Global warming
The reality of global warming can be demonstrated from simple physical principles of physics and chemistry that governs the everyday operations of power plants to cook stoves and light bulbs. At its heart is simple balancing of energy. How much energy comes in, how much goes out and how much is absorbed... and how those ratios change when the matter composition of gases and oceans and land are altered. The principles of physics and chemistry needed are elementary and have been known for over a hundred years. All it requires is middle school algebra.
Energy coming in:
The main energy input to earth is the Sun, whose surface temperature and net energy output is very well known. At earth’s radial distance the energy per square meter is,
Total solar energy Flux from the sun at earth-sun radius is S= 1360 W/m^2
For Venus, which is much closer, it is 2600 W/m^2.
The total effective area on which this sunlight falls is equal to the circular shadow/projection of earth. The radius of earth is R=6400 km. So the total circular area is π*R^2 .
Earth is not black,but a blue planet. So part of this incoming light energy is reflected back.
Part of the sunlight is reflected back and is measured by its albedo α.
Thus total light energy absorbed by earth
E_in = S(1-α)π*R^2
For earth reflectivity α=0.3
This energy is distributed over earth's spherical surface of 4πR^2.
Thus incoming solar energy per unit area of Earth's surface is
(E_in) /A = S(1-α)/4 = 238 W/m^2.
There is large variation on where and how this energy falls and is absorbed. It's concentrated on the day side and equatorial regions get more than high latitudes. Summer hemisphere gets more than winter hemisphere. For one can neglect these when only mean temperature is to be calculated.
Energy radiated if there were no atmosphere
Now suppose earth had no atmosphere. Earth's surface will absorb this incoming energy, attain a certain temperature and radiate this energy back into very cold space. If T be the temperature of earth in Kevins, the rate at which earth will radiate is
E_out/A = σ*T^4 where σ is the well known Stefan-Boltzmann constant.
At equilibrium we must have energy in = energy out
This gives S(1-α)/4 = σ*T^4
Putting in the values, the expected temperature of earth without an atmosphere will be 255 K or -18 Centigrade.
Earth would be entirely frigid if it had no atmosphere.
Energy balance with atmosphere
The atmosphere of planets are composed of gases that absorb the outgoing radiation (partly or wholly) and remit them both upwards and downwards. If the atmosphere is thick, or is made up of especially absorbant gases, then the process may repeat itself several times... with higher layers absorbing the radiation emitted by the lower layers.
Let's consider a simple 1 layer model. Here the idea is that the atmosphere acts as a single layer that absorbs all radiation coming from earth's surface and then radiates it upwards and downwards. The important thing to note here is that energy from the sun comes mostly as light energy that passes through the transparent atmosphere. But Earth radiates it as longer wavelength heat energy and this is absorbed by the gases.
When we have one layer of atmosphere that radiates, for thermal equilibrium, it must radiate the same amount of energy as absorbed by earth. So,
Energy radiated by atmosphere towards space =S(1-α)/4
But the atmosphere will radiate the same amount of energy downwards towards the surface of earth as well.
So net energy incoming for earth’S surface = Net light energy from Sun + Net downward heat energy from atmosphere. = 2*S(1-α)/4.
For energy balance on earth's surface, it's temperature must be such that the net outgoing energy equals this net incoming energy. So
2*S(1-α)/4 =σ*T^4
This gives for earth 2*238 W/m2 =σ*T^4
Or T= 303 K or 30 C
Thus a single fully insulating layer of atmosphere increases the average temperature from - 18C to +30C.
In general for n number of fully insulating layers of atmosphere (n can be fractional for partially transparent atmospheres) we have temperature at the surface
σ*T^4 = (n+1)*S(1-α)/4
For earth, the observed surface temperature is 289 K and hence n=0.65.
For Venus, S=2650 W/m^2 with albedo α = 0.7. The temperature is 735 K and n=82. This attests to the thick and highly thermally insulating nature of the atmosphere of Venus.
Thus we can see that average temperature of the planet can change if
I) There is a change in incoming solar radiation Flux S
2) There is a change in the albedo alpha.
3) There is a change in the composition or thickness of the atmosphere changing n.
All global warming calculations of average temperature boils down to evaluating changes in these three factors.
To be continued...
Questions?
The reality of global warming can be demonstrated from simple physical principles of physics and chemistry that governs the everyday operations of power plants to cook stoves and light bulbs. At its heart is simple balancing of energy. How much energy comes in, how much goes out and how much is absorbed... and how those ratios change when the matter composition of gases and oceans and land are altered. The principles of physics and chemistry needed are elementary and have been known for over a hundred years. All it requires is middle school algebra.
Energy coming in:
The main energy input to earth is the Sun, whose surface temperature and net energy output is very well known. At earth’s radial distance the energy per square meter is,
Total solar energy Flux from the sun at earth-sun radius is S= 1360 W/m^2
For Venus, which is much closer, it is 2600 W/m^2.
The total effective area on which this sunlight falls is equal to the circular shadow/projection of earth. The radius of earth is R=6400 km. So the total circular area is π*R^2 .
Earth is not black,but a blue planet. So part of this incoming light energy is reflected back.
Part of the sunlight is reflected back and is measured by its albedo α.
Thus total light energy absorbed by earth
E_in = S(1-α)π*R^2
For earth reflectivity α=0.3
This energy is distributed over earth's spherical surface of 4πR^2.
Thus incoming solar energy per unit area of Earth's surface is
(E_in) /A = S(1-α)/4 = 238 W/m^2.
There is large variation on where and how this energy falls and is absorbed. It's concentrated on the day side and equatorial regions get more than high latitudes. Summer hemisphere gets more than winter hemisphere. For one can neglect these when only mean temperature is to be calculated.
Energy radiated if there were no atmosphere
Now suppose earth had no atmosphere. Earth's surface will absorb this incoming energy, attain a certain temperature and radiate this energy back into very cold space. If T be the temperature of earth in Kevins, the rate at which earth will radiate is
E_out/A = σ*T^4 where σ is the well known Stefan-Boltzmann constant.
At equilibrium we must have energy in = energy out
This gives S(1-α)/4 = σ*T^4
Putting in the values, the expected temperature of earth without an atmosphere will be 255 K or -18 Centigrade.
Earth would be entirely frigid if it had no atmosphere.
Energy balance with atmosphere
The atmosphere of planets are composed of gases that absorb the outgoing radiation (partly or wholly) and remit them both upwards and downwards. If the atmosphere is thick, or is made up of especially absorbant gases, then the process may repeat itself several times... with higher layers absorbing the radiation emitted by the lower layers.
Let's consider a simple 1 layer model. Here the idea is that the atmosphere acts as a single layer that absorbs all radiation coming from earth's surface and then radiates it upwards and downwards. The important thing to note here is that energy from the sun comes mostly as light energy that passes through the transparent atmosphere. But Earth radiates it as longer wavelength heat energy and this is absorbed by the gases.
When we have one layer of atmosphere that radiates, for thermal equilibrium, it must radiate the same amount of energy as absorbed by earth. So,
Energy radiated by atmosphere towards space =S(1-α)/4
But the atmosphere will radiate the same amount of energy downwards towards the surface of earth as well.
So net energy incoming for earth’S surface = Net light energy from Sun + Net downward heat energy from atmosphere. = 2*S(1-α)/4.
For energy balance on earth's surface, it's temperature must be such that the net outgoing energy equals this net incoming energy. So
2*S(1-α)/4 =σ*T^4
This gives for earth 2*238 W/m2 =σ*T^4
Or T= 303 K or 30 C
Thus a single fully insulating layer of atmosphere increases the average temperature from - 18C to +30C.
In general for n number of fully insulating layers of atmosphere (n can be fractional for partially transparent atmospheres) we have temperature at the surface
σ*T^4 = (n+1)*S(1-α)/4
For earth, the observed surface temperature is 289 K and hence n=0.65.
For Venus, S=2650 W/m^2 with albedo α = 0.7. The temperature is 735 K and n=82. This attests to the thick and highly thermally insulating nature of the atmosphere of Venus.
Thus we can see that average temperature of the planet can change if
I) There is a change in incoming solar radiation Flux S
2) There is a change in the albedo alpha.
3) There is a change in the composition or thickness of the atmosphere changing n.
All global warming calculations of average temperature boils down to evaluating changes in these three factors.
To be continued...
Questions?
