Sensitivity Analysis of the Mascaret model on the Odet River A-L - PowerPoint PPT Presentation

Sensitivity Analysis of the Mascaret model on the Odet River A-L Tiberi-Wadier 1 N Goutal 2 S Ricci 3 P Sergent 4 C Monteil 5 1 Cerema Eau, Mer et Fleuves, Plouzan´ e, France 2 EDF R&D et Laboratoire d’Hydraulique Saint-Venant, Chatou, France 3 CECI, UMR5318, CNRS/CERFACS, Toulouse, France 4 Cerema Eau, Mer et Fleuves, Margny-Les-compi` egne, France 5 EDF R&D, Chatou TELEMAC-MASCARET USER CLUB - Toulouse, 16-17 October, 2019

Introduction Framework SCHAPI and SPC (flood forecasting services in France): majority use deterministic approach for hydrologic and hydraulic models Since inputs and parameters are uncertain, an ensemble approach should be favoured The cascade of uncertainty in a chained ensemble framework is being investigated on the Odet catchment, in Western Brittany Global Sensitivity Analysis (GSA) on the MASCARET model in order to rank the major sources of uncertainties at three observing stations for the simulated water level, considering uncertainties in the upstream and downstream boundary conditions in the area distributed friction parameters values (Strickler coefficients) A-L Tiberi-Wadier 2 / 23 SA of the Mascaret model on the river Odet

Study area Odet catchment coastal river in Western Britany (Quimper, Finistere) astronomical tide ranges between 1.40 and 5.55 m 720 km 2 total lenght of about 60 km Figure: The rivers Odet, 2 tributaries : Jet and Steir Steir and Jet with the rivers location of the hydrologic stations. A-L Tiberi-Wadier 3 / 23 SA of the Mascaret model on the river Odet

Outline 1 Hydrologic and hydraulic models 2 Global Sensitivity Analysis (GSA) Variance decomposition and Sobol’ indices Uncertainty space for GSA Results of GSA - 3 different configurations 3 Conclusion and further work A-L Tiberi-Wadier 4 / 23 SA of the Mascaret model on the river Odet

Outline 1 Hydrologic and hydraulic models 2 Global Sensitivity Analysis (GSA) Variance decomposition and Sobol’ indices Uncertainty space for GSA Results of GSA - 3 different configurations 3 Conclusion and further work A-L Tiberi-Wadier 5 / 23 SA of the Mascaret model on the river Odet

Hydrologic modeling - 3 upstream sub-catchments MORDOR-TS hydrologic model spatialized and continuous conceptual rainfall-runoff model provides hydrologic streamflows at Treodet, Kerjean and Ty-Planche 8 free parameters Figure: The rivers Odet, multi-objective function using Steir and Jet with the caRamel genetic algorithm location of the hydrologic stations. A-L Tiberi-Wadier 6 / 23 SA of the Mascaret model on the river Odet

Hydraulic modeling Mascaret model MASCARET: 1D model based on Saint-Venant equations covers the dowstream part of the catchment, focuses on urban areas Objective: forecating water level at the three observing stations Kervir, Moulin-Vert and Justice Strickler coefficients 12 zones retained riverbed: values ranging [15, 37] Figure: 12 zones of friction flood plains: values ranging [1, 34] coefficents A-L Tiberi-Wadier 7 / 23 SA of the Mascaret model on the river Odet

Outline 1 Hydrologic and hydraulic models 2 Global Sensitivity Analysis (GSA) Variance decomposition and Sobol’ indices Uncertainty space for GSA Results of GSA - 3 different configurations 3 Conclusion and further work A-L Tiberi-Wadier 8 / 23 SA of the Mascaret model on the river Odet

Global Sensitivity Analysis Variance decomposition and Sobol’ indices Notations input : X = ( X 1 , X 2 , ..., X k ) X = ( X 1 , X 2 , ..., X k ) vary on their uncertainty domain output : Y = f ( X ) Variance decomposition Hoeffing decomposition of the variance V ( Y ) : � � � V ( Y ) = V i + V i , j + ... + V 1 , 2 , 3 ,..., K (1) i i j > i where V i is the elementary contribution of X i to V(Y), V i , j is the contribution due to interactions between X i et X j to V(Y), V 1 , 2 ,..., k is the contribution due to interaction between all inputs to V(Y). A-L Tiberi-Wadier 9 / 23 SA of the Mascaret model on the river Odet

Global Sensitivity Analysis Variance decomposition and Sobol’ indices Sobol’ indices Dividing 1 this equation by V ( Y ) leads to � � � S i + S i , j + ... + S 1 , 2 , 3 ,..., K = 1 (2) i i j > i S i : 1 st order Sobol index → normalized elementary contribution of X i to V(Y). Sobol’ indices apportion the variance of the output Y = f ( X ) with X = ( X 1 , X 2 , ..., X k ), to the variation of different inputs ( X 1 , ..., X k ) on their uncertainty domain. In the following: there is very few interaction between the input parameters → only the first order Sobol’ indices will be shown. A-L Tiberi-Wadier 10 / 23 SA of the Mascaret model on the river Odet

Outline 1 Hydrologic and hydraulic models 2 Global Sensitivity Analysis (GSA) Variance decomposition and Sobol’ indices Uncertainty space for GSA Results of GSA - 3 different configurations 3 Conclusion and further work A-L Tiberi-Wadier 11 / 23 SA of the Mascaret model on the river Odet

Uncertainty space for GSA Three types of uncertain inputs minor and flood plain friction coefficients ( Ks i and Ks iM ) 3 hydrologic upstream time series maritime boundary time series Quantity of interest Y measured water level at a forecast station at a specific time GSA applied over time at Kervir, Moulin-Vert and Justice Figure: 12 zones of friction coefficents A-L Tiberi-Wadier 12 / 23 SA of the Mascaret model on the river Odet

Uncertainty space for GSA Friction coefficients and Hydrologic input Friction coefficients Probability Density Functions: supposed to be uniform distribution centered on the calibrated value, width of 5 on each side Hydrologic Ensemble Forecast : 99 members The HEF system is setup by perturbating the value of the 8 free parameters of MORDOR-TS. PDF of the 8 uncertain variables are supposed to be uniform U [ V min , V max ] V min and V max : determined by the realization of a set of calibrations of the MORDOR-TS model over 2 years periods ensemble created with a Halton sequence of 99 members uncertainty in the hydrologic input: index drawn uniform between 1 and 99. A-L Tiberi-Wadier 13 / 23 SA of the Mascaret model on the river Odet

Uncertainty space for GSA Maritime boundary condition Time dependent boundary condition water heigth time-dependent sampling procedure must preserve temporal correlation of errors Time varying perturbation applied on the storm surge s , supposed to be a Gaussian Process Karhunen Loeve decomposition of s 99 perturbed storm surge time series generated uncertainty in the maritime boundary condition: index drawn uniform between 1 and 99 A-L Tiberi-Wadier 14 / 23 SA of the Mascaret model on the river Odet

Uncertainty space for GSA Comparison of the standard deviation of upstream and donwstream perturbations Upstream streamflows → converted into water level by their rating curve Comparison The magnitude of the imposed perturbations are of the same order for the four boundary conditions Figure: std of the upstream and dowstream perturbations (cm) A-L Tiberi-Wadier 15 / 23 SA of the Mascaret model on the river Odet

Outline 1 Hydrologic and hydraulic models 2 Global Sensitivity Analysis (GSA) Variance decomposition and Sobol’ indices Uncertainty space for GSA Results of GSA - 3 different configurations 3 Conclusion and further work A-L Tiberi-Wadier 16 / 23 SA of the Mascaret model on the river Odet

Configuration 1 Pertubation of minor friction coefficients of the 12 zones Figure: Sobol’ indices time series and associated zones A-L Tiberi-Wadier 17 / 23 SA of the Mascaret model on the river Odet

Configuration 2 Pertubation of minor and flood plain friction coefficients of the 6 significant zones Figure: Sobol’ indices time series and associated zones A-L Tiberi-Wadier 18 / 23 SA of the Mascaret model on the river Odet

Configuration 3 Pertubation of minor, flood plain friction coefficients of the 6 significant zones and the boundary conditions Figure: Sobol’ indices time series and associated zones A-L Tiberi-Wadier 19 / 23 SA of the Mascaret model on the river Odet

Outline 1 Hydrologic and hydraulic models 2 Global Sensitivity Analysis (GSA) Variance decomposition and Sobol’ indices Uncertainty space for GSA Results of GSA - 3 different configurations 3 Conclusion and further work A-L Tiberi-Wadier 20 / 23 SA of the Mascaret model on the river Odet

Conclusion Mascaret model of the Odet river studied through GSA Provides Sobol’ indices that rank uncertainty sources When the boundary conditions are not pertubed the simulated water levels are mainly controlled by the immediate downstream friction coefficient flood plains are activated around the peak of the events When the boundary conditions are pertubed they are decisive for the value of the simulated water levels A-L Tiberi-Wadier 21 / 23 SA of the Mascaret model on the river Odet

Further work Results of GSA study will be used for the realization of Hydraulic Ensemble Forecasts for correcting the simulation chain by data assimilation A-L Tiberi-Wadier 22 / 23 SA of the Mascaret model on the river Odet

Thank you for you attention A-L Tiberi-Wadier 23 / 23 SA of the Mascaret model on the river Odet