The current magnitude of the greenhouse effect is measured by the difference between the emission from the surface and the emission from the top of the atmosphere, G=¦ÒTs^4 −¦ÒTe^4 ¡Ö 150 W m-2. What would be the required magnitude of the greenhouse effect to maintain the surface temperature at 288K if the solar constatnt were reduced by 30%? By what distance would the effective emission level of the atmosphere need to rise if the lapse rate is approximately 6 Km -1?
I cannot read your ¡Ö symbols. If one of them is the Stefan-Boltzmann constant, please write "sigma" for that term.
Did you omit some symbols when you wrote ¡Ö 150 W m-2 ? Shouldn't there be an = sign somewhere?
To solve this problem, we'll need to use the formula for the greenhouse effect and then make some calculations based on given information.
First, let's break down the equation for the greenhouse effect:
G = σTs^4 - σTe^4
Where:
G represents the magnitude of the greenhouse effect
σ is the Stefan-Boltzmann constant
Ts is the surface temperature
Te is the effective emission temperature – the temperature at which the Earth would emit radiation into space
We are given that G = 150 W m^-2, and we need to find the required magnitude of the greenhouse effect to maintain the surface temperature at 288K if the solar constant (incoming solar radiation) is reduced by 30%.
Step 1: Calculate the new solar constant after the reduction of 30%.
Let's assume the original solar constant as So. The reduced solar constant, Sr, can be calculated as:
Sr = So - (0.3 * So) = 0.7 * So
Step 2: Calculate the new effective emission temperature, Te.
The change in solar constant directly affects the effective emission temperature. Since the greenhouse effect balances the incoming solar radiation with the outgoing radiation, changing the incoming radiation changes the required outgoing radiation.
To calculate the new effective emission temperature, we can rearrange the greenhouse effect equation:
Te = (G + σTs^4)^(1/4)
Step 3: Substitute the values and solve for Te.
Te = (150 + (σ * (288^4)))^(1/4)
Now, let's move on to the second part of the question, which involves finding the distance by which the effective emission level of the atmosphere needs to rise if the lapse rate is approximately 6 Km^-1.
The lapse rate is the rate at which temperature decreases with increasing altitude. We know that the lapse rate is approximately 6 Km^-1, which means the temperature decreases by 6 degrees Celsius per kilometer.
Step 4: Convert the lapse rate to Kelvin.
Since Te is expressed in Kelvin, we need to convert the lapse rate given in Celsius to Kelvin. We add 273 to the lapse rate.
Lapse rate = 6 Km^-1 = 6 + 273 K^-1
Step 5: Calculate the required rise in the effective emission level.
The change in the effective emission level, Δh, can be found using the lapse rate:
Δh = (Te - Ts) / (lapse rate)
Step 6: Substitute the values and solve for Δh.
Δh = (Te - 288 K) / (6 K^-1)
By following these steps and performing the calculations, you can find the required magnitude of the greenhouse effect and the distance by which the effective emission level of the atmosphere needs to rise.