A la Jodorowski and Pythagoras
Wow. There are so many different takes on this.
I got the associations I use from a combination of Jodorowki (La Via del Tarot) and Pythagorean qualities associated with the elements. The four qualities are moist, dry, warm, and cool. Each of these is associated with a cardinal point, and two each are associated with of the elements. So we get:
Moist: east, the vernal equinox
Warm: south, the summer solstice
Dry: west, the autumnal equinox
Cool: north, the winter solstice
This gives:
Air (Swords) = moist + warm = spring
Fire (Batons) = warm + dry = summer
Earth (Coins) = dry + cool = autumn
Water (Cups) = cool + moist = winter
Clay