The Islamic calendar is based on lunar months, which begin when the thin crescent Moon is actually sighted in the western sky after sunset within a day or so after the New Moon. The Islamic dates begin at sunset on the previous day. The visibility of the lunar crescent as a function of the Moon's age - the time counted from the New Moon - is obviously of great importance to Muslims. The date and time of each New Moon can be computed exactly but the time that the Moon first becomes visible after the New Moon depends on many factors and cannot be predicted with certainty. The sighting of the lunar crescent within one day of New Moon is usually difficult. The crescent at this time is quite thin, has a low surface brightness and can easily be lost in the twilight. Generally, the lunar crescent will become visible to suitably-located, experienced observers with good sky conditions about one day after the New Moon. However, the time that the crescent actually becomes visible varies quite a bit from one month to another. The record for an early sighting of a lunar crescent with a telescope is 12.1 hours after New Moon; for naked-eye sightings, the record is 15.5 hours from New Moon. For Islamic calendar purposes, the sighting must be made with the unaided eye. Obviously, the visibility of the young lunar crescent depends on atmosphere conditions, the location and preparation of the observer.
The prediction of the first sighting of the early crescent Moon is an interesting problem because it simultaneously involves a number of highly non-linear effects. Effects to be considered are the geometry of the Sun, Moon, the width and surface brightness of the crescent, the absorption of the Moon's light and the scattering of the Sun's light in the Earth's atmosphere, the physiology of human vision and natural horizon. The effects of meteorological conditions such as mean sea level pressure, visibility, mean temperature and humidity on Crescent visibility are studied in this paper.
Our studied sites are located in the south, center and eastern part of Iran including Mashad, Bojnord, Birjand, Isfahan, Shiraz and Kerman cities. Two series of data are used in this study. The first one data were sighting and visibility of the lunar crescents which recorded by Moon's sighting groups in the above mentioned cities and the second series of data were the meteorological observations of mean sea level pressure, mean temperature, horizontal visibility and relative humidity in the same dates and locations of Moon's sighting. Horizontal visibility is divided into two categories of bellow and above 10kM. Period of study was 8 years starting from 1423 to 1430 according to Islamic calendar.
Genetic algorithm is used to formulate the relations between moon visibilities and meteorological parameters. Genetic algorithms are one of the best ways to solve a problem for which little is known. They are very general algorithms and so may work well in any search space. Genetic algorithms use the principles of selection and evolution to produce several solutions to a given problem. Two methods of linear and non-linear approaches are used to model the statistical relations between the lunar visibilities and meteorological parameters.
For linear-based method the following formula is used:
We used the bellow formula for the nonlinear approach:
Where MSE is the Mean Square Error, Robs and Rmod represent actual and modeled visibility of the Moon. P, RH, T and V are mean seas level pressure, relative humidity, temperature and visibility, respectively. (n-p) is degree of freedom and ai is constants.
One of the important factors affecting crescent visibility is meteorological parameters, but they have not been considered well up to now. In this paper a Genetic algorithm has been used to find relationship between percentage of crescent lighting and meteorological parameters such as sea level pressure; mean temperature, relative humidity and horizontal visibility. In this regards, observations have been considered during the period of 1423-1430 lunar Hejri(Islamic calender) calendar for Mashad, Kerman, Shiraz, Esfahan, Birjand, and Boujnourd for two cases with about 10 km horizontal visibility.
Error, bias and weighted factor of meteorological impacts on crescent visibility have been calculated after comparing modeled and observed crescent visibility. Results generally show that non-linear parameterization equations have more bias than linear equations. Maximum bias with 3.24 has been occurred in nonlinear model for horizontal visibility less than 10km over Birjand and Bojnourd sites. The minimum bias of crescent visibility has been occurred in Shiraz by 0.01 percent. The minimum and maximum percentages of relative error are found in Shiraz and Birjand by 1.96% and 99%, respectively. We also found that in linear modeling with horizontal visibility more than 10km, weighted effect of pressure increase by decreasing altitude from mean sea level and effect of humidity decreases by increasing altitude from mean sea level.
Our result confirms that the crescent visibility is more sensitive both to pressure and horizontal visibility. Overlay, linear and nonlinear equations have acceptable results for modeling crescent visibility. Results of this paper reveal that meteorological parameterization of crescent visibility can be used for prediction of crescent visibility from meteorological view point.