1. 1
   The solar constant at the orbit of Mars is 590 W m⁻². The mean albedo of Mars is 0.25. Mars has a very thin atmosphere, so assume it has no greenhouse effect and that its surface radiates as a black body.

   (a)

   What is the mean intensity of solar radiation arriving at Mars, averaged over its entire surface?

   [1 mark]

   • A590 W m⁻²
   • B148 W m⁻²
   • C295 W m⁻²
   • D111 W m⁻²

   (b)

   What is the mean intensity absorbed by Mars, averaged over its entire surface?

   [1 mark]

   • A37 W m⁻²
   • B148 W m⁻²
   • C111 W m⁻²
   • D443 W m⁻²

   (c)

   Determine the mean equilibrium surface temperature of Mars predicted by this model.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A satellite measures radiation above two regions at noon. Over a field of fresh snow, 1000 W m⁻² of sunlight is incident and 850 W m⁻² is scattered back to space. Over a dark ocean, 1000 W m⁻² is incident and 60 W m⁻² is scattered back. A thermal camera on the satellite shows that a patch of dry ground at 300 K radiates 410 W m⁻².

   (a)

   What is the albedo of the fresh snow?

   [1 mark]

   • A0.15
   • B1.18
   • C0.060
   • D0.85

   (b)

   What is the emissivity of the dry ground?

   [1 mark]

   • A0.89
   • B0.11
   • C0.41
   • D1.12

   (c)

   Outline why the Earth's albedo varies from day to day and with latitude.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Direct measurements and ice-core records show that atmospheric carbon dioxide rose from about 280 parts per million (ppm) in 1750 to about 420 ppm in 2023. Over the same period methane rose from about 0.72 ppm to 1.92 ppm, and nitrous oxide from about 0.27 ppm to 0.34 ppm. The Sun's radiation peaks at a wavelength of about 0.5 μm, while the radiation emitted by the Earth's surface peaks at about 10 μm.

   (a)

   Explain, with reference to molecular energy levels, why greenhouse gases absorb much of the radiation emitted by the Earth's surface but little of the incoming solar radiation, and how this warms the surface.

   [3 marks]

   (b)

   Using the data, compare the changes in the three gases since 1750, state one human source for each, and suggest why water vapour, despite being the most important greenhouse gas, is not usually treated as a direct cause of the enhanced greenhouse effect.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A simple energy-balance model of the Earth uses the following values: solar constant S = 1361 W m⁻², mean albedo 0.30, and mean surface temperature 288 K. In the model the Earth's surface radiates as a black body, and the Earth–atmosphere system as seen from space is treated as a single emitter with an effective emissivity e.

   (a)

   Determine the equilibrium temperature the Earth would have with no atmosphere (e = 1), and use the model to determine the effective emissivity of the Earth–atmosphere system. Explain what the difference between the two temperatures shows.

   [6 marks]

   (b)

   Suppose melting sea ice reduces the mean albedo to 0.28, and rising greenhouse-gas concentrations reduce the effective emissivity to 0.60. Use the model to predict the new mean surface temperature, and discuss the processes involved and the limitations of this model.

   [6 marks]

   Total for question 4: 12 marks

End of questions