Improving the Reliability of Probabilistic Multi-Step-Ahead Flood Forecasting by Fusing Unscented Kalman Filter with Recurrent Neural Network

It is fundamentally challenging to quantify the uncertainty of data-driven flood forecasting. This study introduces a general framework for probabilistic flood forecasting conditional on point forecasts. We adopt an unscented Kalman filter (UKF) post-processing technique to model the point forecasts made by a recurrent neural network and their corresponding observations. The methodology is tested by using a long-term 6-h timescale inflow series of the Three Gorges Reservoir in China. The main merits of the proposed approach lie in: first, overcoming the under-prediction phenomena in data-driven flood forecasting; second, alleviating the uncertainty encountered in data-driven flood forecasting. Two commonly used artificial neural networks, a recurrent and a static neural network, were used to make the point forecasts. Then the UKF approach driven by the point forecasts demonstrated its competency in increasing the reliability of probabilistic flood forecasts significantly, where predictive distributions encountered in multi-step-ahead flood forecasts were effectively reduced to small ranges. The results demonstrated that the UKF plus recurrent neural network approach could suitably extract the complex non-linear dependence structure between the model’s outputs and observed inflows and overcome the systematic error so that model reliability as well as forecast accuracy for future horizons could be significantly improved.

[1]  Li-Chiu Chang,et al.  Reinforced recurrent neural networks for multi-step-ahead flood forecasts , 2013 .

[2]  Vladan Babovic,et al.  Application of hybrid Kalman filter for improving water level forecast , 2016 .

[3]  A. Raftery,et al.  Probabilistic forecasts, calibration and sharpness , 2007 .

[4]  Hamid Moradkhani,et al.  Improved Bayesian multimodeling: Integration of copulas and Bayesian model averaging , 2014 .

[5]  Yaonan Wang,et al.  Extended and Unscented Kalman filtering based feedforward neural networks for time series prediction , 2012 .

[6]  Li-Chiu Chang,et al.  Explore a deep learning multi-output neural network for regional multi-step-ahead air quality forecasts , 2019, Journal of Cleaner Production.

[7]  Huanhuan Ba,et al.  Evaluation of the BMA probabilistic inflow forecasts using TIGGE numeric precipitation predictions based on artificial neural network , 2018 .

[8]  Florian Pappenberger,et al.  Forecaster priorities for improving probabilistic flood forecasts , 2013 .

[9]  Jianzhong Zhou,et al.  Flood Forecasting Based on an Improved Extreme Learning Machine Model Combined with the Backtracking Search Optimization Algorithm , 2018, Water.

[10]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[11]  N. K. Goel,et al.  Improving real time flood forecasting using fuzzy inference system , 2014 .

[12]  V. Singh,et al.  Novel Hybrid Evolutionary Algorithms for Spatial Prediction of Floods , 2018, Scientific Reports.

[13]  P. Coulibaly,et al.  Two decades of anarchy? Emerging themes and outstanding challenges for neural network river forecasting , 2012 .

[14]  F. Chang,et al.  Explore an evolutionary recurrent ANFIS for modelling multi-step-ahead flood forecasts , 2019, Journal of Hydrology.

[15]  Stefania Tamea,et al.  Verification tools for probabilistic forecasts of continuous hydrological variables , 2006 .

[16]  Alex J. Cannon.  Quantile regression neural networks: Implementation in R and application to precipitation downscaling , 2011, Comput. Geosci..

[17]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[18]  Maria-Helena Ramos,et al.  Willingness-to-pay for a probabilistic flood forecast: a risk-based decision-making game , 2016 .

[19]  J. Nash,et al.  River flow forecasting through conceptual models part I — A discussion of principles☆ , 1970 .

[20]  Faming Liang,et al.  Explicitly integrating parameter, input, and structure uncertainties into Bayesian Neural Networks for probabilistic hydrologic forecasting , 2011 .

[21]  Shenglian Guo,et al.  Methodology that improves water utilization and hydropower generation without increasing flood risk in mega cascade reservoirs , 2018 .

[22]  Paulin Coulibaly,et al.  Bayesian Flood Forecasting Methods: A Review , 2017 .

[23]  Peng Jiang,et al.  State estimation of conceptual hydrological models using unscented Kalman filter , 2018, Hydrology Research.

[24]  Chandranath Chatterjee,et al.  A wavelet-based non-linear autoregressive with exogenous inputs (WNARX) dynamic neural network model for real-time flood forecasting using satellite-based rainfall products , 2016 .

[25]  Ezio Todini.  From HUP to MCP: Analogies and extended performances , 2013 .

[26]  Fi-John Chang,et al.  A nonlinear spatio-temporal lumping of radar rainfall for modeling multi-step-ahead inflow forecasts by data-driven techniques , 2016 .

[27]  Lifeng Luo,et al.  Unscented weighted ensemble Kalman filter for soil moisture assimilation , 2020 .

[28]  Florian Pappenberger,et al.  HESS Opinions "Forecaster priorities for improving probabilistic flood forecasts" , 2013 .

[29]  Manolis I. A. Lourakis.  A Brief Description of the Levenberg-Marquardt Algorithm Implemented by levmar , 2005 .

[30]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[31]  Zhongbo Yu,et al.  Coupled Hydraulic and Kalman Filter Model for Real-Time Correction of Flood Forecast in the Three Gorges Interzone of Yangtze River, China , 2013 .

[32]  William W.-G. Yeh,et al.  Real‐Time Optimal Flood Control Decision Making and Risk Propagation Under Multiple Uncertainties , 2017 .

[33]  Shenglian Guo,et al.  Real-time error correction method combined with combination flood forecasting technique for improving the accuracy of flood forecasting , 2015 .

[34]  Soroosh Sorooshian,et al.  Short‐Term Precipitation Forecast Based on the PERSIANN System and LSTM Recurrent Neural Networks , 2018, Journal of Geophysical Research: Atmospheres.

[35]  Hui Li,et al.  Deep Learning with a Long Short-Term Memory Networks Approach for Rainfall-Runoff Simulation , 2018, Water.

[36]  K. P. Sudheer,et al.  Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models , 2018 .

[37]  Stefan Broda,et al.  Forecasting groundwater levels using nonlinear autoregressive networks with exogenous input (NARX) , 2018, Journal of Hydrology.

[38]  Li-Chiu Chang,et al.  Online multistep-ahead inundation depth forecasts by recurrent NARX networks , 2012 .

[39]  Kuolin Hsu,et al.  HESS Opinions: Incubating deep-learning-powered hydrologic science advances as a community , 2018, Hydrology and Earth System Sciences.

[40]  Sanjeet Kumar,et al.  Reservoir Inflow Forecasting Using Ensemble Models Based on Neural Networks, Wavelet Analysis and Bootstrap Method , 2015, Water Resources Management.

[41]  Shenglian Guo,et al.  Risk analysis for flood control operation of seasonal flood-limited water level incorporating inflow forecasting error , 2014 .

[42]  Eric Huang,et al.  Real-time multi-step-ahead water level forecasting by recurrent neural networks for urban flood control , 2014 .

[43]  Gregory B. Miller,et al.  Conditionally Minimax Nonlinear Filter and Unscented Kalman Filter: Empirical Analysis and Comparison , 2019, Autom. Remote. Control..

[44]  Demetris Koutsoyiannis,et al.  Comparison of stochastic and machine learning methods for multi-step ahead forecasting of hydrological processes , 2019, Stochastic Environmental Research and Risk Assessment.

[45]  Kolbjørn Engeland,et al.  Probabilistic postprocessing models for flow forecasts for a system of catchments and several lead times , 2014 .

[46]  Chong-Yu Xu,et al.  Hydrological uncertainty processor based on a copula function , 2018 .

[47]  Lihua Xiong,et al.  An empirical method to improve the prediction limits of the GLUE methodology in rainfall–runoff modeling , 2008 .

[48]  Madhu S. Nair,et al.  Adaptive Importance Sampling Unscented Kalman Filter based SAR image super resolution , 2019, Comput. Geosci..

[49]  Mark E. Borsuk,et al.  Probabilistic programming: A review for environmental modellers , 2019, Environ. Model. Softw..

[50]  Roman Krzysztofowicz,et al.  Ensemble Bayesian forecasting system Part I: Theory and algorithms , 2015 .

[51]  Giorgio Boni,et al.  A hydrometeorological approach for probabilistic flood forecast , 2005 .

[52]  Jingjing Xie,et al.  Daily reservoir inflow forecasting using multiscale deep feature learning with hybrid models , 2016 .