# Preprints

Filtering by Subject: Applied Mathematics

## Frozen fringe explains sediment freeze-on during Heinrich events

**Published**: 2019-08-17

**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

**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

**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

**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

**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

**Published**: 2019-04-25

**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 [...]

## Matlab/R workflows to assess critical choices in Global Sensitivity Analysis using the SAFE toolbox

**Published**: 2019-04-05

**Subjects**: Applied Mathematics, Civil and Environmental Engineering, Computer Sciences, Earth Sciences, Engineering, Environmental Sciences, Physical Sciences and Mathematics, Risk Analysis, Statistics and Probability

Global Sensitivity Analysis (GSA) is a set of statistical techniques to investigate the effects of the uncertainty in the input factors of a mathematical model on the model’s outputs. The value of GSA for the construction, evaluation, and improvement of earth system models is reviewed in a companion paper by Wagener and Pianosi [n.d.]. The present paper focuses on the implementation of GSA and [...]

## A test case for application of convolutional neural networks to spatio-temporal climate data: Re-identifying clustered weather patterns

**Published**: 2019-01-01

**Subjects**: Applied Mathematics, Computer Sciences, Earth Sciences, Engineering, Environmental Sciences, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics, Planetary Sciences

Convolutional neural networks (CNNs) can potentially provide powerful tools for classifying and identifying patterns in climate and environmental data. However, because of the inherent complexities of such data, which are often spatio-temporal, chaotic, and non-stationary, the CNN algorithms must be designed/evaluated for each specific dataset and application. Yet to start, CNN, a supervised [...]

## Wavelet-based analysis of ground deformation coupling satellite acquisitions (Sentinel-1, SMOS) and data from shallow and deep wells in Southwestern France

**Published**: 2018-10-15

**Subjects**: Aerospace Engineering, Applied Mathematics, Earth Sciences, Engineering, Geophysics and Seismology, Hydrology, Physical Sciences and Mathematics

Acquisitions of the Sentinel-1 satellite are processed and comprehensively analyzed to investigate the ground displacement during a 3-year period above a gas storage site in Southwestern France. Despite quite low vertical displacements (between 4 and 8 mm) compared to the noise level, the local displacements reflects the variations due to charge and discharge during summer and winter periods, [...]

## Statistics and segmentation: Using Big Data to assess Cascades Arc compositional variability

**Published**: 2018-09-25

**Subjects**: Applied Mathematics, Applied Statistics, Earth Sciences, Geochemistry, Geology, Multivariate Analysis, Physical Sciences and Mathematics, Statistics and Probability, Volcanology

Primitive lavas erupted in the Cascades arc of western North America demonstrate significant patterns of along-arc heterogeneity. Such compositional diversity may be the result of differences in mantle melting processes, subduction geometry, regional tectonics, or compositions of the slab, mantle or overlying lithosphere. Previous authors have partitioned the arc into four geochemically distinct [...]

## HYRISK: An R package for hybrid uncertainty analysis using probability, imprecise probability and possibility distributions

**Published**: 2018-08-31

**Subjects**: Applied Mathematics, Engineering, Ordinary Differential Equations and Applied Dynamics, Other Applied Mathematics, Physical Sciences and Mathematics, Risk Analysis

Uncertainty analysis is an unavoidable risk assessment task (for instance for natural hazards, or for environmental issues). In situations where data are scarce, incomplete or imprecise, the systematic and only use of probabilities can be debatable. Over the last years, several alternative mathematical representation methods have been developed to handle in a more flexible manner the lack of [...]

## Higher potential compound flood risk in Northern Europe under anthropogenic climate change

**Published**: 2018-07-18

**Subjects**: Applied Mathematics, Atmospheric Sciences, Climate, Earth Sciences, Environmental Sciences, Hydrology, Multivariate Analysis, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Other Oceanography and Atmospheric Sciences and Meteorology, Other Physical Sciences and Mathematics, Physical Sciences and Mathematics, Physics, Statistics and Probability

The published version of this article is available at https://advances.sciencemag.org/content/5/9/eaaw5531. Compound flooding (CF) is an extreme event taking place in low-lying coastal areas as a result of co-occurring high sea level and large amounts of runoff, caused by precipitation. The impact from the two hazards occurring individually can be significantly lower than the result of their [...]

## Using flood-excess volume to show that upscaling beaver dams for protection against extreme floods proves unrealistic

**Published**: 2018-07-10

**Subjects**: Applied Mathematics, Earth Sciences, Hydrology, Other Applied Mathematics, Physical Sciences and Mathematics

The questions we address in the present article are the following: (i) whether (extreme) river floods can be prevented or seriously mitigated by the introduction of beavers in the wild, and (ii) for which river catchments does flood mitigation by beaver activity (not) work? By using the concept of flood-excess volume (FEV) for four rivers in the UK, in the context of five (extreme) UK flood [...]

## On using flood-excess volume to assess natural flood management, exemplified for extreme 2007 and 2015 floods in Yorkshire

**Published**: 2018-07-10

**Subjects**: Applied Mathematics, Earth Sciences, Hydrology, Other Applied Mathematics, Physical Sciences and Mathematics

This paper offers a protocol for conducting a quantified assessment of the relative merits of both existing and proposed methods of Natural Flood Management (NFM). Assessment is based on the rarely used concept of flood-excess volume (FEV), which approximately quantifies the volume of water one wishes to eliminate via flood-mitigation schemes, and is exemplified using publicly available [...]

## On using flood-excess volume in flood mitigation, exemplified for the River Aire Boxing Day Flood of 2015

**Published**: 2018-07-10

**Subjects**: Applied Mathematics, Earth Sciences, Hydrology, Other Applied Mathematics, Physical Sciences and Mathematics

The goals of this paper are threefold, namely to: (i) define the rarely used concept of flood-excess volume (FEV) as the flood volume above a chosen river-level threshold of flooding; (ii) show how to estimate FEV for the Boxing Day Flood of 2015 of the River Aire in the UK; and, (iii) analyse the use of FEV in evaluating a hypothetical flood-alleviation scheme (FASII+) for the River [...]