Four billion years ago the Sun’s radiative output was 30% less than it is today.
(i) If we assume the radius of the sun is the same, and that the Earth’s atmosphere was the same as it is now (that is, the atmosphere absorbs 10% of the incoming solar radiation and 80% of the outgoing terrestrial radiation), estimate the average surface temperature of the Earth four billion years ago using a single layer atmosphere.
(ii) In fact, the Earth’s atmosphere was drastically different 4 billion years ago (15-20% CO2, 0% O2). Suppose the atmosphere absorbed 5% of the incoming radiation but 95% of the outgoing radiation. What would be the temperature of the early Earth surface and its atmosphere?
Check my answer that I posted yesterday. Show your work if you need further assistance.
It seems yesterday's question was not quite the same, but method of solution should be the same. Perform an energy balance, using the Stefan-Boltzmann Law.
http://www.jiskha.com/display.cgi?id=1264307230
To estimate the average surface temperature of the Earth four billion years ago in both scenarios, we can use the concept of energy balance. The energy received from the Sun equals the energy radiated back into space.
First, let's calculate the current average surface temperature of the Earth, which serves as a baseline for our calculations. The current radiative output of the Sun is taken as 100%. Assuming an albedo (reflectivity) of 30% due to clouds, ice, etc., the Earth absorbs 70% of the incoming solar radiation.
(i) Single Layer Atmosphere:
In this scenario, the Earth's atmosphere absorbs 10% of incoming solar radiation and 80% of outgoing terrestrial radiation.
To calculate the temperature, we need to equate the energy absorbed to the energy radiated. The equation is:
(1 - albedo) * (1 - atmosphere_absorption) * (Sun's radiative output) = atmosphere_absorption * (Earth's radiative output)
Let's denote the average surface temperature of the Earth four billion years ago as T_4bya.
For the current scenario:
0.7 * 0.1 * 1 = 0.1 * (1 - 0.8) * (1 - 0.7) * T
Simplifying:
0.07 = 0.1 * 0.3 * T
Solving for T:
T = 0.07 / (0.03)
T = 2.33
Therefore, the average surface temperature of the Earth four billion years ago, assuming a single layer atmosphere, would be approximately 2.33 times the current average surface temperature, which is around 15°C.
(ii) Drastically Different Atmosphere:
In this scenario, the Earth's atmosphere absorbs 5% of incoming radiation but 95% of outgoing radiation.
Using the same energy balance equation as before:
0.7 * 0.05 * 1 = 0.05 * (1 - 0.95) * (1 - 0.7) * T_4bya
Simplifying:
0.035 = 0.05 * 0.3 * T_4bya
Solving for T_4bya:
T_4bya = 0.035 / (0.015)
T_4bya = 2.33
Therefore, the average surface temperature of the Earth four billion years ago, considering a drastically different atmosphere, would also be approximately 2.33 times the current average surface temperature, which is around 15°C.
In both scenarios, the average surface temperature of the Earth four billion years ago would be roughly the same, assuming the radius of the Sun remained constant.