Graph theory for analyzing pair-wise data: application to geophysical model parameters estimated from interferometric synthetic aperture radar data at Okmok volcano,Alaska

Graph theory is useful for analyzing time-dependent model parameters estimated from interferometric synthetic aperture radar (InSAR) data in the temporal domain. Plotting acquisition dates (epochs) as vertices and pair-wise interferometric combinations as edges defines an incidence graph. The edge-vertex incidence matrix and the normalized edge Laplacian matrix are factors in the covariance matrix for the pair-wise data. Using empirical measures of residual scatter in the pair-wise observations, we estimate the relative variance at each epoch by inverting the covariance of the pair-wise data. We evaluate the rank deficiency of the corresponding least-squares problem via the edge-vertex incidence matrix. We implement our method in a MATLAB software package called GraphTreeTA available on GitHub (https://github.com/feigl/gipht). We apply temporal adjustment to the data set described in Lu et al. (Geophys Res Solid Earth 110, 2005) at Okmok volcano, Alaska, which erupted most recently in 1997 and 2008. The data set contains 44 differential volumetric changes and uncertainties estimated from interferograms between 1997 and 2004. Estimates show that approximately half of the magma volume lost during the 1997 eruption was recovered by the summer of 2003. Between June 2002 and September 2003, the estimated rate of volumetric increase is \((6.2 \, \pm \, 0.6) \times 10^6~\mathrm{m}^3/\mathrm{year} \). Our preferred model provides a reasonable fit that is compatible with viscoelastic relaxation in the five years following the 1997 eruption. Although we demonstrate the approach using volumetric rates of change, our formulation in terms of incidence graphs applies to any quantity derived from pair-wise differences, such as range change, range gradient, or atmospheric delay.     

On the consistency of the current conventional EOP series and the celestial and terrestrial reference frames

Precise transformation between the celestial reference frames (CRF) and terrestrial reference frames (TRF) is needed for many purposes in Earth and space sciences. According to the Global Geodetic Observing System (GGOS) recommendations, the accuracy of positions and stability of reference frames should reach 1 mm and 0.1 mm year\(^{-1}\), and thus, the Earth Orientation Parameters (EOP) should be estimated with similar accuracy. Different realizations of TRFs, based on the combination of solutions from four different space geodetic techniques, and CRFs, based on a single technique only (VLBI, Very Long Baseline Interferometry), might cause a slow degradation of the consistency among EOP, CRFs, and TRFs (e.g., because of differences in geometry, orientation and scale) and a misalignment of the current conventional EOP series, IERS 08 C04. We empirically assess the consistency among the conventional reference frames and EOP by analyzing the record of VLBI sessions since 1990 with varied settings to reflect the impact of changing frames or other processing strategies on the EOP estimates. Our tests show that the EOP estimates are insensitive to CRF changes, but sensitive to TRF variations and unmodeled geophysical signals at the GGOS level. The differences between the conventional IERS 08 C04 and other EOP series computed with distinct TRF settings exhibit biases and even non-negligible trends in the cases where no differential rotations should appear, e.g., a drift of about 20 \(\upmu \)as year\(^{-1 }\)in \(y_{\mathrm{pol }}\) when the VLBI-only frame VTRF2008 is used. Likewise, different strategies on station position modeling originate scatters larger than 150 \(\upmu \)as in the terrestrial pole coordinates.     

Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach

Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63–84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10–30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be connected to and employed in the first computational steps of the space-wise approach, where a time-wise Wiener filter is applied at the first stage of GOCE gravity gradient filtering. The results of this work can be extended to using other adaptive filtering algorithms, such as the recursive least-squares and recursive least-squares lattice filters.     

Enriching the semantics of the directed polyline–polygon topological relationships: the $$\mathcal {}$$-intersection matrix

In this paper, we define an intersection matrix for enriching the semantics of the topological relationships between a directed polyline and a polygon. In particular, we propose the \(\mathcal {DLP}\)-intersection matrix which enables us to model the origin and destination points, as well as the right- and left-hand sides of the directed polyline. This matrix overcomes the limitation of the well-known DE-9IM, because it allows the representation of the different dimensions of the intersection results at the same time. Accordingly, the geo-operators have been revised and extended in order to address the notions of right- and left-hand sides of a directed polyline, as well as additional notions related to the orientation of the polyline. The \(\mathcal {DLP}\)-intersection matrix has been implemented by extending the Java Topology Suite methods in order to address the new geo-operators based on the notion of orientation.     

Change detection of linear features in temporally spaced remotely sensed images using edge-based grid analysis

Automatic change detection of land cover features using high-resolution satellite images, is a challenging problem in the field of intelligent remote sensing data interpretation, and is becoming more and more effective for its applications viz. urban planning and monitoring, disaster assessment etc. In the present study, a change in detection approach based on the image morphology that analyses change in the local image grids is proposed. In this approach, edges from both the images are extracted and grid wise comparison is made by probabilistic thresholding and power spectral density analysis for identifying change area. One of the advantages of the proposed methodology is that the temporal images used in the change analysis need not be radiometrically corrected as analysis is based on edge extractions. The grid-based analysis further reduces the error, which might have been introduced by image mis-registration. The proposed methodology is validated by finding the temporal changes in the linear land cover features in parts of Kolkata city, India using three different image data-sets from LISS IV, Cartosat-1 and Google earth having varied spatial resolutions of 5.8 m, 2.5 m and about 1 m, respectively. The overall accuracy in identifying changes is found to be 64.82, 73.86 and 80.93% for LISS IV, Cartosat-1 and Google earth data-set, respectively.     

A comparative analysis of pansharpening techniques on QuickBird and WorldView-3 images

Nowadays, different image pansharpening methods are available, which combine the strengths of different satellite images that have different spectral and spatial resolutions. These different image fusion methods, however, add spectral and spatial distortions to the resultant images depending on the required context. Therefore, a careful selection of the fusion method is required. Simultaneously, it is also essential that the fusion technique should be efficient to cope with the large data. In this paper, we investigated how different pansharpening algorithms perform, when applied to very high-resolution WorldView-3 and QuickBird satellite images effectively and efficiently. We compared these 27 pansharpening techniques in terms of quantitative analysis, visual inspection and computational complexity, which has not previously been formally tested. In addition, 12 different image quality metrics available in literature are used for quantitative analysis purpose.     

Analysis of urban built-up areas and surface urban heat island using downscaled MODIS derived land surface temperature data

Regional scale urban built-up areas and surface urban heat islands (SUHI) are important for urban planning and policy formation. Owing to coarse spatial resolution (1000 m), it is difficult to use Moderate Resolution Imaging Spectroradiometer (MODIS) Land surface temperature (LST) products for mapping urban areas and visualization, and SUHI-related studies. To overcome this problem, the present study downscaled MODIS (1000 m resolution)-derived LST to 250 m resolution to map and visualize the urban areas and identify the basic components of SUHI over 12 districts of Punjab, India. The results are compared through visual interpretation and statistical procedure based on similarity analysis. The increased entropy value in the downscaled LST signifies higher information content. The temperature variation within the built-up and its environs is due to difference in land use and is depicted better in the downscaled LST. The SUHI intensity analysis of four cities (Ludhiana, Patiala, Moga and Vatinda) indicates that mean temperature in urban built-up core is higher (38.87 °C) as compared to suburban (35.85 °C) and rural (32.41 °C) areas. The downscaling techniques demonstrated in this paper enhance the usage of open-source wide swath MODIS LST for continuous monitoring of SUHI and urban area mapping, visualisation and analysis at regional scale. Such initiatives are useful for the scientific community and the decision-makers.     

Modeling the environmental susceptibility of landfill sites in California

??The proper management of solid waste (SW) is a global environmental challenge. A major issue is the proper disposal of SW while balancing a wide range of criteria and working with different spatial data. In this study, we used geographic information system as a tool to perform multi-criteria decision analysis with an analytical hierarchy process to develop an environmental impact susceptibility model (EISM) for landfills. The model was applied to the state of California, USA and results are presented herein. In particular, the EISM considers factors such as geology, pedology, geomorphology, water resources, and climate as represented by 13 associated environmental indicators. The results of the EISM indicate that more than 75% of California’s territory is situated in areas with very low, low, and medium environmental impact susceptibility categories. However, in the remaining 25% of the state’s land, 61 landfills are located in the high and very high categories. These results are alarming because during the period from 2000 to 2015, these 61 landfills received approximately 308 million tons of SW, which corresponds to more than 57% of all SW disposed in California. The model results can be used toward mitigating the environmental impacts of these facilities.     

Spheroidal equal angular DEMs: The specificity of morphometric treatment

Digital elevation models (DEMs) are commonly constructed using two main types of regular grids: plane square grids and spheroidal equal angular grids. Methods and algorithms intended for plane square‐gridded DEMs should not be directly applied to spheroidal equal angular DEMs. This is because these grids have fundamentally different geometry. However, some researchers continue to apply square‐grid algorithms to spheroidal equal angular DEMs. It seems appropriate to consider once again the specifity of morphometric treatment of spheroidal equal angular DEMs. This article, first, demonstrates possibilities of direct calculation of local, nonlocal, and combined morphometric variables from spheroidal equal angular DEMs exemplified by slope gradient, catchment area, and topographic index. Second, the article shows computational errors when algorithms for plane square‐gridded DEMs are unreasonably applied to spheroidal equal angular DEMs. The study is exemplified by two DEMs. A medium‐resolution DEM of a relatively small, high‐mountainous area (Mount Elbrus) was extracted from the SRTM1 DEM. A low‐resolution DEM of a vast region with the diverse topography (the central and western regions of Kenya) was extracted from the SRTM30_PLUS DEM. The results show that application of square‐grid methods to spheroidal equal angular DEMs leads to substantial computational errors in models of morphometric variables.