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Science 3360 Lecture 5: The Climate System
The Earth’s Orbit and Effective Temperature
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A Brief Review Energy depends inversely on wavelength
Intensity of radiation decreases as 1/r^2 The intensity of radiation reaching the Earth’s surface depends on the angle (beam spreading) All objects with T>0K emit radiation
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The Earth’s Orbit Earth rotates about its axis 24 hours and about the sun every days. Note that the tilt or obliquity remains “constant”. Solstice: Day of the year with the longest amount of daylight Equinox: Day of the year when daytime and nighttime are equal
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Solstice At each solstice, 1 pole is always illuminated, one is always dark From physicalgeography.net
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Equinox Sun is directly overhead at the equator.
Why would the obliquity of the Earth’s orbit cause seasons? There are 3 different reasons… From physicalgeography.net
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The Seasons: Reason 1 The intensity of radiation is affected by the angle the beam makes with the horizontal surface. The higher the angle of incidence, the less the beam is spread and the more energy is received per unit area.
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The Seasons: Reason 2 As light passes through the atmosphere it is scattered, diffused, and reflected. The larger the angle of incidence, the less of the atmosphere the light must pass through to reach the surface. Thus a higher angle means less loss so more energy reaches the surface.
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The Seasons: Reason 3 The length of day changes depending on the day of the year. During the Equinox the day is 12 hours long everywhere. However, on the Solstice the length of day can be anywhere from 0 hours (the dark pole) to 24 hours (the illuminated pole)
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The Seasons: Recap So during the boreal summer, the north hemisphere is warmer because Sunlight hits at a large incident angle so less beam spreading Higher incident angle so less of the atmosphere to travel through Day is longer in the boreal summer so longer period of solar heating
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Kepler’s Laws Johannes Kepler formulated 3 laws that describe how the planets move in the early 1600s The First law states: “Orbit of every planet is an ellipse with the sun at 1 foci” From Wikipedia Why isn’t one summer a lot hotter than the other?
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Kepler’s Laws Because the Earth’s orbit is almost circular
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Planetary Energy Balance
Rough Idea: Amount of energy absorbed by the Earth must equal the amount being emitted Aside: If Global Warming is occurring, are we in balance? Energy In = Energy In Start with the concept of “Effective Temperature”
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Effective Temperature
Think of it as the temperature of the Earth’s surface if no atmosphere was present Also the temperature that a body radiates it energy Remember:
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Energy Balance: An idealized Case
Calculate the temperature of a metallic cube orbiting the Sun at the same distance as the Earth What can we assume? One face of the cube is perpendicular to the sun Ein=Eout (energy is balanced) Assume albedo of cube is 0
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Energy Balance: An idealized Case
Re Sun L What section of the cube receives solar insolation? What is its area? What part of the cube radiates energy?
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Energy Balance: An idealized Case
System is in radiative balance so Ein=Eout Ein is the energy received by the cube. Previously found that flux that Earth receives is 1370 W/m2/second We can ignore time due to radiative balance If Albedo=0, everything is absorbed so
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Energy Balance: An idealized Case
Eout is the energy radiated by the cube. Stefan-Boltzmann says Box radiates from all sides So we can calculate the energy radiated as
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Energy Balance: An idealized Case
We need to solve for T. We have: and Which yields T=252K
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Energy Balance: An idealized Case
What if the albedo of the cube wasn’t 0? Remember that absorptivity = 1 – A Would Eout be affected by albedo?
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Energy Balance What about for a spherical planet?
The area for absorbing radiation is simply a 2-d circle facing the sun so area receiving sunlight is just
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Energy Balance What about the area radiating? The surface area of a sphere is Again using Ein=Eout we can solve for the effective temperature: or
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Effective Temperature of the Earth
Solving for effective temperature yields the equation What is Teff for the Earth? S=1370 W/m2 ; σ = 5.67 x10-8 ; A = .3 Yields Teff of 255K or 0F. Too cold! The average temperature of the Earth is actually about 60F. Why the discrepancy? The Greenhouse Effect!
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