refco¶
- erfa.refco(phpa, tc, rh, wl)[source]¶
Determine the constants A and B in the atmospheric refraction model dZ = A tan Z + B tan^3 Z.
- Parameters:
- phpadouble array
- tcdouble array
- rhdouble array
- wldouble array
- Returns:
- refadouble array
- refbdouble array
Notes
Wraps ERFA function
eraRefco
. The ERFA documentation is:- - - - - - - - - e r a R e f c o - - - - - - - - - Determine the constants A and B in the atmospheric refraction model dZ = A tan Z + B tan^3 Z. Z is the "observed" zenith distance (i.e. affected by refraction) and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo) zenith distance. Given: phpa double pressure at the observer (hPa = millibar) tc double ambient temperature at the observer (deg C) rh double relative humidity at the observer (range 0-1) wl double wavelength (micrometers) Returned: refa double tan Z coefficient (radians) refb double tan^3 Z coefficient (radians) Notes: 1) The model balances speed and accuracy to give good results in applications where performance at low altitudes is not paramount. Performance is maintained across a range of conditions, and applies to both optical/IR and radio. 2) The model omits the effects of (i) height above sea level (apart from the reduced pressure itself), (ii) latitude (i.e. the flattening of the Earth), (iii) variations in tropospheric lapse rate and (iv) dispersive effects in the radio. The model was tested using the following range of conditions: lapse rates 0.0055, 0.0065, 0.0075 deg/meter latitudes 0, 25, 50, 75 degrees heights 0, 2500, 5000 meters ASL pressures mean for height -10% to +5% in steps of 5% temperatures -10 deg to +20 deg with respect to 280 deg at SL relative humidity 0, 0.5, 1 wavelengths 0.4, 0.6, ... 2 micron, + radio zenith distances 15, 45, 75 degrees The accuracy with respect to raytracing through a model atmosphere was as follows: worst RMS optical/IR 62 mas 8 mas radio 319 mas 49 mas For this particular set of conditions: lapse rate 0.0065 K/meter latitude 50 degrees sea level pressure 1005 mb temperature 280.15 K humidity 80% wavelength 5740 Angstroms the results were as follows: ZD raytrace eraRefco Saastamoinen 10 10.27 10.27 10.27 20 21.19 21.20 21.19 30 33.61 33.61 33.60 40 48.82 48.83 48.81 45 58.16 58.18 58.16 50 69.28 69.30 69.27 55 82.97 82.99 82.95 60 100.51 100.54 100.50 65 124.23 124.26 124.20 70 158.63 158.68 158.61 72 177.32 177.37 177.31 74 200.35 200.38 200.32 76 229.45 229.43 229.42 78 267.44 267.29 267.41 80 319.13 318.55 319.10 deg arcsec arcsec arcsec The values for Saastamoinen's formula (which includes terms up to tan^5) are taken from Hohenkerk and Sinclair (1985). 3) A wl value in the range 0-100 selects the optical/IR case and is wavelength in micrometers. Any value outside this range selects the radio case. 4) Outlandish input parameters are silently limited to mathematically safe values. Zero pressure is permissible, and causes zeroes to be returned. 5) The algorithm draws on several sources, as follows: a) The formula for the saturation vapour pressure of water as a function of temperature and temperature is taken from Equations (A4.5-A4.7) of Gill (1982). b) The formula for the water vapour pressure, given the saturation pressure and the relative humidity, is from Crane (1976), Equation (2.5.5). c) The refractivity of air is a function of temperature, total pressure, water-vapour pressure and, in the case of optical/IR, wavelength. The formulae for the two cases are developed from Hohenkerk & Sinclair (1985) and Rueger (2002). The IAG (1999) optical refractivity for dry air is used. d) The formula for beta, the ratio of the scale height of the atmosphere to the geocentric distance of the observer, is an adaption of Equation (9) from Stone (1996). The adaptations, arrived at empirically, consist of (i) a small adjustment to the coefficient and (ii) a humidity term for the radio case only. e) The formulae for the refraction constants as a function of n-1 and beta are from Green (1987), Equation (4.31). References: Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral Atmosphere", Methods of Experimental Physics: Astrophysics 12B, Academic Press, 1976. Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press, 1982. Green, R.M., "Spherical Astronomy", Cambridge University Press, 1987. Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63, 1985. IAG Resolutions adopted at the XXIIth General Assembly in Birmingham, 1999, Resolution 3. Rueger, J.M., "Refractive Index Formulae for Electronic Distance Measurement with Radio and Millimetre Waves", in Unisurv Report S-68, School of Surveying and Spatial Information Systems, University of New South Wales, Sydney, Australia, 2002. Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996. This revision: 2021 February 24 Copyright (C) 2013-2023, NumFOCUS Foundation. Derived, with permission, from the SOFA library. See notes at end of file.