Application of feedback control to stomatal optimisation in a global land surface model

Accurate representations of stomatal conductance are required to predict the effects of climate change on terrestrial ecosystems. Stomatal optimisation theory, the idea that plants have evolved to maximise carbon gain under certain constraints, such as minimising water loss or preventing hydraulic damage, is a powerful approach to representing stomatal behaviour that bypasses the need to represent complex physiological processes. However, while their ability to replicate observed stomatal responses is promising, optimisation models often present practical problems for those trying to simulate the land surface. In particular, when realistic models of photosynthesis and more complex cost functions are used, closed-form solutions for the optimal stomatal conductance are often very difficult to find. As a result, implementing stomatal optimisation in land surface models currently relies either on simplifying approximations, that allow closed-form solutions to be found, or on numerical iteration which can be computationally expensive. Here we propose an alternative approach, using a method motivated by control theory that is computationally efficient and does not require simplifying approximations to be made to the underlying optimisation. Stomatal conductance is treated as the control variable in a simple closed-loop system and we use the Newton-Raphson method to track the time-varying maximum of the objective function. We compare the method to both numerical iteration and a semi-analytical approach by applying the methods to the SOX stomatal optimisation model at multiple sites across the Amazon rainforest. The feedback approach is able to more accurately replicate the results found by numerical iteration than the semi-analytical approach while maintaining improved computational efficiency.