Geostrophic balance

These equations show that stratospheric winds blow approximately parallel to the contours of the geopotential field. An alternative version of the geostrophic balance can be obtained by substituting the hydrostatic approximation as given in (3.23c) into (3.36a,b), after differentiating with respect to z ... 

A vector form of geostrophic balance derived from Eq. (47a,b) is... 

On the /-plane, a third solution can also be obtained (7 = 0 or steady motion. The horizontal momentum equations indicate that this steady but nontrivial flow is geostrophically balanced by pressure gradients. The integrated continuity equation demonstrates that the flow is nondivergent. 

Table I shows the spatial and temporal scales of motion associated with various meteorological phenomena. Large-scale motions, such as planetary waves, were discovered from upper-air observations dining World War II. The work of Jacob Bjerknes (1897-1975), Carl-Gustav Rossby (1898-1957), and others led to the important discoveries that (1) planetary-scale waves are clearly related to weather systems, and (2) planetary-scale waves are predominantly horizontal and in quasi-geostrophic balance, as explained later.

We concentrate on the information obtained from infrared spectroscopy and radiometry, both directly and in conjunction with other data sets, such as those from visible imaging. To provide the necessary background for the subjects of this section, we first review the equations of fluid motion and the succession of approximations leading to a tractable set of equations that can be used to describe the motion of a planetary atmosphere. Eor most of the cases considered, geostrophic balance and the associated thermal wind equations play major diagnostic roles in the inference of atmospheric motions from remotely sensed temperatures. For this reason, the derivation of these relations will be discussed in some detail. Other... 

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