An open-source web service for creating quadrilateral grids based on the rHEALPix Discrete Global Grid System

ABSTRACT

The foundation of modern Digital Earth frameworks is the Discrete Global Grid System (DGGS). To standardize the DGGS model, the Open Geospatial Consortium (OGC) recently created the DGGS Abstract Specification, which also aims to increase usability and interoperability between DGGSs. To support these demands and aid future research, open implementations are necessary. However, several OGC conformant DGGSs are not available for researchers to use. This has motivated us to develop an open-source web service that allows users to create quadrilateral grids based on the rHEALPix DGGS. In this paper, we describe the implementation of the web service, including issues and limitations, and demonstrate how discrete global grids and regional grids can be created. Lastly, we present examples that show how vector data sets can be modeled and integrated at different levels of resolution – a key benefit of the DGGS model.     

Optimal orientations of discrete global grids and the Poles of Inaccessibility

ABSTRACT

Spatial analyses involving binning often require that every bin have the same area, but this is impossible using a rectangular grid laid over the Earth or over any projection of the Earth. Discrete global grids use hexagons, triangles, and diamonds to overcome this issue, overlaying the Earth with equally-sized bins. Such discrete global grids are formed by tiling the faces of a polyhedron. Previously, the orientations of these polyhedra have been chosen to satisfy only simple criteria such as equatorial symmetry or minimizing the number of vertices intersecting landmasses. However, projection distortion and singularities in discrete global grids mean that such simple orientations may not be sufficient for all use cases. Here, I present an algorithm for finding suitable orientations; this involves solving a nonconvex optimization problem. As a side-effect of this study I show that Fuller's Dymaxion map corresponds closely to one of the optimal orientations I find. I also give new high-accuracy calculations of the Poles of Inaccessibility, which show that Point Nemo, the Oceanic Pole of Inaccessibility, is 15?km farther from land than previously recognized.     

On generalised and specialised spatial information grids: are geo-services ready?

Abstract

After the set-up of a spatial data infrastructure (SDI) and a national information infrastructure (NII) in many countries, the provision of geo-services became one of the most important and attractive tasks. With the integration of global positioning system (GPS), geographic information system (GIS) and remote sensing (RS), we can, in principle, answer any geo-spatial related question: when and where what object has which changes? An intelligent geo-service agent could provide end-users with the most necessary information in the shortest time and at the lowest cost. Unfortunately there is still a long way to go to achieve such goals. The central component in such geo-services is the integration of the spatial information system with a computing grid via wire- and wireless communication networks. This paper will mainly discuss the grid technology and its integration with spatial information technology, expounding potential problems and possible resolutions. A novel categorising of information grids in the context of geo-spatial information is proposed: generalised and specialised spatial information grids.     

User Desires and Graphics Capability in the Academic Environment

Abstract

In this paper the cartographic grids engraved on two antique instruments from Iran for finding the sacred direction and distance to Mecca are discussed. It appears that these grids can be well explained in terms of the Mecca-centred retro-azimuthal orthographic projection described in 1968 by J. E. Jackson. In this projection the lines of constant latitude reduce to a set of ellipses with their major axes parallel to the equator and the lines of the constant longitudes reduce to a set of non-equidistant straight lines parallel to the north-south direction. It is shown that the curves actually engraved on the instrument conform to this projection and can be fairly easily constructed. This interpretation of the grid on the Iranian instruments stands in contrast with another explanation, recently proposed by King (1999), which is based on medieval Arabic concepts such as the so-called 'methods of the zijes'. Insufficiently accurate workmanship makes it impossible to distinguish between the two explanations through the study of the instruments themselves. The newly gained insight into the projection itself, however, shows that a direct relation between the Iranian maps and Islamic mappings insight knows from the ninth century, as suggested by King, does not exit. Thus, it is concluded that it is as yet completely unknown when and where the very idea behind the Iranian cartographic grid was first conceived, and that the quest for their historical background is still open.     

Quantitative estimates of collective geo-tagged human activities in response to typhoon Hato using location-aware big data

ABSTRACT

Location-aware big data from social media have been widely used to quantitatively characterize natural disasters and disaster-induced losses. It is not clear how human activities collectively respond to a disaster. In this study, we examined the collective human activities in response to Typhoon Hato at multi spatial scales using aggregated location request data. We proposed a Multilevel Abrupt Changes Detection (MACD) methodological framework to detect and characterize the abrupt changes in location requests in response to Typhoon Hato. Results show that, at the grid level, most anomaly grids were located within a radius of 53?km around the typhoon trajectory. At the city level, there are significant spatial difference in terms of the human activity recovery duration (230?h on average). At the subnational level, the absolute magnitude of abrupt location request changes is strongly correlated with the typhoon-induced economic losses and the population affected.     

Using OpenStreetMap to improve population grids in Europe

ABSTRACT

OpenStreetMap (OSM) database has previously been used to support spatial disaggregation of population data by partly masking out non-residential impervious areas in the European Copernicus imperviousness layer (IL). However, the exact procedure of OSM data incorporation is unknown, and its contribution to the improvement of estimation accuracy has never been studied. In this article, we present a sensitivity study to find out which road categories should be used for masking of IL and how the linear features might be transformed to raster representation. Using Austria and Slovenia as a study area, 2006 commune population counts are disaggregated into 100 m grid cells using 12 versions of modified IL. Further tuning of estimates is performed using CORINE Land Cover (CLC) data in an iterative algorithm. Disaggregated grids are then validated against reference 1 km census-based data. The results show that overall error was reduced thanks to OSM incorporation in all tested scenarios, although the relative improvement varies between as well as within the two countries. The best result (5.3% reduction) was achieved using railways and three major road categories (motorway, trunk, and primary) with double exaggeration of width.     

Enhanced data and methods for improving open and free global population grids: putting ‘leaving no one behind’ into practice

ABSTRACT

Data on global population distribution are a strategic resource currently in high demand in an age of new Development Agendas that call for universal inclusiveness of people. However, quality, detail, and age of census data varies significantly by country and suffers from shortcomings that propagate to derived population grids and their applications. In this work, the improved capabilities of recent remote sensing-derived global settlement data to detect and mitigate major discrepancies with census data is explored. Open layers mapping built-up presence were used to revise census units deemed as ‘unpopulated’ and to harmonize population distribution along coastlines. Automated procedures to detect and mitigate these anomalies, while minimizing changes to census geometry, preserving the regional distribution of population, and the overall counts were developed, tested, and applied. The two procedures employed for the detection of deficiencies in global census data obtained high rates of true positives, after verification and validation. Results also show that the targeted anomalies were significantly mitigated and are encouraging for further uses of free and open geospatial data derived from remote sensing in complementing and improving conventional sources of fundamental population statistics.     

Elevation models for reproducible evaluation of terrain representation

ABSTRACT

This paper proposes elevation models to promote, evaluate, and compare various terrain representation techniques. Our goal is to increase the reproducibility of terrain rendering algorithms and techniques across different scales and landscapes. We introduce elevation models of varying terrain types, available to the user at no cost, with minimal common data imperfections such as missing data values, resampling artifacts, and seams. Three multiscale elevation models are available, each consisting of a set of elevation grids, centered on the same geographic location, with increasing cell sizes and spatial extents. We also propose a collection of single-scale elevation models of archetypal landforms including folded ridges, a braided riverbed, active and stabilized sand dunes, and a volcanic caldera. An inventory of 78 publications with a total of 155 renderings illustrating terrain visualization techniques guided the selection of landform types in the elevation models. The benefits of using the proposed elevation models include straightforward comparison of terrain representation methods across different publications and better documentation of the source data, which increases the reproducibility of terrain representations.     

The geopotential to (14, 14) from a combination of satellite and gravimetric data

A set of2261 5°×5° mean anomalies were used alone and with satellite determined harmonic coefficients of the Smithsonian' Institution to determine the geopotential expansion to various degrees. The basic adjustment was carried out by comparing a terrestrial anomaly to an anomaly determined from an assumed set of coefficients. The (14, 14) solution was found to agree within ±3 m of a detailed geoid in the United States computed using1°×1° anomalies for an inner area and satellite determined anomalies in an outer area. Additional comparisons were made to the input anomaly field to consider the accuracy of various harmonic coefficient solutions. A by-product of this investigation was a new γ_E=978.0463 gals in the Potsdam system or978.0326 gals in an absolute system if −13.7 mgals is taken as the Potsdam correction. Combining this value of γ_E withf=1/298.25, KM=3.9860122·10 ²² cm ³ /sec ² , the consistent equatorial radius was found to be6378143 m.     

Identifying disaster related social media for rapid response: a visual-textual fused CNN architecture

ABSTRACT

In recent years, social media platforms have played a critical role in mitigation for a wide range of disasters. The highly up-to-date social responses and vast spatial coverage from millions of citizen sensors enable a timely and comprehensive disaster investigation. However, automatic retrieval of on-topic social media posts, especially considering both of their visual and textual information, remains a challenge. This paper presents an automatic approach to labeling on-topic social media posts using visual-textual fused features. Two convolutional neural networks (CNNs), Inception-V3 CNN and word embedded CNN, are applied to extract visual and textual features respectively from social media posts. Well-trained on our training sets, the extracted visual and textual features are further concatenated to form a fused feature to feed the final classification process. The results suggest that both CNNs perform remarkably well in learning visual and textual features. The fused feature proves that additional visual feature leads to more robustness compared with the situation where only textual feature is used. The on-topic posts, classified by their texts and pictures automatically, represent timely disaster documentation during an event. Coupling with rich spatial contexts when geotagged, social media could greatly aid in a variety of disaster mitigation approaches.     

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E _Y = (X−E _X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E _Y and E _X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.     

A generalisation of the least-squares method for the adjustment of free networks

Summary The system of normal equations for the adjustment of a free network is a singular one. Therefore, a number of coordinates has to be fixed according to the matrix. The mean square errors and the error ellipses of such an adjustment are dependent on this choice. This paper gives a simple, direct method for the adjustment of free networks, where no coordinates need to be fixed. This is done by minimizing not only the sum of the squares of the weighted errorsV ^T PV=minimun but also the Euclidean norm of the vectorX and of the covariance matrixQ X ^T X=minimum trace (Q)=minimum This last condition is crucial for geodetic problems of this type.     

On non-linear low–low SST observation equations for the determination of the geopotential based on an analytical solution

In satellite data analysis, one big advantage of analytical orbit integration, which cannot be overestimated, is missed in the numerical integration approach: spectral analysis or the lumped coefficient concept may be used not only to design efficient algorithms but overall for much better insight into the force-field determination problem. The lumped coefficient concept, considered from a practical point of view, consists of the separation of the observation equation matrix A=BT into the product of two matrices. The matrix T is a very sparse matrix separating into small block-diagonal matrices connecting the harmonic coefficients with the lumped coefficients. The lumped coefficients are nothing other than the amplitudes of trigonometric functions depending on three angular orbital variables; therefore, the matrix N=B ^T B will become for a sufficient length of a data set a diagonal dominant matrix, in the case of an unlimited data string length a strictly diagonal one. Using an analytical solution of high order, the non-linear observation equations for low–low SST range data can be transformed into a form to allow the application of the lumped concept. They are presented here for a second-order solution together with an outline of how to proceed with data analysis in the spectral domain in such a case. The dynamic model presented here provides not only a practical algorithm for the parameter determination but also a simple method for an investigation of some fundamental questions, such as the determination of the range of the subset of geopotential coefficients which can be properly determined by means of SST techniques or the definition of an optimal orbital configuration for particular SST missions. Numerical results have already been obtained and will be published elsewhere. Received: 15 January 1999 / Accepted: 30 November 1999     

Fehlertheoretische Maxwell-Boltzmann-Verteilung

Summary The probability to find an error vector in multiples of the Helmert-Maxwell-Boltzmann point error σ² δ_ij(δ_ij Kronecker symbol) is calculated. It is found that the probability is for σ39%, for2 σ86% and for3 σ99% in two dimensions, for σ20%, for2 σ74% and for3 σ97% in three dimensions. The fundamental Maxwell-Boltzmann-distribution is tabulated0,02 (0,02) 4,50.      

Terrain radiometric calibration of airborne UAVSAR for forested area

In the field of biomass estimation, terrain radiometric calibration of airborne polarimetric SAR data for forested areas is an urgent problem. Illuminated area correction of σ -naught could not completely remove terrain features. Inspired by Small and Shimada, this paper tested gamma-naught on one mountainous forested area using airborne Uninhabited Aerial Vehicle Synthetic Aperture Radar data and found it could remove most terrain features. However, a systematic increasing trend from far range to near range is found in airborne SAR cases. This paper made an attempt to use the relationship between distance to SAR sensor and γ-naught to calibrate γ -naught. Two quantitative evaluation methods are proposed. Experimental results demonstrate that variation of γ -naught can be constrained to a limited extent from near range to far range. Since this method is based on ground range images, it avoids complicated orthorectification.     

Statistical analysis of discrepancies in high precision levelling

An investigation was made of the behaviour of the variable (where ρ_ij are the discrepancies between the direct and reverse measurements of the height of consecutive bench marks and theR _ij are their distance apart) in a partial net of the Italian high precision levelling of a total length of about1.400 km. The methods of analysis employed were in general non-parametric individual and cumulative tests; in particular randomness, normality and asymmetry tests were carried out. The computers employed wereIBM/7094/7040. From the results evidence was obtained of the existence of an asymmetry in respect to zero of thex _ij confirming the well-known results given firstly by Lallemand. A new result was obtained from the tests of randomness which put in evidence trends of the mean values of thex _ij and explained some anomalous behaviours of the cumulative discrepancy curves. The extension of this investigation to a broader net possibly covering other national nets would be very useful to get a deeper insight into the behaviour of the errors in high precision levelling. Ad hoc programs for electronic computers are available to accomplish this job quickly. Presented at the 14^th International Assembly of Geodesy (Lucerne, 1967).     

CONDITION FOR THE CONSTRUCTION OF A CONFORMAL PROJECTION

Abstract

In the Empire Survey Review for October 1938 (iv, 30, 480) a simple demonstration of the condition to be satisfied for conformal representation was given. This condition may be expressed by the equation w = f(z), where w and z are complex variables representing corresponding points in the w-plane and z-plane respectively, and f(z) is an analytic function of z.     

Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm

In order to achieve to GPS solutions of first-order accuracy and integrity, carrier phase observations as well as pseudorange observations have to be adjusted with respect to a linear/linearized model. Here the problem of mixed integer-real valued parameter adjustment (IRA) is met. Indeed, integer cycle ambiguity unknowns have to be estimated and tested. At first we review the three concepts to deal with IRA: (i) DDD or triple difference observations are produced by a properly chosen difference operator and choice of basis, namely being free of integer-valued unknowns (ii) The real-valued unknown parameters are eliminated by a Gauss elimination step while the remaining integer-valued unknown parameters (initial cycle ambiguities) are determined by Quadratic Programming and (iii) a RA substitute model is firstly implemented (real-valued estimates of initial cycle ambiguities) and secondly a minimum distance map is designed which operates on the real-valued approximation of integers with respect to the integer data in a lattice. This is the place where the integer Gram-Schmidt orthogonalization by means of the LLL algorithm (modified LLL algorithm) is applied being illustrated by four examples. In particular, we prove that in general it is impossible to transform an oblique base of a lattice to an orthogonal base by Gram-Schmidt orthogonalization where its matrix enties are integer. The volume preserving Gram-Schmidt orthogonalization operator constraint to integer entries produces “almost orthogonal” bases which, in turn, can be used to produce the integer-valued unknown parameters (initial cycle ambiguities) from the LLL algorithm (modified LLL algorithm). Systematic errors generated by “almost orthogonal” lattice bases are quantified by A. K. Lenstra et al. (1982) as well as M. Pohst (1987). The solution point of Integer Least Squares generated by the LLL algorithm is = (L')⁻¹[L'◯] ∈ ℤ ^m where L is the lower triangular Gram-Schmidt matrix rounded to nearest integers, [L], and = [L'◯] are the nearest integers of L'◯, ◯ being the real valued approximation of z ∈ ℤ ^m , the m-dimensional lattice space Λ. Indeed due to “almost orthogonality” of the integer Gram-Schmidt procedure, the solution point is only suboptimal, only close to “least squares.” ? 2000 John Wiley & Sons, Inc.     

平面四孔六边形格网系统编码运算

全球离散格网系统是支持多源地球空间信息融合处理的新型数据模型。六边形格网系统具有优良的几何属性,相关研究已引起学术界的关注,单元层次关系描述与编码方案设计是其研究难点。本文根据平面四孔六边形格网系统结构特点,设计“格点四叉树”层次编码结构,定义编码运算并归纳运算规律,据此实现二维直角坐标与单元编码的相互转换。与同类成果相比,格点四叉树从原理上克服了奇（偶）分层编码、单元中心与顶点混合编码导致的诸多缺陷,且编码运算规律简明,易于算法实现。试验结果表明,格点四叉树编码加法运算的效率约是PYXIS的6倍、HQBS的5倍;直角坐标转换到编码的效率约为HQBS的5倍,编码转换到直角坐标的效率约为HQBS的3倍。     

THE CONFORMAL TRANSFORMATION OF A NETWORK OF TRIANGULATION

Abstract

In a recent issue of this Review, an example is given of the conformal transformation of a network of triangulation using Newton's interpolation formula with divided differences. While the application of the method appears to be new, attention should be drawn to the fact that Kruger employed Lagrange's interpolation formula in a discussion and extension of the Schols method in a paper which was published in the Zeitschrift für Vermessungswesen in 1896. A reference to this paper was given at the end of the paper, “Adjustment of the Secondary Triangulation of South Africa”, published in a previous issue of the E.S.R. (iv, 30, 480).