The amount of rainfall that an area receives can certainly
affect the width of tree rings, but so can other factors.
Factors such as temperature, soil conditions, and the gradient
of the slope can have an effect, as can wind, snow
accumulation, and how much sunlight a tree receives.
Complacent
Sensitive
Still, the amount of variation in a tree's rings can vary
between species of trees and between trees of the same
species.
A tree whose rings vary in width are called sensitive.
These trees can have a wide ring if conditions are conducive
to growing and a narrow ring if they aren't.
Sometimes, a tree's annual rings don't show much variation.
The reason can be simply that it's a species that isn't prone
to variation. Or it can be that it's located in a part of the
world where the environment doesn't vary greatly from season
to season. Or it can be that it's growing where the water
table is high enough for it to get all of the water it needs.
Trees whose rings don't show much variation in width are
called complacent.
Tree-ring scientists prefer to work with tree-ring samples
from sensitive trees, as the variation in their annual rings
allows for crossdating.