SME
Meteorology
Weather systems and forecasting
Use this for “A 1,020 hPa high and a 1,004 hPa low are 800 km apart at 45° N. Find the geostrophic wind.”
Diagram
Aloft, away from friction, the geostrophic wind blows along the isobars, the low on its left: clockwise round the high, counterclockwise round the low.
Vg
=
Δp
ρfΔn
=
16.16
m/s.
3 isobars lie between them.
Latitude φ = 45°
Coriolis parameter f = 1.0312 × 10⁻⁴ s⁻¹
Air density ρ = 1.2 kg/m³
Geostrophic wind Vg = 16.1617 m/s
This is an example. Type your own values to start a new problem.
Vg (m/s)
=
1
ρ (kg/m³)
×
f (s⁻¹)
×
Δp (hPa)
Δn (km)
pH
High pressure
example · hPa
pL
Low pressure
example · hPa
φ
Latitude
example · °
Formulas
Δp = pH − pL
16 = 1,020 − 1,004
f
=
2
×
7.292 ×
10
-5
×
sin(
φ
°)
1.0312 ×
10
-4
=
2
×
7.292 ×
10
-5
×
sin(45°)
Vg
=
100
×
Δp
ρ
×
f
× 1,000 × Δn
16.1617
=
100
×
16
1.2 × (1.0312 ×
10
-4
) × 1,000 × 800
Assumptions
•
Straight isobars and no friction (above about 1 km): the pressure-gradient and Coriolis forces balance.
•
Ω = 7.292 × 10⁻⁵ rad/s; Δp in hPa is 100Δp Pa and Δn in km is 1,000Δn m.
•
The wind blows along the isobars, low pressure on its left in the north (on its right in the south).
•
Near the equator f → 0 and the balance fails, so latitudes start at 5°.
Step-by-step
WE KNOW
pH = 1,020 hPa, pL = 1,004 hPa, Δn = 800 km, φ = 45°, ρ = 1.2 kg/m³
FIND
pressure difference (Δp), Coriolis parameter (f), geostrophic wind (Vg)
Step 1 · Find pressure difference (Δp)
Use Δp = pH − pL
How much higher the pressure is at the high.
Δp = 1,020 − 1,004
Δp = 16 hPa
Step 2 · Find Coriolis parameter (f)
Use f = 2 × 7.292 × 10⁻⁵ × sin(φ°)
The Coriolis parameter is twice Earth’s spin rate times the sine of the latitude.
f
=
2
×
7.292 ×
10
-5
×
sin(45°)
f
=
2
×
(7.292
×
10
-5
)
×
0.70711
f
=
0.00014584
×
0.70711
f
=
1.031245 ×
10
-4
s
-1
Step 3 · Find geostrophic wind (Vg)
Use Vg = 100 × Δp ÷ (ρ × f × 1,000 × Δn)
The
wind
blows
just
fast
enough
for
its
Coriolis
force,
ρfV,
to
balance
the
push
Δp
Δn
(in
Pa
and
m).
Vg
=
100
×
16
1.2 × (1.031245 ×
10
-4
) × 1,000 × 800
Vg
=
100
×
16
0.00012375 × 1,000 × 800
Vg
=
100
×
16
0.12375 × 800
Vg
=
100
×
16
99
Vg
=
1,600
99
Vg = 16.1617 m/s
Check
Put the numbers back in. Both sides should match.
16 = 1,020 − 1,004 ✓
1.031245 ×
10
-4
=
2
×
7.292 ×
10
-5
×
sin(45°)
✓
16.1617
=
100
×
16
1.2 × (1.031245 ×
10
-4
) × 1,000 × 800
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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