Chapter 6. Chemical forcing of climate change

https://data.giss.nasa.gov/gistemp

1.5^oC

The Earth has had many different stable climates over its history

Snowball Earth (700 million years ago)

Eocene (35 million years ago)

Cretaceous (100 million years ago)

Last glacial climate (20 thousand years ago)

CO₂ over past 60 million years:�highly correlated with climate transitions

IPCC AR6

By 2100 we may have CO₂ levels not seen since the Eocene

Emission of radiation

• Radiation is energy transmitted by electromagnetic waves
• All objects at T > 0 K emit radiation by oscillation of electric charges in object

emitting object

oscillating

charge

speed of light c

Electric field excites charge in receptor object;

object absorbs radiation, gains energy (heat)

receptor object

emitting object loses energy

(heat)

• Hotter objects have higher

oscillation frequencies and so

shorter emission wavelengths;

frequency ν = c/λ

• Radiation emitted within an object can be reabsorbed by object; actual radiation emitted by object to outside is proportional to area of object

• An object can absorb radiation of a given wavelength only if it has charges that can oscillate at that wavelength

oscillating

charge

Measuring the radiation flux emitted by an object

• A spectrometer measures the radiation flux ΔΦ emitted by an object in discrete wavelength bins [λ, λ+Δλ]

​

​

is the radiation flux distribution function characteristic of the object

We normalize ΔΦ by Δλ

because ΔΦ can be expected to be proportional to Δλ

• Consider now an ideal spectrometer with infinite resolution dλ:

Total radiation emitted by object:

Wavelength λ_max of maximum emission:

Blackbody radiation

• Objects that absorb 100% of incoming radiation are called blackbodies
• For blackbodies, ϕ is given by the Planck function:

​

Φ = σΤ ⁴

where σ = 2π⁵k ⁴/15c²h³ = 5.67x10^-8 W m^-2 K^-4

is the Stefan-Boltzmann constant

λ_max = hc/5kT = 2900/T Wien’s law

h = Planck constant

c = speed of light

k = Boltzmann constant

T = temperature

• Integrate over all λ to get total radiation flux:

• Solve dϕ/dλ = 0 for λ of max emission:

Kirchhoff’s law: emissivity = absorptivity

The absorption spectrum

of an object can be measured

in the lab:

The emission spectrum of that object is then solely determined by its absorption spectrum and its temperature

Emissivity = ratio of emitted radiation flux to that of a blackbody at same T

​

Absorptivity = fraction of incoming radiation that is absorbed

Solar radiation spectrum: blackbody at 5800 K

λ_max = 0.5 μm (green)

0.4 0.7

Terrestrial radiation spectrum measured from satellite:�composite of blackbody radiation spectra for different T

Most terrestrial radiation is emitted in the 5-20 μm range, called the thermal IR

λ_max ≈ 10 μm (IR)

Radiative equilibrium for the Earth�assuming uniform-T blackbody radiation for Sun and Earth

Solar radiation flux intercepted by Earth (solar constant):

F_S = E_S /(4πd²) = σT_S⁴(R_S/d)² = 1360 W m^-2

Radiative equilibrium for the Earth:

flux in = flux out

where A is the albedo (reflectivity) of the Earth

Sun sees Earth disk at any given time

Energy emitted by Sun per unit time: E_S = 4πR_S²σT_S⁴

(1-A)F_S /4 = σT_E⁴

COLD!

Average solar radiation flux received by the Earth: F_SπR_E²/(4πR_E²) = F_S/4

T_E = 255 K is called the effective temperature of the Earth

It’s the mean temperature that would be inferred by an observer in space measuring the radiation flux emitted by the Earth

Earth seen by Voyager-1 25 billion km away

That object has a temperature of 255 K!

• But maybe the observer is not seeing the surface of the Earth but its atmosphere?
• It depends on whether the atmosphere can emit radiation in the 5-20 μm range where most of Earth’s radiation is emitted
• …and thus on whether the atmosphere can absorb radiation in that range

Absorption of radiation by a gas depends on its column abundance following Beer’s law

Propagation of radiation for a given wavelength

extinction coefficient from species X [cm^-1]:

absorption+scattering

Integration yields Beer’s law:

optical depth over [0, Z]

Extinction is proportional to [X]:

extinction cross-section [cm² molecule^-1]

Atmospheric optical depth integrates to top of atmosphere (TOA):

column concentration [molecules cm^-2]

Z

where

Absoption of radiation by gas molecules

…requires quantum transitions in internal energy of molecule.

​

• THREE TYPES OF TRANSITION
• Electronic transition: UV radiation (<0.4 μm)
• Jump of electron from valence shell to higher-energy shell,

may result in photolysis (example: O₃+hν →O₂+O)

• Vibrational transition: near-IR (1-30 μm)
• Increase in vibrational frequency of a given bond

requires change in dipole moment of molecule

• Rotational transition: far-IR (>20 μm)
• Increase in angular momentum around rotation axis

​

• Very little absorption takes place at visible wavelengths (VIS: 0.4-0.7 μm)
• Gases that absorb radiation in the 5-20 μm range where the Earth emits are called greenhouse gases; this requires vibrational transitions and therefore a change in the dipole moment of the molecule

• The main components of the atmosphere (N₂, O₂, Ar) are not greenhouse gases;
• H₂O, CO₂, CH₄, and most other trace constituents are greenhouse gases
• Clouds also exert a powerful greenhouse effect

Normal vibrational modes of CO₂

forbidden

allowed

allowed

Infrared spectrum

of CO₂

bend

asymmetric

stretch

15 μm

4 μm

Major greenhouse gases

�Absorption of terrestrial radiation by the atmosphere

absorptivity

“atmospheric window”

(8-12 μm)

Simple model of greenhouse effect

Earth surface (T_o)

absorptivity 1-A in VIS

1 in IR

Atmospheric layer (T₁)

absorptivity 0 in VIS

f in IR

Incoming

solar flux

Reflected

Solar flux

Surface emission

Transmitted

Surface emission

Atmospheric

emission

Atmospheric

emission

Energy balance equations:

• Earth system

​

​

​

​

• Atmospheric layer

Solution:

T_o=288 K 🢫 f=0.77

T₁ = 241 K

VIS

IR

Solar radiation

Terrestrial radiation

Interpreting the terrestrial radiation spectrum:�composite of blackbody spectra at different T

Gases absorbing in 8-12 μm window

are most effective at warming the Earth

f = 0

f = 1

f = 1

Strength of greenhouse effect depends on altitude of absorber

T_o

T ≈ T_o

Low-altitude absorber:

weak greenhouse effect

Surface

T << T_o

High-altitude absorber:

strong greenhouse effect

Whether a cloud cools or warms the Earth depends on its altitude

T_o

T_cloud≈ T_o

Clouds reflect solar radiation (ΔA > 0) → cooling;

…but also absorb IR radiation (Δf > 0) → warming

σT_o⁴

σT_cloud⁴≈ σT_o⁴

Low cloud (stratus):

cooling

σT_cloud⁴ < σT_o⁴

σT_o⁴

High cloud (cirrus):

warming

Increasing albedo from aerosols

Aerosols cool the Earth by reflecting solar radiation

combustion

industry

dust

aerosol particles (0.1-1 μm)

relative humidity

>100%

cloud droplets condense on particles

solar radiation

Aerosol Optical Depth (nasa.gov)

Solar

Terrestrial

visible infrared

F_in

F_out

increase greenhouse gas by ΔG

F_in

F_out

Climate equilibrium: F_in = F_out

ΔG

Radiative forcing: ΔF = F_in – F_out > 0

Radiative forcing of climate change

increase albedo by ΔA

F_in

F_out

ΔA

Radiative forcing: ΔF = F_in – F_out < 0

visible infrared

visible infrared

positive radiative forcing

warming

negative radiative forcing

cooling

🢡

🢡

radiative fluxes

Computing radiative forcing

• Start from climate equilibrium: F_in = F_out

F_in = F_S(1-A)/4

F_out = (1-f/2)σT_o⁴

Earth surface

Energy flux in Energy flux out

• Now apply an instantaneous greenhouse gas increase df (not allowing T_o to change):

​

ΔF_out = - σT_o⁴ Δf/2 < 0 → F_in > F_out ; the Earth heats

• Or apply an instantaneous increase in albedo: Δ A > 0 → Δ F_in = -F_s ΔA/4 < 0

F_in < F_out and Δ F < 0 ; negative radiative forcing, the Earth cools

ΔF = Δ(F_in – F_out) is called the radiative forcing (ΔF > 0 warms, ΔF < 0 cools);

​

Here Δ F= - Δ F_out an increase of greenhouse gases causes positive radiative forcing

Radiative forcing drives temperature response to restore equilibrium

Temperature adjusts to new equilibrium with ΔT_o = λΔF

​

where λ =(4(1-f/2)σT_o³)^-1 = 0.3 K m² W^-1 is the climate sensitivity parameter

​

Earth system models give λ in range 0.6-1.3 K m² W^-1 (best estimate 0.8 K m² W^-1)

Start from climate equilibrium in our simple greenhouse model,

F_in = F_S(1-A)/4

F_out = (1-f/2)σT_o⁴

Earth surface

Energy flux in Energy flux out

Climate feedbacks to radiative forcing

Temperature response ΔT_o

Physical impacts

• water evaporation
• cloud cover/height
• ice loss
• ocean changes
• ecosystem changes…

climate

feedbacks

drive ΔT_ox3

ΔT_o ∝ ΔF

Surface temperature response

is proportional to radiative forcing

transition to new climate

…until tipping point

Global warming since pre-industrial time

https://data.giss.nasa.gov/gistemp

+1.2^oC

Contributions to radiative forcing since pre-industrial times�and temperature responses

IPCC [2022]

• Temperature response to ΔF is similar for all radiative forcing agents, so total effect on temperature can be obtained by summing the radiative forcings
• Aerosols offset 30% of greenhouse warming, drive uncertainty in radiative forcing
• Total radiative forcing ΔF = 2.7 W m^-2 is only 1% of equilibrium F_in = 245 W m^-2 but drives ΔT_o = 1.3 K

The agents of climate change

+1.3^oC

CO₂ (100+years)

methane

(9 years)

other greenhouse gases (~100 years)

Observed rise in global mean surface temperature, 1880-2024

aerosol

particles

(1 week)

1880

2024

Air quality imperatives drive decrease of aerosol (PM_2.5)�

Future decrease in PM_2.5 must be compensated by more aggressive action on greenhouse gases

HEI, 2019; Li et al., 2023

What kills people around the world?

Dietary Risks

All Cancer

Tobacco

All Air Pollution

Ambient PM_2.5

Indoor Air Pollution

Water Sanitation

Lung Cancer

Unsafe Sex

Breast Cancer

Ambient Ozone

action

National Trends in PM_2.5

Projected temperature responses from aggressive 1.5^oC decarbonization scenarios relative to constant emissions

Decreasing aerosol delays improvement until 2050

Shindell and Smith [2019]

No improvement until 2050

relative to constant emission scenario

Global warming potential

GWP-H of gas X for time horizon H:

How does emitting Δm_X = 1 kg of X compare to emitting 1 kg of CO₂?

where

is the radiative forcing efficiency

General design of climate metrics

https://www.cnn.com/2024/03/18/climate/air-pollution-report-2023-asia-climate-intl-hnk

The agents of climate change

+1.3^oC

CO₂ (100+years)

methane

(9 years)

other greenhouse gases (~100 years)

Observed rise in global mean surface temperature, 1880-2024

aerosol

particles

(1 week)

1880

2024

+0.7^oC

Removing methane decreases temperature

by 0.6^oC within two decades

Methane is a major greenhouse gas… but where does it come from?

Methane has been growing rapidly and its sources are complicated

Wetlands: 100-220 Tg a^-1

Livestock: 90-140

Oil/gas: 40-100

Waste: 50-80

Rice: 20-40

Coal mines: 20-60

Pre-industrial: 650 ppb

Present: 1930 ppb

Simple measures can go a long way, there is no stockage problem like for CO₂

fix leaks, venting practices

flare excess gas

…or use it

recover gas from landfills

digest gas from manure ponds,

wastewater plants

change rice practices

Decreasing methane emissions should be easy

change cattle feed

…but problem is that methane comes from a zillion �of individually small point sources with highly variable emissions

oil field in California

I’m leaking!

I’m venting!

My flare went out!

This translates into order-of-magnitude uncertainties in national oil/gas emissions

Scarpelli et al., 2022

…and little credibility in emissions reported by individual countries under Paris agreement

National methane emission inventories for oil/gas sector (Tg a^-1)

UN reports

Bottom-up

inventories

Lack of confidence in bottom-up methane emission inventories �reported by individual countries to the UNFCCC

• These emission inventories set the basis for Global Stocktake (how the world is doing)

​

• They set the basis for Nationally Determined Contributions to reduce emissions

​

• But they are not very good!

in space

scheduled

canceled

Regional/global mapping

0.1-10 km pixels

high precision

Individual plumes

< 60 m pixels

Jacob et al., ACP 2022

Satellites enable global continuous observations of atmospheric methane

Geostationary observation of methane plumes �from NOAA GOES weather satellite

Pipeline

Pipeline blocking valve in Mexico

Q = 300 tons h^-1, 3-h duration

Watine-Guiu, Varon, et al., PNAS 2023

EELL pipeline from Chihuaha to Durango

supplying Permian gas to Mexico

blocking valve

TROPOMI (2018-): global daily mapping �with 5.5x7 km² pixels, 0.6% precision�

Over 100 million observations per year

Annual mean TROPOMI observations, 2021

Balasus et al.,AMT 2023

coal

livestock

landfills

rice

livestock

landfills

wetlands

oil/gas

rice

oil/gas

livestock

oil/gas

livestock

landfills

Inferring methane emissions from satellite observations�by inversion of an atmospheric transport model

Emissions

transport

Inferring methane emissions from satellite observations�by inversion of an atmospheric transport model

Emissions

inversion

Top ten methane emitting countries [Tg a^-1]

*

Qu et al., ACP 2021

Chen et al., ACP 2022

Nesser et al., ACP 2024

from inversions of GOSAT and TROPOMI satellite data

*

did not sign the Global Methane Pledge

*

*

Attributing the recent rise in methane

Megan He, in prep.

Targeting methane emissions cannot be a substitute for CO₂… �because it does not do much for long-term climate change

​

• Over 10-year horizon, methane is more important than CO₂
• But over 100-year horizon, methane is long gone while CO₂ is still there
• Methane and CO₂ emissions should not be viewed as “equivalent” in climate policy (which they unfortunately are)

Response after 10 years

Response after 100 years

Warming response after 1-year pulse of present-day emissions (IPCC AR6)

CO₂ CH₄

Methane is still a powerful lever for near-term climate action�…while we decrease CO₂ emissions and develop carbon capture technologies

Time

Climate risks

CO₂ emission decrease

+ carbon capture

+ methane emission decrease

Start of climate action

(+solar geoengineering?)

Solar geoengineering

Stratospheric aerosol injection could work technically but raises serious policy, political, and ethical issues