Show that the intensity of the solar radiation incident on the upper atmosphere of the Earth is approximately 1400Wm⁻².

The albedo of the atmosphere is 0.30. Deduce that the average intensity over the entire surface of the Earth is 245Wm⁻².

Estimate the average surface temperature of the Earth.

\(I = \frac{{\sigma A{T^4}}}{{4\pi {d^2}}}\)

\( = \frac{{5.67 \times {{10}^{ - 8}} \times {{\left( {7.0 \times {{10}^8}} \right)}^2} \times {{5800}^4}}}{{{{\left( {1.5 \times {{10}^{11}}} \right)}^2}}}\)

OR \( \frac{{5.67 \times {{10}^{ - 8}} \times 4\pi  \times {{\left( {7.0 \times {{10}^8}} \right)}^2} \times {{5800}^4}}}{{4\pi  \times {{\left( {1.5 \times {{10}^{11}}} \right)}^2}}}\)

I=1397 Wm⁻²

In this question we must see 4SF to award MP3.
Allow candidate to add radius of Sun to Earth–Sun distance. Yields 1386 Wm^–2.

«transmitted intensity =» 0.70 × 1400 «= 980Wm^–2»

\(\frac{{\pi {R^2}}}{{4\pi {R^2}}} \times 980{\rm{W}}{{\rm{m}}^{ - 2}}\)

245Wm^–2