Modélisation des écoulements en milieu poreux hétérogènes 2D / 3D, avec couplages surface / souterrain et densitaires

Dans ce travail, on considère la modélisation des écoulements dans des hydro-systèmes comprenant des sols et des aquifères géologiquement complexes et hétérogènes. On considèrera par exemple le cas d’un aquifère côtier soumis à l’intrusion saline, avec couplage densitaire (eau douce / eau salée), phénomène auquel peuvent se greffer d’autres couplages (écoulements à saturation variable, couplages surface / souterrain). On choisit une approche ayant les caractéristiques suivantes : - le modèle est spatialement distribué afin de représenter l’hétérogénéité du milieu ; - le modèle est fortement couplé afin d’appréhender les écoulements dans leur complexité physique. On utilise dans ce but un modèle fortement intégré, à une seule équation générique de type EDP, basée sur une loi de Darcy généralisée permettant de décrire différents "régimes" d’écoulements la co-existant dans un même domaine, tout en conservant robustesse et efficacité. Le travail est divisé en trois parties : dans une première partie on élabore un nouveau modèle numérique 3D, pour la modélisation des écoulements en milieux poreux à densité variable dans l’hypothèse d’une interface abrupte. Ce nouveau modèle est basé sur des relations ‘effectives’ non linéaires de saturation et de perméabilité, dans une équation d’écoulement de type Richards modifiée. La seconde partie correspond à l’élaboration et l’implémentation d’un modèle verticalement intégré d’intrusion saline en aquifère côtier, permettant d’étudier l’effet de l’hétérogénéité stochastique de l’aquifère. Le modèle, basé sur l’hypothèse ‘interface abrupte’, est implémenté comme un module ‘2D’ dans le code volumes finis BigFlow2D/3D. Le nouveau module 2D est utilisé pour analyser la variabilité de l’interface eau douce / eau salée par simulations stochastiques de type Monte Carlo à échantillonnage spatial (réalisation unique). Ces résultats sont comparés à nouvelle théorie, où l’interface aléatoire auto-corrélée est analysée par transformation de variable, combinée à une méthode de perturbation et à une représentation spectrale (Fourier / Wiener-Khinchine). Dans la troisième et dernière partie, on présente un modèle de couplage fortement "intégré" pour la modélisation des écoulements de surface et souterrain en hypothèses d’écoulement plan, verticalement hydrostatique. On s‘intéresse au cas d’une vallée fluviale avec cours d’eau, plaine d’inondation, et nappe d’accompagnement. L’écoulement en surface est modélisé par l’équation d’onde diffusante et l’écoulement souterrain par l’équation de Dupuit-Boussinesq. Ce modèle couplé est appliqué à la vallée fluviale de la Garonne dans la région de Toulouse - Moissac (France). Cette application a nécessité l’élaboration d’une méthode d’interpolation géostatistique adaptée à l’élaboration d’un Modèle Intégré Numérique de Terrain (‘MINT’), de façon à inclure le fond de la rivière au MNT topographique en haute résolution. Enfin, au-delà de cette application particulière, le modèle d’écoulement couplé surface / souterrain est généralisé au cas d’un couplage densitaire eau douce / eau salée, lorsque la nappe est sujette à l’intrusion saline au voisinage d’une embouchure ou d’un estuaire. ABSTRACT : In this work, we consider water flow modeling in hydro-systems that include geologically complex and heterogeneous soils and aquifers, e.g., a coastal aquifer undergoing seawater intrusion, with density coupling (freshwater / saltwater), along with other coupled phenomena (variable saturation, surface / subsurface coupling). The selected approach has the following characteristics: - the model is spatially distributed in order to represent the heterogeneity of the medium ; - the model is strongly coupled in order to apprehend the physical complexity of flow systems. We use for this purpose a strongly integrated model, governed by a single generic equation (PDE) based on generalized Darcy law, to describe different flow ‘regimes’ co-existing in the same domain, while conserving robustness and efficiency. The work is divided into three parts: in the first part, we develop a new 3D numerical model for variable density flow in porous media under the sharp interface approximation. This new model is based on non-linear ‘effective’ saturation and conductivity relations, in a modified Richards flow equation. The second part corresponds to the development and implementation of a vertically integrated saltwater intrusion model, to study the effect of stochastic heterogeneity in a coastal aquifer. The model, based on the sharp interface hypothesis, is implemented as a 2D module in the finite volumes code BigFlow 2D/3D. The new module is used for analyzing the variability of the salt / fresh interface through Monte Carlo simulations with spatial sampling (single realization). These results are compared to a new theory where the random field interface is analyzed via a transformation combined to a perturbation method and a spectral representation (Fourier / Wiener-Khinchine). In the third and last part, we present a strongly integrated model to simulate coupled surface / subsurface plane flows, such as a river valley with stream, floodplain, and free surface aquifer. Surface flow is modeled via the diffusive wave equation, and subsurface flow is modeled using the Dupuit-Boussinesq equation. This coupled model is applied to the Garonne river valley in the Toulouse-Moissac region (France). This application has required the elaboration of a geostatistical interpolation technique that produces an Integrated Digital Elevation Model (‘IDEM’). The IDEM incorporates a high resolution representation of river channels into the topographic DEM. Finally, beyond this specific application, the coupled surface / subsurface model is generalized to the case of salt / fresh density coupling, where the aquifer is subject to saltwater intrusion near a river mouth or an estuar

Model Coupling for Environmental Flows, with Applications in Hydrology and Coastal Hydrodynamics.

The aim of this paper is to present an overview of “model coupling” methods and issues in the area of environmental hydrodynamics, particularly coastal hydrodynamics and surface/subsurface hydrology. To this end, we will examine specific coupled phenomena in order to illustrate coupling hypotheses and methods, and to gain new insights from analyses of modelling results in comparison with experiments. Although this is to some extent a review of recent works, nevertheless, some of the methods and results discussed here were not published before, and some of the analyses are new. Moreover, this study is part of a more general framework concerning various types of environmental interactions, such as: interactions between soil water flow (above the water table) and groundwater flow (below the water table); interactions between surface and subsurface waters in fluvial environments (streams, floodplains); interactions between coastal flow processes and porous structures (e.g. sea‑driven oscillations and waves through sand beach or a porous dike); feedback effects of flow systems on the geo‑environmental media. This paper starts with a general review of conceptual coupling approaches, after which we present specific modelling and coupling methods for dealing with hydrological flows with surface water / groundwater interactions, and with coastal flows involving the propagation of seawater oscillations through a porous beach (vertically and horizontally). The following topics are treated. (1) Coupled stream‑aquifer plane flow in an alluvial river valley (quasi‑steady seasonal flow regime), assuming aquifer/stream continuity, and using in situ piezometric measurements for comparisons. (2) Water table oscillations induced by sea waves, and propagating through the beach in the cross‑shore direction: this phenomenon is studied numerically and experimentally using a wave canal with an inclined beach equipped with capacitive micro‑piezometers. (3) Tidally driven vertical oscillations of water flow and capillary pressure in a partially saturated / unsaturated sand beach column, studied numerically and experimentally via a “tide machine” contraption (described in some detail): the goal is to apprehend the role of capillary effects, and forcing frequency, on the hydraulic response of a beach column forced by tides from below. At the time of this writing, some of the results from the tide machine are being reinterpreted (ongoing work). We also point out a recent study of vertical flow in the beach, which focuses on the effect of intermittent waves in the swash zone, rather than tidal oscillations

An evaluation of SMOS L-band vegetation optical depth (L-VOD) data sets:high sensitivity of L-VOD to above-ground biomass in Africa

The vegetation optical depth (VOD) measured at microwave frequencies is related to the vegetation water content and provides information complementary to visible/infrared vegetation indices. This study is devoted to the characterization of a new VOD data set obtained from SMOS (Soil Moisture and Ocean Salinity) satellite observations at L-band (1.4 GHz). Three different SMOS L-band VOD (LVOD) data sets (SMOS level 2, level 3 and SMOS-IC) were compared with data sets on tree height, visible/infrared indexes (NDVI, EVI), mean annual precipitation and above-ground biomass (AGB) for the African continent. For all relationships, SMOS-IC showed the lowest dispersion and highest correlation. Overall, we found a strong (R > 0.85) correlation with no clear sign of saturation between L-VOD and four AGB data sets. The relationships between L-VOD and the AGB data sets were linear per land cover class but with a changing slope depending on the class type, which makes it a global non-linear relationship. In contrast, the relationship linking L-VOD to tree height (R = 0.87) was close to linear. For vegetation classes other than evergreen broadleaf forest, the annual mean of L-VOD spans a range from 0 to 0.7 and it is linearly correlated with the average annual precipitation. SMOS L-VOD showed higher sensitivity to AGB compared to NDVI and K/X/C-VOD (VOD measured at 19, 10.7 and 6.9 GHz). The results showed that, although the spatial resolution of L-VOD is coarse (similar to 40 km), the high temporal frequency and sensitivity to AGB makes SMOS L-VOD a very promising indicator for large-scale monitoring of the vegetation status, in particular biomass

Synergistic calibration of a hydrological model using discharge and remotely sensed soil moisture in the Paraná river basin

Hydrological models are useful tools for water resources studies, yet their calibration is still a challenge, especially if aiming at improved estimates of multiple components of the water cycle. This has led the hydrologic community to look for ways to constrain models with multiple variables. Remote sensing estimates of soil moisture are very promising in this sense, especially in large areas for which field observations may be unevenly distributed. However, the use of such data to calibrate hydrological models in a synergistic way is still not well understood, especially in tropical humid areas such as those found in South America. Here, we perform multiple scenarios of multiobjective model optimization with in situ discharge and the SMOS L4 root zone soil moisture product for the Upper Paraná River Basin in South America (drainage area > 900,000 km2), for which discharge data for 136 river gauges are used. An additional scenario is used to compare the relative impacts of using all river gauges and a small subset containing nine gauges only. Across the basin, the joint calibration (CAL-DS) using discharge and soil moisture leads to improved precision and accuracy for both variables. The discharges estimated by CAL-DS (median KGE improvement for discharge was 0.14) are as accurate as those obtained with the calibration with discharge only (median equal to 0.14), while the CAL-DS soil moisture retrieval is practically as accurate (median KGE improvement for soil moisture was 0.11) as that estimated using the calibration with soil moisture only (median equal to 0.13). Nonetheless, the individual calibration with discharge rates is not able to retrieve satisfactory soil moisture estimates, and vice versa. These results show the complementarity between these two variables in the model calibration and highlight the benefits of considering multiple variables in the calibration framework. It is also shown that, by considering only nine gauges inst

Comparison of SMOS and SMAP Soil Moisture Retrieval Approaches Using Tower-based Radiometer Data over a Vineyard Field

The objective of this study was to compare several approaches to soil moisture (SM) retrieval using L-band microwave radiometry. The comparison was based on a brightness temperature (TB) data set acquired since 2010 by the L-band radiometer ELBARA-II over a vineyard field at the Valencia Anchor Station (VAS) site. ELBARA-II, provided by the European Space Agency (ESA) within the scientific program of the SMOS (Soil Moisture and Ocean Salinity) mission, measures multiangular TB data at horizontal and vertical polarization for a range of incidence angles (30-60). Based on a three year data set (2010-2012), several SM retrieval approaches developed for spaceborne missions including AMSR-E (Advanced Microwave Scanning Radiometer for EOS), SMAP (Soil Moisture Active Passive) and SMOS were compared. The approaches include: the Single Channel Algorithm (SCA) for horizontal (SCA-H) and vertical (SCA-V) polarizations, the Dual Channel Algorithm (DCA), the Land Parameter Retrieval Model (LPRM) and two simplified approaches based on statistical regressions (referred to as 'Mattar' and 'Saleh'). Time series of vegetation indices required for three of the algorithms (SCA-H, SCA-V and Mattar) were obtained from MODIS observations. The SM retrievals were evaluated against reference SM values estimated from a multiangular 2-Parameter inversion approach. The results obtained with the current base line algorithms developed for SMAP (SCA-H and -V) are in very good agreement with the reference SM data set derived from the multi-angular observations (R2 around 0.90, RMSE varying between 0.035 and 0.056 m3m3 for several retrieval configurations). This result showed that, provided the relationship between vegetation optical depth and a remotely-sensed vegetation index can be calibrated, the SCA algorithms can provide results very close to those obtained from multi-angular observations in this study area. The approaches based on statistical regressions provided similar results and the best accuracy was obtained with the Saleh methods based on either bi-angular or bipolarization observations (R2 around 0.93, RMSE around 0.035 m3m3). The LPRM and DCA algorithms were found to be slightly less successful in retrieving the 'reference' SM time series (R2 around 0.75, RMSE around 0.055 m3m3). However, the two above approaches have the great advantage of not requiring any model calibrations previous to the SM retrievals

Calibration of DART Radiative Transfer Model with Satellite Images for Simulating Albedo and Thermal Irradiance Images and 3D Radiative Budget of Urban Environment

Remote sensing is increasingly used for managing urban environment. In this context, the H2020 project URBANFLUXES aims to improve our knowledge on urban anthropogenic heat fluxes, with the specific study of three cities: London, Basel and Heraklion. Usually, one expects to derive directly 2 major urban parameters from remote sensing: the albedo and thermal irradiance. However, the determination of these two parameters is seriously hampered by complexity of urban architecture. For example, urban reflectance and brightness temperature are far from isotropic and are spatially heterogeneous. Hence, radiative transfer models that consider the complexity of urban architecture when simulating remote sensing signals are essential tools. Even for these sophisticated models, there is a major constraint for an operational use of remote sensing: the complex 3D distribution of optical properties and temperatures in urban environments. Here, the work is conducted with the DART (Discrete Anisotropic Radiative Transfer) model. It is a comprehensive physically based 3D radiative transfer model that simulates optical signals at the entrance of imaging spectro-radiometers and LiDAR scanners on board of satellites and airplanes, as well as the 3D radiative budget, of urban and natural landscapes for any experimental (atmosphere, topography,…) and instrumental (sensor altitude, spatial resolution, UV to thermal infrared,…) configuration. Paul Sabatier University distributes free licenses for research activities. This paper presents the calibration of DART model with high spatial resolution satellite images (Landsat 8, Sentinel 2, etc.) that are acquired in the visible (VIS) / near infrared (NIR) domain and in the thermal infrared (TIR) domain. Here, the work is conducted with an atmospherically corrected Landsat 8 image and Bale city, with its urban database. The calibration approach in the VIS/IR domain encompasses 5 steps for computing the 2D distribution (image) of urban albedo at satellite spatial resolution. (1) DART simulation of satellite image at very high spatial resolution (e.g., 50cm) per satellite spectral band. Atmosphere conditions are specific to the satellite image acquisition. (2) Spatial resampling of DART image at the coarser spatial resolution of the available satellite image, per spectral band. (3) Iterative derivation of the urban surfaces (roofs, walls, streets, vegetation,…) optical properties as derived from pixel-wise comparison of DART and satellite images, independently per spectral band. (4) Computation of the band albedo image of the city, per spectral band. (5) Computation of the image of the city albedo and VIS/NIR exitance, as an integral over all satellite spectral bands. In order to get a time series of albedo and VIS/NIR exitance, even in the absence of satellite images, ECMWF information about local irradiance and atmosphere conditions are used. A similar approach is used for calculating the city thermal exitance using satellite images acquired in the thermal infrared domain. Finally, DART simulations that are conducted with the optical properties derived from remote sensing images give also the 3D radiative budget of the city at any date including the date of the satellite image acquisition

Soil moisture deficit estimation using satellite multi-angle brightness temperature

Accurate soil moisture information is critically important for hydrological modelling. Although remote sensing soil moisture measurement has become an important data source, it cannot be used directly in hydrological modelling. A novel study based on nonlinear techniques (a local linear regression (LLR) and two feedforward artificial neural networks (ANNs)) is carried out to estimate soil moisture deficit (SMD), using the Soil Moisture and Ocean Salinity (SMOS) multi-angle brightness temperatures (Tbs) with both horizontal (H) and vertical (V) polarisations. The gamma test is used for the first time to determine the optimum number of Tbs required to construct a reliable smooth model for SMD estimation, and the relationship between model input and output is achieved through error variance estimation. The simulated SMD time series in the study area is from the Xinanjiang hydrological model. The results have shown that LLR model is better at capturing the interrelations between SMD and Tbs than ANNs, with outstanding statistical performances obtained during both training (NSE = 0.88, r = 0.94, RMSE = 0.008 m) and testing phases (NSE = 0.85, r = 0.93, RMSE = 0.009 m). Nevertheless, both ANN training algorithms (radial BFGS and conjugate gradient) have performed well in estimating the SMD data and showed excellent performances compared with those derived directly from the SMOS soil moisture products. This study has also demonstrated the informative capability of the gamma test in the input data selection for model development. These results provide interesting perspectives for data-assimilation in flood-forecasting

The Indian COSMOS Network (ICON): validating L-band remote sensing and modelled soil moisture data products

Availability of global satellite based Soil Moisture (SM) data has promoted the emergence of many applications in climate studies, agricultural water resource management and hydrology. In this context, validation of the global data set is of substance. Remote sensing measurements which are representative of an area covering 100 m2 to tens of km2 rarely match with in situ SM measurements at point scale due to scale difference. In this paper we present the new Indian Cosmic Ray Network (ICON) and compare it’s data with remotely sensed SM at different depths. ICON is the first network in India of the kind. It is operational since 2016 and consist of seven sites equipped with the COSMOS instrument. This instrument is based on the Cosmic Ray Neutron Probe (CRNP) technique which uses non-invasive neutron counts as a measure of soil moisture. It provides in situ measurements over an area with a radius of 150–250 m. This intermediate scale soil moisture is of interest for the validation of satellite SM. We compare the COSMOS derived soil moisture to surface soil moisture (SSM) and root zone soil moisture (RZSM) derived from SMOS, SMAP and GLDAS_Noah. The comparison with surface soil moisture products yield that the SMAP_L4_SSM showed best performance over all the sites with correlation (R) values ranging from 0.76 to 0.90. RZSM on the other hand from all products showed lesser performances. RZSM for GLDAS and SMAP_L4 products show that the results are better for the top layer R = 0.75 to 0.89 and 0.75 to 0.90 respectively than the deeper layers R = 0.26 to 0.92 and 0.6 to 0.8 respectively in all sites in India. The ICON network will be a useful tool for the calibration and validation activities for future SM missions like the NASA-ISRO Synthetic Aperture Radar (NISAR)