1. Tropical climatology and general circulation
SO442 Lesson 2
Tropical climatology and general circulation

2. Large-scale high pressure systems feature:
Subsidence (sinking motion)
Surface air divergence
Upper-troposphere air convergence
Large-scale low pressure systems feature:
Ascent (rising motion)
Surface air convergence
Upper-troposphere air divergence

3. Scales in the atmosphere
Atmospheric phenomena tend to self organize depending on their time and space scales
Larger weather and climate phenomena tend to last longer
Why is that??
Duration of the phenomenon tends to depend on how it relates to its “Rossby radius”
Things that are bigger than the Rossby radius tend to last longer
Similarly, weather phenomena that are smaller than their Rossby radius tend to be short-lived
What is the “Rossby radius”?

4. Rossby radius First, the Rossby Number
You heard about Rossby Number in SO335/SO414
It is defined as the ratio between the material derivative and the Coriolis acceleration
If the Rossby # is small (R << 1), then Coriolis is important and the material derivative isn’t
If the Rossby # is large (R >> 1), then Coriolis is not important and the material derivative is
Rossby radius is similarly defined:
A ratio between buoyancy (eg, vertical instability) and Coriolis
U = characteristic horizontal velocity (typically 10 m s-1)
f = characteristic Coriolis (10-4 s-1 in mid-latitudes)
L = characteristic horizontal length scale (1000 km in mid-latitudes)

5. Implications of the Rossby radius

6. Scale analysis of the equation of motion
What are the forces that matter in the tropics? How do they compare to the mid-latitudes?
Expand the left-hand side into 3 terms; replace omega with f
Write each term as scaling parameters U, L, p, and ρ

7. Scale analysis of the equation of motion: mid-latitudes
Typical values of each characteristic scaling parameter in the mid-latitudes:
U = 10 m s-1
W = 10-2 m s-1 (1 cm s-1)
L = 1000 km
Δp = 10 hPa (1000 Pa)
ρ = 1 kg m-3
f = (2)(7.29x10-5)sin(φ). At 40S and 40N, f ≈ 10-4 s-1

8. Scale analysis of the equation of motion: mid-latitudes
Typical values of each characteristic scaling parameter in the mid-latitudes:
U = 10 m s-1
W = 10-2 m s-1 (1 cm s-1)
L = 1000 km
Δp = 10 hPa (1000 Pa)
ρ = 1 kg m-3
f = (2)(7.29x10-5)sin(φ). At 40S and 40N, f ≈ 10-4 s-1

9. Scale analysis of the equation of motion: tropics
Typical values of each characteristic scaling parameter in the tropics:
U = 10 m s-1
W = 10-2 m s-1 (1 cm s-1)
L = 1000 km
Δp = 1 hPa (100 Pa)
ρ = 1 kg m-3
f = (2)(7.29x10-5)sin(φ). At 10S and 10N, f ≈ 10-5 s-1

10. Scale analysis of the equation of motion: deep tropics (5°S-5°N)
Typical values of each characteristic scaling parameter in the deep tropics:
U = 1 m s-1
W = 10-2 m s-1 (1 cm s-1)
L = 1000 km
Δp = 1 hPa (100 Pa)
ρ = 1 kg m-3
f = (2)(7.29x10-5)sin(φ). At 5S and 5N, f ≈ 10-5 s-1

11. Consequences of a rotating planet with unequal heating
Because the planet rotates, and because the heating is concentrated near the equator, we get a general circulation that largely resembles a 3-cell model:
Hadley cell
Rising motion near the equator, sinking motion near 30S and 30N
Ferrell cell
Rising motion near 60S and 60N, sinking motion near 30S and 30N
Polar cell
Rising motion near 60S and 60N, sinking motion near 90S and 90N
Connecting the rising and sinking branches of the Hadley, Ferrell and Polar cells are surface winds:
Easterly trade winds near the equator
Westerly winds in the mid-latitudes
Easterly winds near the poles

12. Mean structure of the global atmosphere that results from the 3 circulation cells

13. Mean structure of sea level pressure and surface winds, by season

14. Winds have tremendous consequences for the oceans