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Illia Horenko

Abstract

Identification and analysis of temporal trends and low-frequency variability in discrete time series is an important practical topic in the understanding and prediction of many atmospheric processes, for example, in analysis of climate change. Widely used numerical techniques of trend identification (like local Gaussian kernel smoothing) impose some strong mathematical assumptions on the analyzed data and are not robust to model sensitivity. The latter issue becomes crucial when analyzing historical observation data with a short record. Two global robust numerical methods for the trend estimation in discrete nonstationary Markovian data based on different sets of implicit mathematical assumptions are introduced and compared here. The methods are first compared on a simple model example; then the importance of mathematical assumptions on the data is explained and numerical problems of local Gaussian kernel smoothing are demonstrated. Presented methods are applied to analysis of the historical sequence of atmospheric circulation patterns over the United Kingdom between 1946 and 2007. It is demonstrated that the influence of the seasonal pattern variability on transition processes is dominated by the long-term effects revealed by the introduced methods. Despite the differences in the mathematical assumptions implied by both presented methods, almost identical symmetrical changes of the cyclonic and anticyclonic pattern probabilities are identified in the analyzed data, with the confidence intervals being smaller than in the case of the local Gaussian kernel smoothing algorithm. Analysis results are investigated with respect to model sensitivity and compared to a standard analysis technique based on a local Gaussian kernel smoothing. Finally, the implications of the discussed strategies on long-range predictability of the data-fitted Markovian models are discussed.

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Illia Horenko

Abstract

A problem of simultaneous dimension reduction and identification of hidden attractive manifolds in multidimensional data with noise is considered. The problem is approached in two consecutive steps: (i) embedding the original data in a sufficiently high-dimensional extended space in a way proposed by Takens in his embedding theorem, followed by (ii) a minimization of the residual functional. The residual functional is constructed to measure the distance between the original data in extended space and their reconstruction based on a low-dimensional description. The reduced representation of the analyzed data results from projection onto a fixed number of unknown low-dimensional manifolds. Two specific forms of the residual functional are proposed, defining two different types of essential coordinates: (i) localized essential orthogonal functions (EOFs) and (ii) localized functions called principal original components (POCs). The application of the framework is exemplified both on a Lorenz attractor model with measurement noise and on historical air temperature data. It is demonstrated how the new method can be used for the elimination of noise and identification of the seasonal low-frequency components in meteorological data. An application of the proposed POCs in the context of the low-dimensional predictive models construction is presented.

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Illia Horenko

Abstract

A numerical framework for data-based identification of nonstationary linear factor models is presented. The approach is based on the extension of the recently developed method for identification of persistent dynamical phases in multidimensional time series, permitting the identification of discontinuous temporal changes in underlying model parameters. The finite element method (FEM) discretization of the resulting variational functional is applied to reduce the dimensionality of the resulting problem and to construct the numerical iterative algorithm. The presented method results in the sparse sequential linear minimization problem with linear constrains. The performance of the framework is demonstrated for the following two application examples: (i) in the context of subgrid-scale parameterization for the Lorenz model with external forcing and (ii) in an analysis of climate impact factors acting on the blocking events in the upper troposphere. The importance of accounting for the nonstationarity issue is demonstrated in the second application example: modeling the 40-yr ECMWF Re-Analysis (ERA-40) geopotential time series via a single best stochastic model with time-independent coefficients leads to the conclusion that all of the considered external factors are found to be statistically insignificant, whereas considering the nonstationary model (which is demonstrated to be more appropriate in the sense of information theory) identified by the methodology presented in the paper results in identification of statistically significant external impact factor influences.

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Illia Horenko

Abstract

Because of the mathematical and numerical limitations, standard statistical methods known from the literature are not applicable to inferring jump processes under exogenous influence. Such processes can be considered, for example, in the atmosphere (transitions between different cloud types) and in the ocean (phase transitions between water and ice). Reasons for these intrinsic limitations of standard methods are investigated and a method for the inference of discrete microscopic jump models based on macroscopic ensemble observations is presented. It significantly extends the recently developed methods of nonstationary Markov model parameterization (which are constrained to a single exogenous factor and to direct individual observations of the jump process realizations). The main advantage of the new method is the possibility of inference from indirect ensemble observations with multiple exogenous factors. Moreover, this method allows for a new possibility to test whether the available time series is best described via stationary or nonstationary and Markovian (with memory) or independent (without memory) processes. It also allows estimation of the relative significance of the exogenous factors and their impact on the jump probabilities. The new framework provides a unified toolkit for data analysis of jump processes with the same level of detail now possible for standard continuous state space tools. The resulting numerical algorithm is applied to analysis of the total relative cloud cover data in the midlatitudes and in the tropics under the influence of some meteorologically relevant local and global exogenous factors.

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Christian Blume, Katja Matthes, and Illia Horenko

Abstract

Sudden stratospheric warmings are prominent examples of dynamical wave–mean flow interactions in the Arctic stratosphere during Northern Hemisphere winter. They are characterized by a strong temperature increase on time scales of a few days and a strongly disturbed stratospheric vortex. This work investigates a wide class of supervised learning methods with respect to their ability to classify stratospheric warmings, using temperature anomalies from the Arctic stratosphere and atmospheric forcings such as ENSO, the quasi-biennial oscillation (QBO), and the solar cycle. It is demonstrated that one representative of the supervised learning methods family, namely nonlinear neural networks, is able to reliably classify stratospheric warmings. Within this framework, one can estimate temporal onset, duration, and intensity of stratospheric warming events independently of a particular pressure level. In contrast to classification methods based on the zonal-mean zonal wind, the approach herein distinguishes major, minor, and final warmings. Instead of a binary measure, it provides continuous conditional probabilities for each warming event representing the amount of deviation from an undisturbed polar vortex. Additionally, the statistical importance of the atmospheric factors is estimated. It is shown how marginalized probability distributions can give insights into the interrelationships between external factors. This approach is applied to 40-yr and interim ECMWF (ERA-40/ERA-Interim) and NCEP–NCAR reanalysis data for the period from 1958 through 2010.

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Christian Franzke, Illia Horenko, Andrew J. Majda, and Rupert Klein

Abstract

In this study the authors apply a recently developed clustering method for the systematic identification of metastable atmospheric regimes in high-dimensional datasets generated by atmospheric models. The novelty of this approach is that it decomposes the phase space in, possibly, overlapping clusters and simultaneously estimates the most likely switching sequence among the clusters. The parameters of the clustering and switching are estimated by a finite element approach. The switching among the clusters can be described by a Markov transition matrix. Possible metastable regime behavior is assessed by inspecting the eigenspectrum of the associated transition probability matrix.

The recently introduced metastable data-analysis method is applied to high-dimensional datasets produced by a barotropic model and a comprehensive atmospheric general circulation model (GCM). Significant and dynamically relevant metastable regimes are successfully identified in both models. The metastable regimes in the barotropic model correspond to blocked and zonal states. Similar regime states were already previously identified in highly reduced phase spaces of just one and two dimensions in the same model.

Next, the clustering method is applied to a comprehensive atmospheric GCM in which seven significant flow regimes are identified. The spatial structures of the regimes correspond to, among others, both phases of the Northern Annular Mode and Pacific blocking. The regimes are maintained predominantly by transient eddy fluxes of low-pass-filtered anomalies. It is demonstrated how the dynamical description of the slow process switching between the regimes can be acquired from the analysis results, and an investigation of the resulting simplified dynamical model with respect to predictability is performed.

A predictability study shows that a simple Markov model is able to predict the regimes up to six days ahead, comparable to the ability of high-resolution state-of-the-art numerical weather prediction models to accurately predict the onset and decay of blockings. The implications of the results for derivation of reduced models for extended-range predictability are discussed.

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Terence J. O’Kane, James S. Risbey, Christian Franzke, Illia Horenko, and Didier P. Monselesan

Abstract

Changes in the metastability of the Southern Hemisphere 500-hPa circulation are examined using both cluster analysis techniques and split-flow blocking indices. The cluster methodology is a purely data-driven approach for parameterization whereby a multiscale approximation to nonstationary dynamical processes is achieved through optimal sequences of locally stationary fast vector autoregressive factor (VARX) processes and some slow (or persistent) hidden process switching between them. Comparison is made with blocking indices commonly used in weather forecasting and climate analysis to identify dynamically relevant metastable regimes in the 500-hPa circulation in both reanalysis and Atmospheric Model Intercomparison Project (AMIP) datasets. The analysis characterizes the metastable regime in both reanalysis and model datasets prior to 1978 as positive and negative phases of a hemispheric midlatitude blocking state with the southern annular mode (SAM) associated with a transition state. Post-1978, the SAM emerges as a true metastable state replacing the negative phase of the hemispheric blocking pattern. The hidden state frequency of occurrences exhibits strong trends. The blocking pattern dominates in the early 1980s, and then gradually decreases. There is a corresponding increase in the SAM frequency of occurrence. This trend is largely evident in the reanalysis summer and spring but was not evident in the AMIP dataset. Further comparison with the split-flow blocking indices reveals a superficial correspondence between the cluster hidden state frequency of occurrences and split-flow indices. Examination of composite states shows that the blocking indices capture splitting of the zonal flow whereas the cluster composites reflect coherent block formation. Differences in blocking climatologies from the respective methods are discussed.

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James S. Risbey, Terence J. O’Kane, Didier P. Monselesan, Christian Franzke, and Illia Horenko

Abstract

This study applies a finite-element, bounded-variation, vector autoregressive method to assess midtropospheric flow regimes characterized by regime switches between metastable states. The flow is assessed in reanalysis data from three different reanalysis sets assimilating surface data only; surface and upper-air data; and ocean, surface, and upper-air data. Results are generally consistent across the reanalyses and confirm the utility of surface-only reanalyses for capturing midtropospheric variability. The method is applied to a set of regional domains in the Northern Hemisphere and for the full-hemispheric domain. Composites of the metastable states for each region yield structures that are consistent with the well-documented teleconnection modes: the North Atlantic Oscillation in the Atlantic Ocean, the Pacific–North America pattern (PNA) in the Pacific Ocean, and Scandinavian blocking over Eurasia. The PNA mode includes a clear waveguide structure in midlatitudes. The Northern Hemisphere domain yields a state composite that reflects aspects of an annular mode (Arctic Oscillation), where the annular component in midlatitudes comprises a circumglobal waveguide. The Northern Hemisphere waveguide is characterized by wavenumber 5. Some of the nodes in this circumglobal waveguide manifest as part of regional dipole structures like the PNA. This situation contrasts with the Southern Hemisphere, where the circumglobal waveguide exhibits wavenumbers 3 and 5 and is monopolar. For each of the regions and modes examined, the annual time series of residence percent in each state displays prominent decadal variability and provides a clear means of identifying regimes of the major teleconnection modes.

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Illia Horenko, Stamen I. Dolaptchiev, Alexey V. Eliseev, Igor I. Mokhov, and Rupert Klein

Abstract

This paper presents an extension of the recently developed method for simultaneous dimension reduction and metastability analysis of high-dimensional time series. The modified approach is based on a combination of ensembles of hidden Markov models (HMMs) with state-specific principal component analysis (PCA) in extended space (guaranteeing that the overall dynamics will be Markovian). The main advantage of the modified method is its ability to deal with the gaps in the high-dimensional observation data. The proposed method allows for (i) the separation of the data according to the metastable states, (ii) a hierarchical decomposition of these sets into metastable substates, and (iii) calculation of the state-specific extended empirical orthogonal functions simultaneously with identification of the underlying Markovian dynamics switching between those metastable substates. The authors discuss the introduced model assumptions, explain how the quality of the resulting reduced representation can be assessed, and show what kind of additional insight into the underlying dynamics such a reduced Markovian representation can give (e.g., in the form of transition probabilities, statistical weights, mean first exit times, and mean first passage times). The performance of the new method analyzing 500-hPa geopotential height fields [daily mean values from the 40-yr ECMWF Re-Analysis (ERA-40) dataset for a period of 44 winters] is demonstrated and the results are compared with information gained from a numerically expensive but assumption-free method (Wavelets–PCA), and the identified metastable states are interpreted w.r.t. the blocking events in the atmosphere.

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