Is the Regge Calculus a consistent approximation to General Relativity?

We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be based on the behaviour of residual errors in the discrete equations when evaluated on solutions of the Einstein equations. We will show that for generic simplicial lattices the residual errors can not be used to distinguish metrics which are solutions of Einstein's equations from those that are not. We will conclude that either the Regge calculus is an inconsistent approximation to General Relativity or that it is incorrect to use residual errors in the discrete equations as a criteria to judge the discrete equations.Comment: 27 pages, plain TeX, very belated update to match journal articl

A simple expression for the ADM mass

We show by an almost elementary calculation that the ADM mass of an asymptotically flat space can be computed as a limit involving a rate of change of area of a closed 2-surface. The result is essentially the same as that given by Brown and York. We will prove this result in two ways, first by direct calculation from the original formula as given by Arnowitt, Deser and Misner and second as a corollary of an earlier result by Brewin for the case of simplicial spaces.Comment: 9 pages, 1 figur

Variations in Remotely-Sensed Phytoplankton Size Structure of a Cyclonic Eddy in the Southwest Indian Ocean

Phytoplankton size classes were derived from weekly-averaged MODIS Aqua chlorophyll a data over the southwest Indian Ocean in order to assess changes in surface phytoplankton community structure within a cyclonic eddy as it propagated across the Mozambique Basin in 2013. Satellite altimetry was used to identify and track the southwesterly movement of the eddy from its origin off Madagascar in mid-June until mid-October, when it eventually merged with the Agulhas Current along the east coast of South Africa. Nano- and picophytoplankton comprised most of the community in the early phase of the eddy development in June, but nanophytoplankton then dominated in austral winter (July and August). Microphytoplankton was entrained into the eddy by horizontal advection from the southern Madagascar shelf, increasing the proportion of microphytoplankton to 23% when the chlorophyll a levels reached a peak of 0.36 mg·m−3 in the third week of July. Chlorophyll a levels declined to 50% of the population. As far as is known, this is the first study to investigate temporal changes in chlorophyll a and community structure in a cyclonic eddy propagating across an ocean basin in the southwest Indian Ocean

Seasonal variation in remotely-sensed phytoplankton size structure around Southern Africa

The three-component model of Brewin et al. (2010) computes fractional contributions of three phytoplankton size classes (micro- (> 20μm), nano- (2–20μm), picophytoplankton ( 1 mgm−3 was limited to shelf regions along the coasts of Southern Africa and Madagascar, while values 50% of the total Chla in these regions with little change throughout the year. The AR shelf differed, with picophytoplankton dominating in summer, and micro- and nanophytoplankton the rest of the year. In the open ocean domains of the NB, SB, and AB regions, nanophytoplankton dominated for most of the year, with picophytoplankton being more prevalent during summer and autumn. In contrast, in the AR open ocean, nanophytoplankton were dominant only during winter and early spring, whereas picophytoplankton dominated throughout the year in the MC open ocean. The refined model characterised previously unknown spatial and temporal changes in size structure in various ecosystems around Southern Africa

Ocean-colour products for climate-change studies: What are their ideal characteristics?

Ocean-colour radiometry is recognised as an Essential Climate Variable (ECV) according to the Global Climate Observing System (GCOS), because of its capability to observe significant properties of the marine ecosystem at synoptic to global scales. Yet the value of ocean colour for climate-change studies depends to a large extent not only on the decidedly important quality of the data per se, but also on the qualities of the algorithms used to convert the multi-spectral radiance values detected by the ocean-colour satellite into relevant ecological, bio-optical and biogeochemical variables or properties of the ocean. The algorithms selected from the pool of available algorithms have to be fit for purpose: detection of marine ecosystem responses to climate change. Marine ecosystems might respond in a variety of ways to changing climate, including perturbations to regional distributions in the quantity and in the type of phytoplankton present, their locations and in their seasonal dynamics. The ideal algorithms would be capable of distinguishing between abundance and type, and would not mistake one for the other. They would be robust to changes in climate, and would not rely on assumptions that might be valid only under current climatic conditions. Based on such considerations, we identify a series of ideal qualitative traits that algorithms for climate-change studies would possess. Necessarily, such traits would have to complement the quantitative requirements for precision, accuracy and stability in the data over long time scales. We examine the extent to which available algorithms meet the criteria, according to the work carried out in the Ocean Colour Climate Change Initiative, and where improvements are still needed

A longitudinal investigation of maternal and child 'anxious cognitions'

Overestimation of threat and underestimation of coping have been frequently reported amongst anxious adults and children. The current study examines the longitudinal relationship between mothers' anxious cognitions and expectations about their child, and children's anxious cognitions. 54 children (aged 10-11 years) and their mothers reported on their interpretation of ambiguous scenarios at two time points. Mothers also reported on their expectations about their child's reaction to ambiguous situations. Significant cross-sectional associations were found between mother and child anticipation of distress. Associations were most consistent between mothers' expectations and children's cognitions. Furthermore, based on regression analyses, mothers' expectations predicted change in children's anxious cognitions over time. Evidence for a reciprocal relationship, that child cognitions predict change in mothers' expectations, was found for girls. The results provide empirical support for potential influences on the development of children's 'anxious cognitive style,' and suggest targets for preventing and reducing maladaptive cognitions in children

Ocean-colour products for climate-change studies: What are their ideal characteristics?

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordOcean-colour radiometry is recognised as an Essential Climate Variable (ECV) according to the Global Climate Observing System (GCOS), because of its capability to observe significant properties of the marine ecosystem at synoptic to global scales. Yet the value of ocean colour for climate-change studies depends to a large extent not only on the decidedly important quality of the data per se, but also on the qualities of the algorithms used to convert the multi-spectral radiance values detected by the ocean-colour satellite into relevant ecological, bio-optical and biogeochemical variables or properties of the ocean. The algorithms selected from the pool of available algorithms have to be fit for purpose: detection of marine ecosystem responses to climate change. Marine ecosystems might respond in a variety of ways to changing climate, including perturbations to regional distributions in the quantity and in the type of phytoplankton present, their locations and in their seasonal dynamics. The ideal algorithms would be capable of distinguishing between abundance and type, and would not mistake one for the other. They would be robust to changes in climate, and would not rely on assumptions that might be valid only under current climatic conditions. Based on such considerations, we identify a series of ideal qualitative traits that algorithms for climate-change studies would possess. Necessarily, such traits would have to complement the quantitative requirements for precision, accuracy and stability in the data over long time scales. We examine the extent to which available algorithms meet the criteria, according to the work carried out in the Ocean Colour Climate Change Initiative, and where improvements are still needed.National Centre for Earth Observation of the Natural Environment Research Council of the U

Regge calculus and Ashtekar variables

Spacetime discretized in simplexes, as proposed in the pioneer work of Regge, is described in terms of selfdual variables. In particular, we elucidate the "kinematic" structure of the initial value problem, in which 3--space is divided into flat tetrahedra, paying particular attention to the role played by the reality condition for the Ashtekar variables. An attempt is made to write down the vector and scalar constraints of the theory in a simple and potentially useful way.Comment: 10 pages, uses harvmac. DFUPG 83/9

Expanding Aquatic Observations through Recreation

Accurate observations of the Earth system are required to understand how our planet is changing and to help manage its resources. The aquatic environment—including lakes, rivers, wetlands, estuaries, coastal and open oceans—is a fundamental component of the Earth system controlling key physical, biological, and chemical processes that allow life to flourish. Yet, this environment is critically undersampled in both time and space. New and cost-effective sampling solutions are urgently needed. Here, we highlight the potential to improve aquatic sampling by tapping into recreation. We draw attention to the vast number of participants that engage in aquatic recreational activities and argue, based on current technological developments and recent research, that the time is right to employ recreational citizens to improve large-scale aquatic sampling efforts. We discuss the challenges that need to be addressed for this strategy to be successful (e.g., sensor integration, data quality, and citizen motivation), the steps needed to realize its potential, and additional societal benefits that arise when engaging citizens in scientific sampling

Expanding aquatic observations through recreation

This is the final version. Available on open access from Frontiers Media via the DOI in this recordAccurate observations of the Earth system are required to understand how our planet is changing and to help manage its resources. The aquatic environment-including lakes, rivers, wetlands, estuaries, coastal and open oceans-is a fundamental component of the Earth system controlling key physical, biological, and chemical processes that allow life to flourish. Yet, this environment is critically undersampled in both time and space. New and cost-effective sampling solutions are urgently needed. Here, we highlight the potential to improve aquatic sampling by tapping into recreation. We draw attention to the vast number of participants that engage in aquatic recreational activities and argue, based on current technological developments and recent research, that the time is right to employ recreational citizens to improve large-scale aquatic sampling efforts. We discuss the challenges that need to be addressed for this strategy to be successful (e.g., sensor integration, data quality, and citizen motivation), the steps needed to realize its potential, and additional societal benefits that arise when engaging citizens in scientific sampling.UK National Centre for Earth ObservationSmartfin/Lostbird FoundationDefr