Deep Learning Integration of Multi-Model Forecast Precipitation Considering Long Lead Times

Abstract

Reliable forecast precipitation can support disaster prevention and mitigation and sustainable socio-economic development. Improving forecast precipitation accuracy remains a challenge. Therefore, a novel method for multi-model forecast precipitation integration considering long lead times was proposed based on deep learning. First, the accuracy of numerical forecast precipitation was evaluated under different lead times. Secondly, an integrated model was built by coupling the attention mechanism and a long short-term memory neural network (LSTM). Finally, integrated forecast precipitation was obtained by taking high-precision numerical forecast precipitation as an input and examining its accuracy and applicability. Considering the example of the Yalong River, the results showed the following: (1) numerical forecast precipitation fails to forecast precipitation of a ≥10 mm/d intensity well, and is less applicable in streamflow forecast; (2) traditional machine learning methods for integrating multi-model forecast precipitation fail to forecast precipitation of a ≥25 mm/d intensity; (3) the LSTM-A integration model formed by attention weighting after the LSTM output can combine the advantages of numerical forecast precipitation under different intensities and improve the forecast precipitation accuracy for 7-day lead times; and (4) the LSTM-A integrated forecast precipitation has the best applicability in streamflow forecast, with an NSE above 0.82 and an MRE below 30% with 7-day lead times. These findings contribute to improving precipitation forecast accuracy at different intensities and enhancing defense against extreme weather events.

1. Introduction

Precipitation is one of the most important environmental factors, crucial in water resource allocation, social development, and human daily life [1,2]. However, due to the combined effects of climate change and human activities, droughts and floods caused by excessive or insufficient precipitation have occurred frequently in recent years [3,4,5]. For example, floods in China have resulted in about 4000 deaths and economic losses of about CNY 160 billion per year, and droughts have caused drinking water difficulties for about 21 million people [6]. These precipitation-induced environmental disasters seriously threaten the safety of people’s lives and property, as well as the development of cities and society. Therefore, it is important to accurately forecast precipitation, which can reduce environmental disaster losses and promote sustainable socio-economic development.

Currently, there are two main ways to obtain forecast precipitation data. One is to use weather radar extrapolation technology for precipitation nowcast, and the other is based on numerical weather prediction models for quantitative precipitation forecast [7,8]. The former uses extrapolation algorithms to predict the future radar echo state based on information such as radar echo intensity, movement speed, and direction, thereby obtaining the distribution and magnitude of the forecast precipitation [9,10]. It has the advantages of timely detection and a high resolution, but can only obtain 0–3 h accurate forecast precipitation data. Subsequently, numerical weather prediction models have been developed to obtain forecast precipitation data for long lead times [9]. They set certain initial and boundary conditions based on the laws of atmospheric motion, and then deduce the future state of the atmosphere by solving dynamical equations through numerical computation methods to forecast precipitation with long lead times [11]. Since the 1950s, many countries have researched numerical weather prediction techniques and established related systems, which can provide up to 16 days of forecast precipitation data [12,13]. Among them, widely used models include the European Centre for Medium-Range Weather Forecasts (ECMWF), China Meteorological Administration (CMA), National Centre for Environmental Prediction (NCEP), and so on. Furthermore, to promote the improvement of global weather prediction accuracy, the World Meteorological Organization established the THORPEX International Grand Global Ensemble (TIGGE) system in 2003 [14]. The TIGGE system is used to collect global numerical weather prediction data for sharing. At present, meteorological centers from 12 countries or regions (such as China, the United States, and Germany) have been attracted to provide data. These have greatly contributed to the development of precipitation forecast research. However, due to the limitations of forecast timeliness, dynamical frameworks, and topographic features, all models have certain errors, which make them difficult to directly apply in actual operations [15]. Thus, to improve precipitation forecast’s accuracy, it is necessary to correct forecast precipitation data according to the forecast error features.

Numerous scholars have studied the error correction of a single model’s forecast precipitation. Common methods include frequency matching, optimal score correction probability matching, and so on [16,17]. For example, Yang et al. [18] corrected the forecast precipitation of the NCEP by the frequency matching method and improved the forecast accuracy of light and moderate precipitation for a 1–8 d lead time. Su et al. [19] evaluated the performance of frequency matching, optimal threat score, optimal percentile, and probability matching, and found that the optimal percentile method could improve forecast precipitation’s accuracy and provide a certain reference for risk decision making for heavy precipitation. However, the correction of a single model’s forecast precipitation fails to integrate the advantages of different numerical weather prediction models, resulting in limited improvement [20]. Therefore, multi-model forecast precipitation integration has emerged and been widely used in forecast precipitation correction.

Multi-model forecast precipitation integration is a method that first comprehensively analyzes the performances of different numerical weather forecast models, and then weights and integrates the different models’ forecast precipitation through statistical analysis, artificial intelligence (AI), and other methods [21,22]. Common methods include weighted integration, multiple regression, Bayesian model averaging, and so on [23,24]. For example, Wu et al. [25] used a multiple linear regression model to integrate three models’ forecast precipitation and applied the integrated results to flood forecast, significantly improving the accuracy of precipitation and flood forecast. Zhi and Zhao [26] integrated five models’ forecast precipitation by the Kalman filter integration method, and the results showed that the effect of multi-model forecast precipitation integration was superior to that of correcting a single model’s forecast precipitation based on the frequency matching method. With the continuous development of AI theory, machine learning models (such as support vector machines, extreme learning machines, and neural networks) have been introduced into multi-model forecast precipitation integration because of their good nonlinear fitting ability and use of few constraints [27,28]. Zhu et al. [29] compared the effects of a feed-forward neural network and optimal threat score weight ensemble method in multi-model forecast precipitation integration, and the results showed that the feed-forward neural network had a better performance and could improve the accuracy of forecast precipitation under different precipitation intensities. Tang et al. [24] proposed a multi-model forecast precipitation integration model that coupled a convolutional neural network and gradient-boosting decision tree, and its performance outperformed multiple linear regression and random forest, effectively improving the accuracy of forecast precipitation in the Fen River basin. Zhang and Ye [27] compared the performance of 21 machine learning models for multi-model forecast precipitation integration in the Yalong River, and found that the light gradient-boosting decision tree performed the best, effectively reducing errors caused by overestimating precipitation.

In practice, sudden heavy precipitation or long-term continuous precipitation are prone to cause flood disasters, threatening human life and property safety, as well as urban development [30,31]. The correction of forecast precipitation is not only to improve their overall accuracy, but also to improve their accuracy under different magnitudes and lead times. Thus, there are still some problems that need to be further explored in multi-model forecast precipitation integration. The main problems are as follows: (1) Precipitation sequences are highly volatile, and most previous methods have only addressed overall correction performance, but have been unable to make good corrections for heavy precipitation and beyond. (2) Because the accuracy of forecast precipitation decreases with an extension of the lead time, how to ensure the accuracy demands under long lead times still needs further research in integration methods. (3) Deep learning models have better time series processing capabilities than traditional machine learning models, but their applicability to multi-model forecast precipitation integration has not yet been explored.

Therefore, the objective of this study was to explore a method for multi-model forecast precipitation integration considering long lead times. The main contributions are as follows:

(1)

The forecast precipitation accuracy of several common numerical weather prediction models was evaluated under different lead times, and the high-accuracy ones were selected as inputs for integration models.

(2)

To utilize the power of deep learning to improve forecasting precipitation accuracy, a novel method for multi-model forecast precipitation integration considering long lead times was proposed based on the attention mechanism and a long short-term memory neural network.

(3)

The accuracy of integrated forecast precipitation was systematically evaluated from the perspective of point precipitation accuracy and applicability in streamflow forecast, and the superiority of deep learning in multi-model forecast precipitation integration was explained.

The remainder of this study is organized as follows. The details of the study area and data are provided in Section 2. The framework for multi-model forecast precipitation integration considering long lead times is described in Section 3. The results and discussion are presented in Section 4. Finally, conclusions are drawn in Section 5.

2. Study Area and Data

In this study, the Yalong River was used as the research area to verify the proposed method’s performance. Information on the study area and data is described below.

2.1. Study Area

Originating in Qinghai Province and flowing into Jinsha River from Panzhihua City in Sichuan Province, the Yalong River (Figure 1) is the largest tributary of the upper Yangtze River with a total length of 1571 km [32]. There are five controlling hydrologic stations, including Ganzi, Yajiang, Maidilong, Jinping, and Tongzilin. Its drainage area is about 136,000 km², spanning 29 counties and cities of three provinces with a permanent population of about 4 million people. The Yalong River has abundant precipitation with a multi-year average of 600–1400 mm, providing a stable water source for rivers. Moreover, it has a large and concentrated drop, which makes it rich in water energy and one of the “rich mines” of hydropower in China. These provide basic guarantees for cities’ development and residents’ livelihoods along the route, such as water supply, power generation, and so on. However, its topographic conditions are complex, and the spatiotemporal distribution of precipitation is uneven, mostly concentrated in flood season, which is prone to natural disasters like landslides, mudslides, and floods. These pose a serious threat to the safety of people’s lives and property, as well as the sustainable development of cities. Thus, accurate forecast precipitation is particularly important for the Yalong River.

2.2. Data Used

In this study, the observed precipitation, forecast precipitation for the following 1–7 days, and five hydrologic stations’ restored streamflow sequences were selected from 2016 to 2020.

(1)

Observed precipitation

In this study, a merged precipitation dataset with a spatial resolution of 0.1° was used as the observed precipitation. This dataset was generated by deep learning methods that spatiotemporally merged satellite precipitation products, terrain and geomorphological factors, temperature, wind, and ground monitoring precipitation [32]. It can significantly correct the temporal or spatial errors of previous precipitation data from along the Yalong River, fully meeting the needs of precipitation forecast research.

(2)

Forecast precipitation

Forecast precipitation was obtained from the TIGGE system. The TIGGE dataset contains deterministic and ensemble forecast results for 30 meteorological variables and can provide global forecast results for up to the following 16 days with a time scale of 6 h. In this study, the interpolated control forecast precipitation with a spatial resolution of 0.1° for the following 1–7 days was selected from the European Centre for Medium-Range Weather Forecasts (ECMWF), China Meteorological Administration (CMA), National Centre for Environmental Prediction (NCEP), Japan Meteorological Agency (JMA), and Korea Meteorological Administration (KMA) in TIGGE (https://apps.ecmwf.int/datasets/data/tigge/levtype=sfc/type=cf/ (accessed on 31 October 2023)). Their forecast time and data format are all 00:00 UTC and grib format, respectively.

(3)

Restored streamflow

In this study, daily-scale restored streamflow from the Ganzi, Yajiang, Maidilong, Jinping, and Tongzilin hydrologic stations was selected, which was provided by Yalong River Hydropower Development Co., Ltd in Chengdu, China.

3. Methodology

In this study, the primary focus was on proposing a rational method for multi-model forecast precipitation integration and evaluating its accuracy and applicability. The general modeling ideas, models, and evaluation indices are described in detail below.

3.1. General Modeling Ideas for Multi-Model Forecast Precipitation Integration

Multi-model forecast precipitation integration is a means of precipitation forecast error correction. It is an effective combination of multiple numerical weather prediction models through statistical analysis, weight assignment, machine learning, and other methods, based on multiple models’ features, improving the accuracy and applicability of forecast precipitation [33]. Its general expression is as follows:

$${\mathit{Y}}_t^F=E({\mathit{W}}_{1,t}\times {\mathit{X}}_{1,t}^F+{\mathit{W}}_{2,t}\times {\mathit{X}}_{2,t}^F+\dots +{\mathit{W}}_{m,t}\times {\mathit{X}}_{m,t}^F)$$

(1)

where ${\mathit{Y}}_t^F$ denotes the integrated forecast precipitation at moment t, m denotes the number of numerical weather prediction models, $E(•)$ denotes the mapping function between the forecast precipitation for each model and integrated forecast precipitation, ${\mathit{X}}_{1,t}^{\mathit{F}},{\mathit{X}}_{2,t}^{\mathit{F}},\dots ,{\mathit{X}}_{m,t}^{\mathit{F}}$ denote the forecast precipitation for each model at moment t, and ${\mathit{W}}_{1,t},{\mathit{W}}_{2,t},\dots ,{\mathit{W}}_{m,t}$ denote weights corresponding to the forecast precipitation for each model.

Combining Equation (1) with a single model forecast correction can lead to two additional modeling ideas. One is to correct the forecast precipitation of each numerical weather model separately based on each model’s forecast performance, and then integrate the corrected results. Its expression is as follows:

$${\mathit{Y}}_t^F=E[{\mathit{W}}_{1,t}\times C_1({\mathit{X}}_{1,t}^F)+{\mathit{W}}_{2,t}\times C_2({\mathit{X}}_{2,t}^F)+\dots +{\mathit{W}}_{m,t}\times C_m({\mathit{X}}_{m,t}^F)]$$

(2)

where $C_1(•),C_2(•),\dots ,C_m(•)$ denote the corrected functions for each single model.

The other is to integrate the forecast precipitation of multiple numerical weather models and then correct the integration results. Its expression is as follows:

$${\mathit{Y}}_t^F=C[E({\mathit{W}}_{1,t}\times {\mathit{X}}_{1,t}^F+{\mathit{W}}_{2,t}\times {\mathit{X}}_{2,t}^F+\dots +{\mathit{W}}_{m,t}\times {\mathit{X}}_{m,t}^F)]$$

(3)

Equations (1)–(3) reflect three different modeling ideas for multi-model forecast precipitation integration. Regarding the integration degree of each model’s advantage, the performances of the latter two are theoretically better than that of the first. The modeling idea of correcting first and integrating later (as shown in Equation (2)) can optimize the forecast performance of each model in a more targeted way and make more flexible use of different models’ advantages to improve the adaptability of forecast precipitation under different scenarios. However, it will increase integration models’ complexity and require greater computational costs. The modeling idea of integration followed by correction (as shown in Equation (3)) enables a more comprehensive consideration of the performance of each model from a holistic perspective and is easy to model. It should be noted that it may not sufficiently improve high-value precipitation forecast accuracy. Thus, choosing modeling ideas should be based on a comprehensive analysis of factors like geographic characteristics and precipitation change laws.

In addition, three different modeling ideas for multi-model forecast precipitation integration can essentially find the correlation between the forecast precipitation of each model and observed precipitation to correct forecast precipitation errors. Deep learning models have powerful temporal feature capture capabilities [34]. From this point of view, deep learning models are naturally suitable for application in multi-model forecast precipitation integration. Thus, this study introduces two popular deep learning models, the attention mechanism and long short-term memory neural network (LSTM), to explore the multi-model forecast precipitation integration method considering long lead times.

3.2. Framework for Multi-Model Forecast Precipitation Integration Considering Long Lead Times

In this study, a novel framework for multi-model forecast precipitation integration considering long lead times was proposed by comprehensively considering different numerical weather prediction models’ performance based on deep learning models (Figure 2). The steps were as follows.

(1)

Data collection and processing: Firstly, forecast precipitation from multiple numerical weather prediction models was collected under different lead times. Secondly, it was processed into the same spatiotemporal resolution as the observed precipitation. Finally, its accuracy was evaluated, and the forecast precipitation of high-precision models was selected under different lead times.

(2)

Model input-output datasets building: For each lead time, model input–output datasets were built by using the forecast precipitation of high-precision models and integrated forecast precipitation at the current time as inputs and outputs. Each dataset was divided into a training set and a validation set.

(3)

Integration model training: Three multi-model forecast precipitation integration models (LSTM, LSTM-A, and A-LSTM) were built by introducing the attention mechanism and LSTM, based on Equations (1)–(3). Based on the training set, the optimal hyperparameter combinations of each integration model were obtained through the Bayesian optimization algorithm under different lead times.

(4)

Comparison of models’ performance: Each integrated forecast precipitation was obtained by driving the trained integration models with test sets under different lead times. Their precipitation forecast accuracy and applicability for forecasting streamflow were evaluated to compare the advantages and disadvantages of each integration model and select the optimal integration model for each lead time.

Figure 2. Framework diagram of methodology.

Figure 2. Framework diagram of methodology.

3.3. Models

The attention mechanism can recognize the importance of each input factor well and assign different weights to different factors [35]. The LSTM network has a strong long-term dependency processing capability and can predict the trend of decision variables according to the relationship between the decision variables and input factors [36]. Thus, the attention mechanism and LSTM can handle complex time series data. In this study, they were introduced, and three multi-model forecast precipitation integration models (LSTM, LSTM-A, and A-LSTM) were built based on Equations (1)–(3). The principles of the attention mechanism, LSTM, LSTM-A, and A-LSTM are briefly described as follows.

3.3.1. Attention Mechanism

The attention mechanism is a deep learning method proposed in 2015, inspired by human visual attention [37]. It can give different weights to input factors according to the importance of the input factors to the decision variables, which gives more attention to the key input factors and reduces the attention on other secondary factors. It has the advantage of enhancing fitting performance, improving computational efficiency, and reducing the complexity of the model structure [38].

The attention mechanism is essentially a feature weight allocation mechanism. It can give different attention weights to each input factor in each computational step, and obtain output results by weighted summation calculation. Thus, it has a continuous distribution of weights and is internally capable of differential computation, making it possible to optimize parameters by the gradient descent method for use in conjunction with other deep learning models [39]. Its general expression is as follows:

$$\begin{array}{c}{\mathit{A}}_i=\mathrm{Softmax}({\mathit{W}}_i\times {\mathit{X}}_i+{\mathit{b}}_i)\\ ={\displaystyle \frac{e^{{\mathit{W}}_i\times {\mathit{X}}_i+{\mathit{b}}_i}}{{\displaystyle \sum _{i=1}^n{e}^{{\mathit{W}}_i\times {\mathit{X}}_i+{\mathit{b}}_i}}}}\end{array}$$

(4)

$$\mathit{X}’=\mathit{A}\times \mathit{X}$$

(5)

where X and $\mathit{X}’$ denote the original and weighted input factors, A denotes the attention weighting vector and W and b denote the weight vector and bias vector of the Softmax function.

3.3.2. LSTM

A long short-term memory neural network (LSTM) is a special form of recurrent neural network (RNN) with a strong ability to time series capture long-term dependent information [40]. Although RNNs can memorize input sequences, retaining a large amount of historical information internally adds many useless computations and leads to the problem of exploding or vanishing gradients. To solve this problem, LSTM designs memory units in the hidden layer to selectively read and store long-term information, improving computational efficiency and fitting ability. The internal structure of LSTM is shown in Figure 3.

In LSTM, the memory unit consists of an input gate, a forgetting gate, and an output gate for selectively retaining or discarding historical information to continuously update the cell. The computational expression within LSTM is as follows:

$${\mathit{F}}_t=\sigma ({\mathit{W}}_{XF}\times {\mathit{X}}_t+{\mathit{W}}_{HF}\times {\mathit{H}}_{t-1}+{\mathit{b}}_F)$$

(6)

$${\mathit{I}}_t=\sigma ({\mathit{W}}_{XI}\times {\mathit{X}}_t+{\mathit{W}}_{HI}\times {\mathit{H}}_{t-1}+{\mathit{b}}_I)$$

(7)

$${\mathit{C}}_t={\mathit{F}}_t\times {\mathit{C}}_{t-1}+{\mathit{I}}_t\times tanh ({\mathit{W}}_{XC}\times {\mathit{X}}_t+{\mathit{W}}_{HC}\times {\mathit{H}}_{t-1}+{\mathit{b}}_C)$$

(8)

$${\mathit{O}}_t=\sigma ({\mathit{W}}_{XO}\times {\mathit{X}}_t+{\mathit{W}}_{HO}\times {\mathit{H}}_{t-1}+{\mathit{b}}_O)$$

(9)

$${\mathit{H}}_t={\mathit{O}}_t\times tanh\left({\mathit{C}}_t\right)$$

(10)

where F_t, I_t,C_t, O_t, and H_t denote the outputs of the forgetting gate, input gate, cell state, output gate, and hidden layer, respectively; W and b denote the weight vector and bias vector, respectively; and tanh and $\sigma$ denote the Tanh and Sigmoid functions for activating variables, respectively.

3.3.3. LSTM-A

Based on Equation (2), an LSTM-A model for multi-model forecast precipitation integration is proposed by adding an attention mechanism component behind the output of LSTM. The internal structure of LSTM-A is shown in Figure 4.

The internal computation of LSTM-A is divided into two main processes, including the correction of each model’s forecast precipitation and integration. The former corrects each model’s forecast precipitation separately by LSTM according to the relationship between the forecast precipitation and decision variables. Subsequently, LSTM’s corrected outputs are weighted and integrated using the attention mechanism, and the final integration results are output after nonlinear transformation in the fully connected layer.

3.3.4. A-LSTM

Based on Equation (3), an A-LSTM model for multi-model forecast precipitation integration is proposed, which adds an attention mechanism component before the input layer of LSTM. The internal structure of A-LSTM is shown in Figure 5.

The internal computation of A-LSTM is also divided into two processes, the integration of multi-model forecast precipitation and correction. The former calculates the weights of models’ forecast precipitation at different periods through the attention mechanism to obtain weighted input factors. Then, these weighted input factors are used to drive LSTM, and the final integration results are output in the fully connected layer.

3.4. Performance Evaluation

The purpose of this study is to improve the accuracy and applicability of forecast precipitation. Thus, the performance of the proposed method needs to be evaluated considering two aspects. On the one hand, the accuracy of integrated forecast precipitation at grid points is evaluated based on the observed precipitation under different lead times. On the other hand, integrated forecast precipitation is used to drive hydrological models to obtain the forecast streamflow under different lead times, and the integrated forecast precipitation’s applicability is tested on the forecast streamflow’s accuracy.

3.4.1. Accuracy Evaluation of Integrated Forecast Precipitation

The accuracy evaluation indices of integrated forecast precipitation contain both continuity and classification indices to evaluate the coincidence degree between the integrated forecast and observed precipitation, as well as the integrated forecast precipitation’s accuracy at different precipitation intensities. In this study, some continuity indices were selected, including Spearman’s correlation coefficient (SCC), mean absolute error (MAE), root mean square error (RMSE), and standard deviation (SD). Their expressions are as follows:

$$SCC=1-{\displaystyle \frac{6{\displaystyle \sum _{i=1}^n{[r(P_{O,i})-r(P_{F,i})]}^2}}{n\times (n^2-1)}}$$

(11)

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|P_{O,i}-P_{F,i}\right|}$$

(12)

$$RMSE=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\left(P_{O,i}-P_{F,i}\right)}^2}}{n}}}$$

(13)

$$SD=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1}^n(P_{F,i}-\overline{P_F})}}{n}}}$$

(14)

where P_O and P_F denote the observed and forecast precipitation, $\overline{P_{\mathit{F}}}$ denotes the mean value of the forecast precipitation, n denotes the precipitation sequence length, and $r(•)$ denotes the precipitation sequence’s rank.

The Taylor diagram is also used to visually evaluate integrated models’ performance. It presents the SCC, SD, and RMSE between the integrated forecast precipitation and observed precipitation on a polar plot, based on the principle of trigonometric functions [41]. On the Taylor diagram, being closer to the observation point indicates a better model performance.

In addition, classification indices included the threat score (TS), missing alarm rate (MAR), and false alarm rate (FAR). Their expressions are as follows:

$$TS={\displaystyle \frac{N_{11}}{N_{11}+N_{10}+N_{01}}}$$

(15)

$$MAR={\displaystyle \frac{N_{10}}{N_{11}+N_{10}+N_{01}}}$$

(16)

$$FAR={\displaystyle \frac{N_{01}}{N_{11}+N_{10}+N_{01}}}$$

(17)

where N_jk denotes the amount of observed precipitation of category j that is identified as category k by forecast precipitation (j, k = 0, 1; 0 denotes no precipitation and 1 denotes precipitation).

3.4.2. Applicability Testing of Integrated Forecast Precipitation

In this study, the Nash–Sutcliffe model efficiency coefficient (NSE), average relative error (MRE), and RMSE were selected to evaluate the forecast streamflow’s accuracy, thereby testing the applicability of integrated forecast precipitation. RMSE’s expression is shown in Equation (13), and other expressions are as follows:

$$NSE=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{(Q_{O,i}-Q_{F,i})}^2}}{{\displaystyle \sum _{i=1}^n{(Q_{O,}{}_i-\overline{Q_{O,}{}_i})}^2}}}$$

(18)

$$MRE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\frac{\left|Q_{O,i}-Q_{F,}{}_i\right|}{Q_{O,}{}_i}}$$

(19)

where Q_O denotes the observed streamflow, Q_F denotes the forecast streamflow, and $\overline{Q_O}$ denotes the mean value of the observed streamflow.

4. Results and Discussion

In this study, the advantages and disadvantages of five numerical weather prediction models’ forecast precipitation, including the ECMWF, CMA, JMA, KMA, and NCEP, were compared and analyzed for the Yalong River. The high-accuracy ones were used as the inputs for integrated models to generate integrated forecast precipitation for the whole basin, and then the performances of different integrated models were comparatively analyzed through the evaluation of forecast precipitation accuracy and applicability testing in streamflow forecast. Relevant results are shown and discussed in detail below.

4.1. Accuracy Evaluation of Original Forecast Precipitation Under Different Lead Times

Based on the observed precipitation, the forecast precipitation accuracy of the ECMWF, CMA, JMA, KMA, and NCEP for the Yalong River for the following 1–7 days was evaluated by the three continuity indices of SCC, MAE, and RMSE. The results are shown in Figure 6.

As presented in Figure 6, the five models’ forecast precipitation accuracy decreases with an extension of the lead time, and their performance for the Yalong River varies. In terms of SCC, the ECMWF is the highest, with values all above 0.4 under different lead times, indicating that the ECMWF forecast precipitation has a high correlation with the observed precipitation; the NCEP is the lowest, with values all below 0.15 under different lead times, implying a weak correlation with the observed precipitation. The values of the remaining models are all between 0.2 and 0.3, but the value of the CMA is only lower than the ECMWF on the following day, and then drops sharply to be only higher than the NCEP over the following 2–7 days. In terms of the RMSE, the JMA has the lowest value and the NCEP has the highest. The value of the ECMWF is 9.5–10 mm/d, probably because the ECMWF forecast precipitation is too high in some periods, resulting in a large degree of dispersion between the observed and forecast precipitation. The CMA is only higher than the JMA, with values all below 9.2 mm/d for the following 1–5 days, while its value sharply increases to 11.2 mm/d for the following 6–7 days. In terms of the MAE, the ECMWF is the lowest, with 4.2–4.3 mm/d, and the NCEP is the highest, with values above 5 mm/d under different lead times. The changes in the CMA, JMA, and KMA results under different lead times are similar to those observed with SCC and RMSE, where the CMA is significantly better than the KMA and JMA over the following 2–5 days. Thus, from the overall evaluation of the three continuity indices, the ECMWF has the best forecast precipitation accuracy for the Yalong River, the NCEP has the worst, and the other models have a similar forecast accuracy.

Accurate forecast precipitation under different intensities can help to reduce flood disasters and improve the scientific management of water resources [42]. According to the grade standard of valley area precipitation, station precipitation intensity can be classified as “light precipitation” (0.1–10 mm/d), “moderate precipitation” (10–25 mm/d), “heavy precipitation” (25–50 mm/d), and “torrential precipitation and above” (≥50 mm/d) [43]. The TS, MAR, and FAR of different model’s forecast precipitation are shown in Figure 7.

It can be seen from Figure 7 that the accuracy of the five models’ forecast precipitation decreases with an increase in the precipitation intensity. At an intensity of 0.1–10 mm/d, all models have certain precipitation forecast capabilities. Among them, the ECMWF has the best performance, with a TS above 0.42, MAR below 0.26, and FAR of around 0.5 for the following 1–7 days, which indicates that the ECMWF has a good ability to forecast light precipitation and its forecast precipitation area can cover the observed precipitation occurrence area to a certain extent, but the coverage is relatively large. The CMA is only inferior to the ECMWF, with a TS of around 0.4, MAR below 0.3, and FAR of around 0.5, but its forecast accuracy deteriorates rapidly in the following 6–7 days. The remaining three models have a TS below 0.4, MAR above 0.3, and FAR above 0.5, among which the KMA is superior to the JMA and NCEP. Thus, for forecasting precipitation of a 0.1–10 mm/d intensity, the ECMWF has the best forecast capability, followed by the CMA and KMA, while the JMA and NCEP are poorer.

However, when the precipitation intensity exceeds 10 mm/d, the five models have a limited forecast capability. At an intensity of 10–25 mm/d, the ECMWF and KMA maintain some forecasting ability, while the CMA, JMA, and NCEP lose their ability to forecast moderate precipitation, with a TS below 0.05, MAR above 0.85, and FAR above 0.94. At an intensity above 25 mm/d, the five models’ TS is below 0.03, with an MAR above 0.92 and FAR above 0.96, indicating that they all lose their ability to forecast heavy precipitation and above for the Yalong River. In particular, the JMA’s MAR and FAR are close to 1, failing to effectively forecast heavy precipitation and above.

The Yalong River covers an area of approximately 136,000 km² with complex topography and large undulation changes from upstream to downstream. Coupled with the influence of the west wind circulation and the southwest monsoon, the climate of the Yalong River is exceptionally complex. Its northern plateau has a continental climate, its central and southern parts have a subtropical climate, and its river valleys and mountainous areas also have different climate characteristics. These make precipitation forecast exceptionally difficult and uncertain in the Yalong River. The forecast precipitation used in this study is all generated based on different initial fields, resolutions, parameterization schemes, and dynamical frameworks, which are oriented to precipitation on a global scale. They cannot fully consider the impacts of the complex topographic characteristics and weather systems of the Yalong River on precipitation forecast. Thus, the precipitation forecast accuracy of the five models is poor for the Yalong River, especially for a precipitation intensity greater than 10 mm/d, and they are not fully applicable to daily operations.

In addition, the five models’ precipitation forecast performance has some variability for the Yalong River. This may be related to the structural composition and counties (or regions) where different patterns occur. The ECMWF is coupled with an ocean model with a vertical resolution of 137 layers, which allows for a more refined consideration of the different factors of precipitation formation, resulting in an optimal precipitation forecast accuracy [44]. The CMA, KMA, and JMA are developed by meteorological centers in Asian countries, and their generation process is naturally more biased towards the precipitation forecast of their own countries and neighboring countries, giving them certain advantages in Asia. The NCEP belongs to the United States Meteorological Center, and its generation process is more biased towards precipitation in the United States, making its precipitation forecast ability inferior to other models for the Yalong River.

4.2. Applicability Evaluation of Original Forecast Precipitation

Precipitation is the main source of streamflow, and the accuracy of precipitation forecast determines the accuracy and reliability of streamflow forecast. Thus, forecast precipitation is often used in streamflow forecast study. In this study, a classical hydrologic model, the lumped Xin’an River model (XAJ), was introduced for streamflow forecast to verify the applicability of forecast precipitation. The parameters of the XAJ model were optimized based on daily observed precipitation with a spatial resolution of 0.1° for the Yalong River. The streamflow simulation of five hydrologic stations was evaluated by NSE, MRE, and RMSE, with 2019–2020 as the validation period and the remaining years as the calibration period. The results are shown in

Table 1. Streamflow simulation accuracy of five hydrologic stations.

Hydrologic Station	Calibration Period			Validation Period
	NSE	MRE (%)	RMSE (m3/s)	NSE	MRE (%)	RMSE (m3/s)
Ganzi	0.872	17.5	106	0.867	18.3	112
Yajiang	0.972	10.2	142	0.961	12.5	158
Maidilong	0.982	3.9	132	0.980	4.3	135
Jinpin	0.985	5.9	141	0.983	6.5	145
Tongzilin	0.983	9.2	227	0.979	9.8	234

.

The streamflow simulation based on observed precipitation achieves good results at the five hydrologic stations. In each hydrologic station, the NSE is above 0.86, MRE is below 10%, and RMSE is also small in the calibration and validation periods. This indicates that the simulated streamflow at each hydrologic station has small errors and deviations, reflecting the main characteristics of the observed streamflow. Thus, the trained XAJ model at each hydrologic station can be used in the applicability testing of forecast precipitation.

Then, the forecast streamflow of five hydrologic stations is obtained by driving the XAJ model with the original forecast precipitation from 2019 to 2020 under different lead times, and their accuracy is evaluated by the NSE, MRE, and RMSE. The results are shown in Figure 8.

It can be seen from Figure 8 that the accuracy of the forecast streamflow for the five hydrologic stations based on the original forecast precipitation decreases with an extension of the lead time. Among them, the NSE of the forecast streamflow based on the ECMWF and CMA at five hydrologic stations is 0–0.5, while the MRE is 40–120% and RMSE is relatively small. This indicates that the applicability of the ECMWF and CMA in streamflow forecast is better than other models’ forecast precipitation. Because the ECMWF has a high vertical resolution and can consider multiple factors related to precipitation formation, it has a high accuracy in precipitation forecast, resulting in a higher accuracy in streamflow forecast. The CMA is developed by the China Meteorological Center, which has more knowledge of the climate and terrain characteristics of the Yalong River, resulting in smaller errors in precipitation forecast and a better accuracy in streamflow forecast. In addition, the forecast streamflow errors of the five hydrologic stations based on the other forecast precipitation are large and spatially superimposed, with the NSE ranging from −13 to 0.1, MRE ranging from 100% to 600%, and a high RMSE. This is because their overestimated precipitation causes a large precipitation forecast error, making the streamflow forecast accuracy poor at Ganzi station. The five hydrologic stations are spatially arranged in sequence, and the upstream streamflow forecast errors inevitably pass down step by step in space, resulting in a poor accuracy of the downstream streamflow forecast.

Furthermore, Tongzilin station is located at the end of the Yalong River, and its streamflow forecast accuracy can represent the overall accuracy of the Yalong River streamflow forecast. It is worth noting that Tongzilin station has an NSE below 0.4, MRE above 50%, and RMSE above 1200 m³/s in streamflow forecast under different lead times. The large forecast errors imply that the five models’ forecast precipitation is still difficult to directly apply to the streamflow forecast along the Yalong River.

From the original forecast precipitation accuracy and its applicability evaluation, it is clear that the ECMWF and CMA have the best precipitation forecast accuracy and applicability, and the NCEP has the worst. However, the ECMWF’s RMSE is relatively high, and the CMA has a poor precipitation forecast accuracy with a lead time of 7 days. The JMA’s RMSE is the lowest under different lead times, and the forecast ability of the KMA for a precipitation intensity greater than 10mm/d is second only to the ECMWF at an intensity above 25 mm/d. Thus, the forecast precipitation data of the ECMWF, CMA, KMA, and JMA were used as the inputs of the integration models.

4.3. Comparison of Integrated Forecast Precipitation Accuracy for Different Models

To fully verify the performance of the proposed method, five typical regression methods, including Multiple Linear Regression (MLR), Support Vector Regression (SVR), Feedforward Neural Network (FNN), Least Squares Boosting Decision Tree (LSBoost), and Bayesian Model Averaging (BMA), were introduced for comparison. All models were built and run on Python 3.9 using a single NVIDIA GeForce GTX 1650 GPU of NVIDIA Corporation in the Santa Clara, CA, USA. BMA was trained with 10,000 iterations by the Expectation Maximization algorithm, and the other seven models were trained with 200 iterations using the Bayesian Optimization algorithm.

To test the performance of the eight integration models, 2019–2020 was used as the test period and the remaining years were used as the training period. Using the ECMWF as a comparison, the performance of each integration model was evaluated through MAE, and the results are shown in

Table 2. The MRE of each model during the test period under different lead times (mm/d).

	Lead Time (Day)	1	2	3	4	5	6	7
Model
LSTM-A		1.56	1.57	1.59	1.61	1.61	1.64	1.75
A-LSTM		1.60	1.61	1.65	1.65	1.67	1.67	1.70
LSTM		1.60	1.62	1.65	1.66	1.69	1.70	1.70
LSBoost		2.16	2.17	2.17	2.17	2.18	2.19	2.20
FNN		2.18	2.18	2.20	2.20	2.21	2.22	2.23
SVR		1.85	1.86	1.95	2.02	2.09	2.09	2.19
MLR		2.25	2.25	2.26	2.26	2.27	2.29	2.30
BMA		2.68	2.69	2.71	2.72	2.82	2.83	2.84
ECMWF		4.26	4.20	4.19	4.20	4.32	4.29	4.30

.

It can be seen from Table 2 that the MAEs of the eight integration models are below 3 mm/d under different lead times, significantly lower than that of the ECMWF, indicating that all integration models can effectively reduce the forecast precipitation error for the Yalong River. Among them, the LSTM-A, A-LSTM, and LSTM integration models significantly outperform the other integration models, with MAEs below 1.8 mm/d under different lead times, reflecting the strong advantages of the attention mechanism and LSTM in time series processing. The LSBoost, FNN, and MLR integration models have similar MAEs under different lead times, slightly inferior to SVR. The MAE of the BMA integration model is 2.68–2.84 mm/d under different lead times, with a poorer forecast performance than the other integration models.

The forecast precipitation accuracy of each integration model is drawn in the Taylor diagram to more intuitively and comprehensively compare the advantages and disadvantages of the integration models. The results are shown in Figure 9.

When the SCC is larger, the RMSE is smaller, and the SD values are closer to the observed sequence, the integration models’ point is closer to the observed point (“red point”) in the Taylor diagram. As seen from Figure 8, each integration model is significantly better than the ECMWF, which shows that it has an obvious enhancement effect on precipitation forecast through integrating the multi-model forecast precipitation for the Yalong River. Among them, A-LSTM and LSTM-A are significantly better than the other integration models, with SCCs of around 0.8 and RMSEs below 3.7 mm/d under different lead times. LSTM-A is slightly better than A-LSTM after 7 days of lead time. The SCC of LSTM is above 0.7, and its RMSE is below 3.8 mm/d under different lead times, which is better than general machine learning models. The SCC, RMSE, and SD of LSBoost are roughly similar to FNN, overall outperforming SVR and MLR. Although the SCC of SVR is higher than that of BMA, the SD of BMA is more similar to the observed sequence and reflects the variation characteristics of the observed precipitation better, making its forecast performance better than that of SVR.

Further, the forecast precipitation accuracy of each integration model is evaluated at different intensities. The results are shown in Figure 10.

It can be seen from Figure 10 that, at an intensity of 0.1–10 mm/d, each integration model has an improved forecast precipitation accuracy. Among them, LSTM-A and A-LSTM have the best forecast precipitation accuracy. Their TS is above 0.7, MAR is around 0.1, and FAR is below 0.3 under different lead times, indicating that they have a good forecast ability for light precipitation and the forecast precipitation area can cover the observed precipitation occurrence area well. The forecast accuracy of LSTM is only inferior to LSTM-A and A-LSTM, with a TS above 0.6, MAR below 0.15, and FAR below 0.4. BMA, LSBoost, and FNN have a roughly equivalent forecast ability, outperforming MLR and SVR. Furthermore, it is worth noting that the MAR of LSBoost, FNN, and MLR is around 0.05, while the FAR is higher than 0.4. This indicates that these three models have a certain accuracy in forecasting light precipitation, but the forecast precipitation area is large.

At an intensity of 10–25 mm/d, the integration models’ forecast precipitation ability has a similar variation to the 0.1–10 mm/d intensity under different lead times, but there is a decrease in accuracy. The TS of A-LSTM is all around 0.4, with an MAR of around 0.36 and FAR of around 0.39 under different lead times, providing a better forecast ability than LSTM-A. The TSs of LSBoost, FNN, SVR, and MLR are all around 0.15, but the MARs are higher than 0.8, showing a low hit rate and high missing rate. The extremely high forecast errors make them inferior to BMA.

At an intensity of 25–50 mm/d, LSTM-A has a certain forecast ability with a TS around 0.32, MAR below 0.6, and FAR of around 0.2, which is better than A-LSTM and LSTM. Instead, the TSs of the remaining five models are close to 0, and the MARs and FARs are both close to 1, indicating a loss of ability to forecast heavy precipitation. At an intensity of ≥50 mm/d, the integration models’ forecast precipitation ability has a similar variation to the 25–50 mm/d intensity under different lead times, with a decrease in accuracy. LSTM-A is the best, followed by A-LSTM and LSTM, and the other models lose their forecast ability. It is worth noting that the FARs of LSBoost, FNN, SVR, MLR, and BMA are all 0, exhibiting extremely high false alarm rates.

The precipitation forecast accuracy of each integration model varies, and the possible reasons are analyzed as follows: precipitation is subject to the synergistic effects of temperature, air pressure, wind speed and direction, and topography and geomorphology, whose change characteristics are stochasticity, mutagenicity, localization, and so on [45,46]. Together with the influence of its vast area, complicated topography, and diverse climate changes, precipitation along the Yalong River is exceptionally complicated. In terms of precipitation intensity, cases of no precipitation or light precipitation are predominant, while the probability of heavy precipitation and above is very small, and nd there are jumping changes between adjacent periods of the precipitation sequence. These make it difficult to accurately capture the change law of precipitation sequences. General machine learning models (FNN, LSBoost, SVR, and MLR) establish a nonlinear mapping between input factors and decision variables based on temporal features. To find smaller computational errors, they usually try to learn the more frequent cases (no precipitation or light precipitation) and fail to capture the less frequent cases (heavy precipitation and above) during their internal optimization, making their integrated forecast precipitation small and unable to forecast high-value precipitation. Thus, they have a good forecast accuracy for light precipitation (0.1–10 mm/d), large errors for moderate precipitation (10–25 mm/d), and lose the ability to forecast heavy precipitation and above (≥25 mm/d). Their integrated forecast precipitation does not reflect high values of a ≥50 mm/d intensity. BMA calculates weights through prior and posterior probability, and can consider precipitation uncertainty, affording it a certain forecast accuracy for light and moderate precipitation. However, BMA cannot better forecast heavy precipitation and above due to the high complexity of the precipitation sequence.

Three multi-model forecast precipitation integration models based on deep learning (LSTM, A-LSTM, and LSTM-A) have a better forecast accuracy than the other five integration models. LSTM has a better ability to deal with long-term dependence through memory gates, and can learn the change law of precipitation better than general machine learning models. This makes LSTM capable of forecasting precipitation of different intensities, especially light precipitation and moderate precipitation. However, subject to the inputs’ mutual interference, LSTM still has some room for improvement in its forecast accuracy for heavy precipitation and above (≥25 mm/d). Combining the attention mechanism and LSTM can more fully exploit the importance of each input or output in the internal calculation, making A-LSTM and LSTM-A superior to LSTM. A-LSTM adds the attention mechanism to LSTM’s input layer to highlight the importance of the inputs at each computational step, which fully utilizes the advantages of each original forecast precipitation under different intensities. Limited by the accuracy of the original precipitation forecast, its forecast accuracy in heavy precipitation and above is weaker than that of LSTM-A. LSTM-A first corrects each original rainfall forecast through LSTM, which can reduce the forecast errors for low, high, and extreme precipitation. Then, it utilizes the performance of each corrected forecast precipitation through the integration of the attention mechanism, improving the accuracy of forecast precipitation under different intensities. Therefore, LSTM-A has an excellent performance in forecasting high-value precipitation.

In summary, the precipitation forecast accuracy of the integration models is improved. Among them, LSTM-A has the best forecast performance, followed by A-LSTM and LSTM, and the other models have a good forecast performance for light precipitation, but cannot accurately forecast heavy precipitation and above.

4.4. Applicability Testing for Integrated Forecast Precipitation

Driving the XAJ model with the integrated forecast precipitation from 2019 to 2020, the forecast streamflow of five hydrologic stations is obtained. Their accuracy is evaluated through NSE, MRE, and RMSE, and the results are shown in Figure 11.

From Figure 11, it can be inferred that, compared with the original forecast precipitation, the accuracy of the streamflow forecast based on the integrated forecast precipitation significantly improves at the five hydrologic stations under different lead times. In terms of the applicability of integrated forecast precipitation in streamflow forecast, LSTM-A is the best, with an NSE above 0.8, MRE below 30%, and small RMSE at the five hydrologic stations under different lead times; LSTM is only inferior to A-LSTM and LSTM-A, and its MRE is quite large at Maidilong, Jinpin, and Tongzilin; LSBoost is roughly equivalent to FNN and slightly better than SVR and MLR; BMA has a good applicability at Ganzi, Yajiang, Maidilong. and Jinping and poor applicability accuracy in Tongzilin; and the applicability of BMA-integrated forecast precipitation is good at Ganzi, Yajiang, Maidilong, and Jinpin but poor in Tongzilin.

The performances of different integrated forecast precipitation models applied to streamflow forecast vary for the Yalong River. After analysis, the possible reasons for this are as follows. Although MLR, SVR, FNN, and LSBoost can correct the errors of the original forecast precipitation to a certain extent, they have a poor forecast ability for precipitation of a >10 mm/d intensity. The additional influences of complex topography and elevation make their integrated forecast precipitation ineffective for streamflow forecast at the Ganzi and Yajiang hydrologic stations. However, their integrated forecast precipitation accuracy is generally good in the region between Yajiang and Tongzilin, and the trained XAJ model parameters are very accurate. This can eliminate the influence of upstream streamflow forecast errors on those downstream to a certain extent, which affords a good streamflow forecast accuracy at Maidilong, Jinpin, and Tongzilin. LSBoost and FNN have a complex structure and slightly better nonlinear mapping ability of input factors to decision variables than SVR and MLR. Thus, the streamflow forecast accuracy based on LSBoost and FNN integrated forecast precipitation is slightly better than that of SVR and MLR. BMA utilizes prior and posterior probability to integrate multi-model forecast precipitation, which can consider precipitation uncertainty and reduce the influence of topographic elevation factors. This causes its integrated forecast precipitation applied to streamflow forecast in Ganzi, Yajiang, Maidilong, and Jinpin to achieve good results. However, the large BMA integrated forecast precipitation error in the region between Jinping and Tongzilin makes the streamflow forecast accuracy low in Tongzilin. Therefore, these five integration models’ integrated forecast precipitation is less applicable to streamflow forecast than LSTM-A, A-LSTM, and LSTM.

LSTM can effectively capture the change characteristics of precipitation to obtain high-accuracy integrated forecast precipitation, achieving a high-accuracy streamflow forecast for the Yalong River. However, its forecast errors for high-value precipitation are large, causing a large MRE for streamflow forecast at each hydrologic station. A-LSTM and LSTM-A are established by coupling LSTM and the attention mechanism. They can effectively identify the importance of inputs or outputs, reduce precipitation forecast errors, and further improve the accuracy of streamflow forecast. LSTM-A, which uses attention weighting after LSTM corrects the original forecast precipitation, can reduce the influence of input errors on the integration model and effectively improve the forecast ability of high-value precipitation, making the streamflow forecast based on the LSTM-A integrated forecast precipitation better than that of A-LSTM.

In summary, in terms of the applicability of integrated forecast precipitation in streamflow forecast, LSTM-A is the best, followed by A-LSTM and LSTM, and the other integrated models are poorer. The NSE of streamflow forecast based on LSTM-A integrated forecast precipitation is above 0.82 at the five hydrologic stations under different lead times, while the MRE is below 30%, indicating the direct applicability in streamflow forecast for the Yalong River.

5. Conclusions

To improve the accuracy of forecast precipitation under different intensities and extend effective lead times, a novel method for multi-model forecast precipitation integration considering long lead times was proposed based on deep learning in this study by combining the advantages of different numerical weather prediction models. First, the accuracy of the ECMWF, CMA, JMA, KMA, and NCEP forecast precipitation was systematically evaluated by continuity and classification indices under different intensities and lead times. Second, multi-model forecast precipitation integration models were built by combining several general modeling ideas with the attention mechanism and LSTM, and the integrated forecast precipitation was obtained for the whole basin under different lead times. Finally, the accuracy of the integrated forecast precipitation and its applicability to streamflow forecast were examined to analyze the superiority of deep learning in multi-model forecast precipitation integration. Taking the Yalong River as an example, the main conclusions are summarized as follows:

(1)

Among five original forecast precipitation models, the ECMWF and CMA had a higher forecast precipitation accuracy under different intensities and a better applicability in streamflow forecast, but they all failed to forecast precipitation of a ≥10 mm/d intensity under different lead times well.

(2)

General machine learning models (LSBoost, FNN, SVR, MLR, and BMA) were unable to adequately learn the fluctuation of precipitation sequences, and lost the ability to forecast precipitation of a ≥25 mm/d intensity because they tended to sacrifice the ability to fit high values during internal training to maintain their overall accuracy.

(3)

Among the integration models, LSTM-A and A-LSTM had the best performance and effectively reduced precipitation forecast errors under different intensities, indicating that deep learning with a strong temporal feature capture ability significantly improves precipitation forecast accuracy.

(4)

Regarding the applicability of forecast precipitation in streamflow forecast, LSTM-A was the best, with an NSE above 0.82 and MRE below 30% at each hydrologic station under different lead times, which can be directly applied in real-time streamflow forecast.

The proposed method can help to improve precipitation forecast accuracy, extend effective lead times, reduce losses from droughts and floods, and promote sustainable socio-economic development. However, due to the extreme complexity of precipitation, there is still room for further improvement of the proposed method for forecasting high-value precipitation. Additionally, the method proposed in this study is mainly deterministic single-value forecasting, and the forecast uncertainty needs further exploration.