3,464 research outputs found
Spatiospectral concentration on a sphere
We pose and solve the analogue of Slepian's time-frequency concentration
problem on the surface of the unit sphere to determine an orthogonal family of
strictly bandlimited functions that are optimally concentrated within a closed
region of the sphere, or, alternatively, of strictly spacelimited functions
that are optimally concentrated within the spherical harmonic domain. Such a
basis of simultaneously spatially and spectrally concentrated functions should
be a useful data analysis and representation tool in a variety of geophysical
and planetary applications, as well as in medical imaging, computer science,
cosmology and numerical analysis. The spherical Slepian functions can be found
either by solving an algebraic eigenvalue problem in the spectral domain or by
solving a Fredholm integral equation in the spatial domain. The associated
eigenvalues are a measure of the spatiospectral concentration. When the
concentration region is an axisymmetric polar cap the spatiospectral projection
operator commutes with a Sturm-Liouville operator; this enables the
eigenfunctions to be computed extremely accurately and efficiently, even when
their area-bandwidth product, or Shannon number, is large. In the asymptotic
limit of a small concentration region and a large spherical harmonic bandwidth
the spherical concentration problem approaches its planar equivalent, which
exhibits self-similarity when the Shannon number is kept invariant.Comment: 48 pages, 17 figures. Submitted to SIAM Review, August 24th, 200
Use of remotely-derived bathymetry for modelling biomass in marine environments
The paper presents results on the influence of geometric attributes of satellite-derived raster bathymetric data, namely the General Bathymetric Charts of the Oceans, on spatial statistical modelling of marine biomass. In the initial experiment, both the resolution and projection of the raster dataset are taken into account. It was found that, independently of the equal-area projection chosen for the analysis, the calculated areas are very similar, and the differences between them are insignificant. Likewise, any variation in the raster resolution did not change the computed area. Although the differences were shown to be insignificant, for the subsequent analysis we selected the cylindrical equal area projection, as it implies rectangular spatial extent, along with the automatically derived resolution. Then, in the second experiment, we focused on demersal fish biomass data acquired from trawl samples taken from the western parts of ICES Sub-area VII, near the sea floor. The aforementioned investigation into processing bathymetric data allowed us to build various statistical models that account for a relationship between biomass, sea floor topography and geographic location. We fitted a set of generalised additive models and generalised additive mixed models to combinations of trawl data of the roundnose grenadier (Coryphaenoides rupestris) and bathymetry. Using standard statistical techniquesâsuch as analysis of variance, Akaike information criterion, root mean squared error, mean absolute error and cross-validationâwe compared the performance of the models and found that depth and latitude may serve as statistically significant explanatory variables for biomass of roundnose grenadier in the study area. However, the results should be interpreted with caution as sampling locations may have an impact on the biomassâdepth relationship
How large are present-day heat flux variations across the surface of Mars?
©2016. American Geophysical UnionThe first in situ Martian heat flux measurement to be carried out by the InSight Discoveryâclass mission will provide an important baseline to constrain the presentâday heat budget of the planet and, in turn, the thermochemical evolution of its interior. In this study, we estimate the magnitude of surface heat flux heterogeneities in order to assess how the heat flux at the InSight landing site relates to the average heat flux of Mars. To this end, we model the thermal evolution of Mars in a 3âD spherical geometry and investigate the resulting surface spatial variations of heat flux at the present day. Our models assume a fixed crust with a variable thickness as inferred from gravity and topography data and with radiogenic heat sources as obtained from gamma ray measurements of the surface. We test several mantle parameters and show that the presentâday surface heat flux pattern is dominated by the imposed crustal structure. The largest surface heat flux peakâto peak variations lie between 17.2 and 49.9 mW mâ2, with the highest values being associated with the occurrence of prominent mantle plumes. However, strong spatial variations introduced by such plumes remain narrowly confined to a few geographical regions and are unlikely to bias the InSight heat flux measurement. We estimated that the average surface heat flux varies between 23.2 and 27.3 mW mâ2, while at the InSight location it lies between 18.8 and 24.2 mW mâ2. In most models, elastic lithosphere thickness values exceed 250 km at the north pole, while the south pole values lie well above 110 km
Advancing a Democratic Pedagogy and Supervision Framework: An Illustrative Case of Teacher Questioning in Secondary Mathematics Instruction
This article pushes back against the evalu-centric view of improvement (Hazi, 2018; 2020) in the supervision literature by advocating for a democratic pedagogy and supervision framework developed to support instructional supervision and evaluation dialogue between teachers and leaders. This democratized approach honors and centers the teacherâs expertise and learning as well as the leaderâs in the observation, debrief, and reflection process. Through this decentering of expertise in the instructional supervision cycle, our goal is to build leadersâ and teachersâ mutual capacity to develop, implement, and sustain democratic instructional supervision cultures in classrooms and schools. Additionally, we illustrate our framework through a subject/discipline-specific case of instructional supervision in secondary mathematics instruction. Through this illustrative case, we demonstrate how the framework provides school leaders and teachers with specific, shared pedagogical language to engage in standards-based mathematical dialogue during the instructional supervision process. Finally, we discuss the implications of our questioning framework for democratic school leadership, supervisorsâ leadership content knowledge, teachersâ discipline-specific work of teaching, and instructional supervision practices, which are often stifled by accountability-driven teacher evaluation education policies that suppress schoolsâ leadership capacity to apply democratic instructional supervision standards and principles
Mercury's lowâdegree geoid and topography controlled by insolationâdriven elastic deformation
©2015. American Geophysical UnionMercury experiences an uneven insolation that leads to significant latitudinal and longitudinal variations of its surface temperature. These variations, which are predominantly of spherical harmonic degrees 2 and 4, propagate to depth, imposing a longâwavelength thermal perturbation throughout the mantle. We computed the accompanying density distribution and used it to calculate the mechanical and gravitational response of a spherical elastic shell overlying a quasiâhydrostatic mantle. We then compared the resulting geoid and surface deformation at degrees 2 and 4 with Mercury's geoid and topography derived from the MErcury, Surface, Space ENvironment, GEochemistry, and Ranging spacecraft. More than 95% of the data can be accounted for if the thickness of the elastic lithosphere were between 110 and 180 km when the thermal anomaly was imposed. The obtained elastic thickness implies that Mercury became locked into its present 3:2 spin orbit resonance later than about 1 Gyr after planetary formation
Nonuniform cratering of the Moon and a revised crater chronology of the inner solar system
International audienceâș We model the cratering of the Moon and terrestrial planets. âș We account for cratering asymmetries and megaregolith. âș We revise the crater chronology method. âș We give new age estimates of key planetary surface
- âŠ