Flexion and Skewness in Map Projections of the Earth

Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map projection metric, flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce new indicatrices that show not only area and isotropy distortions but flexion and skewness as well. We present a table showing error measures for area, isotropy, flexion, skewness, distances, and boundary cuts allowing us to compare different world map projections. We find that the Winkel-Tripel projection (already adopted for world maps by the National Geographic), has low distortion on most measures and excellent quality overall.Comment: 31 pages, including 27 postscript figures. Accepted to Cartographica. Detailed discussion and code at http://www.physics.drexel.edu/~goldberg/projection

Calculation and Visualization of Flexion and Skewness

Nedavnom studijom o kartografskim projekcijama uvedene su dvije nove mjere distorzije: fleksija i asimetrija. Međutim, uvedena je samo za jediničnu sferu. U ovom su redu izvedene formule za rotacijski elipsoid i pokazuje se da tim mjerama distorzije odgovaraju mjerne jedinice. Opisana je nova metoda vizualizacije s pomoću koje se te veličine mogu prikazati na izražajan način.A recent study on map projections expanded two new measures of distortion, namely flexion and skewness. However, it introduced them only for the unit sphere. The present paper derives formulas for the rotational ellipsoid and demonstrates that these kinds of distortion always have a unit of measurement. A new method of illustration is described, by which these quantities can be visualized in an expressive way

Automated map projection selection for GIS

The selection of an appropriate map projection has a fundamental impact on the visualization and analysis of geographic information. Distortion is inevitable and the decision requires simultaneous consideration of several different factors; a process which can be confusing for many cartographers and GIS users. The last few decades have seen numerous attempts to create automated map projection selection solutions based on traditional classification and selection guidelines, but there are no existing tools directly accessible to users of GIS software when making projection selection decisions. This paper outlines key elements of projection selection and distortion theory, critically reviews the previous solutions, and introduces a new tool developed for ESRI’s ArcGIS, employing an original selection method tailored to the specific purpose and geographical footprint characteristics of a GIS project. The tool incorporates novel quantitative projection distortion measures which are currently unavailable within existing GIS packages. Parameters are optimized for certain projections to further reduce distortions. A set of candidate projected coordinate systems are generated that can be applied to the GIS project; enabling a qualitative visual assessment to facilitate the final user selection. The proposed tool provides a straightforward application which improves understanding of the projection selection process and assists users in making more effective use of GIS

Multiple Origins of Sand-Dune Topography Interactions on Titan

The interaction between sand-dune patterns and topographic obstacles is a primary signal of sand transport direction in the equatorial region of Saturn’s moon, Titan. A streamlined, tear drop appearance emerges as dune crestlines wrap around topographic obstacles and a dune-free zone develops on the east side of many obstacles. The morphologies formed by this interaction give the impression that sand transport is from the west to east in Titan’s equatorial region. However, this transport direction is in conflict with the expected wind regime based on Titan’s rotation and many global climate models. The physical mechanism behind the interpretation of the dune-obstacle interaction is not well explained, leaving a gap in the understanding of the sand transport and equatorial wind directions on Titan. In order to better understand this interaction and evaluate wind and sand transport direction on Titan, we take a two-fold approach to studying dune-topography interactions. We use optical imagery on Earth and Cassini radar imagery on Titan in ArcGIS to map spatial variations in dune crestline orientations proximal to obstacles. We also use digital elevation models to analyze the three-dimensional geometry – height, length, width and slope of the dune-topography relationships on Earth. We identify three types of obstacles: positive topography, neutral topography and negative topography. Positive topography is defined as double or more in relief than the surrounding dune height, neutral topography is at the surrounding dune height and negative topography is lower than the surrounding dune heights. Results show that dune patterns are deflected further away from positive relief than neutral or negative relief. Furthermore, positive relief has a dune free obstacle shadow, neutral relief has a smaller dune free obstacle shadow to no obstacle shadow zone, and negative relief has an obstacle shadow zone characterized by increased dune wavelength proximal to the obstacle’s wind-shielded side. The obstacle height, width, slope and wind variability appear to play a role in determining if a lee-dune, rather than a dune-free lee-zone forms. These factors provide further geomorphic evidence that sand transport directions on Titan were from west to east during the formation of the dune-obstacle interaction morphologies

Horizontal Inequalities and Political Violence

While recent quantitative research concludes that economic inequality is unrelated to civil conflict, qualitative case studies suggest that what matters for political violence is so-called ‘horizontal inequalities’ (HIs), or systematic inequalities between identity groups. However, since case studies are not well suited for making broad generalizations, testing the statistical relationship between HIs and conflict is much warranted. Drawing on household surveys from a large number of developing countries, this dissertation offers new systematic data on horizontal inequalities, measured across various group identifiers (ethnic, religious, regional, migrant-status), and along various dimensions (economic, social, political). Specifying various theoretical arguments, the individual articles test the link between HIs and political violence, and whether the relationship is conditioned by different political, economic, and demographic contextual factors. The conflict potential of HIs is evaluated with regard to various forms of politically motivated violence, ranging from civil conflict to low-scale urban violence, and at different levels of analysis (national, regional, local). In sum, the statistical analyses corroborate the findings from the case-based literature, demonstrating that horizontal inequalities are indeed associated with higher levels of political violence

Acoustic/Gravity Wave Phenomena in Wide-Field Imaging: From Data Analysis to a Modeling Framework for Observability in the Mlt Region and Beyond

Acoustic waves, gravity waves, and larger-scale tidal and planetary waves are significant drivers of the atmosphere’s dynamics and of the local and global circulation that have direct and indirect impacts on our weather and climate. Their measurements and characterization are fundamental challenges in Aeronomy that require a wide range of instrumentation with distinct operational principles. Most measurements share the common features of integrating optical emissions or effects on radio waves through deep layers of the atmosphere. The geometry of these integrations create line-of-sight effects that must be understood, described, and accounted for to properly present the measured data in traditional georeferenced frames or in thin-layer representations. These effects include intensity enhancements/cancellations, filtering of scales, and apparent phase shifts relative to the underlying wave dynamics. We have designed a simulation framework that uses 2D and 3D input model data to perform these line-of-sight integrations based on ray tracing and geodesic transformations. The primary objective is to characterize these effects, to define quantifiable impacts on measurable parameters, and to create a basis for synthetic data for processes to be revealed in current and future measurements