Articles | Volume 25, issue 1
https://doi.org/10.5194/npg-25-145-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-25-145-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
05 Mar 2018
Research article |
| 05 Mar 2018
| 05 Mar 2018
A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 1: Frequency analysis
Guillaume Lenoir
CORRESPONDING AUTHOR
Georges Lemaître Centre for Earth and Climate Research, Earth and Life Institute, Université catholique de Louvain, 1348, Louvain-la-Neuve, Belgium
Michel Crucifix
Georges Lemaître Centre for Earth and Climate Research, Earth and Life Institute, Université catholique de Louvain, 1348, Louvain-la-Neuve, Belgium
Belgian National Fund of Scientific Research, rue d'Egmont, 5, 1000 Brussels, Belgium
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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.
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Lilian Vanderveken, Marina Martínez Montero, and Michel Crucifix
Nonlin. Processes Geophys., 30, 585–599, https://doi.org/10.5194/npg-30-585-2023, https://doi.org/10.5194/npg-30-585-2023, 2023
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Mikhail Y. Verbitsky and Michel Crucifix
Earth Syst. Dynam., 12, 63–67, https://doi.org/10.5194/esd-12-63-2021, https://doi.org/10.5194/esd-12-63-2021, 2021
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Mikhail Y. Verbitsky and Michel Crucifix
Earth Syst. Dynam., 11, 281–289, https://doi.org/10.5194/esd-11-281-2020, https://doi.org/10.5194/esd-11-281-2020, 2020
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Mikhail Y. Verbitsky, Michel Crucifix, and Dmitry M. Volobuev
Earth Syst. Dynam., 10, 257–260, https://doi.org/10.5194/esd-10-257-2019, https://doi.org/10.5194/esd-10-257-2019, 2019
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We demonstrate here that nonlinear character of ice sheet dynamics, which was derived naturally from the conservation laws, is an effective means for propagating high-frequency forcing upscale.
Mikhail Y. Verbitsky, Michel Crucifix, and Dmitry M. Volobuev
Earth Syst. Dynam., 9, 1025–1043, https://doi.org/10.5194/esd-9-1025-2018, https://doi.org/10.5194/esd-9-1025-2018, 2018
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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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Paul J. Valdes, Edward Armstrong, Marcus P. S. Badger, Catherine D. Bradshaw, Fran Bragg, Michel Crucifix, Taraka Davies-Barnard, Jonathan J. Day, Alex Farnsworth, Chris Gordon, Peter O. Hopcroft, Alan T. Kennedy, Natalie S. Lord, Dan J. Lunt, Alice Marzocchi, Louise M. Parry, Vicky Pope, William H. G. Roberts, Emma J. Stone, Gregory J. L. Tourte, and Jonny H. T. Williams
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N. Bounceur, M. Crucifix, and R. D. Wilkinson
Earth Syst. Dynam., 6, 205–224, https://doi.org/10.5194/esd-6-205-2015, https://doi.org/10.5194/esd-6-205-2015, 2015
P. A. Araya-Melo, M. Crucifix, and N. Bounceur
Clim. Past, 11, 45–61, https://doi.org/10.5194/cp-11-45-2015, https://doi.org/10.5194/cp-11-45-2015, 2015
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By using a statistical tool termed emulator, we study the sensitivity of the Indian monsoon during the the Pleistocene. The originality of the present work is to consider, as inputs, several elements of the climate forcing that have varied in the past, and then use the emulator as a method to quantify the link between forcing variability and climate variability. The methodology described here may naturally be applied to other regions of interest.
Q. Z. Yin, U. K. Singh, A. Berger, Z. T. Guo, and M. Crucifix
Clim. Past, 10, 1645–1657, https://doi.org/10.5194/cp-10-1645-2014, https://doi.org/10.5194/cp-10-1645-2014, 2014
M. N. A. Maris, B. de Boer, S. R. M. Ligtenberg, M. Crucifix, W. J. van de Berg, and J. Oerlemans
The Cryosphere, 8, 1347–1360, https://doi.org/10.5194/tc-8-1347-2014, https://doi.org/10.5194/tc-8-1347-2014, 2014
M. Crucifix
Clim. Past, 9, 2253–2267, https://doi.org/10.5194/cp-9-2253-2013, https://doi.org/10.5194/cp-9-2253-2013, 2013
Related subject area
Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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The Sampling Method for Optimal Precursors of ENSO Event
Physically constrained covariance inflation from location uncertainty
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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.
Bin Shi and Junjie Ma
EGUsphere, https://doi.org/10.5194/egusphere-2023-2092, https://doi.org/10.5194/egusphere-2023-2092, 2023
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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, 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.
Jonathan M. Lilly, Adam M. Sykulski, Jeffrey J. Early, and Sofia C. Olhede
Nonlin. Processes Geophys., 24, 481–514, https://doi.org/10.5194/npg-24-481-2017, https://doi.org/10.5194/npg-24-481-2017, 2017
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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.
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
Katrin Sedlmeier, Sebastian Mieruch, Gerd Schädler, and Christoph Kottmeier
Nonlin. Processes Geophys., 23, 375–390, https://doi.org/10.5194/npg-23-375-2016, https://doi.org/10.5194/npg-23-375-2016, 2016
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Compound extreme events (e.g., simultaneous occurrence of hot and dry days) are likely to have a big impact on society. In our paper, we propose a new method to analyze the temporal succession of compound extreme events, an aspect that has been largely neglected so far. We analyze past and future changes and identify regions within Europe, which are probably susceptible to a future change in the succession of heavy precipitation and cold days in winter and hot and dry days in summer.
Sri Lakshmi Sunkara and Rama Krishna Tiwari
Nonlin. Processes Geophys., 23, 361–374, https://doi.org/10.5194/npg-23-361-2016, https://doi.org/10.5194/npg-23-361-2016, 2016
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This paper presents a new spectral approach to identifying the periodic patterns from the published Indian temperature variability records. The wavelet analysis of the SSA reconstructed time series highlights the removal of noise in the data and identifies the existence of a high-amplitude, recurrent, multidecadal scale patterns in the Indian continent, confirming the possible influences of sunspot-geomagnetic activity-ENSO through teleconnection.
Michael Weimer, Sebastian Mieruch, Gerd Schädler, and Christoph Kottmeier
Nonlin. Processes Geophys., 23, 307–317, https://doi.org/10.5194/npg-23-307-2016, https://doi.org/10.5194/npg-23-307-2016, 2016
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This paper is the first time that a complex network approach has been used for analysis of decadal climate predictions. We have developed an alternative estimator of heat periods based on network statistics, which turns out to be superior for parts of Europe. This paper opens the perspective that network measures have the potential to improve decadal predictions.
Cited articles
Akaike, H.: A new look at the statistical model identification, IEEE T.
Automat. Contr., 19, 716–723, https://doi.org/10.1109/TAC.1974.1100705, 1974. a
Bretthorst, L.: Nonuniform Sampling: Bandwidth and Aliasing, in: AIP
Conference Proceedings – Bayesian Inference and Maximum Entropy Methods in
Science and Engineering, edited by: Rychert, J., Gary, E., and Smith, R.,
vol. 567, 1–28, Boise, Idaho, USA, https://doi.org/10.1063/1.1381847,
1999. a
Brockwell, P. and Davis, R.: Introduction to Time Series and Forecasting,
Springer Texts in Statistics, Third edn., Springer International Publishing, https://doi.org/10.1007/978-3-319-29854-2, 2016. a, b, c, d
Bronez, T.: Spectral estimation of irregularly sampled multidimensional
processes by generalized prolate spheroidal sequences, IEEE T. Acoust.
Speech, 36, 1862–1873, https://doi.org/10.1109/29.9031, 1988. a
Ferraz-Mello, S.: Estimation of Periods from Unequally Spaced Observations,
Astron. J., 86, 619–624, https://doi.org/10.1086/112924, 1981. a, b, c, d
Fodor, I. and Stark, P.: Multitaper spectrum estimation for time series with
gaps, IEEE T. Signal Proces., 48, 3472–3483,
https://doi.org/10.1109/78.887039, 2000. a
Ghil, M., Allen, M. R., Dettinger, M. D., Ide, K., Kondrashov, D., Mann, M. E.,
Robertson, A. W., Saunders, A., Tian, Y., Varadi, F., and Yiou, P.: Advanced
spectral methods for climatic time series, Rev. Geophys., 40, 1003,
https://doi.org/10.1029/2000RG000092, 2002. a
Harris, F.: On the use of windows for harmonic analysis with the discrete
Fourier transform, Proceedings of the IEEE, 66, 51–83,
https://doi.org/10.1109/PROC.1978.10837, 1978. a, b
Hasselmann, K.: Stochastic climate models Part I. Theory, Tellus, 28,
473–485, https://doi.org/10.1111/j.2153-3490.1976.tb00696.x, 1976. a, b
Jeffreys, H.: An Invariant Form for the Prior Probability in Estimation
Problems, P. Roy. Soc. Lond. A Mat., 186, 453–461,
https://doi.org/10.1098/rspa.1946.0056,
1946. a
Jian, Z., Zhao, Q., Cheng, X., Wang, J., Wang, P., and Su, X.:
Pliocene-Pleistocene stable isotope and paleoceanographic changes in the
northern South China Sea, Palaeogeogr. Palaeocl., 193, 425–442,
https://doi.org/10.1016/S0031-0182(03)00259-1, 2003. a
Jones, R. and Ackerson, L.: Serial correlation in unequally spaced longitudinal
data, Biometrika, 77, 721–731, https://doi.org/10.1093/biomet/77.4.721,
1990. a
Kelly, B., Becker, A., Sobolewska, M., Siemiginowska, A., and Uttley, P.:
Flexible and Scalable Methods for Quantifying Stochastic Variability in the
Era of Massive Time-domain Astronomical Data Sets, Astrophys. J.,
788, 33, https://doi.org/10.1088/0004-637X/788/1/33, 2014. a, b, c, d, e, f, g, h, i
Kemp, D.: Optimizing significance testing of astronomical forcing in
cyclostratigraphy, Paleoceanography, 31, 1516–1531, https://doi.org/10.1002/2016PA002963,
2016. a
Lenoir, G.: Time-frequency analysis of regularly and irregularly sampled time
series: Projection and multitaper methods, PhD thesis, Université
catholique de Louvain – Faculté des Sciences – Georges Lemaître
Centre for Earth and Climate Research, Louvain-la-Neuve, Belgium, available
at: https://dial.uclouvain.be/pr/boreal/object/boreal:191751 (last
access: 22 February 2018), 2017. a
Lenoir, G. and Crucifix, M.: 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, Nonlin.
Processes Geophys., 25, 175–200, https://doi.org/10.5194/npg-25-175-2018, 2018. a, b, c, d, e, f
Lomb, N.: Least-squares frequency analysis of unequally spaced data,
Astrophys. Space Sci., 39, 447–462, https://doi.org/10.1007/BF00648343, 1976. a, b
Mortier, A., Faria, J. P., Correia, C. M., Santerne, A., and Santos, N. C.:
BGLS: A Bayesian formalism for the generalised Lomb-Scargle
periodogram, Astron. Astrophys., 573, A101,
https://doi.org/10.1051/0004-6361/201424908, 2015. a
Mudelsee, M., Scholz, D., Röthlisberger, R., Fleitmann, D., Mangini, A.,
and Wolff, E. W.: Climate spectrum estimation in the presence of timescale
errors, Nonlin. Processes Geophys., 16, 43–56,
https://doi.org/10.5194/npg-16-43-2009, 2009. a
Pardo Igúzquiza, E. and Rodríguez Tovar, F.: Spectral and
cross-spectral analysis of uneven time series with the smoothed
Lomb-Scargle periodogram and Monte Carlo evaluation of statistical
significance, Comput. Geosci., 49, 207–216,
https://doi.org/10.1016/j.cageo.2012.06.018, 2012. a
Provost, S.: Moment-Based Density Approximants, The Mathematica Journal, 9,
727–756, available at: http://www.mathematica-journal.com/issue/v9i4/DensityApproximants.html (last access: 22 February 2018), 2005. a
Rehfeld, K., Marwan, N., Heitzig, J., and Kurths, J.: Comparison of
correlation analysis techniques for irregularly sampled time series, Nonlin.
Processes Geophys., 18, 389–404, https://doi.org/10.5194/npg-18-389-2011,
2011. a
Riedel, K. and Sidorenko, A.: Minimum bias multiple taper spectral estimation,
IEEE T. Signal Proces., 43, 188–195,
https://doi.org/10.1109/78.365298, 1995. a, b
Robinson, P.: Estimation of a time series model from unequally spaced data,
Stoch. Proc. Appl., 6, 9–24, https://doi.org/10.1016/0304-4149(77)90013-8, 1977. a
Schulz, M. and Mudelsee, M.: REDFIT: estimating red-noise spectra directly
from unevenly spaced paleoclimatic time series, Comput. Geosci., 28,
421–426, https://doi.org/10.1016/S0098-3004(01)00044-9, 2002. a, b, c, d
Schulz, M. and Stattegger, K.: SPECTRUM: spectral analysis of unevenly spaced
paleoclimatic time series, Comput. Geosci., 23, 929–945,
https://doi.org/10.1016/S0098-3004(97)00087-3, 1997. a, b, c, d
Stacy, E. W. and Mihram, G. A.: Parameter Estimation for a Generalized Gamma
Distribution, Technometrics, 7, 349–358,
https://doi.org/10.1080/00401706.1965.10490268, 1965.
a, b
Thomson, D.: Spectrum estimation and harmonic analysis, Proceedings of the
IEEE, 70, 1055–1096, https://doi.org/10.1109/PROC.1982.12433, 1982. a, b
Torrence, C. and Compo, G.: A Practical Guide to Wavelet Analysis, B. Am.
Meteorol. Soc., 79, 61–78,
https://doi.org/10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2, 1998. a
Torrésani, B.: Analyse continue par ondelettes, Savoirs actuels/Série
physique, CNRS Editions and EDP Sciences, Paris, France, 1995. a
Uhlenbeck, G. E. and Ornstein, L. S.: On the Theory of the Brownian Motion,
Phys. Rev., 36, 823–841, https://doi.org/10.1103/PhysRev.36.823, 1930. a
Vio, R., Andreani, P., and Biggs, A.: Unevenly-sampled signals: a general
formalism for the Lomb-Scargle periodogram, Astron. Astrophys.,
519, A85, https://doi.org/10.1051/0004-6361/201014079, 2010. a
Walden, A. T.: A unified view of multitaper multivariate spectral estimation,
Biometrika, 87, 767–788, https://doi.org/10.1093/biomet/87.4.767,
2000. a, b
Welch, P.: The use of fast Fourier transform for the estimation of power
spectra: A method based on time averaging over short, modified periodograms,
IEEE T. Acoust. Speech, 15, 70–73,
https://doi.org/10.1109/TAU.1967.1161901, 1967. a, b, c
Zechmeister, M. and Kürster, M.: The generalised Lomb-Scargle
periodogram, Astron. Astrophys., 496, 577–584,
https://doi.org/10.1051/0004-6361:200811296, 2009. a
Short summary
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.
We develop a general framework for the frequency analysis of irregularly sampled time series. We...
