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.     

Stationary spatially modulated fourier transform spectro-radiometer

Journal of the Indian Society of Remote Sensing - A stationary, compact, spatially modulated Fourier Transform spectro-radiometer based on triangular, common path Sagnac interferometer has been...     

Land damage assessment - a case study

The paper discusses the land damage assessment and change detection analysis with reference to a mineral bearing zone in Manjhi, Manuni and Churan valleys. The area is located in environmentally sensitive and fragile region of Himalaya and constitutes of nearly 400 small-scale mines of slate, which were operative since last one hundred years and are stopped by court of law since 1995 on account of environment deterioration. The status of land degradation has been studied using IRS-1B satellite data of 1988,1992 and 1995. The geo-coded data on 1:50,000 scale has been interpreted and an increase in land degradation status was noticed. Finally, the management strategy for arresting the further land damage in a broader perspective is suggested.     

Estimation of recent glacial variations in baspa basin using remote sensing technique

The Himalayas has one of the largest concentrations of glaciers outside the Polar Regions. Various reports suggest that significant number of mountain glaciers is shrinking due to climatic variations. Monitoring of these glaciers is important to assess future availability of water resources in the Himalayan region. However, Himalayan glaciers are normally difficult to monitor due to the rugged, mountainous terrain. Therefore, images of Indian Remote Sensing Satellite were used to monitor glaciers in the Baspa basin. Investigations have shown the presence of 30 glaciers in the basin, with areal extent of 167 km2. Out of these, 19 glaciers, with areal extent of 140 km² were selected to estimate retreat. Investigation suggests that almost all glaciers are retreating in the study basin and overall 19% deglaciation has been observed from 1962 to 2001. In general, altitude distribution appears to have significant influence on glacial retreat. Glaciers located around 5000 m altitude range are showing 24% loss as compared to 14% by glaciers located in altitude range higher than 5400 m. In addition, mean altitude of glacier terminus is shifted upward by 88 m, i.e. from 4482 to 4570 m in last 39 years. The glacial volumes were estimated using regression relationship between area and depth. The investigations have suggested that 19.10 km³ of glacial water stored in the 19 glaciers in 1962, has been reduced to 14.71 km³ in 2001, respectively, an overall loss of 23 percent in a period between 1962 and 2001. These investigations suggest that all glaciers in the Baspa Basin are reducing and in long term, such reducing trend can create scarcity of water in the region.     

The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce “spurious correlation” that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.     

Artificial Neural Network (ANN) Based Inversion of Benthic Substrate Bottom Type and Bathymetry in Optically Shallow Waters - Initial Model Results

Ocean-colour remote sensing in optically shallow waters is influenced by contribution from the water column depth as well as by the substrate type. Therefore, it is required to include the contribution from the water column and substrate bottom type for bathymetry estimation. In this report we demonstrate the use of Artificial Neural Network (ANN) based approach to spectrally distinguish various benthic bottom types and estimate depth of substrate bottom simultaneously in optically shallow waters. We have used in-water radiative transfer simulation modeling to generate simulated top-of-the-water column reflectance the four major benthic bottom types viz. sea grass, coral sand, green algae and red algae using Hydrolight simulation model. The simulated remote sensing reflectance, for the four benthic bottom types having benthic bottom depth up to 30 m were generated for moderately clear waters. A multi-layer perceptron (MLP) type neural network was trained using the simulated data. ANN based approach was used for classification of the benthic bottom type and simultaneous inversion of bathymetry. Simulated data was inverted to yield benthic bottom type classification with an accuracy of ~98% for the four benthic substrate types and the substrate depth were estimated with an error of 0% for sea grass, 1% for coral sand and 1–3% for green and red algae up to 25 m, whereas for substrate bottom deeper than 25 m depth the classification errors increased by 2–5% for three substrate bottom types except sea grass bottom type. The initial results are promising which needs validation using the in-situ measured remote sensing reflectance spectra for implementing further on satellite data.     

Spectral and Spatial Quality Analysis in Pan Sharpening Process

Image fusion is a process to obtain new images containing more information by combining images obtained same or different sensors. With most of the earth observation satellites, high spatial resolution panchromatic images and low spatial resolution multispectral images are obtained. As an example of image fusion ??pan sharpening?? is a process of combining of high spatial resolution panchromatic images and low spatial resolution multispectral images. At the end of the fusion process both high spatial and spectral resolution new images are obtained. In this study, panchromatic and multispectral images gathered from Ikonos were used. Panchromatic and multispectral images belonging to the same sensor were combined by using different image fusion methods. As pan sharpening methods Brovey transform, Modified IHS, Principal Component Analysis (PCA), Wavelet PC transform and Wavelet A Trous transformation methods were used. Quality of fused products was evaluated from the point of view of both visual and statistical criteria. While wavelet based methods are succesfull in terms of protection of spectral quality of original multispectral images, the colorbased and statistical methods are giving better results within the improvement of spatial content.     

Recent advances in accessibility research: Representation,methodology and applications

 In this article we examine recent advances in accessibility research and their implications for future studies. We base our discussion on three intersecting dimensions that are useful for evaluating the contribution of recent studies: representation, methodology and applications. Various examples are selected to show that research concerned with representation and methodological problem solving is often applied to issues of broad concern in policy and planning. It is, however, not clear that the simultaneous treatment of representation, methodological and application issues has ever been fully worked out. The questions raised in this article may serve as a foundation for addressing issues pertinent to accurate representation, improved model building, and more rigorous applications in accessibility research. Received: 9 December 2002 / Accepted: 10 February 2003     

Groebner-basis solution of the three-dimensional resection problem (P4P)

The three-dimensional (3-D) resection problem is usually solved by first obtaining the distances connecting the unknown point P{X,Y,Z} to the known points P_i{X_i,Y_i,Z_i}i=1,2,3 through the solution of the three nonlinear Grunert equations and then using the obtained distances to determine the position {X,Y,Z} and the 3-D orientation parameters {,, }. Starting from the work of the German J. A. Grunert (1841), the Grunert equations have been solved in several substitutional steps and the desire as evidenced by several publications has been to reduce these number of steps. Similarly, the 3-D ranging step for position determination which follows the distance determination step involves the solution of three nonlinear ranging (`Bogenschnitt') equations solved in several substitution steps. It is illustrated how the algebraic technique of Groebner basis solves explicitly the nonlinear Grunert distance equations and the nonlinear 3-D ranging (`Bogenschnitt') equations in a single step once the equations have been converted into algebraic (polynomial) form. In particular, the algebraic tool of the Groebner basis provides symbolic solutions to the problem of 3-D resection. The various forward and backward substitution steps inherent in the classical closed-form solutions of the problem are avoided. Similar to the Gauss elimination technique in linear systems of equations, the Groebner basis eliminates several variables in a multivariate system of nonlinear equations in such a manner that the end product normally consists of a univariate polynomial whose roots can be determined by existing programs e.g. by using the roots command in Matlab.Acknowledgments.The first author wishes to acknowledge the support of JSPS (Japan Society of Promotion of Science) for the financial support that enabled the completion of the write-up of the paper at Kyoto University, Japan. The author is further grateful for the warm welcome and the good working atmosphere provided by his hosts Professors S. Takemoto and Y. Fukuda of the Department of Geophysics, Graduate School of Science, Kyoto University, Japan.