Visibility of the lunar crescent

A model designed to predict whether or not the moon will be visible under any set of observing conditions is presented. It explicitly includes atmospheric clarity, which is calculated from the site's altitude, latitude, temperature, relative humidity, aerosol content, and time of the year. This mathematical model is combined with a lunar and solar ephemeris to yield a computer program which will predict the date of the first crescent sighting from any location. A list of 201 observations of lunar visibility was collected to test this model and other models. It is found that criteria involving the moonset lagtime and the moon's age have zones of uncertainty which typically cover the entire earth.