## Name

CO_REFRACT()

## Purpose

Calculate correction to altitude due to atmospheric refraction.

## Description

CO_REFRACT can calculate both apparent altitude from observed altitude and

vice-versa.

## Calling Sequence

new_alt = CO_REFRACT(old_alt, [ ALTITUDE= , PRESSURE= , $

TEMPERATURE= , /TO_OBSERVED , EPSILON= ])

## Input

old_alt - Observed (apparent) altitude, in DEGREES. (apparent if keyword

/TO_OBSERVED set). May be scalar or vector.

## Output

Function returns apparent (observed) altitude, in DEGREES. (observed if

keyword /TO_OBSERVED set). Will be of same type as input

altitude(s).

## Optional Keyword Inputs

ALTITUDE : The height of the observing location, in meters. This is

only used to determine an approximate temperature and pressure,

if these are not specified separately. [default=0, i.e. sea level]

PRESSURE : The pressure at the observing location, in millibars.

TEMPERATURE: The temperature at the observing location, in Kelvin.

EPSILON: When keyword /TO_OBSERVED has been set, this is the accuracy

to obtain via the iteration, in arcseconds [default = 0.25

arcseconds].

/TO_OBSERVED: Set this keyword to go from Apparent->Observed altitude,

using the iterative technique.

Note, if altitude is set, but temperature or pressure are not, the

program will make an intelligent guess for the temperature and pressure.

## Description

Because the index of refraction of air is not precisely 1.0, the atmosphere

bends all incoming light, making a star or other celestial object appear at

a slightly different altitude (or elevation) than it really is. It is

important to understand the following definitions:

Observed Altitude: The altitude that a star is SEEN to BE, with a telescope.

This is where it appears in the sky. This is always

GREATER than the apparent altitude.

Apparent Altitude: The altitude that a star would be at, if *there were no

atmosphere* (sometimes called "true" altitude). This is

usually calculated from an object's celestial coordinates.

Apparent altitude is always LOWER than the observed

altitude.

Thus, for example, the Sun's apparent altitude when you see it right on the

horizon is actually -34 arcminutes.

This program uses couple simple formulae to estimate the effect for most

optical and radio wavelengths. Typically, you know your observed altitude

(from an observation), and want the apparent altitude. To go the other way,

this program uses an iterative approach.

## Example

The lower limb of the Sun is observed to have altitude of 0d 30'.

Calculate the the true (=apparent) altitude of the Sun's lower limb using

mean conditions of air pressure and temperature

IDL> print, co_refract(0.5) ===> 0.025degrees (1.55')

WAVELENGTH DEPENDENCE:

This correction is 0 at zenith, about 1 arcminute at 45 degrees, and 34

arcminutes at the horizon FOR OPTICAL WAVELENGTHS. The correction is

NON-NEGLIGIBLE at all wavelengths, but is not very easily calculable.

These formulae assume a wavelength of 550 nm, and will be accurate to

about 4 arcseconds for all visible wavelengths, for elevations of 10

degrees and higher. Amazingly, they are also ACCURATE FOR RADIO

FREQUENCIES LESS THAN ~ 100 GHz.

It is important to understand that these formulae really can't do better

than about 30 arcseconds of accuracy very close to the horizon, as

variable atmospheric effects become very important.

## References

1. Meeus, Astronomical Algorithms, Chapter 15.

2. Explanatory Supplement to the Astronomical Almanac, 1992.

3. Methods of Experimental Physics, Vol 12 Part B, Astrophysics,

Radio Telescopes, Chapter 2.5, "Refraction Effects in the Neutral

Atmosphere", by R.K. Crane.

## Dependencies

CO_REFRACT_FORWARD (contained in this file and automatically compiled).

## Author

Chris O'Dell

Univ. of Wisconsin-Madison

Observational Cosmology Laboratory

Email: odell@cmb.physics.wisc.edu

## Revision History

version 1 (May 31, 2002)

Update iteration formula, W. Landsman June 2002

Corrected slight bug associated with scalar vs. vector temperature and

pressure inputs. 6/10/2002

Fixed problem with vector input when /TO_OBSERVED set W. Landsman Dec 2005

Allow arrays with more than 32767 elements W.Landsman/C.Dickinson Feb 2010