This is OT regarding conlanging, but not conworlding; I thought some of our
members might be interested in the following problem.

The world of Angayus has chaotic seasons.  The orbit of the planet, the
eccentricity of the orbit, and the degree of axial tilt tend to vary
year-by-year.  This of course gives human civilizations on the planet a bit
of trouble, especially with regards to agriculture.

Civilizations are probably at the 1100-1400 AD level (pre-Renaissance).

In Streydan, the religious and cultural heart of one such civilization, a
caste of priests has arisen whose job it is to predict the following seasons
and thereby allow agriculture, travel, trade, etc to proceed for the next
year or so.

My first thought is:  is it possible to predict the severity of axial tilt
in a given year, and if so, how?  I would imagine one could plot the
locations of the sunset and sunrise over successive days, and the amount of
drift would give one an idea of how severe the following season is likely to be.

Also, would there be a way to predict the severity of the orbital seasons? 
I.e. if this year, the planet orbits close and hot, then begins to switch to
far and cold, is there any way for a medieval civilization (say, 14th
century) to determine from the stars or the position of the sun the nature
and magnitude of this change?

It would be an interesting world to live in...