Boundary-Layer Meteorology

, Volume 162, Issue 1, pp 91–116 | Cite as

Boundary-Layer Development and Low-level Baroclinicity during High-Latitude Cold-Air Outbreaks: A Simple Model

  • Dmitry G. ChechinEmail author
  • Christof Lüpkes
Research Article


A new quasi-analytical mixed-layer model is formulated describing the evolution of the convective atmospheric boundary layer (ABL) during cold-air outbreaks (CAO) over polar oceans downstream of the marginal sea-ice zones. The new model is superior to previous ones since it predicts not only temperature and mixed-layer height but also the height-averaged horizontal wind components. Results of the mixed-layer model are compared with dropsonde and aircraft observations carried out during several CAOs over the Fram Strait and also with results of a 3D non-hydrostatic (NH3D) model. It is shown that the mixed-layer model reproduces well the observed ABL height, temperature, low-level baroclinicity and its influence on the ABL wind speed. The mixed-layer model underestimates the observed ABL temperature only by about 10 %, most likely due to the neglect of condensation and subsidence. The comparison of the mixed-layer and NH3D model results shows good agreement with respect to wind speed including the formation of wind-speed maxima close to the ice edge. It is concluded that baroclinicity within the ABL governs the structure of the wind field while the baroclinicity above the ABL is important in reproducing the wind speed. It is shown that the baroclinicity in the ABL is strongest close to the ice edge and slowly decays further downwind. Analytical solutions demonstrate that the \(\mathrm{e}\)-folding distance of this decay is the same as for the decay of the difference between the surface temperature of open water and of the mixed-layer temperature. This distance characterizing cold-air mass transformation ranges from 450 to 850 km for high-latitude CAOs.


Baroclinicity Cold-air outbreaks Low-level jet Mixed-layer model 

List of Symbols

\(C_D\), \(C_H\)

Bulk transfer coefficients of momentum (D) and heat (H)


Geostrophic Ekman number


Coriolis parameter


Acceleration due to gravity


Atmospheric boundary-layer (ABL) height scale


Proportionality constant

\(K_M\), \(K_H\)

Eddy diffusivities for momentum (M) and heat (H)


Characteristic length scale of the air-mass transformation

\(U_g\) and \(V_g\)

Horizontal components of large-scale geostrophic wind vector

\(U_{g+}\), \(U_\mathrm{gi}\), \(U_\mathrm{gt}\)

Baroclinic parts of the u-components of the geostrophic wind vector averaged over the ABL height


Friction velocity

\(\mathbf{V_\mathrm{gm}}\), \(u_\mathrm{gm}\), \(v_\mathrm{gm}\)

Geostrophic wind vector averaged over the ABL height and its west-east and north-south components, respectively

\(\mathbf{V_m}\), \(u_m\), \(v_m\)

Horizontal wind vector averaged over the ABL height and its west-east and north-south components, respectively

\(u_+\) and \(v_{+}\)

Wind vector components right above the inversion


Entrainment velocity


Normalized distance from the ice edge along the north-south direction (orthogonal to the ice edge)


Linear function of \(\overline{y}\) (\(\hat{y} = C_1 \overline{y} - C_2\), where \(C_1\) and \(C_2\) are constants as in Eq. 14)

\(z_{0m}\), \(z_{0h}\)

Roughness length for momentum (m) and heat (h)


ABL height defined as the height of the capping inversion

\(z_{i+}\), \(z_{i-}\)

Height just above (\(i+\)) and below (\(i-\)) the capping inversion


ABL height over the sea ice

\((\overline{w'\theta '})_s\)

Vertical kinematic heat flux in the surface layer

\(\alpha \)

Angle between the direction of the large-scale geostrophic wind and y-axis

\(\beta \)

Entrainment coefficient

\(\gamma _h\)

Non-local term in the heat-flux parametrization

\(\gamma _{\theta }\)

Potential temperature lapse rate above the ABL

\(\mathrm{\Delta } \theta \)

Discontinuous jump of potential temperature at the ABL top

\(\mathrm{\Delta } u\) and \(\mathrm{\Delta } v\)

Discontinuous jump of the horizontal components of wind vector u and v, respectively

\(\theta _+\)

Potential temperature right above the inversion

\(\theta _\mathrm{ice}\)

Potential temperature at \(z=z_{0h}\) over the sea-ice and also mixed-layer inflow potential temperature

\(\theta '_\mathrm{ice}\)

Modified \(\theta _\mathrm{ice}\) given by \(\theta '_\mathrm{ice} = \theta _\mathrm{ice} - \gamma _{\theta }z_{i0}(1+\beta )/(1+2\beta )\) and used only for normalization of \(\theta _m\)

\(\theta _w\)

Potential temperature at \(z=z_{0h}\) over the open water

\(\theta _m\)

Potential temperature averaged over the ABL height

\(\phi \)

Angle between the direction of the ABL-averaged wind vector and y-axis



The authors thank Vladimir Gryanik for many inspiring ideas and critical comments on the topic of the paper, Jörg Hartmann for processing the aircraft measurements and Josh Studholme for improving the language. The work is funded by Grants of the Russian Foundation for Basic Research 14-05-00959, 13-05-41443, 14-05-00038, 14-05-91752 and the Russian Federation President Grant MK-7200.2015.5. That part of the work concerning the air-mass transformation process was funded by the Russian Science Foundation Grant 14-17-00647. The NH3D model experiments were supported by the Supercomputing Center of the Lomonosov Moscow State University. We also gratefully acknowledge the support by the SFB/TR172 “ArctiC Amplification: Climate Relevant Atmospheric and SurfaCe Processes, and Feedback Mechanisms (AC)\(^3\)” in Project A03 funded by the Deutsche Forschungsgemeinschaft (DFG).


  1. Andreas EL, Claffy KJ, Makshtas AP (2000) Low-level atmospheric jets and inversions over the Western Weddell Sea. Boundary-Layer Meteorol 97(3):459–486CrossRefGoogle Scholar
  2. Arya SPS (1977) Suggested revisions to certain boundary layer parameterization schemes used in atmospheric circulation models. Mon Weather Rev 105:215–227CrossRefGoogle Scholar
  3. Brümmer B (1996) Boundary layer modification in wintertime cold-air outbreaks from the Arctic sea ice. Boundary-Layer Meteorol 80:109–125CrossRefGoogle Scholar
  4. Brümmer B (1997) Boundary layer mass, water and heat budgets in wintertime cold-air outbreaks from the Arctic sea ice. Mon Weather Rev 125:1824–1837CrossRefGoogle Scholar
  5. Brümmer B, Pohlmann S (2000) Wintertime roll and cell convection over Greenland and Barents Sea regions: a climatology. J Geophys Res 105(D12):15559–15566CrossRefGoogle Scholar
  6. Byun D-W, Arya SPS (1986) A study of mixed-layer momentum evolution. Atmos Environ 20(4):715–728CrossRefGoogle Scholar
  7. Chechin DG, Lüpkes C, Repina IA, Gryanik VM (2013) Idealized dry quasi 2-D mesoscale simulations of cold-air outbreaks over the marginal sea ice zone with fine and coarse resolution. J Geophys Res 118:8787–8813Google Scholar
  8. Chechin DG, Zabolotskikh EV, Repina IA, Shapron B (2015) Influence of baroclinicity in the atmospheric boundary layer and Ekman friction on the surface wind speed during cold-air outbreaks in the Arctic. Izv Atmos Ocean Phys 51(2):127–137CrossRefGoogle Scholar
  9. Deardorff JW (1972) Parameterization of the planetary boundary layer for use in general circulation model. Mon Weather Rev 100:93–106CrossRefGoogle Scholar
  10. Garratt JR (1992) The atmospheric boundary layer. Cambridge University Press, Cambridge, UK 316 ppGoogle Scholar
  11. Gryschka M, Fricke J, Raasch S (2014) On the impact of forced roll convection on vertical turbulent transport in cold air outbreaks. J Geophys Res 119:12513–12532Google Scholar
  12. Grønas A, Skeie P (1999) A case study of strong winds at an Arctic front. Tellus 51:865–879CrossRefGoogle Scholar
  13. Gryanik VM, Hartmann J (2002) A turbulence closure for the convective boundary layer based on a two-scale mass-flux approach. J Atmos Sci 59(18):2729–2744CrossRefGoogle Scholar
  14. Guest PS, Davidson KL, Overland JE, Frederickson PA (1995) Atmosphere-ocean interaction in the marginal ice zones of the Nordic Seas. In: Walker O, Grebmeir J (eds) Arctic oceanography: marginal ice zones and continental shelves. American Geophysical Union, Washington DC, pp 51–95CrossRefGoogle Scholar
  15. Hartmann J, Kottmeier K, Raasch S (1997) Roll vortices and boundary-layer development during a cold air outbreak. Boundary-Layer Meteorol 84(1):44–65CrossRefGoogle Scholar
  16. Hartmann J, Kottmeier K, Wamser C (1992) Radiation and Eddy flux experiment 1991. Reports Polar Res Bremerhaven 105:72Google Scholar
  17. Hartmann J et al (1999) Arctic radiation and turbulence interaction study. Reports Polar Res Bremerhaven 305:81Google Scholar
  18. Holtslag AAM, Moeng C-H (1991) Eddy diffusivity and countergradient transport in the convective atmospheric boundary layer. J Atmos Sci 48(14):1690–1698CrossRefGoogle Scholar
  19. Kottmeier C, Hartmann J, Wamser C, Bochert A, Lüpkes C, Freese D, Cohrs W (1994) Radiation and Eddy flux experiment 1993 (REFLEX II). Reports Polar Res Bremerhaven 132:62Google Scholar
  20. Lavoie RL (1972) A mesoscale numerical model of lake-effect storms. J Atmos Sci 29:1025–1040CrossRefGoogle Scholar
  21. Lüpkes C, Schlünzen KH (1996) Modelling the arctic convective boundary-layer with different turbulence parameterizations. Boundary-Layer Meteorol 79(1):107–130CrossRefGoogle Scholar
  22. Lüpkes C et al (2012) Mesoscale modelling of the Arctic atmospheric boundary layer and its interaction with sea ice. In: Lemke P, Jacobi H-W (eds) ARCTIC climate change the ACSYS decade and beyond. Atmospheric and oceanographic sciences library. Springer, Netherlands, pp 279–324Google Scholar
  23. Miranda PMA (1991) Gravity waves and wave drag in flow past three-dimensional isolated mountains. Ph.D. dissertation, University of Reading, 191pp. (Available from University of Reading, Reading RG6 2AU, UK)Google Scholar
  24. Miranda PMA, James IN (1992) Non-linear three-dimensional effects on gravity-wave drag: splitting flow and breaking waves. Q J R Meteorol Soc 118(508):1057–1081CrossRefGoogle Scholar
  25. Miranda PMA, Valente MA (1997) Critical level resonance in three-dimensional flow past isolated mountains. J Atmos Sci 54(12):1574–1588CrossRefGoogle Scholar
  26. Miller MJ, White AA (1984) On the non-hydrostatic equations in pressure and sigma coordinates. Q J R Meteorol Soc 110(464):515–533CrossRefGoogle Scholar
  27. Noh Y, Cheon WG, Hong SY, Raasch S (2003) Improvement of the K-profile model for the planetary boundary layer based on large eddy simulation data. Boundary-Layer Meteorol 107(2):401–427CrossRefGoogle Scholar
  28. Overland JE, Reynolds RM, Pease CH (1983) A model of the atmospheric boundary layer over the marginal ice zone. J Geophys Res 88:2836–2840CrossRefGoogle Scholar
  29. Rasmussen EA, Turner J (eds) (2003) Polar Lows. Cambridge University Press, Cambridge, 610 ppGoogle Scholar
  30. Renfrew IA, Moore GWK (1999) An extreme cold-air outbreak over the labrador sea: roll vortices and air-sea interaction. Mon Weather Rev 127(10):2379–2394CrossRefGoogle Scholar
  31. Renfrew IA, King JC (2000) A simple model of the convective internal boundary layer and its application to surface heat flux estimates within polynyas. Boundary-Layer Meteorol 94:335–356CrossRefGoogle Scholar
  32. Reynolds M (1984) On the local meteorology at the marginal ice zone of the Bering Sea. J Geophys Res 89:6515–6524CrossRefGoogle Scholar
  33. Savijärvi HI (2011) Anti-heat island circulations and low-level jets on a sea gulf. Tellus A 63:1007–1013CrossRefGoogle Scholar
  34. Stevens B (2002) Entrainment in stratocumuls-topped mixed layers. Quart J Roy Meteorol Soc 128(586):2663–2690Google Scholar
  35. Venkatram A (1977) A model of internal boundary-layer development. Boundary Layer Meteorol 11(4):419–437CrossRefGoogle Scholar
  36. Wacker U, Potty KVJ, Lüpkes C, Hartmann J, Raschendorfer M (2005) A case study on a polar cold air outbreak over Fram Strait using a mesoscale weather prediction model. Boundary Layer Meteorol 117(2):301–336CrossRefGoogle Scholar
  37. Yuen C-W (1985) Simulations of cold surges over the oceans with application to AMTEX’75. J Atmos Sci 42(2):135–154CrossRefGoogle Scholar
  38. Yuen C-W, Young JA (1986) Dynamical adjustment theory for boundary layer flow in cold surges. J Atmos Sci 43(24):3089–3108CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.A.M. Obukhov Institute of Atmospheric Physics of the Russian Academy of SciencesMoscowRussia
  2. 2.Alfred Wegener Institute Helmholtz Zentrum for Polar and Marine ResearchBremerhavenGermany

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