A Variational Data Assimilation Algorithm to Estimate Salinity in the Berre Lagoon with Telemac3D

Variational assimilation of in-situ data for the description of the salinity field in the Berre lagoon is explored. The Berre lagoon is a receptacle of 1000 Mm3 where salty water from the Mediterranean Sea meets fresh water discharged by the hydroelectric plant at SaintChamas and by natural tributaries. Its dynamics are represented by a 3D hydraulic model that simulates the mean tracer and current fields. This simulation should be further improved to allow for the optimization of the operation of the hydroelectric production while preserving the lagoon ecosystem. A 3D-Var FGAT data assimilation algorithm is used to correct the initial salinity state over a 1-hour time window assimilating observations at three fixed buoys each equipped with 5 XBT sensors in the vertical every 15 minutes. The minimization is performed in a space spanned by vectors of the size of the observation vector in order to reduce both memory usage and computational cost. The background error covariance matrix for salinity is modelled using a diffusion operator. The sequential correction of the salinity state improves the representation of the strongly stratified salinity field over the assimilation window as well as in the short-term forecast. The sensitivity of the assimilation to the background error horizontal and vertical length scale was investigated in single observation experiments as well as in a real case study.

[1]  M. Pedder,et al.  Atmospheric data analysis: by Roger Daley, Cambridge University Press. Cambridge atmospheric and space science series, 2. 457 pages. Published 1991. Price: £55,-/U.S. $79.50 ISBN 0 521 382157. , 1992 .

[2]  S. Cohn,et al.  Assessing the Effects of Data Selection with the DAO Physical-Space Statistical Analysis System* , 1998 .

[3]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[4]  P. Courtier,et al.  Correlation modelling on the sphere using a generalized diffusion equation , 2001 .

[5]  Jérôme Vialard,et al.  Three- and Four-Dimensional Variational Assimilation with a General Circulation Model of the Tropical Pacific Ocean. Part I: Formulation, Internal Diagnostics, and Consistency Checks , 2003 .

[6]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

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

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

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

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

[11]  Serge Gratton,et al.  An observation‐space formulation of variational assimilation using a restricted preconditioned conjugate gradient algorithm , 2009 .

[12]  P. Bates,et al.  Progress in integration of remote sensing–derived flood extent and stage data and hydraulic models , 2009 .

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

[14]  A. Weaver,et al.  Representation of correlation functions in variational assimilation using an implicit diffusion operator , 2010 .

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

[16]  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 .

[17]  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 .

[18]  Michael Durand,et al.  The Surface Water and Ocean Topography Mission: Observing Terrestrial Surface Water and Oceanic Submesoscale Eddies , 2010, Proceedings of the IEEE.

[19]  Hernan G. Arango,et al.  The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems Part I - System overview and formulation , 2011 .

[20]  Jacques Sau,et al.  Data assimilation for real-time estimation of hydraulic states and unmeasured perturbations in a 1D hydrodynamic model , 2009, Math. Comput. Simul..

[21]  Serge Gratton,et al.  B‐preconditioned minimization algorithms for variational data assimilation with the dual formulation , 2014 .