Root zone soil moisture prediction models based on system identification: Formulation of the theory and validation using field and AQUACROP data

• Proposes linear time series modelling to represent soil water balance and identifies the model parameters.
• Extends the method for soil under saturation, rule-based irrigation systems, measurement noise
• Evaluates the model fit and adequacy of the modelling using synthetic and field data.
• Investigates the effect of increasing model order for different soil types.
• Demonstrates the application using a real-time closed-loop irrigation control example.

In model-based irrigation control, the root zone soil moisture deficit (RZSMD) is maintained based on the water balance. To predict RZSMD in real-time, effective rainfall, irrigation and crop evapotranspiration need to be calculated online. Estimating the first two variables is more important yet tedious due to practical limitations of knowing the amount of water actually infiltrated into the soil. In order to solve this problem, we propose to apply system identification on water balance data to obtain a linear time series model. We further investigate how to carry out the modelling (i) under saturated conditions, (ii) when there is a rule-based irrigation control, and (iii) under measurement noise in the soil moisture readings. Using synthetic data we obtained a model fit above 80% in all cases. Additionally, we show the model optimality and applicability with an independent dataset, using residual tests. For two sets of field data, we observed model fits of 84% and 63%, and satisfaction in all residual tests. Simplicity in the model reduces calibration efforts whereas its linearity and adequacy recommend it for real-time irrigation control applications. In summary, the results indicate that a first order linear time series model based on system identification can successfully predict RZSMD in a real-time irrigation control system.