3. An infrared radiometer on board a satellite measures the optical power emitted upward from the...

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3. An infrared radiometer on board a satellite measures the optical power emitted upward from the Earth. The radiometer consists of a telescope of diameter 20 cm with a field of view half angle of 0.5 degrees, an optical filter centred on wavelength 10 m with a bandwidth of 0.1 m, and a detector. a) In a cloud free area the measured optical power is 8.16 10-6 Watts. Determine the temperature of the surface. (10 marks) b) In an area with thick clouds the measured optical power is 7.42 10-7 Watts. Determine the temperature of the top of the clouds. (5 marks) c) Estimate the height of the top of the clouds, assuming the atmospheric temperature gradient is -6.5C/km. (5 marks) Assume that the absorptivity of cloud free air is negligible at wavelength 10 m, but that the surface and thick clouds have an emissivity of 1. 3. An infrared radiometer on board a satellite measures the optical power emitted upward from the Earth. The radiometer consists of a telescope of diameter 20 cm with a field of view half angle of 0.5 degrees, an optical filter centred on wavelength 10 m with a bandwidth of 0.1 m, and a detector. a) In a cloud free area the measured optical power is 8.16 10-6 Watts. Determine the temperature of the surface. (10 marks) b) In an area with thick clouds the measured optical power is 7.42 10-7 Watts. Determine the temperature of the top of the clouds. (5 marks) c) Estimate the height of the top of the clouds, assuming the atmospheric temperature gradient is -6.5C/km. (5 marks) Assume that the absorptivity of cloud free air is negligible at wavelength 10 m, but that the surface and thick clouds have an emissivity of 1.