If a geostrophic wind of 30 m/s is observed in Christchurch, then what is the geopotential gradient in m/km at 500hPa required to maintain this wind?
I tried to solve it by assuming that the geopotential gradient is the ratio of the geopotential height.
Let P = 500 hPa = 500 x 10^2 Pa,
R = 287J/kg/K
Assume T = 18 degree C = 291K
Next, I used ??=R?/g_o ln(p_1/p_2 )
??=(287J?kg?^(-1) K^(-1)*(291K))/(9.8ms^(-2) ) ln((1000*?10?^2 Pa)/(500*?10?^2 Pa))
??=5.907*?10?^3 Jkg^(-1) m^(-1) s^2
but I am not sure how does geostrophic wind related to the geopotential gradient and I am stuck on how to convert my geopotential height into m/km, please show some workings, so I can follow to solve similar problems.
Many thanks in advance.
I tried to solve it by assuming that the geopotential gradient is the ratio of the geopotential height.
Let P = 500 hPa = 500 x 10^2 Pa,
R = 287J/kg/K
Assume T = 18 degree C = 291K
Next, I used ??=R?/g_o ln(p_1/p_2 )
??=(287J?kg?^(-1) K^(-1)*(291K))/(9.8ms^(-2) ) ln((1000*?10?^2 Pa)/(500*?10?^2 Pa))
??=5.907*?10?^3 Jkg^(-1) m^(-1) s^2
but I am not sure how does geostrophic wind related to the geopotential gradient and I am stuck on how to convert my geopotential height into m/km, please show some workings, so I can follow to solve similar problems.
Many thanks in advance.