Regularized adaptive long autoregressive spectral analysis

This paper is devoted to adaptive long autoregressive spectral analysis when (i) very few data are available, (ii) information does exist beforehand concerning the spectral smoothness and time continuity of the analyzed signals. The contribution is founded on two papers by Kitagawa and Gersch. The first one deals with spectral smoothness, in the regularization framework, while the second one is devoted to time continuity, in the Kalman formalism. The present paper proposes an original synthesis of the two contributions: a new regularized criterion is introduced that takes both information into account. The criterion is efficiently optimized by a Kalman smoother. One of the major features of the method is that it is entirely unsupervised: the problem of automatically adjusting the hyperparameters that balance data-based versus prior-based information is solved by maximum likelihood. The improvement is quantified in the field of meteorological radar

Tide-surge interaction in the English Channel

The English Channel is characterised by strong tidal currents and a wide tidal range, such that their influence on surges is expected to be non-negligible. In order to better assess storm surges in this zone, tide-surge interactions are investigated. A preliminary data analysis on hourly surges indicates some preferential times of occurrence of large storm surges at rising tide, especially in Dunkerque. To examine this further, a numerical modelling approach is chosen, based on the 2DH shallow-water model (MARS). The surges are computed both with and without tide interaction. For the two selected events (the November 2007 North Sea and March 2008 Atlantic storms), it appears that the instantaneous tide-surge interaction is seen to be non-negligible in the eastern half of the English Channel, reaching values of 74 cm (i.e. 50% of the same event maximal storm surge) in the Dover Strait for the studied cases. This interaction decreases in westerly direction. In the risk-analysis community in France, extreme water levels have been determined assuming skew surges and tide as independent. The same hydrodynamic model is used to investigate this dependence in the English Channel. Simple computations are performed with the same meteorological forcing, while varying the tidal amplitude, and the skew surge differences <i>D</i><sub>SS</sub> are analysed. Skew surges appear to be tide-dependent, with negligible values of <i>D</i><sub>SS</sub> (<0.05 m) over a large portion of the English Channel, although reaching several tens of centimetres in some locations (e.g. the Isle of Wight and Dover Strait)

Uncertainties in shoreline projections to 2100 at Truc Vert Beach (France): Role of sea‐level rise and equilibrium model assumptions

Sandy shorelines morphodynamics responds to a myriad of processes interacting at different spatial and temporal scales, making shoreline predictions challenging. Shoreline modeling inherits uncertainties from the primary driver boundary conditions (e.g., sea-level rise and wave forcing) as well as uncertainties related to model assumptions and/or misspecifications of the physics. This study presents an analysis of the uncertainties associated with future shoreline evolution at the cross-shore transport dominated sandy beach of Truc Vert (France) over the 21st century. We explicitly resolve wave-driven shoreline change using two different equilibrium modeling approaches to provide new insight into the contributions of sea-level rise, and free model parameters uncertainties on future shoreline change in the frame of climate change. Based on a Global Sensitivity Analysis, shoreline response during the first half of the century is found to be mainly sensitive to the equilibrium model parameters, with the influence of sea-level rise emerging in the second half of the century (∼2050 or later), under several simulated scenarios. The results reveal that the seasonal and interannual variability of the predicted shoreline position is sensitive to the choice of the wave-driven equilibrium-based model. Finally, we discuss the importance of the chronology of wave events in future shoreline change, calling for more continuous wave projection time series to further address uncertainties in future wave conditions. Our contribution demonstrates that unmitigated climate change can result in shoreline retreat of several tens of meters by 2100, even for sectors that have been stable or slightly accreting over the last century

The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

We consider an "elastic" version of the statistical mechanical monomer-dimer problem on the n-dimensional integer lattice. Our setting includes the classical "rigid" formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan" EDM systems where the dimer potential is a weighted l1-distance and the auxiliary GRF is a Markov random field of Pickard type which behaves in space like autoregressive processes do in time. For one-dimensional Manhattan EDM systems, we compute the MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a compact transfer operator on a Hilbert space which is related to the annihilation and creation operators of the quantum harmonic oscillator and also recast it as the eigenvalue problem for a pantograph functional-differential equation.Comment: 24 pages, 4 figures, submitted on 14 October 2011 to a special issue of DCDS-

Climate change-driven coastal erosion modelling in temperate sandy beaches: Methods and uncertainty treatment

Developing future projections of shoreline change requires a good understanding of the driving coastal processes. These processes result primarily from the combination of mean sea level, waves, storm surges and tides, which are affected by global and regional climate change, and whose uncertainty increases with time. This paper reviews the current state of the art of methods used to model climate change-induced coastal erosion focusing on how climate change-related drivers and the associated uncertainty are considered. We identify research gaps, describe and analyse the key components of a comprehensive framework to derive future estimates of shoreline change and make suggestions for good practice. Within the scope of the review, we find that although significant progress has been made over the last decade, most of the studies limit uncertainty sampling to considering ranges of variation of forcing variables and ensembles of emissions scenarios, and applications with high level of probabilistic development remain few. Further research is necessary to fully (a) incorporate projected time series of coastal drivers into the erosion models, including bias correction; (b) sufficiently sample the uncertainty associated with each step of the top-down approach, including the consideration of different emission scenarios, inter- and intra-model variability, and multiple runs of erosion models or model ensembles; and (c) reduce uncertainty in shoreline change estimates by developing better datasets and model parameterisations, and progressing in detection and attribution

The Tides They Are A-Changin': A Comprehensive Review of Past and Future Nonastronomical Changes in Tides, Their Driving Mechanisms, and Future Implications:A comprehensive review of past and future non‐astronomical changes in tides, their driving mechanisms and future implications

Scientists and engineers have observed for some time that tidal amplitudes at many locations are shifting considerably due to non-astronomical factors. Here we review comprehensively these important changes in tidal properties, many of which remain poorly understood. Over long geological time-scales, tectonic processes drive variations in basin size, depth, and shape, and hence the resonant properties of ocean basins. On shorter geological time-scales, changes in oceanic tidal properties are dominated by variations in water depth. A growing number of studies have identified widespread, sometimes regionally-coherent, positive and negative trends in tidal constituents and levels during the 19th, 20th and early 21st centuries. Determining the causes is challenging because a tide measured at a coastal gauge integrates the effects of local, regional, and oceanic changes. Here, we highlight six main factors that can cause changes in measured tidal statistics on local scales, and a further eight possible regional/global driving mechanisms. Since only a few studies have combined observations and models, or modelled at a temporal/spatial resolution capable of resolving both ultra-local and large-scale global changes, the individual contributions from local and regional mechanisms remain uncertain. Nonetheless, modelling studies project that sea-level rise and climate change will continue to alter tides over the next several centuries, with regionally coherent modes of change caused by alterations to coastal morphology and ice sheet extent. Hence, a better understanding of the causes and consequences of tidal variations is needed to help assess the implications for coastal defense, risk assessment, and ecological change

The Tides They are A-Changin\u27: A Comprehensive Review of Past and Future Nonastronomical Changes in Tides, Their Driving Mechanisms, and Future Implications

Scientists and engineers have observed for some time that tidal amplitudes at many locations are shifting considerably due to nonastronomical factors. Here we review comprehensively these important changes in tidal properties, many of which remain poorly understood. Over long geological time scales, tectonic processes drive variations in basin size, depth, and shape and hence the resonant properties of ocean basins. On shorter geological time scales, changes in oceanic tidal properties are dominated by variations in water depth. A growing number of studies have identified widespread, sometimes regionally coherent, positive, and negative trends in tidal constituents and levels during the 19th, 20th, and early 21st centuries. Determining the causes is challenging because a tide measured at a coastal gauge integrates the effects of local, regional, and oceanic changes. Here, we highlight six main factors that can cause changes in measured tidal statistics on local scales and a further eight possible regional/global driving mechanisms. Since only a few studies have combined observations and models, or modeled at a temporal/spatial resolution capable of resolving both ultralocal and large-scale global changes, the individual contributions from local and regional mechanisms remain uncertain. Nonetheless, modeling studies project that sea level rise and climate change will continue to alter tides over the next several centuries, with regionally coherent modes of change caused by alterations to coastal morphology and ice sheet extent. Hence, a better understanding of the causes and consequences of tidal variations is needed to help assess the implications for coastal defense, risk assessment, and ecological change

Effective null Raychaudhuri equation

The effects on Raychaudhuri's equation of an intrinsically-discrete or particle nature of spacetime are investigated. This is done through the consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. We do this from an effective point of view, that is through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, this adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point. Further, this results in a non-vanishing of the limiting cross-sectional area itself of the congruence.Comment: 7 pages; v2: some comparisons with other approaches adde

Towards comprehensive observing and modeling systems for monitoring and predicting regional to coastal sea level

A major challenge for managing impacts and implementing effective mitigation measures and adaptation strategies for coastal zones affected by future sea level (SL) rise is our limited capacity to predict SL change at the coast on relevant spatial and temporal scales. Predicting coastal SL requires the ability to monitor and simulate a multitude of physical processes affecting SL, from local effects of wind waves and river runoff to remote influences of the large-scale ocean circulation on the coast. Here we assess our current understanding of the causes of coastal SL variability on monthly to multi-decadal timescales, including geodetic, oceanographic and atmospheric aspects of the problem, and review available observing systems informing on coastal SL. We also review the ability of existing models and data assimilation systems to estimate coastal SL variations and of atmosphere-ocean global coupled models and related regional downscaling efforts to project future SL changes. We discuss (1) observational gaps and uncertainties, and priorities for the development of an optimal and integrated coastal SL observing system, (2) strategies for advancing model capabilities in forecasting short-term processes and projecting long-term changes affecting coastal SL, and (3) possible future developments of sea level services enabling better connection of scientists and user communities and facilitating assessment and decision making for adaptation to future coastal SL change.RP was funded by NASA grant NNH16CT00C. CD was supported by the Australian Research Council (FT130101532 and DP 160103130), the Scientific Committee on Oceanic Research (SCOR) Working Group 148, funded by national SCOR committees and a grant to SCOR from the U.S. National Science Foundation (Grant OCE-1546580), and the Intergovernmental Oceanographic Commission of UNESCO/International Oceanographic Data and Information Exchange (IOC/IODE) IQuOD Steering Group. SJ was supported by the Natural Environmental Research Council under Grant Agreement No. NE/P01517/1 and by the EPSRC NEWTON Fund Sustainable Deltas Programme, Grant Number EP/R024537/1. RvdW received funding from NWO, Grant 866.13.001. WH was supported by NASA (NNX17AI63G and NNX17AH25G). CL was supported by NASA Grant NNH16CT01C. This work is a contribution to the PIRATE project funded by CNES (to TP). PT was supported by the NOAA Research Global Ocean Monitoring and Observing Program through its sponsorship of UHSLC (NA16NMF4320058). JS was supported by EU contract 730030 (call H2020-EO-2016, “CEASELESS”). JW was supported by EU Horizon 2020 Grant 633211, Atlantos