A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin coefficient

In this work, a Reduced Basis (RB) approach is used to solve a large number of boundary value problems parametrized by a stochastic input – expressed as a Karhunen–Loève expansion – in order to compute outputs that are smooth functionals of the random solution fields. The RB method proposed here for variational problems parametrized by stochastic coefficients bears many similarities to the RB approach developed previously for deterministic systems. However, the stochastic framework requires the development of new a posteriori estimates for “statistical” outputs – such as the first two moments of integrals of the random solution fields; these error bounds, in turn, permit efficient sampling of the input stochastic parameters and fast reliable computation of the outputs in particular in the many-query context.United States. Air Force Office of Scientific Research (Grant FA9550-07-1-0425)Singapore-MIT Alliance for Research and TechnologyChaire d’excellence AC

Biological, socio-economic, and administrative opportunities and challenges to moving aquaculture offshore for small French oyster-farming companies

Oyster production has historically taken place in intertidal zones, and shellfish farms already occupy large extents of the French intertidal space. The expansion of French shellfish aquaculture within intertidal areas is therefore spatially limited, and moving production to the subtidal offshore environment is considered to be a possible solution to this problem. Finding new sites along the French Atlantic coast was studied here from the perspective of small oyster companies run by young farmers, who are interested in offshore bivalve aquaculture expansion compatible with their investment capacity. In assessing the feasibility of such offshore production, we considered three main issues: (1) bivalve growth potential and (2) technical feasibility and conflicting uses, both within a spatial framework, as well as (3) the steps and barriers of the administrative licensing process. Oyster spat in an experimental offshore cage showed significantly faster growth, in terms of both weight and length, compared to those in an intertidal cage, mainly due to lower turbidity and full-time feeding capacity (i.e., constant immersion in the water). A combination of Earth Observation data and bivalve ecophysiological modelling was then used to obtain spatial distribution maps of growth potential, which confirmed that offshore sites have better potential for oyster growth than the traditionally oyster-farmed intertidal sites overall, but that this is highly spatially variable. Small-scale producers indicated two technical factors constraining where farms could be located: bathymetry must be between 5 and 20 m and the distance from a harbor no more than five nautical miles. These were included along with maps of various environmental and socio-economic constraints in a Spatial Multi-Criteria Evaluation (SMCE). Touristic traffic and bottom trawling by fisherman were found to be the two other most restrictive variables. The GIS-based SMCE developed in this study showed that there is almost 400 km2 of highly- to very highly-suitable area within which to develop offshore aquaculture using simple, low-cost bottom-cage techniques, and can be used to assist the shellfish industry in the Marine Spatial Planning decision-making process, still in progress in this coastal area. However, the complexity of the administrative processes necessary to obtain an offshore license is perceived as a stronger barrier by farmers owning small companies than site selection, technical feasibility, and required investments, and will be crucial to address in order to realistically proceed to offshore cultivation. The process demonstrated here, and the results are relevant to other coastal and offshore locations throughout the world and can be adapted for other species

Sentinel-2 remote sensing of Zostera noltei-dominated intertidal seagrass meadows

Accurate habitat mapping methods are urgently required for the monitoring, conservation, and management of blue carbon ecosystems and their associated services. This study focuses on exposed intertidal seagrass meadows, which play a major role in the functioning of nearshore ecosystems. Using Sentinel-2 (S2) data, we demonstrate that satellite remote sensing can be used to map seagrass percent cover (SPC) and leaf biomass (SB), and to characterize its seasonal dynamics. In situ radiometric and biological data were acquired from three intertidal meadows of Zostera noltei along the European Atlantic coast in the summers of 2018 and 2019. This information allowed algorithms to estimate SPC and SB from a vegetation index to be developed and assessed. Importantly, a single SPC algorithm could consistently be used to study Z. noltei-dominated meadows at several sites along the European Atlantic coast. To analyze the seagrass seasonal cycle and to select images corresponding to its maximal development, a two-year S2 dataset was acquired for a French study site in Bourgneuf Bay. The po-tential of S2 to characterize the Z. noltei seasonal cycle was demonstrated for exposed intertidal meadows. The SPC map that best represented seagrass growth annual maximum was validated using in situ measurements, resulting in a root mean square difference of 14%. The SPC and SB maps displayed a patchy distribution, influenced by emersion time, mudflat topology, and seagrass growth pattern. The ability of S2 to measure the surface area of different classes of seagrass cover was investigated, and surface metrics based on seagrass areas with SPC >= 50% and SPC >= 80% were computed to estimate the interannual variation in the areal extent of the meadow. Due to the high spatial resolution (pixel size of 10 m), frequent revisit time (<= 5 days), and long-term objective of the S2 mission, S2-derived seagrass time-series are expected to contribute to current coastal ecosystem management, such as the European Water Framework Directive, but to also guide future adaptation plans to face global change in coastal areas. Finally, recommendations for future intertidal seagrass studies are proposed

Hyperspectral remote sensing of wild oyster reefs (Crassostrea gigas)

L’huître creuse Crassostrea gigas, est considérée depuis les années 90 comme une espèce invasive à cause de son impact sur l’environnement. Cependant, suite aux surmortalités qui touchent les huîtres en élevage depuis l’été 2008, les huîtres sauvages sont considérées comme une réelle ressource. Cela nécessite la production de cartes pour localiser et quantifier les gisements naturels. L’objectif de ce travail est d’étudier la capacité de la télédétection visible et proche infrarouge pour identifier les récifs d’huîtres à différentes résolutions spectrales, spatiales et temporelles. Les premières cartographies à l’échelle d’un bassin ostréicole ont montré l’importance des données hyperspectrales, pour distinguer les types de récifs. Les spectres de réflectance ont révélé l’existence inattendue de bandes d’absorptions chlorophylliennes, suggérant la présence d’un biofilm de microalgues sur les coquilles, jusqu’alors invisible à l’oeil nu. L’étude s’est poursuivie à micro-échelle en scannant des coquilles d’huîtres avec une caméra HySpex en laboratoire. L’analyse des pics de dérivés secondes à 462, 524, 571 et 647 nm a révélé la présence de diatomées, cyanobactéries, rhodophycées et chlorophycées. En parallèle, des analyses pigmentaires par chromatographie (CLHP) et des observations microscopiques ont confirmé la présence de ces microalgues epilithes et endolithes. Enfin, malgré la résolution hyperspectrale, les récifs restent difficiles à identifier dans les zones de vasières où la vase et le microphytobenthos recouvrent les coquilles. Cette difficulté peut être surmontée en couplant les données optiques avec les données radar, sensibles à la rugosité de surface.Since the 90’s, the Pacific oyster Crassostrea gigas, is considered as an invasive species because of their negative environmental impacts. However, oyster producers are reconsidering wild oyster populations as a resource due to recent high mortalities affecting cultivated oysters since the summer 2008. The social conflicts existing around natural oyster beds require spatial distribution maps for management purposes. The objective of this work is to evaluate the ability of visible and near infrared remote sensing to identify wild oyster reefs using various spectral, spatial and temporal resolutions. Firstly, maps obtained with an airborne campaign at a shellfish ecosystem scale, showed the importance of hyperspectral data, to identify oysters according to the reef structure. Spectral reflectance shapes surprisingly revealed the existence of chlorophyll absorption bands, suggesting the presence of a visually invisible microalgal biofilm colonizing the shell surface. At microscale, oyster shells were imaged using a hyperspectral HySpex camera in the laboratory with a sub-millimeter spatial resolution. The second derivative peaks at 462, 524, 571 and 647 nm were related to the presence of diatoms, cyanobacteria, rhodophytes and chlorophytes. Further pigment analysis by high performance liquid chromatography (HPLC) and microscopic observations confirmed the presence of these epilithic and endolithic biofilms. Finally, despite the high hyperspectral resolution, misclassification of oyster reefs occurred in muddy areas due to spectral mixing with mud and microphytobenthos. This could be overcome by combining optical data with radar images, sensitive to the surface roughness