Articles | Volume 24, issue 3
https://doi.org/10.5194/npg-24-481-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/npg-24-481-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
21 Aug 2017
Research article |
| 21 Aug 2017
Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion
NorthWest Research Associates, P.O. Box 3027, Bellevue, WA, USA
Adam M. Sykulski
Data Science Institute, Department of Mathematics and Statistics, Lancaster University, Lancaster, UK
Jeffrey J. Early
NorthWest Research Associates, P.O. Box 3027, Bellevue, WA, USA
Sofia C. Olhede
Department of Statistical Science, University College London, Gower Street, London, UK
Related subject area
Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
Evaluation of forecasts by a global data-driven weather model with and without probabilistic post-processing at Norwegian stations
Characterisation of Dansgaard-Oeschger events in palaeoclimate time series using the Matrix Profile
The sampling method for optimal precursors of El Niño–Southern Oscillation events
A comparison of two causal methods in the context of climate analyses
A two-fold deep-learning strategy to correct and downscale winds over mountains
Downscaling of surface wind forecasts using convolutional neural networks
Superstatistical analysis of sea surface currents in the Gulf of Trieste, measured by high-frequency radar, and its relation to wind regimes using the maximum-entropy principle
Representation learning with unconditional denoising diffusion models for dynamical systems
Physically constrained covariance inflation from location uncertainty
Data-driven methods to estimate the committor function in conceptual ocean models
Exploring meteorological droughts' spatial patterns across Europe through complex network theory
Rain process models and convergence to point processes
Integrated hydrodynamic and machine learning models for compound flooding prediction in a data-scarce estuarine delta
Empirical adaptive wavelet decomposition (EAWD): an adaptive decomposition for the variability analysis of observation time series in atmospheric science
Predicting sea surface temperatures with coupled reservoir computers
Lévy noise versus Gaussian-noise-induced transitions in the Ghil–Sellers energy balance model
Using neural networks to improve simulations in the gray zone
Direct Bayesian model reduction of smaller scale convective activity conditioned on large-scale dynamics
A waveform skewness index for measuring time series nonlinearity and its applications to the ENSO–Indian monsoon relationship
The blessing of dimensionality for the analysis of climate data
Empirical evidence of a fluctuation theorem for the wind mechanical power input into the ocean
Producing realistic climate data with generative adversarial networks
Identification of droughts and heatwaves in Germany with regional climate networks
Recurrence analysis of extreme event-like data
Extracting statistically significant eddy signals from large Lagrangian datasets using wavelet ridge analysis, with application to the Gulf of Mexico
Improvements to the use of the Trajectory-Adaptive Multilevel Sampling algorithm for the study of rare events
Ensemble-based statistical interpolation with Gaussian anamorphosis for the spatial analysis of precipitation
Applications of matrix factorization methods to climate data
Beyond univariate calibration: verifying spatial structure in ensembles of forecast fields
Simulation-based comparison of multivariate ensemble post-processing methods
Detecting dynamical anomalies in time series from different palaeoclimate proxy archives using windowed recurrence network analysis
Vertical profiles of wind gust statistics from a regional reanalysis using multivariate extreme value theory
Remember the past: a comparison of time-adaptive training schemes for non-homogeneous regression
On fluctuating momentum exchange in idealised models of air–sea interaction
A prototype stochastic parameterization of regime behaviour in the stably stratified atmospheric boundary layer
Statistical post-processing of ensemble forecasts of the height of new snow
Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach
Statistical hypothesis testing in wavelet analysis: theoretical developments and applications to Indian rainfall
Comparison of stochastic parameterizations in the framework of a coupled ocean–atmosphere model
Idealized models of the joint probability distribution of wind speeds
Nonlinear analysis of the occurrence of hurricanes in the Gulf of Mexico and the Caribbean Sea
A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 1: Frequency analysis
A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 2: Extension to time–frequency analysis
Tipping point analysis of ocean acoustic noise
On the intrinsic timescales of temporal variability in measurements of the surface solar radiation
Optimal heavy tail estimation – Part 1: Order selection
Network-based study of Lagrangian transport and mixing
Multi-scale event synchronization analysis for unravelling climate processes: a wavelet-based approach
A matrix clustering method to explore patterns of land-cover transitions in satellite-derived maps of the Brazilian Amazon
Parameterization of stochastic multiscale triads
John Bjørnar Bremnes, Thomas N. Nipen, and Ivar A. Seierstad
Nonlin. Processes Geophys., 31, 247–257, https://doi.org/10.5194/npg-31-247-2024, https://doi.org/10.5194/npg-31-247-2024, 2024
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During the last 2 years, tremendous progress has been made in global data-driven weather models trained on reanalysis data. In this study, the Pangu-Weather model is compared to several numerical weather prediction models with and without probabilistic post-processing for temperature and wind speed forecasting. The results confirm that global data-driven models are promising for operational weather forecasting and that post-processing can improve these forecasts considerably.
Susana Barbosa, Maria Eduarda Silva, and Denis-Didier Rousseau
Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2024-13, https://doi.org/10.5194/npg-2024-13, 2024
Revised manuscript accepted for NPG
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The characterisation of abrupt transitions in palaeoclimate records allows the understanding of millennial climate variability and of potential tipping points in the context of current climate change. In our study an algorithmic method, the matrix profile, is employed to characterise abrupt warmings designated as Dansgaard-Oeschger (DO) events and to identify the most similar transitions in the palaeoclimate time series.
Bin Shi and Junjie Ma
Nonlin. Processes Geophys., 31, 165–174, https://doi.org/10.5194/npg-31-165-2024, https://doi.org/10.5194/npg-31-165-2024, 2024
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Different from traditional deterministic optimization algorithms, we implement the sampling method to compute the conditional nonlinear optimal perturbations (CNOPs) in the realistic and predictive coupled ocean–atmosphere model, which reduces the first-order information to the zeroth-order one, avoiding the high-cost computation of the gradient. The numerical performance highlights the importance of stochastic optimization algorithms to compute CNOPs and capture initial optimal precursors.
David Docquier, Giorgia Di Capua, Reik V. Donner, Carlos A. L. Pires, Amélie Simon, and Stéphane Vannitsem
Nonlin. Processes Geophys., 31, 115–136, https://doi.org/10.5194/npg-31-115-2024, https://doi.org/10.5194/npg-31-115-2024, 2024
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Identifying causes of specific processes is crucial in order to better understand our climate system. Traditionally, correlation analyses have been used to identify cause–effect relationships in climate studies. However, correlation does not imply causation, which justifies the need to use causal methods. We compare two independent causal methods and show that these are superior to classical correlation analyses. We also find some interesting differences between the two methods.
Louis Le Toumelin, Isabelle Gouttevin, Clovis Galiez, and Nora Helbig
Nonlin. Processes Geophys., 31, 75–97, https://doi.org/10.5194/npg-31-75-2024, https://doi.org/10.5194/npg-31-75-2024, 2024
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Forecasting wind fields over mountains is of high importance for several applications and particularly for understanding how wind erodes and disperses snow. Forecasters rely on operational wind forecasts over mountains, which are currently only available on kilometric scales. These forecasts can also be affected by errors of diverse origins. Here we introduce a new strategy based on artificial intelligence to correct large-scale wind forecasts in mountains and increase their spatial resolution.
Florian Dupuy, Pierre Durand, and Thierry Hedde
Nonlin. Processes Geophys., 30, 553–570, https://doi.org/10.5194/npg-30-553-2023, https://doi.org/10.5194/npg-30-553-2023, 2023
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Forecasting near-surface winds over complex terrain requires high-resolution numerical weather prediction models, which drastically increase the duration of simulations and hinder them in running on a routine basis. A faster alternative is statistical downscaling. We explore different ways of calculating near-surface wind speed and direction using artificial intelligence algorithms based on various convolutional neural networks in order to find the best approach for wind downscaling.
Sofia Flora, Laura Ursella, and Achim Wirth
Nonlin. Processes Geophys., 30, 515–525, https://doi.org/10.5194/npg-30-515-2023, https://doi.org/10.5194/npg-30-515-2023, 2023
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An increasing amount of data allows us to move from low-order moments of fluctuating observations to their PDFs. We found the analytical fat-tailed PDF form (a combination of Gaussian and two-exponential convolutions) for 2 years of sea surface current increments in the Gulf of Trieste, using superstatistics and the maximum-entropy principle twice: on short and longer timescales. The data from different wind regimes follow the same analytical PDF, pointing towards a universal behaviour.
Tobias Sebastian Finn, Lucas Disson, Alban Farchi, Marc Bocquet, and Charlotte Durand
EGUsphere, https://doi.org/10.5194/egusphere-2023-2261, https://doi.org/10.5194/egusphere-2023-2261, 2023
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We train neural networks as denoising diffusion models for state generation in the Lorenz 1963 system and demonstrate that they learn an internal representation of the system. We make use of this learned representation and the pre-trained model in two downstream tasks: surrogate modelling and ensemble generation. For both tasks, the diffusion model can outperform other more common approaches. Thus, we see a potential of representation learning with diffusion models for dynamical systems.
Yicun Zhen, Valentin Resseguier, and Bertrand Chapron
Nonlin. Processes Geophys., 30, 237–251, https://doi.org/10.5194/npg-30-237-2023, https://doi.org/10.5194/npg-30-237-2023, 2023
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This paper provides perspective that the displacement vector field of physical state fields should be determined by the tensor fields associated with the physical fields. The advantage of this perspective is that certain physical quantities can be conserved while applying a displacement vector field to transfer the original physical field. A direct application of this perspective is the physically constrained covariance inflation scheme proposed in this paper.
Valérian Jacques-Dumas, René M. van Westen, Freddy Bouchet, and Henk A. Dijkstra
Nonlin. Processes Geophys., 30, 195–216, https://doi.org/10.5194/npg-30-195-2023, https://doi.org/10.5194/npg-30-195-2023, 2023
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Computing the probability of occurrence of rare events is relevant because of their high impact but also difficult due to the lack of data. Rare event algorithms are designed for that task, but their efficiency relies on a score function that is hard to compute. We compare four methods that compute this function from data and measure their performance to assess which one would be best suited to be applied to a climate model. We find neural networks to be most robust and flexible for this task.
Domenico Giaquinto, Warner Marzocchi, and Jürgen Kurths
Nonlin. Processes Geophys., 30, 167–181, https://doi.org/10.5194/npg-30-167-2023, https://doi.org/10.5194/npg-30-167-2023, 2023
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Despite being among the most severe climate extremes, it is still challenging to assess droughts’ features for specific regions. In this paper we study meteorological droughts in Europe using concepts derived from climate network theory. By exploring the synchronization in droughts occurrences across the continent we unveil regional clusters which are individually examined to identify droughts’ geographical propagation and source–sink systems, which could potentially support droughts’ forecast.
Scott Hottovy and Samuel N. Stechmann
Nonlin. Processes Geophys., 30, 85–100, https://doi.org/10.5194/npg-30-85-2023, https://doi.org/10.5194/npg-30-85-2023, 2023
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Rainfall is erratic and difficult to predict. Thus, random models are often used to describe rainfall events. Since many of these random models are based more on statistics than physical laws, it is desirable to develop connections between the random statistical models and the underlying physics of rain. Here, a physics-based model is shown to converge to a statistics-based model, which helps to provide a physical basis for the statistics-based model.
Joko Sampurno, Valentin Vallaeys, Randy Ardianto, and Emmanuel Hanert
Nonlin. Processes Geophys., 29, 301–315, https://doi.org/10.5194/npg-29-301-2022, https://doi.org/10.5194/npg-29-301-2022, 2022
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In this study, we successfully built and evaluated machine learning models for predicting water level dynamics as a proxy for compound flooding hazards in a data-scarce delta. The issues that we tackled here are data scarcity and low computational resources for building flood forecasting models. The proposed approach is suitable for use by local water management agencies in developing countries that encounter these issues.
Olivier Delage, Thierry Portafaix, Hassan Bencherif, Alain Bourdier, and Emma Lagracie
Nonlin. Processes Geophys., 29, 265–277, https://doi.org/10.5194/npg-29-265-2022, https://doi.org/10.5194/npg-29-265-2022, 2022
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The complexity of geophysics systems results in time series with fluctuations at all timescales. The analysis of their variability then consists in decomposing them into a set of basis signals. We developed here a new adaptive filtering method called empirical adaptive wavelet decomposition that optimizes the empirical-mode decomposition existing technique, overcoming its drawbacks using the rigour of wavelets as defined in the recently published empirical wavelet transform method.
Benjamin Walleshauser and Erik Bollt
Nonlin. Processes Geophys., 29, 255–264, https://doi.org/10.5194/npg-29-255-2022, https://doi.org/10.5194/npg-29-255-2022, 2022
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As sea surface temperature (SST) is vital for understanding the greater climate of the Earth and is also an important variable in weather prediction, we propose a model that effectively capitalizes on the reduced complexity of machine learning models while still being able to efficiently predict over a large spatial domain. We find that it is proficient at predicting the SST at specific locations as well as over the greater domain of the Earth’s oceans.
Valerio Lucarini, Larissa Serdukova, and Georgios Margazoglou
Nonlin. Processes Geophys., 29, 183–205, https://doi.org/10.5194/npg-29-183-2022, https://doi.org/10.5194/npg-29-183-2022, 2022
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In most of the investigations on metastable systems, the stochastic forcing is modulated by Gaussian noise. Lévy noise laws, which describe jump processes, have recently received a lot of attention, but much less is known. We study stochastic versions of the Ghil–Sellers energy balance model, and we highlight the fundamental difference between how transitions are performed between the competing warm and snowball states, depending on whether Gaussian or Lévy noise acts as forcing.
Raphael Kriegmair, Yvonne Ruckstuhl, Stephan Rasp, and George Craig
Nonlin. Processes Geophys., 29, 171–181, https://doi.org/10.5194/npg-29-171-2022, https://doi.org/10.5194/npg-29-171-2022, 2022
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Our regional numerical weather prediction models run at kilometer-scale resolutions. Processes that occur at smaller scales not yet resolved contribute significantly to the atmospheric flow. We use a neural network (NN) to represent the unresolved part of physical process such as cumulus clouds. We test this approach on a simplified, yet representative, 1D model and find that the NN corrections vastly improve the model forecast up to a couple of days.
Robert Polzin, Annette Müller, Henning Rust, Peter Névir, and Péter Koltai
Nonlin. Processes Geophys., 29, 37–52, https://doi.org/10.5194/npg-29-37-2022, https://doi.org/10.5194/npg-29-37-2022, 2022
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In this study, a recent algorithmic framework called Direct Bayesian Model Reduction (DBMR) is applied which provides a scalable probability-preserving identification of reduced models directly from data. The stochastic method is tested in a meteorological application towards a model reduction to latent states of smaller scale convective activity conditioned on large-scale atmospheric flow.
Justin Schulte, Frederick Policelli, and Benjamin Zaitchik
Nonlin. Processes Geophys., 29, 1–15, https://doi.org/10.5194/npg-29-1-2022, https://doi.org/10.5194/npg-29-1-2022, 2022
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The skewness of a time series is commonly used to quantify the extent to which positive (negative) deviations from the mean are larger than negative (positive) ones. However, in some cases, traditional skewness may not provide reliable information about time series skewness, motivating the development of a waveform skewness index in this paper. The waveform skewness index is used to show that changes in the relationship strength between climate time series could arise from changes in skewness.
Bo Christiansen
Nonlin. Processes Geophys., 28, 409–422, https://doi.org/10.5194/npg-28-409-2021, https://doi.org/10.5194/npg-28-409-2021, 2021
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In geophysics we often need to analyse large samples of high-dimensional fields. Fortunately but counterintuitively, such high dimensionality can be a blessing, and we demonstrate how this allows simple analytical results to be derived. These results include estimates of correlations between sample members and how the sample mean depends on the sample size. We show that the properties of high dimensionality with success can be applied to climate fields, such as those from ensemble modelling.
Achim Wirth and Bertrand Chapron
Nonlin. Processes Geophys., 28, 371–378, https://doi.org/10.5194/npg-28-371-2021, https://doi.org/10.5194/npg-28-371-2021, 2021
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In non-equilibrium statistical mechanics, which describes forced-dissipative systems such as air–sea interaction, there is no universal probability density function (pdf). Some such systems have recently been demonstrated to exhibit a symmetry called a fluctuation theorem (FT), which strongly constrains the shape of the pdf. Using satellite data, the mechanical power input to the ocean by air–sea interaction following or not a FT is questioned. A FT is found to apply over specific ocean regions.
Camille Besombes, Olivier Pannekoucke, Corentin Lapeyre, Benjamin Sanderson, and Olivier Thual
Nonlin. Processes Geophys., 28, 347–370, https://doi.org/10.5194/npg-28-347-2021, https://doi.org/10.5194/npg-28-347-2021, 2021
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This paper investigates the potential of a type of deep generative neural network to produce realistic weather situations when trained from the climate of a general circulation model. The generator represents the climate in a compact latent space. It is able to reproduce many aspects of the targeted multivariate distribution. Some properties of our method open new perspectives such as the exploration of the extremes close to a given state or how to connect two realistic weather states.
Gerd Schädler and Marcus Breil
Nonlin. Processes Geophys., 28, 231–245, https://doi.org/10.5194/npg-28-231-2021, https://doi.org/10.5194/npg-28-231-2021, 2021
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We used regional climate networks (RCNs) to identify past heatwaves and droughts in Germany. RCNs provide information for whole areas and can provide many details of extreme events. The RCNs were constructed on the grid of the E-OBS data set. Time series correlation was used to construct the networks. Network metrics were compared to standard extreme indices and differed considerably between normal and extreme years. The results show that RCNs can identify severe and moderate extremes.
Abhirup Banerjee, Bedartha Goswami, Yoshito Hirata, Deniz Eroglu, Bruno Merz, Jürgen Kurths, and Norbert Marwan
Nonlin. Processes Geophys., 28, 213–229, https://doi.org/10.5194/npg-28-213-2021, https://doi.org/10.5194/npg-28-213-2021, 2021
Jonathan M. Lilly and Paula Pérez-Brunius
Nonlin. Processes Geophys., 28, 181–212, https://doi.org/10.5194/npg-28-181-2021, https://doi.org/10.5194/npg-28-181-2021, 2021
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Long-lived eddies are an important part of the ocean circulation. Here a dataset for studying eddies in the Gulf of Mexico is created through the analysis of trajectories of drifting instruments. The method involves the identification of quasi-periodic signals, characteristic of particles trapped in eddies, from the displacement records, followed by the creation of a measure of statistical significance. It is expected that this dataset will be of use to other authors studying this region.
Pascal Wang, Daniele Castellana, and Henk A. Dijkstra
Nonlin. Processes Geophys., 28, 135–151, https://doi.org/10.5194/npg-28-135-2021, https://doi.org/10.5194/npg-28-135-2021, 2021
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This paper proposes two improvements to the use of Trajectory-Adaptive Multilevel Sampling, a rare-event algorithm which computes noise-induced transition probabilities. The first improvement uses locally linearised dynamics in order to reduce the arbitrariness associated with defining what constitutes a transition. The second improvement uses empirical transition paths accumulated at high noise in order to formulate the score function which determines the performance of the algorithm.
Cristian Lussana, Thomas N. Nipen, Ivar A. Seierstad, and Christoffer A. Elo
Nonlin. Processes Geophys., 28, 61–91, https://doi.org/10.5194/npg-28-61-2021, https://doi.org/10.5194/npg-28-61-2021, 2021
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An unprecedented amount of rainfall data is available nowadays, such as ensemble model output, weather radar estimates, and in situ observations from networks of both traditional and opportunistic sensors. Nevertheless, the exact amount of precipitation, to some extent, eludes our knowledge. The objective of our study is precipitation reconstruction through the combination of numerical model outputs with observations from multiple data sources.
Dylan Harries and Terence J. O'Kane
Nonlin. Processes Geophys., 27, 453–471, https://doi.org/10.5194/npg-27-453-2020, https://doi.org/10.5194/npg-27-453-2020, 2020
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Different dimension reduction methods may produce profoundly different low-dimensional representations of multiscale systems. We perform a set of case studies to investigate these differences. When a clear scale separation is present, similar bases are obtained using all methods, but when this is not the case some methods may produce representations that are poorly suited for describing features of interest, highlighting the importance of a careful choice of method when designing analyses.
Josh Jacobson, William Kleiber, Michael Scheuerer, and Joseph Bellier
Nonlin. Processes Geophys., 27, 411–427, https://doi.org/10.5194/npg-27-411-2020, https://doi.org/10.5194/npg-27-411-2020, 2020
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Most verification metrics for ensemble forecasts assess the representation of uncertainty at a particular location and time. We study a new diagnostic tool based on fractions of threshold exceedance (FTE) which evaluates an additional important attribute: the ability of ensemble forecast fields to reproduce the spatial structure of observed fields. The utility of this diagnostic tool is demonstrated through simulations and an application to ensemble precipitation forecasts.
Sebastian Lerch, Sándor Baran, Annette Möller, Jürgen Groß, Roman Schefzik, Stephan Hemri, and Maximiliane Graeter
Nonlin. Processes Geophys., 27, 349–371, https://doi.org/10.5194/npg-27-349-2020, https://doi.org/10.5194/npg-27-349-2020, 2020
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Accurate models of spatial, temporal, and inter-variable dependencies are of crucial importance for many practical applications. We review and compare several methods for multivariate ensemble post-processing, where such dependencies are imposed via copula functions. Our investigations utilize simulation studies that mimic challenges occurring in practical applications and allow ready interpretation of the effects of different misspecifications of the numerical weather prediction ensemble.
Jaqueline Lekscha and Reik V. Donner
Nonlin. Processes Geophys., 27, 261–275, https://doi.org/10.5194/npg-27-261-2020, https://doi.org/10.5194/npg-27-261-2020, 2020
Julian Steinheuer and Petra Friederichs
Nonlin. Processes Geophys., 27, 239–252, https://doi.org/10.5194/npg-27-239-2020, https://doi.org/10.5194/npg-27-239-2020, 2020
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Many applications require wind gust estimates at very different atmospheric altitudes, such as in the wind energy sector. However, numerical weather prediction models usually only derive estimates for gusts at 10 m above the land surface. We present a statistical model that gives the hourly peak wind speed. The model is trained based on a weather reanalysis and observations from the Hamburg Weather Mast. Reliable predictions are derived at up to 250 m, even at unobserved intermediate levels.
Moritz N. Lang, Sebastian Lerch, Georg J. Mayr, Thorsten Simon, Reto Stauffer, and Achim Zeileis
Nonlin. Processes Geophys., 27, 23–34, https://doi.org/10.5194/npg-27-23-2020, https://doi.org/10.5194/npg-27-23-2020, 2020
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Statistical post-processing aims to increase the predictive skill of probabilistic ensemble weather forecasts by learning the statistical relation between historical pairs of observations and ensemble forecasts within a given training data set. This study compares four different training schemes and shows that including multiple years of data in the training set typically yields a more stable post-processing while it loses the ability to quickly adjust to temporal changes in the underlying data.
Achim Wirth
Nonlin. Processes Geophys., 26, 457–477, https://doi.org/10.5194/npg-26-457-2019, https://doi.org/10.5194/npg-26-457-2019, 2019
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The conspicuous feature of the atmosphere–ocean system is the large difference in the masses of the two media. In this respect there is a strong analogy to Brownian motion, with light and fast molecules colliding with heavy and slow Brownian particles. I apply the tools of non-equilibrium statistical mechanics for studying Brownian motion to air–sea interaction.
Carsten Abraham, Amber M. Holdsworth, and Adam H. Monahan
Nonlin. Processes Geophys., 26, 401–427, https://doi.org/10.5194/npg-26-401-2019, https://doi.org/10.5194/npg-26-401-2019, 2019
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Atmospheric stably stratified boundary layers display transitions between regimes of sustained and intermittent turbulence. These transitions are not well represented in numerical weather prediction and climate models. A prototype explicitly stochastic turbulence parameterization simulating regime dynamics is presented and tested in an idealized model. Results demonstrate that the approach can improve the regime representation in models.
Jari-Pekka Nousu, Matthieu Lafaysse, Matthieu Vernay, Joseph Bellier, Guillaume Evin, and Bruno Joly
Nonlin. Processes Geophys., 26, 339–357, https://doi.org/10.5194/npg-26-339-2019, https://doi.org/10.5194/npg-26-339-2019, 2019
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Forecasting the height of new snow is crucial for avalanche hazard, road viability, ski resorts and tourism. The numerical models suffer from systematic and significant errors which are misleading for the final users. Here, we applied for the first time a state-of-the-art statistical method to correct ensemble numerical forecasts of the height of new snow from their statistical link with measurements in French Alps and Pyrenees. Thus the realism of automatic forecasts can be quickly improved.
Jürgen Kurths, Ankit Agarwal, Roopam Shukla, Norbert Marwan, Maheswaran Rathinasamy, Levke Caesar, Raghavan Krishnan, and Bruno Merz
Nonlin. Processes Geophys., 26, 251–266, https://doi.org/10.5194/npg-26-251-2019, https://doi.org/10.5194/npg-26-251-2019, 2019
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We examined the spatial diversity of Indian rainfall teleconnection at different timescales, first by identifying homogeneous communities and later by computing non-linear linkages between the identified communities (spatial regions) and dominant climatic patterns, represented by climatic indices such as El Nino–Southern Oscillation, Indian Ocean Dipole, North Atlantic Oscillation, Pacific Decadal Oscillation and Atlantic Multi-Decadal Oscillation.
Justin A. Schulte
Nonlin. Processes Geophys., 26, 91–108, https://doi.org/10.5194/npg-26-91-2019, https://doi.org/10.5194/npg-26-91-2019, 2019
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Statistical hypothesis tests in wavelet analysis are used to asses the likelihood that time series features are noise. The choice of test will determine which features emerge as a signal. Tests based on area do poorly at distinguishing abrupt fluctuations from periodic behavior, unlike tests based on arclength that do better. The application of the tests suggests that there are features in Indian rainfall time series that emerge from background noise.
Jonathan Demaeyer and Stéphane Vannitsem
Nonlin. Processes Geophys., 25, 605–631, https://doi.org/10.5194/npg-25-605-2018, https://doi.org/10.5194/npg-25-605-2018, 2018
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We investigate the modeling of the effects of the unresolved scales on the large scales of the coupled ocean–atmosphere model MAOOAM. Two different physically based stochastic methods are considered and compared, in various configurations of the model. Both methods show remarkable performances and are able to model fundamental changes in the model dynamics. Ways to improve the parameterizations' implementation are also proposed.
Adam H. Monahan
Nonlin. Processes Geophys., 25, 335–353, https://doi.org/10.5194/npg-25-335-2018, https://doi.org/10.5194/npg-25-335-2018, 2018
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Bivariate probability density functions (pdfs) of wind speed characterize the relationship between speeds at two different locations or times. This study develops such pdfs of wind speed from distributions of the components, following a well-established approach for univariate distributions. The ability of these models to characterize example observed datasets is assessed. The mathematical complexity of these models suggests further extensions of this line of reasoning may not be practical.
Berenice Rojo-Garibaldi, David Alberto Salas-de-León, María Adela Monreal-Gómez, Norma Leticia Sánchez-Santillán, and David Salas-Monreal
Nonlin. Processes Geophys., 25, 291–300, https://doi.org/10.5194/npg-25-291-2018, https://doi.org/10.5194/npg-25-291-2018, 2018
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Hurricanes are complex systems that carry large amounts of energy. Its impact produces, most of the time, natural disasters involving the loss of human lives and of materials and infrastructure that is accounted for in billions of US dollars. Not everything is negative as hurricanes are the main source of rainwater for the regions where they develop. In this study we make a nonlinear analysis of the time series obtained from 1749 to 2012 of the hurricane occurrence in the Gulf of Mexico.
Guillaume Lenoir and Michel Crucifix
Nonlin. Processes Geophys., 25, 145–173, https://doi.org/10.5194/npg-25-145-2018, https://doi.org/10.5194/npg-25-145-2018, 2018
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We develop a general framework for the frequency analysis of irregularly sampled time series. We also design a test of significance against a general background noise which encompasses the Gaussian white or red noise. Our results generalize and unify methods developed in the fields of geosciences, engineering, astronomy and astrophysics. All the analysis tools presented in this paper are available to the reader in the Python package WAVEPAL.
Guillaume Lenoir and Michel Crucifix
Nonlin. Processes Geophys., 25, 175–200, https://doi.org/10.5194/npg-25-175-2018, https://doi.org/10.5194/npg-25-175-2018, 2018
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There is so far no general framework for handling the continuous wavelet transform when the time sampling is irregular. Here we provide such a framework with the Morlet wavelet, based on the results of part I of this study. We also design a test of significance against a general background noise which encompasses the Gaussian white or red noise. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.
Valerie N. Livina, Albert Brouwer, Peter Harris, Lian Wang, Kostas Sotirakopoulos, and Stephen Robinson
Nonlin. Processes Geophys., 25, 89–97, https://doi.org/10.5194/npg-25-89-2018, https://doi.org/10.5194/npg-25-89-2018, 2018
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We have applied tipping point analysis to a large record of ocean acoustic data to identify the main components of the acoustic dynamical system: long-term and seasonal trends, system states and fluctuations. We reconstructed a one-dimensional stochastic model equation to approximate the acoustic dynamical system. We have found a signature of El Niño events in the deep ocean acoustic data near the southwest Australian coast, which proves the investigative power of the tipping point methodology.
Marc Bengulescu, Philippe Blanc, and Lucien Wald
Nonlin. Processes Geophys., 25, 19–37, https://doi.org/10.5194/npg-25-19-2018, https://doi.org/10.5194/npg-25-19-2018, 2018
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We employ the Hilbert–Huang transform to study the temporal variability in time series of daily means of the surface solar irradiance (SSI) at different locations around the world. The data have a significant spectral peak corresponding to the yearly variability cycle and feature quasi-stochastic high-frequency "weather noise", irrespective of the geographical location or of the local climate. Our findings can improve models for estimating SSI from satellite images or forecasts of the SSI.
Manfred Mudelsee and Miguel A. Bermejo
Nonlin. Processes Geophys., 24, 737–744, https://doi.org/10.5194/npg-24-737-2017, https://doi.org/10.5194/npg-24-737-2017, 2017
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Risk analysis of extremes has high socioeconomic relevance. Of crucial interest is the tail probability, P, of the distribution of a variable, which is the chance of observing a value equal to or greater than a certain threshold value, x. Many variables in geophysical systems (e.g. climate) show heavy tail behaviour, where P may be rather large. In particular, P decreases with x as a power law that is described by a parameter, α. We present an improved method to estimate α on data.
Kathrin Padberg-Gehle and Christiane Schneide
Nonlin. Processes Geophys., 24, 661–671, https://doi.org/10.5194/npg-24-661-2017, https://doi.org/10.5194/npg-24-661-2017, 2017
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Transport and mixing processes in fluid flows are crucially influenced by coherent structures, such as eddies, gyres, or jets in geophysical flows. We propose a very simple and computationally efficient approach for analyzing coherent behavior in fluid flows. The central object is a flow network constructed directly from particle trajectories. The network's local and spectral properties are shown to give a very good indication of coherent as well as mixing regions in the underlying flow.
Ankit Agarwal, Norbert Marwan, Maheswaran Rathinasamy, Bruno Merz, and Jürgen Kurths
Nonlin. Processes Geophys., 24, 599–611, https://doi.org/10.5194/npg-24-599-2017, https://doi.org/10.5194/npg-24-599-2017, 2017
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Extreme events such as floods and droughts result from synchronization of different natural processes working at multiple timescales. Investigation on an observation timescale will not reveal the inherent underlying dynamics triggering these events. This paper develops a new method based on wavelets and event synchronization to unravel the hidden dynamics responsible for such sudden events. This method is tested with synthetic and real-world cases and the results are promising.
Finn Müller-Hansen, Manoel F. Cardoso, Eloi L. Dalla-Nora, Jonathan F. Donges, Jobst Heitzig, Jürgen Kurths, and Kirsten Thonicke
Nonlin. Processes Geophys., 24, 113–123, https://doi.org/10.5194/npg-24-113-2017, https://doi.org/10.5194/npg-24-113-2017, 2017
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Deforestation and subsequent land uses in the Brazilian Amazon have huge impacts on greenhouse gas emissions, local climate and biodiversity. To better understand these land-cover changes, we apply complex systems methods uncovering spatial patterns in regional transition probabilities between land-cover types, which we estimate using maps derived from satellite imagery. The results show clusters of similar land-cover dynamics and thus complement studies at the local scale.
Jeroen Wouters, Stamen Iankov Dolaptchiev, Valerio Lucarini, and Ulrich Achatz
Nonlin. Processes Geophys., 23, 435–445, https://doi.org/10.5194/npg-23-435-2016, https://doi.org/10.5194/npg-23-435-2016, 2016
Cited articles
Abramowitz, M. and Stegun, I. A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Washington, D. C., 10th Edn., 1972.
Adler, R. J.: Hausdorff dimension and Gaussian fields, Ann. Probab., 5, 145–151, 1977.
Arató, M., Baran, S., and Ispány, M.: Functionals of complex Ornstein-Uhlenbeck processes, Comput. Math. Appl., 37, 1–13, 1999.
Baillie, R. T.: Long memory processes and fractional integration in econometrics, J. Econometrics, 73, 5–59, 1996.
Barton, R. J. and Poor, H. V.: Signal detection in fractional Gaussian noise, IEEE T. Inform. Theory, 34, 943–959, 1988.
Basset: A Treatise on Hydrodynamics, with Numerous Examples, Cambridge Univ. Press, 1888.
Bateman, H.: Tables of Integral Transforms, McGraw-Hill Book Company, Inc, 1954.
Beran, J.: Statistical methods for data with long-range dependence, Stat. Sci., 7, 404–416, 1992.
Beran, J.: Statistics for Long-Memory Processes, vol. 61 of Monographs on Statitics and Applied Probability, Chapman & Hall/CRC, 1994.
Berloff, P. and McWilliams, J.: Material transport in oceanic gyres. Part II: Hierarchy of stochastic models, J. Phys. Oceanogr., 32, 797–830, 2002.
Bracco, A. and McWilliams, J. C.: Reynolds-number dependency in homogeneous, stationary two-dimensional turbulence, J. Fluid Mech., 646, 517–526, 2010.
Cressie, N.: A graphical procedure for determining nonstationarity in time series, J. Acoust. Soc. Am., 83, 1108–1116, 1988.
Davis, R. E.: Oceanic property transport, Lagrangian particle statistics, and their prediction, J. Mar. Res., 41, 163–194, 1983.
Dietrich, C. R. and Newsam, G. N.: Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix, SIAM J. Sci. Comput., 18, 1088–1107, 1997.
Dritschel, D. G., Scott, R. K., Gottwald, G. A., and Tran, C. V.: Unifying scaling theory for vortex dynamics in two-dimensional turbulence, Phys. Rev. Lett., 101, 94–501, 2008.
Dunbar, S. R., Douglass, R. W., and Camp, W. J.: The divider dimension of the graph of a function, J. Math. Anal. Appl., 167, 403–413, 1992.
Elipot, S. and Lumpkin, R.: Spectral description of oceanic near-surface variability, Geophys. Res. Lett., 35, L05606, https://doi.org/10.1029/2007GL032874, 2008.
Emery, W. J. and Thomson, R. E.: Data Analysis Methods in Physical Oceanography, Elsevier, 3 Edn., 2014.
Falconer, K.: Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, 1990.
Flandrin, P.: On the spectrum of fractional Brownian motion, IEEE T. Inform. Theory, 35, 197–199, 1989.
Flandrin, P.: Time-Frequency/Time-Scale Analysis, Academic Press, San Diego, 1999.
Fofonoff, N. P.: Spectral characteristics of internal waves in the ocean, Deep-Sea Res., 16, 59–71, 1969.
Gneiting, T. and Schlather, M.: Stochastic models that separate fractal dimension and the Hurst effect, SIAM Rev., 46, 269–282, 2004.
Gneiting, T., Kleiber, W., and Schlather, M.: Matérn cross-covariance functions for multivariate random fields, J. Acoust. Soc. Am., 105, 1167–1177, 2010.
Goff, J. A. and Jordan, T. H.: Stochastic modeling of seafloor morphology: Inversion of sea beam data for second-order statistics, J. Geophys. Res., 93, 13589–13608, 1988.
Gonella, J.: A rotary-component method for analyzing meteorological and oceanographic vector time series, Deep-Sea Res., 19, 833–846, 1972.
Gorenflo, R. and Mainardi, F.: Fractals and Fractional Calculus in Continuum Mechanics, vol. 378 of CISM International Centre for Mechanical Sciences Series, chap. Fractional calculus: Integral and differential equations of fractional order, Springer-Verlag Wien, 223–276, 1997.
Gradshteyn, I. S. and Ryzhik, I. M.: The Table of Integrals, Series and Products, 6th Edn., Academic Press, 2000.
Gray, H. L., Zhang, N.-F., and Woodward, W. A.: On generalized fractional processes, J. Time Ser. Anal., 10, 233–257, 1989.
Griffa, A.: Stochastic Modelling in Physical Oceanography, chap. Applications of stochastic particle models to oceanographic problems, Springer, Boston, MA, 113–140, 1996.
Guttorp, P. and Gneiting, T.: Studies in the history of probability and statistics XLIX, On the Matérn correlation family, Biometrika, 93, 989–995, 2006.
Handcock, M. S. and Stein, M. L.: A Bayesian analysis of kriging, Technom, 35, 403–410, 1993.
Hanssen, A. and Scharf, L. L.: A theory of polyspectra for nonstationary stochastic processes, IEEE T. Signal Proces., 51, 1243–1252, 2003.
Hartikainen, J. and Särkkä, S.: Kalman filtering and smoothing solutions to temporal Gaussian process regression models, in: Proceedings of the IEEE International Workshop on Machine Learning for Signal Processing (MLSP), 2010.
Hedevang, E. and Schmiegel, J.: A Lévy based approach to random vector fields: with a view towards turbulence, Int. J. Nonlin. Sci. Num., 15, 411–435, 2014.
Hindberg, H. and Hanssen, A.: Generalized spectral coherences for complex-valued harmonizable processes, IEEE T. Signal Proces., 55, 2407–2413, 2007.
Hunt, G. A.: Random Fourier transforms, Trans. Amer. Math. Soc., 71, 38–69, 1951.
Jeffreys, H.: The variation of latitude, Mon. Not. R. Astron. Soc., 100, 139–155, 1942.
Kadoch, B., del Castillo-Negrete, D., Bos, W. J. T., and Schneider, K.: Lagrangian statistics and flow topology in forced two-dimensional turbulence, Phys. Rev. E, 83, 036314, https://doi.org/10.1103/PhysRevE.83.036314 , 2011.
Kampé de Fériet, J.: Les fonctions aléatoires stationnaires et la théorie statistique de la turbulence homogéne, Ann. Soc. Sci. Brux., 59, 145–194, 1939.
Kirkwood, J. G.: Quantum statistics of almost classical assemblies, Phys. Rep., 44, 31–37, 1933.
Koszalka, I. M. and LaCasce, J. H.: Lagrangian analysis by clustering, Ocean Dynam., 60, 957–972, 2010.
LaCasce, J. H.: Statistics from Lagrangian observations, Prog. Oceanogr., 77, 1–29, 2008.
Li, J.-Y., Lu, X., Li, M., and Chen, S.: Data simulation of Matérn type, WSEAS Transactions on Computers, 9, 696–705, 2010.
Lilly, J. M. and Gascard, J.-C.: Wavelet ridge diagnosis of time-varying elliptical signals with application to an oceanic eddy, Nonlin. Processes Geophys., 13, 467–483, https://doi.org/10.5194/npg-13-467-2006, 2006.
Lilly, J. M. and Olhede, S. C.: Wavelet ridge estimation of jointly modulated multivariate oscillations, in: 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems, and Computers, 452–456, 2009.
Lilly, J. M., Scott, R. K., and Olhede, S. C.: Extracting waves and vortices from Lagrangian trajectories, Geophys. Res. Lett., 38, 1–5, 2011.
Lim, S. C. and Eab, C. H.: Riemann-Liouville and Weyl fractional oscillator processes, Phys. Lett. A, 355, 87–93, 2006.
Lin, J.-T.: Relative dispersion in the enstrophy-cascading inertial range of homogeneous two-dimensional turbulence, J. Atmos. Sci., 29, 394–396, 1972.
Lindgren, F., Rue, H., and Lindström, J.: An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach, J. Roy. Stat. Soc. B Met., 73, 423–498, 2011.
Lumpkin, R. and Pazos, M.: Lagrangian Analysis and Prediction in Coastal and Ocean Processes, chap. Measuring surface currents with Surface Velocity Program drifters: the instrument, its data, and some recent results, Cambridge University Press, 39–67, 2007.
Ma, C.: The use of the variogram in the construction of stationary time series models, J. Appl. Probab., 41, 1093–1103, 2004.
Majda, A. J. and Gershgorin, B.: Elementary models for turbulent diffusion with complex physical features: eddy diffusivity, spectrum and intermittency, Philos. T. Roy. Soc. A, 371, 20120184, https://doi.org/10.1098/rsta.2012.0184, 2013.
Majda, A. J. and Kramer, P. R.: Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena, Phys. Rep., 1999.
Mandelbrot, B. B.: Self-affinity and fractal dimension, Phys. Scripta, 32, 257–260, 1985.
Mandelbrot, B. B. and Van Ness, J. W.: Fractional Brownian motions, fractional noises and applications, SIAM Rev., 10, 422–437, 1968.
Mandelbrot, B. B. and Wallis, J. R.: Computer experiments with fractional Gaussian noises: Part 3, mathematical appendix, Water Resour. Res., 5, 260–267, 1969.
Matérn, B.: Spatial variation: stochastic models and their applications to some problems in forest surveys and other sampling investigations, Meddelanden från Statens Skogsforskningsinstitut, 49, 1–144, 1960.
Matheron, G.: Principles of geostatistics, Econ. Geol., 58, 1246–1266, 1963.
McWilliams, J. C.: The vortices of two-dimensional turbulence, J. Fluid Mech., 219, 361–385, 1990a.
McWilliams, J. C.: The vortices of geostrophic turbulence, J. Fluid Mech., 219, 387–404, 1990b.
Metzner, P.: Transition path theory for Markov processes, PhD thesis, Freien Universität Berlin, available at: http://www.diss.fu-berlin.de/diss/servlets/MCRFileNodeServlet/FUDISS_derivate_000000003512/ (last access: 5 December 2015), 2007.
Molz, F. J., Liu, H. H., and Szulga, J.: Fractional Brownian motion and fractional Gaussian noise in subsurface hydrology: A review, presentation of fundamental properties, and extensions, Water Resour. Res., 33, 2273–2286, 1997.
Monin, A. S.: The structure of atmospheric turbulence, Theor. Probab. Appl., 3, 266–296, 1958.
Monin, A. S. and Yaglom, A. M.: Statistical Fluid Mechanics, Volume II: Mechanics of Turbulence, Dover Publications, Inc., 2007.
Mooers, C. N. K.: A technique for the cross spectrum analysis of pairs of complex-valued time series, with emphasis on properties of polarized components and rotational invariants, Deep-Sea Res., 20, 1129–1141, 1973.
Neeser, F. D. and Massey, J.: Proper complex random processes with applications to information theory, IEEE T. Inform. Theory, 39, 1293–1302, 1993.
Øigård, T. A., Hanssen, A., and Scharf, L. L.: Spectral correlations of fractional Brownian motion, Phys. Rev. E, 74, 1–6, 2006.
Osborne Jr., A. R., A. K., Provenzale, A., and Bergamasco, L.: Fractal drifter trajectories in the Kuroshio extension, Tellus, 41, 416–435, 1989.
Park, J., Vernon III, F. L., and Lindberg, C. R.: Frequency-dependent polarization analysis of high-frequency seismograms, J. Geophys. Res., 92, 12664–12674, 1987.
Pasquero, C., Provenzale, A., and Weiss, J. B.: Vortex statistics from Eulerian and Lagrangian time series, Phys. Rev. Lett., 89, 284–501, 2002.
Percival, D. B.: Exact simulation of complex-valued Gaussian stationary processes via circulant embedding, Signal Process., 86, 1470–1476, 2006.
Percival, D. B. and Walden, A. T.: Spectral Analysis for Physical Applications, Cambridge University Press, New York, 1993.
Picinbono, B. and Bondon, P.: Second-order statistics of complex-valued time series, IEEE T. Signal Proces., 45, 411–420, 1997.
Pollard, R. T. and Millard Jr., R.: Comparison between observed and simulated wind-generated inertial oscillations, Deep-Sea Res., 17, 813–821, 1970.
Qian, H.: Processes with Long-Range Correlations, chap. Fractional Brownian motion and fractional Gaussian noise, Springer, 22–33, 2003.
Rihaczek, A. W.: Signal energy distribution in time and frequency, IEEE T. Inform. Theory, 14, 369–374, 1968.
Rogers, L. C. G.: Arbitrage with fractional Brownian motion, Math. Financ., 7, 95–105, 1997.
Rossby, H. T.: Lagrangian Analysis and Prediction in Coastal and Ocean Processes, chap. Evolution of Lagrangian methods in oceanography, Cambridge University Press, 1–38, 2007.
Rupolo, V., Artalea, V., Huab, B. L., and Provenzale, A.: Lagrangian velocity spectra at 700 m in the western North Atlantic, J. Phys. Oceanogr., 26, 1591–1607, 1996.
Sanderson, B. G. and Booth, D. A.: The fractal dimension of drifter trajectories and estimates of horizontal eddy-diffusivity, Tellus, 43, 334–349, 1991.
Sanderson, B. G., Goulding, A., and Okubo, A.: The fractal dimension of relative Lagrangian motion, Tellus, 42, 550–556, 1990.
Sawford, B. L.: Rotation of trajectories in Lagrangian stochastic models of turbulent dispersion, Bound.-Lay. Meteorol., 93, 411–424, 1999.
Schlather, M.: Advances and Challenges in Space-time Modelling of Natural Events, vol. 207 of Lecture Notes in Statistics, chap. Construction of covariance functions and unconditional simulation of random fields, Springer Berlin Heidelberg, 25–54, 2012.
Schreier, P. J. and Scharf, L. L.: Stochastic time-frequency analysis using the analytic signal: why the complementary distribution matters, IEEE T. Signal Proces., 51, 3071–3079, 2003.
Scott, R. K. and Dritschel, D. G.: Halting scale and energy equilibration in two-dimensional quasigeostrophic turbulence, J. Fluid Mech., 721, 1–12, 2013.
Slepian, D.: Prolate spheriodal wave functions, Fourier analysis, and uncertainty– V: The discrete case, Bell Syst. Tech. J., 57, 1371–1430, 1978.
Solo, V.: Intrinsic random functions and the paradox of l/f noise, SIAM J. Appl. Math., 52, 270–291, 1992.
Summers, D. M.: Impulse exchange at the surface of the ocean and the fractal dimension of drifter trajectories, Nonlin. Processes Geophys., 9, 11–23, https://doi.org/10.5194/npg-9-11-2002, 2002.
Sykulski, A. M., Olhede, S. C., Lilly, J. M., and Danioux, E.: Lagrangian time series models for ocean surface drifter trajectories, J. Roy. Stat. Soc. C App., 65, 29–50, 2016a.
Sykulski, A. M., Olhede, S. C., Lilly, J. M., and Early, J. J.: The Whittle likelihood for complex-valued time series, http://arxiv.org/pdf/1605.06718, in revision, 2016b.
Sykulski, A. M., Olhede, S. C., Lilly, J. M., and Early, J. J.: Frequency-domain stochastic modeling of stationary bivariate or complex-valued signals, IEEE T. Signal Proces., 65, 3136–3151, 2017.
Taylor, C. C. and Taylor, S. J.: Estimating the dimension of a fractal, J. Roy. Stat. Soc. B Met., 353–364, 1991.
Taylor, G. I.: Diffusion by continuous movements, P. Lond. Math. Soc., 20, 196–212, 1921.
Thomson, D. J.: Spectrum estimation and harmonic analysis, Proc. IEEE, 70, 1055–1096, 1982.
Uhlenbeck, G. E. and Ornstein, L. S.: On the theory of the Brownian motion, Phys. Rep., 36, 823–841, 1930.
Vallis, G. K.: Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation, Cambridge University Press, 2006.
Veneziani, M., Griffa, A., Garraffo, Z., and Chassignet, E.: Lagrangian spin parameter and coherent structures from trajectories released in a high-resolution ocean model, J. Mar. Res., 63, 753–788, 2005a.
Veneziani, M., Griffa, A., Reynolds, A. M., Garraffo, Z. D., and Chassignet, E. P.: Parameterizations of Lagrangian spin statistics and particle dispersion in the presence of coherent vortices, J. Mar. Res., 63, 1057–1083, 2005b.
Von Karman, T.: Progress in the statistical theory of turbulence, P. Natl. Acad. Sci. USA, 34, 530–539, 1948.
Watson, G. N.: A Treatise on the Theory of Bessel Functions, Cambridge Univ. Press, 1922.
Weiss, J. B., Provenzale, A., and McWilliams, J. C.: Lagrangian dynamics in high-dimensional point-vortex systems, Phys. Fluids, 10, 1929–1941, 1998.
Whittle, P.: Estimation and information in stationary time series, Ark. Mat., 2, 423–434, 1953.
Wolpert, R. L. and Taqqu, M. S.: Fractional Ornstein-Uhlenbeck Lévy processes and the telecom process: upstairs and downstairs, Signal Process., 85, 1523–1545, 2005.
Wong, R.: Error bounds for asymptotic expansions of integrals, SIAM Rev., 22, 401–435, 1980.
Yagle, A. E. and Levy, B. C.: The Schur algorithm and its applications, Acta Appl. Math., 3, 255–284, 1985.
Short summary
This work arose from a desire to understand the nature of particle motions in turbulence. We sought a simple conceptual model that could describe such motions, then realized that this model could be applicable to an array of other problems. The basic idea is to create a string of random numbers, called a stochastic process, that mimics the properties of particle trajectories. This model could be useful in making best use of data from freely drifting instruments tracking the ocean currents.
This work arose from a desire to understand the nature of particle motions in turbulence. We...
