The Yangtze River, being the longest river in China and the third longest river in the world, runs across China from west to east, plays a vital role in the economic development. Water level prediction is not only helpful for flood control in flood season and vessel navigation in dry season, but also conducive for waterway regulation, port management, etc. Thus, accurately and timely prediction is particularly necessary.

In recent decades, a wide variety of approaches have been investigated for water level prediction, mainly divided into model-driven and data-driven methods. The model-driven methods include experience formulas between water level and water flow [1], generalized extreme value distributions [2], Muskingum model parameters optimal estimation [3], mathematical expression between water level and tide [4], etc. Generally, these models are parameter-based, frequently make a number of hypotheses ideal circumstances, depend on hand-crafted features that are expensive to create and require expert knowledge of the field, in addition, they mainly focus on univariate data excluding the complex joint distributions, resulting in sensitive to disturb. However, water level system in Yangtze River is complicated and uncertain, from the long-term variation trends. Zhang [5] analyzed the annual maximum water level and stream flow during the 1877–2000 year in the Yangtze river basin, and concluded that the periods of water level changes were decreasing over time. Liu [6] explored the annual proportion of flood and dry seasons, and suggested that the water level will emerge an irregular change. As for the factors influencing water level as concerned, such as rainfall-runoff [7], tidal [4], three gorges reservoir [8], natural and anthropogenic changes [9] can dramatically affect the performance of prediction. Thus, the use of model-driven models would be disadvantageous in operational use.

The data-driven models, in the early periods, representative of shallow neural networks, including support vector regression [10,11], artificial neural network [12–16] and hybrid models [17], these models are non-parameter-based, which have the ability to approximate the distribution probability of water level system regardless of its degree of non-linearity and prior knowledge, and have been demonstrated to be effective solutions for hydrological prediction. Based on these models, some algorithms are investigated to improve prediction capabilities, such as Levenberg-Marquard [18], feed-forward back-propagation [19], generalized regression and radial basis function [20], differential evolution, artificial bee colony and ant colony optimization [21], etc.

Neural networks can be specified an arbitrary number of input features, providing support for multivariate prediction, many studies have concentrated on input features selection and extraction, such as stochastic continuum temporal combinations of water level in previous time steps [22], the objective basis on which historical water level have temporal impact on the future. Spatial combinations of different locations according to the travel time that water flows to the downstream [23], the incentive origin is that water level in different locations are spatially dependent, knowledge sharing is practical. Wavelet transform to decompose time series into wavelet components [24–27], which is useful to obtain the periodic components of the measured data, stationarity transform by difference operation that could help explore any other systematic signals for better prediction.

Despite the huge improvements in water level prediction achieved by the above methods, the shallow neural networks that do not have memory, which fail to capture the long-term evolution and can only learn a mapping between input and output patterns, thus incapability to extract the overall temporal interaction of multiple inputs. Recently, deep neural networks called deep learning, has dramatically brought about breakthroughs to the shallow neural networks [28,29], including deep belief network (DBN), convolutional neural network (CNN), stack auto-encoder (SAE) and recurrent neural network (RNN), etc., these models are composed of multiple processing layers to learn representation of features with multiple levels of abstraction, have get great achievements in processing images, video, speech and text, etc. Unlike use the echo state in RNN as a supplier of interesting dynamics from which the desired output is combined, the long short-term memory network (LSTM) [30], a typical RNN, use memory block to store information for an arbitrary duration, effective at capturing long-term temporal correlations in a sequence without suffering from the optimization hurdles that plague simple recurrent networks, which may greatly improve prediction accuracy [31].

In this paper, we propose a deep-learning-based prediction model. Herein, a novel LSTM network is used to learn generic water level features through layer-by-layer feature granulation with a greedy layer wise unsupervised learning algorithm, and the discrete wavelet transform is applied to help to extract the features preliminarily for performance improvement. The remainder of this paper is organized as follows. Section 2 introduces the prediction methodology. Section 3 introduces the study area. Section 4 proposes the prediction model. Section 5 shows the experimental results and some discussions. The conclusions are drawn in Section 6.

LSTM is a special kind of RNN, unlike the repeating module in hidden layer has a very simple structure, such as a single tanh layer in standard RNN, it is known as memory blocks in LSTM, each memory block contains one or more self-connected memory cells and three multiplicative units: input gate, output gate and forget gate. The input gate can allow incoming signal to alter the state of the memory cell or block it, the output gate allows the state of the memory cell to have an effect on other neurons or prevent it, the forget gate decides when to forget the output results and thus selects the optimal time lag for the input sequence, this special structure has the ability of bridging very long time lags.

The discrete wavelet transform (DWT) has recently become a very popular when it comes to analysis and denoising time series [32,33], which is used to decompose time series into a series of wavelet components including both spectral and temporal information, and is beneficial to the detailed analysis in contrast to the Fourier transform that only elucidates frequency information. The corresponding family of the base wavelet is expressed as:

(1) φj,k(t)=s0−j/2φ(s0−jt−kτo)

where j is the wavelet scale, k is the translation parameter, t is the time, φ is the wavelet function, s0=2 and τ0=1 are universally adopted. The wavelet coefficients of a given discrete time series x(t) can be obtained by:

(2) c(j,k)=2−j/2∫−∞+∞⁡x(t)φ(2−jt−k)dt

The coefficients c(j,k) can be divided into two parts: one is the approximation coefficient Aj(n) , which is the high-scale and low-frequency components of x(t) , represents the stationary changing parts, reflects the approximation of information. The other is the detail coefficient Dj(n) , which represents the low-scale and high-frequency components, indicates the non-stationary changing parts, makes up the details of information. The approximation and detail coefficients of the DWT for x(t) at level j can be defined as:

(3) Aj(n)=∑kϵZ⁡hk−2nAj−1(k)

(4) Dj(n)=∑kϵZ⁡hk−2nDj−1(k)

The reference decomposition level L is calculated according to:

(5) L=int[log(N)]

where L is the decomposition level and N is the length of time series.

In this study, six routine surveillance reaches in the middle and lower of Yangtze River, including Jianli, Wuhan, Jiujiang, Anqing, Wuhu and Nanjing are considered as the case study areas (Fig. 2). Water level is measured daily according to the ‘Wusong zero’ baseline, datasets are obtained from the Changjiang Maritime Safety Administration, and collected from January 1, 2010 to December 12, 2019.

Water level in Yangtze River changes daily and shows periodically trends. For instance, the Jianli reaches, in Fig. 3, during 2010–2016, water level experienced three well defined periods: months of 1, 2, 3, 12 were in dry water period; months of 4, 5, 10, 11 were in moderate water period; months of 6, 7, 8, 9 were in flood period. In addition, it would seem obviously that water levels were different and highly irregular at the same time in the past, also, from Tab. 1, it shows clearly that the maximum daily water level difference of different year were quite different, which will bring great challenges to accurate prediction.

Water level differ from the upstream to the downstream. Fig. 4 shows the changes of the proposed reaches in 2010, it appeared that water level presented synchronous trends at Jianli, Wuhan, Jiujiang and Anqing reaches over time, and gradually descended from the upstream to the downstream except Jianli reaches, the same phenomenon can be also found in Wuhu and Nanjing reaches.

In order to train the WA-LSTM model parameters and prove its predictive ability, the dataset is split into two parts, the first 70% dataset is used as the training sample, while the remaining 30% is employed as testing sample for measuring prediction performance of the proposed networks.

In this research, a new WA-LSTM model based on discrete wavelet transform and long short-term memory network for water level prediction in Yangtze River is proposed to help flood control and vessel navigation. In the provided model, water level time series are firstly decomposed into high frequency and low frequency components using wavelet transforms with different scales for a better understanding of temporal properties, then each component is put into the LSTM network for independent prediction, finally, the predicted values are reconstructed to get the predicted water level in one day ahead.

In order to confirm the effectiveness and generalization of the model, six representative reaches including Jianli, Wuhan, Jiujiang, Anqing, Wuhu and Nanjing are applied to study, and several comparisons are developed, including the practicable of temporal and spatial combination, the sensitivity of mother wavelet types and decomposition levels, the efficiency of the state-of-the-art models contained LSTM, WA-ANN and WA-ARIMA. Comprehensive research finds out that 5 or 6 days lag observations as input features using Meyer wavelet transform with decomposition level 4 provides the best performance, which less than 0.045 m on RMSE and less than 0.035 m on MAE in general, extraordinary has only 0.028 m on RMSE and 0.019 m on MAE at Jiujiang reaches. The results are superior to those of competing models, and demonstrates that the WA-LSTM model has strong applicability and generalization, provides references to further research on water level prediction in Yangtze River.

Future research would look into more comprehensive prediction that incorporates with the temporal characteristics like dry season and flood season, or the weather forecasting such as rainstorm, or the waterway tributary characteristics. Furthermore, it would be interesting to investigate other deep learning models for water level prediction.