The reduction correction in North America

An inverse Poisson integral technique has been used to determine a gravity field on the geoid which, when continued by analytic free space methods to the topographic surface, agrees with the observed field. The computation is performed in three stages, each stage refining the previous solution using data at progressively increasing resolution (1^o×1^o, 5′×5′, 5/8′×5/8′) from a decreasing area of integration. Reduction corrections are computed at 5/8′×5/8′ granularity by differencing the geoidal and surface values, smoothed by low-pass filtering and sub-sampled at 5′ intervals. This paper discusses 1^o×1^o averages of the reduction corrections thus obtained for 172 1^o×1^o squares in western North America. The 1^o×1^o mean reduction corrections are predominantly positive, varying from −3 to +15mgal, with values in excess of 5mgal for 26 squares. Their mean andrms values are +2.4 and 3.6mgal respectively and they correlate well with the mean terrain corrections as predicted byPellinen in 1962. The mean andrms contributions from the three stages of computation are: 1^o×1^o stage +0.15 and 0.7mgal; 5′×5′ stage +1.0 and 1.6mgal; and 5/8′×5/8′ stage +1.3 and 1.8mgal. These results reflect a tendency for the contributions to become larger and more systematically positive as the wavelengths involved become shorter. The results are discussed in terms of two mechanisms; the first is a tendency for the absolute values of both positive and negative anomalies to become larger when continued downwards and, the second, a non-linear rectification, due to the correlation between gravity anomaly and topographic height, which results in the values continued to a level surface being systematically more positive than those on the topography.     

Detailed gravimetric geoid for the North Atlantic

A detailed gravimetric geoid in the North Atlantic Ocean, named DGGNA-77, has been computed, based on a satellite and gravimetry derived earth potential model (consisting in spherical harmonic coefficients up to degree and order 30) and mean free air surface gravity anomalies (35180 1°×1° mean values and 245000 4′×4′ mean values). The long wavelength undulations were computed from the spherical harmonics of the reference potential model and the details were obtained by integrating the residual gravity anomalies through the Stokes formula: from 0 to 5° with the 4′×4′ data, and from 5° to 20° with the 1°×1° data. For computer time reasons the final grid was computed with half a degree spacing only. This grid extends from the Gulf of Mexico to the European and African coasts. Comparisons have been made with Geos 3 altimetry derived geoid heights and with the 5′×5′ gravimetric geoid derived byMarsh andChang [8] in the northwestern part of the Atlantic Ocean, which show a good agreement in most places apart from some tilts which porbably come from the satellite orbit recovery.     

Digitized global land-sea map and access software

A computer-efficient global data file, which contains digitized information that enables identification of a given latitude/longitude defined point as over land or over water, was generated from a data base which defines the world's shoreline. The method used in the generation of this land-sea boundary data map and its data structure are discussed. The data file was originally generated on a Control Data Corporation(CDC) computer, but it has been transported to other computer systems, includingIBM, DEC/VAX, UNIVAC and Cray computers. The land-sea boundary map also includes information on islands and inland lakes. The resolution of this map is 5′×5′ or an equivalent of9 km square surface blocks at the equator. The software to access this data base is structured to be easily transportable to different computers. This data base was used in the generation of the Seasat Geophysical Data Record(GDR) to identify whether a spaceborne radar altimeter measurement was over-land or over-ocean.     

Global mean sea surface and marine gravity anomaly from multi-satellite altimetry: applications of deflection-geoid and inverse Vening Meinesz formulae

 Global mean sea surface heights (SSHs) and gravity anomalies on a 2^′×2^′ grid were determined from Seasat, Geosat (Exact Repeat Mission and Geodetic Mission), ERS-1 (1.5-year mean of 35-day, and GM), TOPEX/POSEIDON (T/P) (5.6-year mean) and ERS-2 (2-year mean) altimeter data over the region 0^∘–360^∘ longitude and –80^∘–80^∘ latitude. To reduce ocean variabilities and data noises, SSHs from non-repeat missions were filtered by Gaussian filters of various wavelengths. A Levitus oceanic dynamic topography was subtracted from the altimeter-derived SSHs, and the resulting heights were used to compute along-track deflection of the vertical (DOV). Geoidal heights and gravity anomalies were then computed from DOV using the deflection-geoid and inverse Vening Meinesz formulae. The Levitus oceanic dynamic topography was added back to the geoidal heights to obtain a preliminary sea surface grid. The difference between the T/P mean sea surface and the preliminary sea surface was computed on a grid by a minimum curvature method and then was added to the preliminary grid. The comparison of the NCTU01 mean sea surface height (MSSH) with the T/P and the ERS-1 MSSH result in overall root-mean-square (RMS) differences of 5.0 and 3.1 cm in SSH, respectively, and 7.1 and 3.2 μrad in SSH gradient, respectively. The RMS differences between the predicted and shipborne gravity anomalies range from 3.0 to 13.4 mGal in 12 areas of the world's oceans. Received: 26 September 2001 / Accepted: 3 April 2002 Correspondence to: C. Hwang Acknowledgements. This research is partly supported by the National Science Council of ROC, under grants NSC89-2611-M-009-003-OP2 and NSC89-2211-E-009-095. This is a contribution to the IAG Special Study Group 3.186. The Geosat and ERS1/2 data are from NOAA and CERSAT/France, respectively. The T/P data were provided by AVISO. The CLS and GSFC00 MSS models were kindly provided by NASA/GSFC and CLS, respectively. Drs. Levitus, Monterey, and Boyer are thanked for providing the SST model. Dr. T. Gruber and two anonymous reviewers provided very detailed reviews that improved the quality of this paper.     

联合多种测高数据确定中国边缘海及全球海域的垂线偏差

On the basis of gravity field model （EIGEN_CG01C）, together with multi-altimeter data, the improved deflection of the vertical gridded in 2＇×2＇ in China marginal sea and gridded in 5＇×5＇ in the global sea was determined by using the weighted method of along-track least squares, and the accuracy is better than 1.2^# in China marginal sea. As for the quality of the deflection of the vertical, it meets the challenge for the gravity field of high resolution and accuracy, it shows that, compared with the shipboard gravimetry in the sea, the accuracy of the gravity anomalies computed with the marine deflection of the vertical by inverse Vening-Meinesz formula is 7.75 m.s ^-2.     

Model anomalies for the earth from crustal data

Crustal data of surface elevations and depth of Moho (and densities) can be utilized to form model-earth anomalies. These model-anomalies can closely approximate the free-air anomaly field of the earth, and could thus be used to predict the latter. A review of several such models is presented, with some elaboration on model developments, procedures, data analysis and accuracies. One of the models approaches a prediction accuracy of ±10 mgal for5°×5° mean free-air anomalies, whose r.m.s. value was about30% higher.     

A new gravity map, a new marine geoid around Japan and the detection of the Kuroshio current

About half a million marine gravity measurements over a 30^∘×30^∘ area centered on Japan have been processed and adjusted to produce a new free-air gravity map from a 5′×5′ grid. This map seems to have a better resolution than those previously published as measured by its correlation with bathymetry. The grid was used together with a high-degree and -order spherical harmonics geopotential model to compute a detailed geoid with two methods: Stokes integral and collocation. Comparisons with other available geoidal surfaces derived either from gravity or from satellite altimetry were made especially to test the ability of this new geoid at showing the sea surface topography as mapped by the Topex/Poseidon satellite. Over 2 months (6 cycles) the dynamic topography at ascending passes in the region (23^∘47^∘N and 123^∘147^∘E) was mapped to study the variability of the Kuroshio current. Received: 15 July 1994 / Accepted: 17 February 1997     

Determination of Indian absolute geodetic datum by least-square solution technique

The Everest spheroid, 1830, in general use in the Survey of India, was finally oriented in an arbitrary manner at the Indian geodetic datum in 1840; while the international spheroid, 1924, in use for scientific purposes; was locally fitted to the Indian geoid in 1927. An attempt is here made to obtain the initial values for the Indian geodetic datum in absolute terms on GRS 67 by least-square solution technique, making use of the available astro-geodetic data in India, and the corresponding generalised gravimetric values at the considered astro-geodetic points, as derived from the mean gravity anomalies over1°×1° squares of latitude and longitude in and around the Indian sub-continent, and over5° equal area blocks covering the rest of the earth’s surface. The values obtained independently by gravimetric method, were also considered before actual finalization of the results of the present determination.     

Runoff Estimation and Morphometric Analysis for Hesaraghatta Watershed Using IRS–1D LISS III FCC Satellite Data

The study area, Hesaraghatta watershed is located between 77° 20′ to 77° 42′ E longitude and 13° 10′ to 13° 24′ N latitude with an area of 600.01 km². Thematic layers such as Land Use/Land Cover, drainage, soil and hydrological soil group were generated from IRS–1D LISS III satellite data (FCC). An attempt was made to estimate runoff using Soil Conservation Service (SCS) curve number model and it was estimated to be 1960, 2066, 1870 and 1810 mm for sub-watersheds 1, 2, 3 and 4 respectively. Quantitative morphometric analysis was carried out for the entire watershed and the four sub-watersheds independently by estimating their (a) linear aspects like stream order, stream length, stream length ratio, bifurcation ratio, length of overland flow, drainage pattern (b) aerial aspects like shape factor, circulatory ratio, elongation ratio and drainage density and (c) relief aspects like basin relief, relief ratio, relative relief and ruggedness number. Drainage density was estimated to be 1.23 km/km² designating the study area as a very coarse textured watershed.     

Least-squares prediction of horizontal coordinate distortions in Canada

A least-squares prediction method is described to estimate horizontal coordinate distortions at lower order points of a network using known coordinate differences (NAD27 coordinate distortions Δϕ′s and Δλ′s) at higher order points between NAD27 coordinates and coordinates derived from a recent (MAY 76), relatively distortion free, adjustment of these points. Empirical autocovariance functions of Δϕ and Δλ and crosscovariance function between Δϕ and Δλ are derived from some 5,250 data points and modelled using series of exponential functions. Empirical mean square values of Δϕ and Δλ, which are a measure of the distortions in NAD27 ϕ and λ, are 0.051 and 0.645 arcsecs² respectively. The corresponding mean value of the product ΔϕΔλ, which is a measure of the correlation between Δϕ and Δλ, is 0.056 arcsecs². The accuracy obtainable for predicted Δϕ and Δλ at an arbitrary point (e.g., lower order station) is a function of the accuracy and configuration of known Δϕ′s and Δλ′s in the surrounding area. Accuracies obtainable for various types of data configuration are given. Under favorable conditions taking place in about 60% of cases, accuracies in terms of ms agreement with known values of 0″.02 (0.6 m) and 0″.01 (0.2 m along parallel at latitude 50°) for the predicted latitude and longitude distortions are obtainable. Finally, a comparison with a method based on the use of complex polynomials is made. Presented at International Symposium on Geodetic Networks and Computations, Munich, August–September 1981.     

Sampling Design for Global Scale Mapping and Monitoring of Agriculture

Gathering timely information of the global agriculture production of major and commercially important crops has become essential with globalization of the agriculture commodities. Remote sensing based crop production forecasting and monitoring is emerging as one of the most viable solutions for such large area monitoring task. A suitable sampling strategy is the basic requirement towards this. In the present study, different sampling sizes using agricultural area as the sampling frame has been used to analyse the optimum sampling size for continent level assessment. Land use/cover map of the world using 300 m resolution MERIS data was used to generate the agriculture area mask. Grid size of (i) 5° × 5° (ii) 1° × 1° (iii) 30′ × 30′ (iv) 15′ × 15′ (v) 7.5′ × 7.5′ and (vi) 5′ × 5′ were used. Percent crop area was estimated for the grids of all sizes. The grid size of 15′ × 15′ was found to be optimum for global monitoring, as not much change Ws observed in the distribution of the grids after reducing the sample size. Stratification was done using simple random and stratified random sampling method. Stratification using the ‘cumulative square-root of frequency method that resulted in five strata performed best in terms of the variance of the population.     

Ionospheric tomography based on GNSS observations of the CMONOC: performance in the topside ionosphere

This study carries out a quantitative analysis of the performance of ionospheric tomography in the topside ionosphere, utilizing data of October 2011 collected from 260 Global Navigation Satellite System (GNSS) stations in the Crustal Movement Observation Network of China. This tomographic reconstruction with a resolution of 2° in latitude, 2° in longitude and 20 km in altitude has more than 70 % of voxels traversed by GPS raypaths and is able to provide reliable bottom parts of ionospheric profiles. Compared with the observations measured by the Defense Meteorological Satellite Program (DMSP) satellites (F16, F17 and F18) at an altitude of 830–880 km, the results show that there is an overestimation in the reconstructed plasma density at the DMSP altitude, and the reconstruction is better during daytime than nighttime. In addition, the reconstruction at nighttime also indicates a solar activity and latitudinal dependence. In summary, with respect to DMSP measurements, the daytime bias is on average from ?0.32 × 10⁵/cm³ to ?0.28 × 10⁵/cm³, while the nighttime bias is between ?0.37 × 10⁵/cm³ and ?0.24 × 10⁵/cm³, and the standard deviation at daytime and at nighttime is, respectively, 0.082 × 10⁵/cm³ to 0.244 × 10⁵/cm³ and 0.086 × 10⁵/cm³ to 0.428 × 10⁵/cm³. This study suggests that vertical ionospheric profiles from other sources, such as ionosondes or GNSS occultation satellites, should be incorporated into ground-based GNSS topside tomographic studies.     

Die absolute Lotabweichung in Postdam und die Geod?tischen ausgangswerte des Gesamteurop?ischen netzes auf dem Hayfordschen Ellipsoid

Summary The absolute deviations of the vertical detectable at Potsdam from astronomical-gravity comparisons differ significantly from earlier values obtained from the astronomic-geodetic observations which form the starting elements of the European triangulation network. It is possible to show, by the use of values of the deviation of the vertical extending over the whole of Europe as far as longitude 30°, and referred to the undulations of the geoid ofTanni, that the starting elements adopted at Potsdam are too large by 3″.0 in latitude and 1″.4 in longitude.

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Resumen Las desviaciones absolutas de la vertical obtenidas en Potsdam por procedimiento astronómico-gravimétrico, se alejan sensiblemente de los valores encontrados enteriormente por procedimiento astronómicogeodésico, y que constituyen la base de partida de la red de conjunto europea. Es posible demostrar, basándose en el material de desviaciones de la vertical extendido a toda Europa hasta la longitud de 30°, partiendo de las ondulaciones del geoide deTanni, que los datos de partida adoptados en Potsdam son demasiado grandes en 3″,0 de latitud y 1″,4 de longitud.

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Résumé Les déviations absolues de la verticale relevées à Potsdam par voie astronomico-gravimétrique s’écartent sensiblement des valeurs trouvées autrefois par voie astronomico-géodésique, et qui forment la base de départ du réseau d’ensemble de l’Europe. Il est possible de démontrer, en s’appuyant sur le matériel de déviations de la verticale étendu sur toute l’Europe jusqu’à la longitude de 30°, en partant des ondulations du géo?de deTanni, que les données de départ adoptées à Potsdam sont trop grandes de 3″.0 en latitude et de 1″.4 en longitude.

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Sommario La deviazione assoluta della verticale determinata a Postdam per via astronomico-gravimetrica, si scosta sensibilmente dal valore trovato in precedenza per via astronomico-geodetica, che forma la base della compensazione delle reti europee. Si può dimostrare, appoggiandosi sulle deviazioni della verticale conosciute in Europa fino alla longitudine di 30°, e partendo dalle ondulazioni del geoide diTanni, che i dati di partenza adottati a Postdam sono troppo grandi di 3″,0 in latitudine e di 1″,4 in longitudine.

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Communication présentée à l’Assemblée Générale de Bruxelles     

Bathymetric inversion of South China Sea from satellite altimetry data

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Updating and computing the geoid using two dimensional fast Hartley transform and fast T transform

In the analyses of 2D real arrays, fast Hartley (FHT), fast T (FTT) and real-valued fast Fourier transforms are generally preferred in lieu of a complex fast Fourier transform due to the advantages of the former with respect to disk storage and computation time. Although the FHT and the FTT in one dimension are identical, they are different in two or more dimensions. Therefore, first, definitions and some properties of both transforms and the related 2D FHT and FTT algorithms are stated. After reviewing the 2D FHT and FTT solutions of Stokes' formula in planar approximation, 2D FHT and FTT methods are developed for geoid updating to incorporate additional gravity anomalies. The methods are applied for a test area which includes a 64×64 grid of 3^′×3^′ point gravity anomalies and geoid heights calculated from point masses. The geoids computed by 2D FHT and FTT are found to be identical. However, the RMS value of the differences between the computed and test geoid is ±15 mm. The numerical simulations indicate that the new methods of geoid updating are practical and accurate with considerable savings on storage requirements. Received: 15 February 1996; Accepted: 22 January 1997     

Comparison of undulation difference accuracies using gravity anomalies and gravity disturbances

Errors are considered in the outer zone contribution to oceanic undulation differences as obtained from a set of potential coefficients complete to degree 180. It is assumed that the gravity data of the inner zone (a spherical cap), consisting of either gravity anomalies or gravity disturbances, has negligible error. This implies that error estimates of the total undulation difference are analyzed. If the potential coefficients are derived from a global field of 1°×1° mean anomalies accurate to ε_Δg=10 mgal, then for a cap radius of 10°, the undulation difference error (for separations between 100 km and 2000 km) ranges from 13 cm to 55 cm in the gravity anomaly case and from 6 cm to 36 cm in the gravity disturbance case. If ε_Δg is reduced to 1 mgal, these errors in both cases are less than 10 cm. In the absence of a spherical cap, both cases yield identical error estimates: about 68 cm if ε_Δg=1 mgal (for most separations) and ranging from 93 cm to 160 cm if ε_Δg=10 mgal. Introducing a perfect 30-degree reference field, the latter errors are reduced to about 110 cm for most separations.     

Hydromorphogeology and Remote Sensing applications for groundwater exploration in agnigundala mineralised belt, Andhra Pradesh, India

Hydromorphogeological studies have been carried out around Agnigundala mineralised belt (longitude 70°.39′ - 16°.51′ and latitude 16°.2′ - 16°.15′) using remote sensing IRS-IB and SPOT data for ground water exploration. Based on erosional and depositional characters of various geomorphic units like Hills (Structural and denudational) Pediment, Buried pediment, plains and valley fills have been identified in various lithologies like granite, granite gneiss, biotite schist, phyllite,. quartzite and dolomite. The acclamations of individual geomorphic units through visual interpretation are verified from field data. The groundwater potentials of the individual geomorphologic units have been evaluated to obtain a complete hvdrogcological picture of the area. The field data have further helped in quanlifying various geomorphological units with reference to their potential for ground water occurrence.     

Determination of Geoid over South China Sea and Philippine Sea from Multi-satellite Altimetry Data

A new computational procedure for derivation of marine geoid on a 2.5′×2.5′grid in a non-tidal system over the South China Sea and the Philippine Sea from multi-satellite altimeter sea surface heights is discussed. Single-and dual-satellite crossovers were performed, and components of deflections of the vertical were determined at the crossover positions using Sand-well's computational theory, and gridded onto a 2.5′×2.5′resolution grid by employing the Shepard's interpolation procedure. 2.5′×2.5′grid of EGM96-derived components of deflections of the vertical and geoid heights were then used as reference global geopotential model quantities in a remove-restore procedure to implement the Molodensky-like formula via 1D-FFT technique to predict the geoid heights over the South China Sea and the Philippine Sea from the gridded altimeter-derived components of deflec-tions of the vertical. Statistical comparisons between the altimeter-and the EGM96- derived geoid heights showed that there was a root-mean-square agreement of ±0.35 m between them in a region of less tectonically active geological structures. However, over areas of tectonically active structures such as the Philippine trench, differences of about -19.9 m were obtained.     

Gravimetric and astro-geodetic geoids and mean free-air anomalies in India

A preliminary gravimetric geoid with respect to the International Spheroid and the latest astro-geodetic geoid computed on the Everest and International Spheroids are given in the form of undulation maps over the Indian Sub—continent. 1⁰x1⁰ mean free-air anomalies (modified) on the Geodetic Reference System, 1967 (GRS-67) are also given for the whole country in the form of a chart. For the purpose of computing the gravimetric geoid, 5⁰x5⁰ mean free-air anomalies were used outside the area bounded by latitudes 0⁰ to 40⁰ N and longitudes 60⁰ to 100⁰ E and 1⁰x1⁰ mean free-air anomalies within these limits. The anomalies partly computed by Survey of India and mostly collected from other sources (such as B.G.I.) were utilised for this purpose. The astro-geodetic geoid is based on the astronomical data observed in India up to 1978.     

A comparison of recent Earth gravitational models with emphasis on their contribution in refining the gravity and geoid at continental or regional scale

Since the publication of the Earth gravitational model (EGM)96 considerable improvements in the observation techniques resulted in the development of new improved models. The improvements are due to the availability of data from dedicated gravity mapping missions (CHAMP, GRACE) and to the use of 5′ × 5′ terrestrial and altimetry derived gravity anomalies. It is expected that the use of new EGMs will further contribute to the improvement of the resolution and accuracy of the gravity and geoid modeling in continental and regional scale. To prove this numerically, three representative Earth gravitational models are used for the reduction of several kinds of data related to the gravity field in different places of the Earth. The results of the reduction are discussed regarding the corresponding covariance functions which might be used for modeling using the least squares collocation method. The contribution of the EIGEN-GL04C model in most cases is comparable to that of EGM96. However, the big difference is shown in the case of EGM2008, due not only to its quality but obviously to its high degree of expansion. Almost in all cases the variance and the correlation length of the covariance functions of data reduced to this model up to its maximum degree are only a few percentages of corresponding quantities of the same data reduced up to degree 360. Furthermore, the mean value and the standard deviation of the reduced gravity anomalies in extended areas of the Earth such as Australia, Arctic region, Scandinavia or the Canadian plains, vary between −1 and +1 and between 5 and 10 × 10⁻⁵ ms⁻², respectively, reflecting the homogenization of the gravity field on a regional scale. This is very important in using least squares collocation for regional applications. However, the distance to the first zero-value was in several cases much longer than warranted by the high degree of the expansion. This is attributed to errors of medium wavelengths stemming from the lack of, e.g., high-quality data in some area.