In this problem, you are asked to examine the influence of the atmosphere on the shortwave radiative flux incident at the earth's surface. Incoming solar radiation in the short-wavelength spectra (shortwave) at the top of the atmosphere (TOA) is partially absorbed and scattered (reflected) by atmospheric molecules and particles. As a result, only a fraction of the TOA flux actually reaches the surface. Answer the following questions using the equations provided in Sections 5 and 6. a) Compute declination angle, zenith angle, and incoming top-of-atmosphere (TOA) solar radiative flux for solar noon on December 21 st, 2011 (winter solstice), and June 21st, 2012 (summer solstice) in Hilo, Hawaii (19.73 ∘
N ). For this latitude and days of the year (and time of day), is the sun in the southern sky, northern sky, or directly overhead? [Hint: You can answer this by comparing the latitude to the declination angle]. Is the sun in the same part of the sky throughout the year? Justify your answer. b) What is the predicted shortwave direct beam transmissivity of the atmosphere on June 21 st? To estimate precipitable water assume the surface dewpoint temperature is 25 ∘
C. Assume there is attenuation due to dust using a reasonable parameter value. Based on your answer, approximately what fraction of the incoming direct beam solar radiation is attenuated by the atmosphere? Qualitatively, how would this change if the amount of water vapor increased? So if all else is equal, would you expect more direct beam solar radiation to reach the surface in an area with a dry climate or one with a humid climate? c) What is the predicted scattering coefficient of the atmosphere on June 21 st based on the precipitable water value you estimated in the sample problem in the last chapter? How do the transmissivity and scattering coefficients compare, i.e. which is larger/smaller, etc.? Qualitatively, how would the scattering coefficient change if the amount of water vapor (i.e. cloud cover) increased? d) Using Equation (3.6.5) and the coefficients and variables computed above, compute the incoming shortwave radiation at the surface in Hilo, at noon on June 21 st. Assume a surface albedo of 0.24.