Question about Surface Slope Calculation!

[Springder]

Referring to literature Sayer et al, 2010 , slope calculation equation can be expressed as:

In equation above, $\phi$ is not $\phi_r$ , which represents Relative azimuth angle. But in our Codes below, $\phi$ was replaced by $\phi_r$.

        self.dangle = scenegeom.cos_sza + scenegeom.cos_vza

        self.Zx = da.where(self.dangle > dither_more,
                           -1. * (scenegeom.sin_vza * scenegeom.sin_raa) / self.dangle,
                           0.)
        self.Zy = da.where(self.dangle > dither_more,
                           -1. * (scenegeom.sin_sza + scenegeom.sin_vza * scenegeom.cos_raa) / self.dangle,
                           0.)

Why are we doing this?

[Springder]

@simonrp84 hello! R U here?

[simonrp84]

Please remember to be polite and patient, @Springder. While I always try to assist, this is not my job and I do so in my spare time.

To answer your question, the Sayer paper neglected to include the _R on the azimuth term. Equations 7 and 8 use the relative azimuth.

[Springder]

No offence, I'm just excited about any mistakes I might find. I apologise if I have offended you.
Back to the question. I think $\phi$ should be the azimuth of the normal vector of the slope. Because if you don't consider it that way, then the calculated specular reflection has nothing to do with the undulation of the sea.