It is a common misconception that the data themselves have to be normally distributed, in order to satisify the assumptions of an ordinary least squares (OLS) regression. They do not.
Also, "the data are non-parametric" does not mean "the data are inconsistent with a normal distribution". Usually one would use the non-parametric about a technique that does not assume any underlying distributional properties of the data.
You only mention one variable -- precipitation. I assume you have more than one variable, otherwise a regression isn't even possible.
Please feel free to post your data (ideally in a MAT file, using the paper-clip icon) if you want people to take a look.
