What are the Mathematical Algorithms/Formulas behind hindu Sunrise and Sunset Calculations?
In the linked algorithm,  the &quot;zenith&quot; is the position of the sun at sunrise.  This is the number you need to change.
If you want to calculate the time when the top of the sun reaches the horizon you use the &quot;official&quot; zenith of 90⁰50' This is intended to account for refraction and should estimate the time when the sun first appears over the horizon.
Since the sun in 30' across, if you want the time when the centre of the sun is on the horizon, just subtract 15'  ie use a zenith of 90⁰35' (90.583 degrees)
It isn't possible to be more accurate as the amount of refraction varies with the weather. But this should give values that are correct to the minute.