Capture into first-order resonances and long-term stability of pairs of equal-mass planets

Massive planets form within the lifetime of protoplanetary disks, and therefore, they are subject to orbital migration due to planet–disk interactions. When the first planet reaches the inner edge of the disk, its migration stops and consequently the second planet ends up locked in resonance with the first one. We detail how the resonant trapping works comparing semi-analytical formulae and numerical simulations. We restrict to the case of two equal-mass coplanar planets trapped in first-order resonances, but the method can be easily generalized. We first describe the family of resonant stable equilibrium points (zero-amplitude libration orbits) using series expansions up to different orders in eccentricity as well as a non-expanded Hamiltonian. Then we show that during convergent migration the planets evolve along these families of equilibrium points. Eccentricity damping from the disk leads to a final equilibrium configuration that we predict precisely analytically. The fact that observed multi-exoplanetary systems are rarely seen in resonances suggests that in most cases the resonant configurations achieved by migration become unstable after the removal of the protoplanetary disk. Here we probe the stability of the resonances as a function of planetary mass. For this purpose, we fictitiously increase the masses of resonant planets, adiabatically maintaining the low-amplitude libration regime until instability occurs. We discuss two hypotheses for the instability, that of a low-order secondary resonance of the libration frequency with a fast synodic frequency of the system, and that of minimal approach distance between planets. We show that secondary resonances do not seem to impact resonant systems at low amplitude of libration. Resonant systems are more stable than non-resonant ones for a given minimal distance at close encounters, but we show that the latter nevertheless play the decisive role in the destabilization of resonant pairs. We show evidence that as the planetary mass increases and the minimal distance between planets gets smaller in terms of mutual Hill radius, the region of stability around the resonance center shrinks, until the equilibrium point itself becomes unstable.     

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.     

Classifying zones of suitability for manual drilling using textural and hydraulic parameters of shallow aquifers: a case study in northwestern Senegal

A method is proposed that uses analysis of borehole stratigraphic logs for the characterization of shallow aquifers and for the assessment of areas suitable for manual drilling. The model is based on available borehole-log parameters: depth to hard rock, depth to water, thickness of laterite and hydraulic transmissivity of the shallow aquifer. The model is applied to a study area in northwestern Senegal. A dataset of boreholes logs has been processed using a software package (TANGAFRIC) developed during the research. After a manual procedure to assign a standard category describing the lithological characteristics, the next step is the automated extraction of different textural parameters and the estimation of hydraulic conductivity using reference values available in the literature. The hydraulic conductivity values estimated from stratigraphic data have been partially validated, by comparing them with measured values from a series of pumping tests carried out in large-diameter wells. The results show that this method is able to produce a reliable interpretation of the shallow hydrogeological context using information generally available in the region. The research contributes to improving the identification of areas where conditions are suitable for manual drilling. This is achieved by applying the described method, based on a structured and semi-quantitative approach, to classify the zones of suitability for given manual drilling techniques using data available in most African countries. Ultimately, this work will support proposed international programs aimed at promoting low-cost water supply in Africa and enhancing access to safe drinking water for the population.     

Spatial modelling and uncertainty assessment of pyroclastic cover thickness in the Sorrento Peninsula

Assessing spatial variability of soil thickness is a critical issue for understanding and predicting slope processes. The present work was aimed at estimating the spatial scales at which the variation of pyroclastic cover thickness occurs in a sample area in the Sorrento Peninsula (Italy). Stochastic simulation was used to understand the spatial variability of pyroclastic cover thickness on Mount Pendolo and to assess its spatial uncertainty. In the study area, covering about 0.7 km², thickness measurements were collected using electrical resistivity tomography profiles, continuous core drillings and steel rod penetrometric tests. Variographic analysis revealed the occurrence of an anisotropic behaviour along the N50 and N140 directions. In the latter anisotropic direction, a nested variogram was fitted including (1) a long-range component which could be related to large-scale factors, like the curvature of the slope and contributing area and (2) a shorter scale variation which is probably associated with the occurrence of denudation processes or to the articulate cover/bedrock interface. To assess the spatial variability and uncertainty of pyroclastic cover thickness, a stochastic simulation algorithm was used and 500 equally probable images of cover thickness were yielded. The results showed that a better thickness distribution map can be drawn by simulating the data collected on the slope and at the footslope separately. The approach also allowed delineating the areas characterized by greater uncertainty, suggesting supplementary measurements to further improve the cover thickness distribution model, thus reducing the uncertainty.     

Runoff-generated debris flows: Observation of initiation conditions and erosion–deposition dynamics along the channel at Cancia (eastern Italian Alps)

In the Dolomitic region, abundant coarse hillslope sediment is commonly found at the toe of rocky cliffs. Ephemeral channels originate where lower permeability bedrock surfaces concentrate surface runoff. Debris flows initiate along such channels following intense rainfall and determine the progressive erosion and deepening of the channels. Sediment recharge mechanisms include rock fall, dry ravel processes and channel-bank failures. Here we document debris flow activity that took place in an active debris flow basin during the year 2015. The Cancia basin is located on the southwestern slope of Mount Antelao (3264 m a.s.l.) in the dolomitic region of the eastern Italian Alps. The 2.5 km² basin is incised in dolomitic limestone rocks. The data consist of repeated topographic surveys, distributed rainfall measurements, time-lapse (2 s) videos of two events and pore pressure measurements in the channel bed. During July and August 2015, two debris flow events occurred, following similarly intense rainstorms. We compared rainfall data to existing rainfall triggering thresholds and simulated the hydrological response of the headwater catchment with a distributed model in order to estimate the total and peak water discharge. Our data clearly illustrate how debris entrainment along the channel is the main contributor to the overall mobilized volume and that erosion is dominant when the channel slope exceeds 16°. Further downstream, sediment accumulation and depletion occurred alternately for the two successive events, indicating that sediment availability along the channel also influences the flow behaviour along the prevailing-transport reach. The comparison between monitoring data, topographical analysis and hydrological simulation allows the estimation of the average solid concentration of the two events and suggests that debris availability has a significant influence on the debris flow volume. © 2020 John Wiley & Sons, Ltd.     

Comparison of four meteorite penetration funnels in the Campo del Cielo crater field,Argentina

Abstract– More craters may be discovered in the future, but as it is currently known, the Campo del Cielo crater field is 18 km long by 4 km at its widest point. Such a distribution of craters suggests that the parent meteoroid entered and traversed the atmosphere at a very low angle relative to horizontal. The crater field contains at least 20 small craters produced by the larger fragments of the parent meteoroid. Four of these are explosion analog craters and the rest are penetration funnels. During four field seasons, we have constructed topographic and magnetic maps of four of the penetration funnels as found, and then dug trenches across them to learn their original structures and recover meteorites preserved within them. Structures of these penetration funnels indicate very low angles of impact, i.e., 9–16° relative to horizontal. This supports the idea that the parent meteoroid traversed the atmosphere at a low angle. Data given here for the four penetration funnels include projectile masses, lengths, widths, depths, and estimates of impact angles and azimuths. One of the penetration funnels described here (No. 6) can almost be classified as an explosion analog crater.     

Impact of grid resolution on the integrated and distributed response of a coupled surface–subsurface hydrological model for the des Anglais catchment,Quebec

Digital elevation models (DEMs) at different resolutions (180, 360, and 720 m) are used to examine the impact of different levels of landscape representation on the hydrological response of a 690‐km² catchment in southern Quebec. Frequency distributions of local slope, plan curvature, and drainage area are calculated for each grid size resolution. This landscape analysis reveals that DEM grid size significantly affects computed topographic attributes, which in turn explains some of the differences in the hydrological simulations. The simulations that are then carried out, using a coupled, process‐based model of surface and subsurface flow, examine the effects of grid size on both the integrated response of the catchment (discharge at the main outlet and at two internal points) and the distributed response (water table depth, surface saturation, and soil water storage). The results indicate that discharge volumes increase as the DEM is coarsened, and that coarser DEMs are also wetter overall in terms of water table depth and soil water storage. The reasons for these trends include an increase in the total drainage area of the catchment for larger DEM cell sizes, due to aggregation effects at the boundary cells of the catchment, and to a decrease in local slope and plan curvature variations, which in turn limits the capacity of the watershed to transmit water downslope and laterally. The results obtained also show that grid resolution effects are less pronounced during dry periods when soil moisture dynamics are mostly controlled by vertical fluxes of evaporation and percolation. Copyright © 2010 John Wiley & Sons, Ltd.     

An Analysis of the Coastal Fish Assemblage of the Ustica Island Marine Reserve (Mediterranean Sea)

A study of the coastal fish assemblages in the marine park of Ustica Island (Southern Tyrrhenian Sea, Mediterranean) was conducted from June 1994 to September 1995 and from June 1996 to September 1997. The principal aims of the research were to: (1) define the faunistic features of local fish communities; (2) assess the effectiveness of the protection regime of the marine park on the fish assemblages ('reserve effect'); (3) provide information on the distribution of some Epinephelus and Diplodus species in the shallowest depth zone of the island. During seasonal surveys, underwater visual censuses were carried out at several sites located in three zones of the island, each with a different level of protection. Observations were made along 250 m² transects at 3–5, 10–15 and 25–30 m depth ranges. Additional surveys were made by SCUBA diving and snorkelling. A statistically significant effect of depth on the fish community parameters was observed, whereas differences linked to protection level, zones, sites and seasons were not significant. The abundance and frequency of occurrence of some species, particularly dusky grouper Epinephelus marginatus , were positively correlated with the degree of protection of the different zones of the marine park. Certain sites of the island are important as nursery areas for three species of the genus Diplodus ( i.e., D. puntazzo, D. sargus and D. vulgaris ).