Geostrophic and thermal wind

Reminder Geostrophic wind in pressure coordinates In the free atmosphere, wind is usually close to geostrophic. The departure from geostrophy is the ageostrophic wind Thermal Wind:

Worked Example 10 July 2006 Jet Stream, wind up to 60 m/s 300 mb Same direction, but 20 m/s 700 mb

Weather charts, 10 July 2006 300 mb Consider the geopotential gradient across the solid red line. Δz = 952 – 912 Dm = 400 m,  ΔΦ = 4000 m2 s-2 Δx = 5.5 deg lat = 616 km (1 deg = 111 km) pΦ = 4000 / 616000 = 0.0065 m s-2 Ug = f-1 k x pΦ = 54 ms-1 (f = 1.12 x10-4) Ug = 105 kt compared with 100-105 kt measured (1 knot = I nautical mile hr-1= 1852 m hr-1 = 0.514 ms-1)

700 mb Consider the geopotential gradient across the solid red line. Δz = 316 – 300 Dm = 160 m,  ΔΦ = 1600 m2 s-2 Δx = 5.5 deg lat = 616 km (1 deg = 111 km) pΦ = 1600 / 616000 = 0.0026 m s-2 Ug = f-1 k x pΦ = 23 ms-1 (f = 1.12 x10-4) Ug = 45 kt compared with 45 kt measured (1 knot = I nautical mile hr-1= 1852 m hr-1 = 0.514 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 ΔUg = - (r/f) T Δln p f = 1.46x10-4 sinλ = 1.13x10-4 = (286/1.13x104) x 1.13x10-5 x ln(7/3) = 24 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