Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame

This research represents a continuation of the investigation carried out in the paper of Petrovskaya and Vershkov (J Geod 84(3):165–178, 2010) where conventional spherical harmonic series are constructed for arbitrary order derivatives of the Earth gravitational potential in the terrestrial reference frame. The problem of converting the potential derivatives of the first and second orders into geopotential models is studied. Two kinds of basic equations for solving this problem are derived. The equations of the first kind represent new non-singular non-orthogonal series for the geopotential derivatives, which are constructed by means of transforming the intermediate expressions for these derivatives from the above-mentioned paper. In contrast to the spherical harmonic expansions, these alternative series directly depend on the geopotential coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ . Each term of the series for the first-order derivatives is represented by a sum of these coefficients, which are multiplied by linear combinations of at most two spherical harmonics. For the second-order derivatives, the geopotential coefficients are multiplied by linear combinations of at most three spherical harmonics. As compared to existing non-singular expressions for the geopotential derivatives, the new expressions have a more simple structure. They depend only on the conventional spherical harmonics and do not depend on the first- and second-order derivatives of the associated Legendre functions. The basic equations of the second kind are inferred from the linear equations, constructed in the cited paper, which express the coefficients of the spherical harmonic series for the first- and second-order derivatives in terms of the geopotential coefficients. These equations are converted into recurrent relations from which the coefficients ${\bar{{C}}_{n,m}}$ and ${\bar{{S}}_{n,m}}$ are determined on the basis of the spherical harmonic coefficients of each derivative. The latter coefficients can be estimated from the values of the geopotential derivatives by the quadrature formulas or the least-squares approach. The new expressions of two kinds can be applied for spherical harmonic synthesis and analysis. In particular, they might be incorporated in geopotential modeling on the basis of the orbit data from the CHAMP, GRACE and GOCE missions, and the gradiometry data from the GOCE mission.     

On the evaluation of the gravity effects of polyhedral bodies and a consistent treatment of related singularities

We show that the singularities which can affect the computation of the gravity effects (potential, gravity and tensor gradient fields) can be systematically addressed by invoking distribution theory and suitable formulas of differential calculus. Thus, differently from previous contributions on the subject, the use of a-posteriori corrections of the formulas derived in absence of singularities can be ruled out. The general approach presented in the paper is further specialized to the case of polyhedral bodies and detailed for a rectangular prism having a constant mass density. With reference to this last case, we derive novel expressions for the related gravitational field, as well as for its first and second derivative, at an observation point coincident with a prism vertex and show that they turn out to be more compact than the ones reported in the specialized literature.     

Validation of Chlorophyll-a Algorithms in the Coastal Waters of Bay of Bengal Initial Validation Results from OCM-2

In this paper we report chlorophyll measurements made during an ocean colour validation cruise in April 2011 of the research vessel, Sagar Paschimi in the coastal waters of Northern Bay of Bengal. The chlorophyll-a concentration in these waters range from 0.2 to 4.0 mg/m³. Chlorophyll-a concentration from OCM-2 was estimated using the global ocean colour algorithms namely, OC2, OC3, OC4 and Chl-a algorithms respectively. OCM data was processed using the global SeaWiFS Data Analysis System (SeaDAS) in which all the above mentioned algorithms are embedded for estimating the chlorophyll-a concentration. A comparative study was made between and in-situ and satellite derived chlorophyll-a concentration. Although the matchups between in-situ and satellite data from OCM-2 were sparse, it indicates that direct application of the standard SeaWiFS algorithm-the OC4-V4 algorithm—in the coastal waters of the Bay of Bengal will underestimate chlorophyll-a by up to 30%. The results show a good correlation with an R value of 0.61 using OC2 algorithm. However, all the other global algorithms over estimate the chlorophyll-a concentration even in low chlorophyll concentration range. The comparison between in-situ and all the existing chlorophyll algorithms shows the efficiency of these algorithms for quantification of chlorophyll in coastal waters and hence the need to develop regional algorithms and fluorescence based algorithms for better quantification.     

Geospatial Technologies for National Geomorphology and Lineament Mapping Project – A Case Study of Goa State

A three level classification system, based on the genesis of landforms, was used to map the geomorphology of the Goa state. The first level corresponds to the process that was responsible for landform generation, the second level or the intermediate level was assigned based on the morphography, and the third level corresponds to the individual landforms units identified based on the morphostructure. The mapping was carried out using IRS-P6 LISS-III (23.5 m) satellite image as the primary data source. Ancillary data such as geological map, topographic map, digital elevation model (DEM), field data collected by global positioning system (GPS) and web portals for image visualisation, were also used for the mapping purpose. A new software designed for mapping landforms based on the genesis, was used in this study to create a seamless geomorphology and lineament database of the Goa state in a GIS environment. A total of 58 landforms within six types of genetic classes were mapped in this area. Similarly, structural and geomorphic lineaments were also delineated using the satellite data. The database created has multi-purpose usability such as environmental studies, mining activity assessment, coastal zone management and wasteland development, since the classification system used is focused on processes, not theme specific.     

Effects of reverse geocoding on OpenStreetMap tag quality assessment

OpenStreetMap (OSM), a widely-used open-source geographic information system platform, provides a vast geographic dataset in which users contribute both geometric information (nodes, ways, and relations) and semantic information (tags). This method of voluntary contributions is governed by the collective effort of the users. It is widely acknowledged that the quantity of tag information is substantial, but its quality is often poor. Researchers are therefore trying to assess the quality of the tags and enhance the data through various integration experiments. This article investigates the validity of the tags for geographical objects in metropolitan areas using municipal data and a reverse geocoding technique. The proposed method evaluates the data quality and the matching process carried out by reverse geocoding, using municipal points of interest as a reference. The accuracy of the tag and address information and road network centrality metrics were assessed for the OSM objects that were matched to the locations of interest. The tags were found to match the points of interest with an accuracy of 88%. Furthermore, the tag values were categorized and analyzed based on their similarity. It is concluded that in metropolitan settings where centers of interest are closely located, the accuracy of tags and addresses tends to decrease.     

Statistical data fusion of multi-sensor AOD over the Continental United States

This article illustrates two techniques for merging daily aerosol optical depth (AOD) measurements from satellite and ground-based data sources to achieve optimal data quality and spatial coverage. The first technique is a traditional Universal Kriging (UK) approach employed to predict AOD from multi-sensor aerosol products that are aggregated on a reference grid with AERONET as ground truth. The second technique is spatial statistical data fusion (SSDF); a method designed for massive satellite data interpolation. Traditional kriging has computational complexity O(N³), making it impractical for large datasets. Our version of UK accommodates massive data inputs by performing kriging locally, while SSDF accommodates massive data inputs by modelling their covariance structure with a low-rank linear model. In this study, we use aerosol data products from two satellite instruments: the moderate resolution imaging spectrometer and the geostationary operational environmental satellite, covering the Continental United States.     

A Composite Semisupervised SVM for Classification of Hyperspectral Images

This letter presents a novel composite semisupervised support vector machine (SVM) for the spectral-spatial classification of hyperspectral images. In particular, the proposed technique exploits the following: 1) unlabeled data for increasing the reliability of the training phase when few training samples are available and 2) composite kernel functions for simultaneously taking into account spectral and spatial information included in the considered image. Experiments carried out on a hyperspectral image pointed out the effectiveness of the presented technique, which resulted in a significant increase of the classification accuracy with respect to both supervised SVMs and progressive semisupervised SVMs with single kernels, as well as supervised SVMs with composite kernels.