Parametrization of orographical effects in the planetary boundary layer

Abstract

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.