A New Combined Assessment of Mixed Uncertainty in Spatial Models: Conceptualization and Implementation

Uncertainty quantification is not often performed in spatial modeling applications, especially when there is a mixture of probabilistic and non‐probabilistic uncertainties. Furthermore, the effect of positional uncertainty is often not assessed, despite its relevance to geographical applications. Although there has been much work in investigating the aforementioned types of uncertainty in isolation, combined approaches have not been much researched. This has resulted in a lack of tools for conducting mixed uncertainty analyses that include positional uncertainty. This research addresses the issue by first presenting a new, flexible, simulation‐oriented conceptualization of positional uncertainty in geographic objects called F‐Objects. F‐Objects accommodates various representations of uncertainty, while remaining conceptually simple. Second, a new Python‐based framework is introduced, termed Wiggly and capable of conducting mixed uncertainty propagation using fuzzy Monte Carlo simulation (FMCS). FMCS combines both traditional Monte Carlo with fuzzy analysis in a so‐called hybrid approach. F‐Objects is implemented within the Wiggly framework, resulting in a tool capable of considering any combination of: (1) probabilistic variables; (2) fuzzy variables; and (3) positional uncertainty of objects (probabilistic/fuzzy). Finally, a realistic GIS‐based groundwater contamination problem demonstrates how F‐Objects and Wiggly can be used to assess the effect of positional uncertainty.     

Objects Detection in Hyperspectral Images Using Spectral Derivative

In recent years hyperspectral imaging has proved its significance in the detection and mapping of various objects of interest in a scene. Various methods for object detection in hyperspectral images have been developed with their advantages and limitations. In the present study, a methodology comprising spectral derivative (first order) and spectral information divergence has been investigated for detection of objects in hyperspectral images. The efficacy of the detection scheme has been examined over two different hyperspectral data sets of Hyperion images. Tea plants (Camellia sinensis) and Sal trees (Shorea robusta) (pure pixels) have been detected as the objects of interest in the hyperspectral images independently with reduced false pixels. The proposed methodology may in future be applied for classification of mixed pixels.     

Change of river channel and bank erosion of the burhi dihing river (assam), assessed using remote sensing data and gis

The Burhi Dining river flows in a meandering course for about 220 km through alluvial plains of Assam including a short rocky and hilly tract in between. Sequential changes in the position of banklines of the river due to consistent bank erosion have been studied from Survey of India topographic maps of 1934 and 1972, and digital satellite data of 2001 and 2004 using GIS. Two broad kinds of changes have been observed, e.g. alteration of direction of flow due to neck cut-off and progressive gradual change of the meander bends that accounts for translational, lateral, rotational, extensional and other types of movement of the meander bends. Study of bankline shift due to the bank erosion has been carried out for the periods 1934–1972, 1972–2001, 2001–2004 and 1934–2004 at 13 segments spaced at 5′ longitude interval (average 15 km) as the river course trends nearly east to west. The amounts of the bank area lost due to erosion and gained due to sediment deposition are estimated separately. The total area eroded in both banks during 1934–1972 was more (26.796 km²) as compared to sediment deposition (19.273 km²), whereas total sediment deposition was more (34.61 km²) during 1972-2001 as compared to erosion (23.152 km²). Erosion was again more in 2001–2004 (7.568 km²) as compared to sediment deposition (2.493 km²). During the entire period (1934–2004) of study the overall erosion on the both banks was 31.169 km² and overall sediment deposition was 30.101 km². The highest annual rates of bank erosion as well as bank building of the river are 21055.47 m²/km in 2001–2004 and 9665.81 m²/km in 1972-2001, respectively. Similarly the highest average annual rates of erosion as well as sediment deposition in both banks are observed during 2001–2004 and 1972–2001, respectively. The hard rocks of the hilly tract situated in between result in development of entrenched meandering and this tract has suffered minimum bank erosion.     

The ionospheric eclipse factor method (IEFM) and its application to determining the ionospheric delay for GPS

A new method for modeling the ionospheric delay using global positioning system (GPS) data is proposed, called the ionospheric eclipse factor method (IEFM). It is based on establishing a concept referred to as the ionospheric eclipse factor (IEF) λ of the ionospheric pierce point (IPP) and the IEF’s influence factor (IFF) . The IEF can be used to make a relatively precise distinction between ionospheric daytime and nighttime, whereas the IFF is advantageous for describing the IEF’s variations with day, month, season and year, associated with seasonal variations of total electron content (TEC) of the ionosphere. By combining λ and with the local time t of IPP, the IEFM has the ability to precisely distinguish between ionospheric daytime and nighttime, as well as efficiently combine them during different seasons or months over a year at the IPP. The IEFM-based ionospheric delay estimates are validated by combining an absolute positioning mode with several ionospheric delay correction models or algorithms, using GPS data at an international Global Navigation Satellite System (GNSS) service (IGS) station (WTZR). Our results indicate that the IEFM may further improve ionospheric delay modeling using GPS data.     

The GeoForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C

The recent improvements in the Gravity Recovery And Climate Experiment (GRACE) tracking data processing at GeoForschungsZentrum Potsdam (GFZ) and Groupe de Recherche de Géodésie Spatiale (GRGS) Toulouse, the availability of newer surface gravity data sets in the Arctic, Antarctica and North-America, and the availability of a new mean sea surface height model from altimetry processing at GFZ gave rise to the generation of two new global gravity field models. The first, EIGEN-GL04S1, a satellite-only model complete to degree and order 150 in terms of spherical harmonics, was derived by combination of the latest GFZ Potsdam GRACE-only (EIGEN-GRACE04S) and GRGS Toulouse GRACE/LAGEOS (EIGEN-GL04S) mean field solutions. The second, EIGEN-GL04S1 was combined with surface gravity data from altimetry over the oceans and gravimetry over the continents to derive a new high-resolution global gravity field model called EIGEN-GL04C. This model is complete to degree and order 360 and thus resolves geoid and gravity anomalies at half- wavelengths of 55 km at the equator. A degree-dependent combination method has been applied in order to preserve the high accuracy from the GRACE satellite data in the lower frequency band of the geopotential and to form a smooth transition to the high-frequency information coming from the surface data. Compared to pre-CHAMP global high-resolution models, the accuracy was improved at a spatial resolution of 200 km (half-wavelength) by one order of magnitude to 3 cm in terms of geoid heights. The accuracy of this model (i.e. the commission error) at its full spatial resolution is estimated to be 15 cm. The model shows a reduced artificial meridional striping and an increased correlation of EIGEN-GL04C-derived geostrophic meridional currents with World Ocean Atlas 2001 (WOA01) data. These improvements have led to select EIGEN-GL04C for JASON-1 satellite altimeter data reprocessing. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Efficient GOCE satellite gravity field recovery based on least-squares using QR decomposition

We develop and apply an efficient strategy for Earth gravity field recovery from satellite gravity gradiometry data. Our approach is based upon the Paige-Saunders iterative least-squares method using QR decomposition (LSQR). We modify the original algorithm for space-geodetic applications: firstly, we investigate how convergence can be accelerated by means of both subspace and block-diagonal preconditioning. The efficiency of the latter dominates if the design matrix exhibits block-dominant structure. Secondly, we address Tikhonov-Phillips regularization in general. Thirdly, we demonstrate an effective implementation of the algorithm in a high-performance computing environment. In this context, an important issue is to avoid the twofold computation of the design matrix in each iteration. The computational platform is a 64-processor shared-memory supercomputer. The runtime results prove the successful parallelization of the LSQR solver. The numerical examples are chosen in view of the forthcoming satellite mission GOCE (Gravity field and steady-state Ocean Circulation Explorer). The closed-loop scenario covers 1 month of simulated data with 5 s sampling. We focus exclusively on the analysis of radial components of satellite accelerations and gravity gradients. Our extensions to the basic algorithm enable the method to be competitive with well-established inversion strategies in satellite geodesy, such as conjugate gradient methods or the brute-force approach. In its current development stage, the LSQR method appears ready to deal with real-data applications.     

Ocean tide loading (OTL) displacements from global and local grids: comparisons to GPS estimates over the shelf of Brittany, France

In this paper we examine OTL displacements detected by GPS stations of a dedicated campaign and validate ocean tide models. Our area of study is the continental shelf of Brittany and Cotentin in France. Brittany is one of the few places in the world where tides provoke loading displacements of ∼10–12 cm vertically and a few cm horizontally. Ocean tide models suffer from important discrepancies in this region. Seven global and regional ocean tide models were tested: FES2004 corrected for K2, TPXO.7.0, TPXO.6.2, GOT00.2, CSR4.0, NAO.99b and the most recent regional grids of the North East Atlantic (NEA2004). These gridded amplitudes and phases of ocean tides were convolved in order to get the predicted OTL displacements using two different algorithms. Data over a period of 3.5 months of 8 GPS campaign stations located on the north coast of Brittany are used, in order to evaluate the geographical distribution of the OTL effect. We have modified and implemented new algorithms in our GPS software, GINS 7.1. GPS OTL constituents are estimated based on 1-day batch solutions. We compare the observed GPS OTL constituents of M₂, S₂, N₂ and K₁ waves with the selected ocean tide models on global and regional grids. Large phase-lag and amplitude discrepancies over 20° and 1.5 cm in the vertical direction in the semi-diurnal band of M₂ between predictions and GPS/models are detected in the Bay of Mont St-Michel. From a least squares spectral analysis of the GPS time-series, significant harmonic peaks in the integer multiples of the orbital periods of the GPS satellites are observed, indicating the existence of multipath effects in the GPS OTL constituents. The GPS OTL observations agree best with FES2004, NEA2004, GOT00.2 and CSR4.0 tide models.     

Using a Grid-Based Filter to Solve InSAR Phase Unwrapping

This letter presents a phase-unwrapping (PU) algorithm for synthetic aperture radar interferometry based on a grid-based filter. The proposed PU algorithm, which is based on state-space techniques, simultaneously performs noise filtering and PU. The formulation of this technique provides independence from noise statistics and is not constrained by the nonlinearity of the problem. Results obtained with synthetic data show a significant improvement with respect to other conventional PU algorithms in some situations.     

Accuracy assessment of lidar-derived digital elevation models

Despite the relatively high cost of airborne lidar-derived digital elevation models (DEMs), such products are usually presented without a satisfactory associated estimate of accuracy. For the most part, DEM accuracy estimates are typically provided by comparing lidar heights against a finite sample of check point coordinates from an independent source of higher accuracy, supposing a normal distribution of the derived height differences or errors. This paper proposes a new methodology to assess the vertical accuracy of lidar DEMs using confidence intervals constructed from a finite sample of errors computed at check points. A non-parametric approach has been tested where no particular error distribution is assumed, making the proposed methodology especially applicable to non-normal error distributions of the type usually found in DEMs derived from lidar. The performance of the proposed model was experimentally validated using Monte Carlo simulation on 18 vertical error data-sets. Fifteen of these data-sets were computed from original lidar data provided by the International Society for Photogrammetry and Remote Sensing Working Group III/3, using their respective filtered reference data as ground truth. The three remaining data-sets were provided by the Natural Environment Research Council's Airborne Research and Survey Facility lidar system, together with check points acquired using high precision kinematic GPS. The results proved promising, the proposed models reproducing the statistical behaviour of vertical errors of lidar using a favourable number of check points, even in the cases of data-sets with non-normally distributed residuals. This research can therefore be considered as a potentially important step towards improving the quality control of lidar-derived DEMs.