Wondering if this signature creates space for other approaches to calculate self-shading. What if the arguments are tilt and 'gcr' and passias_masking_angle was private and called within this function? I doubt that the average "masking angle" is general among other models, I could be wrong.

A thought: how is this visible sky dome calculation done in bifacial_vf? Maybe there's some commonality that could inform the interface here, although we wouldn't re-use code from bifacial_vf. If I recall right, that calculation is done with view factors over small increments of angle.

I have a mild preference for sky_diffuse_passias as the function name.

I separated the two functions in anticipation of people wanting to use the "worst-case" angle like SAM does instead of Passias et al.'s average angle. That said, a function that just does 1 - cos(angle/2)^2 does seem strange.

Good idea about bifacial_vf; I haven't had an excuse to get familiar with it before now but am happy to have one.

I looked at the SAM documentation. I think that the low level functions that calculates the average masking_angle is useful, as would be a function that returns masking_angle at a point along the row's surface. Maybe someone would want to use the masking_angle in combination with other sky diffuse models.

Still chewing on the name passias_sky_diffuse for the effects function.

I added a masking_angle function that calculates the angle for a given point and renamed passias_sky_diffuse to sky_diffuse_passias, but am happy to rename if you have a better alternative.

Maybe someone would want to use the masking_angle in combination with other sky diffuse models.

It occurs to me that the masking angle is also useful for comparing with solar position to determine if direct shading is relevant.

The equation below isn't equivalent to the published equation? Or, you couldn't reproduce the published equation [9]?

The latter. The published equation [9] also gives different results from evaluating the integral numerically: https://gist.github.com/kanderso-nrel/2c6c3a1853338cdef5b4bbc67092ccc8

I'm persuaded. Your solution looks correct to me. I computed a few points on the k=1 and k=2 curves to check.

I have a notion that gcr is sometimes defined as gcr := width * cos(tilt) / pitch for fixed-tilt arrays. Is that a common usage? If so, this parameter description and the one in masking_angle_passias should clarify that width / pitch is meant.

In my experience the usual definition of ground coverage ratio is the ratio of module area to ground area, where the "ground area" is left somewhat ambiguous. That's the definition used in Pvsyst, Helioscope and pvlib.tracking.SingleAxisTracker. I think we should stick with gcr = width / pitch. I'd be interested to see where the ratio of projected horizontal width to pitch is used.

Entirely editorial - I'd swap the order of the last and next-to-last sentences, so that the focus stays on the Passias approach.