Question
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I've been trying to find the geostrophic wind at the surface (Vgo), but I'm not sure exactly how to do that. 
I've been trying to use the definition of LTHAD to calculate the direction of the surface wind, but I need the 
magnitude of the geostrophic wind at the surface to do so. I know we can calculate the geostrophic winds at the 
500 mb level using equations 2.6 and 2.7, but how would I go about finding surface geostrophic winds? Is there a 
relationship or simple calculation that I am missing? 

Answer
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The geostrophic wind at the surface will depend on the pressure (geopotential height) gradient, which depends on
how much (or little) you think the central pressure (height) at the cyclone center has changed over the 6-h 
period. To simplify the problem, you might make an assumption about pressure (heights) at some distance from the
cyclone center that makes calculation of the pressure (geopotential height) gradient possible. Geostrophic wind
direction only depends on the shape of the isobars (geopotential height contours) about the cyclone center. Be
sure to clearly state any simplifying assumptions that have been made in making your calculations possible.