Deep dependence in hydroclimatological variables

Abstract

Among artificial intelligence (AI) models, the recurrent neural network (RNN)-based temporal AI, long short-term memory (LSTM) model has been successfully applied to hydroclimatological time series due to its long-lead-time predictions. However, few logical reasons and explanations for its performance by investigating and discovering its deep structure have been made. Therefore, research on the outlook for LSTM models was conducted in the current study by investigating its hidden states and was focused on the dependence structures and statistical behaviors. Here, the three most critical datasets of hydroclimatological variables were applied as the representative climate index data for the Pacific Decadal Oscillation (PDO) and two critical rivers, the Colorado River and Nile River. The results indicate that each hidden unit is responsible for different frequency variations in the input data and is sensitive to special occasions of input data. This separation of the roles of the hidden units leads to variations in the dependence structure along with the numbers of hidden units and the unique characteristics of statistical behaviors. Specifically, the dependence decreases along with the increase in the number of hidden units until the complex structure of the original input data is appropriately separated into the independent hidden units. Overall, the current study reveals that there is a relationship between attaining maturity of the deep learning LSTM model and the dependence structure of the hidden units, especially for hydroclimatological variables, and concludes that the dependence structure of the hidden units can provide valuable information to further extract the explanations of the deep learning model and to select an appropriate model structure, including the number of hidden units. This finding can help to simulate and predict climate and hydrologic conditions whose long-term behaviors are critical for water resource management. Graphical Abstract: (Figure presented.) © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.