Articles | Volume 23, issue 4
https://doi.org/10.5194/npg-23-257-2016
© Author(s) 2016. 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-23-257-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
09 Aug 2016
Research article |
| 09 Aug 2016
Wavelet analysis for non-stationary, nonlinear time series
Justin A. Schulte
CORRESPONDING AUTHOR
The Pennsylvania State University, University Park, Pennsylvania 16802, USA
Related authors
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
J. A. Schulte, C. Duffy, and R. G. Najjar
Nonlin. Processes Geophys., 22, 139–156, https://doi.org/10.5194/npg-22-139-2015, https://doi.org/10.5194/npg-22-139-2015, 2015
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
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
Short summary
Short summary
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.
J. A. Schulte, C. Duffy, and R. G. Najjar
Nonlin. Processes Geophys., 22, 139–156, https://doi.org/10.5194/npg-22-139-2015, https://doi.org/10.5194/npg-22-139-2015, 2015
Related subject area
Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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
Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion
A matrix clustering method to explore patterns of land-cover transitions in satellite-derived maps of the Brazilian Amazon
Parameterization of stochastic multiscale triads
Compound extremes in a changing climate – a Markov chain approach
Wavelet analysis of the singular spectral reconstructed time series to study the imprints of solar–ENSO–geomagnetic activity on Indian climate
A new estimator of heat periods for decadal climate predictions – a complex network approach
Brief Communication: Breeding vectors in the phase space reconstructed from time series data
Transition process of abrupt climate change based on global sea surface temperature over the past century
Cumulative areawise testing in wavelet analysis and its application to geophysical time series
A sequential Bayesian approach for the estimation of the age–depth relationship of the Dome Fuji ice core
Artificial neural networks and multiple linear regression model using principal components to estimate rainfall over South America
Efficient Bayesian inference for natural time series using ARFIMA processes
Review: visual analytics of climate networks
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
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.
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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
Short summary
Short summary
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.
Erin Lynch, Daniel Kaufman, A. Surjalal Sharma, Eugenia Kalnay, and Kayo Ide
Nonlin. Processes Geophys., 23, 137–141, https://doi.org/10.5194/npg-23-137-2016, https://doi.org/10.5194/npg-23-137-2016, 2016
Short summary
Short summary
In this article, bred vectors are computed from a single time series data using time-delay embedding, with a new technique, nearest-neighbor breeding. Since the dynamical properties of the nearest-neighbor bred vectors are shown to be similar to bred vectors computed using evolution equations, this provides a new and novel way to model and predict sudden transitions in systems represented by time series data alone.
Pengcheng Yan, Wei Hou, and Guolin Feng
Nonlin. Processes Geophys., 23, 115–126, https://doi.org/10.5194/npg-23-115-2016, https://doi.org/10.5194/npg-23-115-2016, 2016
Short summary
Short summary
In the previous work (Yan et al., 2015, NPG), we proposed a novel method to detect the transition process of climate change and exposed a new understanding of climate change. In this work, by using this method, we studied several climate changes of the sea surface temperature over the past century. The result shows that the system is bi-stable, and the persist time of transition process is shortened. Besides, a quantitative relation among the transition process parameters is obtained and verified.
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
Short summary
Short summary
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.
Shin'ya Nakano, Kazue Suzuki, Kenji Kawamura, Frédéric Parrenin, and Tomoyuki Higuchi
Nonlin. Processes Geophys., 23, 31–44, https://doi.org/10.5194/npg-23-31-2016, https://doi.org/10.5194/npg-23-31-2016, 2016
Short summary
Short summary
This paper proposes a technique for dating an ice core. The proposed technique employs a hybrid method combining the sequential Monte Carlo method and the Markov chain Monte Carlo method, which is referred to as the particle Markov chain Monte Carlo method. The sequential Monte Carlo method, which is also known as the particle filter, is widely used for nonlinear time-series analysis. This paper demonstrates the usefulness of the approach in time-series analysis for dating an ice core.
T. Soares dos Santos, D. Mendes, and R. Rodrigues Torres
Nonlin. Processes Geophys., 23, 13–20, https://doi.org/10.5194/npg-23-13-2016, https://doi.org/10.5194/npg-23-13-2016, 2016
Short summary
Short summary
Statistical downscaling is widely used in large operational centers around the world, using exclusively linear relations (MLR); this study uses a statistical downscaling methodology using a nonlinear technique known as ANNs with CMIP5 project data. The artificial neural network can perform tasks that a linear program cannot. The main advantages of this are its temporal processing ability and its ability to incorporate several preceding predictor values as input without any additional effort.
T. Graves, R. B. Gramacy, C. L. E. Franzke, and N. W. Watkins
Nonlin. Processes Geophys., 22, 679–700, https://doi.org/10.5194/npg-22-679-2015, https://doi.org/10.5194/npg-22-679-2015, 2015
T. Nocke, S. Buschmann, J. F. Donges, N. Marwan, H.-J. Schulz, and C. Tominski
Nonlin. Processes Geophys., 22, 545–570, https://doi.org/10.5194/npg-22-545-2015, https://doi.org/10.5194/npg-22-545-2015, 2015
Short summary
Short summary
The paper reviews the available visualisation techniques and tools for the visual analysis of geo-physical climate networks. The results from a questionnaire with experts from non-linear physics are presented, and the paper surveys recent developments from information visualisation and cartography with respect to their applicability for visual climate network analytics. Several case studies based on own solutions illustrate the potentials of state-of-the-art network visualisation technology.
Cited articles
Alley, R. B., Marotzke, J., Nordhaus, W. D, Overpeck, J. T., Peteet, D. M., Pielke Jr., R. A., Pierrehumbert, R. T., Rhines, P. B., Stocker, T. F., Talley, L. D., and Wallace, J. M.: Abrupt Climate Change, Science, 299, 2005–2010, 2003.
Benjamini, Y. and Hochberg, Y.: Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing, J. Roy. Stat. Soc., 57, 289–300, 1995.
Benjamini, Y. and Yekutieli, D.: The Control of the False Discovery Rate in Multiple Testing under Dependency, Ann. Stat., 29, 1165–1188, 2001.
Climate Indices: Monthly Atmospheric and Ocean Time Series, http://www.esrl.noaa.gov/psd/data/climateindices/list/, last access: 1 December 2015.
Collis, W. B., White, P. R., and Hammond, J. K.: Higher-order Spectra: The Bispectrum and Trispectrum, Mech. Syst. Signal Pr., 12, 375–394, 1998.
Efron, B.: Bootstrap Methods: Another Look at the Jackknife, Ann. Stat., 7, 1–26, 1979.
Elgar, S. and Chandran, V.: Higher-order Spectral Analysis to Detect Nonlinear Interactions in Measured Time Series and an Application to Chua's Circuit, Int. J. Bifurcat. Chaos, 3, 19–34, 1993.
Elgar, S. and Sebert, G.: Statistics of Bicoherence and Biphase, J. Geophys. Res., 94, 10993–10998,1989.
Elsayed, M. A. K.: Wavelet Bicoherence Analysis of Wind–wave Interaction, Ocean Eng., 33, 458–470, 2006.
Gan, T. Y., Gobena, A. K., and Wang, Q.: Precipitation of Southwestern Canada: Wavelet, Scaling, Multifractal Analysis, and Teleconnection to Climate Anomalies, J. Geophys. Res., 112, D10110, https://doi.org/10.1029/2006JD007157, 2007.
Grinsted, A., Moore, J. C., and Jevrejeva, S.: Application of the Cross Wavelet Transform and Wavelet Coherence to Geophysical Time Series, Nonlinear Proc. Geoph., 11 , 561–566, 2004.
Groppe, D. M, Urbach, T. P, and Kutas, M.: Mass univariate analysis of event-related brain potentials/fields I: a critical tutorial review, Psychophysiology, 48, 1711–1725, 2011.
Hamiliton, K. and Hsieh, W. W.: Representation of the Quasi-biennial Oscillation in the Tropical Stratospheric Wind by Nonlinear Principal Component Analysis, J. Geophys. Res., 107, 4232, https://doi.org/10.1029/2001JD001250, 2002.
Hinich, M. J.: Testing for Gaussianity and linearity of a stationary time series, J. Time Ser. Anal., 3, 169–175, 1982.
Jevrejeva, S., Moore, J. C., and Grinsted, A.: Influence of the Arctic Oscillation and El Nino-Southern Oscillation (ENSO) on Ice Conditions in the Baltic Sea: The wavelet Approach, J. Geophys. Res., 108, D214677, https://doi.org/10.1029/2003JD003417, 2003.
King, T.: Quantifying Nonlinearity and Geometry in Time Series of Climate, Quaternary Sci. Rev., 15, 247–266, 1996.
Kunsch, H. R.: The Jackknife and the Bootstrap for General Stationary Observations, Ann. Stat., 17, 1217–1241, 1989.
Labat, D.: Cross Wavelet Analyses of Annual Continental Freshwater Discharge and Selected Climate Indices, J. Hydrol., 385, 269–278, 2010.
Lee, Y. J. and Lwiza, K. M.: Factors Driving Bottom Salinity Variability in the Chesapeake Bay, Cont. Shelf Res., 28, 1352–1362, 2008.
Lehmann, E.: Testing Statistical Hypothesis, Springer, 1986
Lu, B. W., Pandolfo, L., and Hamilton, K.: Nonlinear Representation of the Quasi-Biennial Oscillation, J. Atmos. Sci., 66, 1886–1904, 2009.
Maccarone, T. J.: The Biphase Explained: Understanding the Asymmetries in Coupled Fourier Components of Astronomical Timeseries, Mon. Not. R. Astron. Soc., 435, 3547, https://doi.org/10.1093/mnras/stu1824, 2013.
MacDonald, G. M. and Case, R. A.: Variations in the Pacific Decadal Oscillation over the Past Millennium, Geophys. Res. Lett., 32, L08703, https://doi.org/10.1029/2005GL022478, 2005.
Maraun, D., Kurths, J., and Holschneider, M.: Nonstationary Gaussian Processes in the Wavelet Domain: Synthesis, Estimation, and Significance Testing, Phys. Rev. E, 75, 016707, https://doi.org/10.1103/PhysRevE.75.016707, 2007.
Moussas, X., Polygiannakis, J. M., Preka-Papadema, P., and Exarhos, G.: Solar cycles: A tutorial, Adv. Sp. Res., 35, 725–738, 2005.
Newman, M., Compo, G. P., and Alexander, M. A.: ENSO-forced variability of the Pacific decadal oscillation, J. Clim., 16, 3853–3857, 2003.
Nidal, K. and Malik, A. S.: EEG/ERP Analysis: Methods and Applications, CRC Press, 334 pp., 2013.
Nikias, C. L. and Raghuveer, M. R.: Bispectrum Estimation: A Digital Signal Processing Framework, IEEE Proceedings, 75, 869–891, 1987.
Olsen, J., Anderson, J. N., and Knudsen, M. F.: Variability of the North Atlantic Oscillation over the past 5,200 years, Nat. Geosci., 5, 808–812, 2012.
Rusu, M. V.: The Asymmetry of the Solar Cycle: A result of Non-linearity, Adv. Sp. Res., 40, 1904–1911, 2007.
Schulte, J. A.: Cumulative areawise testing in wavelet analysis and its application to geophysical time series, Nonlinear Proc. Geophys., 23, 45–57, 2016.
Schulte, J. A.: Higher-order Wavelet Analysis, available at: http://www.mathworks.com/matlabcentral/fileexchange/54671-higher-order-wavelet-analysis, last access: 29 December 2015.
Schulte, J. A., Duffy, C., and Najjar, R. G.: Geometric and Topological Approaches to Significance Testing in Wavelet Analysis, Nonlinear Proc. Geophys., 22, 139–156, 2015.
Schulte, J. A., Najjar, R. G., and Lee, S.: Salinity and Streamflow Variability in the Mid-Atlantic Region of the United States and its Relationship with Large-scale Atmospheric Circulation Patterns, J. Hydrol., in review, 2016.
Timmermann A.: Decadal ENSO Amplitude Modulations: a Nonlinear Paradigm, Global Planet. Change, 37, 135–156, 2003.
Torrence, C. and Compo, G. P.: A Practical Guide to Wavelet Analysis, Bull. Am. Meteorol. Soc., 79, 61–78, 1998.
Torrence, C. and Webster, P. J.: Interdecadal Changes in the ENSO–Monsoon System, J. Clim., 12, 2679–2690, 1999.
Van Milligen, B. P., Saìnchez, E., Estrada, T., Hidalgo, C., Brañas, B., Carreras, B., and Garcìa, L.: Wavelet Bicoherence: A New Turbulence Analysis Tool, Phys. Plasmas, 2, 3017–3032, 1995.
Wilks, D. S.: Resampling Hypothesis Tests for Autocorrelated Fields, J. Clim., 10, 65–82, 1997.
