EOSC 340 Midterm terms

stock

amount of something residing in a particular place at a particular time

flow

rate at which stuff is added or subtracted from a stock

• since it is a rate, it includes the time “per month”

inflow

rate of stuff flowing in

outflow

rate of stuff flowing out

feedback

system’s components interact in a way that again influences the same stock

rate of change in stock

difference between inflow and outflow

• d(stock)/dt = Flow_in - Flow_out

when stock is in equilibrium

no change in stock over time

Flow_in = Flow_out

amplifying feedback

response to a forcing that pushes the system in the same direction as original forcing

• i.e. global warming melts Arctic permafrost, which releases methane (GHG) causing further warming

stabilizing feedback

response to a forcing that pushes the system to respond in the opposite direction, counteracting the forcing, helping move the system toward equilibrium

How do you know when the stock is highest or lowest based on flows/rates? (People in store example)

electromagnetic radiation (EM)

oscillations of both electrical and magnetic fields propagating at the speed of light

what is the range of visible light, and does longer or shorter wavelength mean red light?

visible: 380-750 nm in wavelength

red: longer wavelength

where is the infrared range relative to visible light?

wavelengths just longer that the visible light range

• infra-red = “below”-red

• n (wavenumber) = 1/lambda (wavelength)

power definition and units

rate energy is being used or transferred

• W = J/s

energy flux definition and units

rate energy is transferred through and surface

• W/m²

Plank curve

The radiation that an object absorbs and emits → emission described by planck function

• x-axis can be in wavelength or wavenumber

define blackbody

able to absorb all wavelengths or EM radiation

how do you find total energy flux using the Planck function?

calculate the area under the curve (integrate curve)

What is the Stefan-Boltzmann equation, and how does it relate to the Planck curve?

• I = εσT⁴ ( where σ = 5.67e-8 W/(m²K⁴), and ε is the ratio of energy emitted compared to blackbody)

• when ε = 1 the object is a blackbody

• when ε < 1 the object is a graybody

What is Wien’s Law?

The wavelength of the maximum emission (peak of Planck’s curve for that object) depends on temperature (T)

• λ_max = b/T (b = 2898 μm K)

• Works for both grey- and black-bodies

• Hotter objects peak at shorter wavelengths (closer to solar wavelengths)

how does energy conservation tells us about radiation hitting a material?

radiation is reflected/albedo (α), absorbed (abs), and transmitted (tr)

what is Kirchhoff’s Law?

a body’s absorptivity equals its emissivity (abs = ε) under thermal equilibrium.

based on the second law of thermodynamics ( it is not possible for heat to transfer from a cooler body to a warmer body without external work)

How is the Earth’s climate system (stock of heat energy) expressed?

dE/dt = I_in - I_out

• determines whether or not Earth’s climate is accumulating or losing heat over time

What is the solar constant, and what does it depend on?

• S = 1360 W/m² (total energy received from the sun per unit area)

• Depends on solar output and the Sun-Earth distance

What is the average incoming solar flux of Earth?

circular cross-sectional area (πR²) is distributed over a spherical area (4πR²), therefore the avg solar flux S/4 = 340 W/m²

What is the inverse-square law in relation to solar energy?

• amount of radiation per unit area is inverse the square distance

• i.e. doubling the Sun-Earth distance reduces incoming radiation by a factor of four

describe Planck Feedback

When there is an imbalance of energy on Earth (cooling or warming the Earth), the change in temperature changes the outgoing thermal radiation until I_out = I_in

Is the Plank Feedback a stabilizing or amplifying feedback?

stabilizing

What is albedo?

the fraction of incoming solar radiation that is directly reflected back into space

• across surfaces (ice, forests, oceans, and deserts)

How does urbanization and deforestation change Earth’s albedo?

• urbanization = lower albedo

• deforestation = higher albedo

what are some things humans are doing to increase albedo (counteract warming)?

painting roofs white, glacier blankets, marine cloud brightening (MCB)

Describe Marine cloud brightening

geoengineering to cool earth by increasing the reflectivity (albedo) of low-lying marine clouds

• Spraying sea salt into clouds causes water vapor to condense into smaller droplets (rather than large ones), which makes the clouds denser, whiter, and more reflective.

selective absorption of greenhouse gases

• high absorptivity and emissivity in longwave (thermal) spectrum

• low absorptivity in the shortwave (solar) spectrum

How are greenhouse gases energy trapping?

they let incoming solar radiation through while absorbing outgoing thermal radiation from the surface. This absorbed energy is emitted both upward and downward, trapping heat

what is the greenhouse effect?

GHE = I_LW_{leaving_surface} - I_LW_{leaving_TOA} (W/m²)

• difference in fluxes

Does the greenhouse effect violate the second law of thermodynamics?

no, because the earth-atmosphere system is not an isolated system, the surface is warmer because it absorbs incoming solar radiation that passes straight through the atmosphere

what happens when an extra layer of GHGs are added to the atmosphere?

1. The system temporarily goes out of equilibrium (dE/dt doesn’t equal zero).

2. The Planck feedback, the top layer adjusts first then the lower atmospheric layers, then finally the surface

3. The layers reach a new, warmer radiative equilibrium

What is fundamental difference between climate forcing and climate feedback?

• forcing originates from outside the climate system

• feedback initiated inside the system where a in one component triggers a response in another.

What are major GHGs?

• water vapor (H2O)

• carbon dioxide (CO2)

• methane (CH4)

• nitrous oxide (N2O)

Why is the impact of ozone (O3) on Earth’s radiative balance considered complex compared to other GHGs

the ozone absorbs in the LW spectrum, but it also absorbs in the shortwave spectrum (especially in stratosphere)

what is the “atmospheric window"?

A specific wavelength range (~8 to 13 microns) where atmospheric gases have very low absorption, allowing thermal radiation from Earth’s surface to escape out to space

If two non-reflective layers with emissivity are stacked and intensity is shone through them, how much energy is absorbed by the first layer?

εI_o

what is brightness temperature?

The temperature a blackbody would need to be to emit the observed flux in a particular wavelength band

• The temperature of an object if ε = 1

• T_B = (I/σ)^1/4

what is the kinetic temperature?

The temperature a greybody object ε < 1

• T_k = (I/εσ)^1/4

How does the actual (kinetic) temperature compare to the brightness temperature?

T_k > T_B because an object appears colder than it actually is from a flux perspective since it radiates less energy than ideal blackbody.

how much energy is absorbed by the second layer?

I₂ = ε(1-ε)I_o because the first layer transmits an intensity of I₁ = (1-ε)I_o to the second layer

what are the two core equations required to solve energy balance diagrams and compute planetary temperatures?

1. I_in = I_out (applied at equilibrium)

2. I = εσI (σ = 5.67e-8 W/(m²K⁴)) to convert energy fluxes into temperatures

what happens to the energy transmitted through an atmospheric layer when its emissivity is increased?

The amount of radiation absorbed within the atmosphere increases, which causes the amount of radiation transmitted through it to decrease

What is the cumulative effect of adding more GHG layers or increasing emissivity on the climate system?

It enhances the GHE, decreases longwave cooling escaping to space, and increases the temperature of all atmospheric layers and the surface/layer below.

which GHG is considered the strongest?

water vapor (strong around 6 microns and 18-30 microns)

why is water vapor the strongest GHG?

because it absorbs the widest portion of the longwave spectrum

what are the primary wavelengths or wavenumbers where CO₂ predominantly absorbs?

mostly around 15 microns (~600-800cm^-1)

What are the primary wavelengths or wavenumbers where CH₄ predominantly absorbs?

mostly around 7 microns

what are the primary wavelengths or wavenumbers where O₃ predominantly absorb?

absorbs significantly around 10 microns (1000 cm^-1), unique narrow spike

what is the atmospheric window?

region of wavelengths between ~800-1000cm^-1 (~10-12 microns) where total atmospheric absorptivity is very low, allowing thermal radiation from the surface to escape directly out to space

What is the difference between “broadband emissivity” and “narrow band/spectral emissivity”?

• Broadband uses a single average (ε) for all longwave wavelengths

• Spectral measures absorption within a band for individual gases (using a tool like Modtran)

How can satellite instruments or models like Modtran determine the brightness temperature of a specific GHG layer?

By measuring the longwave radiation flux emitted at a specific absorption band and calculating the temperature an ideal blackbody would need to produce that exact flux (T_b = (I/σ)^1/4).

When a satellite measures upward longwave radiation looking down at the Earth, what do the drops in the spectral curve (absorption bands) represent?

They represent energy emitted the surface that has been absorbed by GHGs in the atmosphere, as well as the cooler thermal radiation emitted upward by those gases themselves

why is the upward radiation emitted by CO₂ reaching the top of the atmosphere significantly less than the total energy absorbed from the surface?

Because CO₂ emits absorbed energy isotropically (both upward to space and downward toward the surface), meaning roughly half of the absorbed energy goes down rather than up.

compare wavenumber Planck Curve looking down from above versus looking up from ground.

important to look within atmospheric window to find surface surface temperature.

how do you use the atmosphere and ground radiation to find the radiation emitted by the ground that is absorbed by GHG in atmosphere?

which GHGs are mostly absorbing at 600-800 cm^-1

• water vapor and CO₂

why is there a spike in the ozone band?

transparent line at 10 microns (1000 cm^-1)

What is the band saturation with respect to carbon dioxide (CO₂)?

after ~10 ppm, the absorption band in the center does note get any deeper because every photon at those wavelengths is already absorbed by the CO₂ layer

If the center of the band is saturated, how does increasing CO₂ concentration still increase absorption?

higher concentrations increase molecular collisions, causing low-probability absorption events to increase at the edges of the absorption band (where e < 1), making the band wider.

why is radiative forcing a logarithmic function of CO₂ concentration rather than linear?

since the band is saturated and absorption only increases at the edges, radiative forcing scales with the logarithm of concentration (Δ F ∝ ln (new/old)).

what is a fractional doubling?

the ratio of new to old CO₂ concentrations divided by natural log of 2, representing the number of doublings (x doublings means multiplying concentration by 2^x)

according to radiative forcing for CO₂ concentrations, what is the radiative forcing increase for every complete doubling of CO₂?

exactly 3.8 W/m² (since ln(2)/ln(2) = 1 when multiplying by 3.8)

How many doublings occur in a tripling of CO₂, and how is it calculated?

~ 1.6 doublings, calculated as x = ln(3)/ln(2) = ~1.585

what is the difference between climate forcing and a climate feedback?

• forcing = outside the coupled ocean-atmosphere-biosphere climate system

• feedback = initiated inside the system where one component changes another

what major modern climate forcings have the highest scientific uncertainty?

aerosol-related forcings (specifically aerosol-cloud interactions) carry the largest error bars and uncertainties.

How do proposed climate solutions like stratospheric aerosols and marine cloud brightening affect radiative forcing?

they act as cooling shortwave forcings by increasing Earth’s albedo (reflecting more incoming solar radiation back to space).

what are stratographic aerosols?

tiny solid particles or liquid droplets suspended in the stratosphere

• found 10-50 km above surface

how do proposed climate solutions like stratospheric aerosols and marine cloud brightening affect radiative forcing?

They act as cooling shortwave forcings by increasing Earth’s albedo (reflecting more incoming solar radiation back to space)

Why can diatomic molecules like N₂ and O₂ act as major atmospheric constituents yet not be greenhouse gases?

because symmetric diatomic molecules cannot absorb radiation in the longwave (thermal) spectrum

why is CO₂ a much more important long-term climate forcing than water vapor?

water vapor has a short atmospheric half-life (~9 days) and condenses out as rain, meaning its concentration is controlled by temperature (making it an amplifying feedback, not forcing). Whereas CO₂ is a long-lived forcing that stays in the atmosphere for centuries

how many times smaller is CH₄ emissions compared to CO₂?

CH₄ is 300x smaller than CO₂

why is methane (CH₄) considered a powerful GHG despite having much lower emissions by weight then CO₂?

methane is less band-saturated and is more powerful (over 20-year timescale, 1 tonne traps ~80x more heat than CO₂), though it has a shorter atmospheric half-life (~10 years).

what is the half life of CH₄ and why?

• ~10 years

• thermodunamically unstable; therefore, it oxidizes into CO₂ and H₂O

  • CH₄ + O₂ → CO₂ + H₂O

what is 1 ppm CO₂ in Gt and GtC?

7.6 Gt CO₂ = 1 ppm CO₂

2.1 Gt C CO₂ = 1 ppm C (carbon)

where does most of the water in the atmosphere sit?

below 10km

• looking at or below 10km is both CO₂ and water vapor

• looking above 10km is mostly CO₂ emission