Optimal seasonal water allocation and model predictive control for precision irrigation

With population growth and a rising demand for meat based diets and energy, the global water demand will grow significantly over the next two decades. Agriculture is the largest global consumer of the available water resources, responsible for almost 70% of annual water withdrawals. Therefore, a pivotal step in addressing the alarming water-scarcity problem is improving water use efficiency in agriculture. This is a complex problem that many farmers face yearly: how to distribute available water optimally to maximize seasonal yield, while considering the uncertainty in future water resources (eg. seasonal rainfall).

In our work, we consider the general problem of optimal soil moisture regulation of multiple fields (e.g., a plantation) for a full growth season, where allocating water optimally over the growth season is considered together with daily irrigation scheduling for multiple fields. This adds complexity to the control problem, as operational constraints need to be included (such as a limited number of fields that can be irrigated in a day) and trade-offs need to be made between irrigation and potential yield of the different fields. Furthermore, the growth stages of the fields can be different, as often not all fields can be planted and harvested at the same time.

We propose a methodology to reduce this complex problem into two separate optimisation problems, which are solved using a two-level structure consisting of a scheduler for seasonal allocation and a model predictive controller for daily irrigation. In this approach, the scheduler determines the optimal allocation of water over the fields for the entire growth season to maximize the summation of each field’s crop yield, by considering a linear approximation of the multiplicative crop productivity function. In addition, the model predictive controller minimizes the daily water stress by regulating the soil moisture of the fields within a water-stress-free zone. This requires a model of the interaction between the soil, the atmosphere, and the crop. A simple water balance model is created for which the saturation dynamics are modeled explicitly using conditionally switched depletion dynamics to improve model quality. To further improve the controller's performance, we create an evapotranspiration model by considering the expected development of the crop over the season using remote-sensing-based measurements of the canopy cover. The presented methodology can handle resource and hydraulic infrastructure constraints. Therefore, our approach is generic as it is not restricted to a specific irrigation method, crop, soil type, or local environment. The performance of the two-level approach is evaluated through a closed-loop simulation in AquaCrop-OS of a real sugarcane plantation in Mozambique. Our optimal control approach boosts water productivity by up to 30% compared to local heuristics and can respect water use constraints that arise in times of drought.