Reference frame stability and nonlinear distortion in minimum-constrained network adjustment

The aim of this paper is to investigate the influence of the minimum constraints (MCs) on the reference frame parameters in a free-net solution. The non-estimable part of these parameters (which is not reduced by the available data) is analysed in terms of its stability under a numerical perturbation of the constrained datum functionals. In practice, such a perturbation can be ascribed either to hidden errors in the known coordinates/velocities that participate in the MCs or to a simple change of their a priori values due to a datum switch on a different fiducial dataset. In addition, a perturbation of this type may cause a nonlinear variation to the estimable part of the reference frame parameters, since it theoretically affects the adjusted observations that are implied by the network’s nonlinear observational model. The aforementioned effects have an impact on the quality of a terrestrial reference frame (TRF) that is established via a minimum-constrained adjustment, and our study shows that they are both controlled through a characteristic matrix which is inherently linked to the MC system (the so-called TRF stability matrix). The structure of this matrix depends on the network’s spatial configuration and the ‘geometry’ of the datum constraints, while its main role is the filtering of any MC-related errors into the least-squares adjustment results. A number of examples with different types of geodetic networks are also presented to demonstrate the theoretical findings of our study.     

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.     

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.     

Crop Residue Discrimination Using Ground-Based Hyperspectral Data

Crop residue has become an increasingly important factor in agriculture management. It assists in the reduction of soil erosion and is an important source of soil organic carbon (soil carbon sequestration). In recent past, remote sensing, especially narrowband, data have been explored for crop residue assessment. In this context, a study was carried out to identify different narrow-bands and evaluate the performance of SWIR region based spectral indices for crop residue discrimination. Ground based hyperspectral data collected for wheat crop residue was analyzed using Stepwise Discriminant Analysis (SDA) technique to select significant bands for discrimination. Out of the seven best bands selected to discriminate between matured crop, straw heap, combine-harvested field with stubbles and soil, four bands were from SWIR (1980, 2030, 2200, 2440 nm) region. Six spectral indices were computed, namely CAI, LCA, SINDRI, NDSVI, NDI5 and hSINDRI for crop residue discrimination. LCA and CAI showed to be best (F?>?115) in discriminating above classes, while LCA and SINDRI were best (F?>?100) among all indices in discriminating crop residue under different harvesting methods. Comparison of different spectral resolution (from 1 nm to 150 nm) showed that for crop residue discrimination a resolution of 100 nm at 2100–2300 m region would be sufficient to discriminate crop residue from other co-existing classes.     

Evaluating the effect of the global ionospheric map on aiding retrieval of radio occultation electron density profiles

Radio occultation (RO) has been proven to be a powerful technique for ionospheric electron density profile (EDP) retrieval. The Abel inversion currently used in RO EDP retrieval has degraded performance in regions with large horizontal gradients because of an assumption of spherical symmetry as indicated by many studies. Some alternative methods have been proposed in the past; the global ionospheric map (GIM)-aided Abel inversion is most frequently studied. Since the number of RO observations will likely increase rapidly in the near future, it is worthwhile to continue to improve retrieval method. In this study, both the simulations and the real data test have been done to evaluate the GIM-aided Abel inversion method. It is found that the GIM-aided Abel inversion can significantly improve upon the standard Abel inversion in either the F or the E region if an accurate GIM is available. However, the current IGS GIM does not appear accurate enough to improve retrieval results significantly, because of the spherical symmetry assumption and sparse global navigation satellite system (GNSS) stations used in its creation. Generating accurate GIM based on dense GNSS network to aid the Abel inversion might be an alternative method.     

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.     

Utilizing the Potential of World View −2 for Discriminating Urban and Vegetation Features Using Object Based Classification Techniques

With the availability of very high resolution multispectral imagery, it is possible to identify small features in urban environment. Because of the multiscale feature and diverse composition of land cover types found within the urban environment, the production of accurate urban land cover maps from high resolution satellite imagery is a difficult task. This paper demonstrates the potential of 8 bands capability of World View 2 satellite for better automated feature extraction and discrimination studies. Multiresolution segmentation and object based classification techniques were then applied for discrimination of urban and vegetation features in a part of Dehradun, Uttarakhand, India. The study demonstrates that scale, colour, shape, compactness and smoothness have a significant influence on the quality of image objects achieved, which in turn governs the classified result. The object oriented analysis is a valid approach for analyzing high spatial and spectral resolution images. World View 2 imagery with its rich spatial and spectral information content has very high potential for discrimination of the less varied varieties of vegetation.