EPS 7: Climate Change Midterm 1

James Watt

He is basically how global warming began

He figured out how to make steam engines much more efficient

- He made industrial factories possible

- His steam engine delivered power

British Industrial Revolution

1700s in Britain

- The scientific revolution and the Age of Enlightenment

- Abundant coal

- James Watt's steam engine efficiency augmentation

Newcomen engine

Invented in 1712

- Heats and cools a single piston with each cycle

- Uses steam condensation to create a partial vacuum

- Invented by Thomas Newcomen

In 1763, James Watt was given the task of fixing a model of a Newcomen steam engine

- He figured out that he could condense the steam in a separate cold chamber, dramatically increasing efficiency

Watt

A unit of power (energy per time)

- The power required to lift one kilogram by ten centimeters every second = 1 watt

- You can make a Watt

James Joule

He discovered the conservation of energy

- He figured out how mechanical work gets converted to heat, conserving energy

- He studied energy and where it goes

Joule

A joule is a unit of energy

- The energy required to lift one kilogram by ten centimeters = 1 Joule

- You can make a Joule

Watt and Joule equations

1 Watt = 1 Joule per second

Convection

Liquid or gaseous matter moves, carrying Joules of energy with it

The movement caused within a fluid/gas by the tendency of hotter and therefore less dense material to rise, and colder, denser material to sink under the influence of gravity, which consequently results in transfer of heat

Conduction

Matter gives Joules of energy to neighboring matter by jiggling against it

The process by which heat is directly transmitted through a substance when there is a difference of temperature between adjoining regions, without movement of the material

Radiation

Matter gives away Joules of energy by emitting photons from its surface

- A process: the transmission of energy by fast-moving elementary particles

- Particles that can radiate (i.e. transmit energy) include electrons, protons, neutrons, and photons

Examples of conduction

Hot handle of a skillet

Hot water pipe

Cold window in the wintertime

Cold handshake

Examples of convection

Hot air balloon

Rising cloud

Fire

Cold air pouring into an open window in the wintertime

Examples of radiation

Sun heats the Earth

Heat lamp heats a person

Laser burns paper

National Ignition Facility at LBNL

Convection oven

It's a regular electric oven with a fan

- Conduction operating over a large distance has slow heat transfer and vice versa

- The fan speeds up the transfer of energy form the heating elements to the toast

How Earth receives and expels energy

Radiation

- Sun radiates Earth and space

- Earth radiates space and gets radiation from the sun

Conduction: matters at the surface, moving heat from the surface into the air

Convection: matters in the atmosphere, moving heat upward within the atmosphere

Radiation: matters at the surface and in the atmosphere, moving energy everywhere

Fahrenheit

0˚F is where salty water freezes

- Stupid

Celsius

0˚C is where pure water freezes

- Stupid

C = (F -30)/2

Kelvin

0˚K is where there is no heat, so there is no kinetic energy, so nothing moves (absolute zero)

- Physics equations use Kelvin

K = C + 273

- Celsius to Kelvin conversion

Basic temperature bench marks in Kelvin

- 0˚K is absolute zero

- 273˚K water freezes

- 280-300˚K is Berkeley

- 288˚K is Earth

- 373˚ water boils

- 450˚K is baking a cake

- 650˚K + is supercritical

- 750˚K is an oven self-clean cycle

- >1000˚K is fire

- 6000˚K is the sun

How to deal with units in an equation

1. Multiply and divide to make units work

2. As needed, multiply by clever versions of 1

Electromagnetic radiation

Radiation by photons

- It's both a particle and a wave (oh, joy)

- The particle is called a photon

- Photons are massless, but have energy

- They all travel at the speed of light

Other names for photons

Radio wave, microwave, infrared radiation, visible light, UV, X-ray, gamma ray

- They're still just photons

How photons are generated

Jiggling particles (electrons, atoms in a molecule, or the molecules themselves) generate photons

Particles, ready to be jiggled, absorb photons

Speed of light

300 million m/s or 600 million mph

- Nothing is faster than light

- That is the universe's speed limit

Wavelength

The distance between adjacent peaks or the distance between adjacent troughs

- Greek letter is lamba λ

Radiowaves

Wavelength of 1-10 meters

- Invisible photons

- Emitted by radio and TV towers

Microwaves

Wavelength of 10-40 cm

- Invisible photons

- Emitted by cell phones and microwaves

Visible light

Wavelength of 0.4 - 0.7 microns (blue to red)

- Visible photons

- Emitted by the sun and a light bulb

Infrared radiation

Wavelength of 3-30 microns

- Invisible photons

- Emitted by Earth and humans

- Ex: sitting next to a fire, sitting under a heat lamp

Micrometer

1 micrometer = 1 micron = 1 millionth of a meter = 1 µm (mu)

Wilhelm Wien

In 1911, he won the Nobel Prize in Physics

- In his laboratory, he discovered how the temperature of an object relates to the peak wavelength of light it emits

Peak wavelength equation

Wien's law

- All objects emit radiation

- Wien's law tells us the peak wavelength of that radiation (in microns)

Peak wavelength = (3000 µm K)/T

T is temperature in K, which cancels out with the top units, leaving only µm for a unit

Solar radiation

The Sun has a peak wavelength of 0.5 µm by Wien's law

Scattered light

The rose problem

- The rose strongly absorbs visible colors other than red from the sun, scatters red light, and emits infrared light that we can't see

Things that have color because they strongly absorb all the other colors and scatters only the colors they don't absorb

Shortwave

Radiation that is emitted by the Sun

- Its wavelengths are short (around 0.5 microns)

- 6000˚K

- Very little overlap with longwave

Longwave

Radiation that is emitted by a planet

- Its wavelengths are long (around 10 microns)

- 288˚K

- Very little overlap with shortwave

Power per area

Radiation is emitted by surfaces

- So, the more surface area, the more radiation

Total power = (Area) * (Power per area)

- Where Area = m^2

- Where Power per area = W/m^2

Stefan-Boltzmann Law

Total power radiated

Power per area = 5.67 * (T/100)^4

- T is temperature in Kelvin

Or, you know, 6 if we're being lazy

Blue vs. red star temperatures

By Wien's law, the blue star has a high temperature because it has a shorter wavelength

The Stefan-Boltzmann law then tells us that the blue star emits more power than the red star

Rocky planets

MVEM

- Mercury

- Venus

- Earth

- Mars

4 rocky planets that are close to the Sun

Gas giants

JSUN

- Jupiter

- Saturn

- Uranus

- Neptune

4 gas giants that are far from the Sun

Mercury

The smallest planet in the solar system

- Closest to the sun

- 88-Earth-day year

- No atmosphere

Total solar irradiance (TSI)

The amount of radiant energy emitted by the Sun over all wavelengths that falls each second at the top of Earth's atmosphere

- Earth's TSI is 1360 W/m^2

Different planets have different TSIs because they are different distances from the sun and have different surface areas

- Area of a planet's surface is 4πr^2

- Area of a shadow is πr^2

For every m^2 of TSI that is intercepted by a planet, there are 4m^2 of planetary surface

If we denote TSI by S, then the average sunlight intercepted by the planet's surface is S/4

Albedo

Not all incident sunlight is absorbed

Albedo is the fraction of sunlight reflected into space

Climate of Mercury

Key parameters to sorting out the climate of Mercury

- Albedo: 7% (dark surface)

- TSI = 9,080 W/m^2 (close to the sun)

- Factor of 4 planet-to-shadow makes this 9,080/4 = 2,270 W/m^2

- Mercury's 7% albedo means that (1 - 0.07) * 2,270 = 2,110 W/m^2 absorbed

Stefan-Boltzmann Law

- 2,110 = 5.67 * (T/100)^4

- Temperature that solves this equation is 440˚K

Mars

The second smallest and last of the rocky planets

- 687 Earth-day years

- Very little atmosphere

Climate of Mars

Key parameters for sorting out the climate of Mars:

- Albedo: 25% (darkish surface)

- TSI: 586 W/m^2 (far from the Sun)

- Factor of 4 (planet-to-shadow) makes this 586/4 = 146 W/m^2

- Mar's albedo of 25% means that (1 - 0.25) * 146 = 110 W/m^2

Stefan-Boltzmann law:

- 110 = 5.67 * (T/100)^4

- Temperature for Mars that satisfies this equation is 210˚K

Climate of Earth

Key parameters for sorting out the climate of Earth:

- Albedo: 30% (darkish surface)

- TSI: 1360 W/m^2 (nice sunny days)

- Factor of 4 (planet-to-shadow) makes this 1360/4 = 340 W/m^2

- Earth's albedo of 30% means that (1 - 0.3) * 340 = 238 W/m^2

Stefan-Boltzmann law:

- 238 = 5.67 * (T/100)^4

- Temperature for Mars that satisfies this equation is 255˚K

- This prediction is pretty far off from our actual temperature of 288˚K

- The prediction by this calculation would have Berkeley as colder than Oymyakon, Siberia, the coldest settlement on Earth

Earth's atmosphere

It's about 10 km thick

- It's made of nitrogen molecules (N2) and oxygen molecules (O2)

- Dry air is composed of 20% oxygen and 80% nitrogen

Reasons for N2 being a primary component of Earth's atmosphere

N2 doesn't like to stay in the magma in which it is produced, so it enters the air

It also does not like to chemically react with stuff

So, nitrogen accumulates above the surface, forming an atmosphere

Reasons for O2 being a primary component of Earth's atmosphere

Cyanobacteria (a.k.a. blue-green algae)

The Great Oxygenation Event (Catastrophe)

- 2.4 billion years ago, cyanobacteria began to photosynthesize and produce oxygen

- However, oxygen in high quantities is toxic, so there was mass extinction

- Also oxygen destroys greenhouse gases, so the Earth froze

Deep atmosphere

The pressure is equal to the weight per area of the overlying air

- Think about the deep ocean and how the pressure is equal to the weight per area of the overlying water

Atmospheric pressure

At the top of the atmosphere, pressure is low

At the bottom of the atmosphere, pressure is high

At the surface, the atmosphere is exerting 10 tons per square meter of pressure

- This is why suction cups work

Bars of pressure

10 tons/m^2 corresponds to 1 bar of pressure

- 1 bar = 1000 millibars (mb) of pressure

Weather and pressure

High pressure results in sunny, fair weather

Low pressures results in cloudy, rainy weather

Typhoon Tip in 1979 had only 8.7 tons of air per square meter

- 870 mb

Ideal gas law

p∝NT

- Pressure is proportional to the number of gas molecules at a given temperature

- Pressure: force per area on a surface from the gas molecules bouncing off of it

- Proportional to: means that these are equal up to a multiplicative constant

- Number: the number of gas molecules per volume

- Temperature

Dalton's law of partial pressures

States that the total pressure of a mixture of gases is equal to the sum of the pressures of all the gases in the mixture

N = N1 + N2 + N3

- If three different gases mixed together

p1 ∝ N1 T, p2 ∝ N2 T, p3 ∝ N3 T

- Then each satisfies its own ideal gas law

p = p1 + p2 +p3

- And the partial pressures simply add up to the total pressure

Example that sums it up:

Air with some water vapor in it

N = Nnitrogen + Noxygen + Nwater

- If Nnitrogen/N = 78%, Noxygen/N = 21%, Nwater/N = 1%

- And pressure = 1000 mb

- Then pnitrogen = 780 mb, poxygen = 210 mb, pwater = 10 mb

Clausius-Clapeyron equation

Sometimes a water molecule at the surface of liquid moves so fast, it shoots off from the surface

- Clausius-Clapeyron tells us the pressure of those molecules shooting off from the surface

pv*(T) = Clausius-Clapeyron expression

Ideal gas law & Clausius-Clapeyron equation

"v" stands for water vapor

- Also "*" tells us that the equation is for liquid

pv ∝ Nv T (ideal gas law)

- This is the pressure of water molecules in the air

pv*(T) (Clausius-Clapeyron expression)

- Pressure of water molecules shooting off a liquid surface at the temperature T

Saturation vapor pressure

pv*(T) = pv

This is the pressure of the vapor in the gas phase when the air is saturated

Saturation

Saturation is a steady state, where the gaseous water molecules get stuck to the liquid surface at the same rate the liquid water molecules escape the liquid surface

pv*

pv* star is a function of temperature only

- It's higher for warmer temperatures

- It increases exponentially with temperature by 7% per degree Kelvin

Relative humidity (RH)

pv gives the rate of water molecules sticking to the liquid surface

- It's given by the ideal gas law

RH = pv/(pv*)

pv* gives the rate of water molecules fleeing the liquid surface

- It's given by the Clausius-Clapeyron equation

If RH < 1 then pv* > pv, so water evaporates

If RH > 1 then pv* < pv, so water condenses

If RH = 1 then pv* = pv, so we have saturation

Evaporation

pv* > pv

Water molecules leave the liquid surface faster than they are replaced

Boiling

pv* > p

The saturation vapor pressure exceeds atmospheric pressure, so evaporation causes bubbles of vapor to form

- Boiling water is exactly what boiling water is doing because it's strong (e.g. steam engines)

Raising the temperature or lowering the total pressure (p) will cause boiling because pv* will exceed pressure

Condensation

pv*(Tglass) < pv

Water molecules stick to it from the air at a faster rate than they shoot off the surface

- Therefore, we get net condensation

Snow and frost formation

pv* is very small at cold temperatures

- If pv tried to be bigger than pv*, we would get snow or frost formation

So: pv < the small pv*

Directionality and temperature

Hot air rises, and cold air sinks

Hot fluid rises, and cold fluid sinks

Atmospheric air temperature and directionality

It's inverse logic in the atmosphere

- The higher up you go, the cold it gets (think of a mountain top)

Height and temperature

Why is there a difference between hot air rising in a house but not in the atmosphere?

Basically the height difference

- Houses are short: the pressure is basically the same in the attic as in the basement

- The atmosphere is tall: the pressure in the upper atmosphere is about 1/10th as much as the pressure in the lower atmosphere

Height and temperature in Earth's atmosphere

The Earth's atmosphere is low pressure at the top of the atmosphere, but high pressure at the bottom

Rising hot air moves to lower pressure, expands, and cools

- Pressurizes

Sinking cold air moves to higher pressure, compresses, and warms

- Depressurizes

When air rises in the atmosphere, it gets cold compared to where it came from

But whether a parcel of air rises or sinks depends on whether it is hot or cold compared to its immediate surroundings

Lapse rate

The rate at which temperature decreases with an increase in altitude

- The slope of the temperature profile

- Air parcels cooling off due to depressurizing

The atmosphere adjusts to have the same lapse rate as the convecting air parcels

For a dry atmosphere, the lapse rate is 10˚K/km

For an atmosphere with water, the lapse rate gets modified to about 6.5˚K/km

- As the air rises, it cools, so pv*(T) decreases until RH =1

- Where RH first equals 1, liquid drops are first formed

- This is the "cloud base"

Clouds

In the base of the cloud, liquid water is beginning to form because the RH = 1

Higher up in the cloud, water vapor condenses and releases heat

- As much heat as would be required to boil that same amount of water

- For every kilometer for ascent, the condensation heats the air by about 3.5˚K

- Thus, the cloud cools by depressurization by 10˚K/km, but heats by 3.5˚K/km from condensation

This gives lapse rate of 6.5˚K/km for an atmosphere with water vapor

- (10 - 3.5) = 6.5˚K/km

When air rises a significant distance, it becomes cloudy

Water vapor take away

Water vapor is a powerful fuel that is capable of heating air by several tens of degrees Kelvin

Reason Earth is so different from Mercury and Mars

It has an atmosphere

How the atmosphere interacts with radiation

1. It scatters some shortwaves (we have already accounted for this by using an albedo of 0.3)

- Evidence for atmospheric scattering of shortwave radiation is that the Sun is orange and the sky is blue

- Scattering by small molecules > Rayleigh scattering > short wavelengths are scattered > the sky is blue

- Also, clouds are visible from space

- Scattering by big cloud drops > Mie scattering > all wavelengths are scattered > clouds are white

2. It absorbs and emits longwaves (we haven't accounted for this yet)

- Evidence for atmospheric absorption and emission of longwave radiation is that we can't use our eyes to see infrared

- Water, like most solids and liquids, is opaque in the infrared, and our eyes are basically balls of water