How to find solar insolation in the IR spectrum

[pondwire]

Homework Statement

Compute the solar irradiance in the near IR range (0.7 - 1.5 microns) at the top of the atmosphere over Denver at noon on August 23rd, and assume that 37 per cent of the solar spectrum is in this range.

Homework Equations

Equations? I=ScosZ where Z is the azimuth angle over Denver at this time, S is 1360Wm-2. Also, there is an equation that's supposed to give actual amount striking surface:
I = I(0) exp(-u secZ), where u is the optical depth.

The Attempt at a Solution

Failed miserably because my computed azimuth angle is 254.8 degrees which results in a negative value for the first equation. I tried the second equation anyway, and the secant of 254.8 is undefined. I spent a lot of time trying to figure out the azimuth angle and could only come up with 254.8 degrees. For that equation (azimuth) I used:

A = 180 deg. + sin-1(cos(11.5)sin(99.8) / sin(90))
Here, 11.5 is the declination angle, which was found from the analemma; 99.8 is the solar hour angle; and 90 is the sun's zenith angle at noon.

Please help. Thanks.

 

[ideasrule]

Why do you need the azimuth angle? You need the altitude of the Sun because that determines what angle the sun's rays hit the ground at. Try calculating the declination of the Sun at the time and work from there, remembering that at noon, the Sun is due south.