Terrestrial refraction

Terrestrial refraction (sometimes called geodetic refraction) is the apparent visual displacement, of terrestrial objects and features, from their assumed or known geometric positions. This observed phenomena is a stochastic (random) in nature and have defied man's ability to create predictive models.

General

Terrestrial refraction appears when both the object and observer are within the Earth’s air. This refraction is responsible for ordinary mirages, image distortion, shimmer, scintillation of light and has been extensively studied for more than 20 centuriesThe following lists some of the known variables that determine the path light travels through air and the resulting image.

• Temperature
• humidity
• air pressure
• turbulence
• wind
• wavelength of electromagnetic radiation
• %CO2 content

These variables interact in a random and complex manner. They are often decorrelated. This fact, severely limits the distance for which precision optical measurements can be made.

"It appears many geodesists share the opinion: geodetic refraction is a nuisance and very little can be done to overcome this hurdle"

Quotes from scholars

"Every one conversant with nautical astronomy is aware that some uncertainty always attends observations made with the natural horizon, from the varying amount of the dip occasioned by terrestrial refraction. The cause of these variations is very obscure. The best authorities seem to regard differences of temperature in the air and water as the sole cause of the irregular density of the lower strata of the atmosphere on which the varieties of the dip depend. It is known that, in general, when the water is warmer than the air, the dip is greater than that given in the tables; and that when the water is colder than the air, the dip is less. But cases occur where the deviations from the tables are found to bear little relation, at least in amount, to the relative temperatures of the air and water. Some other property of the atmosphere must, therefore, be sought after, by the influence of which the effects of temperature are modified."

Young

Citing {Brinkley, J. 1815, Trans. R. Irish Acad., 12, 77} "It is well known to those conversant in observations made with good instruments that near the horizon an irregularity in refraction hitherto unexplained shews itself."... ... "it is not likely the irregularities will ever be submitted to any law, and investigations respecting formulae for refractions for zenith distances greater than about 80� may be considered more curious than useful’’

Citing d, Ivory (1823) ‘‘The refractions are ... affected by circumstances of which the observer has no intimation, and which cannot enter into any theory. The real causes of such anomalies is [sic] undoubtedly the irregular changes that take place in the remote parts of the atmosphere, which are not indicated by the barometer or the thermometer.’’

Citing

Himself "Refraction within about 5° of the horizon is so variable that no a priori formula or table can be expected to give accurate values there."

"Refraction within about 5° of the horizon is so variable that no a priori formula or table can be expected to give accurate values there; the local lapse rate and thickness of the boundary layer above the observer must be known. "

"At and below the astronomical horizon, the refraction depends primarily on atmospheric structure below the observer and varies so much (tens of minutes, or even several degrees) that only very crude predictions can be made."

Burton "Atmospheric refraction is both an astronomical irritant and an intellectual puzzle. A major problem for observational astronomers since Ptolemy, it still baffled Newton who consumed nearly a year of his life finding a correct understanding of the problem in order to aid the astronomer John Flamsteed. 1 Despite its complexity, it has been a delightful puzzle for students of optics and mathematics, and for the armchair astronomer. "

G. A. KHARAGHANI "As in geodetic levelling, the atmospheric refraction can be the main source of error in the trigonometric method." .. ... "A suggested remedy is to shorten the sight length, because the influence of refraction is proportional to the square of the sight distance [e.g. Angus-Leppan, 1985]."

Hilmar "Refraction is a detrimental problem in terrestrial optical measurements and can be regarded as major source of systematic errors in the precise determination of distances and directions."

Flach "The propagation path of light in the atmosphere is influenced by inhomogenities of the refractive index. These refraction effects deteriorate the accuracy of the direction and distance measurements in geodetic applications. As illustrated by two examples in this report, the refraction effects cannot be accurately corrected up to now and, therefore, solutions must be provided which can be implemented into geodetic instruments." ... ... "Although advancing instrument technology allows a high degree of precision and automation, the accuracy and reliability of geodetic measurements is still limited due to atmospheric influences, especially refraction. Up-to-now, refraction is still one of the unsolved problems in numerous applications of surveying."

Baselga, et al. "If temperature vertical profiles are unknown then the refraction coefficient cannot be reliably determined. Some surveyors may customarily use then an average value, e.g. k = 0.13 , perhaps being unaware of the risks involved in such simplistic assumption."

McDaniel and Hahalov "Variations in the refractive index in the atmosphere are caused by inhomogeneities of a wide range of sizes. These include both variations in the mean refractive index and refractive index fluctuations due to turbulence that can not be accounted for by deterministic models"

Gaifillia, D., et al "Refraction is a complex problem in terrestrial optical measurement and can be regarded as a major source of systematic error in the precise determination of height differences using trigonometric weighting." ... " It is important to bear in mind that determination of k by means of a model may turn out to be somewhat inaccurate, but still remains better than the blind use of a universal k of 0.16 (for Greece) or 0.13 (for other parts of Europe)."