Chapter 1: Measures of atmospheric composition

Let’s look at the Sun through the atmosphere…

Radiation intensity

wavelength λ

visible:

0.4-0.7 μm

UV

IR

incident radiation

air molecule

~0.3 nm

absorption

transmission

scatter

Scattering of solar radiation�by air molecules

The atmosphere seen from the space station

Visible solar radiation

wavelength λ = 0.4 µm

0.5

0.6

0.7

• Size of air molecules ~ 0.3 nm << λ
• more scattering in blue (small λ)

Sun is yellow

Sky is blue

Sunset is red

scatter

scatter

cloudy sunset

Sun seen from space station

Aerosols and clouds: the visible part of the atmosphere

Pollution off U.S. east coast

Dust off West Africa

California fire plumes

Aerosols are suspended solid or liquid particles, typically 0.1-1 µm in size

Cloud droplets (1-100 μm in size) form by condensation on particles when relative humidity exceeds 100%

They scatter or absorb visible radiation efficiently

Visible radiation is nearly 100% scattered

Atmospheric gases are “visible” too… if you look in UV or IR

Visible

0.4-0.7 µm

Nitrogen dioxide (NO₂ ) observed by satellite in the UV

Fraction of solar radiation

absorbed by

atmospheric

gases

Ultraviolet (UV)

Infrared (IR)

Nitrogen dioxide (NO₂) observed from satellite

Measure of relative concentration: mole fraction (mixing ratio) C_X [mol mol^-1]

remains constant when air density changes

⇒ stable measure of atmospheric composition

Trace

gases

Air also contains variable H₂O vapor (10^-6-10^-2 mol mol^-1),

aerosol particles, and many trace gases at < 1x10^-6 mol mol^-1

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Trace gas concentration units:

1 ppm = 1 µmol mol^-1 = 1x10^-6 mol mol^-1

1 ppb = 1 nmol mol^-1 = 1x10^-9 mol mol^-1

1 ppt = 1 pmol mol^-1 = 1x10^-12 mol mol^-1

Atmospheric concentrations of greenhouse gases

Concentration units: parts per million (ppm) and parts per billion (ppb)

​

​

Stable gases like CO₂ and methane are generally reported as mole fractions

https://gml.noaa.gov/

Measure of absolute concentration [X]: mass or moles per unit volume of air

Proper measure for absorption of radiation by atmosphere

Proper measure of concentration for

• reaction rates
• optical properties of atmosphere

n_X and C_X are related by the ideal gas law:

(obeyed within 1% at atmospheric pressure)

• Mass concentration (g cm^-3):

n_a = air number density

A = Avogadro’s number

p = pressure

R = Gas constant

T = temperature

M_X= molar mass of X [g mol^-1]

​

• Number density n_X [molecules cm^-3]

Gas-phase reaction rates depend on number densities

A

B

AB*

C

D

reactants

products

activated

complex

rate constant

product of number densities,

proportional to collision frequency

Aerosol concentrations are often expressed as mass per unit volume,�typically in units of [μg m^-3]

Surface PM_2.5 ≡ fine particulate matter < 2.5 μm diameter

EPA air quality standard: 9 μg m^-3 (annual mean)

Daily PM_2.5 concentrations

Surface PM_2.5 ≡ fine particulate matter < 2.5 μm diameter

EPA air quality daily standard: 35 μg m^-3

Air Data - Concentration Map | US EPA

Extinction of radiation depends on column concentration

Radiation flux at top of atmosphere

surface

absorption at altitude z

is proportional to n_Xdz

dz

Total atmospheric extinction is proportional to column concentration (often just called column):

unit area

Extinction = absorption + scatter

Monitoring the ozone column from satellite

Method: UV solar backscatter

Reflection by

Earth surface

λ₁

λ₂

Ozone layer

Ozone

absorption

spectrum

λ₁

λ₂

Thickness of ozone layer is measured

as a column concentration

http://ozonewatch.gsfc.nasa.gov/

Sun

0

50

100

150

Ozone column, 10¹⁷ molecules cm^-2

Absolute concentration of gas can also be measured as partial pressure p_x [Pa]

The partial pressure p_X of a gas X in a mixture is the pressure that the gas would exert if all other gases in the mixture were removed.

Proper measure for phase change

(such as condensation of water vapor)

Thought experiment: consider a pan of water with a lid:

Now heat the pan:

Dalton’s law

saturation vapor pressure

Phase rule: defines the conditions for different phases �to be present at equilibrium in a multicomponent mixture

n = c + 2 - p

• c = number of components
• p = number of phases at equilibrium
• n = number of degrees of freedom (independent variables) determining this equilibrium

Derivation: see chapter 1 of Introduction to Atmospheric Chemistry (2^nd edition)

Example: consider the equilibrium of water between gas and liquid phases.

There are two variables determining the system: p_H2O and T

​

For the gas and liquid phases to be at equilibrium we have

c = 1, p =2 → n = 1 only one degree of freedom which can be either p_H2O or T

(but not both)

This is expressed by p_H2O,SAT = f(T)

Clausius-Clapeyron equation: p_{H2O, SAT} = f(T)

A = 6.11 hPa

B = - 5310 K

T_o = 273 K

p_H2O,SAT (hPa)

T (K)

Phase diagram for water

triple

point (n = 0)

gas-liquid

metastable

equilibrium

Clausius-Clapeyron curve

Even at temperatures < 0 ^oC, water droplets may not freeze…�because creating an ice surface requires energy (surface tension)

Thought experiment: imagine an ice embryo forming in a cloud droplet

Ice molecules at the surface are not happy because they are not bound to their ice neighbors – producing these surfaces requires energy

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Because of this, cloud droplets can remain supercooled liquid in metastable equilibrium down to temperatures as low as -40 ^oC

When supercooled cloud droplets hit surfaces, you get instant freezing because the freezing surface is provided: this produces rime ice

truck on Mt. Washington

Frosted trees near the top of Cannon Mt.

Working with the phase diagram:

Dew point: Temperature T_d such that p_H2O = p_H2O,SAT(T_d)

Initial state (p_H2O, T)

cooling

cloud

current Cambridge weather

p_H2O,SAT

T_d

Relative humidity (%) = 100(p_H2O/p_H2O,SAT)

RUNAWAY GREENHOUSE EFFECT ON VENUS

EARTH

VENUS

due to accumulation of water vapor (a powerful greenhouse gas)

from volcanic outgassing early in its history

…did not happen on Earth because farther from Sun; as water accumulated it reached saturation and precipitated, forming the oceans

Solutes decrease the saturation water vapor pressure

water saturation vapor pressure

over pure liquid water surface

water saturation vapor pressure

over aqueous solution of water

mole fraction x_H2O

An atmosphere of relative humidity RH can contain at equilibrium aqueous solution particles of water mole fraction

solute

molecules

in green

Raoult’s law

Aerosol particles therefore contain water even at RH < 100%, and that water content increases as RH increases so that particles increase in size

Visibility is limited by light scattering by aerosol particles and air molecules

object

Background light

At high RH, aerosol particles grow by uptake of water, decreasing visibility (haze)

scatter

scatter

Haze is a euphemism for air pollution

“winter haze” in Beijing

December 1952 London fog episode (The Crown, season 2)