Model Predictive Control Structures for Periodic ON-OFF Irrigation

Agriculture accounts for approximately 70% of the world’s freshwater consumption. Furthermore, traditional irrigation practices, which rely on empirical methods, result in excessive water usage. This, in turn, leads to increased working hours for irrigation pumps and higher electricity consumption. The main objective of this study is to develop and evaluate periodic model predictive control structures that explicitly account for on-off irrigation, a characteristic of drip irrigation systems where watering can be turned on and off, but flow cannot be regulated. While both proposed control structures incorporate an economic upper layer (Real Time Optimizer, RTO), they differ in the costs associated with the lower layer. The first structure, called Model Predictive Control for Tracking (MPCT), focuses on tracking effectiveness, while the second structure, called Economic Model Predictive Control for Tracking (EMPCT), incorporates the economic cost into the tracking term. These proposed structures are tested in a realistic case study, specifically in a strawberry greenhouse, and both show satisfactory performance. The choice of the best option will depend on specific conditio

State estimation for one-dimensional agro-hydrological processes with model mismatch

The importance of accurate soil moisture data for the development of modern closed-loop irrigation systems cannot be overstated. Due to the diversity of soil, it is difficult to obtain an accurate model for agro-hydrological system. In this study, soil moisture estimation in 1D agro-hydrological systems with model mismatch is the focus. To address the problem of model mismatch, a nonlinear state-space model derived from the Richards equation is utilized, along with additive unknown inputs. The determination of the number of sensors required is achieved through sensitivity analysis and the orthogonalization projection method. To estimate states and unknown inputs in real-time, a recursive expectation maximization (EM) algorithm derived from the conventional EM algorithm is employed. During the E-step, the extended Kalman filter (EKF) is used to compute states and covariance in the recursive Q-function, while in the M-step, unknown inputs are updated by locally maximizing the recursive Q-function. The estimation performance is evaluated using comprehensive simulations. Through this method, accurate soil moisture estimation can be obtained, even in the presence of model mismatch

Economic model predictive control for interactions of water sources connected crop field

Interest in predicting and optimizing irrigation to minimize water usage in agriculture is growing. In this paper, we present how different water sources interconnected in a farm (surface and underground reservoirs) can provide the optimal amount of water to the crop, considering the water available in each water source and the energy cost associated with pumping, without compromising the crop yield. For this purpose, the formulated economic Model Predictive Control makes use of the dynamical non-linear agro-hydrological model, considering the Volumetric Water Content (VWC) at different depths of the soil and the mass balance of the surface reservoir to generate optimal interactions and flow control strategies from the water sources to the crop field to meet future irrigation demands and finally consider the use of these water sources to alleviate the effects of environmental changes and water scarcity

Economic model predictive control for interactions of water sources connected crop field

Interest in predicting and optimizing irrigation to minimize water usage in agriculture is growing. In this paper, we present how different water sources interconnected in a farm (surface and underground reservoirs) can provide the optimal amount of water to the crop, considering the water available in each water source and the energy cost associated with pumping, without compromising the crop yield. For this purpose, the formulated economic Model Predictive Control makes use of the dynamical non-linear agro-hydrological model, considering the Volumetric Water Content (VWC) at different depths of the soil and the mass balance of the surface reservoir to generate optimal interactions and flow control strategies from the water sources to the crop field to meet future irrigation demands and finally consider the use of these water sources to alleviate the effects of environmental changes and water scarcity

Assessing crop water requirements and irrigation scheduling at different spatial scales in Mediterranean orchards using models, proximal and remotely sensed data

Accurate estimations of crop water requirements are necessary to improve water use in agriculture and to optimize the use of available freshwater resource. To this aim, the Agro-Hydrological models represent useful tools to quantify the crop actual evapotranspiration. To define the upper boundary condition of the Agro-Hydrological models it is essential to assess the atmospheric water demand, expressed as crop reference evapotranspiration, ETo. In literature several methods, different in terms of input data requirement and climate variables combinations, have been developed to estimate ETo. Among these methods it is commonly used the well-known FAO56 Penman-Monteith (FAO56-PM) thermodynamic approach. Implementing this method requires access to climate data usually measured by ground weather stations. Unfortunately, these instruments are not always available, in this case recent climate reanalysis databases are useful solution to overcome this limitation. Direct measurements of actual evapotranspiration, ETa, are important to validate the results of the model’s application. These measurements, especially for large scale use, can be time consuming and economically expensive. Moreover, improper installation of the sensors or incorrect calibrations could cause outliers in time series or compromise the continuity of the data time series. Recently Machine Learning (ML) algorithm have been developed to predict and fill the gaps in time series of ETa. The joint use of Agro-Hydrological models with proximity and remotely sensed data is one of the possible ways to accurately estimate crop water requirements. The remote observations of the land surface represent a reliable strategy to identify the spatial distribution of vegetation biophysical parameters, such as, crop coefficient Kc under actual field conditions. The general objective of the research was to assess the crop water requirements in two typical crops (citrus and olive) of the Mediterranean region, using FAO56 Agro-Hydrological model based on functional relationships Kc(VIs) between crop coefficient, Kc, and Vegetation Indices (VIs) calibrate using in situ measurements and VIs obtained by multispectral remotely sensed data. Moreover, it was evaluated the reliability of the reanalysis climate variables provided by ERA5-Land database to assess ETo in Sicily (Italy). The performance of the ERA5-Land reanalysis weather data to estimate ETo, was assessed considering 39 ground weather station distributed in Sicily region. The ETo values estimated on the basis of climate variables from ERA5-L database encourage the use of reanalysis database to assess ETo. In general, the results were in agreement with those obtained from ground measurement, with average Root Mean Square Error (RMSE) equal to 0.73 mm d-1 and corresponding Mean Bias Error (MBE) equal to -0.36 mm d-1. The research activities were carried out in two experimental fields. The first experimental field is a citrus orchard located near the Villabate town whereas the second one was the irrigation district 1/A, managed by “Consorzio di Bonifica della Sicilia” ex “Consorzio di Bonifica Agrigento 3”, Castelvetrano, Sicily (Italy), characterized mainly by olives orchards. The time series of ETa, acquired by the Eddy Covariance (EC) tower installed in the citrus experimental field was processed using the Gaussian Process Regression (GPR) algorithm in order to fill the gaps. The performances were evaluated in terms of Nash Sutcliffe Efficiency (NSE) coefficient and RMSE. The values of NSE ranging between 0.74 and 0.88, whereas the RMSE values lower or equal to 0.55 mm d-1 confirm the suitability of the GPR model, to predict time ETa series. FAO56 Agro-Hydrological model was applied for the irrigation seasons 2018, 2019 and 2020 (Villabate) and for the irrigation seasons 2018 and 2019 (Castelvetrano). For each study areas, using VIs obtained from Sentinel-2 Multi Spectral Images (MSI) level 2A, a Kc(VIs) relationship was developed and then implemented in the model. The model was used to estimates spatial and temporal variability of the actual evapotranspiration, soil water content (SWC), in the root zone, crop coefficient and stress coefficient, as well as, to irrigation scheduling. For the citrus orchard a non-linear Kc(VIs) relationship was identified after assuming that the sum of two VIs, such as Normalized Difference Vegetation Index (NDVI), and Normalized Difference Water Index (NDWI), is suitable to represent the spatio-temporal dynamics of the investigated environment. The application of the FAO56 Agro-Hydrological model indicated that the estimated ETa was characterized by RMSE, and MBE, of 0.48 and -0.13 mm d−1 respectively, while the estimated SWC, were characterized by RMSE = 0.01 cm3 cm−3 and the absence of bias, then confirming that the suggested procedure can produce highly accurate results in terms of dynamics of SWC and ETa under the investigated field conditions. In the Castelvetrano irrigation district 1/A, a linear Kc(VI) relationship was identified following the Allen and Pereira (A&P) procedure which was based on the height of the canopy and the fraction of vegetation cover, the last was estimated by the NDVI. The differences between simulated and measured seasonal values was encouraging for the 2018, with value equal to 3%, while for the 2019 it was equal to 17%. These results highlight that the proposed model, with further improvements, and more accurate information such as the effective depth of root zone and the real volumes delivered by the hydrants, can be a useful tool for supporting the decision in the management of the irrigation demands in the irrigation district

Improving water utilization from a catchment perspective

Water management / Water scarcity / Water use efficiency / Catchment areas / Calibrations / Hydrology / Models / River basins / Participatory management / Water balance / Case studies / Asia / Africa / South Africa / Zimbabwe