Mathematical Optimisation of Smart Irrigation Scheduling Using Climate and Soil-moisture Data: A Simulation Study for Potato Production
Selah Kiplimo
*
Department of Mathematics and Computer Science, University of Eldoret, Eldoret, Kenya.
Jacob Bitok
Department of Mathematics and Computer Science, University of Eldoret, Eldoret, Kenya.
Rotich Titus
Department of Mathematics, Physics and Computing, Moi University, Eldret, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Background: Efficient irrigation scheduling requires simultaneous consideration of soil-water status, atmospheric demand and crop response. Sensor-based monitoring and optimisation methods can support this integration, but model outputs must be interpreted according to the quality and provenance of their inputs.
Objective: This study develops a five-state compartmental framework for potato irrigation and evaluates threshold-based and optimisation-based irrigation scenarios using a 2025 rainfall forcing series associated with Elgeyo-Marakwet County, Kenya.
Methods: The model represents soil water, root-zone water, plant tissue water, biomass and an environmental water compartment through ordinary differential equations. Soil-water retention follows the van Genuchten relation, reference evapotranspiration is represented with the Penman-Monteith formulation, and irrigation is formulated as a constrained quadratic tracking problem. Numerical integration was performed with MATLAB ode45 and Python solve_ivp; constrained optimisation was represented by an SLSQP-based implementation. The analysis is treated as a simulation study rather than as a field-validation study because the underlying station metadata, raw meteorological file and independent crop-calibration dataset were not available for verification.
Results: For the reported loam-soil scenario, total available water was 120 mm m-1, rooting depth was 0.6 m and the adopted depletion fraction was 0.35, giving root-zone total available water of 72 mm and readily available water of 25.2 mm. The supplied simulations produced a rain-fed yield-equivalent output of 3.1 kg m-2 and a threshold-controlled output of 6.3 kg m-2, corresponding to a 103% increase within the model scenario.
Conclusion: The simulations illustrate how climate and soil-moisture information can be incorporated into an irrigation-control framework, but the quantitative outputs should be interpreted as scenario results pending calibration and independent field validation.
Keywords: Smart irrigation, mathematical optimisation, soil moisture, optimal control, potato, water balance, simulation