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-Wadier1 N Goutal2 S Ricci3 P Sergent4 C Monteil5

1Cerema Eau, Mer et Fleuves, Plouzan´

e, France 2EDF R&D et Laboratoire d’Hydraulique Saint-Venant, Chatou, France

3CECI, UMR5318, CNRS/CERFACS, Toulouse, France 4Cerema Eau, Mer et Fleuves, Margny-Les-compi`

egne, France 5EDF 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)

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Study area

Figure: The rivers Odet, Steir and Jet with the location of the hydrologic stations.

Odet catchment coastal river in Western Britany (Quimper, Finistere) astronomical tide ranges between 1.40 and 5.55 m 720 km2 total lenght of about 60 km 2 tributaries : Jet and Steir rivers

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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

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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

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Hydrologic modeling - 3 upstream sub-catchments

Figure: The rivers Odet, Steir and Jet with the location of the hydrologic stations.

MORDOR-TS hydrologic model spatialized and continuous conceptual rainfall-runoff model provides hydrologic streamflows at Treodet, Kerjean and Ty-Planche 8 free parameters multi-objective function using caRamel genetic algorithm

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Hydraulic modeling

Figure: 12 zones of friction coefficents

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] flood plains: values ranging [1, 34]

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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

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Global Sensitivity Analysis

Variance decomposition and Sobol’ indices Notations input : X = (X1, X2, ..., Xk) X = (X1, X2, ..., Xk) vary on their uncertainty domain

• utput : Y = f (X)

Variance decomposition Hoeffing decomposition of the variance V (Y ) : V (Y ) =

• i

Vi +

• i
• j>i

Vi,j + ... + V1,2,3,...,K (1) where Vi is the elementary contribution of Xi to V(Y), Vi,j is the contribution due to interactions between Xi et Xj to V(Y), V1,2,...,k is the contribution due to interaction between all inputs to V(Y).

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Global Sensitivity Analysis

Variance decomposition and Sobol’ indices Sobol’ indices Dividing 1 this equation by V (Y ) leads to

• i

Si +

• i
• j>i

Si,j + ... + S1,2,3,...,K = 1 (2) Si: 1st order Sobol index → normalized elementary contribution of Xi to V(Y). Sobol’ indices apportion the variance of the output Y = f (X) with X = (X1, X2, ..., Xk), to the variation of different inputs (X1, ..., Xk) 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.

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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

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Uncertainty space for GSA

Figure: 12 zones of friction coefficents

Three types of uncertain inputs

minor and flood plain friction coefficients (Ksi and KsiM) 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

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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[Vmin, Vmax] Vmin and Vmax: 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.

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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

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Uncertainty space for GSA

Comparison of the standard deviation of upstream and donwstream perturbations

Figure: std of the upstream and dowstream perturbations (cm)

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

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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

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Configuration 1

Pertubation of minor friction coefficients of the 12 zones

Figure: Sobol’ indices time series and associated zones

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Configuration 2

Pertubation of minor and flood plain friction coefficients of the 6 significant zones

Figure: Sobol’ indices time series and associated zones

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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

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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

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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

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Further work

Results of GSA study will be used for the realization of Hydraulic Ensemble Forecasts for correcting the simulation chain by data assimilation

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Thank you for you attention

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