A real-time probabilistic channel flood-forecasting model based on the Bayesian particle filter approach

Highlights

• A real-time flood-forecasting model is proposed by assimilating real-time stage observations into a hydraulic model.

• Particle filter is adopted as the data assimilation method to update/correct stage, discharge, and roughness coefficient.

• Synthetic experiments are employed to explore model settings and evaluate model performance.

• Model performance is compared with previous studies using Kalman Filter based methods.

• Probabilistic predictions provided by the model are more accurate and reliable.

Abstract

Reliable real-time probabilistic flood forecasting is critical for effective water management and flood protection all over the world. In this study, we develop a real-time probabilistic channel flood-forecasting model by combining a channel hydraulic model with the Bayesian particle filter approach. The new model is tested in the upstream river reach of Three Gorges Dam (TGD) on the Yangtze River, China. Stage observations at seven hydrological stations are used simultaneously to adjust the Manning's roughness coefficients and to update discharges and stages along the river reach to attain reliable probabilistic flood forecasting. The synthetic experiments are applied to demonstrate the new model's correction and forecasting performances. The real-world experiments show that the new model can make accurate flood forecasting as well as derive reliable intervals for different confidence levels. The new probabilistic flood forecasting model not only outperforms the existing deterministic channel flood-forecasting models in accuracy, but also provides a more robust tool with which to incorporate uncertainty into flood-control efforts.

Introduction

Flood disaster is a serious threat to people and property all over the world. Flooding in the Yangtze River in China is a major concern as large economic and population centers sit along the river. For example, the catastrophic flood in 1998 resulted in 3704 deaths, 15 million people left homeless, and economic losses of US$25 billion (Fang and Wang, 2000, Zong and Chen, 2000). The construction of dams has been adopted as an effective measure to regulate and mitigate flood damage. The Three Gorges Dam (TGD) located on the middle reaches of the Yangtze River is the largest flood-control and hydroelectric project in the world. Its operation commenced in 2006 with a flood-control capacity of 22.15 billion cubic meters. Real-time flood forecasting provides essential information for real-time scheduling of dam operations. For example, the TGD can be operated to release water stored in the reservoir before the onset of a predicted flood event, enhancing its regulatory capacity (Fang et al., 2012). However, accurate and reliable flood forecasting in the Yangtze River remains a challenge (Minglei et al., 2010).

Currently, hydraulic models are being used to forecast discharges and stages at cross-sections along rivers and they have been used widely in channel flood forecasting (Chaudhry, 2007, Chow et al., 1988, Costabile and Macchione, 2015, Han et al., 2011, Lamberti and Pilati, 1996, Nguyen and Kawano, 1995, Saavedra et al., 2003). Although hydraulic models are able to simulate the physical processes of flood routing, their performances are highly dependent on the appropriate preparation of their inputs and parameterization and the assumptions of their governing equations (Balica et al., 2013, Costabile and Macchione, 2015). With recent advances in both automatic hydrological monitoring and information transmission technologies, real-time hydrological observations are available for incorporation into hydraulic models to improve their forecasting performance through data assimilation approaches (Costabile and Macchione, 2015, Madsen and Skotner, 2005, Merkuryeva et al., 2014, Schumann et al., 2009, Werner et al., 2013). Data assimilation approaches update model states and parameters against observations to obtain reliable initial conditions and model structures for the next time step's forecasting (Liu et al., 2012a, Liu and Gupta, 2007). One widely used sequential data assimilation methods is the Kalman Filter (KF). The traditional standard KF method can consider both observational and model errors, but is restricted to linear systems (Liu et al., 2016). Recently, the ensemble KF, which is capable of dealing efficiently with nonlinear models, has become a popular approach for assimilating observational data for improving hydraulic models in real-time flood forecasting (Andreadis et al., 2007, Lai et al., 2013, Neal et al., 2007, Neal et al., 2009, Paiva et al., 2013, Schumann et al., 2009).

The ensemble KF, as well as other variants of the KF, has an inherent assumption that the prior distribution of model states observes a Gaussian distribution so that the posterior states are only determined by the first two moments of the prior density. This assumption rarely holds in hydraulic models (Pasetto et al., 2012, Weerts and El Serafy, 2006). Recent researches have allowed for relaxing the assumption of Gaussian priors in EnKF type filters (Anderson, 2010, Borup et al., 2015), but still can't obtain the full flexibility. By contrast, the particle filter (PF), a sequential Monte Carlo method based on the Bayesian theory, can relax the need for restrictive assumptions regarding the forms of the probability densities, i.e., it can handle the propagation of non-Gaussian distributions through nonlinear hydrological and hydraulic models (Bi et al., 2015, Liu et al., 2012b, Moradkhani, 2008, Moradkhani et al., 2005, Noh et al., 2011, Noh et al., 2014, Noh et al., 2012, Seo et al., 2014, Thirel et al., 2013). The main drawback of the PF is that it is more computationally intensive than EnKF, requiring more ensemble members to represent the prior distributions at a reasonable level (Liu et al., 2012b). Recently, Matgen et al. (2010) and Giustarini et al. (2011) successfully used the PF method to assimilate remote-sensing derived water-level data into hydraulic models and achieved significant reductions in the uncertainties of water-level and discharge predictions. However, the Manning's roughness coefficients in their hydraulic models were set as constant values, ignoring the variation of the Manning's roughness coefficients through the course of a flooding event. Kim et al. (2013) examined the inflow and Manning's roughness coefficients of a small-river reach and highlighted the importance of being able to track dynamically the changes of these two variables.

Currently, data assimilation based on the KF method has been applied in several studies to improve real-time channel flood forecasting in the Yangtze River. Ge et al. (2005) constructed a comprehensive state variable vector for the KF method to update a hydraulic model. Wu and Wang (2008) applied the KF method to update the Manning's roughness coefficients dynamically. Wu et al. (2013) developed an alternative coupled method to compute stages and discharges alternately using the KF. In all of the above studies, either the state variables or the parameters in the hydraulic model were updated, but not simultaneously.

To improve flood forecasting for the TGD, we aim to develop a new modeling approach using the PF to derive probabilistic ensemble flood forecasts. In this study, a real-time probabilistic channel flood-forecasting model is developed for the river reach from Cuntan to the TGD, by assimilating real-time observed stages at multiple hydrological stations along the river channel using the PF. This approach not only updates model state variables (i.e., discharge and stage), but also corrects model parameters (i.e., Manning's roughness coefficient).

The rest of this paper is organized as follows. In the methodology section, the real-time channel flood-forecasting model is formulated by coupling a hydraulic model with the PF. Next, the coupled modeling approach is examined against synthetic data to test the validity of the developed modeling approach. In the real-world experiment section, we evaluate and verify the new model's applicability to three observed flooding events. In the discussion section, we compare the proposed modeling approach with other models applied previously to the Three Gorges river reach, and we highlight both its novel capability in achieving improved deterministic predictions and its reliability in quantifying forecasting uncertainties.