Estimation de l'équivalent en eau du couvert nival au moyen d'images radar satellitaires

L'objectif de cette étude est de vérifier le potentiel des images radar à synthèse d'ouverture (RSO) pour estimer l'équivalent en eau du couvert nival sur le bassin de la rivière La Grande (Baie de James, Québec). Il s'agit d'un milieu dominé par une forêt ouverte d'épinettes noires, des brûlis et des tourbières. Cette information intéresse grandement Hydro-Québec qui gère plusieurs installations hydro-électriques dans cette région subarctique. Durant deux ans, six campagnes de terrain ont été réalisées sur le bassin de la rivière La Grande et une dizaine d'images RSO du satellite européen ERS-1 ont été acquises, étalonnées et géoréférencées, afin de déterminer la relation entre les coefficients de rétrodiffusion des images radar (hiver et automne) et la résistance thermique du couvert nival. Cette relation constitue la première partie d'un algorithme d'estimation de l'équivalent en eau. Elle utilise plus spécifiquement le rapport de rétrodiffusion, qui est la différence entre une image avec neige et une image sans neige. La deuxième partie de cette algorithme déduit l'équivalent en eau du couvert de neige à partir de sa résistance thermique et de sa densité, en se basant sur la relation physique établie par les mesures de terrain. L'équivalent en eau du couvert nival a donc été estimé pour quatre images de février et mars 1994 et 1995. L'erreur moyenne sur l'estimation de l'équivalent en eau de la neige au sol est de 2% à 3% (-5 à 7mm) sur l'ensemble des sites d'échantillonnage avec un écart-type de 14 à 19% (-35 à 45mm). Ces résultats ont encouragé Hydro-Québec à poursuivre la recherche avec les données du satellite canadien RADARSAT (opérationnel depuis le 1er avril 1996) et à développer un prototype pour la cartographie de l'équivalent en eau du couvert nival à partir d'images radar.The goal of this study was to evaluate the potential of synthetic aperture radar (SAR) images for estimating the snow water equivalent (SWE) on the La Grande river watershed (James Bay area, Québec). This information is of major interest for Hydro-Québec, which exploits many hydroelectric complexes throughout this subarctic region. The La Grande watershed is composed of moderately dense to opened black spruce forests, opened areas, burned areas and peat bogs. Over two years (1994-1995), six field campaigns were carried out on a study site located between the LG4 and Laforge1 reservoir, in the center of the La Grande river watershed. The field measurements were of two types: 20 snow lines (depth, snow water equivalent (SWE), density) and 8 snow profiles (depth, density, grain size, temperature, dielectric constant). With these data, the thermal resistance of the snowpack was calculated for every test-site, using the depth, density and thermal conductivity of each layer. Concurrently, more than 10 SAR images (European Satellite ERS-1) of the study site were acquired, calibrated and georeferenced. The backscattering coefficients of all winter images were extracted. Using a reference image (snow-free), backscattering ratios were calculated. They are the difference between a winter image and a snow-free image. This process is used to reduce the impact of vegetation and topography. Then, the relationship between the backscattering ratios and the snowpack thermal resistance of february and march 1994 are established, as the first part of an algorithm developed to estimate the snow water equivalent. The second part of the algorithm infers the snowpack water equivalent from its thermal resistance and density, based on the physical relationship established with field data. This approach is based on studies conducted by INRS-Eau in a southern Quebec agricultural area (BERNIER and FORTIN (1998)). The hypothesis are based on the following: - The snowpack characteristics influence the underlying soil temperature;- The dielectric constant of the soil varies with the soil temperature under 0°C;- The radar signal is influenced by the soil dielectric constant;- Thus, the snowpack characteristics (thermal resistance) influence the radar signal. However, due to variations of soil humidity on the date of the reference image (september 1994), two slightly different relationships were obtained. One for open areas and open forests and one for burned areas and peat bogs. This shows the importance of using a good reference image, with homogeneous soil conditions. It could be better to obtain an image later in the fall, when the soil is frozen. The relationships established here are preliminary, as they use a small dataset. It is estimated that a better regression should be obtained with the acquisition of more images and with a greater range of snow characteristics. However, the algorithm is applied to test the applicability of the method. First, the algorithm was applied on the test-sites, using the images from February and March of 1994 and 1995. The mean error on the estimation of the snow water equivalent is 2% to 3% ( 5 to 7mm), with a deviation of 14% to 19% ( 35 to 45mm). The results are comparable for both years, even if the algorithm is based on 1994 data only. Secondly, the algorithm is applied on the whole images. A classification of a Landsat-TM image is used to identify the land cover of every pixel, which determines the regression and the snow density to be used in the algorithm. Four maps of the SWE are produced and resampled to a resolution of 500m. These are compared with the field measurements from the four nearest Hydro-Quebec snow survey sites. The SWE measured by Hydro-Quebec are all within the most dominant SWE class of each map. Further validation of the results will be possible when the algorithm can be applied on a sub-watershed, which is the actual scale used by Hydro-Quebec. However, the results of this study were sufficiently promising to Hydro-Quebec to support a follow up research with data from the canadian satellite RADARSAT (operational since april 1996). Meanwhile, to improve the algorithm, it is important to obtain a good and homogeneous reference image, to better assess the impact of the land cover and to acquire a dataset with a greater range of snow characteristics

Stability of an oscillating tip in Non-Contact Atomic Force Microscopy: theoretical and numerical investigations

This paper is a theoretical and a numerical investigation of the stability of a tip-cantilever system used in Non-Contact Atomic Force Microscopy (NC-AFM) when it oscillates close to a surface. No additional dissipative force is considered. The theoretical approach is based on a variationnal method exploiting a coarse grained operation that gives the temporal dependence of the nonlinear coupled equations of motion in amplitude and phase of the oscillator. Stability criterions for the resonance peak are deduced and predict a stable behavior of the oscillator in the vicinity of the resonance. The numerical approach is based on results obtained with a virtual NC-AFM developped in our group. The effect of the size of the stable domain in phase is investigated. These results are in particularly good agreement with the theoretical predictions. Also they show the influence of the phase shifter in the feedback loop and the way it can affect the damping signal

On the Hausdorff volume in sub-Riemannian geometry

For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous function. We then prove that up to dimension 4 it is smooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4 on every smooth curve) but in general not C^5. These results answer to a question addressed by Montgomery about the relation between two intrinsic volumes that can be defined in a sub-Riemannian manifold, namely the Popp and the Hausdorff volume. If the nilpotent approximation depends on the point (that may happen starting from dimension 5), then they are not proportional, in general.Comment: Accepted on Calculus and Variations and PD

Heat transport by turbulent Rayleigh-B\'enard convection for $\Pra\ \simeq 0.8and and 3\times 10^{12} \alt \Ra\ \alt 10^{15}:Aspectratio: Aspect ratio \Gamma = 0.50$

We report experimental results for heat-transport measurements, in the form of the Nusselt number \Nu, by turbulent Rayleigh-B\'enard convection in a cylindrical sample of aspect ratio $\Gamma \equiv D/L = 0.50$ ($D = 1.12$ m is the diameter and $L = 2.24$ m the height). The measurements were made using sulfur hexafluoride at pressures up to 19 bars as the fluid. They are for the Rayleigh-number range 3\times 10^{12} \alt \Ra \alt 10^{15} and for Prandtl numbers \Pra\ between 0.79 and 0.86. For \Ra < \Ra^*_1 \simeq 1.4\times 10^{13} we find \Nu = N_0 \Ra^{\gamma_{eff}} with $\gamma_{eff} = 0.312 \pm 0.002$, consistent with classical turbulent Rayleigh-B\'enard convection in a system with laminar boundary layers below the top and above the bottom plate. For \Ra^*_1 < \Ra < \Ra^*_2 (with \Ra^*_2 \simeq 5\times 10^{14}) $\gamma_{eff}$ gradually increases up to $0.37\pm 0.01$. We argue that above \Ra^*_2 the system is in the ultimate state of convection where the boundary layers, both thermal and kinetic, are also turbulent. Several previous measurements for $\Gamma = 0.50$ are re-examined and compared with the present results.Comment: 44 pages, 18 figures, submitted to NJ

Boolean Chaos

We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may find application as an ultra-wide-band source of radio wavesComment: 10 pages and 4 figur

Segregation and ordering at the (1×2) reconstructed Pt80Fe20(110) surface determined by low-energy electron diffraction

The surface of an ordered Pt80Fe20(110) crystal exhibits (1×2) and (1×3) reconstructions depending on the annealing treatment after ion bombardment. The (1×3) structure occurs after annealing in the range 750 to 900 K. Annealing above 1000 K leads to the (1×2) structure, which is, from the present result, unambiguously attributed to the same geometrical reconstruction as Pt(110) but with smaller relaxation amplitudes: a detailed low-energy electron-diffraction analysis concludes to a missing-row structure with row pairing in layers 2 and 4 accompanied by a buckling in layers 3 and 5. The top layer spacing is contracted by 13%, and further relaxations are detectable down to the fifth layer. The specific diffraction spots associated with the bulk chemical ordering along the dense [1¯10] rows are very weak: The I(V) analysis shows that this chemical ordering is absent in the outermost ‘‘visible’’ rows but gradually recovers over five to six layers deep. General Pt enrichment is found in the surface ‘‘visible’’ rows (in layers 1–3), but segregation and order yield a subtle redistribution of Pt and Fe atoms in deeper rows: For example, in layer 2, the visible row is Pt rich, whereas the other row (buried under layer 1) is enriched with Fe. Because of the many parameters considered, a fit procedure was applied to a large data basis to solve the structure; the results were confirmed and illustrated subsequently by a standard I(V) analysis for the most relevant parameters. The final r factors are RDE=0.36, RP=0.34, and RZJ=0.14 for two beam sets at normal and oblique incidence consisting of 26 and 21 beams, respectively

Numerical simulations of compressible Rayleigh-Taylor turbulence in stratified fluids

We present results from numerical simulations of Rayleigh-Taylor turbulence, performed using a recently proposed lattice Boltzmann method able to describe consistently a thermal compressible flow subject to an external forcing. The method allowed us to study the system both in the nearly-Boussinesq and strongly compressible regimes. Moreover, we show that when the stratification is important, the presence of the adiabatic gradient causes the arrest of the mixing process.Comment: 15 pages, 11 figures. Proceedings of II Conference on Turbulent Mixing and Beyond (TMB-2009

AC Losses in the First ITER CS Module Tests: Experimental Results and Comparison to Analytical Models

The ITER Central Solenoid (CS) will be manufactured by assembling a stack of six modules, which are under fabrication by the US ITER organization and its subcontractors. The tests of the first CS Module have been performed at the premises of the General Atomics (GA) facility in Poway (US), in order to check compliance to the ITER requirements. Among other tests, the magnet was submitted to exponential dumps of the transport current from different initial values (10, 15, 20, 22.5, 25, 35, 40 kA) down to 0 kA. These tests are aimed at conducting DC breaker commissioning of the test facility and were used to measure the AC losses in the coil during electrodynamic transients. This paper presents the results of these measurements, along with a comparison with analytical computations of the losses in the magnet

Reconstructing the primordial power spectrum from the CMB

We propose a straightforward and model independent methodology for characterizing the sensitivity of CMB and other experiments to wiggles, irregularities, and features in the primordial power spectrum. Assuming that the primordial cosmological perturbations are adiabatic, we present a function space generalization of the usual Fisher matrix formalism, applied to a CMB experiment resembling Planck with and without ancillary data. This work is closely related to other work on recovering the inflationary potential and exploring specific models of non-minimal, or perhaps baroque, primordial power spectra. The approach adopted here, however, most directly expresses what the data is really telling us. We explore in detail the structure of the available information and quantify exactly what features can be reconstructed and at what statistical significance.Comment: 43 pages Revtex, 23 figure