Analytical ray-tracing in planetary atmospheres

Ground-based astro-geodetic observations and atmospheric occultations, are two examples of observational techniques requiring a scrutiny analysis of atmospheric refraction. In both cases, the measured changes in observables are geometrically related to changes in the photon path and the light time of the received electromagnetic signal. In the context of geometrical optics, the change in the physical properties of the signal are related to the refractive profile of the crossed medium. Therefore, having a clear knowledge of how the refractivity governs the photon path and the light time evolution is of prime importance to clearly understand observational features. Analytical studies usually focused on spherically symmetric atmospheres and only few aimed at exploring the effect of the non-spherical symmetry on the observables. In this paper, we analytically perform the integration of the photon path and the light time of rays traveling across a planetary atmosphere. We do not restrict our attention to spherically symmetric atmospheres and introduce a comprehensive mathematical framework which allows to handle any kind of analytical studies in the context of geometrical optics. To highlight the capabilities of this new formalism, we carry out five realistic applications for which we derive analytical solutions. The accuracy of the method of integration is assessed by comparing our results to a numerical integration of the equations of geometrical optics in the presence of a quadrupolar moment $J_2$. This shows that the analytical solution leads to the determination of the light time and the refractive bending with relative errors at the level of one part in $10^8$ and one part in $10^5$, for typical values of the refractivity and the $J_2$ parameter at levels of $10^{-4}$ and $10^{-2}$, respectively

Integrated model for beach nourishment design, post-nourishment monitoring and beach-maintenance refills

The Grain-size Nourishment Model (GNM) is a new numerical model that forecasts in 3D the littoral features following the nourishment intervention. Its predictions concern: (a) beach and shoreface morphology; (b) shoreline position; (c) geometry of the artificial deposit; (d) sediment amount for the intervention; (e) geographic distribution of sedimentological parameters (mean size, sorting, percentage of sand and mud). Theory and principles of calculation are presented in this paper together to two applications of the model

Experimental verification of a simple method for accurate center of gravity determination of small satellite platforms

We propose a simple and relatively inexpensive method for determining the center of gravity (CoG) of a small spacecraft. This method, which can be ascribed to the class of suspension techniques, is based on dual-axis inclinometer readings. By performing two consecutive suspensions from two different points, the CoG is determined, ideally, as the intersection between two lines which are uniquely defined by the respective rotations. We performed an experimental campaign to verify the method and assess its accuracy. Thanks to a quantitative error budget, we obtained an error distribution with simulations, which we verified through experimental tests. The retrieved experimental error distribution agrees well with the results predicted through simulations, which in turn lead to a CoG error norm smaller than 2mm with 95% confidence level

Transgressive coastal systems (1st part): barrier migration processes and geometric principles

Coastal processes during transgression have been explored through morpho-kinematic simulations using the Shoreface Translation Model (STM). Our STM experiments show that the landward migration of coastal system is controlled by the rate of sea level rise (SLR), the rate of sediment supply (Vs), the shelf slope (?), and the morphology of the coastal profile (M). Additionally, the geometric relationships between shoreface and plane of translation govern three kinematic modes of coastal barrier migration: (1) roll-over, (2) hybrid, (3) encroachment. Each mode exhibits differences along the coastal profile in relation to zones of erosion (cut) and redeposition (fill) and to the consequent sediment exchanges across the profile (from the cut to the fill). Each mode produces distinctive facies architectures and specific stratigraphic position of the shoreface-ravinement surface. Environmental conditions (rates of sea-level rise, sediment supply (±), barrier morphology) and kinematic modes both control stratal preservation. Transgressive roll-over, in particular, occurs on gently sloping shelves and involves erosion along the entire shoreface and landward sediment redeposition (by overwash and tidal inlet processes). Three different types of roll-over are possible depending on the conditions of sediment supply (Vs) to the coastal cell: neutral roll-over (Vs=0 m3), which produces no effect on the shelf; depositional roll-over (Vs >0) and erosional (Vs<0) roll-over, which modify the shelf through stratal preservation and erosion, respectively. These differences are quantified in simulations by tracking parameters that principally relate to the trajectory of a ‘neutral point’ (maximum depth of shoreface erosion). The shoreface-ravinement defines the trajectory in all the transgressions and in principle is preserved in the rock record, making it a much more useful tracking point than the shoreline trajectory analysed in other studies. Coastal migration in all kinematic modes includes state-dependent inertial effects, experimentally well evident when, after a perturbation, the drivers (SLR, Vs, ?, M) are maintained constant for a long interval of time. Kinematic inertia appears as progressive geometric self-adjustments of the barrier until it acquires a shape that is stable under prevailing conditions (constant drivers). At this stage (kinematic equilibrium), which is unlikely ever to be attained in nature, simulated transgressions finally evolve with processes and geological products that remain invariant. Kinematic inertia is likely to be an additional factor that governs the real transgressions under most circumstances

Transgressive coastal systems (2nd part): geometric principles of stratal preservation on gently sloping continental shelves

This study focuses on the causes and mechanisms of coastal-lithosome preservation during transgressions driven by roll-over processes of barrier migration. Using the Shoreface Translation Model, a large range of idealised coastal settings was simulated to identify the environmental conditions of stratal preservation. Preservation occurs within two broad categories of experimental conditions. The first category relates to transgressive phases evolving under relatively constant conditions in which stratal preservation takes place only if the coastal barrier experiences positive net sediment supplies. The resulting deposits show tabular geometries, have poorly differentiated internal architectures and tend to extend continuously with quite uniform thickness upslope across plain regions of the shelf. In the second category, by comparison, deposits are thicker and stratal preservation is more localised. Moreover preservation occurs as an adaptive morpho-kinematic response to environmental perturbations due to variations in: (1) the ratio of sediment supply (Vs) to accommodation generated by sea-level rise (SLR); (2) the substrate topography; (3) the morphology of the barrier profile. More specifically, changes of the ratio Vs /SLR, where SLR is an approximate surrogate for added accommodation space, directly promotes growth of the barrier (Vs /SLR >> 0) and its subsequent drowning (Vs /SLR?0). The topographic variations of the substrate may include minor irregularities as well as sudden changes in gradient that afford other types of preservation, such as local fills and residual littoral packages. Finally, barrier-profile changes inducing stratal preservation may include the reduction in barrier width and depth of surf base as well as the increment in shoreface concavity and shoreface length. Simplified methods are given for relating the geometry of preserved deposits to rates of sea-level rise and sediment supply over different shelf slopes, and for identifying the position of the shoreline at specific times. Holocene evolution of some coastal deposits from the Tuscan shelf (Italy) is presented in a morpho kinematic reconstruction to illustrate the geometric relationships for stratal preservation

MATNet: Multi-Level Fusion and Self-Attention Transformer-Based Model for Multivariate Multi-Step Day-Ahead PV Generation Forecasting

The integration of renewable energy sources (RES) into modern power systems has become increasingly important due to climate change and macroeconomic and geopolitical instability. Among the RES, photovoltaic (PV) energy is rapidly emerging as one of the world's most promising. However, its widespread adoption poses challenges related to its inherently uncertain nature that can lead to imbalances in the electrical system. Therefore, accurate forecasting of PV production can help resolve these uncertainties and facilitate the integration of PV into modern power systems. Currently, PV forecasting methods can be divided into two main categories: physics-based and data-based strategies, with AI-based models providing state-of-the-art performance in PV power forecasting. However, while these AI-based models can capture complex patterns and relationships in the data, they ignore the underlying physical prior knowledge of the phenomenon. Therefore, we propose MATNet, a novel self-attention transformer-based architecture for multivariate multi-step day-ahead PV power generation forecasting. It consists of a hybrid approach that combines the AI paradigm with the prior physical knowledge of PV power generation of physics-based methods. The model is fed with historical PV data and historical and forecast weather data through a multi-level joint fusion approach. The effectiveness of the proposed model is evaluated using the Ausgrid benchmark dataset with different regression performance metrics. The results show that our proposed architecture significantly outperforms the current state-of-the-art methods with an RMSE equal to 0.0460. These findings demonstrate the potential of MATNet in improving forecasting accuracy and suggest that it could be a promising solution to facilitate the integration of PV energy into the power grid

Stochastic Gravitational Wave Background: Upper Limits in the 10–6 to 10–3 Hz Band

We have used precision Doppler tracking of the Cassini spacecraft during its 2001-2002 solar opposition to derive improved observational limits to an isotropic background of low-frequency gravitational waves. Using the Cassini multilink radio system and an advanced tropospheric calibration system, the effects of heretofore leading noises—plasma and tropospheric scintillation—were, respectively, removed and calibrated to levels lower than other noises. The resulting data were used to construct upper limits to the strength of an isotropic background in the 10-6 to 10-3 Hz band. Our results are summarized as limits on the strain spectrum Sh( f), the characteristic strain (hc = the square root of the product of the frequency and the one-sided spectrum of strain at that frequency), and the energy density (Ω = energy density in bandwidth equal to center frequency assuming a locally white energy density spectrum, divided by the critical density). Our best limits are Sh( f) < 6 × 10-27 Hz-1 at several frequencies in the millihertz band, hc < 2 × 10-15 at about 0.3 mHz, and Ω < 0.025 × h, where h75 is the Hubble constant in units of 75 km s-1 Mpc-1, at 1.2 × 10-6 Hz. These are the best observational limits in the low-frequency band, the bound on Ω, for example, being about 3 orders of magnitude better than previous constraints from Doppler tracking

Analytical study of the radio signals propagation in planetary atmospheres

The ESA JUICE (JUpiter ICy moons Explorer) mission is planned for launch in 2022 and arrival at Jupiter around 2030. The mission is dedicated to the study of the giant gaseous and its largest moons. While the spacecraft will probe the Jovian system it will be occulted by the atmosphere of Jupiter or its satellites as seen from antennas on Earth. Such a configuration offers a great opportunity to study remotely the physical properties of the occulting atmosphere using radio links as the probe is being occulted. Indeed, non-unity index of refraction causes the electromagnetic waves to depart from the straight line and also impacts the propagation speed of the waves. Both changes modify the wave frequency and conversely, from the time variation of the Doppler measurements the index of refraction profile can be retrieved. In the literature, there are different approaches devoted to the retrieval of the refractive profile from these observables. Let mention, i) the analytic formulation of the Abel inversion which is employed for spherically symmetric atmospheres, and ii) the ray tracing method which is a numerical integration of the fundamental equations of optics and which is well suited for atmospheres with more complicated shapes. Both possess their own advantages and inconveniences. For instance, to invert a complete set of data, the ray tracing method requires more computational time than the Abel transformation. In return, the Abel inversion is based on the spherical symmetry assumption while the ray tracing technique can handle non-radial gradient in the refractive profile. In the context of the future occultations of JUICE by Jupiter, we discuss the benefit of a new formalism based on a full reformulation of the fundamental equations of optics. This new approach let to provide a very comprehensive description of the light trajectory inside a planetary atmosphere with no assumption on the refractive profile. In the special case where the departure from the spherical symmetry is small, we present an analytic solution which is well suited for the data processing of radio occultation experiments. Indeed, this solution can handle the effect of a non-spherically symmetric atmosphere with a low computational cost. We use this solution to process the Cassini Doppler data acquired during an occultation by the oblate atmosphere of Saturn. The validity of the proposed approach is assessed comparing the results with other studies available in the literature

Detection of rapid orbital expansion of Saturn’s moon Titan

The Saturn satellite system is a complex dynamical system with several gravitational interactions happening between the satellites, the rings and the central body, such as resonances, librations and tides. These intricate dynamics carry information on the formation and evolution of the Saturn and Solar systems