An accurate irrigation volume prediction method based on an optimized LSTM model

Construction of the model

Construction of the irrigation water demand model

This article has used the AquaCrop model to construct an optimal irrigation water demand model. Based on principles of crop physiology and soil water balance, the model provides an accurate estimate of crop irrigation requirements by combining factors such as meteorological data, soil properties, and crop parameters. We have combined the AquaCrop model with the BiLSTM-CNN-Attention algorithm to determine the optimal irrigation strategy and accurately predict the water requirements for crop irrigation, as shown in Fig. 1.

The detailed process for performing the proof has been outlined as follows:

The first step involves acquiring various meteorological station data, soil data, crop parameter data, and field management data for the planting area. The second step involves local debugging of the AquaCrop model through a trial-and-error method. Third, the model simulates different irrigation systems using the AquaCrop model to select an appropriate irrigation strategy. Then, the output of AquaCrop model simulation results is obtained. Finally, the BiLSTM-CNN-Attention model was used to predict the daily irrigation water requirement of the crop for the following year’s reproductive period.

This study combines crop models, machine learning methods, and existing meteorological stations and crop management data. We select suitable irrigation strategies based on the water supply and demand conditions in different areas and the water demand characteristics of crop growth.

Based on Chen et al. (2019), Zhang & Zhang (2013), Kuschel-Otárola et al. (2020), and Aemro, Mekete & Hailu (2022) Mathias models, we developed five irrigation strategies, namely rainfed, 80 mm irrigation, 60 mm irrigation, 45 mm irrigation, and optimal irrigation. Table 1 shows our specific irrigation strategies. Using the results of the AquaCrop model simulations, we select the best irrigation strategy based on the water requirements of each crop growth cycle.

Table 1:

Irrigation strategies.

Irrigation strategies	Acronyms	Standard
Rain irrigation	RF	The crop’s water needs can only be met by rainfall
80 mm irrigation	80 CI	When soil water content (SWC) reaches a threshold value, crops are irrigated with 80 mm of water.
60 mm irrigation	60 CI	When soil water content (SWC) reaches a threshold value, the crop is irrigated with 60 mm of water.
30 mm irrigation	45 CI	When soil water content (SWC) reaches a threshold value, the crop is irrigated with 45 mm of water.
Optimal	TBI	Irrigate the crop according to the amount of water required. Irrigation is carried out according
Irrigation		To the date and depth calculated.

DOI: 10.7717/peerjcs.2112/table-1

The Penman–Monteith method recommended by the Food and Agriculture Organization of the United Nations (FAO) calculates crop water requirements and irrigation. This method calculates ET0, as shown in Eq. (1): (1)${\displaystyle E{T}_o=\frac{0.408\Delta \left(R_n-G\right)+\gamma \frac{900}{T+273}{U}_2\left(e_S-e_a\right)}{\Delta +\gamma \left(1+0.34U_2\right)}}$

where ET₀ is the reference crop evapotranspiration and mm/dR_n is the net canopy surface radiation .MJ/(m²⋅d)G is the soil heat flux ; G = 0 .32MJ/(m²⋅d)γ is the thermometer constant; T is the mean air temperature; ⁰CU₂ is the wind speed at 2.0 m above ground level; and e_s is the saturated water vapor pressure of air. KP_ae_a is the actual water vapor pressure of air, and KP_aΔ isthe slope of the soaking water vapor pressure–temperature relationship curve.

We determined the fixed irrigation schedules and crop water requirements using CROPW version 8.0, based on FAO-56 (Bodner, Loiskandl & Kaul, 2007; Kassaye et al., 2020). The reference irrigation treatment (K_c) had a crop factor of 100%. For the spring maize crop, the crop coefficients used in the reference irrigation treatment (K_c) were 100%, based on the nutrient growth stages, which were 0.42 at the seedling stage, 0.753 at the growing stage, 1.288 at the flowering set, and 0.769 at maturity. For the soybean crop, the growth coefficients were 0.40 at the seedling stage, 0.64 at the growing stage, 1.14 at the flowering set, and 0.68 at maturity. We obtained 0.68. K_c for each growth stage from the literature (Li et al., 2020; Wang, 2020), and crop evapotranspiration (ET_c, mm) was determined from Eq. (2): (2)${\displaystyle E{T}_c=E{T}_0\ast K_c}$

where ET₀ is the reference evapotranspiration in mm. Since the model is based on evapotranspiration, the net irrigation water requirement (NIR) can be quantified by subtracting the adequate rainfall for the experimental season (P), described by Eq. (3): (3)${\displaystyle \mathrm{NIR}=\mathrm{E}{\mathrm{T}}_{\mathrm{C}}-\mathrm{P}.}$

BiLSTM-CNN-Attention prediction model structure

This study proposes a crop irrigation prediction method based on the BiLSTM-CNN-Attention model, and the specific implementation is shown in Fig. 2. We construct a BiLSTM-CNN-Attention model, and the data are first processed by a BiLSTM layer and a CNN layer to exploit the sequential coding capabilities of BiLSTM better. However, using the CNN layer first can lead to information loss about the data sequence. This model design can improve the accuracy of crop irrigation prediction.The technique involves pre-processing and splitting the collected irrigation data into training and test sets.

This study also uses the BiLSTM model to extract the time series information by combining the model with three layers of 1D convolutions to construct a CNN framework for automatically extracting internal features from irrigation volume data. The convolutional layers efficiently remove the nonlinear local features of the irrigation volume data. Following the first two convolutional layers, batch normalization is also introduced to reduce the input bias by normalizing the batch samples’ net input. Then, we add residual join after the first and third convolutional layers to address the gradient vanishing and weight matrix degradation issues. Using the model design can improve the extraction of features from irrigation data and the accuracy of crop irrigation prediction.

The method utilized features extracted from the CNN layer to improve the attention mechanism. By applying the attention mechanism, the temporal information extracted from the CNN layer is weighted, helping to uncover deep temporal correlations and making more effective use of the time-series properties of the irrigation data. The attention mechanism also reduces the loss of historical information. It highlights information at key historical time-points, reducing redundant data’s impact on the irrigation volume prediction results. Next, the output of the attention layer is used as input to the fully connected layer, which produces the final irrigation volume prediction result. This approach takes full advantage of the time series information and reduces unnecessary interference factors, resulting in more accurate and predicting results.

The method also introduces a random deactivation (Dropout) technique to prevent the occurrence of over-fitting. Studies have used stochastic inactivation techniques to improve the generalization of models’ performance and reduce the training time. This technique improved model performance and efficiency during training. Regarding network parameter optimization, the method uses the adaptive moment estimation optimization algorithm (Adam) to update the network parameters of each layer. However, we used the MSE as the loss function. Finally, we saved the trained BiLSTM-CNN-Attention model and verified its effectiveness using a test set. We identified the model shortcomings by analyzing the irrigation prediction results and optimized the predictive models continuously. We followed this procedure to enhance its robustness and improve the predictive model’s performance.

Local sensing and weight sharing of CNN can significantly reduce the number of parameters and improve the model efficiency. These convolutional and pooling layers play crucial roles in this process. Each convolutional layer contains multiple kernels, and features are calculated using Eq. (10). The convolutional layer extracts the data features, but the feature dimension is steep. Adding a pooling layer after the convolutional layer can effectively reduce the feature dimension and contribute to the training cost. (10)${\displaystyle l_t=\mathit{tanh}\left(x_t\ast k_t+b_t\right)}$

where l_t is the output value after convolution; tanh is the activation function ; x_t is the input vector; k_t is the weight of the convolution kernel; and b_t is the bias of the convolution kernel.

RNNs are either many-to-one or many-to-many with variable input and output lengths. RNNs are suitable for small-scale problems. Large-scale problems require a Transformer, and RNNs are not ideal for this application.

Moreover, LSTM only considers forward data dependencies. Therefore, BiLSTM uses LSTM networks in two opposite directions, front and back, to obtain complete information. The model also processes the input data and determines the current input by processing the data dependencies in both directions, as shown in Fig. 3. Our experiments demonstrate that the model performs better when backward data dependencies are considered. This approach improves the expressiveness of the model without requiring more data and reduces the risk of underfitting by re-using weights.

The LSTM calculation results are as follows:

In the first step, the LSTM determines the information that can be passed through the “cell state”. This decision is controlled by the “forget gate” layer (forgetting layer) through the sigmoid cell. The sigmoid function outputs a value between (0,1), filtering the information passed at the last moment and the information entered at the current moment. The calculation is shown in Eq. (11): (11)${\displaystyle f_t=\sigma \left(W_{xf}{x}_t+W_{hf}{h}_{t-1}+b_f\right).}$

The second step uses the “input gate” layer (input layer) to generate the data that can be updated when employing sigmoid cells. The calculation is shown in Eqs. (12), (13), (14) and (15): (12)${\displaystyle {\mathrm{i}}_{\mathrm{t}}=\sigma \left({\mathrm{W}}_{\mathrm{xi}}{\mathrm{x}}_{\mathrm{t}}+{\mathrm{W}}_{\mathrm{hi}}{\mathrm{h}}_{\mathrm{t}-1}+{\mathrm{b}}_{\mathrm{i}}\right)}$ (13)${\displaystyle {\mathrm{c}}_{\mathrm{t}}={\mathrm{f}}_{\mathrm{t}}{\mathrm{c}}_{\mathrm{t}-1}+{\mathrm{i}}_{\mathrm{t}}\text{tanh}\left({\mathrm{W}}_{\mathrm{xc}}{\mathrm{x}}_{\mathrm{t}}+{\mathrm{W}}_{\mathrm{hc}}{\mathrm{h}}_{\mathrm{t}-1}+{\mathrm{b}}_{\mathrm{c}}\right)}$ (14)${\displaystyle {\mathrm{o}}_{\mathrm{t}}=\sigma \left({\mathrm{W}}_{\mathrm{xo}}{\mathrm{x}}_{\mathrm{t}}+{\mathrm{W}}_{\mathrm{ho}}{\mathrm{h}}_{\mathrm{t}-1}+{\mathrm{b}}_{\mathrm{c}}\right)}$ (15)${\displaystyle {\mathrm{h}}_{\mathrm{t}}={\mathrm{o}}_{\mathrm{t}}\text{tanh}\left({\mathrm{c}}_{\mathrm{t}}\right)}$

where x_t is the input; i_t is the input gate; f_t is the forgetting gate; c_t is the state of the cell at the moment t; o_t is the cell state at the output at moment t; h_t is the production at moment t; σ is the sigmoid function; tanh is the hyperbolic tangent function; b_i, b_f, b_c, b_o are the paranoid vectors; and W_xi, W_hi, W_xf, W_hf, W_xc, W_hc, W_xo, W_ho are the weighting factors.

When inputting computational irrigation data into a neural network, it is common to encounter vectors of varying sizes, each with specific relationships between them. These differences in vectors can pose a challenge. Therefore, it is challenging to sufficiently exploit these relations during practical training, resulting in poor model results. Introducing the attention mechanism allows critical information to be selected and highlights essential inputs. This study used a forward-attentive model, learning through attention weights, which involved adding a feed-forward network to the existing network structure. The attention weights of the feed-forward network are functions of the hidden state values of the encoder and decoder. Therefore, we used a feed-forward network trained jointly with the previous network architecture.

(16)${\displaystyle {\mathrm{e}}_{\mathrm{t}}=\text{tanh}\left({\mathrm{h}}_{\mathrm{t}}\right)}$

(17)${\displaystyle {\alpha }_{\mathrm{t}}=\frac{exp\left({\mathrm{e}}_{\mathrm{t}}\right)}{{\sum }_{\mathrm{t}=1}^{\mathrm{m}\sum \left({\mathrm{e}}_{\mathrm{t}}\right)}exp}.}$

The generated attention weights are assigned to the corresponding hidden layer h_t so that the attention weights generated by the model are functional. Its h_t weighted average and the consequences α_t are shown in Eq. (18). (18)${\displaystyle {\mathrm{c}}_{\mathrm{t}}=\sum _{\mathrm{t}=1}^{\mathrm{m}}{\alpha }_{\mathrm{t}}\cdot {\mathrm{h}}_{\mathrm{t}}.}$

BiLSTM-CNN-Attention training process

The BiLSTM-CNN-Attention training process is shown in Fig. 4.

The main steps of the BiLSTM-CNN-Attention training are as follows.

(1) Input data: The first step is to input data for BiLSTM-CNN-Attention training.

(2) Input data normalization: We used the z-score normalization method to normalize the input data to train the model due to the significant variation in the input data.

(3) Network initialization: We initialize the BiLSTM-CNN-Attention layer weights and biases.

(4) BiLSTM layer calculation: Then, we extract the time series information from the irrigation data, calculate the input data of the CNN layer through the hidden layer of the BiLSTM layer, and obtain the output value.

(5) CNN layer calculation: The input data are sequentially passed through 3 CNN layers within a convolutional layer to perform feature extraction on the input data and obtain the output value.

(6) Residual calculation: The residuals are accumulated from the output values of the first convolutional layer after passing through the BiLSTM layers and the third convolutional layer normalized by batch normalization.

(7) Attention layer calculation: The attention layer calculates the output data of the CNN layer to obtain the output value.

(8) Output layer calculation: We calculate the output value of the attention layer to obtain the model output value.

(9) Calculation error: We compared the output value calculated with the actual value of this data set. This process enables us to calculate the corresponding error and assess our model’s accuracy.

(10) We determine if the end conditions for the prediction process are met: The requirements for a successful end are the completion of a predetermined number of cycles, a weight below a certain threshold, and a prediction error rate below a certain point. The training is completed if at least one of the end conditions is met. Otherwise, the movement continues.

(11) Error backpropagation: The calculated error is propagated in the opposite direction, updating the weights and biases of each layer and returning to step (4) to continue the network training.

BiLSTM-CNN-attention training process

BiLSTM-CNN-Attention is only possible if BiLSTM-CNN-Attention has been trained (Fig. 5).

The steps are as follows:

(1) Input data: We input data required for the forecast.

(2) Input data normalization: The input data are normalized according to (11).

(3) Prediction: The normalized data are fed into the trained BiLSTM-CNN-Attention to obtain the corresponding output values.

(4) Data normalization recovery: The output values obtained by BiLSTM-CNN-Attention are normalized, and the normalization formula is shown in Eq. (19):

(19)${\displaystyle x_i=y_i\ast s+\bar{x}}$

where x_i is the normalized recovery value ; y_i is the output value of BiLSTM-CNN-Attention ; s is the input data’s standard deviation; and $\overline{X}$ is the mean of the input data x.

(5) Output results: We output the recovered results to complete the prediction process.

Evaluation indicators

We evaluated the prediction accuracy of the BiLSTM-CNN-Attention model by comparing it with other models, such as RNN, LSTM, BiLSTM, and BiLSTM-CNN. This process helps to predict the amount of irrigation for spring corn from May 1, 2020 to September 30, 2022 in Changchun, Jilin Province, China. Then, we evaluated the proposed model performance using MAE, MSE, RMSE, and R². The model performs better when MAE, MSE, and RMSE are smaller. However, a larger value of the R² indicates a better fit of the model to the data.

The calculation formula is as follows:

(20)${\displaystyle MAE=\frac{1}{n}{\sum }_{i=1}^n\left|{\hat{y}}_i-y_i\right|}$

(21)${\displaystyle \mathrm{MSE}=\frac{1}{n}{\sum }_{i=1}^n{\left({\hat{y}}_i-y_i\right)}^2}$

where ${\hat{y}}_i$ is the predicted value and y_i is the actual value.

The calculation formula of RMSE is as follows:

(22)${\displaystyle RMSE=\sqrt{\frac{1}{n}{\sum }_{i=1}^n{\left({\hat{y}}_i-y_i\right)}^2}}$

where ${\hat{y}}_i$ is the predicted value and y_i is the actual value.

The calculation formula of R² isas follows:

(23)${\displaystyle R^2=1-\frac{\left({\sum }_{i=1}^n{\left(y_i-{\hat{y}}_i\right)}^2\right)/n}{\left({\sum }_{i=1}^n{\left(\overline{y_i}-{\hat{y}}_i\right)}^2\right)/n}}$

where ${\hat{y}}_i$ is the predicted value, y_i is the actual value, and ${\bar{y}}_i$ is the average value.

Data sources

The model requires daily meteorological data values and annual mean atmospheric CO2 concentrations. We obtained meteorological data from the WheatA Small Malt-Agricultural Meteorological Big Data System V1.5.4a. For the training set, we opted for irrigation data from May 1, 2000 to September 30, 2020. However, irrigation data has been designated for the independent prediction dataset from May 1, 2021 to September 30, 2022. Detailed information regarding the training data is presented in Table 2, while specifics concerning the prediction data are presented in Table 3.

The GCA has been utilized to analyze the correlation between each feature value from the daily monitored meteorological data in Changchun, Jilin Province, China. The data span from May 2000 to September 2020, providing a comprehensive understanding of the meteorological patterns in the region. The Pycharm environment has been employed to implement the GCA, as shown in Fig. 6.

In Fig. 6, We used AT–average temperature, rainfall (mm)–rainfall, WindV (m/s)–average wind speed, HoursS (peak, hours)–hours of sunshine, MaxT (°C)–maximum temperature, MinT (°C)–minimum temperature, and RelativeH (%)–relative humidity for the correlation analysis. As shown in Table 4, the correlation between maximum temperature and crop water requirement is the best, with a correlation coefficient of 0.88. Average temperatures and rainfall subsequently showed the highest correlation with crop water requirements, with a correlation coefficient of 0.87. Wind speed and sunshine hours were also strongly correlated with crop water requirements, with coefficients ranging from 0.7 to 0.85. Figure 6 shows that the more significant the correlation between the influence factor and the target series, the darker the corresponding module color, indicating a closer relationship.

Model parameter settings

Table 4 shows the parameters of the BiLSTM-CNN-Attention model set for this experiment, exhibiting that the training parameters are the same for all our methods, with epochs of 500, loss function MSE, optimizer Adam, time step of 20, and learning rate of 0.001.

Results of the irrigation prediction model

The processed training set data were used to train CNN, RNN, LSTM, BiLSTM, CNN-LSTM, BiLSTM-CNN, and BiLSTM-CNN-Attention. The trained model was used to predict the test set data, and the valid values were compared with the predicted values.

Based on the analysis of Figs. 7–12, the fold fit between the predicted and fundamental values of six prediction methods follows from highest to lowest: BiLSTM-CNN-Attention, BiLSTM-CNN, BiLSTM, LSTM, CNN, and RNN. Notably, RNN had the lowest fold fit. Based on each method’s predicted and actual values, the evaluation error indicators are calculated by comparing the results of the six methods shown in Table 5.

The MSE, RMSE, and MAE of RNN are the largest, and R² is the smallest, as shown in Table 6 and Figs. 13–16. Moreover, MSE, RMSE, and MAE of BiLSTM-CNN-Attention are the smallest, and R² is the largest and closest to 1. The prediction performance of the six methods is in descending order: BiLSTM-CNN-Attention, BiLSTM-CNN, BiLSTM, LSTM, CNN, and RNN. -CNN, BiLSTM, LSTM, CNN, RNN. However, LSTM has smaller MSE, RMSE, and MAE and larger R² than RNN. Its MAE (0.020867 vs. 0.026724) was 21.59% lower, and its MSE (0.000464 vs. 0.000767) was 39.5% lower than RNN. Its RMSE (0.021549 vs. 0.027701) was 22.2% lower than RNN. Its R² is 4.01% larger than RNN. Therefore, LSTM outperforms RNN. BiLSTM reduces MAE from 0.020867 to 0.018530, MSE from 0.000464 to 0.000376, RMSE from 0.021549 to 0.019387, R² from 0.9032 to 0.9147 compared with LSTM, indicating that the prediction accuracy of BiLSTM has been improved compared with LSTM.

The BiLSTM decreases in MAE and RMSE and increases in R² compared to the BiLSTM after CNN layers. Moreover, MAE decreased from 0.018530 to 0.013423. MSE decreased from 0.000376 to 0.000203, and RMSE decreased from 0.019387 to 0.014247. R² increased to 0.9518. The results show that BiLSTM-CNN-Attention performs best among the six methods. Its MAE is 0.004599, RMSE is 0.005968, and R² is 0.9926. Therefore, among the six methods, the proposed BiLSTM-CNN-Attention method exhibits a higher accuracy in predicting the future crop irrigation amount, providing a reference for agricultural workers to make correct irrigation decisions.

We are currently performing additional verification to validate the optimized LSTM model. In addition to investigating irrigation practices for spring corn in agricultural bases in Changchun City, Jilin Province, we are currently studying the irrigation conditions for greenhouse tomatoes at the “Good Yunlai” agricultural base in Yuncheng County, Heze City, Shandong Province. This extended research aims to verify the model’s applicability under different geographical and crop conditions.