kai.reduce.slalib

Functions

`refco`(HM, TDK, PMB, RH, WL, PHI, TLR, EPS)	Determine the constants A and B in the atmospheric refraction
`refro`(ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR, EPS)	Atmospheric refraction for radio and optical/IR wavelengths.
`atmt`(R0, T0, ALPHA, GAMM2, DELM2, C1, C2, C3, C4, C5, ...)	Internal routine used by REFRO
`atms`(RT, TT, DNT, GAMAL, R)	Internal routine used by REFRO
`da1p`(ANGLE)	Normalize angle into range +/- pi (double precision)

Module Contents

kai.reduce.slalib.refco(HM, TDK, PMB, RH, WL, PHI, TLR, EPS)[source]

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:: HM d height of the observer above sea level (metre) TDK d ambient temperature at the observer (deg K) PMB d pressure at the observer (millibar) RH d relative humidity at the observer (range 0-1) WL d effective wavelength of the source (micrometre) PHI d latitude of the observer (radian, astronomical) TLR d temperature lapse rate in the troposphere (degK/metre) EPS d precision required to terminate iteration (radian)
Returned:: REFA d tan Z coefficient (radian) REFB d tan**3 Z coefficient (radian)

Called: refco

Notes:

1 Typical values for the TLR and EPS arguments might be 0.0065D0 and: 1D-10 respectively.

2 The radio refraction is chosen by specifying WL > 100 micrometres.

3 The routine is a slower but more accurate alternative to the: slRFCQ routine. The constants it produces give perfect agreement with slRFRO at zenith distances arctan(1) (45 deg) and arctan(4) (about 76 deg). It achieves 0.5 arcsec accuracy for ZD < 80 deg, 0.01 arcsec accuracy for ZD < 60 deg, and 0.001 arcsec accuracy for ZD < 45 deg.

P.T.Wallace Starlink 3 June 1997

Migrated from SLALIB (fortran) to python: J. R. Lu – 2015-05-13

kai.reduce.slalib.refro(ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR, EPS)[source]

Atmospheric refraction for radio and optical/IR wavelengths.

Given:: ZOBS d observed zenith distance of the source (radian) HM d height of the observer above sea level (metre) TDK d ambient temperature at the observer (deg K) PMB d pressure at the observer (millibar) RH d relative humidity at the observer (range 0-1) WL d effective wavelength of the source (micrometre) PHI d latitude of the observer (radian, astronomical) TLR d temperature lapse rate in the troposphere (degK/metre) EPS d precision required to terminate iteration (radian)
Returned:: REF d refraction: in vacuo ZD minus observed ZD (radian)

Notes:

1 A suggested value for the TLR argument is 0.0065. The

refraction is significantly affected by TLR, and if studies of the local atmosphere have been carried out a better TLR value may be available.

2 A suggested value for the EPS argument is 1D-8. The result is

usually at least two orders of magnitude more computationally precise than the supplied EPS value.

3 The routine computes the refraction for zenith distances up

to and a little beyond 90 deg using the method of Hohenkerk and Sinclair (NAO Technical Notes 59 and 63, subsequently adopted in the Explanatory Supplement, 1992 edition - see section 3.281).

4 The code is a development of the optical/IR refraction subroutine

AREF of C.Hohenkerk (HMNAO, September 1984), with extensions to support the radio case. Apart from merely cosmetic changes, the following modifications to the original HMNAO optical/IR refraction code have been made:

. The angle arguments have been changed to radians.

. Any value of ZOBS is allowed (see note 6, below).

. Other argument values have been limited to safe values.

. Murray’s values for the gas constants have been used: (Vectorial Astrometry, Adam Hilger, 1983).
. The numerical integration phase has been rearranged for: extra clarity.
. A better model for Ps(T) has been adopted (taken from: Gill, Atmosphere-Ocean Dynamics, Academic Press, 1982).
. More accurate expressions for Pwo have been adopted: (again from Gill 1982).
. Provision for radio wavelengths has been added using: expressions devised by A.T.Sinclair, RGO (private communication 1989), based on the Essen & Froome refractivity formula adopted in Resolution 1 of the 13th International Geodesy Association General Assembly (Bulletin Geodesique 70 p390, 1963).

. Various small changes have been made to gain speed.

None of the changes significantly affects the optical/IR results with respect to the algorithm given in the 1992 Explanatory Supplement. For example, at 70 deg zenith distance the present routine agrees with the ES algorithm to better than 0.05 arcsec for any reasonable combination of parameters. However, the improved water-vapour expressions do make a significant difference in the radio band, at 70 deg zenith distance reaching almost 4 arcsec for a hot, humid, low-altitude site during a period of low pressure.

5 The radio refraction is chosen by specifying WL > 100 micrometres.

Because the algorithm takes no account of the ionosphere, the accuracy deteriorates at low frequencies, below about 30 MHz.

6 Before use, the value of ZOBS is expressed in the range +/- pi.

If this ranged ZOBS is -ve, the result REF is computed from its absolute value before being made -ve to match. In addition, if it has an absolute value greater than 93 deg, a fixed REF value equal to the result for ZOBS = 93 deg is returned, appropriately signed.

7 As in the original Hohenkerk and Sinclair algorithm, fixed values

of the water vapour polytrope exponent, the height of the tropopause, and the height at which refraction is negligible are used.

8 The radio refraction has been tested against work done by

Iain Coulson, JACH, (private communication 1995) for the James Clerk Maxwell Telescope, Mauna Kea. For typical conditions, agreement at the 0.1 arcsec level is achieved for moderate ZD, worsening to perhaps 0.5-1.0 arcsec at ZD 80 deg. At hot and humid sea-level sites the accuracy will not be as good.

9 It should be noted that the relative humidity RH is formally

defined in terms of “mixing ratio” rather than pressures or densities as is often stated. It is the mass of water per unit mass of dry air divided by that for saturated air at the same temperature and pressure (see Gill 1982).

Called: slDA1P, slATMT, slATMS

P.T.Wallace Starlink 3 June 1997

kai.reduce.slalib.atmt(R0, T0, ALPHA, GAMM2, DELM2, C1, C2, C3, C4, C5, C6, R)[source]

Internal routine used by REFRO

Refractive index and derivative with respect to height for the troposphere.

Given:: R0 d height of observer from centre of the Earth (metre) T0 d temperature at the observer (deg K) ALPHA d alpha ) GAMM2 d gamma minus 2 ) see HMNAO paper DELM2 d delta minus 2 ) C1 d useful term ) C2 d useful term ) C3 d useful term ) see source C4 d useful term ) of slRFRO C5 d useful term ) C6 d useful term ) R d current distance from the centre of the Earth (metre)
Returned:: T d temperature at R (deg K) DN d refractive index at R RDNDR d R rate the refractive index is changing at R

Note that in the optical case C5 and C6 are zero.

P.T.Wallace Starlink 30 May 1997

kai.reduce.slalib.atms(RT, TT, DNT, GAMAL, R)[source]

Internal routine used by REFRO

Refractive index and derivative with respect to height for the stratosphere.

Given:: RT d height of tropopause from centre of the Earth (metre) TT d temperature at the tropopause (deg K) DNT d refractive index at the tropopause GAMAL d constant of the atmospheric model = G MD/R R d current distance from the centre of the Earth (metre)
Returned:: DN d refractive index at R RDNDR d R rate the refractive index is changing at R

P.T.Wallace Starlink 14 July 1995

kai.reduce.slalib.da1p(ANGLE)[source]

Normalize angle into range +/- pi (double precision)

Given:: ANGLE dp the angle in radians

The result (double precision) is ANGLE expressed in the range +/- pi.

P.T.Wallace Starlink 23 November 1995