Sister Day — For a given location, let C denote the calendar date with the lowest long-term average daily temperature. The sister day of a date D is the unique date D′ equidistant from C on the opposite side of the annual temperature cycle — if D falls n days after C, then D′ falls n days before C, and vice versa.
warming
⟷
cooling
Warming side
Cooling side
Coldest day
Warmest day
Winter solstice
Summer solstice
Why not the solstice?
The winter solstice marks the day the sun sits lowest in the sky — the most oblique angle of incidence and the least solar energy per square metre of ground. Yet the coldest day arrives weeks later. This is thermal lag: the earth and atmosphere keep radiating stored heat even after the sun begins its climb back. It's the same reason late afternoon is hotter than solar noon, scaled to an entire hemisphere.
Winter solstice (min sun angle)
Coldest day (min temperature)
For , this thermal lag is — the atmosphere needs that long to exhaust its stored warmth after the solstice turns the corner.