Multiple stable states and catastrophic shifts in coastal wetlands: Progress, challenges, and opportunities in validating theory using remote sensing and other methods

open5siThe analysis by K.B. Moffett was partially supported by National Science Foundation grant EAR-1013843 to Stanford University. Any opinions, findings, and onclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The analysis by W. Nardin was partially supported by Office of Naval Research Award N00014-14-1-0114 to Boston University. The analysis by C. Wang was partially supported by National Natural Science Funds of China (41376120 and 41401413). The analysis by C. Wang and S. Temmerman was also partially supported by the European Union Programme Erasmus Mundus External Cooperation Window (EMECW)-Lot 14-China. K.B. Moffett thanks B.C. Smith for the analysis for the Wax Lake Delta example of Section 4.2 and S.M. Gorelick for the funding leading to the San Francisco Bay example of Section 4.3. W. Nardin thanks S. Fagherazzi and C. Woodcock for the funding leading to the Mekong River Delta example of Section 4.1. S. Silvestri thanks M. Marani for inspiring ideas and research on coastal wetland processes.Multiple stable states are established in coastal tidal wetlands (marshes, mangroves, deltas, seagrasses) by ecological, hydrological, and geomorphological feedbacks. Catastrophic shifts between states can be induced by gradual environmental change or by disturbance events. These feedbacks and outcomes are key to the sustainability and resilience of vegetated coastlines, especially as modulated by human activity, sea level rise, and climate change. Whereas multiple stable state theory has been invoked to model salt marsh responses to sediment supply and sea level change, there has been comparatively little empirical verification of the theory for salt marshes or other coastal wetlands. Especially lacking is long-term evidence documenting if or how stable states are established and maintained at ecosystem scales. Laboratory and field-plot studies are informative, but of necessarily limited spatial and temporal scope. For the purposes of long-term, coastal-scale monitoring, remote sensing is the best viable option. This review summarizes the above topics and highlights the emerging promise and challenges of using remote sensing-based analyses to validate coastal wetland dynamic state theories. This significant opportunity is further framed by a proposed list of scientific advances needed to more thoroughly develop the field.openMoffett K.B.; Nardin W.; Silvestri S.; Wang C.; Temmerman S.Moffett K.B.; Nardin W.; Silvestri S.; Wang C.; Temmerman S

Stochastic timeseries analysis in electric power systems and paleo-climate data

In this thesis a data science study of elementary stochastic processes is laid, aided with the development of two numerical software programmes, applied to power-grid frequency studies and Dansgaard--Oeschger events in paleo-climate data. Power-grid frequency is a key measure in power grid studies. It comprises the balance of power in a power grid at any instance. In this thesis an elementary Markovian Langevin-like stochastic process is employed, extending from existent literature, to show the basic elements of power-grid frequency dynamics can be modelled in such manner. Through a data science study of power-grid frequency data, it is shown that fluctuations scale in an inverse square-root relation with their size, alike any other stochastic process, confirming previous theoretical results. A simple Ornstein--Uhlenbeck is offered as a surrogate model for power-grid frequency dynamics, with a versatile input of driving deterministic functions, showing not surprisingly that driven stochastic processes with Gaussian noise do not necessarily show a Gaussian distribution. A study of the correlations between recordings of power-grid frequency in the same power-grid system reveals they are correlated, but a theoretical understanding is yet to be developed. A super-diffusive relaxation of amplitude synchronisation is shown to exist in space in coupled power-grid systems, whereas a linear relation is evidenced for the emergence of phase synchronisation. Two Python software packages are designed, offering the possibility to extract conditional moments for Markovian stochastic processes of any dimension, with a particular application for Markovian jump-diffusion processes for one-dimensional timeseries. Lastly, a study of Dansgaard--Oeschger events in recordings of paleoclimate data under the purview of bivariate Markovian jump-diffusion processes is proposed, augmented by a semi-theoretical study of bivariate stochastic processes, offering an explanation for the discontinuous transitions in these events and showing the existence of deterministic couplings between the recordings of the dust concentration and a proxy for the atmospheric temperature

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Developing small scale fracture tests for polycrystalline diamond

Opening ceramics up to a wider range of applications, where their high hardness and high strength are required, necessitates our understanding and improving of their fracture properties. In the last three decades, such improvements have been sought through developing our understanding of toughening mechanisms, typically involving microstructure control that focuses on crack deflection and grain bridging at grain boundaries and interfaces. However, these are often difficult to engineer, as changing microstructural processing (e.g. through heat treatment, chemistry or powder processing) does not result in a one-to-one correlation with performance, since the influence of microstructure on crack path is varied and complex. Recent developments on characterisation at the micro-scale therefore present an opportunity to broaden our understanding of the role of individual factors on the bulk performance. To investigate the fracture properties of individual features (i.e. individual crystallographic planes, grain boundaries or interfaces), a testing method was developed. This approach is based on the double cantilever wedging to measure the fracture energy change during stable crack growth and was successfully applied at the micron scale inside a scanning electron microscope. Direct view of the crack growth in the sample and measurement of the energy absorbed during fracture, without use of load-displacement data, is afforded through the combination of a stable test geometry with an image based analysis strategy. In addition to these precise tests, characterisation of the role of microstructure on crack paths in polycrystalline metal-ceramic composites was carried out. The focus has been on using high angular resolution electron backscatter diffraction combined with microindentation, to correlate intragranular residual stress gradients, due to thermal expansion mismatches, to crack deflection. Fracture energy of individual crystallographic planes and interfaces was measured in both brittle and brittle/ductile systems. In addition, local residual stresses and microstructure in diamond were related to fracture path.Open Acces

Complexity, aftershock sequences, and uncertainty in earthquake statistics

Earthquake statistics is a growing field of research with direct application to probabilistic seismic hazard evaluation. The earthquake process is a complex spatio-temporal phenomenon, and has been thought to be an example of the self-organised criticality (SOC) paradigm, in which events occur as cascades on a wide range of sizes, each determined by fine details of the rupture process. As a consequence, deterministic prediction of specific event sizes, locations, and times may well continue to remain elusive. However, probabilistic forecasting, based on statistical patterns of occurrence, is a much more realistic goal at present, and is being actively explored and tested in global initiatives. This thesis focuses on the temporal statistics of earthquake populations, exploring the uncertainties in various commonly-used procedures for characterising seismicity and explaining the origins of these uncertainties. Unlike many other SOC systems, earthquakes cluster in time and space through aftershock triggering. A key point in the thesis is to show that the earthquake inter-event time distribution is fundamentally bimodal: it is a superposition of a gamma component from correlated (co-triggered) events and an exponential component from independent events. Volcano-tectonic earthquakes at Italian and Hawaiian volcanoes exhibit a similar bimodality, which in this case, may arise as the sum of contributions from accelerating and decelerating rates of events preceding and succeeding volcanic activity. Many authors, motivated by universality in the scaling laws of critical point systems, have sought to demonstrate a universal data collapse in the form of a gamma distribution, but I show how this gamma form is instead an emergent property of the crossover between the two components. The relative size of these two components depends on how the data is selected, so there is no universal form. The mean earthquake rate—or, equivalently, inter-event time—for a given region takes time to converge to an accurate value, and it is important to characterise this sampling uncertainty. As a result of temporal clustering and non-independence of events, the convergence is found to be much slower than the Gaussian rate of the central limit theorem. The rate of this convergence varies systematically with the spatial extent of the region under consideration: the larger the region, the closer to Gaussian convergence. This can be understood in terms of the increasing independence of the inter-event times with increasing region size as aftershock sequences overlap in time to a greater extent. On the other hand, within this high-overlap regime, a maximum likelihood inversion of parameters for an epidemic-type statistical model suffers from lower accuracy and a systematic bias; specifically, the background rate is overestimated. This is because the effect of temporal overlapping is to mask the correlations and make the time series look more like a Poisson process of independent events. This is an important result with practical relevance to studies using inversions, for example, to infer temporal variations in background rate for time-dependent hazard estimation

Modelling and Forecasting Human Populations using Sigmoid Models

Early this century "S-shaped" curves, sigmoids, gainedpopulari ty among demographers. However, by 1940, the approachhad "fallen out of favour", being criticised for giving po,orresults and having no theoretical validity. It was alsoconsidered that models of total population were of littlepractical interest, the main forecasting procedure currentlyadopted being the bottom-up "cohort-component" method.In the light of poor forecasting performance fromcomponent methods, a re-assessment is given in this thesis of theuse of simple trend models. A suitable means of fitting thesemodels to census data is developed, using a non-linear leastsquares algorithm based on minimisation of a proportionatelyweighted residual sum of squares. It is demonstrated that usefulmodels can be obtained from which, by using a top-downmethodology, component populations and vi tal components can bederived. When these models are recast in a recursiveparameterisation, it is shown that forecasts can be obtainedwhich, it is argued, are superior to existing officialprojections.Regarding theoretical validity, it is argued that sigmoidmodels relate closely to Malthusian theory and give a mathematicalstatement of the demographic transition.In order to judge the sui tabili ty of extrapolating fromsigmoid models, a framework using Catastrophe Theory is developed.It is found that such a framework allows one quali tati vely tomodel population changes resulting from subtle changes ininfluencing variables. The use of Catastrophe Theory hasadvantages over conventional demographic models as it allows amore holistic approach to population modelling