evidence of Suppression of the Unequal Refraction Error in Geodetic Leveling

Analyses of historic data indicate that procedures in force since the nineteenth century have effectively suppressed the unequal refraction error (URE) in geodetic leveling. Although theoretical considerations argue that large refraction errors should accumulate where levelings traverse gentle slopes permitting long sight lengths, extensive examination of routinely developed results lends little support to this argument. Our analyses of the historic record consider (1) height differences based on otherwise similar levelings over the same route but characterized by substantially different sight length, (2) modeled refraction error differences and actually measured elevation changes on both a section‐by‐section and a line‐by‐line basis, (3) misclosures produced from levelings identified with significantly different procedural constraints in technically stable areas of comparable variation in terrain and climate, and (4) alternatively and sequentially developed heights in areas of tectonic stability and areas of persisting instability. All of these analyses indicate that the URE is generally small and unpredictable and hence inconsistent with both theoretical expectations and the results of two conceptually different experimental studies. This inconsistency probably is attributable to the inability of the theoretical models and the failure of the experiments to incorporate in their design those procedures, especially the rejection criteria at the setup, section, and circuit level, that normally minimize refraction error. Traditionally invoked procedural specifications may have suppressed the URE through biasing of observations toward less refractive conditions, whereas all of the theoretical models assume an averaged sampling of the atmosphere. Alternatively, a variety of real world complexities that are disregarded in the models may take on added importance in normally constrained leveling. Thus refraction corrections based on simplified models and mean atmospheric and terrain conditions tend to overcompensate substantially for refraction errors associated with routinely constrained surveys.