Integrated Markov chains and uncertainty analysis techniques to more accurately forecast floods using satellite signals

Abstract

Utilizing the readily available, inexpensive, remotely-sensed satellite data products in combination with Markov Chain methods for estimating water levels and discharge anywhere along the vast river networks around the world is one of the most interesting and promising fields in hydrology. This study presents two new extensions of Markov Chain (MC) methods, namely the Online-Markov Chains (O-MC) and Extreme Online-Markov Chains (EO-MC) methods to improve the prediction accuracy. The O-MC method has the advantage of the online implementation of the correct variable states, and the EO-MC method has the advantage of online updating the Markov Matrix (MM) along with the online implementation of the correct variable states. The new O-MC and the EO-MC methods were evaluated using short-term satellites signal predictions for six different case study rivers. The Monte Carlo uncertainty analysis was used to measure the reliability of the new MC-based methods. Each model was developed 1000 times to calculate two indices, namely the 95 Percent Predicted Uncertainties (95PPU) and average distance factor (d-factor). The performances of MC and two extensions of O-MC and EO-MC were also examined for cases where we lack the training data. The Training Percent (TrPr) of the entire dataset gradually decreased from 90% to 1%, and the performance of the models in producing accurate future signals in the non-observed dataset is calculated. The Input Variable Imitation (IVI) problem was considered for the MC-based methods, and the results were compared with the Linear Regression (LR), Multi-Layer Perceptron (MLP), Extreme Learning Machine (ELM), and Radial Basis Function (RBF) regression methods. The results showed that the performance of EO-MC and O-MC are better than the simple MC method. In addition, it is concluded that EO-MC and O-MC have very similar performance in the uncertainty analysis and both methods are robust techniques. The main advantage of EO-MC compared with the O-MC method is highlighted when the number of training samples are very low. Finally, considering the IVI problem, the new O-MC and EO-MC methods significantly outperformed the LR, MLP, ELM, and RBF methods.