Adjust an unrefracted zenith distance to include the effect of atmospheric refraction, using the simple A tan Z $+$ B tan$\ast$$\ast$3 Z model (plus special handling for large ZDs).

void palRefz ( double zu, double refa, double refb, double $\ast$zr );

zu = double (Given)

refa = double (Given)

refb = double (Given)

zr = double $\ast$ (Returned)

• This routine applies the adjustment for refraction in the opposite sense to the usual one - it takes an unrefracted (in vacuo) position and produces an observed (refracted) position, whereas the A tan Z $+$ B tan$\ast$$\ast$3 Z model strictly applies to the case where an observed position is to have the refraction removed. The unrefracted to refracted case is harder, and requires an inverted form of the text-book refraction models; the formula used here is based on the Newton-Raphson method. For the utmost numerical consistency with the refracted to unrefracted model, two iterations are carried out, achieving agreement at the 1D-11 arcseconds level for a ZD of 80 degrees. The inherent accuracy of the model is, of course, far worse than this - see the documentation for palRefco for more information.

• At ZD 83 degrees, the rapidly-worsening A tan Z $+$ B tan^3 Z model is abandoned and an empirical formula takes over. For optical/IR wavelengths, over a wide range of observer heights and corresponding temperatures and pressures, the following levels of accuracy (arcsec, worst case) are achieved, relative to numerical integration through a model atmosphere:

ZR error

80 0.7 81 1.3 82 2.4 83 4.7 84 6.2 85 6.4 86 8 87 10 88 15 89 30 90 60 91 150 } relevant only to 92 400 } high-elevation sites

For radio wavelengths the errors are typically 50% larger than the optical figures and by ZD 85 deg are twice as bad, worsening rapidly below that. To maintain 1 arcsec accuracy down to ZD=85 at the Green Bank site, Condon (2004) has suggested amplifying the amount of refraction predicted by palRefz below 10.8 deg elevation by the factor (1$+$0.00195$\ast$(10.8-E_t)), where E_t is the unrefracted elevation in degrees.

The high-ZD model is scaled to match the normal model at the transition point; there is no glitch.

• Beyond 93 deg zenith distance, the refraction is held at its 93 deg value.

• See also the routine palRefv, which performs the adjustment in Cartesian Az/El coordinates, and with the emphasis on speed rather than numerical accuracy.

Condon,J.J., Refraction Corrections for the GBT, PTCS/PN/35.2, NRAO Green Bank, 2004.