Spatial Modeling and Analysis for Shoreline Change Detection and Coastal Erosion Monitoring

Coastal erosion presents a serious problem throughout U.S. coastal areas. The Ohio Geological Survey estimates that more than 3,200 acres of Ohio's Lake Erie shore have been lost to erosion since the 1870s, resulting in economic losses exceeding tens of millions of dollars per year. This article presents research results of a project that monitors shoreline erosion using high-resolution imagery and examines erosion causes. Spatial modeling and analysis methods are applied to the project area along the south shore of Lake Erie. The shoreline is represented as a dynamically-segmented linear model that is linked to a large amount of data describing shoreline changes. A new method computes an instantaneous shoreline using a digital water level model, a coastal terrain model, and bathymetric data. This method provides an algorithm for deriving the Mean-Lower Low Water (MLLW) and the Mean High Water (MHW) shorelines that are essential to navigation charts. The results describe a part of our effort towards a coastal spatial information infrastructure to support management and decision-making in the dynamic coastal environment.     

On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms

The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E _Y = (X−E _X ) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E _Y and E _X . Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition. For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion matrix of the estimated parameters.     

Compression of intensity interferometry signals

Correlations between photon currents from separate light-collectors provide information on the shape of the source. When the light-collectors are well separated, for example in space, transmission of these currents to a central correlator is limited by band-width. We study the possibility of compression of the photon fluxes and find that traditional compression methods have a similar chance of achieving this goal compared to compressed sensing.     

Calibration of oxygen isotope fractionation and calcite-corundum thermometry in emery at Naxos,Greece

Corundum (Crn), including sapphire, occurs in emery pods surrounded by marble on the island of Naxos, Greece. The emery formed from bauxite deposited in karst that was metamorphosed to 400–700°C at 20–15 Ma. Many of these rocks initially appeared well suited for refractory accessory mineral (RAM) thermometry, which uses oxygen isotope fractionation between a RAM – corundum – and a modally dominant phase with faster diffusion of oxygen – calcite (Cc) – to determine peak metamorphic temperatures. However, previous attempts at oxygen isotope thermometry were confounded by highly variable fractionations (Δ¹⁸O) measured at mm-scale and the uncertain calibration of Δ¹⁸O(Cc-Crn) versus temperature. Secondary ion mass spectrometry (SIMS) permits in situ analysis of δ¹⁸O in corundum and calcite at the 10-μm scale in adjacent grains where textures suggest peak metamorphic equilibrium was attained. SIMS analyses of adjacent mineral pairs in eight rocks yield values of Δ(Cc-Crn) that systematically decrease from 7.2 to 2.9‰ at higher metamorphic grade. Pairing these data with independent temperature estimates from mineral isograds yields an empirical calibration of 1,000 lnα(Cc-Crn) = 2.72 ± 0.3 × 10⁶/T² (T in K). The new fractionations (2.7‰ at 1,000 K) are significantly smaller than those calculated from the modified increment method (6.5‰ at 1,000 K; Zheng, Geochimica et Cosmochimica Acta, 1991, 55:2299–2307; Zheng, Mineral Mag, 1994, 58A:1000–1001), which yield unreasonably high temperatures of 630 to 1,140°C when applied to the new Naxos data. The new calibration of Δ(Cc-Crn) can be combined with published fractionations to calculate A-factors for corundum versus a range of 14 other minerals. These new fractionation factors can be used for thermometry or to constrain the genesis of corundum. A compilation of gem corundum δ¹⁸O values shows that many igneous sapphires, including important deposits of basalt-associated sapphire, are mildly elevated in δ¹⁸O relative to the calculated range in equilibrium with mantle values (4.4–5.7‰) and formed from evolved magmas.     

Estimation of surface roughness (z0) over a stabilizing coastal dune field based on vegetation and topography

Accurate knowledge of the surface roughness and the resultant wind speed are important for many applications, such as climatic models, wind power meteorology, agriculture and erosion hazards, especially on sand dunes in arid and semi‐arid environments, where vegetation cover is scarce. In this study we aimed at quantifying the effects of vegetation cover and topography on surface roughness over a stabilizing dune field on the southern coast of Israel. Forty‐six wind measurements were made at various distances from the coastline, ranging from 10 to 2800 m, and z₀ values were calculated from the wind measurements based on the ratio between the wind gust and the average wind speed. We estimated vegetation cover using the soil adjusted vegetation index (SAVI) from Landsat satellite images for the upwind sector at various lengths, ranging from 15 to 400 m, and based on digital elevation models and differential GPS field measurements we calculated the topographic variable of the relative heights of the stations. z₀ values were positively correlated with the winter SAVI values (r = 0·87 at an upwind length of 200 m) and negatively correlated with the relative height (r = ?0·68 at an upwind length of 200–400 m for the inland dune stations). Using these variables we were able to create a map of estimated z₀ values having an accuracy of over 64%. Such maps provide a better understanding of the spatial variability in both wind speed and sand movement over coastal dune areas. Copyright © 2007 John Wiley & Sons, Ltd.     

Tracking fluid flow during deep crustal anatexis: metasomatism of peridotites (Naxos, Greece)

Horizons of ultramafic lenses were metamorphosed with host felsic gneisses at upper amphibolite facies conditions during the M2 event on the island of Naxos, Greece. The synkinematic peak M2 Ol-Opx-Hbl-Chl-Spl assemblage of the Main, migmatite-associated, Ultramafic Horizon (MUH) retains mantle-like chemical and oxygen isotope compositions and thus shows no evidence of infiltration of fluids from the host rocks. A bimodal distribution of temperatures, grouped at 700 and 1,200 °C, is given by oxygen isotope Opx-Ol thermometry in the MUH meta-peridotites and indicates partial oxygen exchange during M2 superposed over previous mantle fractionation. The Agia Ultramafic Horizon (AUH), a coarser-grained and unfoliated peridotite, occurs within sillimanite gneisses in northwest Naxos and contains talc-enstatite and olivine domains. Recrystallization of the AUH peridotite during post-peak M2 infiltration of silica-rich, high '¹⁸O fluids is indicated by lack of deformation, increased activity of silica required to stabilize the talc-enstatite assemblage, extremely high '¹⁸O values of Ol and Opx and (¹⁸O_(Opx-Ol) temperatures of 520-650 °C. The source for these fluids is inferred to be aplitic and pegmatitic dikes emanating from the migmatitic core of Naxos and intruding the AUH. At peak M2 temperatures and during anatexis of gneisses, volumes of fluid were small and fluid composition was locally buffered in the deeper part of the Naxos section. Crystallization of melts within the migmatitic core released siliceous fluids and initiated an episode of retrograde hydrous metamorphism in the overlying sequences, as observed in the AUH.     

Early Carboniferous anorogenic magmatism in the Levant: implications for rifting in northern Gondwana

The Variscan orogenesis in Europe peaked during the Late Devonian–Early Carboniferous times when Gondwanan terranes collided with Laurasia. Hitherto it has been thought that Carboniferous tectonics in northern Arabia and the adjacent parts of NE Africa were broad swells (‘arches’) and depressions (‘basins’) that formed as a far-field contractional effect of the Variscan compression. The discovery of a 351 ± 3 Ma (U–Pb in zircon) within-plate felsic volcanism in the Helez borehole, southern coastal Israel, suggests that the Levant Arch is, instead, extensional in origin. Felsic volcanism was associated with gabbro underplating of the crust, an extreme (~50°C/km) crustal thermal gradient, major uplift, and truncation of the ≥2.5 km section. Taken together with the recent discovery of the ~340 Ma oceanic crust in the Eastern Mediterranean, the Levant Arch is interpreted as an uplifted shoulder of a rift, preceding ocean spreading.