Inflow and initial conditions for direct numerical simulation based on adjoint data assimilation

International audienceA method for generating inflow conditions for direct numerical simulations (DNS) of spatially-developing flows is presented. The proposed method is based on variational data assimilation and adjoint-based optimization. The estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint system defined by the adjoint of the discrete scheme associated to the dynamical system. The approach's robustness is evaluated on two synthetic velocity field sequences provided by numerical simulation of a mixing layer and a wake flow behind a cylinder. The performance of the technique is also illustrated in a real world application by using PIV measurements to acquire the database. This method allows to denoise experimental velocity fields and to reconstruct a continuous trajectory of motion fields from discrete and unstable measurements

DassFlow v1.0: a variational data assimilation software for river flows

Dassflow is a computational software for river hydraulics (floods), especially designed for variational data assimilation. The forward model is based on the bidimensional shallow-water equations, solved by a finite volume method (HLLC approximate Riemann solver). It is written in Fortran 95. The adjoint code is generated by the automatic differentiation tool Tapenade. Thus, Dassflow software includes the forward solver, its adjoint code, the full optimization framework (based on the M1QN3 minimization routine) and benchmarks. The generation of new data assimilation twin experiments is easy. The software is interfaced with few pre and post-processors (mesh generators, GIS tools and visualization tools), which allows to treat real data

Mitigation of flash floods in arid regions using adjoint sensitivity analysis

This paper presents an analysis of the sensitivities of flood wave propagation to variations in certain control variables and boundary conditions by means of the adjoint method. This uses a variational technique to find the relationships between changes in predicted flood water levels and changes in control variables such as the inflow hydrograph, bed roughness, and bed elevation. The sensitivities can be used for optimal control of hydraulic structures, for data assimilation, for decision makers' procedures, for the analysis of the effects of uncertainties in control variables on the predictions of floods water levels, and for investigating both the sensitivities of model flood forecasts to model parameters, boundary and initial conditions. Example of the last application of the sensitivity analysis is presented and discussed These methods are developed and implemented through a numerical hydraulic model of channel flow based on the Shallow Water Equations (SWEs) and the corresponding adjoint model. The equations are integrated using finite difference methods and a new modified method of characteristics is used to define the open boundaries. Results of validation tests on both the forward hydraulic model and on the adjoint model are presented

Modelling uncertainty for flash floods in coastal plains using adjoint methods

This paper shows the application of adjoint sensitivity analysis to flash flood wave propagation in a river channel. The adjoint sensitivity analysis is used to assess flood hazard in a coastal area caused by river discharge. The numerical model determines the sensitivities of predicted water levels to uncertainties in key controls such as inflow hydrograph, channel topography, frictional resistance and infiltration rate. Sensitivities are calculated using the adjoint equations and are specified in terms of water levels being greater than certain safe threshold levels along the channel. The flood propagation model is based on the St. Venant equations while the propagation of sensitivity information is based on the corresponding adjoint equations. This analysis is achieved using a numerical model that integrates The St. Venant equations forward in time using a staggered finite difference scheme. An enhanced method of characteristics at the downstream boundary provides open boundary conditions and overcomes the problem of reflections from the boundaries. Then, the adjoint model is integrated backwards in time to trace the sensitivity information back through the model domain towards the inflow control boundary. The adjoint model has been verified by means of an identical twin experiment

Robust finite volume schemes for 2D shallow water models. Application to flood plain dynamics

This study proposes original combinations of higher order Godunov type finite volume schemes and time discretization schemes for the 2d shallow water equations, leading to fully second-order accuracy with well-balanced property. Also accuracy, positiveness and stability properties in presence of dynamic wet/dry fronts is demonstrated. The test cases are the classical ones plus extra new ones representing the geophysical flow features and difficulties

A particle filter to reconstruct a free-surface flow from a depth camera

We investigate the combined use of a Kinect depth sensor and of a stochastic data assimilation method to recover free-surface flows. More specifically, we use a Weighted ensemble Kalman filter method to reconstruct the complete state of free-surface flows from a sequence of depth images only. This particle filter accounts for model and observations errors. This data assimilation scheme is enhanced with the use of two observations instead of one classically. We evaluate the developed approach on two numerical test cases: a collapse of a water column as a toy-example and a flow in an suddenly expanding flume as a more realistic flow. The robustness of the method to depth data errors and also to initial and inflow conditions is considered. We illustrate the interest of using two observations instead of one observation into the correction step, especially for unknown inflow boundary conditions. Then, the performance of the Kinect sensor to capture temporal sequences of depth observations is investigated. Finally, the efficiency of the algorithm is qualified for a wave in a real rectangular flat bottom tank. It is shown that for basic initial conditions, the particle filter rapidly and remarkably reconstructs velocity and height of the free surface flow based on noisy measurements of the elevation alone

Inverse computational algorithms for flood plain dynamic modelling

Flood plain dynamic modelling remains a challenge because of the complex multi-scale data, data uncertainties and the uncertain heterogeneous flow measurements. Mathematical models based on the 2d shallow water equations are generally suitable but wetting-drying processes can be driven by small scale data features. The present study aims at deriving an accurate and robust direct solver for dynamic wet-dry fronts and a variational inverse method leading to sensitivity analyses and data assimilation processes. The numerical schemes and algorithms are assessed on academic benchmarks representing well some flood dynamic features and a real test case (Lèze river, southwestern of France). Original sensitivity maps with respect to the (friction , topography) fields are performed and discussed. Furthermore, the identification of inflow discharges (time series) or roughness coefficients defined by land covers (spatially distributed parameters) demonstrate the relevance of the approach and the algorithm efficiency. Inverse computational methods may contribute to breakthrough in flood plain modelling

DassFow-Shallow, Variational Data Assimilation for Shallow-Water Models: Numerical Schemes, User and Developer Guides

DassFlow is a computational software for free-surface flows includingvariational data assimilation (4D-VAR), sensitivity analysis, calibration features (adjoint method). The code version "shallow" solves shallow-water like models (Saint-Venant's type).The other version (ALE, not detailed in the present document) includes free-surface Stokes like models (low Reynolds, power-law rheology, ALE surface dynamics). All source files are written in Fortran 2003 / MPI. For more details and references, please consult DassFlow website.In the present manuscript, we describe: the equations, the compilation/execution instructions, the input / output files (user guide), the finite volume schemes, few validation test cases included in the archive, and the code structure (developer guide)

Modelling the Eddy Pattern in the harbour of Zeebrugge

Hydrodynamic

Correction of upstream flow and hydraulic state with data assimilation in the context of flood forecasting

The present study describes the assimilation of river water level observations and the resulting improvement in flood forecasting. The Kalman Filter algorithm was built on top of a one-dimensional hydraulic model which describes the Saint-Venant equations. The assimilation algorithm folds in two steps: the first one was based on the assumption that the upstream flow can be adjusted using a three-parameter correction; the second one consisted of directly correcting the hydraulic state. This procedure was applied using a four- day sliding window over the flood event. The background error covariances for water level and discharge were repre- sented with anisotropic correlation functions where the cor- relation length upstream of the observation points is larger than the correlation length downstream of the observation points. This approach was motivated by the implementation of a Kalman Filter algorithm on top of a diffusive flood wave propagation model. The study was carried out on the Adour and the Marne Vallage (France) catchments. The correction of the upstream flow as well as the control of the hydraulic state during the flood event leads to a significant improve- ment in the water level and discharge in both analysis and forecast modes