Long-term inflow forecast using meteorological data based on long short-term memory neural networks

In recent decades, researchers have devoted efforts to hydrological long-term runoff prediction, which is extremely important for water resource planning (Liu et al. 2021), reservoir operations (Maddu et al. 2022), risk management (Huang et al. 2022), flood control (Bahramian et al. 2023) and water abandonment (Jiang et al. 2018), especially in areas with concentrated rainfall (Liang et al. 2017). The main challenges with respect to inflow forecasting include complex structure prediction methods, low accuracy inflow predictions and multiple influence meteorological data that are caused by changeable climate, excessive human activities and complex and various natural runoff.

To address these challenges, researchers have devoted efforts to monthly runoff prediction and its prediction methods. Generally, the research approaches can be divided into three categories: statistical methods (Taormina & Chau 2015), physical methods (Duan 1992; Robertson et al. 2013) and machine learning methods (Wang et al. 2023a). However, there has been no single identified method that is universally appropriate for runoff prediction for any scenario because the hydrological characteristics of river basins and regions change with variations in time and space (Cheng et al. 2015).

Statistical methods represented by autoregressive models are usually based on historical inflow records and assume that the inflow series are stationary, linear and accurate. In other words, the relationship of the method is simply between the input and output. Nevertheless, real inflow series are in nature complex, nonlinear and chaotic (Dhanya & Nagesh Kumar 2011), and it is difficult to obtain high-accuracy predictions using statistical methods based on real inflow data. Physical methods such as the Soil and Water Assessment Tool (SWAT) (Ebod E 2023) have a clear physical mechanism of inflow generation and confluence. The method can reflect the characteristics of the study site but is highly dependent on the initial conditions and input data (Bennett et al. 2016). In addition, the parameters are not easy to determine, and the predictive ability is limited in many situations.

To further improve the runoff prediction results and accuracy, machine learning methods, such as artificial neural networks (ANNs) (Samantaray et al. 2022), support vector machines (SVMs) (Xu et al. 2023), and evolutionary algorithms (EAs) (Chadalawada et al. 2020; Cai et al. 2022) and so forth, have been proposed because they have shown excellent performance with respect to inflow prediction and are effective in handling the nonlinear relationship between input and output. Herath et al. (2021) utilized genetic programming (GP) as a rainfall–runoff method, preserving the prediction power of the short-term forecasting approach while benefiting from a better understanding of the catchment runoff dynamics. Sedighi et al. (2016) used SVR and ANN in rainfall–runoff modeling. Humphrey et al. (2016) carried out streamflow estimation using ANN. However, despite the use of the above methods, there still exist several limitations and drawbacks. For instance, ANNs are prone to being trapped by local minima and cannot avoid long-term dependency. To address this shortcoming, a novel method, long short-term memory neural network (LSTM), in which the central idea is a memory cell that can maintain its state over time, and nonlinear gating units, which regulate the information flow into and out of the cell (Greff et al. 2017), is formed.

In recent years, LSTM has been applied to many areas due to its strong nonlinear prediction ability, shorter convergence time and capture of the long-term correlation of time series. For example, Shahid et al. (2020) proposed deep learning methods to predict COVID-19, and the results can be exploited for pandemic prediction for better planning and management. Jiang et al. (2022) uncovered the flooding mechanisms across the contiguous United States through interpretive deep learning represented by LSTM on representative catchments. Zhang et al. (2020) studied LSTM to predict public environmental emotions and then used a variety of error assessment methods to quantitatively analyze the prediction results and verified LSTM's performance in prediction achievements. Qu et al. (2020) constructed a method with an M-B-LSTM hybrid network to predict short-term traffic flow, and the results showed that the proposed method has a better ability to solve uncertainty and overfitting problems. Wang et al. (2021) presented an ensemble hybrid forecasting method for annual runoff, which provided higher accuracy and consistency for annual runoff prediction. These studies proved the competitiveness of LSTM in many fields. Thus, LSTM is employed for monthly inflow prediction in this paper. For comparison purposes, the backpropagation neural network (BPNN) and support vector regression (SVR) were employed to forecast monthly inflow and are considered to be benchmark methods.

Moreover, a single prediction method still cannot accurately predict runoff, and a method of incorporating advances in both meteorological understanding and observations has been proposed (Abbs 1999), which aimed to attain a higher inflow prediction accuracy. For example, Yu et al. (2017) constructed using meteorological and hydrological data as inputs a method to forecast monthly inflow values, but only the monthly average air temperature was considered. Gauch et al. (2021) investigated two multitimescale LSTM architectures to forecast rainfall runoff based on adding meteorological data. The meteorological variables closely related to rainfall runoff were not filtered. However, it is not enough to use unscreened meteorological data series as input because strictly relevant sufficient potential input factors are a prerequisite for obtaining reliable and accurate prediction results.

However, now, to accurately and quickly select effective inputs, the maximal information coefficient (MIC) is employed to select input factors for inflow forecasting, which is a robust measure of the degree of correlation between two variables (Sun et al. 2018). Therefore, many researchers have proposed adding filtered meteorological data via the MIC to further enhance the accuracy of inflow forecasting. For instance, Liao et al. (2020) used the ERA-Interim reanalysis dataset as input, and ulteriorly adopted gradient-boosting regression trees and the MIC to forecast daily inflow.

To elevate the inflow forecasting accuracy, meteorological data generated by the European Centre for Medium-Range Weather Forecasts (ECMWF) of THORPEX Interactive Grand Global Ensemble (TIGGE) (Tao et al. 2014) were used as input (Saedi et al. 2019). The TIGGE network is a World Meteorological Organization project that searches to capture other sources of uncertainties associated with the meteorological model structure and the ensemble size (Velázquez et al. 2011). The meteorological dataset has the advantages of long time series and wide spatial distribution and can greatly compensate for the problems of uneven time-space distribution and lack of observation data.

Motivated by the above discussion, a novel forecast framework, the M-LSTM, aims to provide a reliable runoff prediction method for monthly inflow forecasting. The forecast framework adopts meteorological data as input, which ensures that ample information is supplied to depict inflow. Inverse distance weighting (IDW) was employed to obtain meteorological data. The MIC is used to identify effective features from massive features to reduce the computational burden. LSTM has good robustness and strong nonlinear fitting ability and is used as a prediction method to improve the monthly inflow forecasting accuracy.

This paper is organized as follows: Section 2 describes a case study and collected data. Section 3 introduces the theory and process of the methods used, including IDW, MIC and LSTM. Section 4 shows the results and discussion of the data, followed by the conclusions in Section 5.

The MIC (Reshef et al. 2011) is a relatively new measure for associations between two variables that applies mutual information (MI) to continuously distributed random variables (Lu et al. 2021). The calculation of the MIC is based on concepts of MI (Kinney & Atwal 2014), and the process is described as follows:

Given two variables ⁠, such as observed inflow, and ⁠, such as meteorological data, the MI between X and Y is given by:

We perform feature selection from meteorological data in two steps via the MIC. First, we compute the MIC of each meteorological data and observed inflow. Then, we sort features based on the MIC in descending order and determine the optimum inputs using a trial-and-error procedure.

To test the performance of prediction methods, the root-mean-squared error (RMSE), the Pearson correlation coefficient (CORR), the mean absolute error (MAE), the Nash–Sutcliffe efficiency (NSE), the Kling–Gupta efficiency scores (KGE) and the index of agreement (IA) are used to evaluate the performance on the basis of the forecasting and fitted values of the method compared with observed data.

The LSTM method:

Step 1: Lag selection of observed inflow

We measure the relevance of the different lags in observed inflow using the partial autocorrelation function (PACF) and further select appropriate lags as predictors for the method using hypothesis testing and trial-and-error procedures.

Step 2: Normalizing the data

The data are normalized to improve the speed of the method and accuracy of prediction, and the dataset is transformed into supervised learning (in Section 2.3). Furthermore, the dataset is divided into a training set, validation set, and testing set according to the length of each dataset specified in advance (in Section 2.2).

Step 3: Obtaining the forecasted inflow of the LSTM method

The LSTM, a grid search algorithm, is used to guide the optimization of the method parameters by the evaluation of the validation set via MAE, and then, the prediction results are evaluated based on the testing set.

M-LSTM uses the screened meteorological dataset by the MIC as input and adopts LSTM to forecast monthly inflow.

The M-LSTM method:

The M-LSTM fully incorporates the advantages of LSTM and meteorological data to forecast inflow. Specifically, the meteorological data obtained by IDW further identifies effective features from a large number of features via the MIC. Similarly, the MAE of the training set and validation set are used as the fitness of the M-LSTM, which can determine the ideal hyperparameter and realize the optimal search.

To compare the performance of the M-LSTM, the meteorological data backpropagation neural network (M-BPNN), and meteorological data support vector regression (M-SVR), which were obtained by replacing LSTM in the framework with BPNN and SVR, respectively, are also employed for monthly inflow forecasting. As mentioned previously, six indices, RMSE, CORR, MAE, NSE, KGE and IA, are used to evaluate the performance of these methods (Liao et al. 2020). In addition, the feature importance based on the M-LSTM is explored. All computations carried out in this paper were performed on a personal computer with 1.70 GHz processor and 16 GB RAM.

Finally, a total of 18 variables, including nine observed variables and nine meteorological variables, are selected as the method inputs (Table 4). As shown in Table 4, Nos. 10–18 are meteorological variables, and the range of the MIC of the meteorological variables selected is 0.92 to 0.48. Moreover, No. 10 and No. 11 are variables related to the water content of the atmosphere. The total column water (No. 10) is the sum of water vapor, liquid water, cloud ice, rain and snow in a column extending from the surface of the Earth to the top of the atmosphere. The 2-meter dewpoint temperature (No. 11) is a measure of the humidity of the air; in general, it can be used to calculate the relative humidity combined with temperature and pressure. Nos. 12 and 16 are variables related to rainfall. The total cloud cover (No. 12) is the fraction of the sky covered by all visible clouds. Cloud cover can refer to a genus, species, variety, layer, or a certain combination of clouds. The soil moisture in the top 20 cm (No. 16) is the volumetric soil moisture in the top 20 cm of the soil layer. Nos. 13–15 are variables related to temperature. The 2-meter temperature (No. 13) is the temperature of air at 2 m above the surface of land, sea or inland waters, which is calculated by interpolating between the lowest model level and the Earth's surface. The skin temperature (No. 14) is the temperature of the surface of the Earth, which represents the temperature of the uppermost surface layer. The soil temperature in the top 20 cm (No. 15) is the average soil temperature in the top 20 cm of the soil layer. In summary, all selected predictors are interpretable and have a good physical connection with inflow.

Every machine learning system has hyperparameters, which are a parameter set before training and cannot be directly learned from the routine training process. It is imperative to tune the hyperparameters of the method to improve the performance of the machine learning. The grid search method is used to optimize the hyperparameters of LSTM, M-LSTM, M-BPNN and M-SVR. Tables 5 and 6 show the results of various hyperparameter values in different methods, respectively.

Table 6

Tunig parameters for M-SVR

Method .	No. .	Tuning range .			Evaluation criteria .
		C .	.	.	MAE(m3/s) .
M-SVR	1	5,000	0.2	0.2	659.04
	2	3,000	0.2	0,3	645.40
	3	1,000	0.2	0.35	650.05
	4	100	0.2	0.25	624.88
	5	10	0.15	0.2	543.94
	6	30	0.05	0.1	498.71

Method .	No. .	Tuning range .			Evaluation criteria .
		C .	.	.	MAE(m3/s) .
M-SVR	1	5,000	0.2	0.2	659.04
	2	3,000	0.2	0,3	645.40
	3	1,000	0.2	0.35	650.05
	4	100	0.2	0.25	624.88
	5	10	0.15	0.2	543.94
	6	30	0.05	0.1	498.71

Note: The bold numbers represent the values of performance criterion for the best fitted methods.

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The M-LSTM is used as the training algorithm of the neural network, and the hidden layers are fixed in three layers. The activation functions are selected as tanh and sigmoid, and batch_Size chooses 1. To select the optimal parameter, 40 LSTM are trained for each parameter combination to alleviate the influence of random initialization of weights. The optimal epoch is determined by selecting the minimal MAE of the validation set. Table 5 shows the result of hyperparameter optimization. It is clear that the optimum result can be obtained when the epoch = 50 for the M-LSTM. Hyperparameter optimization of the M-BPNN is similar to that of the M-LSTM, and the optimum result can be obtained when epoch = 200.

For M-SVR, the radial basis function (RBF) is selected as the core function in inflow simulation according to Lin et al. (2006), and the RBF outperforms other kernel functions for runoff modeling. Therefore, the RBF is used as a contrast method in this study. There are three parameters that need to be tuned. First, the appropriate parameter setting range is determined by the trial-and-error procedure. Then, MAE is used to optimize these parameters by a grid search algorithm to obtain the optimal selection of these parameters. The optimal tuning parameters of SVR are shown in Table 6. The results show that the optimum results can be obtained when = 0.1, C = 30 and = 0.05.

The M-LSTM, M-SVR and M-BPNN with the optimal hyperparameters are employed for monthly inflow forecasting. The summarized results for the six indices of the testing set are presented in Table 7. The M-LSTM provides great performance compared to M-BPNN and M-SVR. The RMSE and MAE of the M-LSTM achieve 7.15 and 3.19% and 30.58 and 30.41% reductions for testing set forecasting compared with M-SVR and M-BPNN, respectively. The CORR, NSE, KGE, and IA of the M-LSTM increase by 0.68, 2.03, 0.98 and 0.38% for testing set forecasting compared with M-SVR and 1.43, 15.41, 50.56 and 6.78% for testing set forecasting compared with the M-BPNN, respectively. In general, the M-LSTM has higher prediction accuracy than the M-SVR and M-BPNN methods.

The M-LSTM is employed to make monthly inflow forecasts, and the M-BPNN and M-SVR are proposed for comparison with the M-LSTM in this study. The meteorological data were obtained by IDW and further screened by MIC. These methods are compared using six evaluation criteria: RMSE, CORR, MAE, NSE, KGE and IA. We find that the performances of the M-LSTM outperform the M-BPNN and M-SVR at the monthly inflow forecast. According to a comparison of the forecasted results of LSTM and M-LSTM, it is shown that the M-LSTM can be used for more accurate and reliable inflow forecasting and that meteorological data selected by the MIC greatly improve upon LSTM forecasting. Moreover, the feature importance achieved by the M-LSTM demonstrates that the total amount of water vapor in a column, dewpoint temperature near the ground and the fraction of the sky covered by all visible clouds contribute to increasing the prediction accuracy of inflow. In summary, the research results are of great significance for guiding hydropower stations to formulate reservoir management schedules, improve water resource planning and reduce water abandonment. Another possibility to improve the results may be the consideration of a parallel algorithm to optimize the method parameters, which could search optimization parameters more quickly.

This research is supported by the National Natural Science Foundation of China (No. 52379004 and No. 51979023). We are grateful for meteorological data provided by European Centre for Medium-Range Weather Forecasts.

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

The authors declare there is no conflict.