Improvement of streams hydro‐geomorphological assessment using LiDAR DEMs

Hydro‐geomorphological assessments are an essential component for riverine management plans. They usually require costly and time‐consuming field surveys to characterize the spatial variability of key variables such as flow depth, width, discharge, water surface slope, grain size and unit stream power throughout the river corridor. The objective of this research is to develop automated tools for hydro‐geomorphological assessments using high‐resolution LiDAR digital elevation models (DEMs). More specifically, this paper aims at developing geographic information system (GIS) tools to extract channel slope, width and discharge from 1 m‐resolution LiDAR DEMs to estimate the spatial distribution of unit stream power in two contrasted watersheds in Quebec: a small agricultural stream (Des Fèves River) and a large gravel‐bed river (Matane River). For slope, the centreline extracted from the raw LiDAR DEM was resampled at a coarser resolution using the minimum elevation value. The channel width extraction algorithm progressively increased the centerline from the raw DEM until thresholds of elevation differences and slopes were reached. Based on the comparison with over 4000 differential global positioning system (GPS) measurements of the water surface collected in a 50 km reach of the Matane River, the longitudinal profile and slope estimates extracted from the raw and resampled LiDAR DEMs were in very good agreement with the field measurements (correlation coefficients ranging from 0 · 83 to 0 · 87) and can thus be used to compute stream power. The extracted width also corresponded very well to the channel as seen from ortho‐photos, although the presence of bars in the Matane River increased the level of error in width estimates. The estimated maximum unit stream power spatial patterns corresponded well with field evidence of bank erosion, indicating that LiDAR DEMs can be used with confidence for initial hydro‐geomorphological assessments. Copyright © 2013 John Wiley & Sons, Ltd.     

A semi-numerical expansion of the averaged disturbing function for some very-high-eccentricity orbits

A note on the construction of expansions of the disturbing function valid for any eccentricity and on some applications.     

Backwater effects in the Amazon River basin of Brazil

The Amazon River mainstem of Brazil is so regulated by differences in the timing of tributary inputs and by seasonal storage of water on floodplains that maximum discharges exceed minimum discharges by a factor of only 3. Large tributaries that drain the southern Amazon River basin reach their peak discharges two months earlier than does the mainstem. The resulting backwater in the lowermost 800 km of two large southern tributaries, the Madeira and Purús rivers, causes falling river stages to be as much as 2–3 m higher than rising stages at any given discharge. Large tributaries that drain the northernmost Amazon River basin reach their annual minimum discharges three to four months later than does the mainstem. In the lowermost 300–400 km of the Negro River, the largest northern tributary and the fifth largest river in the world, the lowest stages of the year correspond to those of the Amazon River mainstem rather than to those in the upstream reaches of the Negro River.     

Tidal synchronization of an anelastic multi-layered body: Titan’s synchronous rotation

Tidal torque drives the rotational and orbital evolution of planet–satellite and star–exoplanet systems. This paper presents one analytical tidal theory for a viscoelastic multi-layered body with an arbitrary number of homogeneous layers. Starting with the static equilibrium figure, modified to include tide and differential rotation, and using the Newtonian creep approach, we find the dynamical equilibrium figure of the deformed body, which allows us to calculate the tidal potential and the forces acting on the tide generating body, as well as the rotation and orbital elements variations. In the particular case of the two-layer model, we study the tidal synchronization when the gravitational coupling and the friction in the interface between the layers is added. For high relaxation factors (low viscosity), the stationary solution of each layer is synchronous with the orbital mean motion (n) when the orbit is circular, but the rotational frequencies increase if the orbital eccentricity increases. This behavior is characteristic in the classical Darwinian theories and in the homogeneous case of the creep tide theory. For low relaxation factors (high viscosity), as in planetary satellites, if friction remains low, each layer can be trapped in different spin-orbit resonances with frequencies \(n/2,n,3n/2,2n,\ldots \). When the friction increases, attractors with differential rotations are destroyed, surviving only commensurabilities in which core and shell have the same velocity of rotation. We apply the theory to Titan. The main results are: (i) the rotational constraint does not allow us to confirm or reject the existence of a subsurface ocean in Titan; and (ii) the crust-atmosphere exchange of angular momentum can be neglected. Using the rotation estimate based on Cassini’s observation (Meriggiola et al. in Icarus 275:183–192, 2016), we limit the possible value of the shell relaxation factor, when a deep subsurface ocean is assumed, to \(\gamma _s\lesssim 10^{-9}\,\hbox {s}^{-1}\), which corresponds to a shell’s viscosity \(\eta _s\gtrsim 10^{18}\,\hbox {Pa}\,\hbox {s}\), depending on the ocean’s thickness and viscosity values. In the case in which a subsurface ocean does not exist, the maximum shell relaxation factor is one order of magnitude smaller and the corresponding minimum shell’s viscosity is one order higher.     

Modeling the 3-D secular planetary three-body problem: Discussion on the outer υ Andromedae planetary system

The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in geometrical pictures allowing us to investigate a large domain of the phase space of this problem without time-expensive numerical integrations of the equations of motion and without any restriction on the magnitude of the planetary eccentricities, inclinations and mutual distance. Several regimes of motion of the system are observed. With respect to the secular angle Δ?, possible motions are circulations, oscillations (around 0° and 180°), and high-eccentricity/inclination librations in secular resonances. With respect to the arguments of pericenter, ω₁ and ω₂, possible motions are direct circulation and high-inclination libration around ±90° in the Lidov-Kozai resonance. The regions of transition between domains of different regimes of motion are characterized by chaotic behavior. We apply the analysis to the case of the two outer planets of the υ Andromedae system, observed edge-on. The topology of the 3-D phase space of this system is investigated in detail by means of surfaces of section, periodic orbits and dynamical spectra, mapping techniques and numerical simulations. We obtain the general structure of the phase space, and the boundaries of the spatial secular stability. We find that this system is secularly stable in a large domain of eccentricities and inclinations.     

Dynamic portrait of the planetary 2/1 mean-motion resonance – I. Systems with a more massive outer planet

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant domain, we show the existence of two families of periodic orbits, one associated to the librational motion of resonant angle (σ-family) and the other related to the circulatory motion of the difference in longitudes of pericentre (  Δϖ  -family). The well-known apsidal corotation resonances (ACR) appear as intersections between both families. A complex web of secondary resonances is also detected for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system.
The construction of dynamical maps for various values of the total angular momentum shows the evolution of the families of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. For low–moderate eccentricities, several different stable modes exist outside the ACR. For larger eccentricities, however, all stable solutions are associated to oscillations around the stationary solutions.
Finally, we present a possible link between these stable families and the process of resonance capture, identifying the most probable routes from the secular region to the resonant domain, and discussing how the final resonant configuration may be affected by the extension of the chaotic layer around the resonance region.     

A Perturbative Treatment of The Co-Orbital Motion

We develop a formalism of the non-singular evaluation of the disturbing function and its derivatives with respect to the canonical variables. We apply this formalism to the case of the perturbed motion of a massless body orbiting the central body (Sun) with a period equal to that of the perturbing (planetary) body. This situation is known as the co-orbital motion, or equivalently, as the 1/1 mean motion commensurability. Jupiter's Trojan asteroids, Earth's co-orbital asteroids (e.g., (3753) Cruithne, (3362) Khufu), Mars' co-orbital asteroids (e.g., (5261) Eureka), and some Jupiter-family comets are examples of the co-orbital bodies in our solar system. Other examples are known in the satellite systems of the giant planets. Unlike the classical expansions of the disturbing function, our formalism is valid for any values of eccentricities and inclinations of the perturbed and perturbing body. The perturbation theory is used to compute the main features of the co-orbital dynamics in three approximations of the general three-body model: the planar-circular, planar-elliptic, and spatial-circular models. We develop a new perturbation scheme, which allows us to treat cases where the classical perturbation treatment fails. We show how the families of the tadpole, horseshoe, retrograde satellite and compound orbits vary with the eccentricity and inclination of the small body, and compute them also for the eccentricity of the perturbing body corresponding to a largely eccentric exoplanet's orbit.This revised version was published online in October 2005 with corrections to the Cover Date.