The Sky Quality Meter (SQM) and the supporting observations allowed the project to address many of the factors when trying to establish the best approximation for both dawn and Isha.
The reason why any calculation method can only 'approximate' the time for dawn and Isha is because of the many atmospheric and climate conditions which can affect twilight, some of which are illustrated in this project.
The 15 month study using the SQM allowed the project to established the earliest point at which dawn can occur (Tipping Point) and likewise the last point at which Isha (Shafaq al-Abyad) has definitely started (Levelling Point), although due to flexibility in Shariah Isha could be set earlier.
Through the SQM data analysis, it is very clear that dawn is occurring after the sun passes the depression angle of 18° (closer to 14.5°) and similarly Isha (Shafaq al-Abyad) is achieved before the sun reaches the depression angle of 18°, this is not to say that the project totally discounts the important use of 18° as part of the dawn and Isha calculation which will be come clear later in section.
For ease of understanding, there are two district periods when calculating dawn and Isha:
- Dates when the sun reaches the depression angle of 18° or beyond for some part of the night. We will refer this to at the "Normal Period"
- Dates when the sun does not reach the depression angle of 18° during any part of the night. We will refer this to at the "Adjusted Period"
All locations below 48.5° latitude (Majority of the Islamic World), the sun reaches the depression angle of 18° and hence can apply the same calculation method for the complete year as there is no requirement for any alternative method as part of any "Adjusted Period". Even in a high latitude country like the UK, the SQM data for the "Normal Period" was able to establish a strong correlation between magnitudes per square arcsecond (MPAS) reading of 19.5 where dawn was observed and the depression angle of 14.5°. Other international studies using the SQM were also able to establish dawn at approximately 14.5°.
The use of the depression angle of the sun when establishing dawn and Isha is widely used especially since this gives comparable times for all locations below 48.5° latitude (Majority of the Islamic World), but does not address the issue for locations which have an "Adjusted Period" (locations above 48.5° latitude). The exploration of the sun depression rate of change answers some the questions for the transition from "Normal Period" and "Adjusted Period".
Using the minute-by-minute SQM data gathered for the 15 month period, allowed the project the apply a LOWESS function to illustrate the changes in twilight from the darkest part of the night to sunrise (illustrated below).
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What this shows is the constant and regular change in light levels leading to sunrise as the depression angle of the sun decreases. After 19 MPAS, the tight regular bands of MPAS begin to spread. As 20 MPAS there seems to be no correlation between the fixed depression angle and the resulting MPAS light reading. This indicates that the sun continues to have a direct impact levels of twilight which can be measured up until around 19.5 MPAS. All dawn observations have been achieved at this MPAS level. After 19.5 MPAS the sun depression angle and resulting twilight levels have no coloration and must be the random conditions of the night.
When the corresponding depression angles are calculated, 19.5 MPAS results at approximately 14.5° during the "Normal Period". The following chart shows the relationship between the MPAS reading and the depression angle of the sun:
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As described in the project, the MPAS reading at which dawn is observed may well be relative (to location) and not a fixed reading, but all studies indicate that once the sun reaches a depression angle of 14.5° the MPAS reading no longer has a tight relationship indicating the influence of the sun on twilight no longer remains.
The incorrect use of a fixed depression angle throughout the year in higher latitude countries (above 48.5° latitude) is demonstrated with the following chart. The raw MPAS data for the year is shown against the sun depression angle of 14.5°. There is a close relationship during the "Normal Period" and less so in the "Adjusted Period":
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This difference between the "Normal Period" and "Adjusted Period" is better illustrated when the LOWESS function is applied:
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There is almost no difference between the LOWESS 19.5 MPAS result and the depression angle of 14.5° during the "Normal Period". The "Adjusted Period" shows a dawn time calculated by the LOWESS function not bound to a fixed depression angle. The separation between the two (LOWESS calculation and 14.5°) begin and ends at the "Adjusted Period" - when the sun does not go below 18°.
The rate of change analysis indicates that despite the period of time (in minutes) continuing to increase during the "Adjusted Period", it has little or no impact on the observable dawn and the LOWESS function on 19.5 MPAS. The following chart shows the principle method for establishing dawn during the "Adjusted Period". At the point the sun stops reaching the depression angle of 18°, the time difference between sunrise and 14.5° can be set in minutes and this time difference is substracted from each sunrise time during the "Adjusted Period" to give you the approximate dawn time.
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With the combination of a fixed depression angle of 14.5° during the "Normal Period" and the application of the calculated time difference during the "Adjusted Period" you get a very good approximation of dawn times supported by the SQM readings and naked-eye observations.
For Isha the same principle is applied where the fixed depression angle of 14.5° is used during the "Normal Period" and the application of the calculated time difference during the "Adjusted Period" is added to sunset time to give you an Isha time which can be observed as Shafaq al-Abyad.