Chapter 4: Atmospheric transport

Forces in the atmosphere:

• Gravity g = 9.8 m s^-2
• Pressure-gradient
• Coriolis
• Friction at surface

to R of direction of motion (NH) or L (SH)

Angular velocity ω = 2π/24h

Wind speed v

Latitude λ

Friction coefficient k

for x-direction (also y, z directions)

Explaining the Coriolis force:

over North Pole

Forces in the atmosphere:

• Gravity g = 9.8 m s^-2
• Pressure-gradient
• Coriolis
• Friction at surface

to R of direction of motion (NH) or L (SH)

Equilibrium of forces:

Angular velocity ω = 2π/24h

Wind speed u

Latitude λ

Friction coefficient k

for x-direction (also y, z directions)

Geostrophic flow: �equilibrium between pressure-gradient and Coriolis forces

• steady
• parallel to isobars
• speed ~ pressure gradient

NH perspective

Circulation around Highs (a.k.a. anticyclones) �and Lows (a.k.a cyclones) in northern hemisphere

Geostrophic flow is clockwise around High, counterclockwise around Low

• Near surface, friction force causes air to diverge from High and converge toward Low
• High pressure is associated with clear weather, low pressure with clouds and rain

(in southern hemisphere it would be the other way around)

The Hadley circulation (1735): global sea breeze

Explains:

• Intertropical Convergence Zone (ITCZ)
• Wet tropics, dry poles
• Easterly trade winds in the tropics

​

But… Direct meridional transport of air between Equator and poles is not possible because Coriolis force is too strong

Hadley circulation only extends to about 30^o latitude

• Easterly trade winds in the tropics at low altitudes
• Subtropical anticyclones at about 30^o latitude
• Westerlies at mid-latitudes

Climatological surface winds and pressures�(January)

Climatological surface winds and pressures �(July)

Time scales for horizontal transport (troposphere)

• ~1 month to go around a latitudinal band;
• ~ 3 months to mix within a hemisphere
• 1 year to transfer between hemispheres

⁸⁵Kr source: nuclear fuel reprocessing

sink: radioactive decay, t_1/2= 11 years

NH

SH

E

• Derive E from knowledge of (m₁+m₂), t_1/2
• Derive interhemispheric transfer time 1/k₁₂ =1.1 years from knowledge of E, (m₁-m₂)

Buoyancy in the atmosphere

Air parcel (T)

Background air (T_B)

Consider an air parcel at a different temperature than the surrounding background air:

Ideal gas law: air density

so ρ↑ as T↓

T > T_B 🢫 ρ < ρ_B the air parcel is accelerated upward;

​

T < T_B 🢫 ρ > ρ_B the air parcel is accelerated downward.

But air parcel cools as it rises

• As air rises it expands, which requires work: dW = -pdv
• In absence of external heat source (adiabatic process), this cooling must come at expense of internal energy of air parcel U = Q + W
• Since U depends only on T, decreasing U decreases T

rising

air parcel

For adiabatic process, Γ = -dT/dz = g/C_p = 9.8 K km^-1

specific heat of air

at constant pressure

Γ is called the adiabatic lapse rate

(lapse rate is meteorological jargon for –dT/dz)

Whether the rising air parcel keeps accelerating upwards depends on the lapse rate for the background atmosphere (-dT_B / dz)

z

T

rising air parcel

Γ

background

atmosphere

-dT_B/dz > Γ

Air parcel continues upward acceleration;

atmosphere is unstable against vertical motions

z

T

rising air parcel

Air parcel decelerates and stops;

atmosphere is stable against vertical motions

OR

Γ

background

atmosphere

-dT_B/dz < Γ

The vertical temperature gradient (atmospheric lapse rate)�determines the stability of the atmosphere

z

Γ = 9.8 K km^-1

z

Background

T_B

unstable

very stable

neutral

stable

• In unstable conditions, strong up/down vertical motions drive rapid vertical mixing
• In stable conditions, vertical motions are suppressed and atmosphere is stratified
• The stability of the atmosphere is solely determined by its lapse rate.

T

Temperature inversion in a mountain valley

dT/dz > 0 is called an inversion: very stable

nighttime

valley floor

cooling

cooling

very

cold

What determines the atmospheric lapse rate?

• An atmosphere left to evolve adiabatically from an initial state would eventually tend to neutral conditions (-dT/dz = Γ ) at equilibrium
• Consider now solar heating of the surface. This disrupts the equilibrium and produces an unstable atmosphere:

Initial equilibrium

state: - dT/dz = Γ

z

T

z

T

Solar heating of surface: unstable atmosphere

T_B

Γ

Γ

T_B

z

T

initial

final

Γ

buoyant motions relax

unstable atmosphere back towards –dT/dz = Γ

​

• Fast vertical mixing in an unstable atmosphere maintains the lapse rate to Γ.

Observation of -dT/dz ≈ Γ is indicator of an unstable atmosphere.

In cloudy air parcel, heat release from water condensation decreases the lapse rate

RH > 100%:

Cloud forms

“Latent” heat release

as H₂O condenses

Γ = 9.8 K km^-1

Γ_W = 2-7 K km^-1

RH

​

100%

T

z

Γ

Γ_W

Wet adiabatic lapse rate Γ_W = 2-7 K km^-1

Subsidence inversion

typically

2 km altitude

Typical summer afternoon vertical profile over Boston

DIURNAL CYCLE OF SURFACE HEATING/COOLING:�ventilation of urban pollution

VERTICAL PROFILE OF TEMPERATURE�Mean values for 30^oN, March

Altitude, km

Surface heating

Latent heat release

- 6.5 K km^-1

+2 K km^-1

- 3 K km^-1

Absorption of UV radiation by ozone

TYPICAL TIME SCALES FOR VERTICAL MIXING