Articles | Volume 22, issue 2
https://doi.org/10.5194/npg-22-139-2015
© Author(s) 2015. 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-22-139-2015
© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
10 Mar 2015
Research article |
| 10 Mar 2015
Geometric and topological approaches to significance testing in wavelet analysis
J. A. Schulte
CORRESPONDING AUTHOR
Department of Meteorology, Pennsylvania State University, University Park, Pennsylvania, USA
Department of Civil Engineering, Pennsylvania State University, University Park, Pennsylvania, USA
R. G. Najjar
Department of Meteorology, Pennsylvania State University, University Park, Pennsylvania, USA
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Justin Schulte, Frederick Policielli, and Benjamin Zaitchik
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Wavelet coherence is now a commonly used method for detecting scale-dependent relationships between time series. In this study, the concept of wavelet coherence is generalized to higher-order wavelet coherence methods that quantify the relationship between higher-order statistical moments associated with two time series. The methods are applied to the El Niño–Southern Oscillation (ENSO) and the Indian monsoon to show that the ENSO–Indian monsoon relationship is impacted by ENSO nonlinearity.
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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.
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Connections between Long Island Sound (LIS) water temperature variability and modes of tropical sea surface temperature (SST) variability have yet to be explored. It is shown that intense LIS cold-water temperature events are related to central equatorial Pacific SSTs. The decay phase of such events may be related to canonical El Niño events. Furthermore, a ridge–trough atmospheric pattern related to LIS water temperature variability fluctuates coherently with central equatorial Pacific SSTs.
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The paper presents a new method called cumulative areawise testing that allows scientists to better extract important signals from geophysical time series. The method was found to be able to distinguish aspects of time series that are random from those of potential physical importance better than existing methods in wavelet analysis.
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Robert Ladwig, Paul C. Hanson, Hilary A. Dugan, Cayelan C. Carey, Yu Zhang, Lele Shu, Christopher J. Duffy, and Kelly M. Cobourn
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Using a modeling framework applied to 37 years of dissolved oxygen time series data from Lake Mendota, we identified the timing and intensity of thermal energy stored in the lake water column, the lake's resilience to mixing, and surface primary production as the most important drivers of interannual dynamics of low oxygen concentrations at the lake bottom. Due to climate change, we expect an increase in the spatial and temporal extent of low oxygen concentrations in Lake Mendota.
Justin Schulte, Frederick Policielli, and Benjamin Zaitchik
Hydrol. Earth Syst. Sci., 24, 5473–5489, https://doi.org/10.5194/hess-24-5473-2020, https://doi.org/10.5194/hess-24-5473-2020, 2020
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Wavelet coherence is now a commonly used method for detecting scale-dependent relationships between time series. In this study, the concept of wavelet coherence is generalized to higher-order wavelet coherence methods that quantify the relationship between higher-order statistical moments associated with two time series. The methods are applied to the El Niño–Southern Oscillation (ENSO) and the Indian monsoon to show that the ENSO–Indian monsoon relationship is impacted by ENSO nonlinearity.
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Over the past century, estuaries have experienced global (atmospheric CO2 concentrations and temperature) and regional changes (river inputs, land use), but their relative impact remains poorly known. In the Chesapeake Bay, we find that global and regional changes have worked together to enhance how much atmospheric CO2 is taken up by the estuary. The increased uptake is roughly equally due to the global and regional changes, providing crucial perspective for managers of the bay's watershed.
Lele Shu, Paul A. Ullrich, and Christopher J. Duffy
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Justin A. Schulte
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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.
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Justin A. Schulte and Sukyoung Lee
Ocean Sci., 15, 161–178, https://doi.org/10.5194/os-15-161-2019, https://doi.org/10.5194/os-15-161-2019, 2019
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The Ocean Model Intercomparison Project (OMIP) is a model comparison effort under Phase 6 of the Coupled Model Intercomparison Project (CMIP6). Its physical component is described elsewhere in this special issue. Here we describe its ocean biogeochemical component (OMIP-BGC), detailing simulation protocols and analysis diagnostics. Simulations focus on ocean carbon, other biogeochemical tracers, air-sea exchange of CO2 and related gases, and chemical tracers used to evaluate modeled circulation.
Justin A. Schulte
Nonlin. Processes Geophys., 23, 257–267, https://doi.org/10.5194/npg-23-257-2016, https://doi.org/10.5194/npg-23-257-2016, 2016
Justin A. Schulte
Nonlin. Processes Geophys., 23, 45–57, https://doi.org/10.5194/npg-23-45-2016, https://doi.org/10.5194/npg-23-45-2016, 2016
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The paper presents a new method called cumulative areawise testing that allows scientists to better extract important signals from geophysical time series. The method was found to be able to distinguish aspects of time series that are random from those of potential physical importance better than existing methods in wavelet analysis.
Related subject area
Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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Bin Shi and Junjie Ma
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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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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.
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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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.
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