The relation between rigorous and Helmert’s definitions of orthometric heights

Following our earlier definition of the rigorous orthometric height [J Geod 79(1-3):82–92 (2005)] we present the derivation and calculation of the differences between this and the Helmert orthometric height, which is embedded in the vertical datums used in numerous countries. By way of comparison, we also consider Mader and Niethammer’s refinements to the Helmert orthometric height. For a profile across the Canadian Rocky Mountains (maximum height of ~2,800 m), the rigorous correction to Helmert’s height reaches ~13 cm, whereas the Mader and Niethammer corrections only reach ~3 cm. The discrepancy is due mostly to the rigorous correction’s consideration of the geoid-generated gravity disturbance. We also point out that several of the terms derived here are the same as those used in regional gravimetric geoid models, thus simplifying their implementation. This will enable those who currently use Helmert orthometric heights to upgrade them to a more rigorous height system based on the Earth’s gravity field and one that is more compatible with a regional geoid model.     

＂Digital Region＂ in the Context of the ＂Grid Computing＂

This paper is to construct a “digital local, regional, region“ information framework based on the technology of “SIG“ and its significance and application to the regional sustainable development evaluation system. First, the concept of the “grid computing“ and “SIG“ is interpreted and discussed, then the relationship between the “grid computing“ and “digital region“ is analyzed, and the framework of the “digital region“ is put forward. Finally, the significance and application of “grid computing“ to the “region sustainable development evaluation system“ are discussed.     

Triangulated spherical splines for geopotential reconstruction

We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations. The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite. Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (n _max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics of satellite coverage, which could not be done using a global spherical harmonic representation. The results in this paper are based on the research supported by the National Science Foundation under the grant no. 0327577.     

Confidence regions for GPS baselines by Bayesian statistics

 The global positioning system (GPS) model is distinctive in the way that the unknown parameters are not only real-valued, the baseline coordinates, but also integers, the phase ambiguities. The GPS model therefore leads to a mixed integer–real-valued estimation problem. Common solutions are the float solution, which ignores the ambiguities being integers, or the fixed solution, where the ambiguities are estimated as integers and then are fixed. Confidence regions, so-called HPD (highest posterior density) regions, for the GPS baselines are derived by Bayesian statistics. They take care of the integer character of the phase ambiguities but still consider them as unknown parameters. Estimating these confidence regions leads to a numerical integration problem which is solved by Monte Carlo methods. This is computationally expensive so that approximations of the confidence regions are also developed. In an example it is shown that for a high confidence level the confidence region consists of more than one region. Received: 1 February 2001 / Accepted: 18 July 2001     

Modeling global Hammond landform regions from 250‐m elevation data

In 1964, E.H. Hammond proposed criteria for classifying and mapping physiographic regions of the United States. Hammond produced a map entitled “Classes of Land Surface Form in the Forty‐Eight States, USA”, which is regarded as a pioneering and rigorous treatment of regional physiography. Several researchers automated Hammond?s model in GIS. However, these were local or regional in application, and resulted in inadequate characterization of tablelands. We used a global 250 m DEM to produce a new characterization of global Hammond landform regions. The improved algorithm we developed for the regional landform modeling: (1) incorporated a profile parameter for the delineation of tablelands; (2) accommodated negative elevation data values; (3) allowed neighborhood analysis window (NAW) size to vary between parameters; (4) more accurately bounded plains regions; and (5) mapped landform regions as opposed to discrete landform features. The new global Hammond landform regions product builds on an existing global Hammond landform features product developed by the U.S. Geological Survey, which, while globally comprehensive, did not include tablelands, used a fixed NAW size, and essentially classified pixels rather than regions. Our algorithm also permits the disaggregation of “mixed” Hammond types (e.g. plains with high mountains) into their component parts.     

Economic convergence or divergence? Modeling the interregional dynamics of EU regions, 1985–1999

In this paper we start from a continuous time framework derived from the classical predator-prey model in order to analyze the recent dynamics of regional evolution in the EU. The model describes a system of interrelated units obeying a complex functional dynamics that at any moment may encompass divergent forces. After briefly reviewing the modeling framework presented elsewhere (Arbia and Paelinck 2002), we consider the dynamics of per-capita income in 119 NUTS-2 European regions in the years 1985–1999, and fit the model using Simultaneous Dynamic Least Squares (Paelinck 1996b). The model is shown to fit the empirical data well. The – potential divergence – leads up to a formidable coordination task for public authorities responsible for regional policies, as they are supposed – if their aim is absolute convergence in an economic sense, meaning equalizing incomes per head – to produce at any time a consistent set of regional policies for all the regions concerned, and not only for the less developed ones.     

Quantification of Urban Landscape Dynamics Using Patch Parameters and Landscape Indices: An Analytical Study of Ranchi

Urbanization incepts serious challenges of growth and its management. The issues of urbanization manifest in the form of overcrowding, congestion, insufficient infrastructure, inadequate service provisioning, environmental degradation, pollution etc and affect the socioeconomic development of the city. Ranchi, the capital of newly formed state of Jharkhand (India) has been witnessing the same scenario; raising the question of its planning and management of growth to make it more efficient and sustainable. It hoists the necessity to study the pattern of urbanization and its impact on other landuse/landcover categories in Ranchi city. In order to assess the urbanization pattern and spatio-temporal dynamics in the study area, the changing pattern of the three significant patch parameters viz. patch frequency, largest patch size and average patch size of all affected landuse/landcover categories over a time gradient representing the pre-capital and post-capital formation phases of the Ranchi city have been analyzed. The two conventional landscape indices viz. Shannon’s diversity Index and Simpson’s diversity index and a newly developed index ‘Normalized Patch size Range Index’ have been employed in the analyses which not only ascertained the finding derived but also provided meaningful insights pertaining to the spatio-temporal urban landscape dynamics prevailing in the Ranchi city.     

Modeling of earth’s gravity fields visualization based on Quad Tree

The problems of the earth’s gravity fields’ visualization are both focus and puzzle currently. Aiming at multiresolution rendering, modeling of the Earth’s gravity fields’ data is discussed in the paper by using LOD algorithm based on Quad Tree. First, this paper employed the method of LOD based on Quad Tree to divide up the regional gravity anomaly data, introduced the combined node evaluation system that was composed of viewpoint related and roughness related systems, and then eliminated the T-cracks that appeared among the gravity anomaly data grids with different resolutions. The test results demonstrated that the gravity anomaly data grids’ rendering effects were living, and the computational power was low. Therefore, the proposed algorithm was a suitable method for modeling the gravity anomaly data and has potential applications in visualization of the earth’s gravity fields.     

Urban growth analysis using spatial and temporal data

Urban growth identification, quantification, knowledge of rate and the trends of growth would help in regional planning for better infrastructure provision in environmentally sound way. This requires analysis of spatial and temporal data, which help in quantifying the trends of growth on spatial scale. Emerging technologies such as Remote Sensing, Geographic Information System (GIS) along with Global Positioning System (GPS) help in this regard. Remote sensing aids in the collection of temporal data and GIS helps in spatial analysis. This paper focuses on the analysis of urban growth pattern in the form of either radial or linear sprawl along the Bangalore — Mysore highway. Various GIS base layers such as built-up areas along the highway, road network, village boundary etc. were generated using collateral data such as the Survey of India toposheet, etc. Further, this analysis was complemented with the computation of Shannon’s entropy, which helped in identifying prevalent sprawl zone, rate of growth and in delineating potential sprawl locations. The computation Shannon’s entropy helped in delineating regions with dispersed and compact growth. This study reveals that the Bangalore North and South taluks contributed mainly to the sprawl with 559% increase in built-up area over a period of 28 years and high degree of dispersion. The Mysore and Srirangapatna region showed 128% change in built-up area and a high potential for sprawl with slightly high dispersion. The degree of sprawl was found to be directly proportional to the distances from the cities.     

Wavelet Modeling of Regional and Temporal Variations of the Earth’s Gravitational Potential Observed by GRACE

This work is dedicated to the wavelet modeling of regional and temporal variations of the Earth’s gravitational potential observed by the GRACE (gravity recovery and climate experiment) satellite mission. In the first part, all required mathematical tools and methods involving spherical wavelets are provided. Then, we apply our method to monthly GRACE gravity fields. A strong seasonal signal can be identified which is restricted to areas where large-scale redistributions of continental water mass are expected. This assumption is analyzed and verified by comparing the time-series of regionally obtained wavelet coefficients of the gravitational signal originating from hydrology models and the gravitational potential observed by GRACE. The results are in good agreement with previous studies and illustrate that wavelets are an appropriate tool to investigate regional effects in the Earth’s gravitational field. Electronic Supplementary Material Supplementary material is available for this article at     

Application of remote sensing and GIS to assess land use changes in Jhunjhunun district of arid Rajasthan

Over the last four decades exploitation of natural resources to meet increasing societal demands for land based products has caused significant changes in land use and land cover not only in nature’s best gifted regions but also environmentally sensitive arid regions. Through digital interpretation of IRS LISS-III data of 2004 supported with field survey, the present land use map of Jhunjhunun district of arid Rajasthan has been prepared. Agriculture is the dominant land use constituting 84% (including 38% irrigated cropland) area. The land use changes over time and space are worked out by comparing with Landsat 2 MSS data of 1975 and Land use/land cover map of 1988–89. These changes are correlated by analyzing historical land use and cropping pattern data from 1957–58 to 2004–05. The region witnessed record increase in irrigated area but sharply depleted ground water and rendered hectares of irrigated double cropland into dry land agriculture. Strategies and technologies are suggested for sustainable use and management of different category of land.     

Productivity convergence and spatial dependence among Spanish regions

This paper estimates the evolution of labor productivity disparities among 48 Spanish regions over 1980–1996 according to the concepts of - and -convergence. The results of -convergence emphasize the importance of including the impact of neighboring locations productivity and a disaggregate analysis at a sectoral level. In order to measure the narrowing of inequalities, we examine -convergence and reveal that convergence occurs in aggregate labor productivity but not in productivities per sector. The reason comes from a transfer of resources from agriculture towards more productive sectors that has been more pronounced in the poor regions than in the rich ones.The author would like to thank Julie Le Gallo, an anonymous referee, and the participants of the 50th North American Meetings of the RSAI and of the 43rd Annual Meeting of the WRSA for their valuable comments. This paper won the first place the 2004 Tiebout Prize competition, which was awarded at the WRSA meeting, Hawaii, USA, February 26–28.     

The change of land use/cover and characteristics of landscape pattern in arid areas oasis: An application in Jinghe,Xinjiang

This paper uses 3S technology in macroscopic. Combining the integrated technology of ecological quantity analytical method with GIS technology through ArcGIS and Fragstats, the authors study the images of 1972, 1990, 2001, and 2005 and obtained land use data in Jinghe County. Then, the change of land use/cover and landscape pattern had been analyzed in the Jinghe County of Xinjiang. The conclusions were as follows: (1) The trend of LUCC is that the area of oasis expands slowly in nearly 33 years between 1972 to 2005 in Jinghe County. (2) The water area is mainly influenced by Ebinur Lake, so the area expands a little in this period. (3) The area of salinization-land expands at first and reduces later. The area of sand land decreases and the other land class increases, while the probability of transfer is always high. (4) Landscape change is also obvious throughout the decades. Overall, landscape density increases, the largest path index decreases at first and expends later, the weight area index decreases, and the shape of landscape becomes regulated. The nearest distances, the degrees of reunite, and outspread decreases. It shows that the connection of the main path in 1972 is better than 2005, wherein the patch becomes more complex. From the changes of Shannon’s Diversity Index and Shannon’s Evenness Index, we know that the diversity of landscape and the Interspersion Juxtaposition Index increase. The degree of diversity landscape and fragmentation increase also shows that the land uses become more complex. All in all, it is essential to intensify the spatial relationships among landscape elements and to maintain the continuity of landscape ecological process and pattern in the course of area expansion.     

Phase transitions and path dependence in urban evolution

There is a long history of recognising and interpreting discontinuous change—phase transitions—in urban systems. In this paper, we use the aggregate retail model as an archetype to explore some new ideas. For example, we argue that the dependence of paths of development on initial conditions has been understudied, and we offer a new graphical analysis that demonstrates explicitly their influence on discrete change. We introduce an order parameter, and we plot this on a ‘results grid’ to facilitate the discovery of possible phase transitions. We illustrate the use of these new developments with an application to London. We show how retail developers can change the ‘initial conditions’ at a point in time and possibly bring about phase transitions by their actions. This also shows that it should be possible to account for the history of urban development as a sequence of initial conditions, illustrating path dependence. Secondly, the model could be deployed in relation to a new shopping zone, and the tools developed here used to calculate the minimum size of a new development in order for it to compete. We explore the ‘minimum size’ idea in relation to a new shopping zone in London.     

Hierarchical spatial interaction among the Italian regions: a nonlinear relative dynamics approach

Regional interactions and spillover effects should be considered as important factors in growth analysis of regional economies. Using modified versions of the Dendrinos–Sonis model, this paper analyses the spatial hierarchical system of Italy. The interaction among Italian regions is considered at three different levels of spatial aggregation, the NUTS-1, NUTS-2 and NUTS-3 levels. Compared to more popular spatial econometric approaches, the Dendrinos–Sonis model and its extensions provide greater flexibility in the way interaction between regions is handled but the results strongly depend on the choice of a reference region.

Nonlinear regional economic dynamics: continuous-time specification,estimation and stability analysis

This paper presents an innovative approach to the study of regional economic dynamics within a nonlinear continuous-time econometric framework—a generalized specification of the Lotka–Volterra system of equations. This specification, which accounts for interdependent behavior of three industrial sectors and spillover effects of activities in neighboring regions, is employed in an analysis of five Italian regions between 1980 and 2003. For these regions, we report estimation results, characterize the varying systems dynamics, analyze the models’ local and global stability properties, and determine via sensitivity analyses which structural features appear to exert the greatest influence on these properties.

Transformation from Cartesian to Geodetic Coordinates Accelerated by Halley’s Method

By using Halley’s third-order formula to find the root of a non-linear equation, we develop a new iterative procedure to solve an irrational form of the “latitude equation”, the equation to determine the geodetic latitude for given Cartesian coordinates. With a limit to one iteration, starting from zero height, and minimizing the number of divisions by means of the rational form representation of Halley’s formula, we obtain a new non-iterative method to transform Cartesian coordinates to geodetic ones. The new method is sufficiently precise in the sense that the maximum error of the latitude and the relative height is less than 6 micro-arcseconds for the range of height, −10 km ≤ h ≤ 30,000 km. The new method is around 50% faster than our previous method, roughly twice as fast as the well-known Bowring’s method, and much faster than the recently developed methods of Borkowski, Laskowski, Lin and Wang, Jones, Pollard, and Vermeille.     

Ocean tidal parameters from starlette data

Starlette was launched in 1975 in order to study temporal variations in the Earth’s gravity field; in particular, tidal and Earth rotation effects. For the period April 1983 to April 1984 over12,700 normal points of laser ranging data to Starlette have been sub-divided into49 near consecutive 5–6 day arcs. Normal equations for each arc as obtained from a least-squares data reduction procedure, were solved for ocean tidal parameters along with other geodetic and geodynamic parameters. The tidal parameters are defined relative to Wahr’s body tides and Wahr’s nutation model and show fair agreement with other satellite derived results and those obtained from spherical harmonic decomposition of global ocean tidal models.     

Evaluation of the first GOCE static gravity field models using terrestrial gravity,vertical deflections and EGM2008 quasigeoid heights

Recently, four global geopotential models (GGMs) were computed and released based on the first 2 months of data collected by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission. Given that GOCE is a technologically complex mission and different processing strategies were applied to real space-collected GOCE data for the first time, evaluation of the new models is an important aspect. As a first assessment strategy, we use terrestrial gravity data over Switzerland and Australia and astrogeodetic vertical deflections over Europe and Australia as ground-truth data sets for GOCE model evaluation. We apply a spectral enhancement method (SEM) to the truncated GOCE GGMs to make their spectral content more comparable with the terrestrial data. The SEM utilises the high-degree bands of EGM2008 and residual terrain model data as a data source to widely bridge the spectral gap between the satellite and terrestrial data. Analysis of root mean square (RMS) errors is carried out as a function of (i) the GOCE GGM expansion degree and (ii) the four different GOCE GGMs. The RMS curves are also compared against those from EGM2008 and GRACE-based GGMs. As a second assessment strategy, we compare global grids of GOCE GGM and EGM2008 quasigeoid heights. In connection with EGM2008 error estimates, this allows location of regions where GOCE is likely to deliver improved knowledge on the Earth’s gravity field. Our ground truth data sets, together with the EGM2008 quasigeoid comparisons, signal clear improvements in the spectral band ~160–165 to ~180–185 in terms of spherical harmonic degrees for the GOCE-based GGMs, fairly independently of the individual GOCE model used. The results from both assessments together provide strong evidence that the first 2 months of GOCE observations improve the knowledge of the Earth’s static gravity field at spatial scales between ~125 and ~110 km, particularly over parts of Asia, Africa, South America and Antarctica, in comparison with the pre-GOCE-era.     

Geospatial modeling of Brown oak (<Emphasis Type="Italic">Quercus semecarpifolia</Emphasis>) habitats in the Kumaun Himalaya under climate change scenario

The study explores the use of multiple criteria decision techniques in predicting spatial niche of Brown oak (also known as Kharsu oak, Quercus semecarpifolia Sm.) formation in midaltitude (2,400–3,500 meter amsl) Kumaun Himalaya. Predictive models using various climatic and topographical factors influencing Brown oak’s growth and survival were developed to define its current ecological niche. Analytical Hierarchical Process (AHP) method involving Saaty’s pair-wise comparison was performed to rank the explanatory powers of each compared variable. Variables were suitably weighted using fuzzy factor standardization scheme to reflect their relative importance in defining species niche. An optimum indicator was then chosen for deriving a site suitability map of brown oak. This study establishes the role of aspect in the current distribution of the species along with known influence of altitude. Future niches of oak has been tracked in the projected climate change scenario of +1°C and +2°C rise in temperature and 20 mm in precipitation. The results show that on predicted +1°C and +2°C increase in temperature, present habitat of brown oak distribution may be reduced by 40 per cent and 76 per cent respectively.