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## Global Warming; Understanding the Forecast

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**Global Warming; Understanding the Forecast**David Archer**Reading assignment, Module 5**• Global Warming Book • Chapters I, 2, 3 and 4**Chapter 2, Blackbody Radiation**How light can carry heat energy through empty space**Heat**• A thermometer is like an atomic speedometer • Heat is the kinetic energy of atoms • Atoms move faster if it is hot and slower when it is cold • Too much heat energy can cause the chemical bonds to break (cooking food denatures the protein) • Touching a hot object is an example of heat conduction**Light**• A vacuum is an excellent insulator, because it contains no molecules to absorb heat energy (Thermos bottle). • Between Earth and the Sun is 150 million km of vacuum, how can heat travel through this space? • Electromagnetic waves carry energy through a vacuum.**Electromagnetic waves:**• Electric and magnetic fields in a vacuum fit together to form a closed, self replicating cycle, travelling at light speed • The electromagnetic radiation comes in a full range of frequencies, denoted by the Greek letter ν, and in units of Hz = cycles / second • The waves have wavelength, λ • The constant speed of light makes it possible to relate the frequency and the wavelength c=λ ν**Wave number**• Scientists who discuss infrared (IR) light use a third way of describing different colors called wave number • Wave number is the number of cycles per cm of length • Wave number is designated with “n” • Wavelength in cm / cycle is inverted, to get the wave number in cycles / cm**Blackbody Radiation**• A substance that can interact with light (absorb) at all possible frequencies is called a blackbody • The light emitted is called blackbody radiation • A plot of intensity vs. wavelength of light is called a spectrum • The IR light emission spectrum of a blackbody depends only on the temperature of the object • intensity given by the Stefan-Boltzmann equation**Stefan-Boltzmann Equation**• is the intensity and represents the total rate of energy emission from the object at all frequencies in units of Watts/m2 • is a number from 0 to 1, for a perfect blackbody =1 • is a constant • is the Kelvin temperature raised to the fourth power**Value of σ**The value of the Stefan–Boltzmann constant is given in SI units by σ = 5.670373(21)×10−8 W m−2 K−4**Blackbody spectra**• A room temperature object “glows” in the infrared region, we can’t see it • As objects get hotter, their energy glows in the visible range • The Sun glows in the visible range • The Earth glows in the IR range • “Earth light” called terrestrial radiation, is IR**Take Home Points Chapter 2**• Light carries energy through the vacuum of space • If an object can absorb light, it can also emit light • An object that can emit all frequencies of light is called a blackbody, and emits light energy at a rate equal to εσT4**Chapter three**The Layer Model Our first Climate Model**Layer Model**• A toy, demonstrating an idea • Demonstrates how the greenhouse effect works • First step - construct a Bare Rock Model without an atmosphere • Step two – demonstrate the greenhouse effect by adding an atmospheric layer**Algebraic Model (math )**• First assumption: energy flux Flux out = Flux in • 1350 W/m2 incoming, some is reflected back, called albedo, designated with α • Mars, 15% reflected, α = 0.15 (no clouds) • Venus, 70% reflected, α = 0.7 (acid clouds) • Earth, 30%reflected, α = 0.3 • So 70% is absorbed, or (1-α)**In the Real World**When sunlight hits the Earth it comes from the same direction. The Earth makes a circular shadow. Therefore the Earth receives an influx of energy = the intensity of the sunlight, multiplied by the area of the circle.**Intensity of the sunlight actually absorbed by the Earth is**• Iabsorbed = 1350 W/m2 (1-α) ≈ 1000 W/m2 • To get incoming flux for the planet instead of a square meter of the planet, we need to multiply by the planet area. The amount of head on sunlight can be calculated by the area of the Earth’s shadow. earth • Putting it together… • Fin = earth (1-α) I sunlight • In words, flux in = Earth’s area x amount absorbedx intensity of sunlight**Flux in, Flux out**• Fin= earth (1-α) Isunlight (one direction) • The rate at which Earth loses energy by radiation to space is given by the Stefan-Boltzmann equation (ignoring temperature fluctuations for simplicity) • Fout = A εσT4 (all directions, next slide)**IR leaving Earth**The surface of the earth is four times larger than its shadow. When IR leaves the Earth, the rate of heat loss is the intensity of the Earthlight times the area of the surface of a sphere (the Earth)**Put them together**• Incoming solar radiation, outgoing IR (heat) • Fin= earth (1- α) Isunlight • Fout = εσT4 εσT4 = earth (1- α) Isunlight**Simplify the terms**• εσT4 = earth (1- α) I sunlight • Cancel • Divide by 4 • Equation is in units of W/m2 εσT4 ground =(1-α) I in 4 As though full strength sunlight only shines on one-fourth of the Earth**The unknown is T**• Rearrange to solve for T • ] • Solving for the temperature of the Earth gives a value of 255 K, or about -15°C • The average temperature of the Earth is closer to +15°C • Repeating the calculations for Venus and Mars, Bare Rock Model results in temperatures that are too cold for all three of the terrestrial planets**Frequency ranges of IR, divided into three parts**• Far IR – the water in the atmosphere absorbs so strongly in this range that it renders the atmosphere, in effect, opaque • Mid IR – blackbody radiators can radiate strongly in the range (human skin radiates strongly at the lower end). This IR is absorbed by molecular vibration • Near IR – infrared photography (next to visible)**The Layer Model with a Greenhouse Effect**Figure 3.4 An Energy diagram for a planet with a single pane of glass for an atmosphere. The glass is transparent to incoming visible light but a blackbody to infrared light.**Greenhouse effect adds heat to the model**• Very simple – a pane of glass suspended by magic above the ground • Incoming sunlight goes through the glass because it is transparent to visible light, and goes to the ground like before • Planet radiates IR as before, εσT4 • In The IR range, the glass pane is a blackbody, absorbing and emitting all frequencies of IR**Two unknowns**• Temperature of the ground, and • Temperature of the glass • The rate of energy going out of the layer equals the rate of energy going in (the layers are in a state of energy balance) • There is only one temperature for each of the layers at which both energy budgets will be in balance • Solve for one and substitute to back to solve for the other**Energy budget for the pane of glass**• Intensity in = intensity out I up, glass + I down, glass = I up, ground This is IR intensity, so use the S-B equation 2εσT4 (glass)=εσT4(ground) (eq. 3-7) Both the ground and the glass have to be in a state of balance**Energy budget for the ground**• Different that the Bare Rock Model because now there is heat flowing down from the pane of glass I up, ground + I in, solar= I down, glass • These intensities expand to 3-8 • Combine 3-7, and 3-8, eliminate one of the temperatures, solve for the other, and substitute back to the original equation to get the second temperature.**Solving for the temperature of the glass gives the same**answer as solving for the temperature of the ground in the Bare Rock Model. • The skin temperature of the model is always the same • The place in the Earth system where the temperature is the most directly controlled by incoming sunlight is at the top layer, where infrared radiates to space. • We will call this temperature the skin temperature of the Earth • Plug in the skin temperature for the outermost glass temperature, and we see that the ground temperature is warmer than the skin temperature by a factor of the fourth root of 2 (comes out to about 19%) • The glass layer warms the ground by trapping outgoing heat**Kitchen sink analogy**• Used throughout the book • Read page 26 and understand the analogy • Water flows into the sink at some rate • Water flows down the drain at some rate • As the sink fills the water is heavier and goes down the drain faster • Eventually the sink reaches an equilibrium between inflow and outflow of water**Greenhouse effect**• Water is analogous to energy flowing into and out of the Earth system • Outgoing IR flows faster as the temperature of the earth increases by εσT4 • Greenhouse effect is like a piece of carrot in the drain • Watery (energy) outflow is slower until the level in the sink rises and pushes the water out faster, coming into balance again.**Take home points, Chapter 3**• The outflow of IR energy from a planet must balance heating from the sun. • The planet accomplishes this act of energetic housekeeping by adjusting its temperature • Absorption of outgoing IR light by the atmosphere warms the surface of the planet as the planet strives to balance its energy budget**Chapter four**Greenhouse Gases Why some gases are greenhouse gases, but most aren’t, and some are stronger than others**Models**• In Chapter 3 the Layer Model was an idealization • Chapter 4 and beyond, we will add things to the model one at a time • Before adding atmospheric components, we need to study the gases**About Gases:**• Concentration is the amount of “stuff” in a given volume • Concentration changes as gases expand or contract • Better to use proportions, such as % • The CO2 concentration in the atmosphere is about 0.039% • This corresponds to 390 ppm • ppm is a mixing ratio of CO2 in the atmosphere**Pressure:**• The total pressure of a mixture of gases is the sum of the partial pressures exerted by each gas • Written as pCO2 = partial pressure of CO2 • ppm ≈ μatm • So the concentration of CO2 is approximately equal to the partial pressure of CO2 • 390 ppm CO2≈ 390 μatm CO2**Kinetic Energy:**• Kinetic Energy is ~ equal for all gases • Heavier gases will move slower, depending on their mass • KE = ½mv2 • As the mass gets larger, the velocity of the gas is slower, keeping the KE constant**Gases, Vibrations and Light**• Atoms – the mass is in the nucleus, the electrons are in shells (orbitals) • Outer orbitals participate in sharing electrons, forming covalent bonds • There is an optimal nuclear distance that is low energy • If the nuclei get too close or too far apart, they readjust to the optimal distance • This is a stretching vibration**Molecular vibration**• If a molecule has more than two atoms, there is flexibility in the bond angles • This is a bending vibration • To interact with IR light, the molecule must be electrically lopsided • A charge separation results in a dipole moment • One side is partially positive while the other is partially negative • Written δ+ and δ-**Molecular gases**• Symmetrical molecules with only two of the same atom are never greenhouse gases • O2 and N2 are the two major components of the atmosphere • These gases do not absorb or emit IR light**Simple example:**• The gases NO and CO have their bonding electrons drown toward the more electronegative atom • Electronegativity increases across a period • Electronegativity decreases down a group • Both of these molecules are electrically lopsided, but in low concentrations and not very reactive**Better example:**• 3 or more atoms with two or more bonds (think springs for the bonds and weights for the atoms) • Particularly carbon dioxide, it is symmetrical, but the stretching and bending sets up a dipole moment • Or water that has a permanent dipole**Vibrational modes of a CO2molecule that interact with IR in**the atmosphere.**Vibration modes of a water molecule that interact with IR**light in the atmosphere Water vapor is very electrically lopsided and can absorb and emit lots of frequencies of infrared light.**Figure 4-3**• The solid line is a model generated spectrum of the infrared light escaping to space from the top of the atmosphere • Broken lines are blackbody spectra at different temperatures • Atmospheric window is between about 900-1000 cm-1 where no gases absorb or emit IR light • CO2, H2O, O3 and CH4 absorb IR emitted from the ground and emit lower intensity IR from high altitudes where air temps are colder**How a Greenhouse Gas Interacts with Earthlight**The area under the curve is the amount of emitted IR light**Figure 4-3 is constructed so the area under the curve of a**spectrum is proportional to the total energy flux • You can eyeball the energy change as the area change • This trick works with the jagged spectrum as well, representing the total energy loss of the planet to space • The atmospheric absorption band takes a bite out of the energy lost to space, decrease the area, decrease the outgoing energy • Carbon dioxide absorbs in the middle of the Earthlight • Methane absorbs on the fringes of the Earthlight region • Water absorbs over a wide range of frequencies**Thick and Thin:**• The atmosphere is call optically thick in the 700 cm-1 in the CO2 bend frequency range • The atmosphere is called optically thin in the atmospheric window**The Band Saturation Effect**As the CO2 concentration is increased to 100 ppm, the center of the peak runs into the blackbody curve from just a bit colder than 220K, and it doesn’t get any deeper as the CO2 concentration is raised to 1000 ppm. This is the band saturation effect, the band is the range of frequencies, and the saturation means “used up”, all absorbed by the CO2

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