Radiation and Atmospheric Behavior

Global Environmental Change – Lecture 3 Spring 2015

What is Radiation?• Radiation describes a process in which energetic particles

or waves travel through a medium or space

• Radiation is often referred to as electromagnetic radiation (EMR)

• It comprises both electric and magnetic field components

• These components oscillate in phase perpendicular to each other, and usually perpendicular to the direction of energy propagation

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EM Radiation

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• Relation between electric field, magnetic field, and direction of propagation

Classification of Radiation• Electromagnetic radiation is classified into

several types according to the frequency, or alternatively its related property wavelength, of the wave

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Frequency• Frequency is the number of occurrences of a

repeating event per unit time.

• The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency

• It is usually measured in the unit Hertz, formerly known as cycles per second

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Wavelength• Wavelength of a sinusoidal wave is the spatial

period of the wave, the distance over which the wave's shape repeats

• It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or null crossings

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Wavelength Diagram

• Wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests, or troughs, or corresponding null crossings as shown

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Relationship of Frequency and Wavelength

• λ = c/ν c is the speed of light in vacuum, a fundamental

constant of nature (cm/s) ν is the frequency, measured in Hertz (Hz) λ is the wavelength (cm/cycle)

c = 29,979,245,800 cm/sec (29.979 x 109 cm/sec)

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Electromagnetic Spectrum• The EM spectra ranges

from long waves with low energy to short wave X-ray and γ rays with high energy

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Size and Sources

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Radiation Interactions with Matter• If an atom absorbs a photon of

electromagnetic radiation and remains intact, there is a strong tendency for it to return to its ground state

• All physical systems will tend to move to lower energy levels, much as water runs downhill

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Absorption of Radiation• It is the absorption of radiation by matter that is

of concern in an effect that has come to be known as the Greenhouse Effect

• The name comes from the use of glass structures to grow plants during times when temperatures are below the normal range for plant growth

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Greenhouse

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Giant Amazon waterlilies in a large greenhouse at the Saint Petersburg Botanical Garden, Russia

Why Do Greenhouses Work?• Glass is essentially transparent to visible radiation

• Light striking the Greenhouse enters freely

• Light is absorbed by interaction with matter inside the Greenhouse

• Various forms of interaction transform the visible light radiation to heat, in the form of bond vibration and stretching

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Re-radiation• The warmed structures and plants inside the greenhouse re-

radiate this energy in the infra-red, to which glass is partly opaque, and that energy is trapped inside the glasshouse

• Although there is some heat loss due to conduction, there is a net increase in energy (and therefore temperature) inside the greenhouse

• Air warmed by the heat from hot interior surfaces is retained in the building by the roof and wall

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Temperature Scales• Scientists (and most of the world) use the Celsius

temperature scale, a temperature scale that is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale two years before his death

• From 1744 until 1954, 0°C was defined as the freezing point of water and 100°C was defined as the boiling point of water, both at a pressure of one standard atmosphere

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Definition of Celsius Scale• By international agreement, the unit "degree Celsius" and

the Celsius scale are currently defined by two different points: absolute zero, and the triple point of VSMOW (Vienna Standard Mean Ocean Water - specially prepared water)

• This definition also precisely relates the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature (symbol: K)

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Relation to Absolute Temperature Scale

• Absolute zero, the hypothetical but unattainable temperature at which matter exhibits zero entropy, is defined as being precisely 0 K and −273.15°C

• The temperature value of the triple point of water is defined as being precisely 273.16 K and 0.01°C The triple point is where water, ice, and water vapor coexist

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Infrared Blanket• If the earth's atmosphere were transparent to infrared radiation,

the earth would lose heat rapidly and would have a low average temperature This temperature would be about 254 K, or about -19°C

• While life would probably exist at these temperatures, it would be difficult and life on earth would likely be much different from life as we know it

• Fortunately, some gases in the earth's atmosphere absorb some outgoing infrared radiation These gases as known as Greenhouse gases, often denoted GHG

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Polyatomic Gases• The most abundant polyatomic gas is water

Water is the most important greenhouse gas in the sense that it accounts for the major portion of the natural greenhouse effect

• Other polyatomic gases in the atmosphere Carbon dioxide (CO2)

Methane (CH4)

Nitrogen gases (NOx)

Sulfur Gases (H2S, DMS or (CH3)2S, SO2, SO3)

Chlorofluorocarbons (CFC’s)20

Absorption of IR Radiation• IR radiation is absorbed by polyatomic molecules

It excites rotational and vibrational states and raises the molecules to a higher energy state

• They return to the ground state by radiating IR radiation in all directions Some of this radiation is directed at the ground and will likely be

reabsorbed by the ground Other rays are directed sideways, or upward These rays will likely encounter other greenhouse gas molecules before

escaping from the atmosphere 21

Dipole Moments• Polyatomic gases which absorb IR radiation must

possess one or more moving electric dipole moments

• The electric dipole moment is a measure of the separation of positive and negative electrical charges in a system of electric charges, It is a measure of the charge system's overall polarity

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Dipole Moment Diagrams

Moving charges generate a changing electric field around the ions

A water molecule possesses a dipole, with the oxygen (red) being megative, and the hydrogens (blue) being positive

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Dipole Moment Video

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GLY 6746

IR Absorption• Each polyatomic gas adsorbs IR radiation at a

discrete set of wavelengths

• Combinations of gases are more effective at absorbing across the electromagnetic spectrum than any single gas

• Some gases are much more effective than others

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Liquid Water Absorption Spectra

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CO2 IR Absorption

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Methane IR Absorption

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Combined IR Absorption

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Atmospheric Windows

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Effect of Concentration• As the concentration increases, so does absorption• Eventually, the absorption is nearly 100% (saturation)• Further increases in concentration have little effect on

absorption, or so it was long thought• The next slide illustrates the effect for C2F6

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C2F6 Transmissivity vs. Wavenumber and Concentration

Wavenumber (k) is defined as

where λ is the wavelength

• Animation made from a sequence of still images (double-click to play)

Svante August Arrhenius• Arrhenius, a Swedish scientist, published an article in

April, 1896, called “On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground”

• This was one of the first times anyone realized that atmospheric gases might influence temperature

• In 1881,Arrhenius had received a fourth class doctorate, later upgraded to third class after his defense, so was not highly regarded at the time

• In 1903 his later work in the same area as his doctorate was recognized by the Nobel Prize in Chemistry

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Knut Angström• Angström, a Physics professor at Uppsela University,

challenged Arrhenius work in the Monthly Weather Review of the American Meteorlogical Society

• “He infers, therefore, that a layer so thick as to be equivalent to that contained in the earth’s atmosphere will absorb about 16 per cent of the earth’s radiation, and that this absorption will vary very little with any changes in the proportion of carbon dioxid (sic) gas in the air”

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Error• For many years, this stopped consideration of

Arrhenius’ idea

• But that was a flaw in Angström’s approach

• This error is described in a RealClimate web page, written by Spencer Weart

• http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument

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Fluid Properties• Before investigating this error, we need to think about the

properties of fluid Incompressible Compressible

• Compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change

• Objects may be said to be compressible or incompressible, depending on the degree of volume change they experience per unit of pressure

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Compression of Water• Water is often said to be incompressible

• At a depth of 4 km, with pressures are around 40 megapascals, water has a volume decrease of 1.8%

• At 0º C, the compressibility is less than one part in a billion per Pascal

• (One atmosphere is 101,000 Pascals)

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Linear Pressure Response• As the figure shows,

this means that water shows a linear response to an increase in pressure

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Non-Linear Pressure Response• The figure is a graph of the actual

change in pressure with increasing altitude, and is clearly non-linear

• At an altitude of 8 kilometers, pressure is half as much as at sea-level

• This is because the atmosphere is compressible

Vertical scale is km 39

Compressible vs. Incompressible• The figure shows a response to pressure

by a compressible substance (air), and an incompressible substance, water

• There is more air per meter at low altitude than at higher altitude

• The amount of water per meter does not depend on the depth to a significant extent

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Exponential Function• The change in pressure with altitude is an example of an

exponential function

• Q = ekx, where: Q = quantity in question k is a constant, which may be positive or negative x is a variable e is an irrational number (sometimes called Euler’s number) equal to

2.7182818284590452353602874713527…. , and is the base of the natural logarithms

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Change of Pressure with Altitude• Pressure clearly decays (grows smaller) with

altitude

• We can calculate the change in pressure as follows P(z) = 1 atm • e-z[km]/8 km

• z is the height above the ground, measured in kms

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Temperature • Temperature is related to the average

kinetic energy of the molecules in the volume under consideration

• The faster molecules move, the higher the temperature

• It does not matter how many molecules there are per unit volume

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Heat Content (Enthalpy)• The heat content is equal to the energy required to

create a system, plus the energy required to displace the surroundings, creating room for the system

• If a gas is compressed, it warms up – we did work on the system to compress it, which added energy

• If a gas expands, it cools down – the gas expanded, doing work on the universe

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Adiabatic Change• Adiabatic change refers to change with no

change in heat content

• Adiabatic expansion – a gas occupies a bigger volume, but the molecules move slower

• Adiabatic compression - a gas occupies a smaller volume, but the molecules move faster

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Lapse Rate• As gas rises in the

atmosphere, it expands, because pressure is less

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• If conditions are adiabatic, the gas will behave as shown in the diagram, depending on how much water it holds

Lapse Rate Definition• The lapse rate is defined as the change with

height of an atmospheric variable

• The variable is usually temperature

• The adiabatic lapse rate is the change with constant heat content

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Phase Changes• Substances, such as water, can exist in any of three

phases Gas (Water vapor) Liquid Solid (Water ice)

• A change in phase involves heat Water vapor → Water + heat Ice + heat → Water

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Latent Heat• If you stick your hand in an oven at 100º C for a short

time, you will not be burned

• If steam from a kettle contacts your hand, you probably will be

• Steam has extra energy, called latent heat

• When the steam hits your hand, some of it condenses, transferring energy to your hand, and burns you

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Vapor Pressure• Water molecules in the air

contribute to the total pressure within a system

• The pressure is known as the vapor pressure

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• Vapor pressure is primarily a function of the temperature• The higher the temperature, the higher the vapor pressure

Saturation• At any given temperature, air can hold a certain amount of

water vapor at equilibrium

• Equilibrium means if one water molecule evaporates, another will condense

• If the water vapor content is below the equilibrium value, the air is undersaturated – water will tend to evaporate

• If it is above the equilibrium value, it is supersaturated – water will tend to condense

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Humidity• Relative humidity is the water vapor pressure divided by

the saturation pressure

• As relative humidity increases, it is harder to evaporate water – sweating as a means of cooling becomes less and less efficient

• Absolute humidity is the amount of water the air holds, per unit volume Usually expressed as grams per m3

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Latent Heat of Vaporization (Lv)

• The quantity of heat necessary to change one gram of liquid to one gram of vapor with no temperature change, again measured in calories per gram

• Water has the highest value of all substances (539.55 cal/g at 100[ C).

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Latent Heat of Fusion (Lf)• The quantity of heat necessary to change one gram of

solid to one gram of liquid with no temperature change, usually measured in calories per gram

• Except for ammonia, water has the highest known value for the heat of fusion

• For water at 0[ C the value is 79.71 calories per gram

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Lv Compared to Lf • When a solid is heated, turning it into a liquid, the kinetic energy of its

molecules is increased, moving them further apart until the forces of attraction are reduced to allow the liquid to flow freely

• However, the forces of attraction still exist

• When a liquid is heated, turning it into a gas, the kinetic energy of the molecules are increased to a point where there are no forces of attraction between the molecules

• The energy required to completely separate the molecules, moving from liquid to gas, is much greater than the energy required to just to reduce their separation, solid to liquid

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Condensation and Energy Transfer• When water evaporates from the surface into the atmosphere,

it rises and enters encounters regions of lower temperature

• Eventually, it reaches saturation, and condenses

• Condensing water transfers a lot of energy to the atmosphere

• This is the energy that drives a big thunderstorm, or a tropical cyclone

• Heat transferred to the atmosphere causes temperature to increase, and the air mass to expand

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Ideal Gas Law• PV = nRT

P = pressure V = Volume n = number of moles R = universal gas constant = 8.3145 J/mol K T = absolute temperature (in K)

For a given air mass, n and R are constants, so if T increases, the product PV must also increase

Since the air mass is relatively unconfined, pressure remains nearly constant and thus the volume must increase

Having the same mass of material in a larger volume decreases density, and the air mass rises

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Convection• Convection is a movement of molecules within

a fluid, either liquid or gas

• It is sometimes used to mean the heat transfer produced by such motion As such, it is a third means of heat transfer, along

with radiation and conduction

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Convective Clouds• Convective clouds are formed in vertical motions that result from the

instability of the atmosphere

• This instability can be caused by: a. Heating at the bottom of an air layer b. Cooling at the top of an air layer c. Lifting or saturation of a potentially unstable layer d. A combination of all the above

Convection is a common process in thunderstorms and hurricanes The photos on the following slides show a typical pattern of convective

cloud formation in Juneau, Alaska

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Sunrise• At sunrise, only

very few clouds form, and they are transient, whispy phenomena

60Picture lightened to improve cloud visibility

Midmorning• Later in the day, the cloud

formation is somewhat stronger

• Clouds tend to form over mountain peaks, not over open water

• No strong cloud development occurs over Taku glacier in the upper left, despite its high altitude, as the ice surface does not become heated in the sun

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Noon• At noon, the thermal

updrafts become stronger and consequently the clouds become more well-defined

• While in the morning the upward motion of air rarely exceeds 0.5 m/s, around noon this becomes rather 1 m/s, to strengthen even more in the afternoon

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Midafternoon• A few hours later, the

number of clouds decreases again as the thermal irradiation by the sun weakens

• Typically fewer, but stronger, thermals with larger cap clouds are found

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Sunset• Towards sunset, there is still

significant thermal energy left to lead to sizeable cloud development, although the number of clouds as well as the typical strength of thermals is decreasing again

• During the night, the development of convective clouds breaks more or less down completely as there is no thermal energy from the sun available

64Picture lightened to improve cloud visibility

Convection Diagram - 1

• In A, a fluid has a uniform temperature, and is well-mixed In this situation, the fluid is stable

• In B, the fluid is heated from below, increasing the temperature and decreasing the density The fluid is now convectively unstable

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Convection Diagram - 2

• If the fluid consists of two immiscible components, the heated portion will rise to the top, float until it cools, and then sink – the principle of a lava lamp, as shown in C

• If the fluid is a single component, it will mix, and the entire fluid will become warmer, as shown in D

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Lava Lamps

• Slow heating • Rapid heating

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Layer by Layer Heating• As radiation moves up, layer by layer, through the atmosphere,

some is stopped in each layer

• Specifically, a molecule of carbon dioxide, water vapor or some other GHG absorbs a bit of energy from the radiation

• The molecule may radiate the energy back out again in a random direction, or it may transfer the energy into velocity in collisions with other air molecules, so that the layer of air where it sits gets warmer – in-situ heating

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Skin Layer• Each layer of air radiates some of the energy it has

absorbed back toward the ground, and some upwards to higher layers

• With increasing altitude, the atmosphere gets thinner and colder

• Eventually the energy reaches a layer so thin that radiation can escape into space - this layer is known as the skin layer

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Raising the Skin Layer• The addition of carbon dioxide, or other GHG, to layers, so

high and thin that much of the heat radiation from lower down slips through, means the layer will absorb more of the rays

• So the place from which most of the heat energy finally leaves the Earth will shift to higher layers

• Those are colder layers, so they do not radiate heat as well

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Establishing a New Balance• The planet as a whole is now taking in more energy

than it radiates , our current situation

• Higher levels radiate some of the excess downwards, so all the lower levels down to the surface warm up

• The imbalance must continue until the high levels get hot enough to radiate as much energy back out as the planet is receiving

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Convection in Compressible Fluids

• Figure a represents a stable situation in the troposphere, with temperature decreasing with altitude

• Figure b shows heating from below – the heated air is less dense, so it rises, but along its own adiabat – it can rise to the top of the gas column if mixing does not occur

• If mixing occurs, the temperature profile of the whole column is increased

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Dry vs. Wet Adiabats

• If air with relative humidity = 100% rises in the atmosphere, it will expand and cool

• Cool air holds less moisture, so the water vapor will start to condense to form droplets

• Condensing water releases latent heat, helping to offset the cooling due to expansion

• This accounts for the dry and wet adiabats in the diagram

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Radiative vs. Convective Equilibrium

• If only radiative transfer is considered, the radiative equilibrium lapse rate is about 16K/km

• The convective lapse rate for a dry adiabat is around 10K/km, and for a wet adiabat around 6K/km

• This is called radiative-convective equilibrium, and is a much better model for the real atmosphere than radiation alone

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Radiation Altitude• Some IR radiation goes directly into space, through IR windows

• Other IR wavelengths are absorbed and reradiated from the coldest part of the atmosphere, the tropopause

• We can imagine an equilibrium altitude that averages the different wavelengths, and this was the skin altitude encountered earlier

• Skin temperature is commonly defined as the temperature of the interface between the earth's surface and its atmosphere

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Increasing Skin Altitude• As GHG concentration

goes up, more radiation is trapped, and more radiation to space comes from the tropopause

• This raises the skin altitude, which we can denote as zskin

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Calculating Ground Temperature• We can calculate the worldwide average ground

temperature if we know the skin temperature altitude and the lapse rate

• If the lapse rate is 6K/km, and the skin altitude is 5 km, the calculation is as follows: Tground = Tskin + 6K/km • 5 km, or

Tground = Tskin + 30K

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Changing Skin Altitude

• If GHG concentration goes up, so does skin altitude

• This shifts the point at which the moist adiabat intercepts the ground to a higher temperature

• Thus, greenhouse warming

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Calculating Changing Skin Altitude• We can rewrite the equation for changing ground

temperature with changing skin altitude, as follows: ΔT= Δzskin • 6K/km , where

• ΔT is the change in temperature

• Δzskin is the change in skin altitude

• If we know the increase in ground temperature and the lapse rate, we can calculate the new skin altitude

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Incompressible Atmosphere• If the atmosphere were incompressible, convection

would keep the temperature equal at all altitudes, thus making the lapse rate zero ΔT= Δzskin • 0K/km = 0

• There would be no greenhouse effect

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Ground Temperature Sensitivity

• The lapse rate determines the sensitivity of the ground temperature to increasing GHG concentration

• Thus, this is a critical parameter for model calculations

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John Tyndall• Saturation of GHG at lower levels would not change the

surface temperature directly, but does raise the layers from which radiation escape, and this determines the planet’s heat balance

• John Tyndall, an American physicist, understood this in 1862: "As a dam built across a river causes a local deepening of the stream, so our atmosphere, thrown as a barrier across the terrestrial [infrared] rays, produces a local heightening of the temperature at the Earth’s surface."

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Incoming vs. Outgoing Radiation• To fully understand the Greenhouse Effect, we

need to look at the radiation balance of earth What radiation is reaching the earth? For what radiation is earth a source? What is the balance between incoming and

outgoing radiation?

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Incoming Radiation• The earth receives radiation from our sun, as well as

cosmic radiation from other stars, and reflected radiation from the moon and other planets

• Since almost all of the energy reaching earth comes from the sun, we will neglect other sources

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Solar Flux and Flux Density• �Solar Luminosity (L) is the constant flux of energy

put out by the sun

• L = 3.9 x 1026 W

• Solar Flux Density (S� d) is the amount of solar energy per unit area on a sphere centered at a distance d from the Sun

• Sd = L/(4πd2) W/m2

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Solar Flux Density Reaching Earth• Solar Constant (S) = the solar energy density at the

mean distance of Earth from the sun (1.5 x 1011m)• S = L/(4πd2) =

(3.9 x 1026W)/[4 x 3.14 x (1.5 x 1011m)2] = 1370 W/m2

• This figure is for a disc with the earth’s diameter

• The actual area of the earth is four times larger, so the flux per square meter averaged over the whole surface is 1370 W/m2 ÷ 4 = 343 W/m2

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Blackbody• A blackbody is something that emits (or absorbs)

electromagnetic radiation with 100% efficiency at all wavelengths

• Since no light is reflected, the object is perfectly black at absolute zero (0 K)

• As a blackbody is heated above 0 K, it begins to emit radiation

• The wavelength of the emitted radiation decreases as temperature increases

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Blackbody Spectrum• Radiation intensity

increases as temperature increases

• Wavelength decreases as temperature increases

• Remember that the shorter the wavelength, the more energetic is the radiation

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Sun vs. Earth• Comparison of the

radiation from the sun and the earth

• Note that the earth’s radiation is entirely in the IR

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Greenhouse Effect Diagram

• The Sun’s radiation, largely in the visible, passes through the earth’s atmosphere

• Some is reflected, some is absorbed in the atmosphere, and some is absorbed by the ground, where it is converted to heat

• Heat is radiated back to space as longwave radiation, in the IR part of the spectrum

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Factors Affecting the Greenhouse• Three main factors directly influence the greenhouse

effect: (1) Total energy influx from the sun, which depends on the

earth's distance from the sun and on solar activity (2) Chemical composition of the atmosphere (what gases

are present and in what concentrations) (3) Albedo, the ability of the earth's surface to reflect light

back into space

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Why the Earth is Warming• The only factor that has changed significantly

over the last two hundred years is the chemical composition of the atmosphere, which is a direct result of human influence

• In the near future, albedo changes will become important

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Factor Diagrams

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CO2 IR Absorption

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Natural Greenhouse Effect• The atmosphere naturally contains carbon

dioxide, methane and nitrous oxide

• These gases--together with water vapor--create the natural greenhouse effect

• They trap some of the sun's energy and keep the Earth warm enough to sustain life

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Cumulative Absorption

• The animation shows the absorbance of carbon dioxide, methane, water, and nitrous oxide

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Enhanced Greenhouse Effect

• An increase in the natural process of the greenhouse effect, brought about by human activities, whereby greenhouse gases such as carbon dioxide, methane, chlorofluorocarbons and nitrous oxide are being released into the atmosphere at a far greater rate than would occur through natural processes

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Carbon dioxide• In 2013 we added more than 36 billion tons of

carbon dioxide to the air mainly by: Burning fossil fuels Cutting down and burning trees

• Deforestation accounts for about 20 percent of the carbon dioxide increase from human activities

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Deforestation• Until 50 years ago most of the carbon dioxide

from deforestation was released from temperate zones

• Now tropical deforestation is the largest source

• Tropical forests are being burned and cut for farming, mining and raising cattle

Stefan-Boltzmann Equation• The emission of radiation by a Blackbody

radiator is governed by the Stefan-Boltzmann equation F = σT4 where σ is 5.67x10-8 W/m2/K4

Note the fourth order dependence on the absolute temperature

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Using the Albedo• The average albedo of the earth is about 30%

• The heat input into earth is therefore 343 W/m2 x (1 – 0.3) = 240 W/m2

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Apply Stefan-Boltzmann• 240 W/m2 = 5.67x10-8 W/m2/K4 x T4

• Solving for T T4 = 240 ÷ 5.67x10-8 = 4.232 x 109

T = 255 K

If the earth were a pure Blackbody radiator, with no atmosphere, the earth’s surface temperature would be about 255 K

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Earth Without an Atmosphere• Zero Celsius is 273 K, so 255 K is about -18C• Although life might survive at these temperatures, it

would be difficult and life on earth would likely be much different from life as we know it

• Fortunately, some gases in the earth's atmosphere absorb some outgoing infrared radiation

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Natural Greenhouse Effect• The earth’s average surface temperature is

about 15C, or 288 K

• Thus, the Greenhouse Effect raises the temperature about 33C, making the earth a much more pleasant place for most forms of life

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Effective Level of Radiation • Since the effect of adding more GHG to the

atmosphere is to raise the effective level of radiation to space, it gets colder in the effective level

• Colder temperatures greatly decrease the intensity of radiation, trapping more heat

• The earth should retain more heat

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