515-2014 CrossRefGoogle Scholar
  30. Louis J-F (1979) A parametric model of vertical eddy fluxes in the atmosphere. Boundary-Layer Meteorol 17:187–202CrossRefGoogle Scholar
  31. Louis J-F, Tiedtke M, Geleyn J-F (1982) A short history of the operational PBL-parameterization at ECMWF. In: Proceedings of the ECMWF workshop on boundary layer parameterization, November 1981. European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, UK, pp 59–79Google Scholar
  32. Lüpkes C, Gryanik VM (2015) A stability-dependent parametrization of transfer coefficients for momentum and heat over polar sea ice to be used in climate models. J Geophys Res Atmos 120:552–581. doi: 10.1002/2014JD022418 CrossRefGoogle Scholar
  33. Lüpkes C, Gryanik VM, Hartmann J, Andreas EL (2012) A parametrization, based on sea ice morphology, of the neutral atmospheric drag coefficients for weather prediction and climate models. J Geophys Res 117:D13112. doi: 10.1029/2012JD017630 CrossRefGoogle Scholar
  34. Mahrt L (1999) Stratified atmospheric boundary layers. Boundary-Layer Meteorol. 90:375–396CrossRefGoogle Scholar
  35. Monin AS, Yaglom AM (1971) Statistical fluid mechanics: mechanics of turbulence, vol 1. MIT Press, Cambridge, 769 ppGoogle Scholar
  36. Obukhov AM (1946) Turbulence in an atmosphere with a non-uniform temperature. Trudy Inst Theoret Geofiz Akad NAuk SSSR 1:95–115Google Scholar
  37. Sein DV, Mikolajewicz U, Gröger M, Fast I, Cabos W, Pinto JG, Hagemann S, Semmler T, Izquierdo A, Jacob D (2015) Regionally coupled atmosphere ocean sea ice marine biogeochemistry model ROM: 1. Description and validation. J Adv Model Earth Syst 7:268–304. doi: 10.1002/2014MS000357 CrossRefGoogle Scholar
  38. Sidorenko D, Rackow T, Jung T, Semmler T, Barbi D, Danilov S, Dethloff K, Dorn W, Fieg K, Goessling HF, Handorf D, Harig S, Hiller W, Juricke S, Losch M, Schröter J, Sein DV, Wang Q (2015) Towards multi-resolution global climate modeling with ECHAM6-FESOM. Part I: mdel formulation and mean climate. Clim Dyn 44:757–780. doi: 10.1007/s00382-014-2290-6 CrossRefGoogle Scholar
  39. Uttal T, Curry JA, McPhee MG, Perovich DK, Moritz RE, Maslanik JA, Guest PS, Stern HL, Moore JA, Turenne R, Heiberg A, Serreze MC, Wylie DP, Persson OG, Paulson CA, Halle C, Morison JH, Wheeler PA, Makshtas A, Welch H, Shupe MD, Intrieri JM, Stamnes K, Lindsey RW, Pinkel R, Pegau WS, Stanton TP, Grenfeld TC (2002) Surface heat budget of the Arctic Ocean. Bull Am Meteorol Soc 83:255–275CrossRefGoogle Scholar
  40. Viterbo P, Beljaars A, Mahfouf J-F, Teixeira J (1999) The representation of soil moisture freezing and its impact on the stable boundary layer. Q J R Meteorol Soc 125:2401–2426CrossRefGoogle Scholar
  41. Webb EK (1970) Profile relationships: the log-linear range, and extension to strong stability. Q J R Meteorol Soc 96:67–90CrossRefGoogle Scholar
  42. Wouters H, De Ridder K, van Lipzig NPM (2012) Comprehensive parametrizations of surface-layer transfer coefficients for use in atmospheric numerical models. Boundary-Layer Meteorol 145:539–550CrossRefGoogle Scholar
  43. Yang K, Tamai N, Koike T (2001) Analytical solution of surface layer similarity equations. J Appl Meteorol 40:1647–1653CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Alfred-Wegener-Institut Helmholtz-Zentrum für Polar- und MeeresforschungBremerhavenGermany
  2. 2.A.M. Obukhov Institute of Atmospheric PhysicsRussian Academy of SciencesMoscowRussia

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