Streamflow Forecasting Using a Long Short-Term Memory Network

1 INTRODUCTION

The reliable prediction of streamflow plays a significant role in reservoir management, risk evaluation, irrigation and flood prevention, and water planning and management. Considerable efforts have been made to develop model for streamflow and precipitation forecasting over the past few decades. Generally, these methods can be divided into two categories: process-based model and data-driven model.

Process-based models usually have the advantage of assisting physically understanding about the hydrological process. However, they are subject to many simplification assumptions or excessive data requirements about the physics of the catchment. One the other hand, data-driven models, mainly emphasize the direct role of historical observations. They have gained popularity in hydrological prediction due to their simplicity, rapid development time, less information requirements and ease of implementation in real time. At present, statistical models and machine learning methods are often employed to develop data-driven models.

Traditional statistical data-driven methods including multiple linear regression, autoregressive moving average (AMRA) and its variants, have been applied for streamflow forecasting since 1970s. Previous studies have shown that statistical models produce satisfactory prediction when the time series are linear or near-linear, but they perform badly in nonstationary series as they poorly capture the nonlinear and nonstationary patterns hidden in the series. However, hydrological forecasting is characterized by high complexity, dynamism and non-stationarity. More recently, machine learning techniques have received considerable attention from hydrologists for their strong deep learning ability and suitability for modeling the complex and nonlinear process. A variety of machine learning models such as artificial neural networks (ANN), support vector regression (SVR), genetic programming (GP), and adaptive neuro-fuzzy inference system (ANFIS) have shown their superior performance for forecasting nonlinear hydrological process.

The central idea behind LSTM architecture is a memory cell, which can maintain its state over time, and nonlinear gating units, which regulate the information flow into and out of the cell. LSTM networks have subsequently prove to be more effective than conventional RNNs. Stimulated by the success of LSTM on many domains related to sequential data, a few studies have explored the power of LSTM on hydrological problems and obtained promising results.

The objective of this study is to explore the potential of the LSTM in forecasting monthly hydrological time series, and developed a model containing a two-layer LSTM with a dense layer atop advance the multi-step ahead prediction accuracy. Cuntan and Hankou monthly streamflow volume data, are considered in this study. Additionally, MLP was employed as the benchmark model.

2 a lstm model for hydrological time series forecasting

The procedure of the LSTM approach for hydrological time series forecasting is described as follows.

• Let X, t= 1, 2, ..., n denote the time series. Divide time series into training and testing sets, X_train and X_test
• Decide the lag-time (q, the number of previous time steps to use as input variables) and the lead-time (p, the number of next time period we want to predict) and sliding windows method to create a combination of inputs and outputs. That is, .
• Use training set to train the network (containing two-layer LSTM and a dense layer atop) for p-step ahead forecast.
• Apply the trained network to predict p-step ahead values.

3 appilication

Monthly streamflow volume data from Cuntan and Hankou stations in Yangtze River basin, China, were selected for the applications of the developed LSTM approach. The Yangtze River is the longer river in China and the third longest river in the world at the length of 6280km. Cuntan station is the inflow gauge point of the upper Yangtze River, while Hankou station is located at the middle Yangtze River. Both of the data sets spans for the period 1959-2008, consisting of 600 records. The last 10 years records are used as testing data.

In this study, We explored the potential use of LSTM on 1-, 3-, 6-, 9-, and 12-steps ahead forecasting with previous streamflow data (3 month-lag) to camper the performance of a three-layer MLP. All the hyper-parameters of neural network (NN), was set though trial-and-error procedures. And a dropout method (Srivastava et al., 2014) was applied to prevent overfitting.

The RMSE, NSE, MARE statistics of the LSTM, MLP in training and testing are given in Tables 1. The best error measures are highlighted in red. The tables point that the LSTM outperformed MLP in terms of all the performance criteria.

As shown in the results, the model prediction accuracy reduced as the prediction steps increase. For the one-step ahead prediction, LSTM and MLP showed satisfying results, with low RMSE and MARE, and high NSE. When turning the prediction time steps to three, the performance of MLP deteriorated immediately. With longer time steps, MLP performance decreased continually. While the performance of LSTM did not decrease quickly with longer time steps.

4 Conclusions

Due to nonlinear and non-stationary nature of streamflow, novel models are required to predict streamflow. Long short-term memory (LSTM) is a popular neural network (NN) suitable for sequential data. This paper explored the potential use of LSTM in streamflow forecasting, and proposed a model containing a two-layer LSTM with dense layer atop, perform multi-step ahead prediction. The model was applied to predict monthly streamflow at Cuntan and Hankou station of Yangtze River, and compared with MLP. The obtained results indicate that LSTM is applicable for streamflow forecasting, and significantly outperform MLP. LSTM is superior alternatives when longer time steps ahead prediction are expected.