Estimating the uncertainty of video-based flow velocity and discharge measurements due to the conversion of field to image coordinates

Video-based hydrometry continues to develop for contactless discharge measurements, automated flood gauging stations and the use of crowd-sourced flood videos for discharge reconstruction. Irrespective of the velocimetry algorithm used (LSPIV, STIV, PTV…), orthorectification of the images is necessary beforehand, so that each pixel has the same known physical size. Most times, the orthorectification transformation is a plane-to-plane projection from the water surface to the camera sensor. Two approaches are typically used to compute the coefficients of this transformation: their calibration from ground reference points (GRPs) with known image and real-world coordinates (“implicit calibration”) or their calculation from the values of the intrinsic (focal length, sensor size) and extrinsic (position, angles) parameters of the camera (“explicit calibration”). In this paper, we develop a Bayesian method which makes it possible to combine the implicit and explicit approaches in a probabilistic framework. The Bayesian approach can be used from situations suitable for the implicit approach (plenty of GRPs) to situations propitious to the explicit approach (well-known camera parameters). The method is illustrated using synthetic views of a typical streamgauging scene with known true values of the parameters and GRP coordinates. We show that combining observational and prior information is generally beneficial to get precise estimates. Further tests carried out with a real scene of the Arc River at Randens, France, in flood conditions illustrate the impact of the number, uncertainty and spatial distribution of GRPs on the final uncertainty of flow velocity and discharge.     

Structure of the Barents Sea from seismic refraction

The Barents Sea is underlain by a thick (up to 5 km) sedimentary basin. Seismic refraction has outlined four main velocity discontinuities which have been correlated with geological units on the basis of the geological history of the region. The basin is underlain by a crystalline basement, the nature of which cannot be determined on the basis of seismic velocity alone. Metamorphosed Paleozoic units (velocities around 5–4 km/sec) lie over this basement. Their thickness is not well established but appears to reach 1 or 2 km in some cases. A very distinct and thick (up to 2.5 km) layer (4.1 km/sec) is found almost everywhere and is thought to correspond to a major discontinuity at the end ot the Paleozoic. This discontinuity is followed by a variable velocity layer (2.4–4 km/sec, up to 1.2 km thick) which includes Mesozoic and Cenozoic sediments and is limited to the south of the Barents Sea. The absence of thick Tertiary deposits support the idea that the Barents shelf was emergent at that time. Recent low-velocity sediments are found close to the shelf edge.Gravity anomaly trends reflect a series of depressions of the 5.4-km/sec layer isobath map and suggest that the deeper part of the basin is made of a succession of faulted blocks or intense folds.     

Oxidation modes and thermodynamics of Fe oxyhydroxycarbonate green rust: Dissolution-precipitation versus in situ deprotonation

Fe^II-III hydroxycarbonate green rust GR(CO₃²⁻), Fe^II₄ Fe^III₂ (OH)₁₂ CO₃·3H₂O, is oxidized in aqueous solutions with varying reaction kinetics. Rapid oxidation with either H₂O₂ or dissolved oxygen under neutral and alkaline conditions leads to the formation of ferric oxyhydroxycarbonate GR(CO₃²⁻)∗, Fe^III₆ O₁₂ H₈ CO₃·3H₂O, via a solid-state reaction. By decreasing the flow of oxygen bubbled in the solution, goethite α-FeOOH forms by dissolution-precipitation mechanism whereas a mixture of non-stoichiometric magnetite Fe_(3−x)O₄ and goethite is observed for lower oxidation rates. The intermediate Fe^II-III oxyhydroxycarbonate of formula Fe^II_6(1−x) Fe^III_6x O₁₂ H_2(7−3x) CO₃·3H₂O, i.e. GR(x)∗ for which x ? [1/3, 1], is the synthetic compound that is homologous to the fougerite mineral present in hydromorphic gleysol; in situ oxidation accounts for the variation of ferric molar fraction x = [Fe^III]/{[Fe^II]+[Fe^III]} observed in the field as a function of depth and season but limited to the range [1/3, 2/3]. The domain of stability for partially oxidized green rust is observed in the E_h-pH Pourbaix diagrams if thermodynamic properties of GR(x)∗ is compared with those of lepidocrocite, γ-FeOOH, and goethite, α-FeOOH. Electrochemical equilibrium between GR(x)∗ and Fe^II in solution corresponds to E_h-pH conditions close to those measured in the field. Therefore, the reductive dissolution of GR(x)∗ can explain the relatively large concentration of Fe^II measured in aqueous medium of hydromorphic soils containing fougerite.     

Automatic Variogram Modeling by Iterative Least Squares: Univariate and Multivariate Cases

In this paper, we propose a new methodology to automatically find a model that fits on an experimental variogram. Starting with a linear combination of some basic authorized structures (for instance, spherical and exponential), a numerical algorithm is used to compute the parameters, which minimize a distance between the model and the experimental variogram. The initial values are automatically chosen and the algorithm is iterative. After this first step, parameters with a negligible influence are discarded from the model and the more parsimonious model is estimated by using the numerical algorithm again. This process is iterated until no more parameters can be discarded. A procedure based on a profiled cost function is also developed in order to use the numerical algorithm for multivariate data sets (possibly with a lot of variables) modeled in the scope of a linear model of coregionalization. The efficiency of the method is illustrated on several examples (including variogram maps) and on two multivariate cases.     

Non-numeric computation for high eccentricity orbits

Geocentric orbits of large eccentricity (e=0.9 to 0.95) are significantly perturbed in cislunar space by the Sun and Moon. The time-history of the height of perigee, subsequent to launch, is particularly critical. The determination of ‘launch windows’ is mostly concerned with preventing the height of perigee from falling below its low initial value before the mission lifetime has elapsed. Between the extremes of high accuracy digital integration of the equations of motion and of using an approximate, but very fast, stability criteria method, this paper is concerned with the development of a method of intermediate complexity using non-numeric computation. The computer is used as the theory generator to generalize Lidov's theory using six osculating elements. Symbolic integration is completely automatized and the output is a set of condensed formulae well suited for repeated applications in launch window analysis. Examples of applications are given.     

Etude geochimique de la fraction carbonatee d'un facies de bordure de depot gypseux (exemple du gypse ludien du Bassin de Paris) (geochemical study of a carbonate-rich facies in the northern border-area of the Ludian gypsum in the Paris Basin)

The bore-hole of Mont-Pagnotte (Oise, France), located in the northern border-area of the Ludian gypsum in the Paris Basin, shows a facies richer in carbonate than those of the centre of the basin. It is possible to relate this facies to the typical formations of the centre of the basin. Samples from the Middle Bartonian (Calcaire de Saint-Ouen) to the Stampian (argile verte) are studied. In this part of the core, the proportion of argillaceous minerals is very low, but there are many variations which are related to the evolution of the area of sedimentation. Alizarine-coloured thin-section study and X-ray analysis show that the microfacies is constant: it is always a calcimicrite. This constancy is very important in geochemical study, because we can eliminate a possible action of mineralogic and diagenetic factors on the distribution coefficient of the different elements studied. Results of the atomic absorption analysis of the trace elements (on the carbonate part of the samples) are positive for 8 elements (Sr, Na, K, Mg, Zn, Mn, Cr, Ni). After a critical discussion (based on much experimental data) of the comportment of those elements during carbonate sedimentation, the Sr, Na, K, Mg, Zn contents appear to represent an indicator of the salinity of the water in the area of sedimentation; the Mn concentration as an indicator of oxydo-reduction conditions in the sediment and the Ni and Cr contents as an indicator of variation in the quality of continental supplies (in ionic or detritic form). It is possible to relate this variation to weathering conditions on the continent.The study shows an evolution of the salinity in the Middle Bartonian: the basal part has the characteristics of a marine deposit, the top has those of a continental (fresh-water) deposit. The Mg contents are constant in the carbonate part, but this is related to a competition between an argillaceous phase and a carbonate phase towards magnesium. This evolution of the sedimentation area is confirmed by the distribution of Characeae in the Middle Bartonian.The Ludian gypsums of the Paris Basin are really a continental deposit, the lateral, calcareous facies equivalent to the gypsum deposits always present the geochemical characteristics of a continental deposit: carbonates in gypsum formations always have the lowest concentrations of Sr, Na, K, Mg and Zn.Comparison between the evolution of argillaceous and carbonate sediments shows that argillaceous sedimentation is not affected by variations in salinity, but it is very sensitive to variations of the quality and quantity of continental supplies in the sedimentation area.To conclude, an evolutionary paleogeography of this region of the Paris Basin from the middle Bartonian to the Stampian (salinity of water, weathering on the continent…) is proposed.     

The transport and redistribution of atmospheric gases in regions of frontal rain

Gases emitted in the planetary boundary layer can be transported very efficiently to the free troposphere through vertical motion along a frontal surface. A mesoscale numerical model was used to simulate the vertical transport of a tracer by clouds during frontogenesis in a moist atmosphere (an evolving Eady wave) in order to illustrate such vertical transport conditions. It is shown that the efficient vertical transport of a tracer occurs only when clouds are present, either when a surface or an in-situ source is considered. Insoluble, partially soluble, and soluble tracers are studied in order to determine the relative importance of vertical transport and scavenging on their redistribution.     

Effect of Surface Morphology on the Dissipation During Shear and Slip Along a Rock–Rock Interface that Contains a Visco-elastic Core

High resolution topography measurements of the Vuache–Sillingy fault (Alps, France) reveal a characteristic roughness of the fault zone. We investigate the effect of roughness on the rheology of a planar shear configuration by using a model system consisting of a visco-elastic layer embedded into a rigid solid. The model is discussed in the context of several geological cases: a damage fault zone, a fault smeared with a clay layer, and a shear zone with strain weakening. Using both analytical approaches and finite element simulations, we calculate to linear order the relation between wall roughness and the viscous dissipation in the fault zone as well as the average shear rate.     

Parallel Multiple-Point Statistics Algorithm Based on List and Tree Structures

Multiple-point statistics are widely used for the simulation of categorical variables because the method allows for integrating a conceptual model via a training image and then simulating complex heterogeneous fields. The multiple-point statistics inferred from the training image can be stored in several ways. The tree structure used in classical implementations has the advantage of being efficient in terms of CPU time, but is very RAM demanding and then implies limitations on the size of the template, which serves to make a proper reproduction of complex structures difficult. Another technique consists in storing the multiple-point statistics in lists. This alternative requires much less memory and allows for a straightforward parallel algorithm. Nevertheless, the list structure does not benefit from the shortcuts given by the branches of the tree for retrieving the multiple-point statistics. Hence, a serial algorithm based on list structure is generally slower than a tree-based algorithm. In this paper, a new approach using both list and tree structures is proposed. The idea is to index the lists by trees of reduced size: the leaves of the tree correspond to distinct sublists that constitute a partition of the entire list. The size of the indexing tree can be controlled, and then the resulting algorithm keeps memory requirements low while efficiency in terms of CPU time is significantly improved. Moreover, this new method benefits from the parallelization of the list approach.     

Influence of food supply on the δ13C signature of mollusc shells: implications for palaeoenvironmental reconstitutions

Compared to oxygen isotopes, the carbon isotope composition of biogenic carbonates is less commonly used as proxy for palaeoenvironmental reconstructions because shell δ¹³C is derived from both dissolved inorganic (seawater) and organic carbon sources (food), and interactions between these two pools make it difficult to unambiguously identify any independent effect of either. The main purpose of this study was to demonstrate any direct impact of variable food supply on bivalve shell δ¹³C signatures, using low/high rations of a ¹³C-light mixed algal diet fed to 14-month-old (adult) cultured Japanese Crassostrea gigas under otherwise essentially identical in vitro conditions during 3 summer months (May, June and July 2003, seawater temperature means at 16, 18 and 20 °C respectively) in experimental tanks at the Argenton laboratory along the Brittany Atlantic coast of France. At a daily ration of 12% (versus 4%) oyster dry weight, the newly grown part of the shells (hinge region) showed significantly lower δ¹³C values, by 3.5‰ (high ration: mean of −5.8  ± 1.1‰, n = 10; low ration: mean of −2.3  ± 0.7‰, n = 6; ANOVA Scheffe’s test, p < 0.0001). This can be explained by an enhanced metabolic activity at higher food supply, raising ¹³C-depleted respiratory CO₂ in the extrapallial cavity. Based on these δ¹³C values and data extracted from the literature, and assuming no carbon isotope fractionation between food and shell, the proportion of shell metabolic carbon would be 26  ± 7 and 5  ± 5% for the high- and low-ration C. gigas shells respectively; with carbon isotope fractionation (arguably more realistic), the corresponding values would be 69  ± 14 and 24  ± 9%. Both groups of cultured shells exhibited lower δ¹³C values than did wild oysters from Marennes-Ol éron Bay in the study region, which is not inconsistent with an independent influence of diet type. Although there was no significant difference between the two food regimes in terms of δ¹⁸O shell values (means of 0.1  ± 0.3 and 0.4  ± 0.2‰ at high and low rations respectively, non-significant Scheffe’s test), a positive δ¹³C vs. δ¹⁸O relationship recorded at high rations supports the interpretation of a progressive temperature-mediated rise in metabolic activity fuelled by higher food supply (in this case reflecting increased energy investment in reproduction), in terms not only of δ¹³C (metabolic signal) but also of δ¹⁸O (seawater temperature signal). Overall, whole-shell δ¹⁸O trends faithfully recorded summer/winter variations in seawater temperature experienced by the 17-month-old cultured oysters.