Reduction of the uncertainties in the water level-discharge relation of a 1D hydraulic model in the context of operational flood forecasting

Abstract This paper presents a data-driven hydrodynamic simulator based on the 1-D hydraulic solver dedicated to flood forecasting with lead time of an hour up to 24 h. The goal of the study is to reduce uncertainties in the hydraulic model and thus provide more reliable simulations and forecasts in real time for operational use by the national hydrometeorological flood forecasting center in France. Previous studies have shown that sequential assimilation of water level or discharge data allows to adjust the inflows to the hydraulic network resulting in a significant improvement of the discharge while leaving the water level state imperfect. Two strategies are proposed here to improve the water level-discharge relation in the model. At first, a modeling strategy consists in improving the description of the river bed geometry using topographic and bathymetric measurements. Secondly, an inverse modeling strategy proposes to locally correct friction coefficients in the river bed and the flood plain through the assimilation of in situ water level measurements. This approach is based on an Extended Kalman filter algorithm that sequentially assimilates data to infer the upstream and lateral inflows at first and then the friction coefficients. It provides a time varying correction of the hydrological boundary conditions and hydraulic parameters. The merits of both strategies are demonstrated on the Marne catchment in France for eight validation flood events and the January 2004 flood event is used as an illustrative example throughout the paper. The Nash–Sutcliffe criterion for water level is improved from 0.135 to 0.832 for a 12-h forecast lead time with the data assimilation strategy. These developments have been implemented at the SAMA SPC (local flood forecasting service in the Haute-Marne French department) and used for operational forecast since 2013. They were shown to provide an efficient tool for evaluating flood risk and to improve the flood early warning system. Complementary with the deterministic forecast of the hydraulic state, the estimation of an uncertainty range is given relying on off-line and on-line diagnosis. The possibilities to further extend the control vector while limiting the computational cost and equifinality problem are finally discussed.

[1]  John C. Gille,et al.  Inverse modeling of carbon monoxide surface emissions using Climate Monitoring and Diagnostics Laboratory network observations , 2002 .

[2]  Yuqiong Liu,et al.  Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework , 2007 .

[3]  Hamid Moradkhani,et al.  Toward reduction of model uncertainty: Integration of Bayesian model averaging and data assimilation , 2012 .

[4]  C. Diks,et al.  Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation , 2005 .

[5]  D. Lettenmaier,et al.  Prospects for river discharge and depth estimation through assimilation of swath‐altimetry into a raster‐based hydrodynamics model , 2007 .

[6]  J. Kirchner.  Getting the right answers for the right reasons: Linking measurements, analyses, and models to advance the science of hydrology , 2006 .

[7]  Seong Jin Noh,et al.  Advancing data assimilation in operational hydrologic forecasting: progresses, challenges, and emerging opportunities , 2012 .

[8]  C. M. DeChant,et al.  Improving the characterization of initial condition for ensemble streamflow prediction using data assimilation , 2011 .

[9]  Samuel Buis,et al.  PALM: a computational framework for assembling high-performance computing applications , 2006 .

[10]  Ashish Sharma,et al.  Bayesian calibration and uncertainty analysis of hydrological models: A comparison of adaptive Metropolis and sequential Monte Carlo samplers , 2011 .

[11]  Florian Pappenberger,et al.  A data assimilation approach to discharge estimation from space , 2009 .

[12]  Keith Beven,et al.  Uncertainty and equifinality in calibrating distributed roughness coefficients in a flood propagation model with limited data , 1998 .

[13]  Kuolin Hsu,et al.  Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter , 2005 .

[14]  J. Stedinger,et al.  Appraisal of the generalized likelihood uncertainty estimation (GLUE) method , 2008 .

[15]  J. S. Verkade,et al.  Estimation of Predictive Hydrological Uncertainty using Quantile Regression , 2010 .

[16]  Christopher K. Wikle,et al.  Atmospheric Modeling, Data Assimilation, and Predictability , 2005, Technometrics.

[17]  C. M. DeChant,et al.  Radiance data assimilation for operational snow and streamflow forecasting , 2011 .

[18]  Delwyn Moller,et al.  Estimation of bathymetric depth and slope from data assimilation of swath altimetry into a hydrodynamic model , 2008 .

[19]  Peter M. Atkinson,et al.  Flood inundation model updating using an ensemble Kalman filter and spatially distributed measurements , 2007 .

[20]  Jaap Schellekens,et al.  Recent developments in operational flood forecasting in England, Wales and Scotland , 2009 .

[21]  J. M. Van Der Knijff,et al.  LISFLOOD : a GIS-based distributed model for river basin scale water balance and flood simulation , 2008 .

[22]  R. De Keyser,et al.  Towards the sequential assimilation of SAR-derived water stages into hydraulic models using the Particle Filter: proof of concept , 2010 .

[23]  Soroosh Sorooshian,et al.  Evolution of ensemble data assimilation for uncertainty quantification using the particle filter‐Markov chain Monte Carlo method , 2012 .

[24]  Didier Lucor,et al.  Interactive comment on “Towards predictive data-driven simulations of wildfire spread – Part I: Reduced-cost Ensemble Kalman Filter based on a Polynomial Chaos surrogate model for parameter estimation” , 2014 .

[25]  Henrik Madsen,et al.  Adaptive state updating in real-time river flow forecasting—a combined filtering and error forecasting procedure , 2005 .

[26]  A. Weerts,et al.  Particle filtering and ensemble Kalman filtering for state updating with hydrological conceptual rainfall‐runoff models , 2006 .

[27]  G. Thirel,et al.  A past discharges assimilation system for ensemble streamflow forecasts over France - Part 1: Description and validation of the assimilation system , 2010 .

[28]  K. Beven,et al.  Development of a European flood forecasting system , 2003 .

[29]  Nelly Jean-Baptiste Dit Parny.  Assimilation de données pour l'estimation de l'état hydraulique d'un aménagement hydroélectrique du Rhône équipé de la commande prédictive , 2011 .

[30]  D. Seo,et al.  Ensemble prediction and data assimilation for operational hydrology , 2014 .

[31]  Johan Valstar,et al.  A representer‐based inverse method for groundwater flow and transport applications , 2004 .

[32]  George Kuczera,et al.  Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors , 2010 .

[33]  Cajo J. F. ter Braak,et al.  Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation , 2008 .

[34]  Dong-Jun Seo,et al.  Real-Time Variational Assimilation of Hydrologic and Hydrometeorological Data into Operational Hydrologic Forecasting , 2003 .

[35]  Dong Jun Seo,et al.  Automatic state updating for operational streamflow forecasting via variational data assimilation , 2009 .

[36]  Soroosh Sorooshian,et al.  Dual state-parameter estimation of hydrological models using ensemble Kalman filter , 2005 .

[37]  DATA ASSIMILATION AND DISTRIBUTED FLASH FLOOD MODELING , 2007 .

[38]  Hamid Moradkhani,et al.  Examining the effectiveness and robustness of sequential data assimilation methods for quantification of uncertainty in hydrologic forecasting , 2012 .

[39]  Dusanka Zupanski,et al.  An ensemble data assimilation system to estimate CO2 surface fluxes from atmospheric trace gas observations , 2005 .

[40]  N. Gouta,et al.  A finite volume solver for 1D shallow‐water equations applied to an actual river , 2002 .

[41]  A. Piacentini,et al.  Correction of upstream flow and hydraulic state with data assimilation in the context of flood forecasting , 2010 .

[42]  W. Kinzelbach,et al.  Real‐time groundwater flow modeling with the Ensemble Kalman Filter: Joint estimation of states and parameters and the filter inbreeding problem , 2008 .

[43]  Jery R. Stedinger,et al.  Appraisal of the generalized likelihood uncertainty estimation (GLUE) method , 2008 .

[44]  Keith Beven,et al.  A dynamic TOPMODEL , 2001 .