The refraction graph is about as I expected. The change from 40 to 25 degrees is on the order of an arcmin POSITION. Colors refract differentially, so we'd expect HFR to increase perpendicular to the horizon. Whether refraction or airmass is the major driver, I consider elevation to be a good proxy for modeling/controlling the effect (and it's readily available).
It's not a position graph, it's a graph of the Index of refraction versus the elevation angle at standard temperature and pressure (STP). It is a number representing the angular displacement of incident light rays through the atmosphere showing the effect of thickness of the transited airmass between the observer and the celestial target. The calculated index is directly influenced by temperature and pressure (among other things, but these are the two largest factors), Elevation angle is a scalar value, and it's change due to earth rotation, is based on the location data, which doesn't change (or shouldn't)., so it has no mathematical relationship to temperature, and isn't a proxy value for anything. Unless your mount is on a moving object, it will not have have a direct impact of tracking error, unless .
Temperature has several effects. It causes the materials in the mount or gear to expand or contract, which can change the elevation angle slightly, and the error it produces will be relatively constant, and always in the same direction relative to the direction of the temperature change. So you wouldn't expect to see a lot of tracking error scattered about the regression line, instead you'd see the directrix of the parabolic regression line move up or down the Y axis, but the parabola itself doesn't change its shape.
The principle effect of temperature changes is that they change the index of refraction (RI), and thus change the apparent size of celestial objects. If the atmosphere were still and well regulated, then this wouldn't be a problem, but it isn't. It roils, changes density, and the stratification of the air changes, and this produces inherent error in the RI, and that translates directly to focusing, tracking and guiding errors, and those will be randomly scattered about the calculated RI.
In your post, you refer to Temperature Compensation as though it is a single term, but it's not. It's an ephemeral value calculated specifically for each value modified. There is no one "Temperature Compensation" value. Theres one for refraction, one for expansion/contraction, and probably others. A programmer would have to discuss how they used temperature in the various processes, to discuss it in more specific terms, but the main takeaway, is that temperature compensation is only a meaningful term when it includes the process or value being compensated. It will be different for every process.
dmsummers wrote: I consider elevation to be a good proxy for modeling/controlling the effect (and it's readily available).
It's not. The elevation angle is fixed (or should be) and does not change during a session. It is used for the initial calculation of the RI (and alignment, etc), but thereafter is constant, and so has no further effect on focusing or focus error.