1. The maximum radiance of a blackbody is at wavelength = A um. a) At what temperature does this occur? b) Estimate the brightness temperature for a grey body at this wavelength if the emissivity coefficient is &. (Use full formula.) (15 points). 2. The imaginary planet is at X AU from the Sun, its effective temperature is T1 K and radius r. a) What is the solar constant for this planet if the Earth solar constant is 1380 W/m? b) What is the albedo of this planet with respect to the Earth albedo? Assume effective temperature for the Earth 270K. c) What fraction of radiative flux emitted by the Sun is absorbed by this planet? (20 points). A 9 3. The solar irradiance at some band is 10 mW/cm/um. The surface irradiance is measured to be Il mW/cm/um with a solar zenith angle of 01 degrees. The surface albedo is R%. a) what would be the atmospheric optical thickness at this band? b) what is the optical thickness of aerosols if Rayleigh optical thickness is 0.05? 4. Optical thickness of the atmosphere at some wavelength is Tau, concentration of aerosol particles is N*E6 1/m and the sun zenith angle is a degrees. Calculate the transmittance of atmosphere at this wavelength. What is the scattering and absorption cross-sections of aerosols if Rayleigh optical thickness is 0.1, the thickness of aerosol layer is 8 km and the absorption cross-section is X2 of the scattering cross-section? (20 points). c) what is the transmittance of the atmosphere at this band? d) what is the radiance detected by the satellite sensor if the sensor viewing angle is 02 degrees? Assume the surface is uniform (Lambertian)? (25 points) 5. The diameter of the field of view of the satellite sensor on the surface is D km and the sensor is at the height of H km. Determine the radiance from the surface if the diameter of the telescope is d m and the flux measured at the detector is P mW (20 points) I 1 2 8 X T1 T 0.65 8 280 3693 Page 10 3 4 Na 8 X2 D H d P 7+44 1.5 0.4 80 730 0.4 30