THE TRANSVERSE MERCATOR PROJECTION

Abstract

I. Introduction.—Map projection is a branch of applied mathematics which owes much to J. H. Lambert (v. this Review, i, 2, 91). In his “Beyträge zum Gebrauche der Mathematik und deren Anwendung” (Berlin, 1772) he arrived at a form of projection whereof the Transverse Mercator is a special case, and pointed out that this special case is adapted to a country of great extent in latitude but of small longitudinal width. Germain (“Traité des Projections”, Paris, 1865) described it as the Projection cylindrique orthomorphe de Lambert, but he also introduced the name Projection de Mercator transverse or renversée; he shows that Lambert's treatment of the projection was remarkably simple.     

BOWDITCH TRAVERSE ADJUSTMENT AND A MODIFICATION: NOTES

Abstract

In the second part of the paper on this subject in the last issue (30, 483) the references to the relative angular and linear closures are rather misleading. Mr Clendinning points out that the probable angular error at a station must be considered; the mean error is clearly different.     

SOME PROBLEMS OF RESECTION AND COUNTERSECTION-I

Abstract

“A Well-Defined mountain, though miles inland and never visited by the surveyors, will often prove the very keystone of a chart which cannot be regularly and theoretically triangulated” (“Hydrographic Surveying”, by Rear-Adm. Sir Wm J. L. Wharton, K.C.B., and Rear-Adm. Mostyn Field, F.R.S. 3rd Ed. 1909, p. 128). To many the reasons prohibiting the occupation of inland stations may be unknown; it may suffice to state that, in the past, British hydrographers have mapped many coastal waters where penetration of the land was at least inadvisable. Since the charts so made were in general sold to the world, seamen of all nations have benefited from the surveys.     

Geocenter variations derived from a combined processing of LEO- and ground-based GPS observations

GNSS observations provided by the global tracking network of the International GNSS Service (IGS, Dow et al. in J Geod 83(3):191–198, 2009) play an important role in the realization of a unique terrestrial reference frame that is accurate enough to allow a detailed monitoring of the Earth’s system. Combining these ground-based data with GPS observations tracked by high-quality dual-frequency receivers on-board low earth orbiters (LEOs) is a promising way to further improve the realization of the terrestrial reference frame and the estimation of geocenter coordinates, GPS satellite orbits and Earth rotation parameters. To assess the scope of the improvement on the geocenter coordinates, we processed a network of 53 globally distributed and stable IGS stations together with four LEOs (GRACE-A, GRACE-B, OSTM/Jason-2 and GOCE) over a time interval of 3 years (2010–2012). To ensure fully consistent solutions, the zero-difference phase observations of the ground stations and LEOs were processed in a common least-squares adjustment, estimating all the relevant parameters such as GPS and LEO orbits, station coordinates, Earth rotation parameters and geocenter motion. We present the significant impact of the individual LEO and a combination of all four LEOs on the geocenter coordinates. The formal errors are reduced by around 20% due to the inclusion of one LEO into the ground-only solution, while in a solution with four LEOs LEO-specific characteristics are significantly reduced. We compare the derived geocenter coordinates w.r.t. LAGEOS results and external solutions based on GPS and SLR data. We found good agreement in the amplitudes of all components; however, the phases in x- and z-direction do not agree well.     

Enriching the semantics of the directed polyline–polygon topological relationships: the $$\mathcal {}$$-intersection matrix

In this paper, we define an intersection matrix for enriching the semantics of the topological relationships between a directed polyline and a polygon. In particular, we propose the \(\mathcal {DLP}\)-intersection matrix which enables us to model the origin and destination points, as well as the right- and left-hand sides of the directed polyline. This matrix overcomes the limitation of the well-known DE-9IM, because it allows the representation of the different dimensions of the intersection results at the same time. Accordingly, the geo-operators have been revised and extended in order to address the notions of right- and left-hand sides of a directed polyline, as well as additional notions related to the orientation of the polyline. The \(\mathcal {DLP}\)-intersection matrix has been implemented by extending the Java Topology Suite methods in order to address the new geo-operators based on the notion of orientation.     

A spatial error model with continuous random effects and an application to growth convergence

We propose a spatial error model with continuous random effects based on Matérn covariance functions and apply this model for the analysis of income convergence processes (\(\beta \)-convergence). The use of a model with continuous random effects permits a clearer visualization and interpretation of the spatial dependency patterns, avoids the problems of defining neighborhoods in spatial econometrics models, and allows projecting the spatial effects for every possible location in the continuous space, circumventing the existing aggregations in discrete lattice representations. We apply this model approach to analyze the economic growth of Brazilian municipalities between 1991 and 2010 using unconditional and conditional formulations and a spatiotemporal model of convergence. The results indicate that the estimated spatial random effects are consistent with the existence of income convergence clubs for Brazilian municipalities in this period.     

Change detection of linear features in temporally spaced remotely sensed images using edge-based grid analysis

Automatic change detection of land cover features using high-resolution satellite images, is a challenging problem in the field of intelligent remote sensing data interpretation, and is becoming more and more effective for its applications viz. urban planning and monitoring, disaster assessment etc. In the present study, a change in detection approach based on the image morphology that analyses change in the local image grids is proposed. In this approach, edges from both the images are extracted and grid wise comparison is made by probabilistic thresholding and power spectral density analysis for identifying change area. One of the advantages of the proposed methodology is that the temporal images used in the change analysis need not be radiometrically corrected as analysis is based on edge extractions. The grid-based analysis further reduces the error, which might have been introduced by image mis-registration. The proposed methodology is validated by finding the temporal changes in the linear land cover features in parts of Kolkata city, India using three different image data-sets from LISS IV, Cartosat-1 and Google earth having varied spatial resolutions of 5.8 m, 2.5 m and about 1 m, respectively. The overall accuracy in identifying changes is found to be 64.82, 73.86 and 80.93% for LISS IV, Cartosat-1 and Google earth data-set, respectively.     

Analysis of urban built-up areas and surface urban heat island using downscaled MODIS derived land surface temperature data

Regional scale urban built-up areas and surface urban heat islands (SUHI) are important for urban planning and policy formation. Owing to coarse spatial resolution (1000 m), it is difficult to use Moderate Resolution Imaging Spectroradiometer (MODIS) Land surface temperature (LST) products for mapping urban areas and visualization, and SUHI-related studies. To overcome this problem, the present study downscaled MODIS (1000 m resolution)-derived LST to 250 m resolution to map and visualize the urban areas and identify the basic components of SUHI over 12 districts of Punjab, India. The results are compared through visual interpretation and statistical procedure based on similarity analysis. The increased entropy value in the downscaled LST signifies higher information content. The temperature variation within the built-up and its environs is due to difference in land use and is depicted better in the downscaled LST. The SUHI intensity analysis of four cities (Ludhiana, Patiala, Moga and Vatinda) indicates that mean temperature in urban built-up core is higher (38.87 °C) as compared to suburban (35.85 °C) and rural (32.41 °C) areas. The downscaling techniques demonstrated in this paper enhance the usage of open-source wide swath MODIS LST for continuous monitoring of SUHI and urban area mapping, visualisation and analysis at regional scale. Such initiatives are useful for the scientific community and the decision-makers.     

SVLBI用于大地测量的卫星轨道及其跟踪网设计

SVLBI （space very long baseline interferometry） has some important potential applications in geodesy and geodynamics, for which one of the most difficult tasks is to precisely determine the orbit of an SVLBI satellite. This work studies several technologies that will possibly be able to determine the orbit of a space VLBI satellite. Then, according to the types and charac- teristics of the satellite and the requirements for geodetic study and the geometry of the GNSS （GPS, GALILEO） satellite to track the space VLBI satellite, the six Keplerian elements of the SVLBI satellite （TEST-SVLBI） are determined. A program is designed to analyze the coverage area of space of different altitudes by the stations of the network, with which the tracking network of TEST-SVLBI is designed. The efficiency of tracking TEST-SVLBI by the network is studied, and the results are presented.