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The Physics of Climate and Climate Change. A/Professor Michael Box Dr. Gail Box School of Physics, UNSW. Radiation and Climate Thermal radiation laws The Greenhouse Effect Global energy budget Simple models Climate Forcing Aerosol and gas forcings Feedback Mechanisms

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the physics of climate and climate change

The Physics of Climate andClimate Change

A/Professor Michael Box

Dr. Gail Box

School of Physics, UNSW

Radiation and Climate
    • Thermal radiation laws
  • The Greenhouse Effect
    • Global energy budget
    • Simple models
  • Climate Forcing
    • Aerosol and gas forcings
  • Feedback Mechanisms
    • Ice-albedo feedback
  • Global Climate Models
    • Strengths and weaknesses
  • Climate Prediction
    • Scenarios and uncertainties
radiation and climate
Radiation and Climate
  • The Earth’s climate, at both global and regional scales, is the result of dynamic balances (equilibrium) in the flows of energy (heat), when averaged over sufficiently large time and space scales.
  • The only energy exchange mechanism between the Earth and space is via thermal (electromagnetic) radiation, so we’ll start our physics lesson here.
radiation laws 1
Radiation laws: 1.
  • In order to understand radiation exchange, we need to know the laws of (thermal) radiation.
  • Law 1: All bodies with temperatures above 0 K (absolute zero) emit electromagnetic radiation.
  • A ‘black body’ is an ideal body which absorbs all radiation incident on it, and reflects none. (Thus it appears black!) A black body is also the most efficient emitter of radiation. We will start be examining the physics of blackbody radiation.
radiation laws 2
Radiation laws: 2.
  • Law 2: A blackbody at temperature T (°K) emits radiation from its surface at the rate

Watts per square metre

Here is the Stephen-Boltzmann constant.

For a body which is not ‘black’, we may interpret this temperature as an ‘effective temperature’.

energy balance
Energy balance
  • The Earth’s climate is governed by the balance between
    • incoming solar radiation, S, minus the fraction, α, which is reflected (both are measured by satellite);
    • and the emission of ‘terrestrial’ radiation.
  • If we assume that the Earth is a blackbody with an unknown (effective) temperature T, then we can determine T by ensuring this balance:
energy balance8
Energy balance
  • To determine the effective temperature of the Earth, we balance these two terms:

where we have used F = 1368 Wm-2 and α = 0.3.

  • Seems a bit cold! (Average surface temp is 14.5° C.)
  • Is the physics wrong? No, it’s just incomplete.
radiation laws 3
Radiation laws: 3.
  • Law 3. The emission spectrum of blackbody radiation follows Planck’s law. (This law has a very interesting history, and was in fact the first step in the development of Quantum Physics.)
  • Law 4. The wavelength at which this spectrum peaks is inversely proportional to temperature. (This is known as Wien’s law, and was actually discovered some years before Planck’s law.)
the greenhouse effect
The Greenhouse Effect
  • An examination of the spectra for 5750 K (the sun’s temperature ), and 250 K (the Earth’s effective temperature), shows quickly that
    • 99% of sunlight has wavelength less than 4.0 μm; known as shortwave radiation:
    • 99% of ‘earthlight’ has wavelength more than 4.0 μm; known as longwave radiation.
  • Our atmosphere contains a number of gases which absorb in the longwave region: these are greenhouse (or ‘radiatively active’) gases. These include H2O, CO2, CH4, N2O, O3, CFCs.
radiation laws 4
Radiation laws: 4.
  • A body which is not ‘black’ (any gas) will absorb a fraction, aλof the radiation incident upon it: this usually varies (strongly) with wavelength, λ. It will also emit a fraction, eλ of the radiation that a black body would emit at that wavelength.
  • Law 5. Fractional absorptivity equals fractional emissivity, at all wavelengths (Kirchhoff’s law):
  • Because of its temperature, the Earth’s surface emits radiation in the 4.0 to 100.0 μm region.
  • Most of this is absorbed by greenhouse gases.
  • But the atmosphere is at a similar temperature, so by Kirchhoff’s law these gases will re-emit much of this radiation, some to space, but more back to the surface, making the surface warmer.
  • This is known as the greenhouse effect, or more correctly, the ‘atmosphere effect’. I now display it both qualitatively, and quantitatively.
measuring the greenhouse effect
Measuring the greenhouse effect
  • There are two ways of measuring the greenhouse effect.
  • The first is the 33° difference between the effective temp (-18°C) and the actual (average) surface temp (15°C).
  • The second is the difference between the 390 Wm-2 surface emission and the 237 Wm-2 emission to space.
  • Of this 153 Wm-2, H2O accounts for about 95, CO2 for about 50, and N2O, CH4, O3 and CFCs about 2 each.
  • The interesting question which now confronts us is: how are these numbers changing, as a result of our actions?
a simple one layer model
A simple one-layer model
  • We can construct a very simple model of an absorbing atmosphere as follows:
    • Assume that the incoming shortwave radiation (after removing the reflected component) is transmitted by the atmosphere, and is all absorbed at the ground.
    • Assume that the ground emits as black body with Tg.
    • Assume the atmosphere absorbs all of this energy, and re-emits energy, as a black body with Ta, from both surfaces: i.e. to space; and back to ground.

Energy balance at the surface, and at the top-of-atmosphere, givesWhen these equations are solved for the two temperatures we obtainTa = 255 KTg = 300 K = 27 CThis time it is a little too warm, but it is an improvement.

more realistic models
More realistic models
  • For teaching purposes we use a model which allows some solar radiation to be absorbed in the atmosphere, and also allows some longwave radiation to pass right through the atmosphere (i.e. fractional emissivity < 1.0).
  • A radiative-convective model allows for an atmosphere with many layers, each with it’s own temperature and gas concentration (and hence fractional emissivity). This model can only be solved iteratively, but it serves as a first step in realistic modelling of radiation flows.
modified one layer greenhouse model
Modified one layer greenhouse model

Solar Radiation

  •  reflected
  • a absorbed in atmosphere
  • (1 – a - ) absorbed at surface
modified one layer greenhouse model25
Modified one layer greenhouse model

Terrestrial Radiation

  • e Tg4 absorbed in atmosphere
  • (1 – e) Tg4emitted to space
modified one layer greenhouse model26
Modified one layer greenhouse model

Terrestrial Radiation

  • e Tg4 absorbed in atmosphere
  • (1 – e) Tg4emitted to space


  • e Ta4emitted to space AND to ground
For radiative balance:

Incoming absorbed = Outgoing emitted

In atmospheric layer

aE + eTg4 = 2eTa4


(1 – a – )E + eTa4 = eTg4

Solve the simultaneous equations for two unknowns.

climate forcing
Climate Forcing
  • Any change in the radiation balance (at TOA) caused by changes in atmospheric composition, etc., is a called a “radiative forcing”.
  • We can evaluate radiative forcings with a very high precision by running a 1D radiative-convective model ‘before’ and ‘after’.
  • IPCC 4AR: “very high confidence” (>90%).
  • What forcings have been identified? The major ones are greenhouse gases and aerosols.
atmospheric aerosols
Atmospheric aerosols
  • Atmospheric aerosols are small particles with sizes ranging from ~10nm to ~10μm. They have atmospheric residence times ~1 week.
  • They may be produced by both natural and anthropogenic processes (or a combination).
  • Primary particles are directly injected into the atmosphere (e.g. dust, sea salt, soot).
  • Secondary particles are created by gas-to-particle conversion, from precursor gases (e.g. SO2 to sulphate aerosols).
aerosol forcing 1
Aerosol forcing: 1.
  • Aerosols are very efficient light scatterers, and will reflect (some) sunlight back to space.
  • Increasing levels of (anthropogenic) aerosols provide a negative forcing (cooling the surface). This is known as the aerosol direct effect.
  • Some particles, mainly soot, but also mineral dust, are efficient absorbers. They may affect the vertical heating rate in the atmosphere.
aerosol forcing 2
Aerosol forcing: 2.
  • At the heart of every cloud droplet is an aerosol particle (CCN), which is essential for it’s startup.
  • Increasing levels of aerosols may lead to more, but smaller, cloud droplets (for fixed l.w.c.).
  • Such a cloud will be more reflective (brighter) – this is the first aerosol indirect effect.
  • Smaller droplets also take longer to grow large enough to precipitate, so a longer-lived cloud – this is the second aerosol indirect effect.

These shiptracks, seen from space, are an example of the indirect effect. Ships sailing beneath these clouds have released particles which have seeded them with more CCN, creating lines of enhanced reflectivity.

feedback mechanisms
Feedback Mechanisms
  • A radiative-convective model is only a first step in understanding climate change, as we must now allow the climate system to respond. This involves ‘simple’ dynamics, plus feedbacks.
  • Feedbacks can be positive, enhancing any initial warming (or cooling), or negative, damping out any initial climatic change.
  • Unfortunately, many of the feedbacks which have been identified are positive.
feedback examples
Feedback examples
  • The simplest feedback involves water vapour. Warmer ocean temperatures lead to increased evaporation, hence more water vapour in the atmosphere. This is a powerful greenhouse gas, which leads to more warming, which leads to….
  • Other feedbacks involve the carbon cycle and the biosphere – both positive and negative.
  • As the oceans warm, their ability to dissolve CO2 decreases, so more will stay in the atmosphere.
ice albedo feedback
Ice-albedo feedback
  • Surface warming at high latitudes leads to the melting of ice and snow.
  • Ice has a much higher albedo (reflectivity) than ocean: 80% vs. 5%. Less snow cover means more solar energy is absorbed, causing more warming, and hence more ice melting, etc.
  • This is the reason polar regions are warming faster than the rest of the globe.
  • It is also a key to the glacial/interglacial cycle. (The Milankovitch ice-age mechanism.)
climate models
Climate Models
  • Climate models are an attempt to encapsulate everything we know about the Earth System.
  • This involves the atmosphere, the oceans and sea ice, vegetation, biogeochemistry, aerosols and atmospheric chemistry…. along with all of the interconnections and feedbacks involved.
  • The growth of computer power, plus of our knowledge of planetary systems, has allowed these models to become increasingly powerful.
atmospheric models
Atmospheric models
  • An atmospheric General Circulation Model (GCM), like a numerical weather model, solves the equations of motion for the fluid, plus equations for conservation of energy (including radiative transfer), mass and water vapour.
  • To do this the (continuous) atmosphere is replaced by a collection grid-boxes: maybe 20 vertical layers, and a horizontal spacing of around 100 km (or more).
sub grid scale phenomena
Sub-grid-scale phenomena
  • All processes which take place on scales smaller than the grid scale must be ‘parameterized’. This is one of the major sources of uncertainty in using these models.
  • Major examples include clouds (still the main problem), topography and coastlines.
  • This is one reason why global predictions are more reliable than regional predictions.
  • Sometimes we run ‘nested models’.
planetary heat transport
Planetary heat transport
  • Both the atmosphere and ocean act to transport heat from equatorial regions to polar regions.
  • Temperature gradients drive the weather.
  • For day-to-day weather forecasting, we can ignore the ocean, as it’s conditions will not change in the next week.
  • For longer time-scales we need to understand how the atmosphere affects the oceans, and how changes in ocean circulation (e.g. El Nino) can feed back to affect weather patterns.
climate prediction
Climate Prediction
  • To predict the climate in the year 2100, we run the best climate models available.
  • To do this, we need to decide on the conditions which are significant – e.g. the composition of the atmosphere – over the next 100 years, and run the model for 100 years of computer time.
  • Since we can’t know in advance what will be the atmospheric conditions, we use ‘scenarios’.
climate scenarios
Climate scenarios
  • The CO2 content of the atmosphere in 2050 depends on inputs and outputs between now and 2050. Thus we need ‘emissions scenarios’, and a good understanding of the carbon cycle.
  • The IPCC asks modelers to run their models for a range of emissions scenarios, which are based on assumptions about technological changes and economic decisions.
  • The main focus is usually on what used to be called the business-as-usual scenario.
changing climate statistics
Changing climate statistics
  • What do we look for in model predictions?
    • A major focus is on global mean temperature.
    • However other, statistical, predictions are studied (we extract both means and variation from model runs):
    • Rainfall: how is it distributed spatially and seasonally; does it come as more intense downpours; is it likely to rapidly re-evaporate due to higher temperatures?
    • Changes in winter storms or tropical cyclones?
    • Temperature: will there be more heatwaves (periods of several days that are ‘too hot’) or other extremes?
prediction uncertainties
Prediction uncertainties
  • Predictions of our ‘climatic future’ naturally contain many uncertainties.
    • Emissions scenarios are clearly an uncertainty, but one which we understand (and control).
    • Models are never perfect – for example, sub-grid-scale phenomena; or simplified chemistry.
    • There are always processes (and feedbacks) which are missing from the models, for different reasons.
what s missing
What’s missing?

There will always be processes missing from the models, and for a variety of reasons:

  • Processes which are just too complex: e.g. a full atmospheric chemistry/aerosol package.
  • Feedbacks we are not sure just when they’ll ‘kick in’: e.g. icecaps being lubricated, and sliding off; permafrost melting, releasing trapped methane.
  • Processes that haven’t even entered our thinking yet. For this reason, we must always monitor as many aspects of the climate system as possible, and be on the lookout for the unexpected (eggs and baskets).