Evaluating the impact of different decomposition methods on the accuracy of reference evapotranspiration forecasts in humid regions

Evapotranspiration (ET) is the physical process by which liquid water is transferred from the soil and plant surfaces into the atmosphere as water vapor. It is a crucial factor in the interactions among soil, plants, and the atmosphere, playing a significant role in the water balance and energy equilibrium at the Earth's surface (Allen et al. 1998; Liu et al. 2013). Moreover, is an indispensable component in the terrestrial water, energy, and carbon cycles, making it crucial for water resource planning and management (Tao et al. 2018). To make irrigation systems work better, accurate predictions of crop evapotranspiration are needed. These predictions need to cover a long enough time in the future to take into account changes in water supply over time (Torres et al. 2011a). Similarly, accurate forecasting of crop water requirements (i.e., actual evapotranspiration, ⁠) is crucial for designing and planning irrigation scheduling (Perera et al. 2014). For large-scale irrigation system forecasting, Cetin et al. (2023) used the mapping evapotranspiration at high resolution and the internalized calibration (METRIC) model to estimate using satellite and meteorological data, highlighting the importance of estimating for enhancing water efficiency.

Crop evapotranspiration (⁠⁠) can be estimated by multiplying the reference evapotranspiration (⁠⁠) with the crop coefficient ⁠. represents the ratio between (Jensen 1968). Alternatively, can be measured directly using an atmometer. However, this method is time-consuming and costly, making it less suitable for research purposes (Wright 1988; Tao et al. 2018). Simultaneously, research on data is also highly noteworthy. Başakın et al. systematically summarized the process of estimating missing data. From these studies, the complexity and nonlinearity of data can be inferred (Başakın et al. 2023). Currently, the most well-known mathematical formula for determining is the FAO-56 Penman–Monteith (PM) equation. This formula was proposed by the Food and Agriculture Organization of the United Nations (FAO) (Allen et al. 1998). The FAO-56 PM model, taking into account both thermodynamic and aerodynamic effects, is more accurate than existing empirical models. As a result, the FAO-56 PM method has been widely applied as a reference method in various regions and climates (Tao et al. 2018; Zhang et al. 2018; Granata 2019; Tikhamarine et al. 2019; Wu et al. 2019b; Lu et al. 2023). However, this model has a notable drawback. It requires a substantial amount of input meteorological data to be effectively utilized, including parameters such as maximum/minimum temperature, wind speed, relative humidity (RH), and solar radiation (Feng et al. 2017b). Therefore, the FAO-56 PM model can only be optimally employed when comprehensive meteorological data is available. For scenarios with limited meteorological data, it is advisable to use models that require fewer meteorological variables (Wen et al. 2015). In the past few decades, efforts have been made to address the issue of requiring extensive meteorological inputs by relying on empirical models (Mehdizadeh et al. 2017). Pendiuk et al. reduced the data requirements for estimating by utilizing superconducting gravimeter data to calculate cumulative (Pendiuk et al. 2023). In addition, many studies based on radiation, humidity, and temperature, and have aimed to estimate reference evapotranspiration using limited meteorological data (Xu & Singh 2002; Bickici Arikan et al. 2021). For example, there are temperature-based methods such as the Hargreaves and the modified Hargreaves methods (Hargreaves & Samani 1985; Luo et al. 2014), radiation-based methods including the Priestley–Taylor, Marking, and Ritchie models (Priestley & Taylor 1972; Feng et al. 2016), as well as the mass-transfer-based Trabert model (Trabert 1896). Additionally, these models are more suitable for forecasting on weekly and monthly cycles and may not be as well-suited for daily forecasting (Torres et al. 2011a). We employ Chen's nonlinear theoretical model within a dual-source trapezoid framework based on dry/wet edges to estimate land surface ET. This model enhances the estimation of daily-scale ⁠, thereby improving the prediction accuracy of regional evapotranspiration and its components. This research is closer to a physical model for prediction (Chen et al. 2023). These models involve complex physical processes, and predictive accuracy still has room for improvement.

In contrast to attempts with empirical models, researchers have sought to address the challenges associated with empirical models by employing data-driven artificial intelligence (AI) and machine learning (ML) methods to establish mathematical models for forecasting ⁠. Due to the high nonlinearity of meteorological data, traditional empirical models struggle to accurately capture the relationships between meteorological variables, thereby hindering their ability to forecast effectively. However, ML does not require a clear understanding of data variables in advance and can offer simple solutions to nonlinear and multivariate problems (Kisi 2015; Wang et al. 2017). Due to its capability to operate without prior knowledge of the underlying data and physical processes and its ability to handle nonlinearity, ML becomes robust, efficient, and reliable in problem-solving and decision-making (Goyal et al. 2023). In past research, various ML techniques have been applied to forecast ⁠. For instance, Ferreira et al. used artificial neural networks (ANNs) and support vector machines (SVMs) with limited meteorological data to forecast at 203 stations in Brazil. The results indicated that ANN and SVM exhibited good forecasting performance (Ferreira et al. 2019). Vosoughifar et al. established equations for coastal areas using multi-adaptive regression splines (MARS) and genetic expression programming (GEP), discovering they possess a more accurate estimation capability than traditional regression-based formulas (Vosoughifar et al. 2023). In addition to that, other models such as M5 model trees (Pal & Deswal 2009; Rahimikhoob 2014; Kisi & Kilic 2016), random forest (RF) (Feng et al. 2017a), gradient boosting decision tree (GBDT) (Fan et al. 2018; Wu et al. 2019a), and ANN-based models like multi-layer perceptron (MLP) (Torres et al. 2011a; Ladlani et al. 2014; Traore et al. 2016), generalized regression neural network (KiŞI 2006), radial basis function neural network (RBFNN) (Trajkovic 2005; Ladlani et al. 2012), and extreme learning machine (ELM) (Abdullah et al. 2015; Gocic et al. 2016) have been employed to forecast ⁠. In previous studies, to further improve the forecasting accuracy of within the framework of ML, bio-inspired optimization algorithms have been incorporated. For example, in the forecasting of for arid and humid regions in China, a hybrid model combining the whale optimization algorithm (WOA) with extreme gradient boosting (XGBoost) was employed. The results indicated that this strategy could provide a more accurate estimation of daily evaporation (Yan et al. 2021). Wu et al. utilized four bio-inspired optimization algorithms – ant colony optimization, genetic algorithm, flower pollination algorithm, and cuckoo search algorithm – to optimize the ELM model for daily forecasting. The results indicated that the ELM-FPA and ELM-CAS models outperformed the base ELM model regarding forecasting accuracy (Wu et al. 2019b). Zhao et al. (2022) combined two bio-inspired optimization algorithms, golden eagle optimization (GEO) and sparrow search algorithm (SSA), with ELM. The ELM model with the SSA was considered the optimal model for forecasting ⁠.

While conventional ML models have made significant strides in the daily forecasting of ⁠, there are still limitations to these theoretical models when it comes to forecasting with higher nonlinearity, larger datasets, and more complex cycles. In recent years, deep learning (DL) has been applied to various fields, and its performance has surpassed that of traditional ML models (Shi et al. 2018; Ghimire et al. 2019; Du et al. 2021; Luo et al. 2021; Yan et al. 2023). Furthermore, a growing body of research employs DL for the time-series forecasting of ⁠. This differs from traditional forecasting methods, as time-series forecasting involves forecasting a sequence using a sequence, distinct from the conventional regression task where independent variables are used to forecast dependent variables. Time-series forecasting also provides a better understanding of the forecasted trends and aligns well with real-world variations. Sabanci et al. (2023) predicted for 12 stations with variable climatic characteristics in the Central Anatolia region (CAR) using long short-term memory (LSTM), ANN, and MARS models. The results indicated that LSTM, ANN, and ML-based MARS showed high accuracy in estimating ⁠. Yin et al. (2020) forecasted daily based on a limited set of meteorological variables using a hybrid bidirectional LSTM (Bi-LSTM) model. The results indicated that the Bi-LSTM model yielded the best forecasting for all stations. Saggi & Jain (2019) estimated reference evapotranspiration in the northern region of Punjab, India, using a DL-MLP in comparison with traditional ML models such as generalized linear model (GLM), RF, and gradient boosting machine (GBM). The results indicated that the DL model achieved the best forecasting performance. Additionally, by combining DL models with convolutional neural networks (CNNs), one can further enhance the training of DL models through the convolutional calculations of CNN. For instance, Ferreira & da Cunha (2020a) used a hybrid CNN-LSTM model to forecast lagged ⁠, combining a one-dimensional CNN with an LSTM model. The results suggest that CNN-LSTM performs slightly better than RF and ANN but does not demonstrate the highest accuracy. In addition, combining ML with metaheuristic algorithms to optimize model parameters is also a common strategy. For example, Yuan et al. optimized the parameters of an LSTM model using the ant lion optimization (ALO) algorithm (LSTM-ALO) for monthly runoff prediction (Yuan et al. 2018). Ikram et al. utilized the reptile search algorithm and the weighted vector optimizer to enhance the performance of the LSTM model (LSTM-INFO) in predicting water temperature (Ikram et al. 2023). The application of DL in forecasting still requires further analysis and exploration to maximize its inherent value.

Despite extensive studies and proven effectiveness of ML and DL models in forecasting ⁠, bias toward data dependency persists. If 's increased nonlinearity, uncertainty, and randomness fail to capture relevant features/patterns in the time series, including trends, periodicity, seasonality, anomalies, and abrupt change peaks, it becomes increasingly difficult for DL to produce accurate forecasts (Ali et al. 2023). By decomposing the original data to obtain signal components and forecasting each signal component separately, even though there are multiple features in actual problems, each feature undergoes one decomposition at a time (Prasad et al. 2019). The decomposed signals become smoother with more robust periodicity, making them better suited for DL forecasting. Ali et al. employed the multivariate variational mode decomposition (MVMD) and monotonic empirical mode decomposition (MEMD) to decompose the original data. They then used a combination of RF, convolutional feedforward neural network (CFNN), ELM, and boosted regression trees (BRT) to forecast daily ⁠. The results indicated that MVMD-BRT, compared with the baseline model (BRT), could provide more accurate daily forecasting accuracy (Ali et al. 2023). Zheng et al. employed the MVMD method combined with the soft feature filter (SoFeFilter) and gated recurrent unit (GRU) model to predict for t + 1 day. Experimental results demonstrated that at the Gympie station, the MVMD-SoFeFilter-GRU model achieved the highest performance metrics. These findings confirm that the MVMD-SoFeFilter-GRU model provides the most accurate predictions for 1 day ahead (Zheng et al. 2023). Similarly, by integrating LSTM with the MEMD method and the Boruta-RF algorithm, ET was forecasted for drought-prone areas in Queensland, Australia. The results indicated that the MEMD-Boruta-LSTM hybrid model outperformed standalone models such as deep neural network (DNN), decision tree (DT), and LSTM, achieving the highest predictive performance across all study locations (Jayasinghe et al. 2021). In addition, time-varying correlation decomposition methods have been applied to forecasting. Karbasi et al. employed the time-varying filter-based empirical mode decomposition (TVF-EMD) technique, coupled with the partial autocorrelation function (PACF), to calculate significant lag values from the decomposed subsequences (i.e., IMFs). The extra tree-Boruta feature selection algorithm was then used to extract key features from the IMFs. By integrating TVF-EMD with the bidirectional recurrent neural network (Bi-RNN), MLP, RF, and XGBoost, weekly evaporation was predicted and evaluated using various performance metrics. The results demonstrated that, compared to models without decomposition, the TVF-EMD hybrid ML models achieved superior forecasting accuracy for weekly at the Redcliffe and Gold Coast stations (Karbasi et al. 2023). Lu et al. combined the variational mode decomposition (VMD) algorithm with the backpropagation neural network (BPNN) model. The results showed that the VMD-BPNN hybrid forecasting model outperformed the empirical mode decomposition (EMD) algorithm with the BPNN (EMD-BPNN) and the ensemble empirical mode decomposition (EEMD) algorithm with BPNN (EEMD-BPNN) models. Additionally, the forecasting accuracy of the VMD-BPNN model was significantly higher than that of single models such as BPNN, support vector regression (SVR), and gradient boosting regression tree (GBRT) (Lu et al. 2023). Commonly used decomposition algorithms include Fourier spectrum analysis (Soman et al. 2015) and discrete wavelet transform (Mallat 1989). Karbasi et al. proposed a time-series decomposition technique known as empirical Fourier decomposition (EFD). Autocorrelation analysis was employed to determine significant lag values, and EFD was applied to decompose the data. Based on the EFD results, lagged data were created, and the K-best feature selection algorithm was used to identify key features. Models were evaluated using the correlation coefficient (R) and root mean square error (RMSE). The results demonstrated that incorporating EFD-decomposed data significantly enhanced the predictive performance of ML models (Karbasi et al. 2024). Katipoğlu estimated monthly ET values for the Hakkari Province by combining SVM, bagging trees, and boosting trees with wavelet transformation. Model performance was evaluated using RMSE, MAE, the coefficient of determination (R²), and Taylor diagrams. The results indicated that hybrid wavelet-ML models, constructed by decomposing input combinations into subcomponents via wavelet transformation, generally produced more accurate predictions compared with standalone ML models (Katipoğlu 2023). Additionally, a method different from the decompositions mentioned above is complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) (Yeh et al. 2010), which has been applied to many other fields with satisfactory results (Zhang et al. 2017; Gao et al. 2020; Yan et al. 2023). It is generally believed that decomposition methods have advantages, but in geographically complex environments, where numerous influencing factors and frequent meteorological changes occur, time series-based methods can be risky. This study verifies this risk from multiple perspectives. However, based on the author's understanding, there is currently no specific analysis of the application of CEEMDAN combined with CNN and DL for forecasting ⁠. A detailed analysis of this algorithm is of significant reference value for future research on forecasting.

Due to the nonlinearity among climate variables, accurately predicting has become a challenge. Related literature shows few studies on DL-based models combined with CEEMDAN models to forecast in China. This study proposes four new methods for forecasting using CNN, LSTM, Bi-LSTM, and CNN-Bi-LSTM combined with CEEMDAN. This study compared hybrid models that integrate different decomposition algorithms, including EEMD, CEEMD, and CEEMDAN, with standalone model approaches, offering a more accurate forecasting strategy for multi-period prediction. Therefore, the objectives of this study are as follows: (1) Determine the importance and forecasting potential of CEEMDAN combined with base models XGBoost, SVM, RF, CNN, LSTM, Bi-LSTM, CNN-LSTM, and CNN-Bi-LSTM for forecasting; (2) Develop the base model and CEEMDAN models for forecasting at different periods; (3) Compare the accuracy, stability, and computational cost of baseline models with models based on EEMD, CEEMD, and CEEMDAN for predicting over different periods, and identify the optimal model; (4) Analyze the compatibility of the base model with the combination of CEEMDAN and CNN models for predicting at different periods, aiming to explore potential synergies and optimize overall predictive performance.

Researchers have widely applied conventional ML models in forecasting, yielding excellent forecasting results (Fan et al. 2018; Wu et al. 2019a; Ferreira & da Cunha 2020b; Yan et al. 2021). In previous studies, XGBoost (Fan et al. 2018), SVM (Granata 2019), and RF (Ali et al. 2023) have demonstrated stable performance in forecasting. This study used XGBoost, SVM, and RF as baseline models to compare with DL models, thereby enhancing the rigor of the DL forecasting results.

XGBoost is an algorithm or engineering implementation based on GBDT proposed by Chen & Guestrin (2016). The basic idea of XGBoost is similar to GBDT, but XGBoost introduces the concept of ‘boosting’, aggregating forecasting from ‘weak’ learners to generate a strong learner. Additionally, XGBoost incorporates second-order derivative optimization, making the loss function more precise. The regularization term optimization helps prevent the overfitting of trees. In addition, XGBoost is an efficient distributed implementation, making its training speed faster.

SVM is a supervised ML algorithm proposed by Cortes & Vapnik (1995). Based on the principle of structural risk minimization (SRM), SVMs seek to minimize the upper bound of generalization error rather than the upper bound of empirical error. To make predictions in problems that are not linearly related, SVM models can use a set of high-dimensional linear functions to make regression functions (Pai & Lin 2005). SVM employs different kernel functions as a key component to address nonlinear problems. Kernel functions can transform the original features of the data from a lower-dimensional space to a higher-dimensional feature space, making the data linearly separable in the new space. This study utilized the RBF kernel function because, compared with other kernel functions, it demonstrated better performance in forecasting (Kisi 2015).

RF was introduced by Breiman (2001). An ensemble learning method utilizes the ‘bagging’ concept to integrate a collection of decision trees with controlled variance. By combining multiple decision trees, RF aims to enhance the accuracy of the model. The ensemble nature of RF, which uses the voting results of multiple decision trees, makes it more robust than a single DT and better able to handle overfitting problems. RF randomly selects the best factor from a subset of forecasters at each node to split it, thereby improving forecasting performance (Liaw & Wiener 2002).

This paper employs time series models, including CNN, LSTM, and Bi-LSTM, which are capable of capturing complex linear relationships in time series data. In this study, multi-period forecasting was conducted, where LSTM better captures long-term temporal dependencies.

CNN has been applied to various fields to address problems, yielding favorable results (Cao et al. 2018; Hoseinzade & Haratizadeh 2019; Viton et al. 2020). Traditional CNN structures consist of three different types of essential layers: convolutional layers, pooling layers, and fully connected layers. For feature extraction, CNN can automatically extract features from input data, which is very different from manually extracting features, and it eliminates the need for data preprocessing (Ferreira & da Cunha 2020b). Moreover, CNN has the characteristic of parameter sharing, where weight parameters are shared at different locations, reducing model complexity, training time, and memory requirements and enhancing robustness. Since CNN is commonly used for image processing problems, it employs 2D convolutional filtering, as images are typically composed of two-dimensional arrays (matrices) (Ferreira & da Cunha 2020a). However, when dealing with time series-based problems in this experiment, CNN with one-dimensional (1D) convolutional filters was used.

This paper uses the decomposition algorithm CEEMDAN, developed by Torres et al., based on the EEMD algorithm (Torres et al. 2011b). The EMD and EEMD algorithms share the common feature of decomposing the original signal into high-frequency signals called intrinsic mode functions (IMFs) after multiple iterations. EMD and EEMD algorithms can alleviate mode mixing issues by adding positive and negative Gaussian noise to the decomposed signals. This characteristic is also present in CEEMDAN. However, both of these algorithms inevitably leave some white noise in the obtained IMFs from the decomposition of the original signal, which can impact the model's forecasting performance. CEEMDAN, on the other hand, differs in that its key advantage lies in its adaptability. It can automatically adjust noise estimation based on the signal's local characteristics, thereby improving signal decomposition's accuracy and stability. The implementation process of CEEMDAN is as follows:

• (1). Add white noise with a standard deviation of to the original signal ⁠:

  

  (14)

  where k represents a real number.
• (2). Decompose the signal set using EMD, then average each decomposition's combined parts.

  

  (15)
• (3). Calculate the first-order residuals.

  

  (16)
• (4). Further, decompose the signal using EMD and calculate the second IMF mode.

  

  (17)

  where represents the IMF mode component obtained by EMD.
• (5). In the next stage, the component and residue are calculated, as given by the following equations:

  

  (18)

  

  (19)
• (6). Repeat Equations (18) and (19) until the residual component no longer satisfies the decomposition conditions, and the decomposition stops. Finally, the original signal can be represented as:

  

  (20)

  where denotes the final residuals.

To further validate the robustness and complexity analysis of CEEMDAN decomposition, this study proposes a comparison with hybrid ML methods based on EEMD and CEEMD. EEMD is an improvement on the original EMD. EEMD introduces multiple iterations of white noise into the original signal, performs EMD on each noise-added signal, and averages the results. This approach effectively mitigates the mode mixing problem, enhancing the robustness and accuracy of the decomposition (Wu & Huang 2009). CEEMD further refines EEMD. While EEMD reduces mode mixing, residual noise can still occur in some cases. CEEMD addresses this issue by introducing symmetrically distributed positive and negative white noise into the signal, completely eliminating residual noise and ensuring the completeness of the decomposition (Torres et al. 2011a). The forecast structures of hybrid ML models for based on EEMD and CEEMD algorithms are consistent with the structure shown in Figure 3. By replacing the CEEMDAN components with EEMD or CEEMD, the corresponding schematic diagram of the hybrid ML models for prediction is obtained.

This study employed the grid search (GS) hyperparameter optimization method. Since the parameter space of ML and DL algorithms may consist of actual values or have infinite space, GS involves setting multiple values for each parameter within defined bounds. This approach is beneficial for parallelization, making it easy to explore the parameter space and find the optimal model parameters (Liashchynskyi & Liashchynskyi 2019). The ML models, XGBoost, SVM, and RF, have relatively few model parameters, so hyperparameter optimization was not performed on them. XGBoost chose the reg:squarederror parameter, commonly used in regression tasks, as the objective function. The RBF kernel function generally has good generalization ability and is increasingly used in nonlinear mapping SVM (Han et al. 2012). RBF was chosen as the kernel function for SVM. The number of decision trees (N_Estimators) for RF and XGBoost are 100 and 42, respectively. RF requires more decision trees to reduce prediction bias, while XGBoost, with its gradient boosting technique, improves each tree based on the previous one. Therefore, XGBoost uses fewer trees (N_Estimators = 42) for training. In the RF model, random_state serves as the random seed to ensure result reproducibility. In this study, setting it to 50 achieved better forecasting results. In the RF model, setting n_jobs to 1 uses only one computing core, saving computational resources and avoiding interference with other tasks. Setting oob_score = True provides an additional performance evaluation metric, which is useful for tuning model parameters. Setting max_features = 1 ensures that each tree uses all features. min_samples_leaf = 10 specifies that each leaf node must contain at least 10 samples to prevent overfitting. DL models have more parameters. The best model parameters for the DL parameters were determined through GS. In CNN, filters and kernel_size refer to the number of convolutional kernels used for feature extraction and the size of the 1 × 1 kernels, respectively. In LSTM and Bi-LSTM models, the unit parameter represents the number of neurons in the LSTM layer. Higher units increase the model's learning capacity and complexity, but they also lead to greater computational demands and training time, as well as a higher risk of overfitting (Yu et al. 2019). Through multiple experiments and grid searches, this study determined that 150 units is the most suitable choice. Dropout = 0.1 means that each neuron has a 10% chance of being dropped during training, reducing the network's dependence on the training data. A lower dropout value does not affect the model's training stability while helping to prevent overfitting and improve generalization. This study used the Adam optimizer for all DL models. Adam has shown superior performance in model training, as validated by Kingma & Ba (2014). In this study, the forecast is a scalar value, resulting in a single prediction output for the task, so Dense is set to 1. The mean squared error (MSE) was employed as the loss function to monitor the error between the actual values continuously and forecasted values in real-time, aiding in the tuning of model parameters (Kingma & Ba 2014). The batch_size represents the sample size used in each training iteration, while epochs denote the number of iterations for model training. The epochs and batch_size values are the optimal model parameters determined by GS. Suitable epochs and batch_size can enhance the model's prediction speed and stability. The activation function for all DL models is set as a rectified linear unit (ReLU), a nonlinear function with a range from 0 to 1. This function aids the model in learning more complex data relationships. Specific parameters are detailed in Table 2.

To validate the importance of EEMD, CEEMD, and CEEMDAN decomposition algorithms for prediction, an initial comparison was conducted to evaluate the predictive accuracy of various models without using the CEEMDAN decomposition algorithm over different time periods. Tables 3–5 describe the statistical results of forecasting using three conventional ML models and five DL models in Nanchang, Dongxiang, and Xinjian, respectively. These tables present the statistical analysis of forecasting for the XGBoost (XGB), SVM, RF, CNN, LSTM, Bi-LSTM, CNN-LSTM, and CNN-Bi-LSTM models during the testing phase under six different periods: 1, 3, 5, 7, 10, and 15 days.

Table 3

The statistical values of forecasting for different periods by various models in Nanchang station

Note: In the table, the cells with a yellow background represent the best forecasting results, while the text in bold indicates the best forecasting results among the three conventional ML models.

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Table 4

The statistical values of forecasting for different periods by various models in Dongxiang station

Note: In the table, the cells with a yellow background represent the best forecasting results, while the text in bold indicates the best forecasting results among the three conventional ML models.

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Table 5

The statistical values of forecasting for different periods by various models in Xinjian station

Note: In the table, the cells with a yellow background represent the best forecasting results, while the text in bold indicates the best forecasting results among the three conventional ML models.

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As shown in Table 3, the forecast results vary significantly depending on forecasting models and periods. Compared with forecasting for multiple periods, the forecasting for with a period of 1 day achieved the highest (0.9768) and the lowest ⁠, NSE, CA, and ⁠, which are 0.2016 ⁠, 0.2630 ⁠, 0.9768, and 0.161, respectively. The forecasting model that achieved the best results is Bi-LSTM. Compared with several conventional ML models, including XGB, SVM, and RF, the DL-based Bi-LSTM demonstrates higher and lower and in forecasting different periods of ⁠. It is worth noting that, in the forecasting of with a period of 10 days, Bi-LSTM's is higher than the model with the lowest forecasting accuracy, XGB, by 16.94%. In addition, the ⁠, ⁠, ⁠, and of Bi-LSTM are respectively 25.83, 37.04, 38.51, and 16.94% higher than those of XGB in terms of forecasting performance. Table 3 shows that, when forecasting for periods of 3, 5, and 7 days, the best-performing model is LSTM. Comparing the results of Bi-LSTM and LSTM for forecasting with periods of 3, 5, and 7 days, the difference in forecasting results is at the level of the third decimal place, indicating a difference of 0.001. Due to the varying patterns of at different periods, the optimal forecasting model does not achieve uniformity. However, with the statistical difference at the 0.001 level, it can be considered an approximate forecasting accuracy in both statistical and practical terms. From Table 5, we can see that when forecasting for different periods, the prediction accuracy of DL algorithms, precisely the LSTM and Bi-LSTM models, is higher than that of ML models such as XGB, SVM, and RF. This indicates that DL algorithms outperform ML algorithms in the forecasting of based on time series. In Table 3, the highest forecasting accuracy is achieved by Bi-LSTM for forecasting for 1 day. When grouped by forecasting period and sorted in descending order of forecasting accuracy, the sequence is as follows: Bi-LSTM forecasting with a period of 1 day, Bi-LSTM forecasting with a period of 10 days, Bi-LSTM forecasting with a period of 15 days, LSTM forecasting with a period of 5 days, LSTM forecasting with a period of 7 days, and LSTM forecasting with a period of 3 days. Tables 4 and 5 show similar trends in forecasting accuracy as Table 3. Table 3 shows that Bi-LSTM has an advantage in forecasting short periods (1 day) of and longer periods (10 and 15 days) of compared with other models. On the other hand, LSTM performs better in forecasting medium periods (3, 5, and 7 days) of compared with other models. This pattern is consistent in both Tables 4 and 5. From the experimental results, Bi-LSTM demonstrates a more stable advantage in forecasting short and long periods of ⁠, while LSTM exhibits an advantage in forecasting medium periods of ⁠.

To further illustrate its periodicity and the forecasting relationship of LSTM and Bi-LSTM models, Figure 8 provides an analysis of the forecasting results (three-dimensional curve graph) of for different periods in Nanchang, Dongxiang, and Xinjian. It is clear from the graph that for different stations, the two models show significant differences in forecasting for the same period. From Figure 8, it is evident that for forecasting a period of 3 days of ⁠, when compared with the curve of the actual values, the forecasting curve of LSTM is closer to the actual values than Bi-LSTM for all three different stations. Conversely, from the graph of the forecasting period of 15 days for ⁠, it is clear that the forecasting curve of Bi-LSTM is closer to the actual curve of ⁠. Figure 8 effectively illustrates that Bi-LSTM and LSTM have different advantages in forecasting for different periods. Although the difference in their forecasting accuracy is small, Figure 8 suggests that Bi-LSTM is more suitable for forecasting long-period ⁠. At the same time, LSTM is more suitable for forecasting shorter periods of ⁠. In this study, LSTM and Bi-LSTM accurately forecasted over different periods. Short-term forecasts can provide more precise guidance for daily irrigation, while long-term forecasts contribute to long-term water resource planning.

This study aims to investigate whether adding the CEEMDAN algorithm on top of the base models can lead to higher forecasting accuracy and, consequently, to analyze the importance of CEEMDAN in forecasting ⁠. Tables 6–8 provide a clear overview of the forecasting accuracy of for different stations and periods based on the CEEMDAN algorithm. Analysis of Table 6 reveals that CEEMDAN-Bi-LSTM achieved the best forecasting results when forecasting for a period of 15 days. However, there is no consistent optimal forecasting model for different periods. A different pattern from Tables 3–5 is observed, wherein the CEEMDAN-based algorithms, forecasting for a 1-day period yielded better accuracy with CEEMDAN-XGB compared with the forecasting accuracy of CEEMDAN-CNN-LSTM, a DL-based model. The same pattern is observed when forecasting the Dongxiang and Xinjian stations. Tables 3–8 clearly show that in forecasting for different periods, all DL-based algorithms outperform ML-based XGB, SVM, and RF. However, forecasting the for a period of 1 day shows different results, which is in stark contrast to Tables 3–5. Figure 9 shows the distribution of the optimal models for forecasting for different stations and periods between the base models and those based on CEEMDAN. Analysis of Figure 9 reveals that adding the CEEMDAN algorithm to the forecasting for different periods does not follow a consistent pattern, significantly reducing the stability of the forecasting and the universality of the models.

Table 6

Statistical values of the CEEMDAN model for forecasting ET₀ over different periods at the Nanchang station

Note: In the table, the cells with a yellow background represent the best forecasting results, while the text in bold indicates the best forecasting results among the three conventional ML models.

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Table 7

Statistical values of the CEEMDAN model for forecasting ET₀ over different periods at the Dongxiang station

Note: In the table, the cells with a yellow background represent the best forecasting results, while the text in bold indicates the best forecasting results among the three conventional ML models.

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Table 8

Statistical values of the CEEMDAN model for forecasting ET₀ over different periods at the Xinjian station

Note: In the table, the cells with a yellow background represent the best forecasting results, while the text in bold indicates the best forecasting results among the three conventional ML models.

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To further validate the impact and significance of the CEEMDAN decomposition model on multi-period forecasting in humid regions, this study introduced EEMD and CEEMD methods combined with the same ML models as CEEMDAN. The forecasting performance of EEMD and CEEMD-based hybrid ML models was analyzed for multi-period predictions at the Nanchang, Dongxiang, and Xinjian stations. Experimental analysis revealed that EEMD and CEEMD demonstrated similar forecasting patterns and comparable performance across all three stations for multi-period predictions. Therefore, detailed analyses of EEMD and CEEMD forecasting results were conducted based on the results from the Nanchang station. Table 9 presents the model evaluation metrics for the EEMD-based hybrid ML models at Nanchang station over six different periods. Except for predictions at 1- and 3-day periods, EMMD-LSTM and EEMD-Bi-LSTM were identified as the best forecasting models for all other periods, consistent with the results observed for standalone models and CEEMDAN hybrid models. Moreover, Table 9 shows that the EEMD hybrid DL models outperformed the EEMD hybrid traditional ML models in forecasting accuracy.

Table 9

Statistical values of the EEMD model for forecasting over different periods at the Nanchang station

Note: In the table, the cells with a yellow background represent the best forecasting results, while the text in bold indicates the best forecasting results among the three conventional ML models.

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Notably, for predictions at 10- and 15-day forecasting periods, the EEMD-LSTM and EEMD-Bi-LSTM models outperformed EEMD-SVM in terms of R² by approximately 20 and 15.49%, respectively, and in terms of the comprehensive CA metric by approximately 39.47 and 34.37%, respectively. It is worth highlighting that EEMD demonstrated forecasting performance comparable to CEEMDAN across different forecasting periods for ⁠. Moreover, in certain forecasting periods, the EEMD method showed superior performance compared with CEEMDAN. However, significant differences remained when compared with the baseline model. For the 10-day forecasting period, Bi-LSTM emerged as the best-performing model. Compared with EEMD-Bi-LSTM, Bi-LSTM achieved superior performance in the comprehensive CA metric, with its forecasting accuracy exceeding that of EEMD-Bi-LSTM by approximately 53.87% under the same forecasting conditions.

In addition to EEMD, this study employed CEEMD combined with the same models as CEEMDAN to analyze the effects of different decomposition methods on predictions across various time periods. Table 10 presents the detailed evaluation metrics for the predictive performance of the CEEMD method. As shown in Table 10, CEEMD-LSTM emerged as the best-performing model for the 5-, 7-, and 10-day forecasting periods, accounting for three out of the six best models across all periods. This result aligns with the predictive patterns observed for the baseline model, the CEEMDAN-based hybrid models, and the EEMD-based hybrid models. LSTM and Bi-LSTM were consistently identified as the most effective models for multi-period prediction in humid regions. Furthermore, hybrid DL models outperformed hybrid traditional ML models, a trend consistent with the results from CEEMDAN and EEMD models. One distinguishing feature of CEEMD compared with EEMD and CEEMDAN was its superior accuracy in predicting for the 15-day forecasting period, where CEEMD-CNN exhibited higher predictive precision. Regarding the comprehensive CA metric, CEEMD-CNN's performance surpassed that of CEEMDAN-CNN and EEMD-CNN by approximately 16.09 and 17.71%, respectively. Nonetheless, the overall predictive performance of CEEMD remained comparable to that of CEEMDAN and EEMD. Compared with the baseline model, CEEMD still demonstrated a noticeable gap in predictive performance for multi-period prediction in humid regions.

Table 10

Statistical values of the CEEMD model for forecasting over different periods at the Nanchang station

Statistical values of the CEEMDAN model for forecasting ET₀ over different periods at the Xinjian station In the table, the cells with a yellow background represent the best forecasting results, while the text in bold indicates the best forecasting results among the three conventional ML models.

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The error analysis presented in Figure 11 clearly illustrates that the CEEMDAN, EEMD, and CEEMD methods exhibit significant performance gaps compared with the baseline model in multi-period forecasting in humid regions. This finding further highlights the influence and limitations of decomposition methods in predicting over multiple periods in humid environments.

Accurate forecasting of at different periods is crucial for addressing practical issues, and the model's accuracy varies significantly for different periods. The results of this study indicate that both LSTM and Bi-LSTM models achieve satisfactory results in forecasting at different periods. However, there are some inconsistencies, and as the forecasting period lengthens, the forecasting accuracy tends to decrease. Lu et al. (2023) used VMD-BPNN to forecast at different periods and found that the forecasting accuracy decreases as the forecasting period lengthens. This result is similar to the patterns observed in this study's forecasting of CNN and XGB models. However, in contrast, the forecasting accuracy of LSTM and Bi-LSTM in this study is less affected by the length of the forecasting period and consistently achieves good results across all periods. Multi-step forward forecasting and nonperiodic forecasting of have different meanings. Multi-step forward forecasting allows for advanced knowledge and understanding of the specific data of ⁠. Malik et al. (2022) used the MVMD-RR technique to optimize the KELM model for accurate forecasting of for the next 3 and 7 days. However, there is still a phenomenon of decreasing forecasting accuracy as the forecasting length increases. Compared with this experiment, forecasting for different periods allows for a more precise understanding of the specific trends in each period. The results indicate that LSTM and Bi-LSTM do not exhibit a linear decline in forecasting accuracy with changes in the forecasting period length.

The basic DL models, LSTM and Bi-LSTM, exhibited similar performance in forecasting for different periods across all stations, outperforming other base models and CEEMDAN models. Mandal & Chanda (2023) found that LSTM had higher forecasting accuracy than SVR, RF, MLP, and MARS in real-time and 28-day ahead forecasting using DL. Ayaz et al. (2021) estimated in two different climatic regions using ML. The evaluation of results indicated that LSTM models outperformed GBR, SVR, and RF models. Long et al. (2022) decomposed the original data through a DWT decomposition model and used LSTM, ANN, and ELM models as base models to estimate in Beijing and Baoding in the northern part of the North China Plain. The results indicated that single ML models (LSTM, ANN, and ELM) were more stable than models based on DWT (wavelet-coupled) decomposition, and they generally exhibited better overall performance. It is worth noting that in a considerable amount of previous research on estimating and forecasting ⁠, good results have been obtained using non-CEEMDAN decomposition models. For example, Kang et al. (2022) achieved satisfactory results in forecasting at 10 stations in the Weihe River Basin in China by combining VMD and Box–Cox transformation (BC) with SVM. Jayasinghe et al. (2021) demonstrated the utility of combining MEMD and Boruta with LSTM in forecasting daily datasets, showing its usefulness compared with independent LSTM models. Yan et al. (2023) achieved excellent water-level forecasting results by combining the CEEMDAN decomposition model with LSTM and Bi-LSTM models. The specific analysis of the experimental results above is shown in Table 11. From Table 11, in previous studies, the combination of decomposition algorithms and ML models has yielded satisfactory results for various forecasting tasks. However, in this experiment, the opposite forecasting effect was obtained. In this study, the addition of EEMD, CEEMD, and CEEMDAN led to a decrease in prediction accuracy compared with the base model. The reason for this phenomenon is that the incorporation of EEMD, CEEMD, and CEEMDAN generates components for each feature in the original data. LSTM accepts different component features within a fixed parameter range, greatly increasing the difficulty of generalizing the LSTM model. This significantly increases the dependence on parameters of LSTM and other models, resulting in a significant decrease in forecasting accuracy with parameters that are not suitable for component features, ultimately leading to lower forecasting results than the base model. Additionally, due to the high quality of the data in this experiment, even without using a decomposition algorithm to denoise the raw data, decompose the original signal with higher nonlinearity, and then sequentially forecast each IMF mode, the base model still maintains a high level of forecasting accuracy. The basic LSTM and Bi-LSTM models achieved the best results in forecasting for different periods in this experiment. However, models based on EEMD, CEEMD, and CEEMDAN have lower prediction accuracy than the base models. This is closely related to the data decomposition by EEMD, CEEMD, and CEEMDAN, which introduce changes in input features, requiring the derivation of optimal model parameters corresponding to the altered data. This complexity suggests that EEMD, CEEMD, and CEEMDAN decomposition methods may not be suitable for predicting multi-period forecasts in humid regions ⁠.

Table 11

Literature on the combination of decomposition algorithms and ML

Author/References .	Research objective .	Best model used .	Performance of models .
Long et al. (2022)	Reference evapotranspiration estimation using long short-term memory network and wavelet-coupled long short-term memory network	Wavelet-coupled-LSTM	= 0.998, RMSE = 0.08 ⁠, MAE = 0.059 ⁠, NSE = 0.997, when Rn, T, RH, U is input.
Kang et al. (2022)	Machine learning framework with decomposition–transformation and identification of key modes for estimating reference evapotranspiration	VMD-Box–Cox (BC)-SVM	The correlation coefficient (R) is consistently greater than 0.96; both MAPE (mean absolute percentage error) and RMSE are less than 8.41% and 0.38 mm day−1, respectively.
Jayasinghe et al. (2021)	Deep multi-stage reference evapotranspiration forecasting model	MEMD-Boruta-LSTM	R = 0.9668, RMSE = 0.5307 ⁠, MAE = 0.4204 ⁠, NSE = 0.8960.
Yan et al. (2023)	Forecasting water levels using CEEMDAN decomposition algorithm with machine learning and deep learning ensemble	CEEMDAN-Bi-LSTM	= 0.9846, MAE = 0.501 ⁠, RMSE = 0.0641 ⁠, nRMSE = 0.0235.

Author/References .	Research objective .	Best model used .	Performance of models .
Long et al. (2022)	Reference evapotranspiration estimation using long short-term memory network and wavelet-coupled long short-term memory network	Wavelet-coupled-LSTM	= 0.998, RMSE = 0.08 ⁠, MAE = 0.059 ⁠, NSE = 0.997, when Rn, T, RH, U is input.
Kang et al. (2022)	Machine learning framework with decomposition–transformation and identification of key modes for estimating reference evapotranspiration	VMD-Box–Cox (BC)-SVM	The correlation coefficient (R) is consistently greater than 0.96; both MAPE (mean absolute percentage error) and RMSE are less than 8.41% and 0.38 mm day−1, respectively.
Jayasinghe et al. (2021)	Deep multi-stage reference evapotranspiration forecasting model	MEMD-Boruta-LSTM	R = 0.9668, RMSE = 0.5307 ⁠, MAE = 0.4204 ⁠, NSE = 0.8960.
Yan et al. (2023)	Forecasting water levels using CEEMDAN decomposition algorithm with machine learning and deep learning ensemble	CEEMDAN-Bi-LSTM	= 0.9846, MAE = 0.501 ⁠, RMSE = 0.0641 ⁠, nRMSE = 0.0235.

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The stability of the model is an important factor to consider when forecasting reliable ⁠. In this study, the three conventional ML models, XGB, SVM, and RF, exhibit the highest percentage variations in ⁠, ⁠, ⁠, ⁠, and in forecasting for different periods across all stations. Among them, XGB shows the most noticeable variation in RMSE in forecasting for different periods. This phenomenon also reveals that ML-based XGB, SVM, and RF models, when forecasting different periods of ⁠, exhibit a decrease in forecasting performance as the period changes, leading to a reduction in stability. However, for models based on CEEMDAN, judging stability based on the increase in RMSE as a criterion for stability in forecasting different periods of is more stable than the base model. However, for models based on EEMD, CEEMD, and CEEMDAN, the increase in and metrics serves as a criterion for evaluating the stability of predictions across different time periods, revealing that their stability is lower than that of the baseline model. Nevertheless, models based on EEMD, CEEMD, and CEEMDAN should be considered as a cohesive system rather than being evaluated against the stability criteria of the baseline model. These models fail to achieve optimal solutions for different stations and time periods. Figure 10 clearly demonstrates that models based on EEMD, CEEMD, and CEEMDAN demonstrate weaker generalization capabilities, making them incapable of adapting to changes in input features. Consequently, these models produce inconsistent predictions and fail to reliably forecast variations. In contrast, the base models, LSTM and Bi-LSTM, obtained similar forecasting results for at different stations and periods. The percentage increase in RMSE for these models is smaller than for all models in this experiment. Moreover, Figure 12 also shows that the baseline model has the best overall performance compared with the EEMD, CEEMD, and CEEMDAN decomposition models. It also responds more steadily to changes in features, making predictions that are consistent and accurate. Additionally, LSTM and Bi-LSTM based on DL have a large number of parameters that need to be adjusted in real-time based on changes in input features. Therefore, further parameter optimization using GS methods is needed to select the best model parameters to ensure the excellent stability of the models.

The results indicate that the runtime of models based on CEEMDAN is significantly higher than the corresponding base models. Specifically, at the Nanchang station, the computational cost of the CEEMDAN-LSTM model is approximately 8.9 times that of the base LSTM model, and the computational cost of the CEEMDAN-Bi-LSTM model is about 8.5 times that of the base Bi-LSTM model. However, the high multiple of runtime costs comes at the expense of an inversely proportional impact on the final forecasting accuracy. Models based on CEEMDAN exhibit very low operational efficiency. Moreover, the runtime costs for models based on CEEMDAN and CNN are even higher for LSTM and Bi-LSTM. The computational costs of the three conventional ML models, XGB, RF, and SVM, are significantly lower than those of various DL models. However, their forecasting accuracy and stability are lower than those of LSTM and Bi-LSTM. The computational costs of ML increase with the values and quantity of the model parameters used (Fan et al. 2018). DL shares similar principles with ML. LSTM and Bi-LSTM, based on DL, have many parameters, leading to higher computational costs than ML. However, obtaining better forecasting results through higher computational time costs is acceptable. In this experiment, the base models were more efficient in computation time than the CEEMDAN algorithm. Combining high-precision forecasting by LSTM and Bi-LSTM with lower computational time costs than CEEMDAN makes them better models for forecasting ⁠. CEEMDAN, which is effective for complex nonlinear problems, decomposes each variable into complex-to-simple signals through multiple iterations and aggregates them to produce a forecast. However, in this study, using CEEMDAN did not improve forecasting performance. This is likely due to the strong correlation within the data itself. For instance, the regional limitations of the forecast area cause significant periodic variations in ⁠. This might lead to substantial learning errors when CEEMDAN decomposes signals into simpler components, resulting in inaccurate forecasts. Additionally, decomposing multiple variables with CEEMDAN and reusing them as model inputs results in forecasts equivalent to those based on different datasets, causing a loss of accuracy due to the inconsistency of inputs.

Additionally, we conducted a detailed analysis of the computational time costs for the EEMD and CEEMD models. The results indicate that the EEMD model, when combined with traditional ML methods, demonstrates lower computational time costs compared with the CEEMDAN model. However, this difference is negligible when comparing the computational costs of EEMD and CEEMD combined with DL models. For instance, in the case of EEMD combined with the Bi-LSTM model, the computational cost exceeds 10,000 s, which is 2.6 times higher than that of CEEMDAN-Bi-LSTM. Furthermore, the computational cost of the decomposition methods shows a substantial increase compared with the baseline model. To address this, in this study, EEMD and CEEMD combined with CNN-LSTM and CNN-Bi-LSTM underwent model parameter adjustments. To minimize the impact on forecast accuracy, the model parameters were set to be identical to those of CEEMDAN-CNN-LSTM and CEEMDAN-CNN-Bi-LSTM. Experimental results show that under these parameter settings, computational time was reduced by a factor of five.

However, even without the need for hyperparameter GS algorithms, the computational costs of EEMD and CEEMD models combined with CNN-LSTM and CNN-Bi-LSTM under a single parameter setting still approached half an hour. When using the same GS algorithms as the CEEMDAN and baseline models, the computational time costs for EEMD and CEEMD combined with CNN-LSTM and CNN-Bi-LSTM models remained significantly higher than those of the baseline and CEEMDAN models. This study recommends using LSTM and Bi-LSTM as forecasting models for in future studies of humid regions. Additionally, it provides valuable insights into the use of decomposition models combined with ML for forecasting.

In this study, we compared the performance of LSTM and Bi-LSTM models with other models in forecasting across different periods. The results indicate that the LSTM and Bi-LSTM models demonstrate high accuracy and stability in predicting ⁠, consistent with the findings of Mandal & Chanda (2023), who observed that LSTM showed greater forecasting accuracy than SVR, RF, MLP, and MARS in prediction. Additionally, the research by Ayaz et al. (2021) also indicated that the LSTM model outperformed the GBR, SVR, and RF models in estimating in two distinct climate regions. Moreover, a key finding of this study is that EEMD, CEEMD, and CEEMDAN did not outperform the basic LSTM and Bi-LSTM models in multi-period prediction for humid regions of China. This could be due to changes in the correlation between -decomposed IMFs and corresponding IMFs of other meteorological variables after decomposition, potentially weakening these correlations. Furthermore, the temporal dependencies in time-series data may be affected, limiting the model's ability to capture the time-dependent nature of the data accurately, thus leading to a decline in prediction accuracy. It was also observed that these decomposition methods generate multiple IMFs, requiring repetitive predictions for each IMF followed by an aggregation process, which significantly increases the computational cost of the EEMD, CEEMD, and CEEMDAN models. In conclusion, this study highlights the potential of EEMD, CEEMD, and CEEMDAN decomposition methods for multi-period prediction in humid regions of China while emphasizing that prediction should consider not only model accuracy but also computational cost and stability. Due to their superior performance in these aspects, the LSTM and Bi-LSTM models are recommended for multi-period forecasting research in humid regions of China. Our research also provides valuable insights and recommendations for the application of ML combined with decomposition models in forecasting.

In this study, three conventional ML models, XGB, RF, SVM, and DL models, including CNN, LSTM, Bi-LSTM, CNN-LSTM, and CNN-Bi-LSTM, were utilized. In addition, a hybrid model that combines EEMD, CEEMD, and CEEMDAN with the aforementioned models, respectively, was introduced. The objective was to evaluate the accuracy and stability of forecasting different periods of ⁠. In the forecasting of for the Nanchang station, the base models, LSTM (⁠ = 0.968, MAE = 0.2245 ⁠, RMSE = 0.2686⁠, NSE = 0.968, CA = 0.1727) and Bi-LSTM (⁠ = 0.9768, MAE = 0.2016⁠, RMSE = 0.2630⁠, NSE = 0.9768, CA = 0.1610), achieved satisfactory results. For this station, the best-performing model within the CEEMDAN-based hybrid framework is CEEMDAN-Bi-LSTM (R² = 0.8872, MAE = 0.4853⁠, RMSE = 0.3863 ⁠, NSE = 0.8872, CA = 0.3249). Within the EEMD-based hybrid framework, the best-performing model is CEEMD-Bi-LSTM (⁠ = 0.8905, MAE = 0.3606⁠, RMSE = 0.4759 ⁠, NSE = 0.8905, CA = 0.3122). Meanwhile, the best-performing model within the CEEMD-based hybrid framework is CEEMD-CNN (⁠ = 0.9038, MAE = 0.3477 ⁠, RMSE = 0.4461 ⁠, NSE = 0.9038, CA = 0.2937). However, compared with the best-performing model (Bi-LSTM) for the 1-day forecast at the Nanchang station, the EEMD-, CEEMD-, and CEEMDAN-based hybrid Bi-LSTM models exhibited significantly lower forecasting performance in terms of the comprehensive metric CA for the 1-day forecast. Specifically, the prediction performances of the three decomposition models were approximately 193.30, 187.02, and 191.91% lower than that of the baseline Bi-LSTM model, respectively. Furthermore, a statistical analysis of the best models for different stations reveals that the base models consistently obtained a more unified best-performing model for forecasting across various stations and periods. However, the CEEMDAN-based hybrid models exhibited inconsistent best models for forecasting across different stations and periods. This indicates that introducing the CEEMDAN model resulted in poorer forecasting stability. Surprisingly, the analysis of model computational costs revealed an unacceptable increase in the running costs for each CEEMDAN-based hybrid model. The base model Bi-LSTM achieved satisfactory results in forecasting different stations, with an average runtime cost of around 8 min across the three stations. However, after incorporating CEEMDAN, the runtime cost for CEEMDAN-Bi-LSTM increased to approximately 1 h and 10 min. This represents an increase of about 8–9 times in runtime costs after adding CEEMDAN, which is unacceptable. Furthermore, both EEMD and CEEMD demonstrated even higher computational costs compared with CEEMDAN while still showing lower stability than the baseline model, with the computational cost of EEMD-Bi-LSTM being 2.6 times that of CEEMDAN-Bi-LSTM. In conclusion, based on the experimental results, the EEMD, CEEMD, and CEEMDAN models are not suitable for forecasting over different time periods. It is worth noting that incorporating LSTM and Bi-LSTM with CNN is also a decision that requires attention. In this experiment, adding CNN to LSTM and Bi-LSTM did not yield good forecasting results and increased runtime costs. The probable reason for this phenomenon is that the research data in this experiment has high quality, and excessive preprocessing, further feature extraction, and noise reduction methods may have had a counterproductive effect. Similar to enhancing positive relationships but diminishing negative relationships, this could have led to poorer forecasting outcomes. This study investigated the use of EEMD, CEEMD, and CEEMDAN decomposition methods combined with ML to predict in humid regions. The results indicated that the EEMD, CEEMD, and CEEMDAN hybrid models did not outperform the baseline model. It is recommended to use LSTM and Bi-LSTM models for forecasting at different periods in humid regions. Based on the findings, caution should be exercised when using EEMD, CEEMD, or CEEMDAN combined with ML for prediction. Given their accuracy and computational costs, EEMD, CEEMD, or CEEMDAN combined with ML are not optimal choices for forecasting in humid regions and are therefore not recommended for this purpose. Conversely, single models such as XGB, RF, and SVM can be considered for forecasting in humid regions due to their accuracy and time efficiency. It is important to note that this study has some limitations. The integration of EEMD, CEEMD, or CEEMDAN with DL did not show significant improvement in prediction and demonstrated unstable performance across multiple stations and time periods. Additionally, the introduction of EEMD, CEEMD, and CEEMDAN significantly increased the computational cost of the models. In this research, LSTM and Bi-LSTM achieved precise multi-period forecasts for humid regions in China, but they were not validated in other regions, so it cannot be ensured that similar accuracy would be achieved in those areas. In future studies, forecasting for more regions will be conducted to verify the accuracy and stability of LSTM and Bi-LSTM models for multi-period forecasting across different regions.

We would like to express our special thanks to the National Meteorological Information Center of China Meteorological Administration for providing the foundational data for this research.

Conceptualization, Z.Y. and L.W.; methodology, Z.Y. and L.W.; software, Z.Y.; validation, Z.Y., L.W., and X.L.; formal analysis, Z.Y. and L.W.; investigation, Z.Y., L.W., and X.L.; resources, Z.Y. and L.W.; data curation, Z.Y.; writing – original draft preparation, Z.Y.; writing – review and editing, Z.Y. and L.W.; visualization, Z.Y. and L.W.; supervision, Z.Y., L.W., and X.L.; project administration, X.L.; funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript.

This research was funded by the General Project of Natural Science Foundation of Jiangxi Province (Grant No. 20232BAB205031), the National Natural Science Foundation of China (Grant No. 52269013), and the Key Project of Natural Science Foundation of Jiangxi Province (Grant No. 20242BAB26081).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.