(1) Hydrostatic balance states Әр Equation -1 where p is pressure, z is altitude, p is density and g is the acceleration due to gravity. It can be shown that the reciprocal of hydrostatic balance also applies. That is Equation -2 дz Əz Әр =-pg, 1 pg Use the ideal gas law (p= pRT, where Ra is the gas constant for dry air and T is temperature) to eliminate p from (2). (2) Under geostrophic balance, the following balance is approximately satisfied Equation -3 fu=-g ¹(³), ду where f is the Coriolis parameter, u is the zonal wind, y is meridional distance and z is altitude. (Note that the derivative on the right hand side is taken at constant pressure.) Differentiate (3) with respect to p, and use your expression from part 1 to obtain an expression relating du/ap and T/ay. This expression is called "thermal wind balance".

(1) Hydrostatic balance states Әр Equation -1 where p is pressure, z is altitude, p is density and g is the acceleration due to gravity. It can be shown that the reciprocal of hydrostatic balance also applies. That is Equation -2 дz Əz Әр =-pg, 1 pg Use the ideal gas law (p= pRT, where Ra is the gas constant for dry air and T is temperature) to eliminate p from (2). (2) Under geostrophic balance, the following balance is approximately satisfied Equation -3 fu=-g ¹(³), ду where f is the Coriolis parameter, u is the zonal wind, y is meridional distance and z is altitude. (Note that the derivative on the right hand side is taken at constant pressure.) Differentiate (3) with respect to p, and use your expression from part 1 to obtain an expression relating du/ap and T/ay. This expression is called "thermal wind balance".