Using the equations described in class, compute the top of atmosphere (TOA) radi
ID: 235202 • Letter: U
Question
Using the equations described in class, compute the top of atmosphere (TOA) radiation over a location in the Sierra Nevada Mountains (latitude of 36.535 degrees) for 9am, noon, and 3pm (local solar time) on October 17^th (Day of Year, DOY = 290). What fraction of the solar constant is coming in perpendicular to the TOA at these times? Explain (using physical arguments) why the fractions are less than 1.0. For each of the three times (i.e. 9am, noon, and 3pm) listed above, answer the following questions. b) Assuming that the shortwave (SW) transmissivity, equal to 0.444, is representative for this day over the Sierras, what is the magnitude of the direct beam flux incident on a horizontal plane at the surface? c) Assuming that the scattering coefficient beta, equal to 0.215, is representative for this day over the Sierras, what is the magnitude of the diffuse flux incident on a horizontal plane at the surface? d) Assuming the average surface albedo is 0.25 in this region, what is the magnitude of the backscatlered shortwave flux incident on a horizontal plane at the surface? e) What is the total shortwave radiation incident on a horizontal plane at the surface? In general, how do the three components compare in magnitude? f) What is the net shortwave radiation absorbed by the surface?Explanation / Answer
Solar constant (Io=1367w/m2)
n=290
a. I0= Is( 1+0.034 cos(2pi n/265.25)
=1367(1+0.034 cos (2 pi* 290/265.25)
=1367(1+0.034cos(6.865)
=1367(1+0.034*0.99)
=1367(1+0.03366)
=1367*1.03366
=1413.013
TOA=1413.013
b. Shortwave transmissivity=0.444
Q=K +L
Q=1413.013
K= 0.444
L=?
1413.013-0.444
=1412.569
d. average surface albedo=0.25
surface albedo= reflected solar radiation/ incoming short wave radiation
0.25=reflected(backscattered short wave solar radiation)/1412.569
=353.142
e. Total short wave incident on a horizontal plane at the surface is the total amount of short wave radiation recieved from above by a surface horizonatal to the ground. It includes both direct normal irriadiance and diffuse normal irradiance. DNI is direct solar radiation comes in a straight line from the direction of the current position of the sun in the sky. DFI is not come directly from the sun but has been scattered by molecules in the air and comes equally from all directions.
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