Geostrophic and thermal wind

ReminderGeostrophic wind in pressure

coordinates

In the free atmosphere, wind is usually close to geostrophic.

The departure from geostrophy is the ageostrophic wind

Thermal Wind:

zfg

f ppg kkU 1

dtd

aU

kU f1

TfT

g

z

U or T

f

r

p

U GG

kkln

Worked Example

300 mb

700 mb

10 July 2006

Jet Stream, wind up to 60 m/s

Same direction, but 20 m/s

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

= (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

Temperature gradient coincides with a front