Efficient water management is a key factor for agriculture in India. Particularly, it is aiding in the estimation of crop water requirements (CWR) to enhance yields and profitability. This study aims to improve crop water demand forecasting through a neural network-based time series model tailored for agricultural applications.
A hybrid forecasting model is proposed which combines an Ensemble of Hyperparameter-Tuned Nonlinear Autoregression Neural Network (E-NLARNN) for crop yield prediction with a Generalized Regression Neural Network (GRNN) for prediction error correction. E-NLARNN aggregates forecasts from multiple optimized NLARNNs to improve robustness in crop yield prediction. It combines prediction from multiple hyperparameter-tuned NLARNNs. GRNN models the residual errors to further refine predictions. Five different crop yield datasets were used to demonstrate the effectiveness of the proposed work. Its performance was benchmarked against traditional NLAR and E-NLARNN models using RMSE and R-value metrics.
This hybrid model demonstrated significant improvements, achieving RMSE reductions between 9.6% and 19.5% compared to E-NLARNN models and between 19.3% and 30.5% compared to the best TA-NLARNN variants across datasets. It consistently outperformed baseline methods in terms of accuracy and stability.
This study presents a novel hybrid neural network approach that integrates ensemble learning and regression-based error correction for agricultural time series forecasting. By enhancing prediction accuracy and offering interpretable insights, the proposed model supports more reliable irrigation planning and sustainable water resource management.
1. Introduction
For a country like India, an important aspect of agriculture is crop water demand estimation, which helps the farmer to optimize irrigation and increase crop production. Traditionally, process-based models and empirical techniques have been used to estimate the amount of water required for each crop in India. These methods are used to estimate crop water requirements (CWR) by considering various factors, including crop type, soil type, climate and irrigation system. However, these traditional techniques are often expensive, time-consuming and labor-intensive for small-scale farmers. Therefore, it is very important to have accurate and efficient techniques to calculate CWR for better water management.
In recent years, the advent of smart agriculture powered by Internet of Things (IoT) and Artificial Intelligence (AI) technologies has transformed agricultural practices by enabling real-time monitoring and predictive decision making. Smart sensors, remote sensing devices and IoT network facilitate the continuous collection of field data, while AI models offer enhanced capabilities to predict crop yield, water requirements and environmental stress factors with high accuracy.
Consequently, machine learning and deep learning techniques such as artificial neural networks (ANNs), have gained significant traction for modelling and predicting crop water demand. These methods provide precise and trustworthy predictions, as prior studies have amply demonstrated. Farmers can greatly benefit from this by upgrading their irrigation systems and increasing crop yields. Farmers may enhance their practices and increase production and sustainability in agriculture by adopting these advances.
Farmers can choose which crops to plant and how to manage them during the growing season with the help of crop production forecasts using machine learning models (Van Klompenburg, Kassahun, & Catal, 2020; Akhil Varma & Teja Naidu, 2023). The aforementioned models took into account a number of factors, such as meteorological and soil data (Shahhosseini, Hu, Huber, & Archontoulis, 2021). Combining machine learning and crop modelling may enhance crop yield forecasts, according to studies of Rammohan, Niveditha, Amandeep Singh, and Yuvarani (2021). One study, for example, used machine learning techniques to predict crop harvests based on weather data and transfer information about production trends (Kuradusenge et al., 2023). Moreover, recent research highlights the integration of IoT and AI to enhance agricultural forecasting capabilities (Sciullo, Trotta, Bosi, Bononi, & Felice, 2024; Basavaraju, Mahadevaswamy, & Mallikarjunaswamy, 2024; Fondaj, Hamit, Krrabaj, Zenuni, & Ajdari, 2024).
Despite these advancements, existing approaches continue to face challenges in handling nonlinear dependencies and error accumulation, both of which critically undermine the accuracy in crop water demand estimation. This underscores the necessity for hybrid, explainable and computationally efficient models that can bridge this limitation and provide more reliable decision support for farmers. In response to this identified gap, this study proposes the E-NLARNN-GRNN hybid system to enhance prediction accuracy and facilitate more efficient agricultural water management.
1.1 Problem statement
In India, sustainable agriculture is critically challenged by water scarcity and inefficient crop water estimation methods impact agricultural productivity. Traditional models struggle with nonlinear dependencies and lack adaptability, while ML based models struggles to capture complex nonlinear interactions and dynamic variations leading to inaccurate predictions. Hence, there is a need for hybrid predictive framework that enhances prediction accuracy, mitigate errors and supports optimized water resource management.
1.2 Design goals: it can be summarized as follows:
To develop and optimize training algorithm based NLAR neural network model (TA-NLARNN) for crop yield prediction using multiple training algorithms and hyperparameter tuning.
To construct an ensemble framework (E-NLARNN) by selecting the best performing TA-NLARNN model through a panel selection strategy.
To design a GRNN model for error prediction based on historical residual patterns of the E-NLARNN.
To integrate E-NLARNN model and GRNN into a hybrid framework that enhances prediction accuracy and enables reliable crop yield and water demand estimation.
Unlike some existing approaches that rely on a single model for crop yield prediction or water demand estimation, the proposed hybrid model integrates two different neural network models: the E-NLARNN model for crop yield prediction and the GRNN model for error prediction. This combination allows for a more comprehensive and accurate forecasting methodology. Hence, this predictive model empowers farmers to improve agricultural yield, water management and irrigation efficiency.
The remainder of the paper is divided into sections. Section 1 introduces the research problem being studied. Section 2 provides a summary of the previous related work. The preliminaries are described in Section 3. The proposed work is explained in Section 4. The findings and discussion are presented in Section 5. The conclusion and future work are included in Section 6, the last section.
2. Literature review
Neural network-based crop yield prediction is an emerging area of study. A study has proposed a machine learning model that demonstrated the potential use of ANNs for forecasting agricultural productivity. With weather, soil and management practices as input factors and crop production as output variable, the study used Feedforward Back Propagation Network (FFBP) with one hidden layer as ANN method (Cheng et al., 2022). The results of the FFBP model showed how accurately this model can predict crop production [6]. The performance of temporal and spatial neural network models for crop forecasting was investigated in a different study (Guo & Xue, 2014). It found that both types of models could be used to predict agricultural yields but recommended against using specific neural network types due to inconsistent prediction and training effects. Deep neural network (DNN)-based crop production prediction offered real-world uses for food security, including recommendations regarding food transportation, food storage and influencing policy choices for farmers (Malviya & Solanki, 2022). Farmers can enhance their harvests and planting strategies by precisely forecasting crop yields.
ANN models are used to estimate crop yield by considering environmental factors such as temperature, rainfall, soil type, tillage practices, elevation and irrigation strategies. Temperature, rainfall and soil type are the parameters most often used in crop yield prediction models (Van Klompenburg et al., 2020; Hara, Piekutowska, & Niedbała, 2021). The most popular machine learning methods for estimating agricultural productivity are neural networks, although other methods have also been used, including elastic net, k-nearest neighbour, support vector regression, AdaBoost (Adaptive Boosting), decision trees, random forest, association rule mining, linear regression and extreme gradient (XG) Boost (Lontsi Saadio et al., 2022; Haque, Abdelgawad, Yanambaka, & Yelamarthi, 2020; Sunil, Nagaveni, & Shruthi, 2022; Gupta et al., 2022; Bennett & Harms, 2011; Charoen-Ung & Mittrapiyanuruk, 2018).
Accurate crop productivity forecast and CWR are essential for effective agricultural management. Forecasts that are trustworthy can be used to assess the need for irrigation, carry out feasibility studies, raise productivity and enhance farmers’ profits. Crop yield estimates can be used to determine the amount of water required by crops. Using relationships between yield and field water supply for different crops, limited water resources during severe droughts can be distributed to diverse crops as efficiently as feasible (Dalei, Subudhi, & Panigrahi, 2017). Accurate and high-resolution datasets on crop yield and crop water productivity are required to assess and forecast spatio-temporal variability in agricultural production systems (Leng & Hall, 2020). The research work was carried out to forecast agricultural water requirements and effective rainfall utilizing data analysis techniques (Abishek, Priyatharshini, Eswar, & Deepika, 2017).
Crop yield, energy consumption, financial time series and food demand can all be predicted with NARNNs (Ruiz, Cuéllar, Calvo-Flores, & Jiménez, 2016; Lutoslawski et al., 2021). NARNNs can be used to predict agricultural yield in crop prediction. A study that forecasts wheat yield in China using NARNNs found that NARNNs performed better than other models, including Multilayer Perceptron (MLP) and Nonlinear Autoregressive with Exogenous Inputs (NARX), as explained in Boussaada, Curea, Remaci, Camblong, and Mrabet Bellaaj (2018). NARNNs were also used in a study that predicted the demand for food in India. NARNNs performed better than other models, including Support Vector Regression (SVR) and MLP, according to the study carried out in the works of Paidipati et al. (2021); Rathod, Bandumula, and Chitikela (2022). A type of radial basis neural network known as a generalized regression neural network (GRNN) can be used for predictions based on regression, and classification. The holdout method removes one sample from the entire set to apply GRNN for prediction. With a smaller amount of training data, GRNN is used again to predict this sample for a fixed sigma (Ding, Rangaraju, & Poursaee, 2019; Martinez-Blanco et al., 2016). Li, Zhao, and Yang (2021) conducted a study that applied a neural network-based model to calculate the water required to grow maize in China. They gathered soil and meteorological data and inputted it into a neural network that had been trained with a backpropagation method. The findings indicated that the model had a mean absolute error of less than 10% and could accurately estimate the crop water requirement.
In a related study (Mokhtar et al., 2023), the authors estimated crop water needs using a hybrid neural network. They collected weather and soil data and used the Penman-Monteith Method to determine the reference evapotranspiration. Next, they computed the crop coefficient using a neural network, and the crop water requirement was calculated by multiplying the result by the reference evapotranspiration. The findings showed that the hybrid neural network could estimate the crop’s need for water with an absolute mean error of less than 5%.
Habeeb et al. (2025) showcased innovative hybrid modelling techniques for enhancing evapotranspiration prediction and optimizing water resource management in agriculture. Liliopoulos et al. (2025) have developed, trained and evaluated novel hybrid classical-quantum multilayer neural networks, comparing their efficacy with conventional classical networks for agricultural activities. The hybrid back-propagation neural network models proposed in Zhao et al. (2024), used for estimating maize evapotranspiration, primarily rely on meteorological data.
The results of the previous studies are compiled in Table 1. It finds out that there is evidence to support the estimation of CWR using crop yield forecasts. Using the connection between crop production and field water availability for different crops, it is possible to distribute limited water resources among different crops during drought periods. In order to forecast CWR for any given location, one must have a thorough understanding of spatio-temporal differences in agricultural production systems, crop output and effective rainfall levels.
Summary of the related work
| Topic | Descriptions |
|---|---|
| Crop yield prediction using neural network models | Environmental factors considered include temperature, rainfall, soil type, tillage systems, elevation and irrigation techniques. (Van Klompenburg et al., 2020; Hara et al., 2021) ANN algorithm with one hidden layer is commonly used (Cheng et al., 2022). Deep neural networks (DNNs) have practical applications for food security (Malviya & Solanki, 2022). Other techniques include decision trees (Gupta et al., 2022), association rule mining (Bennett & Harms, 2011), linear regression (Haque et al., 2020), elastic net (Lontsi Saadio et al., 2022), k-nearest neighbor (Charoen-Ung & Mittrapiyanuruk, 2018), support vector regression (Haque et al., 2020), XGBoost and AdaBoost (Sunil et al., 2022) |
| Crop water requirements prediction using neural network models | Crop water requirements can be estimated using crop yield forecasts (Dalei et al., 2017). Neural network models have been used to predict effective rainfall and water needs (Abishek et al., 2017). NARNNs and GRNNs have been applied for accurate estimation (Ruiz et al., 2016; Ding et al., 2019). Hybrid neural networks have improved accuracy in crop water requirement predictions (Mokhtar et al., 2023; Habeeb et al., 2025; Zhao et al., 2024) |
| Prediction of crop yield, energy consumption, financial time series and food demand | NARNNs have been employed for agricultural yield prediction (Ruiz et al., 2016; Boussaada et al., 2018), wheat yield prediction in China (Boussaada et al., 2018) and food demand forecasting in India (Paidipati et al., 2021; Rathod et al., 2022). Hybrid classical-quantum multilayer neural networks are emerging for agricultural predictions (Liliopoulos et al., 2025) |
3. Preliminaries
This section contains relevant techniques and methods needed to understand the proposed methodology.
3.1 Nonlinear AutoRegressive neural network
The Nonlinear AutoRegressive (NLAR) neural network is a specific type of neural network that is applied to time-series forecasting problems (Ruiz et al., 2016). The foundation of this network architecture is the notion that future values of a time series can be predicted from past values. It has one hidden layer and is a feedforward network. The network’s output layer makes predictions about the time series’ future values, while the input layer gets the time series data’s historical values. The representation for the NLAR neural network can be written as in Equation (1):
where W1 and W2 are weight matrices, b1 and b2 are bias vectors, f is the activation function and y(t) is the forecast crop production data at time t. x(t–1) is the input data at time t–1.
3.2 Hyperparameter tuning
The de facto method for boosting the NLAR neural network's performance is called hyperparameter tuning. Analysis of hyperparameters of TA-NLARNN, such as HNC, FD are used in this study to improve their predictive performance. Here is a detailed description of the hyperparameters analyzed:
Training Algorithm (TA):
Various training techniques used to train the NLARNN architecture include Levenberg–Marquardt (LM), Bayesian Regularization (BR), Conjugate Gradient Fletcher (CGF) optimization and Scaled Conjugate Gradient (SCG) approach (Bhojani & Bhatt, 2020). The choice of training algorithm can have a significant impact on the performance and training time of the NLARNN framework. An optimal training algorithm can be selected using a grid search method. A validation set is used to test several training methods, and the algorithm with the best performance is selected.
Hidden Neuron Count (HNC):
The studies revealed that there is a strong correlation between the HNC in the hidden layer and the performance of the NLARNN framework (Bhojani & Bhatt, 2020). Increasing the hidden neuron quantity in the model can improve its ability to explain complex interactions in the data, but it also increases the possibility of overfitting. Therefore, in this work, attention should be paid to adjust the number of hidden neurons using grid search that can be used to determine the optimal number of hidden neurons in the hidden layer. It evaluates multiple hidden neurons counts in the validation set to see which configuration performs best.
Feedback Delay (FD): It is the time interval between the input and output of the NLARNN structure. The ability to record lag between input and output time series makes it a useful tool. The best FD can be found by phase searching, which involves testing a range of FD values in the validation set and selecting the configuration that performs best.
Generalized Regression Neural Network (GRNN): This type of radial basis function neural network is used for regression problems. The foundation of this network architecture is the notion that the input-output mapping of a dataset can be approximated using radial basis functions. The Gaussian function is used as the radial basis function by a fixed number of neurons in a single hidden layer of the GRNN.
In GRNN model, the prediction formula can be written as in Equation (2):
In this case, “x” stands for the input crop yield data, “y” for the predicted crop yield data, “w'i” for the weight connected to the “ith” input and “gi(x)” for the Gaussian function centered at the ith input.
The Gaussian function is represented as in Equation (3):
where “σ” stands for the width parameter, which regulates the Gaussian function’s smoothness, and “xi” is the ith input.
3.3 Panel selector
The ensemble of TA-NLAR neural network models is created by combining the strengths of multiple TA-NLAR neural network models and selecting the best model based on the panel selector. The panel selector selects the TA-NLARNN models with the lowest RMSE value as the E-NLARNN model. E-NLARNN is the best-performing training algorithm-based hyperparameter-tuned NLARNN model (TA-NLARNN).
4. Proposed scheme: hybrid NLARNN model for agriculture data
4.1 Problem statement
To enhance the accuracy and reliability of crop yield predictions, propose a hybrid methodology that combines an ensemble of training algorithms based on a hyperparameter-tuned NLAR neural network and a GRNN for crop yield prediction. The goal is to estimate CWR by utilizing forecasted crop yield data generated by the proposed hybrid neural network model.
4.2 Proposed scheme
This scheme aims to improve the crop yield prediction accuracy by combining the strengths of two different neural network models. Figure 1 depicts the workflow of the proposed scheme. Table 2 shows the pseudocode of the hybrid neural network model using E-NLARNN and GRNN algorithms. The detail explanation of the pseudocode is followed as:
The flowchart begins with the text box labeled “Historical Crop Yield Dataset.” From “Historical Crop Yield Dataset,” a downward arrow leads to the text box labeled “Define Range for Hyperparameters for N L A R Model.” From “Define Range for Hyperparameters for N L A R Model,” four downward arrows extend and point to four boxes arranged horizontally and labeled from left to right as follows: “Hyperparameter Tuned T A underscore N L A R underscore L M Model,” “Hyperparameter Tuned T A underscore N L A R underscore B R Model,” “Hyperparameter Tuned T A underscore N L A R underscore S C G Model,” and “Hyperparameter Tuned T A underscore N L A R underscore C G F Model.” From these four boxes, downward arrows merge and point to a text box labeled “Ensemble using Panel Selection.” From “Ensemble using Panel Selection,” a downward arrow arises and points to the text box labeled “Winning Model.” From “Winning Model,” a downward arrow arises and points to the text box labeled “Hybrid E-N L A R N N with G R N N Model.” From “Hybrid E-N L A R N N with G R N N Model,” a downward arrow arises and points to the text box labeled “Predict the Crop Yield.” From “Predict the Crop Yield,” a rightward arrow arises and points to the text box labeled “Crop Water Requirement Estimation equals Forecasted Crop yield data times Water required for 1 kilogram yield.”Workflow of proposed work. Source: Figure by authors
The flowchart begins with the text box labeled “Historical Crop Yield Dataset.” From “Historical Crop Yield Dataset,” a downward arrow leads to the text box labeled “Define Range for Hyperparameters for N L A R Model.” From “Define Range for Hyperparameters for N L A R Model,” four downward arrows extend and point to four boxes arranged horizontally and labeled from left to right as follows: “Hyperparameter Tuned T A underscore N L A R underscore L M Model,” “Hyperparameter Tuned T A underscore N L A R underscore B R Model,” “Hyperparameter Tuned T A underscore N L A R underscore S C G Model,” and “Hyperparameter Tuned T A underscore N L A R underscore C G F Model.” From these four boxes, downward arrows merge and point to a text box labeled “Ensemble using Panel Selection.” From “Ensemble using Panel Selection,” a downward arrow arises and points to the text box labeled “Winning Model.” From “Winning Model,” a downward arrow arises and points to the text box labeled “Hybrid E-N L A R N N with G R N N Model.” From “Hybrid E-N L A R N N with G R N N Model,” a downward arrow arises and points to the text box labeled “Predict the Crop Yield.” From “Predict the Crop Yield,” a rightward arrow arises and points to the text box labeled “Crop Water Requirement Estimation equals Forecasted Crop yield data times Water required for 1 kilogram yield.”Workflow of proposed work. Source: Figure by authors
Hybrid neural network model for crop water estimation algorithm
| Algorithm | |
|---|---|
| Data source: https://desagri.gov.in/document-report-category/agriculture-statistics-at-a-glance/ Region of study: India Duration: 1950–2023 Time series length: 74 entries Input Historical crop yield data: X_train historical error data: y_train Test crop yield data: X_test Crop yield data for a specific region: X_new Range of hidden neuron count: neuron_range Range of feedback delay: delay_range Set of training algorithms: alg_set Output Predicted crop yield for the test set: y_pred Estimated CWR for the specific region: cwr_est | Step 3: Error forecasting using GRNN
For each crop yield dataset in the test set
|
Step 1: Data Preprocessing
| |
In Step 1, the data is pre-processed and split into training, validation and test sets, denoted as X_train, y_train, X_val, y_val, X_test and y_test. In Step 2, an ensemble of TA-NLAR neural networks is trained using a set of training algorithms (alg_set), neuron range (neuron range) and FD range (delay range). The best model is selected based on the lowest RMSE on the validation set and named the E-NLARNN model (e_nn).
In Step 3, a grnn (error train) is trained on the historical error data for error forecasting where historical error data is the difference between actual crop yield and predicted crop yield. In Step 4, the E-NLARNN model is used to predict the expected crop yield for each dataset in the test set. The GRNN model is used to forecast the expected error in the E-NLARNN prediction, and the final predicted crop yield (y_final) is obtained by adding the E-NLARNN prediction and the GRNN error forecast. In Step 5, evaluate the performance of the hybrid ensemble neural network model on the test set using the benchmark error metric RMSE metric. It is denoted as RMSE = sqrt (mean_squared_error (y_test, y_final)). After that, analyze the effect of different hyperparameters on the model's accuracy, and optimize the hyperparameters to improve the model's accuracy.
In Step 6, predict the crop yield for a particular crop in a given region based on the historical crop yield data using the trained E-NLARNN model as y_new = e_nn.predict (X_new). Then, crop water requirement (CWR) is calculated using predicted crop yield data and water requirement data. It is given in Equation (4) which is used to estimate the crop water requirement based on crop yield value and water requirement per 1 kg of yield.
CWR is the total amount of water needed by a crop during its growth cycle, expressed in terms of depth (usually in mm) or volume (usually in liters or cubic meters).
To scientifically validate the effectiveness of the proposed hybrid approach, a comparative analysis was conducted between the hybrid E-NLARNN + GRNN model and individual baseline models. The results are illustrated through figures, demonstrate a significant improvement in prediction accuracy and error reduction. The time complexity of neural network models like E-NLARNN, NLARNN and GRNN can be expressed using variables and constraints as follows. Let P represent the total number of parameters in the neural network model, N denote the number of training samples in the dataset, L signify the number of layers in the neural network and B represent the batch size used during training. The time complexity of training these models can be expressed as:
O (P * N*L*B), for NLARNN and E− NLARNN,
O (P*N*B), for GRNN
These expressions outline the computational complexity in terms of parameters, training samples, layers and batch size of the neural network models.
5. Performance analysis
This section depicts the discussions the results and the performance metrics.
5.1 Data description
The crop yield dataset is taken from Agriculture Statistics at a Glance 2023 published by the Department of Economics and Statistics, The Government of India. The website link is https://desagri.gov.in/document-report-category/agriculture-statistics-at-a-glance/. This website is designed to collect data related to various features of agricultural development including soil health, crop yield, irrigation and farmer welfare.
5.1.1 Performance metrics
The benchmark performance measurements for evaluating the performance of the proposed method are listed and discussed in this section.
5.1.1.1 Correlation Coefficient (R-Value)
Equation (6) represents the Correlation Coefficient (R-value) which is used to measure a linear relationship between the predicted and actual data.
where “A” is the actual data value, “p” is the predicted data, “t1’” is the mean of actual data, “p1” is the mean predicted data and “n’” is the total number of data items in the dataset.
5.1.1.2 Root Mean Square Error (RMSE)
It defines the “difference in the square root of the sample between the values predicted and the values observed” as shown in Equation (7).
Where “n’” represents the total number of years, “A'”i is the actual value of crop yield and “Pi” is the expected value of crop yield.
5.2 Results and discussions
The crop yield dataset is split into a 70:30 ratio for training and testing. Table 3 provides parameter settings for the configuration of the NLARNN model and GRNN model for building the hybrid neural network for crop yield prediction. Both models share some similarities in terms of their architectures, such as using one or two hidden layers with linear output activation functions and mean squared error loss functions. However, they differ in several parameter settings, such as the number of neurons per layer, the learning rate and the training algorithm.
Parameter setting for TA-NLARNN model and GRNN model
| Parameter | NLARNN model | GRNN model |
|---|---|---|
| Network Type | Recurrent Neural Network (RNN) | Recurrent Neural Network (RNN) |
| Activation Function | Hidden layer activation function:Hyperbolic Tangent (tanh) Output layer activation function: Linear | Hidden layer activation function:Gaussian Output layer activation function: Linear |
| Hidden Units | 5–25 | 50 |
| Learning Rate | 0.001–0.01 | 0.001–0.1 |
| Training Algorithm | LM. BR, CGF, SCG | BR |
| Input Scaling | Standardize or Normalize | Normalize |
| Loss Function | Root Mean Squared Error (RMSE) | Root Mean Squared Error (RMSE) |
| Epochs | Typically 100–1,000 | Typically 50–500 |
| Early Stopping | Enabled | Enabled |
| Spread | N/A | 0–10 |
| Feedback delay | 1–4 | N/A |
Based on the result given in Table 4, the set of hyperparameters with the lowest RMSE is considered to be the best-performing prediction model for each crop dataset. Generally, lower RMSE values indicate better performance of the model in terms of predicting the crop yield. It can be seen that for rice, the best set of hyperparameters based on RMSE with a training algorithm is BR, a hidden layer size of 19 and a delay of 2. For wheat, the best set of hyperparameters based on RMSE with a training algorithm is BR, a hidden layer size of 15 and a delay of 1.
Optimal hyperparameter values for TA-NLARNN models for all crop datasets
| Crop dataset | HNC | FD | RMSE | R | HNC | FD | RMSE | R |
|---|---|---|---|---|---|---|---|---|
| TA-NLARNN-LM | TA-NLARNN-BR | |||||||
| Paddy | 11 | 4 | 22.9 | 0.86 | 19 | 2 | 4.16 | 0.99 |
| Wheat | 19 | 4 | 24.14 | 0.87 | 15 | 1 | 2.51 | 1 |
| Maize | 7 | 4 | 8 | 0.84 | 18 | 3 | 0.79 | 0.96 |
| Groundnut | 18 | 2 | 1.47 | 0.53 | 20 | 3 | 0.88 | 0.59 |
| Cotton | 13 | 4 | 11.72 | 0.89 | 17 | 1 | 1.11 | 0.96 |
| Sugarcane | 13 | 3 | 73.15 | 0.89 | 18 | 1 | 16.79 | 0.95 |
| TA-NLARNN-SCG | TA-NLARNN-CFG | |||||||
|---|---|---|---|---|---|---|---|---|
| Paddy | 20 | 2 | 4.66 | 0.99 | 11 | 2 | 5.91 | 0.97 |
| Wheat | 20 | 3 | 2.63 | 1 | 5 | 1 | 3.56 | 1 |
| Maize | 17 | 1 | 0.92 | 0.99 | 19 | 3 | 1.68 | 0.98 |
| Groundnut | 20 | 2 | 0.95 | 0.8 | 19 | 3 | 1.26 | 0.6 |
| Cotton | 20 | 1 | 1.21 | 0.99 | 17 | 1 | 1.99 | 0.94 |
| Sugarcane | 20 | 4 | 16.83 | 0.98 | 9 | 1 | 23.79 | 0.96 |
For maize, the best set of hyperparameters based on RMSE with a training algorithm is BR, a hidden layer size of 18 and a delay of 3. For groundnut, the best set of hyperparameters based on RMSE with a training algorithm is BR, a hidden layer size of 20 and a delay of 3. For cotton, the best set of hyperparameters based on RMSE with a training algorithm is BR, a hidden layer size of 17 and a delay of 1. For sugarcane, the best set of hyperparameters based on RMSE with a training algorithm is BR, a hidden layer size of 18 and a delay of 1.
The panel selector selects the best E-NLAR neural network model for each crop, with a specific architecture consisting of a certain number of neurons in the hidden layer and FDs, as given in Table 5.
Hyperparameter values of the E-NLARNN model for crop datasets
| Crop dataset | Training algorithm | HNC | FD |
|---|---|---|---|
| Paddy | BR | 19 | 1 |
| Wheat | BR | 18 | 1 |
| Maize | BR | 20 | 1 |
| Groundnut | BR | 20 | 3 |
| Cotton | BR | 12 | 1 |
| Sugarcane | BR | 17 | 1 |
Table 6 shows the performance metrics of different models for predicting crop yield using the crop dataset. The E-NLARNN model and the hybrid NLARNN model are compared. In terms of individual crops, the hybrid NLARNN model shows the lowest RMSE and highest R-value values for paddy, millets, maize and cotton. For groundnut, the hybrid NLARNN model has a lower RMSE value but a slightly lower R-value than the E-NLARNN model. In comparison to the E-NLARNN model, the hybrid NLARNN model for sugarcane exhibits a higher RMSE value; however, the R-value of the E-NLARNN model is higher than that of the hybrid NLARNN model. The hybrid NLARNN model appears to perform better overall than the E-NLARNN model in predicting crop yield, while the E-NLARNN model is useful in determining which hyperparameters of the NLARNN architecture generate the best results.
Performance of E-NLARNN and hybrid NLARNN models for crop dataset
| Crop dataset | RMSE | R-value | ||
|---|---|---|---|---|
| E-NLARNN Model | Hybrid NLARNN model | E-NLARNN Model | Hybrid NLARNN model | |
| Paddy | 4.66 | 3.76 | 0.99 | 0.99 |
| Wheat | 2.65 | 2.10 | 1 | 1.00 |
| Maize | 0.95 | 0.66 | 0.99 | 0.99 |
| Groundnut | 0.96 | 0.71 | 0.79 | 0.85 |
| Cotton | 1.39 | 0.98 | 0.99 | 1.00 |
| Sugarcane | 17.97 | 13.51 | 0.98 | 0.99 |
Figure 2 compares the performance of several NLARNN models performed in predicting crop data for sis types of crops. The x-axis on both charts lists the crops. The left chart shows the RMSE on the y-axis which indicates how much error is in the prediction-where lower values are better. The right chart shows the R-value on the y-axis, which indicate how closely the model's predictions match the real data where higher values are better, ideally close to 1.
The figure shows two vertical bar graphs side by side. The graph on the left side is titled “R M S E Comparison Graph.” The details of this graph are as follows. The vertical axis is labeled “R M S E” and ranges from 0 to 70 in increments of 10 units. The horizontal axis is labeled “Crops” and includes the following crops from left to right: “Paddy,” “Wheat,” “Maize,” “Groundnut,” “Cotton,” and “Sugarcane.” Each crop has six bars labeled with different models, with the following colors and labels: Blue: “T A - N L A R N N - L M,” Orange: “T A - N L A R N N - B R,” Green: “T A - N L A R N N - S C G,” Red: “T A - N L A R N N - C F G,” Purple: “E - N L A R N N,” and Brown: “Hybrid N L A R N N.” The data from the bars is as follows: Paddy: T A - N L A R N N - L M: 22.95. T A - N L AR N N - B R: 4.35. T A - N L AR N N - S C G: 4.95 T A - N L AR N N - C F G: 6.13. E - N L AR N N: 5.14. Hybrid NLARNN: 4.15. Wheat: T A - N L A R N N - L M: 24.5. T A - N L AR N N - B R: 2.77. T A - N L AR N N - S C G: 2.97. T A - N L AR N N - C F G: 3.56. E - N L AR N N: 2.97. Hybrid NLARNN: 2.18. Maize: T A - N L A R N N - L M: 8.11. T A - N L AR N N - B R: 0.99. T A - N L AR N N - S C G: 1.38. T A - N L AR N N - C F G: 1.78. E - N L AR N N: 1.19. Hybrid NLARNN: 0.99. Groundnut: T A - N L A R N N - L M: 1.78. T A - N L AR N N - B R: 1.19. T A - N L AR N N - S C G: 1.20. T A - N L AR N N - C F G: 1.58. E - N L AR N N: 1.19. Hybrid NLARNN: 1.1. Cotton: T A - N L A R N N - L M: 12.07. T A - N L AR N N - B R: 1.38. T A - N L AR N N - S C G: 1.4. T A - N L AR N N - C F G: 2.18. E - N L AR N N: 1.58. Hybrid NLARNN: 1.19. Sugarcane: T A - N L A R N N - L M: 73.21. T A - N L AR N N - B R: 17.02. T A - N L AR N N - S C G: 17.04. T A - N L AR N N - C F G: 23.9. E - N L AR N N: 18.2. Hybrid NLARNN: 13.65. The graph on the right side is titled “R-Value Comparison Graph.” The details of this graph are as follows. The vertical axis is labeled “R-Value” and ranges from 0 to 14 in increments of 2 units. The horizontal axis is labeled “Crops” and includes the following crops from left to right: “Paddy,” “Wheat,” “Maize,” “Groundnut,” “Cotton,” and “Sugarcane.” Each crop has six bars labeled with different models, with the following colors and labels: Blue: “T A - N L A R N N - L M,” Orange: “T A - N L A R N N - B R,” Green: “T A - N L A R N N - S C G,” Red: “T A - N L A R N N - C F G,” Purple: “E - N L A R N N,” and Brown: “Hybrid N L A R N N.” The data from the bars is as follows: Paddy: T A - N L A R N N - L M: 3.8. T A - N L AR N N - B R: 3.8. T A - N L AR N N - S C G: 3.8. T A - N L AR N N - C F G: 3.8. E - N L AR N N: 3.8. Hybrid NLARNN: 3.8. Wheat: T A - N L A R N N - L M: 2.1. T A - N L AR N N - B R: 2.1. T A - N L AR N N - S C G: 2.1. T A - N L AR N N - C F G: 2.1. E - N L AR N N: 2.1. Hybrid NLARNN: 2.1. Maize: T A - N L A R N N - L M: 0.69. T A - N L AR N N - B R: 0.69. T A - N L AR N N - S C G: 0.69. T A - N L AR N N - C F G: 0.69. E - N L AR N N: 0.69. Hybrid NLARNN: 0.69. Groundnut: T A - N L A R N N - L M: 0.8. T A - N L AR N N - B R: 0.8. T A - N L AR N N - S C G: 0.8. T A - N L AR N N - C F G: 0.8. E - N L AR N N: 0.8. Hybrid NLARNN: 0.8. Cotton: T A - N L A R N N - L M: 1.03. T A - N L AR N N - B R: 1.03. T A - N L AR N N - S C G: 1.03. T A - N L AR N N - C F G: 1.03. E - N L AR N N: 1.03. Hybrid NLARNN: 1.03. Sugarcane: T A - N L A R N N - L M: 13.5. T A - N L AR N N - B R: 13.5. T A - N L AR N N - S C G: 13.5. T A - N L AR N N - C F G: 13.5. E - N L AR N N: 13.5. Hybrid NLARNN: 13.5. Note: All numerical data values are approximated.Comparative performance of all NLARNN models. Source: Figure by authors
The figure shows two vertical bar graphs side by side. The graph on the left side is titled “R M S E Comparison Graph.” The details of this graph are as follows. The vertical axis is labeled “R M S E” and ranges from 0 to 70 in increments of 10 units. The horizontal axis is labeled “Crops” and includes the following crops from left to right: “Paddy,” “Wheat,” “Maize,” “Groundnut,” “Cotton,” and “Sugarcane.” Each crop has six bars labeled with different models, with the following colors and labels: Blue: “T A - N L A R N N - L M,” Orange: “T A - N L A R N N - B R,” Green: “T A - N L A R N N - S C G,” Red: “T A - N L A R N N - C F G,” Purple: “E - N L A R N N,” and Brown: “Hybrid N L A R N N.” The data from the bars is as follows: Paddy: T A - N L A R N N - L M: 22.95. T A - N L AR N N - B R: 4.35. T A - N L AR N N - S C G: 4.95 T A - N L AR N N - C F G: 6.13. E - N L AR N N: 5.14. Hybrid NLARNN: 4.15. Wheat: T A - N L A R N N - L M: 24.5. T A - N L AR N N - B R: 2.77. T A - N L AR N N - S C G: 2.97. T A - N L AR N N - C F G: 3.56. E - N L AR N N: 2.97. Hybrid NLARNN: 2.18. Maize: T A - N L A R N N - L M: 8.11. T A - N L AR N N - B R: 0.99. T A - N L AR N N - S C G: 1.38. T A - N L AR N N - C F G: 1.78. E - N L AR N N: 1.19. Hybrid NLARNN: 0.99. Groundnut: T A - N L A R N N - L M: 1.78. T A - N L AR N N - B R: 1.19. T A - N L AR N N - S C G: 1.20. T A - N L AR N N - C F G: 1.58. E - N L AR N N: 1.19. Hybrid NLARNN: 1.1. Cotton: T A - N L A R N N - L M: 12.07. T A - N L AR N N - B R: 1.38. T A - N L AR N N - S C G: 1.4. T A - N L AR N N - C F G: 2.18. E - N L AR N N: 1.58. Hybrid NLARNN: 1.19. Sugarcane: T A - N L A R N N - L M: 73.21. T A - N L AR N N - B R: 17.02. T A - N L AR N N - S C G: 17.04. T A - N L AR N N - C F G: 23.9. E - N L AR N N: 18.2. Hybrid NLARNN: 13.65. The graph on the right side is titled “R-Value Comparison Graph.” The details of this graph are as follows. The vertical axis is labeled “R-Value” and ranges from 0 to 14 in increments of 2 units. The horizontal axis is labeled “Crops” and includes the following crops from left to right: “Paddy,” “Wheat,” “Maize,” “Groundnut,” “Cotton,” and “Sugarcane.” Each crop has six bars labeled with different models, with the following colors and labels: Blue: “T A - N L A R N N - L M,” Orange: “T A - N L A R N N - B R,” Green: “T A - N L A R N N - S C G,” Red: “T A - N L A R N N - C F G,” Purple: “E - N L A R N N,” and Brown: “Hybrid N L A R N N.” The data from the bars is as follows: Paddy: T A - N L A R N N - L M: 3.8. T A - N L AR N N - B R: 3.8. T A - N L AR N N - S C G: 3.8. T A - N L AR N N - C F G: 3.8. E - N L AR N N: 3.8. Hybrid NLARNN: 3.8. Wheat: T A - N L A R N N - L M: 2.1. T A - N L AR N N - B R: 2.1. T A - N L AR N N - S C G: 2.1. T A - N L AR N N - C F G: 2.1. E - N L AR N N: 2.1. Hybrid NLARNN: 2.1. Maize: T A - N L A R N N - L M: 0.69. T A - N L AR N N - B R: 0.69. T A - N L AR N N - S C G: 0.69. T A - N L AR N N - C F G: 0.69. E - N L AR N N: 0.69. Hybrid NLARNN: 0.69. Groundnut: T A - N L A R N N - L M: 0.8. T A - N L AR N N - B R: 0.8. T A - N L AR N N - S C G: 0.8. T A - N L AR N N - C F G: 0.8. E - N L AR N N: 0.8. Hybrid NLARNN: 0.8. Cotton: T A - N L A R N N - L M: 1.03. T A - N L AR N N - B R: 1.03. T A - N L AR N N - S C G: 1.03. T A - N L AR N N - C F G: 1.03. E - N L AR N N: 1.03. Hybrid NLARNN: 1.03. Sugarcane: T A - N L A R N N - L M: 13.5. T A - N L AR N N - B R: 13.5. T A - N L AR N N - S C G: 13.5. T A - N L AR N N - C F G: 13.5. E - N L AR N N: 13.5. Hybrid NLARNN: 13.5. Note: All numerical data values are approximated.Comparative performance of all NLARNN models. Source: Figure by authors
From the RMSE chart, TA-NLARNN-LM model performs poorly especially for Sugarcane where its error exceeds 70, The other TA-NLARNN variants (BR, SCG and CFG) perform slightly better but still show higher error values compared to the ensemble and hybrid approaches. The E-NLARNN and Hybrid NLARNN models achieve significantly lower RMSEs. In the R-value chart, hybrid NLARNN model shows the highest correlation across all crops, indicating that its predictions closely follow actual trends. The E-NLARNN also perform strongly, though slightly behind Hybrid NLARNN. The ensemble approach (E-N: ARNN) also enhances perdition quality over the baselines TA-NLARNN models, which generally perform less reliably.
Table 7 shows the crop water requirement (in mm) for the entire growing period of each crop and yield of crop per hectare, and water use efficiency (WUE) (liters/kg). It should be noted that these values are general guidelines and vary depending on various factors such as climate, soil type and crop type. These information are taken from the Indian government websites like https://desagri.gov.in/, https://agriwelfare.gov.in/ and https://www.ikisan.com/. These values can be used as a reference for irrigation planning and water management practices. It is important to ensure that crops receive the right amount of water at the right time to maximize yield and minimize water use.
Approximate water requirements in India
| Crops | Crop water need per hectare (mm/total growing period) | Yield (kg/Ha) | Water use Efficiency(L/kg) |
|---|---|---|---|
| Paddy | 900–2,500 | 2,809 | 3,000–5,000 |
| Millets | 450–650 | 3,507 | 900–2,000 |
| Maize | 500–800 | 3,349 | 900–1,250 |
| Groundnut | 500–700 | 1,759 | 500–700 |
| Cotton | 700–1,300 | 445 | 22,500–24,000 |
| Sugarcane | 1,500–2,500 | 83,887 | 1,500–3,000 |
Table 8 presents the percentage improvement in RMSE for E-NLARNN and Hybrid NLARNN models over the best baseline TA-NLARNN model for each crop. The improvement is calculated using the formula:
Percentage of RMSE improvement for baseline TA-NLARNN model
| Crop | Best TA-NLARNN RMSE | E-NLARNN RMSE | Hybrid NLARNN RMSE | Best TA-NLARNN vs hybrid E-NLARNN improvement (%) | E-NLARNN RMSE vs Hybrid NLARNN improvement (%) |
|---|---|---|---|---|---|
| Paddy | 4.16 (BR) | 4.66 | 3.76 | 19.3% | 9.6% |
| Wheat | 2.51 (BR) | 2.65 | 2.1 | 20.8% | 16.3% |
| Maize | 0.79 (BR) | 0.95 | 0.66 | 30.5% | 16.5% |
| Groundnut | 0.88 (BR) | 0.96 | 0.71 | 26.0% | 19.3% |
| Cotton | 1.11 (BR) | 1.39 | 0.98 | 29.5% | 11.7% |
| Sugarcane | 16.79 (BR) | 17.97 | 13.51 | 24.8% | 19.5% |
From the results, it is evident that the Hybrid NLARNN model consistently outperforms both the best TA-NLARNN and the E-NLARNN models across all crop datasets. Specifically, the Hybrid NLARNN achieved RMSE reductions ranging from 19.3% to 30.5% compared to the best TA-NLARNN variants. Moreover, when compared against the E-NLARNN model, the Hybrid NLARNN demonstrated further RMSE reductions between 9.6% and 19.5%.
The hybrid NLARNN model outperforms other models such as E-NLARNN and NLARNN models. This is due to the hybrid model's ability to better capture different patterns in the data, reduce overfitting and handle non-linear relationships more effectively. In addition, the hybrid model's ability to refine forecasts using GRNN for error estimation improves its overall performance in agricultural time series forecasting tasks.
Table 9 presents the predicted yields for six major crops – paddy, wheat, maize, groundnut, cotton and sugarcane – for the years 2024–2030. The forecasted production is expressed in million tons (MT). The corresponding estimated water requirements, expressed in billion liters (BL), were derived from these yield forecasts using the WUE values provided in Table 7. The water requirement calculation (Equation 4) accounts for the total growing season water demand of each crop in relation to the predicted production. These estimates provide valuable insights for irrigation planning and sustainable water resource management.
Forecasted crop yield and estimated water requirement
| Year | Paddy (MT) | Water (BL) | Wheat (MT) | Water (BL) | Maize (MT) | Water (BL) | Groundnut (MT) | Water (BL) | Cotton (MT) | Water (BL) | Sugarcane (MT) | Water (BL) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2024 | 110.84 | 443360.0 | 98.57 | 142916.5 | 5.00 | 5375.0 | 6.75 | 4050.0 | 35.59 | 827467.5 | 337.62 | 759645.0 |
| 2025 | 112.84 | 451360.0 | 100.52 | 145754.0 | 6.88 | 7396.0 | 5.45 | 3270.0 | 36.09 | 839092.5 | 357.18 | 803655.0 |
| 2026 | 112.90 | 451600.0 | 101.05 | 146522.5 | 6.25 | 6718.8 | 7.50 | 4500.0 | 37.91 | 881407.5 | 353.53 | 795442.5 |
| 2027 | 114.04 | 456160.0 | 101.91 | 147769.5 | 6.08 | 6536.0 | 7.27 | 4362.0 | 39.03 | 907447.5 | 350.29 | 788152.5 |
| 2028 | 114.91 | 459640.0 | 102.40 | 148480.0 | 7.14 | 7675.5 | 7.63 | 4578.0 | 40.76 | 947670.0 | 336.72 | 757620.0 |
| 2029 | 116.01 | 464040.0 | 103.70 | 150365.0 | 4.96 | 5332.0 | 6.57 | 3942.0 | 42.02 | 976965.0 | 358.21 | 805972.5 |
| 2030 | 118.50 | 474000.0 | 105.02 | 152279.0 | 6.74 | 7245.5 | 5.58 | 3348.0 | 44.34 | 1030905.0 | 353.84 | 796140.0 |
Note(s): MT = million tonnes; BL = billion liters. Water requirements are computed using forecasted yields and water use efficiency values from Table 7
In short, briefly the findings of these studies indicate that there is no one best model for forecasting crop yield data. The best model to implement will vary depending on the unique characteristics of the crop yield data, the research question being addressed and other variables (like data accessibility, geographic location and model interpretability). The hybrid E-NLARNN + GRNN model demonstrates superior performance across most crops, particularly in capturing complex nonlinear relationships and refining error estimations. However, to improve water demand estimation precision, detailed comparative analyses considering climate variability, soil–water interactions and crop stages are needed.
6. Conclusion
This study proposed a novel hybrid neural network approach for crop water requirement estimation based on the predicted yield. A hybrid model was developed by combining the E-NLARNN and the GRNN models. Proposed model performance was evaluated using benchmark metrics such as RMSE and R-value. According to the findings, the Bayesian regularization training method provided superior prediction results. Sensitivity analysis showed that variations in the hidden neurons and the FD had minimal impact on prediction accuracy. The hybrid neural network model outperformed the E-NALRNN model and both traditional baseline models such as NLARNN and E-NLARNN models in estimating the agricultural water demand.
However, this study is limited to a univariate forecasting framework based only on historical yield data, without incorporating climatic factors such as rainfall or temperature. Future work will extend the model to a multivariate setting by including rainfall and other weather variables, enabling more robust and climate-resilient crop yield prediction. Additionally, the proposed approach will eventually be applied to additional crops and geographical areas, which will help manage water resources and promote sustainable agriculture. The proposed hybrid approach has substantial implications for agricultural sustainability in water-limited countries and offers a promising approach for crop water requirement assessment.
