A New Precipitation Prediction Method Based on CEEMDAN-IOWA-BP Coupling

: Precipitation is the most basic part of the water cycle process. Aiming at the problem of low prediction accuracy caused by the nonlinear and unstable characteristics of the precipitation series, a new precipitation prediction method based on the CEEMDAN-IWOA-BP coupling model is proposed. This method first uses the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to decompose the original precipitation sequence, and obtains a series of intrinsic mode function (IMF) and residual terms (Res) as inherent potential influencing factors, innovatively introduce TENT chaotic mapping and roulette algorithm to improve the Whale Optimization Algorithm (WOA), use IMFs and Res as the input of the Improve Whale Optimization Algorithm (IWOA) to optimize Back Propagation (BP) neural network prediction model, and finally superimpose the predicted values as ultima result.The present method was applied to predict the annual precipitation from 1958 to 2017 in Sichuan Province.Compared with the prediction results of other models, the CEEMDAN-IWOA-BP coupled model has significantly improved prediction accuracy than the single model, and the prediction error index of the Back Propagation(BP) neural network optimized by the Genetic Algorithm (GA) and Particle Swarm


Introduction
The issue of water resources is one of the important scientific issues that the scientific community attaches importance to (Xia et al. 2011), and precipitation is the most basic link in the cycle of water resources (Yang 2020). For many years, the forecast of mid-and long-term precipitation has mainly adopted statistical forecasting methods, which include two types of time series analysis and multivariate analysis (Lei 2020). However, the statistical analysis model lacks adaptability, which makes it difficult to update the model itself. At the same time, the uncertainty of the model also causes the instability of prediction and inspection accuracy (Xu et al. 2006). Therefore, there is an urgent need for more effective forecasting methods.
Since David et al (1986). proposed the BP neural network model, the crossdiscipline of machine learning has gradually been applied to wind power load (Wang and Sun, 2015), operation and maintenance (Peng and  Compared with other algorithms, the Whale Optimization Algorithm has the advantages of simple structure, fewer parameters, and faster iteration speed. This article uses the whale optimization algorithm to build the model. In view of the disadvantages of the traditional whale algorithm such as weak global search ability, the TENT chaotic map is introduced to the population Initialization, to further improve the global search capability of the algorithm, and introduce the roulette algorithm to enhance the local optimization capability of the algorithm as IWOA. In practical applications, the coupling model uses various decomposition methods to combine with different prediction models. Based on the decomposition algorithm, the data is preprocessed to reduce the non-stationarity of the sequence to achieve the purpose of improving the accuracy of the model (Xu et al. 2021). In this paper, the items decomposed by CEEMDAN are used as the input of the IWOA-BP prediction model, and the weights and thresholds of the BP neural network are optimized through IWOA to improve the robustness and accuracy of the BP neural network, then superimpose the output of the BP neural network as the prediction result. Finally, the model is applied to the measured precipitation sequence, and the superiority of the CEEMDAN-IWOA-BP prediction model is verified through the prediction fitting of different models and the comparison of multiple error indicators. Where X(t) is the original sequence, R(t) is the residual term, and IMF k is the internal mode component of the decomposed series. The final sequence is decomposed by CEEMDAN to obtain a series of IMFs ranging from high frequency to low frequency, and the original sequence can be accurately and completely reconstructed by using the characteristics of noise adaptation.

Basic WOA Algorithm
The Whale Optimization Algorithm is an intelligent optimization algorithm proposed by Mirjalili (2016). The proposed algorithm is affected by the predation of humpback whales and imitates the hunting process of whales, as follows.
(1) Search for prey. Whales achieve their hunting goals by updating their positions when searching the space, this behavior is represented by equations (2) and (3).
Where D is the distance between the current optimal individual and other individuals; φ is the current it eration number; X * ⃗⃗⃗⃗ is the vector position of the current optimal individual; X ⃗ ⃗ is the position vector of other individuals; A ⃗ ⃗ and C ⃗ is a vector  Among them, the shrinking and enclosing mechanism is realized by reducing a ⃗ , and the range of A ⃗ ⃗ is [-a, a]. As it approaches the optimal individual, the whale will surround its prey in a spiral manner. This behavior is described below.
Where D ′ ⃗⃗⃗ is the distance between the best position and the current optimal solution; m is the shape constant of the spiral; l is a random number between [-1,1].
When whales are hunting, there is a 50% probability of choosing the above two hunting methods. The behavior is described as follows.
(3) Simulate predation. When | | < 1, the position of the optimal individual is the position of the prey, and other individuals in the group will adjust their positions to hunt according to the optimal individual; when | | ≥ 1, the group is forced to update the position information of randomly selected individuals Until the optimal solution is obtained, the process is described as follows.
Where is the position vector of randomly selected individuals in the group.

Improved WOA Algorithm
The basic WOA has shortcomings such as weak global search ability and easy to fall into local optimum, slow local optimization speed and so on. The traversal of the TENT chaotic map has uniformity and randomness, which can make the algorithm easy to escape from the local optimal solution, thereby maintaining the diversity of the population and improving the global search ability. This paper first uses TENT chaotic mapping to initialize the population, which greatly eliminates the randomness of the initial population, makes the initial population more evenly distributed within the parameter range, and further improves the global search ability of the WOA. The TENT chaotic map is as follows.
In the formula, α ∈ (0,1), when α =0.5, the system will present a short period state and not belong to a chaotic system. In this study, the value of α is 0.6.
The basic WOA is blind in the process of optimizing and predation, and cannot fully integrate the iterative experience to update the population. Secondly, this paper

Improved WOA Optimized BP Neural Network
BP neural network is a multi-layer feedforward neural system. Its main characteristics are signal propagates forward and error propagates backward. BP neural network has self-learning ability and nonlinear function mapping ability. The structure of the three-layer BP neural network is shown in Figure 4.

Example Application
Sichuan Province is located in the inland of southwest China, with complex topography and large differences in topography, the topography is high in the west and low in the east, affected by the monsoon and topography, the annual variation of precipitation varies greatly. A more accurate forecast of annual precipitation will provide corresponding reference value for the protection and management of water resources, water environmental protection and governance, and disaster prevention and mitigation in the province. The measured precipitation sequence of the province from is high, and the representativeness of the data can be guaranteed. Fig. 6 The precipitation sequence of Sichuan Province from 1958 to 2017

CEEMDAN Decomposition of Annual Precipitation Series
The CEEMDAN method is used to decompose the precipitation sample data of Sichuan Province from 1958 to 2017 to reduce the volatility of the original precipitation series. Set the CEEMDAN algorithm parameters Nstd to 0.2, NE to 500, and Maxlter to 5000, the original precipitation sequence is finally decomposed into 6 IMF and one Res. The Res indicates that the 60-year precipitation series in Sichuan Province has shown a downward trend as a whole, and the decomposition results are shown in Figure   7.

Model Construction and Prediction
In  Where N is the number of samples involved in the calculation, ŷ(t) is the predicted value of precipitation in year t, y is the average value of the sample, and y(t) is the true value of precipitation in year t. Table 1 shows the evaluation index values of different models, and Figure 8 shows the comparison of the prediction errors of different models.
It can be seen from Table 1 and Figure

Conclusion
In order to reduce the non-stationarity of the precipitation series and improve the accuracy of precipitation prediction, this paper constructs a hybrid prediction model of achieving a more accurate precipitation prediction provides a new approach for midand long-term precipitation prediction, and also provides reference value for related prediction research in other regions.

Author Contribution
All authors contributed to the study conception and design. Writing and editing: Fuping Liu and Chen Yang; chart editing: Ying Liu; preliminary data collection: Ruixun Lai. All authors read and approved the final manuscript.

Data Availability
Data and materials are available from the corresponding author upon request.

Declarations
Ethics Approval: Not applicable.
Consent to Participate: Not applicable.
Consent for Publication: Written informed consent for publication was obtained from all participants.
Competing Interests: The authors declare no competing interests.