HELP! Stats method for comparing curves?

Hello all,
I was hoping you guys might be able to assist me, I'm in the middle of writing a biology honors thesis and I'm trying to compare the thermal accumulation of different years to see if there's a correlation between them thermal accumulation trend line and an epidemic or non-epidemic year. I'm working with seasonal thermal accumulation curves and can't figure out how to compare a trend line with a nominal variable like epidemic or non-epidemic.
Any thoughts or suggestions would be greatly appreciated!
So you want to test for year-to-year differences in trendlines. If you think one set is quadratic and the other is linear, you could run a test for the significance of the quadratic component in each curve. You could also take a meta-analytic approach and find the average linear and quadratic regression coefficients for each set of years. Alternately, you could specify each trendline using an ARIMA model, if that's part of your toolbox. But I wonder whether simply graphing the curves and in so doing enforcing the epidemic/non-epidemic year comparisons would accomplish what you need.