The Hilbert Transform on the Two-Sphere: A Spectral Characterization

The local analysis of signals arising on the sphere is a common task in earth sciences. On the real line the analytic signal turned out to be an important representation in local one-dimensional signal processing. Its generalization to two dimensions is the monogenic signal, and the properties of the analytic and the monogenic signal in the Fourier domain are well known. A generalization to the sphere is given by the Hilbert transform on the sphere known from Clifford analysis. To obtain a spectral characterization, the transform has to be decomposed into spherical harmonic functions. In this paper, we derive the spherical harmonic coefficients of the Hilbert transform on the sphere and give a series expansion. This will show that it acts as a differential operator on the spherical harmonic basis functions of the Laplace equation solution, analogously to the Riesz transform in two dimensions. This allows an interpretation of the Hilbert transform suitable for signal processing of signals naturally arising on the two-sphere. We show that the scale space naturally arising is a Poisson scale space in the unit ball. In addition, the obtained interpretation of the Hilbert transform is used for orientation analysis of plane waves. This representation is justified as a novel signal model on the sphere which can be used to construct intensity and rotation-invariant operators for local signal analysis in a scale-space concept.     

“Wet” low angle subduction: a possible mechanism below the Tanzania craton 2 Ga ago

The hypothesis that much of the lithosphere of the Archaean Tanzania Craton was hydrated, by the dehydration of a buoyant subduction 2 Ga ago is presented in this study. Buoyant subduction is a potential mechanism for thermal erosion and metasomatism of extensive regions of the cold overlying continental lithosphere. This hypothesis could explain why the Tanzania Craton forms an undeformed island within the intensely deformed mobile belts. Furthermore, it would explain the formation of the eclogite and lherzolite bearing kimberlites within the Tanzania Craton far away from the trench. A buoyant, slow subduction is required because this would provide sufficient cooling from the overlying cratonic lithosphere and therefore the dipping slab could retain hydrous minerals such as antigorite in hydrated aureoles in peridotites. To test this hypothesis, the release of water during prograde metamorphism of a flat-subducting plate was modeled. It is shown that water can be transported ～800 km laterally, inboard of the trench, which is close to the north-south extension of the Archaean Tanzania Craton.     

Woolly mammoth (Mammuthus primigenius Blum.) and its environment in northern Europe during the last glaciation

Woolly mammoths were large, herbivorous, cold-adapted mammals of the Late Pleistocene. The diet and habitat requirements of the species set certain constraints on the palaeoenvironments it could occupy. The relationship between the mammoth’s shifting range and changing environments can be explored using independent data on ice sheet configuration, temperature, and vegetation, provided the locality and age of the fossil remains can be validated. Here we present a comprehensive record of occurrence of the woolly mammoth in the circum-Baltic region of northern Europe during the last glaciation, based on a compilation of radiocarbon-dated remains. The record shows that the mammoth was widespread in northern and north-eastern Europe during Marine Isotope Stage 3 (MIS 3), at 50,000–30,000 calibrated years ago (50–30 ka). The presence of the species up to 65°N latitude supports the restriction of the Scandinavian Ice Sheet (SIS) during MIS 3. The widest distribution range round 30 ka was followed by a decline that led to the disappearance of mammoths from the area during the maximum extent of the SIS, from 22 to 18 ka. The woolly mammoth re-colonized the Baltic region and southern Scandinavia after the onset of the late-glacial deglaciation at 17 ka. The late-glacial record suggests a markedly fluctuating population changing its range in tune with the rapid environmental changes. The last appearance of mammoth in our study region was in Estonia during the Younger Dryas (Greenland Stadial 1; GS1) at about 12 ka. The two major periods of occurrence during MIS 3 and the late-glacial stadial suggest that mammoth had a wide tolerance of open to semi-open tundra and steppe-tundra habitats with intermediately cold climate, whereas the 22–18 ka disappearance suggests a major southward and/or eastward retreat in response to extremely cold, glacial conditions near the SIS margin. The final regional extinction correlates with the re-forestation during the rapid warming at the Younger Dryas–Holocene boundary.     

Hydrating laterally extensive regions of continental lithosphere by flat subduction: A pilot study from the North American Cordillera

It has been suggested that much of the lithopheric mantle beneath the Colorado Plateau was hydrated by the dehydration of the Farallon plate when it was undergoing low angle subduction during the Laramide orogeny. If correct, low angle subduction could be a viable mechanism for weakening laterally extensive regions of continental lithosphere, allowing such lithosphere potentially to be recycled back into the Earth's interior and into the asthenospheric mantle wedge. To test this hypothesis, we model the release of water during prograde metamorphism of a flat-subducting Farallon plate by considering a thermal model for flat subduction and tracking open-system metamorphic phase equilibria. Our model indicates that significant amounts of water can be laterally transported ∼700 km inboard of the trench, close to the width of the North American Cordillera. The amount of water released is shown here to have been large enough to influence the rheology of the overriding North American lithosphere and the potential for melting at its base. Anomalously high S-velocities in the lithospheric mantle supports our modeled calculations of laterally extensive weakening at the base of the continental lithosphere.     

The trophic importance of epiphytic algae in a freshwater macrophyte system (<Emphasis Type="Italic">Potamogeton perfoliatus</Emphasis> L.): stable isotope and fatty acid analyses

Stable isotope and fatty acid analyses were used to study carbon sources for animals in a submerged plant bed. Epiphytes growing on Potamogeton perfoliatus, sand microflora, and alder leaves were the most important carbon sources. The most abundant macrophyte, P. perfoliatus was unimportant as a food source. Modelling (IsoSource) showed that epiphytes were the most important food source for the most abundant benthic invertebrates, the isopod Asellus aquaticus (annual mean contribution 64%), the amphipod Gammarus pulex (66%), and the gastropod Potamopyrgus antipodarum (83%). The mean annual contributions of sand microflora were, respectively, 21, 19, and 9%; and of alder leaves, 15, 15, and 8% for these three species. The relative importance of carbon sources varied seasonally. The relative contribution of epiphytes was lowest for all three grazer species in July: A. aquaticus 38%, G. pulex 43%, and P. antipodarum 42%. A decline in epiphyte biomass in summer may have caused this switch to less attractive food sources. P. perfoliatus provided habitat and shelter for consumers, but food was mainly supplied indirectly by providing space for attached epiphytes, which are fast-growing and provide a highly nutritious food source.     

Nutrient limitation of phytoplankton growth in the freshwater tidal zone of a turbid,Mediterranean estuary

Identification of the limiting nutrient(s) is a requirement for the rational management of eutrophication. Here, we present the first experimental analysis of nutrient limitation of phytoplankton growth and its seasonal variation in the Guadiana estuary (SE Portugal-SW Spain). Ten microcosm experiments were performed during 2005 and 2008, using water samples collected in the freshwater tidal zone of the Guadiana estuary. Nitrate, phosphate and silicate were added in a single pulse, alone and in combinations. Experimental treatments were incubated for 4 days under controlled laboratory conditions. Phytoplankton response to nutrient enrichment was evaluated through changes in biomass (Chla), and abundance of specific phytoplankton groups.     

Modeling the Effects of Future Outflow on the Abiotic Habitat of an Imperiled Estuarine Fish

Future development and climate change pose potentially serious threats to estuarine fish populations around the world. We examined how habitat suitability for delta smelt (Hypomesus transpacificus), a state and federally protected species, might be affected by changes in outflow in the San Francisco Estuary due to future development and climate change. Forty years of sampling data collected during fall from 1967 to 2008 were examined to define abiotic habitat suitability for delta smelt as a function of salinity and water transparency, and to describe long-term trends in habitat conditions. The annual habitat index we developed, which incorporated both quantity and quality of habitat, decreased by 78% over the study period. Future habitat index values under seven different development and climate change scenarios, representing a range of drier and wetter possibilities, were predicted using a model which related estuarine outflow to the habitat index. The results suggested that each of the scenarios would generally lead to further declines in delta smelt habitat across all water year types. Recovery targets for delta smelt will be difficult to attain if the modeled habitat conditions are realized.     

Operationalizing the Adaptation Fund: challenges in allocating funds to the vulnerable

The Adaptation Fund of the Kyoto Protocol marks a change in the international climate change financing architecture due to its independence from official development assistance, direct access and the majority of developing countries in governance. A major goal of the Adaptation Fund is to finance concrete adaptation projects and programmes in developing countries that are particularly vulnerable to the effects of climate change. The presented analysis considers the results of operationalization of the fund between 2008 and 2010, and the role vulnerability had in the allocation of funds. The definition of ‘vulnerability’ remains broad and currently does not allow for a prioritization in the allocation of funds. Criteria like ‘level of vulnerability’ or ‘adaptive capacity’ still need to be specified. The possibilities for the Adaptation Fund Board to implement a vulnerability-oriented funding approach are limited by the legal basis of the Kyoto Protocol and the principle of a country-driven approach. The effective support of vulnerable communities primarily depends on the institutional capacities and the institutional arrangement at the national level and the quality of analysis the adaptation projects and programmes are based on.     

Thermal performance and heat transport in aquifer thermal energy storage

Aquifer thermal energy storage (ATES) is used for seasonal storage of large quantities of thermal energy. Due to the increasing demand for sustainable energy, the number of ATES systems has increased rapidly, which has raised questions on the effect of ATES systems on their surroundings as well as their thermal performance. Furthermore, the increasing density of systems generates concern regarding thermal interference between the wells of one system and between neighboring systems. An assessment is made of (1) the thermal storage performance, and (2) the heat transport around the wells of an existing ATES system in the Netherlands. Reconstruction of flow rates and injection and extraction temperatures from hourly logs of operational data from 2005 to 2012 show that the average thermal recovery is 82 % for cold storage and 68 % for heat storage. Subsurface heat transport is monitored using distributed temperature sensing. Although the measurements reveal unequal distribution of flow rate over different parts of the well screen and preferential flow due to aquifer heterogeneity, sufficient well spacing has avoided thermal interference. However, oversizing of well spacing may limit the number of systems that can be realized in an area and lower the potential of ATES.     

Saxo‐Thuringia in the Variscan belt from a geodynamic point of view

Saxo‐Thuringia is a suture bounded part of the Variscan belt in central Europe and represents a fragment of the Armorica microplate. Structural investigations and a critical review of other geologic data allow the reconstruction of its geodynamic history. Two south‐dipping subduction zones, corresponding to the Rheno‐Herzynian and the Tepla sutures, delimited Saxo‐Thuringia before the Variscan orogeny. As a result of the continental collision between Avalonia to the north and a further fragment of Armorica to the south, both outer realms of Saxo‐Thuringia record high‐grade metamorphism and a subsequent uplift between 340 and 310 Ma. Contemporaneously, the low‐grade metamorphic internal zone of Saxo‐Thuringia records thrust contraction of the late Pre‐Cambrian basement and the formation of a fold belt in the overlaying Palaeozoic deposits. Two pre‐Variscan tectonic imprints are distinguishable: (1) the consolidation of late Pre‐Cambrian basement in the Cadomian–Avalonian belt and (2) a Cambrian and early Ordovician rift setting related to the opening of the Rheic ocean and the fragmentation and separation of Armorica.