Exploring the Factors Controlling the Error Characteristics of the Surface Water and Ocean Topography Mission Discharge Estimates

The Surface Water and Ocean Topography (SWOT) satellite mission will measure river width, water surface elevation, and slope for rivers wider than 50–100 m. SWOT observations will enable estimation of river discharge by using simple flow laws such as the Manning-Strickler equation, complementing in situ streamgages. Several discharge inversion algorithms designed to compute unobserved flow law parameters (e.g., friction coefficient and bathymetry) have been proposed, but to date, a systematic assessment of factors controlling algorithm performance has not been conducted. Here, we assess the performance of the five algorithms that are expected to be used in the construction of the SWOT product. To perform this assessment, we used synthetic SWOT observations created with hydraulic model output corrupted with SWOT-like error. Prior information provided to the algorithms was purposefully limited to an estimate of mean annual flow (MAF), designed to produce a “worst case” benchmark. Prior MAF error was an important control on algorithm performance, but discharge estimates produced by the algorithms are less biased than the MAF; thus, the discharge algorithms improve on the prior. We show for the first time that accuracy and frequency of remote sensing observations are less important than prior bias, hydraulic variability among reaches, and flow law accuracy in governing discharge algorithm performance. The discharge errors and error sensitivities reported herein are a bounding benchmark, representing worst possible expected errors and error sensitivities. This study lays the groundwork to develop predictive power of algorithm performance, and thus map the global distribution of worst-case SWOT discharge accuracy

Assimilation variationnelle de données satellitaires dans un modèle hydraulique Saint-Venant complet dans le contexte de bassins non instrumentés

[Departement_IRSTEA]Eaux [TR1_IRSTEA]GEUSI [ADD1_IRSTEA]Gestion intégrée de la ressource et des infrastructures [Encadrant_IRSTEA]Malaterre, P.O. ; Gejadze I.The present thesis investigates the potential of variational data assimilation (DA) in discharge estimation from the future Surface Water and Ocean Topography (SWOT) satellite mission, using a 1.5D full Saint-Venant hydraulic model in the context of fully ungauged basins. Two distinct approaches for treating the model error are being investigated; the extended control vector approach, and a novel approach based on a modified covariance matrix. Adjoint sensitivity analysis was first performed to assess the local influence of the hydraulic model inputs, on the model response, defined using an objective function of the model state. The latter is highly sensitive to the upstream boundary condition on discharge as well as the river bed elevation and roughness coefficient. Sensitivities indicate the control sections of the river that have major influence on the flow hydraulics, which emphasizes the need of accurate measurements and/or at these locations. Second, the estimation of river discharge from simulated SWOT observations using a variant of the conventional variational DA method '4D-Var' has been investigated. The variational DA scheme involves an extended control vector and is developed to apply the method to fully ungauged basins. The method was tested using two experimental set-ups: (i) Observing System Simulation Experiments over the Garonne River and a more realistic and general framework using (ii) the SWOT hydrology simulator, which simulates the radar system on-board the satellite, over the Po and Sacramento Rivers. Water surface elevation was assimilated leading to local improvements on bathymetry and roughness which allowed successful estimation of discharge. Nevertheless, the estimates of the space distributed variables are subjected to the equifinality issue which may prevent their use for subsequent applications. Moreover, results emphasize that successful estimation of discharge over the whole study period requires an observation frequency comparable to the characteristic time of the hydraulic system. Finally, a novel method for the treatment of the model error using the variational approach is proposed. Based on the 'nuisance parameter' idea, it allows implicit treatment of the model error by using a modified observation covariance matrix. The equivalency theorem substantiating the method has been proved. A case of the biased model error is also considered. Numerical experiments involving the 1D generalized Burger's equation and the 1.5D full Saint-Venant equations illustrate the presented theory.Ce sujet de thèse s'inscrit dans le cadre général de la mission satellitaire Surface Water and Ocean Topography (SWOT) et a pour objectif d'évaluer l'apport de l'assimilation de données (AD) variationnelle en utilisant un modèle hydraulique 1.5D basé sur le système d'équations Saint-Venant complet. De plus, la méthode proposée est conçue pour une application dans le contexte général de bassins non instrumentés. Une première analyse de sensibilité avec la méthode de l'adjoint a été effectuée pour évaluer l'influence locale des variables et paramètres d'entrée du modèle sur ses sorties. La réponse du modèle est définie à partir d'une fonction objective des variables d'état. Celle-ci s'avère significativement sensible à la condition limite en débit amont, ainsi qu'aux variables de géomorphologie fluviale; le niveau du lit du fleuve et ses coefficients de frottements. Les sensibilités calculées renseignent sur les sections de contrôle qui ont une influence majeure sur l'hydraulique du fleuve et qui requièrent des relevés ou un calage plus précis. L'estimation du débit des fleuves à partir de données SWOT, a été ensuite étudiée, en utilisant une variante de la méthode conventionnelle '4D-Var'. Celle-ci permet d'estimer simultanément le débit, ainsi que la bathymétrie et les frottements dans le contexte de bassins non instrumentés, observés uniquement depuis l'espace. Deux configurations ont été analysées: (i) les expériences jumelles dans le cadre du fleuve Garonne, puis un cadre plus représentatif des données SWOT, en utilisant (ii) le simulateur SWOT d'hydrologie, sur les fleuves Po et Sacramento. En assimilant des données de hauteur d'eau, la bathymétrie et les frottements sont corrigés localement, permettant une meilleure estimation du débit. Toutefois, les variables estimées (bathymétrie et frottements) sont sujettes au problème d'équifinalité, et ne peuvent être exploitées pour des applications ultérieures. De plus, les résultats obtenus renseignent sur la fréquence temporelle des observations permettant une bonne estimation du débit et qui se doit d'être au moins équivalente au temps caractéristique du fleuve étudié. Pour finir, une nouvelle approche pour le traitement de l'erreur modèle en utilisant l'AD variationnelle a été proposée. Elle implique un traitement implicite basé sur une matrice de covariance des erreurs d'observations modifiée. Le théorème proposé est démontré et illustré par une application à l'équation 1D de Burger généralisée, ainsi qu'au cadre hydraulique en utilisant le modèle 1.5D saint-Venant complet

Implicit treatment of model error using inflated observation-error covariance

International audienceData assimilation involving imperfect dynamical models is an important topic in meteorology, oceanography and other geophysical applications. In filtering methods, the model error is compensated for by inflation. In variational data assimilation, authors usually try to estimate it, which means that all uncertainty-loaded model inputs are included into the control vector. However, this approach suffers from implementation difficulties. In this paper we suggest an alternative method, motivated by the 'nuisance parameter' concept known in statistics. This method allows the model error to be treated implicitly by inflating the observation-error covariance. The equivalency theorem substantiating the method has here been proved. We also consider a case with a biased model error. In the corresponding mixed formulation, the spatially distributed mean error is included into the control vector, whereas the time-dependent fluctuations around the mean are subjected to the proposed implicit treatment. Numerical experiments for the 1D generalized Burgers' equation illustrate the presented theory. In these experiments the model error related to uncertainty in the advection coefficient has been considered

Estimation of Multiple Inflows and Effective Channel by Assimilation of Multi-satellite Hydraulic Signatures: The Ungauged Anabranching Negro River

International audienceWith the upcoming SWOT satellite mission, which should provide spatially dense river surface elevation, width and slope observations globally, comes the opportunity to assimilate such data into hydrodynamic models, from the reach scale to the hydrographic network scale. Based on the HiVDI (Hierarchical Variational Discharge Inversion) modeling strategy (Larnier et al. [#Larnier2019]), this study tackles the forward and inverse modeling capabilities of distributed channel parameters and multiple inflows (in the 1D Saint-Venant model) from multisatellite observations of river surface. It is shown on synthetic cases that the estimation of both inflows and distributed channel parameters (bathymetry-friction) is achievable with a minimum spatial observability between inflows as long as their hydraulic signature is sampled. Next, a real case is studied: 871 km of the Negro river (Amazon basin) including complex multichannel reaches, 21 tributaries and backwater controls from major confluences. An effective modeling approach is proposed using (i) WS elevations from ENVISAT data and dense in situ GPS flow lines (Moreira [#DanielPhD]), (ii) average river top widths from optical imagery (Pekel et al. [#Pekel_Nature]), (iii) upstream and lateral flows from the MGB large-scale hydrological model (Paiva et al. [#paiva2013]). The calibrated effective hydraulic model closely fits satellite altimetry observations and presents real like spatial variabilities; flood wave propagation and water surface observation frequential features are analyzed with identifiability maps following Brisset et al. [#Brisset_2018]. Synthetic SWOT observations are generated from the simulated flowlines and allow to infer model parameters (436 effective bathymetry points, 17 friction patches and 22 upstream and lateral hydrographs) given hydraulically coherent prior parameter values. Inferences of channel parameters carried out on this fine hydraulic model applied at a large scale give satisfying results using noisy SWOT-like data at reach scale. Inferences of spatially distributed temporal parameters (lateral inflows) give satisfying results as well, with even relatively small scale hydrograph variations being inferred accurately on this long reach. This study brings insights in: (i) the hydraulic visibility of multiple inflows hydrographs signature at large scale with SWOT; (ii) the simultaneous identifiability of spatially distributed channel parameters and inflows by assimilation of satellite altimetry data; (iii) the need for prior information; (iv) the need to further tailor and scale network hydrodynamic models and assimilation methods to improve the fusion of multisource information and potential information feedback to hydrological modules in integrated chains