1. In class we stated that linearized vorticity equation that governs barotropic dynamics is ag' ag' + u = 0 at ax dy2 Starting from the horizontal momentum equations, show the steps in deriving the linearized vorticity equation, but this time allow the planet's rotation rate to vary: f = fo + By. (Because of this change, your final linearized equation will differ slightly from what's given above.). As in class, linearize around a background state with a zonal wind that varies with y only; there is no meridional component to the background wind