The correct answers are b, c, e.

In scaling the vertical momentum equation, it only needs to be shown that Dw/Dt is much smaller than gravity, not zero, hence a) is incorrect. Because there is no term involving time, the equation is only useful for diagnosing the current state of the atmosphere, not for predicting future states, and hence d) is incorrect. Finally, the physical significance of the equation is that the vertical pressure gradient ∂P/∂z is balanced by the weight ρg, which is why we can ignore vertical accelerations, and hence f) is incorrect.

The hydrostatic equation preserves stability within the forecast model and is used to calculate the height field necessary for determining geostrophic balance in the wind forecast equations. This diagnostic equation links the mean temperature in a layer of the model to the difference in height between the upper and lower isobaric surfaces serving as the top and bottom of the layer. Updated temperatures obtained from the temperature forecast equation are used here to calculate heights, which are then used in the wind forecast equations.