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.     

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.     

On the theoretical link between LLL-reduction and Lambda-decorrelation

The LLL algorithm, introduced by Lenstra et al. (Math Ann 261:515–534, 1982), plays a key role in many fields of applied mathematics. In particular, it is used as an effective numerical tool for preconditioning the integer least-squares problems arising in high-precision geodetic positioning and Global Navigation Satellite Systems (GNSS). In 1992, Teunissen developed a method for solving these nearest-lattice point (NLP) problems. This method is referred to as Lambda (for Least-squares AMBiguity Decorrelation Adjustment). The preconditioning stage of Lambda corresponds to its decorrelation algorithm. From an epistemological point of view, the latter was devised through an innovative statistical approach completely independent of the LLL algorithm. Recent papers pointed out some similarities between the LLL algorithm and the Lambda-decorrelation algorithm. We try to clarify this point in the paper. We first introduce a parameter measuring the orthogonality defect of the integer basis in which the NLP problem is solved, the LLL-reduced basis of the LLL algorithm, or the $\Lambda $ -basis of the Lambda method. With regard to this problem, the potential qualities of these bases can then be compared. The $\Lambda $ -basis is built by working at the level of the variance-covariance matrix of the float solution, while the LLL-reduced basis is built by working at the level of its inverse. As a general rule, the orthogonality defect of the $\Lambda $ -basis is greater than that of the corresponding LLL-reduced basis; these bases are however very close to one another. To specify this tight relationship, we present a method that provides the dual LLL-reduced basis of a given $\Lambda $ -basis. As a consequence of this basic link, all the recent developments made on the LLL algorithm can be applied to the Lambda-decorrelation algorithm. This point is illustrated in a concrete manner: we present a parallel $\Lambda $ -type decorrelation algorithm derived from the parallel LLL algorithm of Luo and Qiao (Proceedings of the fourth international C $^*$ conference on computer science and software engineering. ACM Int Conf P Series. ACM Press, pp 93–101, 2012).     

An Improved Band Selection Technique for Hyperspectral Data Using Factor Analysis

This paper discusses a statistical and band transformation based approach to select bands for hyperspectral image analysis. Hyperspectral images contain large number of spectral bands with redundant information about the spectral classes in the image scene. It is necessary to reduce the high dimensionality of the data for the processing of hyperspectral data. We report a feature selection technique that removes correlated spectral bands using band decorrelation technique and obtains maximum variance image bands based on factor analysis. Factor analysis method of band selection technique is also validated against existing methods of band selection. The study is carried out for the agriculturally rich area of Musiri region of South India that has varied landcover types. Evaluation of the band selection procedure is done using signature separability measures such as Euclidean distance, Divergence, Transformed divergence and Jeffries Matusita distance. Results indicated that selected bands exhibited maximum separability and also occurred predominantly at wavelength 700 nm, 850, 1000 nm, 1200 nm, 1648 nm and 2200 nm.     

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.     

Understanding the Spatial Variability of Chlorophyll a and Total Suspended Matter Distribution Along the Southwest Bay of Bengal Using In-Situ and OCM-2 & MODIS-Aqua Measurements

Spatial and temporal distribution of chlorophyll a (chl a) and Total Suspended Matter (TSM) and inter comparison of Ocean Color Monitor-2 (OCM-2) and Moderate Resolution Imaging Spectro-radiometer (MODIS-Aqua) derived chlorophyll a and TSM was made along the southwest Bay of Bengal (BoB). The in-situ chl a and TSM concentration measured during different seasons were ranged from 0.09 to 10.63 μgl^?1 and 11.04–43.75 mgl^?1 respectively. OCM-2 and MODIS derived chl a showed the maximum (6–8 μgl^?1) at nearshore waters and the minimum (0–1 μgl^?1) along the offshore waters. OCM-2 derived TSM imageries showed the maximum (50–60 mgl^?1) along the nearshore waters of Palk Strait and the moderate concentration (2–5 mgl^?1) was observed in the offshore waters. MODIS derived minimum TSM concentration (13.244 mgl^?1) was recorded along the offshore waters, while the maximum concentration of 15.78 mgl^?1 was found along the Kodiakarai region. The inter-comparison of OCM-2 and MODIS chl a data (R ² ?=?0.549, n?=?49, p?<?0.001, SEE?=?±0.117) indicate that MODIS data overestimates chl a concentration in the nearshore waters of the southern BoB compared to the OCM-2. The correlation between OCM-2 and MODIS-Aqua TSM data (R ² ?=?0.508, N?=?53, P?<?0.001 and SEE?=?±0.024) confirms that variation in the range of values measured by OCM-2 (2–60 mgl^?1) and the MODIS (13–16 mgl^?1) derived TSM values. Despite problems in range of measurements, persistent cloud cover etc., the launch of satellites like OCM-2 with relatively high spatial resolutions makes job easier and possible to monitor chl a distribution and sediment discharges on day to day basis in the southwest BoB.     

Negotiating on location, timing, duration, and participant in agent-mediated joint activity-travel scheduling

Agent-based simulation has become an important modeling approach in activity-travel analysis. Social activities account for a large amount of travel and have an important effect on activity-travel scheduling. Participants in joint activities usually have various options regarding location, participants, and timing and take different approaches to make their decisions. In this context, joint activity participation requires negotiation among agents involved, so that conflicts among the agents can be addressed. Existing mechanisms do not fully provide a solution when utility functions of agents are nonlinear and non-monotonic. Considering activity-travel scheduling in time and space as an application, we propose a novel negotiation approach, which takes into account these properties, such as continuous and discrete issues, and nonlinear and non-monotonic utility functions, by defining a concession strategy and a search mechanism. The results of experiments show that agents having these properties can negotiate efficiently. Furthermore, the negotiation procedure affects individuals’ choices of location, timing, duration, and participants.     

Estimation and testing of higher-order spatial autoregressive panel data error component models

This paper develops an estimator for higher-order spatial autoregressive panel data error component models with spatial autoregressive disturbances, SARAR(R,S). We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define a generalized two-stage least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators, derive their joint asymptotic distribution, and provide Monte Carlo evidence on their small sample performance.     

GIS Course Planning: A Comparison of Syllabi at US College and Universities

Despite the enormous growth of college courses dealing with spatial information, curriculum planning involving geographic information science (GIS) courses and programs has received little attention within the GIS literature. As the number and variety of GIS courses expands, so too does the importance of both systematic and inclusive planning and campus‐wide coordination. In this article we explore course planning through an exploration of 312 GIS course syllabi used at US colleges and universities with the goal of characterizing the degree to which learning resources, student evaluation methods, and course topics have become standardized across institution types, academic levels, and disciplines. Our findings reveal a consensus in the use of GIS software across courses but no similar agreement in the use of textbooks. Hands‐on activities were used as evaluation methods in nearly every course in the sample regardless of institution type or academic level. However, quizzes, tests and final exams were used more often in community colleges while papers and projects were used more frequently in four‐year and comprehensive research universities. The frequency of topic categories listed on syllabi was relatively consistent across institutions, academic levels and disciplines with a few topics such as vector analytic operations, data models, and data creation/acquisition/editing included on more than 50% of syllabi.