Data Assimilation (4D-VAR) for Shallow-Water Flow: The Case of the Chicoutimi River

This is a web presentation of the work presented at the 10th Annual Conference of the CFD Society of Canada, “CFD 2002”, at the University of Windsor on June 9-11, 2002. This discussion paper presents the four-dimensional variational data assimilation (4D-VAR) technique as a tool to forecast floods. This discussion will be limited to hydrological forecast. We assume that the weather, here a large rainstorm, had already been forecasted by the meteorological services. In the 4D-VAR technique, we need to minimize, in the sense of Lagrange, a cost function which measures the difference between the forecast and the observations. The physical equations acts as a set of constraints. Here, the model is the shallow-water equations modified to include sediment transport. The minimum was found by using the steepest descent algorithm. This is made possible because the gradient of the cost function can be calculated analytically by using the adjoint equations of the model. To illustrate the 4D-VAR technique, the bypass of a simple theoretical dam as well as the more complex overflowing of the Chicoutimi River at the Chute-Garneau dam (during the 1996 flood) are investigated.     

Osmium-strontium-neodymium-lead isotopic covariations in mid-ocean ridge basalt glasses and the heterogeneity of the upper mantle

Osmium, strontium, neodymium, and lead isotopic data have been obtained for 30 hand picked samples of basaltic glass from the Pacific, Atlantic and Indian mid-oceanic ridges. Large variations in Os isotopic ratios exist in the glasses, from abyssal peridotite-like values to radiogenic compositions similar to oceanic island basalts (¹⁸⁷Os/¹⁸⁶Os and ¹⁸⁷Os/¹⁸⁸Os ratios range from 1.06 to 1.36 and from 0.128 to 0.163, respectively). Os isotopic and elemental data suggest the existence of mixing correlations. This relationship might be ascribed to secondary contamination processes; however, such a hypothesis cannot account for the negative correlation observed between Os and Nd isotopes and the existence of complementary covariations between Os and SrPb isotopes. In this case, OsSrNdPb isotopic variations are unrelated to late post-eruption or shallow level contamination. These relationships provide strong evidence that the Os isotopic composition of the samples are derived from the mantle and thus implies a global chemical heterogeneity of the oceanic upper mantle. The results are consistent with the presence of recycled oceanic crust in the mantle sources of mid-ocean ridge basalts, and indicate that the unique composition of the upper mantle below the Indian ocean results from its contamination by a mantle component characterized by radiogenic Os and particularly unradiogenic Nd and Pb isotopic compositions.     

Crystal morphologies in pillow basalts: implications for mid-ocean ridge processes

We present the results of a detailed petrological study of a sparsely phyric basalt (MAPCO CH98-DR11) dredged along the Mid-Atlantic Ridge (30°41′N). The sample contains microphenocrysts of olivine that display four different rapid-growth morphologies. Comparison of these morphologies with those obtained in dynamic crystallization experiments allows us to constrain the thermal history of the sample. The dendritic morphology (swallowtail, chain and lattice olivine) is directly related to the final quenching during magma–seawater interaction. In contrast, the three other morphologies, namely the complex polyhedral crystal, the closed hopper and the complex swallowtail morphology result from several cycles of cooling–heating (corresponding to a maximum degree of undercooling of 20–25°C) during crystal growth. These thermal variations occurred before eruption and are interpreted to be the result of turbulent convection in a small magmatic body beneath the ridge. The results suggest that the Mid-Atlantic Ridge is underlain by a mush zone that releases batches of liquid during tectonic segregation. Aphyric basalts are emitted during eruptions controlled by the tectonic activity, whereas phyric basalts correspond to small fractions of magma from the mush zone mobilized by reinjections of primitive magmas.     

Magnetic fabrics and rock magnetism of Proterozoic dike swarm from the southern São Francisco Craton, Minas Gerais State, Brazil

Magnetic fabric and rock magnetism studies were performed on 32 mafic dikes of a Proterozoic dike swarm from the southern São Francisco Craton (SFC; Minas Gerais State, SE Brazil). Magnetic anisotropies were determined by applying anisotropy of low-field magnetic susceptibility (AMS) and anisotropy of remanent magnetization (ARM). The latter was performed imposing both anhysteretic (total (AAR) and partial pAAR)) and isothermal remanence magnetizations (AIRM). Partial anhysteretic remanence anisotropy was performed based on remanent coercivity spectra from a pilot specimen of each site. In most sites, AMS is dominantly carried by ferromagnetic minerals, however, in some sites, the paramagnetic contribution exceeds 70% of bulk susceptibility. Rock magnetism and thin section analysis allow classifying the dikes as non-hydrothermalized and hydrothermalized. Magnetic measurement shows that the mean magnetic susceptibility is usually lower than 5×10⁻³ (SI). Ti-poor titanomagnetites up to pure magnetite pseudo-single-domain (PSD) grain sizes carry the majority of magnetic fabrics for non-hydrothermalized dikes whereas coarse to fine grained Ti-poor titanomagnetites carry the majority of magnetic fabrics for hydrothermalized dikes.Three primary AMS fabrics are recognized which are coaxial with ARM fabric, except for two dikes, from both non-hydrothermalized and hydrothermalized dikes. Normal AMS fabric surprisingly is not dominant (31%). The parallelism between AMS, pAAR_0–30, pAAR_30–60 and pAAR_60–90 fabrics in the hydrothermalized dikes indicates that magnetic grains formed due to late-stage crystallization or to remobilization of iron oxides due to hydrothermal alteration after dike emplacement have acquired a mimetic fabric coaxial with the primary fabric given by coarse-grained early crystallized Ti-poor titanomagnetites. This fabric is interpreted as magma flow in which the analysis of K_max inclination permitted the inference that the dikes were fed by horizontal or subhorizontal fluxes (K_max<30°). Intermediate AMS fabric is the most important (41%) in the investigated swarm. It is interpreted as due to vertical compaction of a static magma column with the minimum stress along the dike strike. ARM determinations for these sites also remained intermediate except for two dikes. In one of them, AIRM fabric resulted in normal AMS fabric while for the other AAR fabric resulted in inverse AMS fabric. A combination of AMS and ARM fabrics suggest that magmatic fabric for both dikes were overprinted by some late local event, probably related to Brasiliano orogenic processes after dike emplacement. InverseInverse AMS fabric is a minority (four dikes). ARM determinations also remained inverse suggesting a primary origin for inverse AMS fabric.     

Fitting the Linear Model of Coregionalization by Generalized Least Squares

In geostatistical studies, the fitting of the linear model of coregionalization (LMC) to direct and cross experimental semivariograms is usually performed with a weighted least-squares (WLS) procedure based on the number of pairs of observations at each lag. So far, no study has investigated the efficiency of other least-squares procedures, such as ordinary least squares (OLS), generalized least squares (GLS), and WLS with other weighing functions, in the context of the LMC. In this article, we compare the statistical properties of the sill estimators obtained with eight least-squares procedures for fitting the LMC: OLS, four WLS, and three GLS. The WLS procedures are based on approximations of the variance of semivariogram estimates at each distance lag. The GLS procedures use a variance–covariance matrix of semivariogram estimates that is (i) estimated using the fourth-order moments with sill estimates (GLS₁), (ii) calculated using the fourth-order moments with the theoretical sills (GLS₂), and (iii) based on an approximation using the correlation between semivariogram estimates in the case of spatial independence of the observations (GLS₃). The current algorithm for fitting the LMC by WLS while ensuring the positive semidefiniteness of sill matrix estimates is modified to include any least-squares procedure. A Monte Carlo study is performed for 16 scenarios corresponding to different combinations of the number of variables, number of spatial structures, values of ranges, and scale dependence of the correlations among variables. Simulation results show that the mean square error is accounted for mostly by the variance of the sill estimators instead of their squared bias. Overall, the estimated GLS₁ and theoretical GLS₂ are the most efficient, followed by the WLS procedure that is based on the number of pairs of observations and the average distance at each lag. On that basis, GLS₁ can be recommended for future studies using the LMC.     

Petrology and geochemistry of a diamondiferous lherzolite from the Premier diamond mine, South Africa

This paper reports on the petrology and geochemistry of a diamondiferous peridotite xenolith from the Premier diamond mine in South Africa.

The xenolith is altered with pervasive serpentinisation of olivine and orthopyroxene. Garnets are in an advanced state of kelyphitisation but partly fresh. Electron microprobe analyses of the garnets are consistent with a lherzolitic paragenesis (8.5 wt.% Cr₂O₃ and 6.6 wt.% CaO). The garnets show limited variation in trace element composition, with generally low concentrations of most trace elements, e.g. Y (<11 ppm), Zr (<18 ppm) and Sr (<0.5 ppm). Garnet rare earth element concentrations, when normalised against the C1 chondrite of McDonough and Sun (Chem. Geol. 120 (1995) 223), are characterised by a rare earth element pattern similar to garnet from fertile lherzolite.

All diamonds recovered are colourless. Most crystals are sharp-edged octahedra, some with minor development of the dodecahedral form. A number of crystals are twinned octahedral macles, while aggregates of two or more octahedra are also common. Mineral inclusions are rare. Where present they are predominantly small black rosettes believed to consist of sulfide. In one instance a polymineralic (presumably lherzolitic) assemblage of reddish garnet, green clinopyroxene and a colourless mineral is recognised.

Infrared analysis of the xenolith diamonds show nitrogen contents generally lower than 500 ppm and variable nitrogen aggregation state, from 20% to 80% of the ‘B’ form. When plotted on a nitrogen aggregation diagram a well defined trend of increasing nitrogen aggregation state with increasing nitrogen content is observed. Carbon isotopic compositions range from −3.6 ‰ to −1.3 ‰. These are broadly correlated with diamond nitrogen content as determined by infrared spectroscopy, with the most negative C-isotopic compositions correlating with the lowest nitrogen contents.

Xenolith mantle equilibration temperatures, calculated from nitrogen aggregation systematics as well as the Ni in garnet thermometer are on the order of 1100 to 1200 °C.

It is concluded that the xenolith is a fertile lherzolite, and that the lherzolitic character may have resulted from the total metasomatic overprinting of pre-existing harzburgite. Metasomatism occurred prior to, or accompanied, diamond growth.     

Modélisation morphodynamique cross-shore d'un estran vaseux

Numerical experiments were performed to simulate the profile evolution of an intertidal mudflat with a 1D cross-shore morphodynamical model. First, the hydrodynamical forcing is a cross-shore tidal current due to semi-diurnal variations of the free surface elevation at the open boundary. Further, considering the conservation of the action density of surface gravity waves, a wave height (and resulting bottom shear stress) calculation is added to the morphodynamical model. Results of the numerical experiments show that the shape of the profile reaches equilibrium. The mudflat progrades continually when the forcing is tide only, whereas it can be steady under the simultaneous action of tide and waves. To cite this article: B. Waeles et al., C. R. Geoscience 336 (2004).