The Iranian calendar defines its new year based on the exact moment of the northern equinox; if the equinox is before noon (Iran standard time, I believe) then

The Iranian calendar defines its new year based on the exact moment of the northern equinox; if the equinox is before noon (Iran standard time, I believe) then the new year is on that day, while if it's after noon the new year is on the next day. As a bonus, the month lengths are designed to be longer near aphelion, when the corresponding solar months (periods between 30-degree solar longitudes) are longer. The Chinese calendar is defined (since 1644) based on the days of true new moons and solar terms (corresponding to 15-degree solar longitudes), which also makes it purely astronomically defined. The various Indian calendars are mostly defined using traditional astronomical texts, but I think there have been occasional attempts to update them to modern astronomical knowledge. I'm not sure where the rate 0.003% of a day per year comes from in your comment; even the error in the Gregorian calendar is longer than this (if measured based on the northern equinox, about 12 seconds; if measured based on the mean tropical year, about 27 seconds).