The Calculation of Astronomical Refraction in Marine Navigation

Abstract

Since programmable electronic calculators were first employed in marine navigation, a variety of formulae has been used for calculating astronomical refraction. As the choice is wide, some formulae have been selected from commonly used reference sources and their accuracy and suitability examined. No attempt has been made to assess the validity of the selected formulae to represent astronomical refraction in practical circumstances. Accuracy comparisons have been made using the refraction algorithm proposed by Garfinkel 1 -the standard adopted by the British and American Nautical Almanac Offices. New formulae are given that are simple and accurate, even over a wide range of temperature and pressure, and which for all practical purposes may be considered equivalent to the tables of refraction given in the Nautical Almanac.i. I N T R O D U C T I O N A number of attempts, with varying degrees of success, have been made to devise a single, simple formula to represent astronomical refraction accurately. The problem is difficult when one considers the complexity of the algorithm of Garfinkel. 1 If observations are confined to altitudes above i j°, where refraction does not exceed about one-tenth of that at o° altitude, a good approximation to the unsigned mean refraction (ft M ) in minutes of arc is given by:where h is the observed altitude in degrees at a sea-level air temperature of i o° C and pressure of i o i o mb and K is a constant close to unity. Not only is this refraction formula simple, but also variations between the computed and actual refraction are expected to be small. As altitude decreases, the size of the refraction correction and its uncertainty increase -the uncertainty arising when atmospheric anomalies are present.Occasionally observations need to be made at low altitudes, and for these situations either the range of validity of the above formula can be extended by suitable modifications or a separate formula provided. In these circumstances it is not uncommon to find significant differences between the values of refraction corrections calculated using Garfinkel's algorithm and formulae that purport to represent the generally accepted standard of Garfinkel. One must accept the fact that atmospheric anomalies may be present at the time of observation, but the estimated value of the refraction correction should not be further degraded by the use of a poor formula. NAV 35

Optical intensity interferometry through atmospheric turbulence

“…is shown in the top part of the figure, with latitude φ, declination δ and hour angle ω (Woolf 1968) and a small heuristic correction R of at most 34 arc minutes due to the refraction in the atmosphere (Bennett 1982). Over that measurement time where weather and building geometry permitted to collect data, the elevation angle α covers a range from about 70 • around noon to 20 • in the evening, making the length of the air column s = h0/ sin α the light has to pass through to range from 1.06h0 to 2.92h0, where h0 is the effective height of the atmosphere.…”

Metrology of solar spectral irradiance at the top of the atmosphere in the near infrared measured at Mauna Loa Observatory: the PYR-ILIOS campaign

“…Solar zenith angles (SZAs) are calculated with the NOAA Solar Position Calculator (https://www.esrl.noaa.gov/gmd/ grad/solcalc/index.html, last access: 12 December 2018) that implements Meeus (1998) algorithms and are subsequently corrected for atmospheric refraction effects according to Bennett (1982). AMFs are calculated using the Kasten and Young algorithm (Kasten and Young, 1989).…”

Analytical formulas for refraction of radiowaves from exoatmospheric sources

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