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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

Abstract

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.

Keywords

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)

\(E_m\)

Geostrophic Ekman number

f

Coriolis parameter

g

Acceleration due to gravity

H

Atmospheric boundary-layer (ABL) height scale

K

Proportionality constant

\(K_M\), \(K_H\)

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

\(L_\mathrm{tr}\)

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

\(u_*\)

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

\(w_e\)

Entrainment velocity

\(\overline{y}\)

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

\(\hat{y}\)

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)

\(z_i\)

ABL height defined as the height of the capping inversion

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

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

\(z_{i0}\)

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

Notes

Acknowledgments

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).

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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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