What is a good approximate functional form for an equation relating plant growth to sunlight?

Question is in the title. I've got daily measurements of daily mean shortwave radiation at the surface, and annual measurements of plant growth (some measure, be it height or biomass or something).

I want to fit a statistical model

$$growth = f(light) + \epsilon$$

Assume that all other conditions are near-optimal, for simplicity. What is a good first-order approximation for how to specify $f$?

For example, could it be:

• Average daily light over the growing season? $$growth = \beta_0 + \beta_1\bar{light} + \epsilon$$
• Average daily light for each month? $$growth = \beta_0 + \displaystyle\sum_{months}\beta_m\bar{light_m} + \epsilon$$
• Maybe it's quadratic?

$$growth = \beta_0 + \beta_1\bar{light} + \beta_2\bar{light}^2 + \epsilon$$

Obviously something so simplified will never be perfect, but what's a good rule-of-thumb that'd cover most situations reasonably well?

• You need to write more about the specific system/plant species you are modelling to get useful answers. Is it a crop plant? Annual or perennial plant? Strongly seasonal environment? Generally, and since it seems like you are not testing a specific hypothesis, you should try several models and see what fits your data best. After all, the goal should be a biological reasonable model that describes the patterns in your data. – fileunderwater May 12 '18 at 7:37
• Ok, let's say an annual in a temperate climate. – generic_user May 12 '18 at 12:25
• And I take your point that cross-validation is how to do model selection. But domain knowledge is usually the best starting point. – generic_user May 12 '18 at 12:27