Atmos 1020 Lecture Slides 2/5 and 2/7 2020 The Sun is a weakly variable star, and its energy fluctuates. Over the course of about 11 years ( the solar sunspot cycle) , the Sun’s emitted energy varies on average about 0.1 % Venus is 107 Million Km (1.07x1011m) from the sun.
Area of the enclosing sphere is 1.44x1023 m2
So then take the total energy output of the sun and divide by the area of the enclosing sphere…
In each square meter at Venus there is 2641 W/m2 or almost twice as much as at Earth.
Mars is 229 Million Km (2.29x1011m) from the sun.
So Area of the enclosing sphere=4�(2.29x1011m)2=6.6x1023m2 In each square meter at Mars there is 576 W/m2 or less than half as much at Earth. Venus: at 107 Million Km the Solar Constant is 2641 W/m2 1.4x 1.9x Earth: at 150 Million Km the Solar Constant is 1360 W/m2 1.5X 2.4x Mars: at 229 Million Km the Solar Constant is 576 W/m2
Earth is 40% farther away than Venus with ~ ½ the Solar constant
Mars is twice farther away than Venus but gets about 1/3 the sunlight
The changes in solar constant are much bigger than the relative differences in distance! Why? https://en.wikipedia.org/wiki/Inverse-square_law
Inverse Square Law of Electromagnetic Radiation
r 2r
So by doubling the radius of the sphere we are putting the same amount of energy into a 4 times larger area.
The amount of energy per unit area Or by tripling the radius of the decreases as the square of the distance sphere (i.e. tripling the distance, we from the source. are putting the same energy into a 9 times larger area. • If we set up a screen behind the Earth, • the Earth would cast a circular shadow on the screen, • and the shadow would have the radius of the Earth. • The amount of sunlight falling on the Earth is equal to the amount that would have fallen into the shadow area if the Earth were not there.
Area of shadow=πR2 Multiplied by the Solar Constant.
R=6.4x106 meters Radius of the Earth W/m2 x m2= W Total energy falling on the Earth’s surface How is this energy distributed on the Earth’s surface? 1360 W/m
1360 W/m2 at the top of the atmosphere 1.8E17 W total energy for the entire Earth 2
This number 349 W/m2 is an important quantity since it gives an average upper limit on solar energy input to the Earth (without considering any reflection)
349 W/m2 represents the external forcing of the Earth by the Sun!!! To summarize so far…
• Energy leaves the Sun and expands as the inverse square of the distance it travels while conserving energy. • By the time the energy reaches the Earth (150 million km away) it has an energy density of just 1360 Watts in every square meter (called the solar constant). • The Earth intercepts an amount of energy equal to the area of a circle that has the radius of the Earth. The total energy= solar constant π R2 =1.8E17 Watts • This energy is distributed onto the sphere of the Earth. Divide total intercepted energy by the area of a sphere with a radius of the earth. This is 349 W/m2 349 Watts/m2 represents the external forcing of the Earth by the Sun!!
Important Definitions:
Forcing: Something that can modify the climate system – causes it to respond in some way.
Internal Forcing: Something within the climate system that can modify the climate system but that can itself be modified by the climate system.
External Forcing: Something that can modify the climate system but cannot be changed by the climate system. So we have two important results so far: 2 1. 1360 W/m is the solar constant 1360 W/m 2. 349 W/m2 is the external forcing
What is the difference? 2 • Solar constant is what would be measured by an instrument at the top of Earth’s atmosphere pointing directly at the Sun. • External Forcing takes that energy and spreads it out over the globe.
The number (349 W/m2) is fixed. But what is absorbed by Earth will be less than 349 due to reflection of sunlight back to space. Reflection occurs when an EM wave strikes an object and bounces off of it. Not all of the photons from the Sun that fall on the Earth are absorbed by it. A fraction of the solar energy is reflected back to space by clouds, ice, and other reflective elements. Albedo: Reflectivity of a planet
Total rate of energy in (Ein) for the Earth is α = the fraction of photons reflected. 1-α = the fraction of photons that are absorbed. For the Earth α=0.3 We want to know how that energy is distributed over the sphere so we divide by the energy of the sphere The Earth absorbs an average of 238 W/m2 from the Sun. That does not mean that every square meter of the Earth absorbs this amount. The amount of solar energy absorbed varies widely across the planet. • Night half receiving no energy • Variation in the incoming energy with latitude • Albedo of the planet varies widely. The primary reflectors in the Earth-Atmosphere system are?
1. Clouds 2. Earth’s surface (snow/ice,desert, other land, ocean, in order of reflectance. 3. Aerosols (both anthropogenic from combustion, etc. and natural from volcanoes, biological, and geochemical processes 4. Ocean (very low reflectivity except at certain angles) 5. Atmospheric gasses
https://www.youtube.com/watch?v=d1U7X1k3d0Y Atmos 1020 – Lecture 2 The Radiation Balance of the Atmosphere
We define albedo as the total reflectance of the earth system.
Reflectance just means the fraction of incident light that is reflected.
The albedo of the earth is right around 0.3 or 30%. This means that (1 minus 0.3)=0.7 is the fraction of 349 W/m2 that is actually absorbed by the earth system. 238 w/m2
Is the albedo an internal or external forcing mechanism? Atmos 1020 – Lecture 2 The Radiation Balance of the Atmosphere
The albedo can be viewed as an internal forcing mechanism.
While the albedo determines how much solar energy is available to the climate, changes within the climate can modify the albedo and in turn modify the absorbed solar energy – Very much like a feedback loop. Atmos 1020 – Lecture 2 The Radiation Balance of the Atmosphere
Many things can alter the earth albedo including • Changes in snow/ice extent • Changes in cloud cover • Changes in surface type and land use • Volcanic events, Dust, etc. • Impacts (i.e. demise of the dinosaurs) • BIG human events (nuclear war) • Lesser human activity – industrial and agricultural
https://www.youtube.com/watch?v=O0B8Yi7AZvQ The Seasons
Northern Summer
Sunlight sunlight
Southern Summer
The seasons are due to the tilt The combination of more direct rays of sunlight of the Earth’s rotation axis and more hours of daylight cause the relative the orbital plane hemisphere tilted toward the sun to receive more solar radiation and have warmer temperatures
Source: I, Dennis Nilsson, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=3262268 Atmos 1020 – Lecture 2 The Radiation Balance of the Atmosphere Seasonal variations in incoming solar radiation:
Perihelion: 147 Mkm
Aphelion: 152 Mkm
Seasons Simulator https://astro.unl.edu/classaction/animations/coordsmotion/eclipticsimulator.html Atmos 1020 – Lecture 2 The Radiation Balance of the Atmosphere
What we don’t often consider are seasonally averaged changes in the energy balance. The earth-sun distance actually varies by season!
The earth-sun distance varies.
This variation causes the amount of energy we receive at the top of the atmosphere to vary by 16 w/m2 over the course of 1 year.
Since this oscillation averages to 0 annually, it is typically neglected. Energy Loss to Space
• In the early 19th century, Joseph Fourier, one of history’s great mathematicians, asked a deceptively simple question. • Because energy is always falling on the Earth from the Sun, why doesn’t the Earth heat up until it is the same temperature as the Sun? • The Earth is losing energy at a rate equal to the rate at which it is receiving energy from the Sun. • Earth loses energy back to space by Solve for T blackbody radiation.
T=255K S=1360 W/m2 Actual temp is 288K. Our Estimate is too cold. α=0.3 We have neglected the heating of the planet by the Earth’s atmosphere. σ=5.67X10-8 (W/m2)/K4