1. Assume the surface emits like a blackbody at 290 ^oK.

(a) Calculate the total flux across the spectrum emitted by the surface.
 

(b) What is the wavelength of peak emission?

(c) Calculate the monochromatic flux at the wavelength of peak emission. Over how wide a spectral interval would this monochromatic flux have to be emitted to equal the flux from part (a)?

2. Calculate the solar constant S and radiative equilibrium temperature T_e for Venus and Mars. Use a solar constant of S=1380 W^-2 for the Earth.

Planet     Distance from Sun     Albedo     Avg. Sfc.             Avg. Sfc.
                        (km)                                 Temperature (K) Pressure (mb)

 Venus         108x10⁶                 0.77             730                         92000
Earth            150x10⁶                0.30             288                         1013
Mars             228x10⁶                         0.24            218                               7
 

3. The optical depth of sunlight at sea level due to Rayleigh scattering from air molecules is about

d _R = 0.0090 l^-4 where the wavelength l is in m m.
 

(a) Compute the clear sky transmissivity of collimated solar flux in the blue (l =0.47 m m) and the red (l =0.64 m m) at solar zenith angles of j =30^o and j =85^o (four cases). Ignore absorption by ozone and water vapor (which is small at these wavelengths) and the effects of aerosols. Assume the atmosphere is a planar slab (i.e. ignore the curvature of the Earth).
 

(b) Use these results to explain why the sky is blue and why the setting sun is red.
 
 

4. - we may not do this problem - please ask instructor first!
(a) Calculate the visible optical depth of a cloud of thickness D Z=250 m, liquid water content of W=0.2 g m^-3, and droplet number concentration of 50 cm^-3 droplets. Assume the droplets all have the same size. Use a scattering efficiency (scattering area coefficient) of K=2. Why is the scattering efficiency equal to 2 for these cloud droplets?
 

(b) Calculate the visible albedo (reflectivity) of this cloud for a solar zenith angle with cosj ₀=2/3. Use an asymmetry parameter of g=0.85.

(c) Emissions of sulfate aerosols by industry have the potential to change cloud properties. This is called the indirect effect of aerosols on climate. Calculate the albedo of this cloud if the number of cloud condensation nuclei, and hence cloud droplets, doubled, and assuming the liquid water content remains constant.