I'm digitizing and stitching together a number of adjacent/overlapping property surveys.
The most recent ones provide clear UTM/MTM grid bearings and distances, and in some cases coordinates of ORPs, plus relative bearing corrections applied to adjacent older surveys. These corrections are consistent with mathematical calculations of grid convergence (see Calculating grid convergence (True North to Grid North)). This helps me digitize those surveys in turn, even if they lack as much information.
A couple of the older surveys are pretty wide in the east-west direction, so bearing convergence should mathematically vary by over 90 arc seconds over the one survey. While this is not huge, taken in combination with other surveys, it is significant enough to contribute to closure errors in my resultant model, if I do it wrong.
In coding a wide survey, should the bearing correction (vs grid) be varied across the survey based on longitude/easting? And if so, how? Should a line defining point B from point A have its bearing adjusted based on the grid convergence angle at point A? At point B? At the midpoint? If it's long (some of my lines are 6000'/1800m), do I even need to transcribe as a curve, or break into several line segments at slightly different grid angles? Or, alternatively, is that all taken care of by the single bearing correction implied by the reference bearing specified on the survey?
Here is an exaggerated illustration. In blue, each survey is digitized with a constant bearing correction, as specified by A itself, and calculated relative to it for B,C,D. In red, B's bearing correction is varied according to differences in grid convergence across its width. When C and D are then corrected relative to B, the difference is significant for points on the far right side.
The surveys where I'm encountering this issue date to the 1980s or 90s, so the distances are implicitly ground rather than grid. The bearings are described as "astronomic", relative to a specified reference bearing. This is typically a boundary line shared with a neighbouring survey (and so its bearing reference frame is being borrowed, deviating further away from true north when this happens several times), or a meridian near the midpoint.
I've tried it both ways and there are some improvements in apparent empirical accuracy, but not wholly conclusive due to other surveying imprecisions. So I'd love to know the right answer in theory.
[And no, I'm not infringing on surveyors' bailiwick. I'm not establishing property boundaries for anyone, just trying to reconcile data placement issues for some research.]
