Question

Calculate the expected solar radiative flux at our latitude (40°N) at solar noon (time of peak radiation) at three times of year: equinox, and both summer and winter solstice. (Please ignore the role of the atmosphere here – in other words calculate your answer as if there were no atmosphere altering the incoming radiation.)

Answer 1

H = 15⁰ *(time - 12), where H is hour angle

Z = cos^-1 (sinXsinY + cosXcosYcosH), where Z is the zenith angle, X is latitude and Y is the solar declination angle

Y at equinox is 0⁰ , Y during summer solstice is 23.45⁰ and Y during winter solstice is -23.45⁰.

Solar radiative flux = ScosZ, where S is the solar constant 1000 W/m²

H = 15⁰*(12-12) = 0, X = 40⁰

During  equinox

Z = cos^-1 (sin40⁰sin0⁰ + cos40⁰cos0⁰cos0⁰) = cos^-1 (0+cos40⁰*1*1) = 40⁰

Solar radiative flux = 1000*cos40⁰ = 766.044443 W/m²

During summer solistice

Z = cos^-1 (sin40⁰sin23.45⁰ + cos40⁰cos23.45⁰cos0⁰) = cos^-1 (0.25579645+0.70277507) = cos^-1 (0.95857152) = 16.5499999⁰

Solar radiative flux = 1000*cos16.5499999⁰ = 958.57152 W/m²

During Winter solistice

Z = cos^-1 (sin40⁰sin(-23.45⁰) + cos40⁰cos(-23.45⁰)cos0⁰) = cos^-1 (-0.255796449+0.70277507) = cos^-1 (0.446978621) = 63.45⁰

Solar radiative flux = 1000*cos63.45⁰ = 446.978621 W/m²