Non-linear effects

The yields of crops such as wheat are clearly affected by the amount of moisture available in the soil, as well as the temperature. More if generally better, but up to a point. Yields increase and then drop off. It looks like a reversed U-shaped curve. The usual way of modeling this would be with a quadratic term, that is including a squared term in the regression. That has been the approach taken by leading reasearchers looking into the effects of climate change on agriculture. But what if the two variables act on each other in a non-linear fashion? I have been working on this problem using regression splines, allowing the relationship to be flexible or ‘wiggly’. The estimation is non-parametric but so far seems to show more accurate results than the rather rigid parameterization of the quadratic method. The plot below shows wheat yields from the 1830s, against temperature and precipitation in August. The non-linearity is clear. I used the mgcv package in R for this.