Why the Site Diffuse Solar Radiation Rate per Area is smaller than the Surface Outside Face Incident Sky Diffuse Solar Radiation Rate per Area

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NOT a definitive answer - suggestions if you wanted to take a deeper dive.

Assuming the model is in the Northern Hemisphere, a south-facing surface will see the sun rise on its left (~SE) and set on its right (~SW) in early January. Depending on the Perez Sky Model calculations, a south-facing vertical surface may receive more diffuse irradiance than a horizontal surface ("Site Diffuse Solar Radiation Rate"), when the sun is fairly low (morning & afternoon), mainly due to circumsolar and horizon brightening. The south-facing surface would also receive diffuse radiation reflected off the ground (more so when the sun is low). Your results seems to reflect that.

A deeper dive would involve reproducing the calculations in the link above, e.g. isolate the contributions from sky dome vs horizon vs circumsolar. In the meantime, here a few simple tests (may help):

• rotate the model 90° so the subsurface is east-facing: same phenomenon only in the morning?
• rotate the model 90° so the subsurface is west-facing: same phenomenon only in the afternoon?
• adjust ground reflectance (to isolate its contribution)

Because of the view factors of the surfaces with the sky.