Question[s] #4
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When calculating the GRVT using the petterssen development equation all of the terms are at the 500Hpa level. Does this 
imply that our GRVT is at the 500Hpa level as well? We believe that in order to calculate the geopotential height at 
1000Hpa we need the 1000Hpa GRVT. If so, do we need to derive a relationship between the 500Hpa GRVT and the 1000Hpa 
GRVT before calculating the 1000Hpa geopotential height?

Answer to #4
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If you look closely at Eq. (3.47), you see the subscript "p0" on the GRVT term. This indicates that ALL terms on the RHS
of the equation are contributing to changing GRV at the 1000 hPa level. GAVA represents an upper boundary condition, 
while the other terms are internal to the 1000 - 500 hPa layer (overbars are layer mean averages...we are assuming 700 hPa
omega is identical to the 1000 -500 layer average omega in the LAD term). But, ALL RHS terms contribute either to 
increasing, decreasing, or no change of 1000 hPa level GRV with time.