1. Geostrophic and thermal wind

2. 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:

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

4. 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 / = m s-2
Ug = f-1 k x pΦ = 54 ms (f = 1.12 x10-4)
Ug = 105 kt compared with kt measured
(1 knot = I nautical mile hr-1= 1852 m hr-1 = ms-1)

5. 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 / = m s-2
Ug = f-1 k x pΦ = 23 ms (f = 1.12 x10-4)
Ug = 45 kt compared with 45 kt measured
(1 knot = I nautical mile hr-1= 1852 m hr-1 = ms-1)

6. 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.

7. Surface chart
Temperature gradient coincides with a front