Geostrophic and thermal wind

Weather charts, 3 July mb Consider the geopotential gradient across the solid red line. Δz = 952 – 912 Dm = 400 m,  ΔΦ = 4000 m 2 s -2 Δx = 5.5 deg lat = 616 km (1 deg = 111 km)  p Φ = 4000 / = m s -2  U g = f -1 k x  p Φ = 54 ms -1 (f = 1.12 x10 -4 )  U g = 105 kt compared with kt measured (1 knot = I nautical mile hr -1 = 1852 m hr -1 = ms -1 )

700 mb Consider the geopotential gradient across the solid red line. Δz = 316 – 300 Dm = 160 m,  ΔΦ = 1600 m 2 s -2 Δx = 5.5 deg lat = 616 km (1 deg = 111 km)  p Φ = 1600 / = m s -2  U g = f -1 k x  p Φ = 23 ms -1 (f = 1.12 x10 -4 )  U g = 45 kt compared with 45 kt measured (1 knot = I nautical mile hr -1 = 1852 m hr -1 = ms -1 )

Thermal wind 700 mb 300 mb Camborne temperature at 700 mb = 5°, at 300 mb = -37° Valentia temperature at 700 mb = -1°, at 300 mb = -40° ΔT = 6° at 700 mb, 3° at 300 mb, mean around 4.5° Δx = 3.7 degrees latitude = 411 km   T = 1.13x10 -5 K m -1 ΔU g = - (r/f)  T Δln p = (286x10 4 ) 1.13x10 -5 ln(7/3) = 27 ms -1 Actual value is 30 ms -1 but the calculation is considerably cruder than the 3-figure precision implies.

Surface chart Temperature gradient coincides with a front