Environmental Physics PRELIM1

Why do we have seasons?

We have seasons because Earth’s 23.5° axial tilt causes the subsolar point to shift north and south between the Tropics throughout the year. This changes the solar elevation angle and length of daylight at each location, producing the seasons.

Equinoxes & Solstices

March 21 = march equinox
June 21 = summer solstice
Sep 21 = sep equinox
Dec 21 = dec solstice

What is an equinox?

Both hemispheres receive equal day and night (12 hours)

Declination angle

The latitude where the sun’s rays are directly overhead at noon

Why is S_mod bigger in the summer than winter?

Sun is higher, α is larger

When α is larger, α + β is larger, so S_mod is larger S_mod = S₀sin(α + β)

kwh definition

unit of energy; it kwh * hours.

kW = how fast energy is being used/produced

kWh = how much energy is used/produced

Why is module power similar to incident power in the summer but less in the winter?

Because the tilt of the panel is closest to being normal to the solar beam (declination angle) at elevation angles occuring in the summer

Why is incident power less in winter than in summer?

Because the days are longer in the summer. S_incident doesn’t change value btwn seasons; the days are longer so you get more energy per area per day

Units for total enery over the time period of a day

kWhr / m² / day

Why does the total energy per day overestimate?

It assumes:
- it’s always daytime
- it’s always noon

What solar panel orientation receives the most solar radiation on a cloudy day?

Parallel to sky; facing flat up

bc the horizontal gets more energy on cloudy days

What EM radiation is emitted most by the sun?

Visible light

Planck’s Law

Wien’s Law

Wavelength of maximum emissions shifts to shorter wavelengths for higher temperatures

Stefan-Boltzmann Law

Total energy emitted by a m² of an object is equal to a constant times temperature ⁴. E_t = area under each curve

How do we know the temperature of the sun?

We analyze a spectral irradiance graph of the sun and compare it to the spectral insensity distribution of planck’s black-body radiation as a function of wavelength for different temperatures. see what the temperature is of the sun.

Kirchhoff’s Law

For a given temp, whichever wavelengths you emit, you must absorb the same wavelengths — applies to black bodies

Not the same intensity for all wavelengths

Molecular absorption spectra

What does LANDSAT do?

Records electromagnetic radiation reflected off of Earth so we can analyze the surface - can be used to show land use changes, etc

Healthy vs. stressed vegetation reflection landsat

Healthy vegetation: Absorbs most radiation in the visible (VIS) part of the spectrum and reflects radiation in the near infrared (NIR) part of the spectrum

Stressed vegetation: Absorbs less radiation in VIS and reflects more in NIR

(makes sense bc healthier plants do more photosynthesis and stuff, so absorb more visible light)

NDVI & what it means

NDVI = relationship to determine healthy or stressed vegetation

Higher NDVI = healthier vegetation

NDVI can be used to map the density of vegetative cover & track vegetative health throughout growing seasons bc low NDVI = stress

Blackbody model vs sun

Emissivity ε & its effect on Stefan-Boltzmann law

How to compute the TOTAL POWER of an object

Irradiance (E_T) = Wm^-2 = how many joules produced per second for each m²

Total power = E_T * SA_sun = power produced by entire surface of sun

How to calculate solar irradiance that Earth actually receives per 1m² at the top of Earth’s atmosphere

The sun produces its Total Power by the entire surface of the sun in ALL directions, but only a proportion of that actually hits Earth

You get P_total by multiplying the E_T by the surface area of the sun

This is the average incoming radiation for the sun “solar constant”

How to calculate how much total power reaches the top of the Earth’s atmosphere?

Multiply the Solar constant (average irradiance (W/m² )) by surface area of imaginary circle w/ radius of Earth

If the Earth’s albedo is 0.3, how much power actually enters the Earth’s atmosphere

Energy Balance

If E_in = E_out, what should a planet’s temperature be?

How to derive Energy Balance temperature equation

Total power out = power flux emitted by Earth * Earth’s SA

E_out = (E_T⁾ (SA)
E_out = (σT_earth^4₎ * (4πr_earth²)

E_in = (1-A) * (S₀ x πr_earth²)

E_in = E_out

E_in = (1-A) * (S₀ x 4πr_earth²) = (σT_earth^4₎ * (4πr_earth²)
Cancel stuff to get
(1-A) = σT^_earth4

T_earth⁴ = S₀ (1-A) / 4σ

Why is Earth’s surface warmer than the expected temperature of -18?

The sun emits shortwave radiation and is let in through the atmosphere, which is this absorbed by the earth and reemitted as longwave radiation. Atmospheric molecules absorb longwave radiation and reemit it, keeping some energy in the system and causing heat

Solar geoengineering