[fesempuw] Seasonal lag and astronomical seasons

It seems strange that the day with the most sun, the summer solstice, is marked as the beginning of summer and not the midpoint of summer.  However, this is fine if there is a 1.5 month seasonal lag, essentially how long it takes for the air to heat up (or cool down) after the sun does its thing.  (If there were not seasonal lag, seasons should start on the cross-quarter days.)

The amount of seasonal lag depends on local environment and season, so we consider defining the seasons locally, allowing every place to celebrate the start of various seasons on different days.  How should the seasons be defined based on historical temperature data?  Some possibilities:

1. Each season is exactly 3 months (1/4 year) long, providing exactly one degree of freedom: what is the location's average seasonal lag (which might be more or less than 1.5 months)?  Order the days of the year by average temperature.  Ideally the top 25% warmest days get assigned to summer and the bottom 25% winter.  Rotate the dial of seasonal lag to best fit, scoring using some goodness-of-fit function against the ideal.

2. Simply assign the 25% warmest days to summer and 25% coldest to winter, playing some tricks to make sure the days are contiguous for each season.  Spring and fall get assigned the days in between, which might not be 1/4 year each.

3. Summer is the interval between the solstice and highest average temperature.  Similarly for winter.  Spring and fall are the times in between, typically very long.  Inspired by, there really are only two seasons: things becoming more and things becoming less (it's all downhill from here): the meanings of the words spring and fall respectively.  Some people care about light; others temperature.

4. Summer starts at the solstice.  Take note of the average temperature on the solstice.  Summer extends through increasing temperatures then decreasing temperatures until the average temperature drops below the average temperature of the summer solstice.  Similarly for winter.  Spring and fall are the times in between.

5. The boundaries between summer and winter are the points of inflection on the smoothed temperature function over the whole year.  Spring and fall are eliminated.