Geodetic Refraction

Refraction, Geodetic


a general term sometimes used to refer to different types and manifestations of refraction of electromagnetic waves associated with geodetic measurements. When such refraction occurs, the object being observed, that is, the source of the observed electromagnetic waves, is located within the earth’s atmosphere, whereas in the case of astronomical refraction (seeREFRACTION, ATMOSPHERIC), the object is located beyond the earth’s atmosphere and may even be at an infinitely great distance compared with the earth’s radius.

A distinction is made between the geodetic refraction of light waves, including the refraction of rays of the invisible (infrared) part of the spectrum, and the refraction of radio waves. The reason for this is that the curvature of rays of both types of waves depends on the refractive index n along the waves’ path in the atmosphere, and the refractive index is itself a function of wavelength.

The earth’s atmosphere is nonuniform in structure: the refractive index is different at different points of the atmosphere and varies with time. For this reason, an electromagnetic ray is a space curve of variable curvature and twist. The projection of this curve on the vertical and horizontal planes at the point of observation results in what is called vertical refraction and horizontal, or lateral, refraction. Vertical refraction shows up in trigonometric leveling (terrestrial refraction), in geometric leveling (leveling refraction), in aerial photography (photogram-metric refraction), and in observations of artificial earth satellites (satellite refraction). Lateral refraction is one to two orders of magnitude less than vertical refraction and accompanies all types of refraction; it directly affects results in the measurement of horizontal angles, in triangulation, in traversing, and in astronomical observations of azimuths.

If we know the refractive index of the atmosphere along and near the path of propagation of the electromagnetic waves and if we know the relative position of the source and receiver (observer) of the waves, we can formulate an equation for the ray and determine the effect of refraction on various kinds of observations. In practice, however, this direct method of determining the magnitude of refraction cannot be used because we cannot know the exact refractive index n of the atmosphere at the time of observation. The refractive index exhibits a complex dependence on the temperature, pressure, and humidity of the atmosphere, on the physicogeographical conditions, on the topography, and on the character of the underlying cover. Geodesy usually employs indirect methods of determining the refraction and of reducing the effect of the refraction on individual types of geodetic measurements. Such indirect methods may be, for example, of a meteorological, geodetic, or statistical nature. There are being developed instrumental methods of determining refraction wherein measuring devices are used to determine directly the actual total refractive index of the air in the path of the electromagnetic waves or to measure the angle of refraction.


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