A symbolic regression approach to illuminate the water-energy-food-ecosystem interlinkages in a rainwater harvesting system

Nature-based solutions (NBS) are increasingly considered as components of strategies aiming to address climate-related challenges, since their impact expands across more than one aspect of the water, energy, food, and ecosystems (WEFE) nexus. Therefore, searching for tangible evidence on the impact of NBS requires addressing the complexities of the WEFE nexus, which is characterized by dynamic and highly nonlinear relationships. These complexities may challenge traditional modeling approaches, which would rely heavily on human intuition and the cumbersome integration of individual sub-models.

Driven by the continuous improvement of monitoring capabilities, the increase of computational power, and the emergence of efficient algorithms, data-oriented solutions gather momentum in the efforts to identify dynamic systems in a multitude of domains. Nonetheless, such solutions are rarely adopted by the nexus community.

In this work we aim to investigate the potential of data-driven approaches to identify the underlying dynamics of systems that exhibit properties commonly encountered in many WEFE nexus systems, such as nonlinearity, high dimensionality and non-stationarity (e.g., the exposure to extreme events).

To unravel these complexities, we employed a symbolic regression (SR) approach within a case study of a rainwater harvesting system operating in Mykonos, Greece. This system is designed to collect, treat, and store rainwater for agricultural reuse. A sub-surface collection system captures rainwater, diverting it into two storage tanks. The collected water irrigates an agricultural field using precision irrigation, optimizing water usage and minimizing waste. The system integrates components of the WEFE nexus, enhancing water security through rainwater collection and treatment, promoting energy security by reducing reliance on groundwater abstraction, improving soil quality, and enhancing food security through sustainable agricultural practices.

A one-year long dataset was generated from a set of individual process-based sub-models that simulate diverse components of the nexus, including (a) the system’s water balances (comprising infiltration, surface runoff and evapotranspiration), (b) water quality dynamics in the storage tanks, (c) energy consumption, and (d) plant growth dynamics, based on the estimated water stress and nutrient limitations that affect growth and yield. To mimic real-world conditions, we introduced random noise and incorporated missingness, simulating the variability and incompleteness of observational data. SR was applied to the dataset, aiming to inversely estimate the equations that describe the functional behavior of the NBS. SR employs a multi-population evolutionary algorithm, which navigates within the space of analytic expressions in search of accurate and parsimonious models.

The results unveiled parsimonious expressions that captured the dynamics of the system across different external hydrometeorological forcings with reasonable accuracy. These equations provided interpretable insights into the mechanisms underpinning this rainwater harvesting system, resonating, at the same time, with existing scientific understanding. This approach is an example of the potential of data-driven methodologies to enhance the understanding of NBS and their capacity to address multifaceted challenges. Even if a globally valid analytical expression for such systems is probably infeasible, this work managed to set-up a data-driven methodology for deciphering the WEFE nexus at a local scale, providing also a tool for optimizing NBS performance and informing decision-making.