Correcting the Atmospheric Refraction of Fireball Observations at Low Elevation Angles and Significance of the Correction

We introduce a new atmospheric refraction correction method which allows to retrieve fireball position with high accuracy without the need to consider at which distance from the observer or height above the Earth's surface the fireball is situated.
Traditional refraction correction is valid for objects positioned at infinite distance and it overcompensates when an object is situated inside the atmosphere. In this numerical study the overcompensated correction is reduced by artificially increasing the observing site height above the sea level, called the delta-z correction. We use analytically derived formula for the delta-z correction with different refraction models and compare these results to the numerical solution where light ray is traced through the atmosphere. Ray tracing technique is implemented on the finely meshed atmospheric layers in order to derive value of the correction.
We parametrize the viewing angle and the fireball height above sea level in order to define whether this delta-z correction is significant or negligible. Significance is defined by studying the errors caused by the observed horizontal altitude, height of the fireball above the sea-level, and height of the observing site. We find that the delta-z correction should be performed if a fireball is observed within 20 degrees altitude above the horizon or with negative altitudes. We also find that delta-z correction is always accurate if fireball is situated 20km or higher above the sea level and hence it can be safely applied in processing of all observational cases of fireballs.