The optimal Mercator projection and the optimal polycylindric projection of conformal type – case-study Indonesia

As a conformal mapping of the sphere S ² _R or of the ellipsoid of revolution E ² _A , _B the Mercator projection maps the equator equidistantly while the transverse Mercator projection maps the transverse metaequator, the meridian of reference, with equidistance. Accordingly, the Mercator projection is very well suited to geographic regions which extend east-west along the equator; in contrast, the transverse Mercator projection is appropriate for those regions which have a south-north extension. Like the optimal transverse Mercator projection known as the Universal Transverse Mercator Projection (UTM), which maps the meridian of reference Λ₀ with an optimal dilatation factor &ρcirc;=0.999 578 with respect to the World Geodetic Reference System WGS 84 and a strip [Λ₀−Λ _W ,Λ₀ + Λ _E ]×[Φ _S ,Φ _N ]= [−3.5^∘,+3.5^∘]×[−80^∘,+84^∘], we construct an optimal dilatation factor ρ for the optimal Mercator projection, summarized as the Universal Mercator Projection (UM), and an optimal dilatation factor ρ₀ for the optimal polycylindric projection for various strip widths which maps parallel circles Φ₀ equidistantly except for a dilatation factor ρ₀, summarized as the Universal Polycylindric Projection (UPC). It turns out that the optimal dilatation factors are independent of the longitudinal extension of the strip and depend only on the latitude Φ₀ of the parallel circle of reference and the southern and northern extension, namely the latitudes Φ _S and Φ _N , of the strip. For instance, for a strip [Φ _S ,Φ _N ]= [−1.5^∘,+1.5^∘] along the equator Φ₀=0, the optimal Mercator projection with respect to WGS 84 is characterized by an optimal dilatation factor &ρcirc;=0.999 887 (strip width 3^∘). For other strip widths and different choices of the parallel circle of reference Φ₀, precise optimal dilatation factors are given. Finally the UPC for the geographic region of Indonesia is presented as an example. Received: 17 December 1997 / Accepted: 15 August 1997     

Determination of the boundary values for the Stokes–Helmert problem

 The definition of the mean Helmert anomaly is reviewed and the theoretically correct procedure for computing this quantity on the Earth's surface and on the Helmert co-geoid is suggested. This includes a discussion of the role of the direct topographical and atmospherical effects, primary and secondary indirect topographical and atmospherical effects, ellipsoidal corrections to the gravity anomaly, its downward continuation and other effects. For the rigorous derivations it was found necessary to treat the gravity anomaly systematically as a point function, defined by means of the fundamental gravimetric equation. It is this treatment that allows one to formulate the corrections necessary for computing the `one-centimetre geoid'. Compared to the standard treatment, it is shown that a `correction for the quasigeoid-to-geoid separation', amounting to about 3 cm for our area of interest, has to be considered. It is also shown that the `secondary indirect effect' has to be evaluated at the topography rather than at the geoid level. This results in another difference of the order of several centimetres in the area of interest. An approach is then proposed for determining the mean Helmert anomalies from gravity data observed on the Earth's surface. This approach is based on the widely-held belief that complete Bouguer anomalies are generally fairly smooth and thus particularly useful for interpolation, approximation and averaging. Numerical results from the Canadian Rocky Mountains for all the corrections as well as the downward continuation are shown. Received: 9 March 1998 / Accepted: 16 November 1998     

Generalization Services on the Web—Classification and an Initial Prototype Implementation

Much progress has been made in the field of web-based cartography through standards developed by the Open Geospatial Consortium (OGC). While automated access and presentation of cartographic data have been defined, the services for automated generalization are yet to be standardized. This paper aims to show advantages of applying the service concept to generalization and suggests several classification schemas of generalization services at different levels of granularity. A detailed explanation of a real implemented Generalization Service is provided. We show how software developers can make their generalization functionality available as a service and how these services can be accessed dynamically. For the implementation, the open source Java Unified Mapping Platform (JUMP) was extended to work as a framework for generalization. Generalization services could be used in different application scenarios, for instance as a middleware component extending a web map service with adaptive zooming or as stand-alone services supporting the production of topographic maps by national mapping agencies. They may also allow the development of a common research platform, where researchers would have access to a common generalization framework.     

On the indirect effect in the Stokes–Helmert method of geoid determination

The classical integral formula for determining the indirect effect in connection with the Stokes–Helmert method is related to a planar approximation of the sea level. A strict integral formula, as well as some approximations to it, are derived. It is concluded that the cap- size truncated integral formulas will suffer from the omission of some long-wavelength contributions, of the order of 50 cm in high mountains for the classical formula. This long-wavelength information can be represented by a set of spherical harmonic coefficients of the topography to, say, degree and order 360. Hence, for practical use, a combination of the classical formula and a set of spherical harmonics is recommended. Received: 10 March 1998 / Accepted: 16 November 1998     

Improvement of edge effect of the wavelet time–frequency spectrum: application to the length-of-day series

 The edge effect in the wavelet time–frequency spectrum of a time series is treated. The time series is first extended on both ends by applying a non-linear model, namely the leap-step time series analysis (LSTSA) model, prior to the wavelet transform. The results of a series of simulation experiments and an application to the observed length-of-day (LOD) series demonstrate that the edge effect is effectively reduced this way. Thus, the application of the LSTSA model improves the wavelet time–frequency spectrum, especially enhancing the ability to detect the low-frequency signals. Received: 15 September 1998 / Accepted: 4 October 1999     

A swash–backwash model of the single epidemic wave

While there is a large literature on the form of epidemic waves in the time domain, models of their structure and shape in the spatial domain remain poorly developed. This paper concentrates on the changing spatial distribution of an epidemic wave over time and presents a simple method for identifying the leading and trailing edges of the spatial advance and retreat of such waves. Analysis of edge characteristics is used to (a) disaggregate waves into ‘swash’ and ‘backwash’ stages, (b) measure the phase transitions of areas from susceptible, S, through infective, I, to recovered, R, status (S → I → R) as dimensionless integrals and (c) estimate a spatial version of the basic reproduction number, R ₀. The methods used are illustrated by application to measles waves in Iceland over a 60-year period from 1915 to 1974. Extensions of the methods for use with more complex waves are possible through modifying the threshold values used to define the start and end points of an event.

The solution of the Korn–Lichtenstein equations of conformal mapping: the direct generation of ellipsoidal Gauß–Krüger conformal coordinates or the Transverse Mercator Projection

The differential equations which generate a general conformal mapping of a two-dimensional Riemann manifold found by Korn and Lichtenstein are reviewed. The Korn–Lichtenstein equations subject to the integrability conditions of type vectorial Laplace–Beltrami equations are solved for the geometry of an ellipsoid of revolution (International Reference Ellipsoid), specifically in the function space of bivariate polynomials in terms of surface normal ellipsoidal longitude and ellipsoidal latitude. The related coefficient constraints are collected in two corollaries. We present the constraints to the general solution of the Korn–Lichtenstein equations which directly generates Gau?–Krüger conformal coordinates as well as the Universal Transverse Mercator Projection (UTM) avoiding any intermediate isometric coordinate representation. Namely, the equidistant mapping of a meridian of reference generates the constraints in question. Finally, the detailed computation of the solution is given in terms of bivariate polynomials up to degree five with coefficients listed in closed form. Received: 3 June 1997 / Accepted: 17 November 1997     

Temperature dependence of variations in the end of the growing season from 1982 to 2012 on the Qinghai–Tibetan Plateau

A growing number of studies have focused on variations in vegetation phenology and their correlations with climatic factors. However, there has been little research on changes in spatial heterogeneity with respect to the end of the growing season (EGS) and on responses to climate change for alpine vegetation on the Qinghai–Tibetan Plateau (QTP). In this study, the satellite-derived normalized difference vegetation index (NDVI) and the meteorological record from 1982 to 2012 were used to characterize the spatial pattern of variations in the EGS and their relationship to temperature and precipitation on the QTP. Over the entire study period, the EGS displayed no statistically significant trend; however, there was a strong spatial heterogeneity throughout the plateau. Those areas showing a delaying trend in the EGS were mainly distributed in the eastern part of the plateau, whereas those showing an advancing trend were mostly scattered throughout the western part. Our results also showed that change in the vegetation EGS was more closely correlated with air temperature than with precipitation. Nonetheless, the temperature sensitivity of the vegetation EGS became lower as aridity increased, suggesting that precipitation is an important regulator of the response of the vegetation EGS to climate warming. These results indicate spatial differences in key environmental influences on the vegetation EGS that must be taken into account in current phenological models, which are largely driven by temperature.     

Fifty Years of the British Cartographic Society, 1963–2013

The British Cartographic Society has been in existence for 50 years. During that time it has sought to pursue its central aim of promoting the art and science of cartography through a variety of publications and events to its members and beyond. The Society has been on a journey of continual development in response to the way maps are created and used. In this short history we touch on some of the factors that have influenced its evolution and what the future may hold.     

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.     

The pyrogeography of sub-Saharan Africa: a study of the spatial non-stationarity of fire–environment relationships using GWR

This study analyses the relationship between fire incidence and some environmental factors, exploring the spatial non-stationarity of the phenomenon in sub-Saharan Africa. Geographically weighted regression (GWR) was used to study the above relationship. Environment covariates comprise land cover, anthropogenic and climatic variables. GWR was compared to ordinary least squares, and the hypothesis that GWR represents no improvement over the global model was tested. Local regression coefficients were mapped, interpreted and related with fire incidence. GWR revealed local patterns in parameter estimates and also reduced the spatial autocorrelation of model residuals. All the covariates were non-stationary and in terms of goodness of fit, the model replicates the data very well (R ² = 87%). Vegetation has the most significant relationship with fire incidence, with climate variables being more important than anthropogenic variables in explaining variability of the response. Some coefficient estimates exhibit locally different signs, which would have gone undetected by a global approach. This study provides an improved understanding of spatial fire–environment relationships and shows that GWR is a valuable complement to global spatial analysis methods. When studying fire regimes, effects of spatial non-stationarity need to be incorporated in vegetation-fire modules to have better estimates of burned areas and to improve continental estimates of biomass burning and atmospheric emissions derived from vegetation fires.     

Topographic effects by the Stokes–Helmert method of geoid and quasi-geoid determinations

The topographic potential and the direct topographic effect on the geoid are presented as surface integrals, and the direct gravity effect is derived as a rigorous surface integral on the unit sphere. By Taylor-expanding the integrals at sea level with respect to topographic elevation (H) the power series of the effects is derived to arbitrary orders. This study is primarily limited to terms of order H ². The limitations of the various effects in the frequently used planar approximations are demonstrated. In contrast, it is shown that the spherical approximation to power H ² leads to a combined topographic effect on the geoid (direct plus indirect effect) proportional to H˜² (where terms of degrees 0 and 1 are missing) of the order of several metres, while the combined topographic effect on the height anomaly vanishes, implying that current frequent efforts to determine the direct effect to this order are not needed. The last result is in total agreement with Bjerhammar's method in physical geodesy. It is shown that the most frequently applied remove–restore technique of topographic masses in the application of Stokes' formula suffers from significant errors both in the terrain correction C (representing the sum of the direct topographic effect on gravity anomaly and the effect of continuing the anomaly to sea level) and in the term t (mainly representing the indirect effect on the geoidal or quasi-geoidal height). Received: 18 August 1998 / Accepted: 4 October 1999     

Review of the development of digital earth research during 1998–2015 based on a bibliometric analysis

ABSTRACT

Since Al Gore created the vision for Digital Earth in 1998, a wide range of research in this field has been published in journals. However, little attention has been paid to bibliometric analysis of the literature on Digital Earth. This study uses a bibliometric analysis methodology to study the publications related to Digital Earth in the Science Citation Index database and Social Science Citation Index database (via the Web of Science online services) during the period from 1998 to 2015. In this paper, we developed a novel keyword set for ‘Digital Earth’. Using this keyword set, 11,061 scientific articles from 23 subject categories were retrieved. Based on the searched articles, we analyzed the spatiotemporal characteristics of publication outputs, the subject categories and the major journals. Then, authors’ performance, affiliations, cooperation, and funding institutes were evaluated. Finally, keywords were examined. Through keyword clustering, research hotspots in the field of Digital Earth were detected. We assume that the results coincide well with the position of Digital Earth research in the context of big data.     

Simulation of permafrost changes on the Qinghai–Tibet Plateau,China, over the past three decades

ABSTRACT

Permafrost is one of the largest elements of the terrestrial cryosphere and is extremely sensitive to climate change. Based on mean annual ground temperature (MAGT) data from 189 boreholes on the Qinghai–Tibet Plateau (QTP), terrain factors, and climate data from China Meteorological Forcing Dataset, we propose a new mean annual ground air temperature (MAGAT) statistical model between meteorological parameters with subsurface temperatures to simulate permafrost distribution and variation of MAGT on the QTP over the past three decades (1981–2010). Validation of the model with MAGT data from 13 boreholes and permafrost maps of the QTP indicated that the MAGAT model is applicable to simulate the distribution and evolution of permafrost on the QTP. Simulation results show that the spatiotemporal MAGT of permafrost significantly increased by 0.37°C, or 0.25°C/10 yr, and the total area of permafrost decreased by 2.48?×?10⁵?km² on the QTP over the past three decades. Regionally, the changes of permafrost in the southwestern QTP were greater than other regions of the QTP.     

A preliminary evaluation of the performance of multiple ionospheric models in low- and mid-latitude regions of China in 2010–2011

Ionospheric delay is a dominant error source in Global Navigation Satellite System (GNSS). Single-frequency GNSS applications require ionospheric correction of signal delay caused by the charged particles in the earth’s ionosphere. The Chinese Beidou system is developing its own ionospheric model for single-frequency users. The number of single-frequency GNSS users and applications is expected to grow fast in the next years in China. Thus, developing an appropriate ionospheric model is crucially important for the Chinese Beidou system and worldwide single-frequency Beidou users. We study the performance of five globally accessible ionospheric models Global Ionospheric Map (GIM), International Reference Ionosphere (IRI), Parameterized Ionospheric Model (PIM), Klobuchar and NeQuick in low- and mid-latitude regions of China under mid-solar activity condition. Generally, all ionospheric models can reproduce the trend of diurnal ionosphere variations. It is found that all the models have better performances in mid-latitude than in low-latitude regions. When all the models are compared to the observed total electron content (TEC) data derived from GIM model, the IRI model (2012 version) has the best agreement with GIM model and the NeQuick has the poorest agreement. The RMS errors of the IRI model using the GIM TEC as reference truth are about 3.0–10.0 TECU in low-latitude regions and 3.0–8.0 TECU in mid-latitude regions, as observed during a period of 1 year with medium level of solar activity. When all the ionospheric models are ingested into single-frequency precise point positioning (PPP) to correct the ionospheric delays in GPS observations, the PIM model performs the best in both low and mid-latitudes in China. In mid-latitude, the daily single-frequency PPP accuracy using PIM model is ~10 cm in horizontal and ~20 cm in up direction. At low-latitude regions, the PPP error using PIM model is 10–20 cm in north, 30–40 cm in east and ~60 cm in up component. The single-frequency PPP solutions indicate that NeQuick model has the lowest accuracy among all the models in both low- and mid-latitude regions of China. This study suggests that the PIM model may be considered for single-frequency GNSS users in China to achieve a good positioning accuracy in both low- and mid-latitude regions.     

MacLeod,MI4, and the Directorate of Military Survey 1919–1943

Abstract

The organization lineage of the UK Defence Geographic and Imagery Intelligence Agency can be traced back to the seventeenth century. For much of this time the organization, bearing a succession of different titles, formed only a very small section of the armed forces, and, until the World War of 1914–1918, its main duties were the creation and maintenance of a map collection and the acquisition of geographical data of foreign countries. The survey and mapping innovations made during the war greatly enlarged the remit of what was now termed the Geographical Section General Staff (MI4). This paper outlines the work of MI4 in the inter-war years taking account of the principal personalities involved, and traces the controversial background to the creation in 1943 of the Directorate of Military Survey — the immediate predecessor of the DGIA.