State what is meant by green house effect.

A researcher uses the following data for a simple climatic model of the earth without an atmosphere, incident solar radiation $350 \mathrm{W} {\mathrm{m}}^{-2}$, absorbed solar radiation$250 \mathrm{W} {\mathrm{m}}^{-2}$.

Make an energy flow diagram of these data.

A researcher uses the following data for a simple climatic model of the earth without an atmosphere, incident solar radiation $350 \mathrm{W} {\mathrm{m}}^{-2}$, absorbed solar radiation$250 \mathrm{W} {\mathrm{m}}^{-2}$.

Determine the average albedo for the earth that is to be used in modelling.

A researcher uses the following data for a simple climatic model of the earth without an atmosphere, incident solar radiation $350 \mathrm{W} {\mathrm{m}}^{-2}$, absorbed solar radiation$250 \mathrm{W} {\mathrm{m}}^{-2}$.

Determine the intensity of outgoing long radiation.

A researcher uses the following data for a simple climatic model of the earth without an atmosphere, incident solar radiation $350 \mathrm{W} {\mathrm{m}}^{-2}$, absorbed solar radiation$250 \mathrm{W} {\mathrm{m}}^{-2}$.

Estimate the temperature (in Kelvin) of the earth according to this model,assuming a constant Earth temperature.

The diagram shows a more involved model of the greenhouse effect.

The average incoming radiation intensity $\frac{\mathrm{S}}{4}=350 \mathrm{W} {\mathrm{m}}^{-2}$. The albedo of the atmosphere is $0.300$. Assume that the fraction $t$ of the energy radiated by the earth actually escapes the earth and the surface behaves as a black body. The model assumes that part of the radiation from the earth is reflected back down from the atmosphere.

The intensity radiated by the earth is $I_1$ and the intensity radiated by the atmosphere is $I_2$ and the fraction of intensity escaping the earth is $I_3$.By examining the energy balance of the atmosphere and the surface seperately. Show that 

$I_1=\frac{2}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$

$I_2=\frac{1-\alpha -t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$

$I_3=\frac{2t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$

The diagram shows a more involved model of the greenhouse effect.

The average incoming radiation intensity $\frac{\mathrm{S}}{4}=350 \mathrm{W} {\mathrm{m}}^{-2}$. The albedo of the atmosphere is $0.300$. Assume that the fraction $t$ of the energy radiated by the earth actually escapes the earth and the surface behaves as a black body. The model assumes that part of the radiation from the earth is reflected back down from the atmosphere.

Show that as much energy enters the earth's atmosphere as leaves it.

Given $I_2=\frac{1-\alpha -t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$ and $I_3=\frac{2t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$

The diagram shows a more involved model of the greenhouse effect.

The average incoming radiation intensity $\frac{\mathrm{S}}{4}=350 \mathrm{W} {\mathrm{m}}^{-2}$. The albedo of the atmosphere is $0.300$. Assume that the fraction $t$ of the energy radiated by the earth actually escapes the earth and the surface behaves as a black body. The model assumes that part of the radiation from the earth is reflected back down from the atmosphere.

Show that a surface temperature of $\mathrm{T}= 288 \mathrm{K}$ implies that $t=0.556$

Given $I_2=\frac{1-\alpha -t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$ and $I_3=\frac{2t}{1-\alpha +t}\times \frac{(1-\alpha )S}{4}$ and $I_1=\frac{(1-\alpha )S}{4}\times \frac{2}{1-\alpha +t}$, Solar constant $\mathrm{S}=1400 \mathrm{W} {\mathrm{m}}^{-2}$ Stefan's constant $\mathrm{\sigma }=5.6\times {10}^{-8 }\mathrm{W}/{\mathrm{m}}^2 {\mathrm{K}}^4$