Preprints

Filtering by Subject: Applied Mathematics

Quantification and interpretation of the climate variability record

Anna S von der Heydt, Peter Ashwin, Charles D. Camp, Michel Crucifix, Henk A Dijkstra, Peter Ditlevsen, Timothy M Lenton

Published: 2020-05-24
Subjects: Applied Mathematics, Earth Sciences, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

This paper is currently in review for Global and Planetary Change. \\ The spectral view of variability is a compelling and adaptable tool for understanding variability of the climate. In the Mitchell (1976) seminal paper, it was used to express, on one graph with log scales, a very wide range of climate variations from millions of years to days. The spectral approach is particularly useful for [...]

A mixed $RT_0 - P_0$ Raviart-Thomas finite element implementation of Darcy Equation in GNU Octave

Agah D. Garnadi, Corinna Bahriawati

Published: 2020-04-14
Subjects: Applied Mathematics, Bioresource and Agricultural Engineering, Chemical Engineering, Computational Engineering, Earth Sciences, Engineering, Environmental Sciences, Hydrology, Numerical Analysis and Computation, Partial Differential Equations, Physical Sciences and Mathematics, Water Resource Management

In this paper we shall describe mixed formulations -differential and variational- of Darcys flow equation, an important model of elliptic problem. We describe * Galerkin method with finite dimensional spaces; * Local matrices and assembling; * Raviart-Thomas $RT_0 - P_0$ elements; * Edge basis and local matrices for $RT_0 - P_0$ FEM; * Model problem with corresponding local matrices, right hand [...]

SymAE: an autoencoder with embedded physical symmetries for passive time-lapse monitoring

Pawan Bharadwaj, Matt Li, Laurent Demanet

Published: 2020-04-13
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Geophysics and Seismology, Physical Sciences and Mathematics

We introduce SymAE, an auto-encoder architecture that learns to separate multichannel passive-seismic datasets into qualitatively interpretable components: one component corresponds to path-specific effects associated with subsurface properties while the other component corresponds to the spectral signature of the passive sources. This information is represented by two latent codes produced by [...]

Global Sensitivity Analysis to Optimize Basin-Scale Conductive Model Calibration - Insights on the Upper Rhine Graben

Denise Degen, Karen Veroy, Jessica Freymark, Magdalena Scheck-Wenderoth, Florian Wellmann

Published: 2020-04-01
Subjects: Applied Mathematics, Earth Sciences, Physical Sciences and Mathematics

Geothermal simulations are widely used in both scientific and applied industrial contexts. Typically, the temperature state is evaluated on the basis of the heat equation, with suitable parameterizations of the model domain and defined boundary conditions, which are calibrated to obtain a minimal misfit between measured and simulated temperature values. We demonstrate the essential need for [...]

Hydro-morphodynamics 2D modelling using a discontinuous Galerkin discretisation

Mariana C A Clare, James Percival, Athanasios Angeloudis, Colin Cotter, Matthew Piggott

Published: 2020-01-09
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Geomorphology, Numerical Analysis and Computation, Partial Differential Equations, Physical Sciences and Mathematics, Sedimentology

The development of morphodynamic models to simulate sediment transport accurately is a challenging process that is becoming ever more important because of our increasing exploitation of the coastal zone, as well as sea-level rise and the potential increase in strength and frequency of storms due to a changing climate. Morphodynamic models are highly complex given the non-linear and coupled nature [...]

Goal-Oriented Error Estimation and Mesh Adaptation for Shallow Water Modelling

Joseph Wallwork, Nicolas Barral, Stephan C. Kramer, David Ham, Matthew Piggott

Published: 2019-12-31
Subjects: Applied Mathematics, Computer Sciences, Engineering, Non-linear Dynamics, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Partial Differential Equations, Physical Sciences and Mathematics

Numerical modelling frequently involves a diagnostic quantity of interest (QoI) - often of greater importance than the PDE solution - which we seek to accurately approximate. In the case of coastal ocean modelling the power output of a tidal turbine farm is one such example. Goal-oriented error estimation and mesh adaptation can be used to provide meshes which are well-suited to achieving this [...]

Redshift of Earthquakes via Focused Blind Deconvolution of Teleseisms

Pawan Bharadwaj, Chunfang Meng, Aimé Fournier, Laurent Demanet, Mike Fehler

Published: 2019-10-13
Subjects: Applied Mathematics, Earth Sciences, Electrical and Computer Engineering, Engineering, Geophysics and Seismology, Physical Sciences and Mathematics, Signal Processing

We present a robust factorization of the teleseismic waveforms resulting from an earthquake source into signals that originate from the source and signals that characterize the path effects. The extracted source signals represent the earthquake spectrum and its variation with azimuth. Unlike most prior work on source extraction, our method is data-driven, and it does not depend on any [...]

Controls on the development and termination of failed continental rifts: Insights from the crustal structure and rifting style of the North Sea via ambient noise tomography

Emily Crowder, Nick Rawlinson, David G. Cornwell, Carmelo Sammarco, Erica Galetti, Andrew Curtis

Published: 2019-09-21
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Geophysics and Seismology, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Physical Sciences and Mathematics, Probability, Statistics and Probability

The mid to lower crust plays an important role in rift initiation and evolution, particularly when large scale sutures and/or terrane boundaries are present. These inherited features can focus strain or act as inhibitors to extensional deformation. Ancient tectonic features are known to exist beneath the iconic failed rift system of the North Sea making it the ideal location to investigate the [...]

An Adaptive Discontinuous Galerkin Method for the Simulation of Hurricane Storm Surge

Nicole Beisiegel, Stefan Vater, Jörn Behrens, Frederic Dias

Published: 2019-09-09
Subjects: Applied Mathematics, Other Applied Mathematics, Physical Sciences and Mathematics

Numerical simulations based on solving the 2D shallow water equations using a Discontinuous Galerkin (DG) discretisation have evolved to be a viable tool for many geophysical applications. In the context of flood modelling, however, they have not yet been methodologically studied to a large extent. On geographic scale, hurricane storm surge can be interpreted as a localised phenomenon making it [...]

Frozen fringe explains sediment freeze-on during Heinrich events

Colin R. Meyer, Alexander Robel, Alan Rempel

Published: 2019-08-16
Subjects: Applied Mathematics, Earth Sciences, Glaciology, Physical Sciences and Mathematics

Anomalous coarse-grained sediment layers beneath the North Atlantic likely originated from sediment freeze-on to the base of ice sheets during the last glacial period. These layers represent periods of extreme ice discharge, called Heinrich events, and are variously attributed to ice stream flow instability, ice shelf collapse, or enhanced terminus melting due to ocean warming. In this paper, we [...]

Certified Reduced Basis Method in Geosciences Addressing the challenge of high dimensional problems

Denise Degen, Karen Veroy, Florian Wellmann

Published: 2019-06-28
Subjects: Applied Mathematics, Earth Sciences, Numerical Analysis and Computation, Partial Differential Equations, Physical Sciences and Mathematics

One of the biggest challenges in Computational Geosciences is finding ways of efficiently simulating high-dimensional problems. In this paper, we demonstrate how the RB method can be gainfully exploited to solve problems in the Geosciences. The reduced basis method constructs low-dimensional approximations to (high-dimensional) solutions of parametrized partial differential equations. In contrast [...]

Dynamical Systems Theory Sheds New Light on Compound Climate Extremes in Europe and Eastern North America

Paolo De Luca, Gabriele Messori, Flavio M. E. Pons, Davide Faranda

Published: 2019-06-27
Subjects: Applied Mathematics, Atmospheric Sciences, Climate, Dynamic Systems, Earth Sciences, Meteorology, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics, Physics, Statistical, Nonlinear, and Soft Matter Physics

We propose a novel approach to the study of compound extremes, grounded in dynamical systems theory. Specifically, we present the co-recurrence ratio (α), which elucidates the dependence structure between variables by quantifying their joint recurrences. This approach is applied to daily climate extremes, derived from the ERA-Interim reanalysis over the 1979-2018 period. The analysis focuses on [...]

Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM

Ashesh Kumar Chattopadhyay, Pedram Hassanzadeh, Devika Subramanian

Published: 2019-06-20
Subjects: Applied Mathematics, Artificial Intelligence and Robotics, Atmospheric Sciences, Climate, Computer Sciences, Dynamic Systems, Earth Sciences, Fluid Dynamics, Non-linear Dynamics, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics, Physics

In this paper, the performance of three deep learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The methods are: echo state network (a type of reservoir computing, RC-ESN), deep feed-forward artificial neural network (ANN), and recurrent neural network with long short-term memory [...]

Implicitly localized ensemble observational update to cope with nonlocal/nonlinear data constraints in large-size inverse problems

Jean-Michel Brankart

Published: 2019-05-30
Subjects: Applied Mathematics, Earth Sciences, Physical Sciences and Mathematics

Many practical applications involve the resolution of large-size inverse problems, without providing more than a moderate-size sample to describe the prior probability distribution. In this situation, additional information must be supplied to augment the effective dimension of the available sample. This is the role played by covariance localization in the large-size applications of the ensemble [...]

A heuristic model inversion for coupled thermo-hydro-mechanical modeling of triaxial experiments

Jack Lin, Mustafa Sari, Sotiris Alevizos, Emmanouil Veveakis, Thomas Poulet

Published: 2019-04-24
Subjects: Applied Mathematics, Civil and Environmental Engineering, Engineering, Geotechnical Engineering, Physical Sciences and Mathematics

As multiphysics geomechanical models get developed, their increasing complexity and number of parameters make it particularly difficult to calibrate against experimental data. In this contribution, we present a heuristic workflow to invert for parameters of a coupled Thermo-Hydro-Mechanical (THM) model in a way that helps the theoretical modellers refine their definition of the underlying [...]

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