How does solar altitude affect the length of the path of solar radiation through earth's atmosphere?

The angle of the Sun above the horizon, which is the solar altitude, influences the intensity ofsolar radiation received at Earth’s surface. At the place on Earth where the Sun is directlyoverhead, the local solar altitude has its maximum value of 90 degrees and solar rays are mostconcentrated. Whenever the Sun is positioned lower in the sky, solar radiation spreads over alarger area of Earth’s horizontal surface and thus is less intense. Solar radiation reaches theplanet essentially as parallel beams of uniform intensity. The nearly spherical Earth presents acurved surface to incoming solar radiation so that the noon solar altitude always varies withlatitude. The intensity of solar radiation actually striking Earth’s atmosphere is greatest at thelatitude where the noon Sun is in the zenith and decreases with distance north and south of thatlatitude. Decreasing solar altitude lengthens the path of the Sun’s rays through the atmosphere. As the path lengthens, the greater interaction of solar radiation with clouds, gases and aerosols reduces its intensity