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Geostrophic and thermal wind. Weather charts, 3 July 2006. 300 mb. Consider the geopotential gradient across the solid red line. Δ z = 952 – 912 Dm = 400 m,  ΔΦ = 4000 m 2 s -2 Δ x = 5.5 deg lat = 616 km (1 deg = 111 km)  p Φ = 4000 / 616000 = 0.0065 m s -2

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weather charts 3 july 2006
Weather charts, 3 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)

slide3

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
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

= (286x104) 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
Surface chart

Temperature gradient coincides with a front