A method of determining optimum scales for averaging the earth's topography in quantitative studies of atmospheric cyclo- and anti-cyclogenesis

A method for optimum modelling of the earth's topography, corresponding to differing meteorological phenomena, is presented.The optimum averaging scale for mountains in terms of orographic cyclo- and anti-cyclogenesis is shown to be of the order of 150 km. The use of larger or smaller averaging scales decreases the correlation between the degree of cyclo- and anti-cyclogenesis and the parameters which describe the orography.A quantitative relation between orographic cyclo- and anti-cyclogenesis and the form of orography determined by the Laplacian ² Z ₀ of the terrain function Z ₀ = Z ₀(x, y) is presented.     

Wind profile and vertical motions above an abrupt change in surface roughness and temperature

A review is presented of some Russian-language papers published as early as 1952–1954 that are unknown to most English-speaking readers. In these papers the influence of an abrupt change in the surface friction velocityv _*, surface roughnessz ₀ and surface temperature or heat flux on the wind velocity profile and vertical motions has been investigated analytically and numerically. Most of the theories are based on the exchange-coefficient approximation for momentum and heat. In terms of this approximation, further generalization and development of the problem is discussed.In an appendix, the Shwetz method for approximate solution of the boundary-layer partial differential equations is briefly described, using as an example an equation for which an exact solution is also possible.     

Parametrization of orographical effects in the planetary boundary layer

Studies of the influence of orography on the dynamics of atmospheric processes usually assume the following relation as a boundary condition at the surface of the Earth, or at the top of the planetary layer: $$w = u\frac{{\delta z_0 }}{{\delta x}} + v\frac{{\delta z_0 }}{{\delta y}}$$ where u, v and w are the components of wind velocity along the x, y and z axes, respectively, and z ₀ = z₀(x, y) is the equation of the Earth's orography. We see that w, and consequently the influence of orography on the dynamics of atmospheric processes, depend on the wind (u, v) and on the slope of the obstacle (δz ₀/δx, δz₀/δy). In the present work, it is shown that the above relation for w is insufficient to describe the influence of orography on the dynamics of the atmosphere. It is also shown that the relation is a particular case of the expression: $$\begin{gathered} w_h = \left| {v_g } \right|\left[ {a_1 (Ro,s)\frac{{\delta z_0 }}{{\delta x}} + a_2 (Ro,s)\frac{{\delta z_0 }}{{\delta y}}} \right] + \hfill \\ + \frac{{\left| {v_g } \right|^2 }}{f}\left[ {b_1 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta x^2 }} + b_2 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta y^2 }} + b_3 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta x\delta y}}} \right] \hfill \\ \end{gathered} $$ where ¦vv _g¦ is the strength of the geostrophic wind, a ₁, a₂, b₁, b₂, b₃ are functions of Rossby number Ro and of the external stability parameter s. The above relation is obtained with the help of similarity theory, with a parametrization of the planetary boundary layer. Finally, the authors show that a close connection exists between the effects described by the above expression and cyclo- and anticyclogenesis.