So for that reason only average the temp and precip and the SOI only over the winter season. Note that either a positive or a negative correlation is equally important and show a useful signal. It is the near-zero values that don't mean much. You can see by these plots that the more values you have the more meaningful it gets. You have to have at least a few of them to see the pattern.
Correlation is the basic statistical measure of the relation between two variables.
The correlation is a number between -1 and 1. A correlation of 1 means the relation is perfect, a correlation of 0.5 means a partial relation, a correlation of 0 means no relation, while a correlation of -1 means one thing varies exactly oppositely to another. How about some examples. If you took two unrelated things, say, the number of student absences in a high school in Seattle compared to the number of computers sold in New York, the correlation would be near 0. In case you haven't covered correlation coefficients in math, I can explain it.