GEO214 Midterm Class 2.1-2.2

What are the parent questions for class 2.1?

1. Why does the outgoing longwave spectrum seen from space look jagged, with gaps at specific wavelengths?

2. Why is tropical air so much more humid than polar air?

The simple “why’s” for parent questions 2.1

1. Why does the outgoing longwave spectrum seen from space look jagged, with gaps at specific wavelengths?

Greenhouse gases absorb only specific infrared wavelengths → because molecules absorb radiation that matches their vibrational frequency → they work as tuning forks → so only respond to certain frequencies → because only the vibration that changes the dipole movement can interact with IR → so H2O, CO2, CH4, and O3 have IR-vibrations → N2 and O2 do not → because symmetric molecules like N2 and O2 do not have dancing dipoles → so less outgoing IR can escape to space → the photon’s energy is turned into motion = equal → so later new photons are emitted higher in the atmosphere → so higher air is colder than the surface atmospheric layers → because colder air emits less radiation to space → because E = σT4 → so because less energy escapes, Earth will warm toward energy balance

2. Why is tropical air so much more humid than polar air?

Warm air can hold more water vapor than cold air → because evaporation happens faster with higher temperatures → because only the fast moving water molecules can escape from the liquid water into the air (evaporation) → and warming also fuels the energy needed to escape → higher temperatures = increased molecular speed → increased evaporation → the amount of water vapor needed for saturation thus increases with temperature → so warm air therefore has a higher saturation vapor pressure → it takes more water vapor for warm tropical air to become saturated → so it becomes really humid → in comparison to cold polar air which doesn’t have any of this therefore can reach saturation with less water vapor → so trppical air can stay unsaturated while holding a lot more moisture

The in-depth “why’s” for “Why does the outgoing longwave spectrum seen from space look jagged, with gaps at specific wavelengths?”

The main idea is:

• Earth emits infrared longwave radiation

• If that radiation went straight into space with no obstacles, it would be a smooth spectrum as seen in a blackbody curve

• BUT: Instead we see a jagged spectrum with these dips

• Those DIPS are from the atmosphere absorbing some wavelengths while others escape

• This is called the “greenhouse effect”

To understand this, we need to go over some terms.

1. Blackbody Radiation

Any object ABOVE 0 K emits radiation.

The amount that is emitted is denoted as E=σT4, known as the Stefan-Boltzmann Law. Hotter objects = more emitted radiation. λmax​=Tb​, Wien’s Law, also states that hotter objects also = shorter wavelength peak.

• The spectrum should be smooth if the radiation from Earth’s surface went directly to space, if measured at the surface

2. Selective Absorption

Atmospheric gases don’t absorb all wavelengths equally.

Certain wavelengths are absorbed, some aren’t. This is why there is jagged “bites” in the spectrum.

• Imagine a tuning fork. It responds to one frequency. A molecule is essentially the same in that it only absorbs radiation whose frequency matches it’s preferred vibration. If there’s no match, there is no absorption. If there is, there is absorption.

• Non-greenhouse gases such as O2 and N2 do not for this reason.

- This is due to “molecular symmetry”. When they vibrate, the distribution of charges stays balanced so the dipoles don’t “dance”. If the dipoles do not dance, there is no interaction with IR and therefore no absorption. For example, noise-cancelling headphones work by matching the outside noise frequency to the noise coming from your headphones which cancel each other out therefore removing the outside noise.

• “Greenhouse” gasses H2O, CO2, CH4, and O3 all absorb infrared.

- CO2 and H2O are asymmetric with a “bend” in their structure. Thus therefore separates their charges and changes them, which make their dipoles dance. Dancing dipoles make room for IR absorption as it stretches, unlike a symmetric stretch which does not have dancing dipoles.

3. Thermalization

The answer is not simply it “bounces back” with some light going back down, however.

When greenhouse gases absorb the IR photons, that photon energy becomes a vibration which collides with the N2 and O2 surrounding it converting it to kinetic energy. This is what releases HEAT, destroying the original photon. This is thermalization, and is what warms up the atmosphere.

Now, re-emission occurs.

• Increased temperature from thermalization = increased molecular speed

• Increased speed = stronger and faster collisions

• Stronger and faster collisions = light emission, or new IR photons

The culmination: warming.

1. Earth’s surface is warm, radiating infrared upward

2. If the atmosphere was transparent, the radiation would go from the surface to space straight. You could see the warm surface from space

3. But greenhouse gases in the troposphere absorb the IR. Then it thermalizes, then it is re-emitted

4. But because the greenhouses gases are at the surface, the newly created IR photons are absorbed over and over by the gases

5. So photons cannot escape within the troposphere

6. However, the higher you go the less greenhouse gasses there are as the air gets thinner

7. When the air is thin enough, so the concentration of greenhouse gases has decreased enough, the photons can finally escape. This is called the emission height

8. But now when you look down from space, you don’t see the surface but you see the upper cold troposphere

9. And according to Stefan-Boltzmann, colder things emit less radiation, so a colder emission height = less outgoing longwave radiation

This leaves an energy imbalance, where the incoming solar radiation from the Sun is the same but the outgoing radiation from the Earth is smaller.

• Energy in > Energy out

• This means the planet will continue to warm until the energy leaving, which is colder than the energy coming in, is equal to the incoming energy temperature from the Sun

The in-depth “why’s” for “Why is tropical air so much more humid than polar air?”

We know that warm air can hold more water vapor than cold air. But why?

1. Evaporation

Where a water molecule has enough kinetic energy to break free of the strong hydrogen bonds.

For the needed kinetic energy, a molecule must be very fast. But what makes it fast?

2. Temperature

The temperature of a molecule controls it’s speeds, as denoted by the Maxwell-Boltzmann distribution.

• Some molecules are fast, some are slow

• When temperature increases, the area under the curve exceeds the threshold needed for breaking hydrogen bonds exponentially

3. Clausius-Clapeyron Relation

The law that states that the saturation vapor pressure increases exponentially with temperature, as stated above,

• The saturation vapor pressure (esat​) is the maximum vapor pressure air can support at a given temperature before condensation begins.

• Warm air has a higher esat, cold air has a lower esat.

• So, tropical air can hold much more moisture before becoming saturated.

• Vapor pressure (e) is the partial pressure exerted by water vapor alone.

Tropical air is therefore more humid because at higher temperatures:

• The molecules move faster, building enough energy to break the hydrogen bond

• The broken hydrogen bond is evaporation

• Because evaporation is happening at higher rates, much more water vapor is needed to hit saturation. Hence, the saturation vapor pressure is higher

Note: Water vapor is a feedback, not a forcing

• Temperature controls water vapor, water vapor does NOT control temperature

As CO2 increases first, the Earth warms, and that warmer air can hold more H2O.

The more H2O there is, as a greenhouse gas, the more warming.

Thus, water vapor is a positive feedback.

What are the parent questions for class 2.2?

1. Why does indoor air feel so dry in winter, even when the outdoor air is humid?

2. Why is the observed tropospheric temperature profile nearly linear with height, rather than the exponential-like profile that pure radiative equilibrium predicts?

3. Why does a rising dry parcel cool at roughly 10 K per km?

The simple “why’s” for parent questions 2.2

1. Why does indoor air feel so dry in winter, even when the outdoor air is humid?

Cold outdoor air can’t hold much water vapor → because it has a low saturation vapor pressure → since temperature controls saturation → so when cold air comes indoor, we heat it → that increases the water vapor it can hold, even though we didn’t add more water vapor → the moisture stays the same but the capacity it can hold goes up → so relative humidity drops → RH being the comparison between present vapor and storage capacity → low RH makes the air feel dry → so our skin, throats, and noses lose moisture faster

2. Why is the observed tropospheric temperature profile nearly linear with height, rather than the exponential-like profile that pure radiative equilibrium predicts?

Radiation by itself cools the atmosphere too strongly with height → because the surface absorbs most of the sunlight and warms it → and since warm surface air becomes buoyant and rises → since warm air is less dense than cold air → the rising air then transports the heat up through convection → which mixes the atmosphere vertically → but the atmosphere cant stay steep and unstable with respect to its temp profile → so convection adjusts the profile toward a stable one → this creates a shallow, linear temp that decreases with height → because the real troposphere is controlled by both convection and radiation, not the exponential radiation alone

3. Why does a rising dry parcel cool at roughly 10 K per km?

Air rises → pressure around it decreases → because less air above it pushing down → so the parcel expands to match the surrounding pressure → which requires work → so the parcel uses its own internal energy to do work → because energy used for work isn’t available as temp anymore → thus the parcel cools → which happens without exchanging heat with surroundings → called adiabatic process → because gravity controls how much pressure changes with height → and heat capacity controls how much temp changes for some amount of energy loss → which gives the dry adiabatic lapse rate of 10 K/km

The in-depth “why’s” for “Why does indoor air feel so dry in winter, even when the outdoor air is humid?”

If the air outside was:

• temperature = 0°C

• relative humidity = 100%

Then the air is saturated. It’s humid outside because the air is holding it’s maximum capacity for water at that temperature. Cold air, however, cannot hold as much water vapor. It has a low saturation vapor pressure, which means even at 100% RH the actual amount of water vapor cold air is holding is small (especially in comparison to hot air).

This is the Clausius-Clapeyron relationship: where warmer air has a higher saturation vapor pressure, and colder air is vice versa.

Now imagine that air came inside and is heated to 20°C.

• Note that only heat was added, not water

• So the vapor pressure is the same, but something isn’t

We know hot air holds more moisture, so now that same air which didn’t hold much water vapor before now has the ability to hold more moisture. However, the amount of moisture currently in it did not change.

But then why does it feel dry indoors in the winter, even when the air outside is humid?

Because that dry air begins to pull the moisture from your:

• Skin

• Nose

• Throat

• Eyes

So all of those feel dry, because the air inside has the same low moisture from the cold outside air.

THINK, the outdoor winter air is cold so it’s humid because it’s capacity to hold water vapor is smaller so it is closer to saturation. When that relative humidity changes from a colder temperature with low capacity to a hotter temperature inside with a high capacity it just means a 6oz cup with 1oz of water in it became a 12 oz cup with that same 1 oz in it. So the air is drier, because the 6oz cup has more water in it relative to it’s size than the 12oz cup even though it’s the same amount of water. As such, the air is drier and thus the moisture is pulled.

The in-depth “why’s” for “Why is the observed tropospheric temperature profile nearly linear with height, rather than the exponential-like profile that pure radiative equilibrium predicts?”

If the atmosphere were solely controlled by radiation, this is what would play out.

• The sun emits shortwave radiation as sunlight

• The surface absorbs all sunlight, warming it

• The Earth’s surface would emit it’s infrared back upward

• The IR meets the atmosphere however, which absorbs it (greenhouse gasses)

• So after the atmosphere absorbs the IR, with the greenhouse effect, everything below remains heated as that’s the source while everything above begins to cool exponentially the farther you get from the troposphere

Thus, an atmosphere with only radiation as a control would exhibit exponential cooling with no other input.

However, reality is not that simple. The troposphere cools linearly at a rate of 6.5 K/km, and that means there is another input other than radiation. What is it?

That input is convection. This is the play:

• The sun warms the surface

• The warm surface heats the air directly above it

• Warmer air is less dense, becoming positively buoyant and rises

Before, heat moved only by radiation but now the convection input provided a new mode of transport for heat. The warm air parcel carries the heat upward, mixing with the atmosphere above, preventing the steep temperature gradient as the warm buoyant air mixes.

The in-depth “why’s” for “Why does a rising dry parcel cool at roughly 10 K per km?”

First, begin with an air parcel.

• It rises when it is warmer than the surrounding air

• It expands as it rises as the pressure decreases with height

• This expansion requires work, as the outward push takes energy

• But that energy comes from the parcel’s own internal energy and nowhere else

• Thus, as the internal energy begins to decrease there is less energy for the molecule to move fast, and slower molecules are colder than fast moving molecules

• So the once fast and hot molecule begins to slow down and cool

Think of a moving wall. If the molecule hits a wall moving away from it, it’ll bounce off but pretty slowly because it’s energy is given to the moving wall. Same thing happens with parcel expansion as the boundary is moving away from the molecule, thus losing speed and dropping it’s temperature.

Adiabatic, which means no heat exchange, is what the air parcel experiences. The parcel rises quickly enough that cooling happens from the work of expansion and not the transfer of heat. Thus, the process is adiabatic.

According to the first law of thermodynamics, energy cannot be created or destroyed but can be changed. So, the change in energy = heat added, or dU = Q, but that would mean the only way energy could change is by heat. However, the adiabatic process puts a wrench in that law because the parcel still cools even when no heat is removed or added. So, what’s missing?

Work is what is missing, as we said before. Expansion requires work as to expand, the air parcel must push on the surrounding air. The process of pushing needs energy, so that transfer of energy is therefore called work. Now, the law of thermodynamics is changed to add work: dU = Q - W.

So, since the internal energy drops as work is done, and temperature is the average molecular kinetic energy, less energy therefore means the temperature will drop and the parcel cools.