A hurricane with a central pressure of 940 hPa is surrounded by a region with a

Question

A hurricane with a central pressure of 940 hPa is surrounded by a region with a pressure of 1010 hPa. The storm is located over an ocean region. At 200 hPa the depression in the pressure field vanishes (i.e., the 200-hPa surface is perfectly flat). Estimate the average temperature difference between the center of the hurricane and its surroundings in the layer between the surface and 200 hPa. Assume that the mean temperature of this layer outside the hurricane is 3 °C and ignore the virtual temperature correction.

Explanation / Answer

We will use

.H= (R/G) * Tmean * ln(P0 /Pp1) where:
H = layer thickness, in meters
R = ideal gas constant (287 m2 s-2 k-1)
G = gravity (9.8 m/s^2)
Tmean = mean temperature for the P0 to P1 layer

Converting Temperature ino Kelvin

3degree C + 273.15K = 276.15K

H = (287 / 9.8) * 276.15 * ln (P0 / P1) where ln (P0 / P1) = ~1.55
H (above center) = ~12,516 m

1mb = ~10m; so we add 700 meters to the 940-200 thickness (12,515m) to estimate the 1010-200 thickness as 13,215m.
h = (R/g) * Tmean * ln(p0 / p1) then now solving for solve for Tmean in the 1010-200 layer

Tmean = (H * G) / (R * lnP0/P1))...where P0 = 1010
Tmean = (13,215 * 9.8) / (287 * ln(P0/P1 ) where ln(P0/P1) = ~1.62
Tmean = ~278.5 K
Tmean = ~5.4°C

Tdifference = 3°C - 5.4°C = -2.4°C

Thank you

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