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The monthly anomaly sea surface temperature field over the global ocean exhibit probabilistic dependencies between remote points and lagged times, which are explained eventually by some oceanic or atmospheric bridge of information transfer. Despite much of the bivariate SST dependencies appear to be linear, others are characterized by robust and statistically significant nonlinear correlations. In order to enhance that, we present a general method of extracting bivariate (X,Y) dependencies, seeking for pairs of polynomials P(X) and Q(Y) which are maximally correlated. The method relies on a Canonical correlation Analysis (CCA) between sets of standardized monomials of X and Y, up to a certain (low) degree (e.g. 4). Polynomial coefficients are obtained from the leading CCA eigenvector. Polynomials are calibrated and validated over independent periods, being afterwards subjected to marginal Gaussian anamorphoses. The bivariate non-Gaussianity in the space of marginally Gaussianized polynomials remains residual because of the correlation concentration and maximization. Consequently, the bivariate Gaussian pdf or in alternative, a copula pdf in the space of maximally correlated polynomials can accurately approximate the bivariate dependency. That probabilistic model is then used to determine conditional pdfs, cdfs and probabilities of extremes.The method is applied to various (X,Y) pairs. In the first example, X is an optimized polynomial of the El-Niño 3.4 index while Y is that index lagged to the future. For lags between 6 and 18 months, the nonlinear El-Niño forecast clearly surpasses the linear one, contributing to lower the El-Niño seasonal predictability barrier. In the second example, we relate El-Niño (X) with the lagged Atlantic multidecadal oscillation index (Y). Nonlinear, robust correlations appear, both for positive and negative lags up to 5 years putting in evidence Pacific-Atlantic basin oceanic teleconnections.The above probabilistic (polynomial based) model appears to be a good candidate tool for the statistical (seasonal up to decadal) forecast of regime probabilities (e.g. dry/wet) and extremes, given certain antecedent precursors.This work was funded by the Portuguese Fundação para a Ciência e a Tecnologia (FCT) I.P./MCTES through national funds (PIDDAC) – UIDB/50019/2020- IDL and the project JPIOCEANS/0001/2019 (ROADMAP: ’The Role of ocean dynamics and Ocean–Atmosphere interactions in Driving cliMAte variations and future Projections of impact–relevant extreme events’). Acknowledgements are also due to the International Meteorological Institute (IMI) at Stockholm University.

The ability to find and recognize patterns in high-dimensional geophysical data is fundamental to climate science and critical for meaningful interpretation of weather and climate processes. Archetypal analysis (AA) is one technique that has recently gained traction in the geophysical science community for its ability to find patterns based on extreme conditions. While traditional empirical orthogonal function (EOF) analysis can reveal patterns based on data covariance, AA seeks patterns from the points located at the edges of the data distribution. The utility of any objective pattern method depends on the properties of the data to which it is applied and the choices made in implementing the method. Given the relative novelty of the application of AA in geophysics it is important to develop experience in applying the method. We provide an assessment of the method, implementation, sensitivity, and interpretation of AA with respect to geophysical data. As an example for demonstration, we apply AA to a 39-yr sea surface temperature (SST) reanalysis dataset. We show that the decisions made to implement AA can significantly affect the interpretation of results, but also, in the case of SST, that the analysis is exceptionally robust under both spatial and temporal coarse graining. Significance Statement Archetypal analysis (AA), when applied to geophysical fields, is a technique designed to find typical configurations or modes in underlying data. This technique is relatively new to the geophysical science community and has been shown to be beneficial to the interpretation of extreme modes of the climate system. The identification of extreme modes of variability and their expression in day-to-day weather or state of the climate at longer time scales may help in elucidating the interplay between major teleconnection drivers and their evolution in a changing climate. The purpose of this work is to bring together a comprehensive report of the AA methodology using an SST reanalysis for demonstration. It is shown that the AA results are significantly affected by each implementation decision, but also can be resilient to spatiotemporal averaging. Any application of AA should provide a clear documentation of the choices made in applying the method.

The low-frequency variability of the extratropical atmosphere involves hemispheric-scale recurring, often persistent, states known as teleconnection patterns or regimes, which can have a profound impact on predictability on intra-seasonal and longer timescales. However, reliable data-driven identification and dynamical representation of such states are still challenging problems in modeling the dynamics of the atmosphere. We present a new method, which allows us both to detect recurring regimes of atmospheric variability and to obtain dynamical variables serving as an embedding for these regimes. The method combines two approaches from nonlinear data analysis: partitioning a network of recurrent states with studying its properties by the recurrence quantification analysis and the kernel principal component analysis. We apply the method to study teleconnection patterns in a quasi-geostrophical model of atmospheric circulation over the extratropical hemisphere as well as to reanalysis data of geopotential height anomalies in the mid-latitudes of the Northern Hemisphere atmosphere in the winter seasons from 1981 to the present. It is shown that the detected regimes as well as the obtained set of dynamical variables explain large-scale weather patterns, which are associated, in particular, with severe winters over Eurasia and North America. The method presented opens prospects for improving empirical modeling and long-term forecasting of large-scale atmospheric circulation regimes.

This chapter describes the idea behind, and develops the theory of empirical orthogonal functions (EOFs) along with a historical perspective. It also shows different ways to obtain EOFs and provides examples from climate and discusses their physical interpretation. Strength and weaknesses of EOFs are also mentioned.

This chapter describes patterns obtained based on proximity or similarity measures, i.e. multidimensional scaling (MDS). Conventional EOFs correspond to the case of quadratic distance. In this chapter other forms of similarities are discussed, with climate application, and which can yield structures that cannot be revealed by classical MDS.

Weather and Climate data contain a myriad of processes including oscillating and propagating features. In general EOF method is not suited to identify propagating patterns. In this chapter describes a spectral method based on Hilbert transform to identify propagating features, with application to the stratospheric quasi-biennial oscillation.

Weather and climate data are in general discrete and result from sampling a continuous system. This chapter attempts to take this into account when computing EOFs. The first part of the chapter describes methods to construct EOFs/PCs of profiles with application to oceanography. The second part of the chapter describes regularised EOFs with application to reanalysis data.

EOF method is essentially an exploratory method to analyse the modes of variability of multivariate weather and climate data, with no model is involved. This chapter describes a different method, Principal Oscillation Pattern (POP) analysis, that seeks the simplest dynamical system that can explain the main features of the space–time data. The chapter also provides further extension of POPs by including nonlinearity. Examples from climate data are also given.

Hilbert EOFs presented in Chap. 5 are based on a spectral method to identify propagating or oscillating features. This chapter describes a time domain method, the extended EOFs, to identify propagating patterns from spatio-temporal data sets. The method is similar to the EOF method except that the spatial dimension is extended to include lagged information. Examples from the Madden–Julian oscillation are also provided.

This chapter introduces some basic terminologies that are used in subsequent chapters. It also presents some basic summary statistics of data sets and reviews basic methods of data filtering and smoothing.

Conventional EOFs yield orthogonal spatial patterns and uncorrelated time series. Non-correlation does not necessarily yield independence, which is a strong constraint compared to non-correlation. This chapter discusses the concept of independence, and its relation to non-normality and describes different ways to obtain independent components. The chapter also discusses the application to climate data.

This chapter describes further the drawbacks of EOFs mentioned in Chap. 3. It also provides different ways to overcome those drawbacks, including EOF rotation and simplified EOFs. A number of applications to climate data are also provided.

Previous chapters focussed mostly on single fields, such as EOFs of seal level pressure. This chapter is an extension of previous methods. It describes different methods that mostly deal with two fields to identify coupled patterns that covary coherently. The chapter discusses both the conventional and regularised problems. It also explores the predictive power of coupled pattern analysis.

Previous chapters discuss methods with no particular predictive power. This chapter describes further advanced linear methods that are more related to prediction. Three related methods, involving extrapolation (or prediction) and interpolation, with climate applications are discussed in this chapter.

We studied the inter-annual variability of the vertically integrated zonal/meridional moisture transport in the lower troposphere over the northern Indian Ocean using observed data from 1971-2016 f ...

Understanding the effects of climate change and global warming on the South Asian summer monsoon rainfall trend is critically important for millions of inhabitants of this region. This study invest ...

Conventional analysis methods in weather and climate science (e.g., EOF analysis) exhibit a number of drawbacks including scaling and mixing. These methods focus mostly on the bulk of the probability distribution of the system in state space and overlook its tail. This paper explores a different method, the archetypal analysis (AA), which focuses precisely on the extremes. AA seeks to approximate the convex hull of the data in state space by finding “corners” that represent “pure” types or archetypes through computing mixture weight matrices. The method is quite new in climate science, although it has been around for about two decades in pattern recognition. It encompasses, in particular, the virtues of EOFs and clustering. The method is presented along with a new manifold-based optimization algorithm that optimizes for the weights simultaneously, unlike the conventional multistep algorithm based on the alternating constrained least squares. The paper discusses the numerical solution and then applies it to the monthly sea surface temperature (SST) from HadISST and to the Asian summer monsoon (ASM) using sea level pressure (SLP) from ERA-40 over the Asian monsoon region. The application to SST reveals, in particular, three archetypes, namely, El Niño, La Niña, and a third pattern representing the western boundary currents. The latter archetype shows a particular trend in the last few decades. The application to the ASM SLP anomalies yields archetypes that are consistent with the ASM regimes found in the literature. Merits and weaknesses of the method along with possible future development are also discussed.

The anomalous decadal warming of the subpolar North Atlantic Ocean (SPNA), and the northward spreading of this warm water, has been linked to rapid Arctic sea ice loss and more frequent cold Europe ...

The study of regional rainfall trends over South Asia is critically important for food security and economy, as both these factors largely depend on the availability of water. In this study, South Asian summer monsoon rainfall trends on seasonal and monthly (June–September) time scales have been investigated using three observational data sets. Our analysis identify a dipole-type structure in rainfall trends over the region north of the Indo–Pak subcontinent, with significant increasing trends over the core monsoon region of Pakistan and significant decreasing trends over the central-north India and adjacent areas. The dipole is also evident in monthly rainfall trend analyses, which is more prominent in July and August. We show, in particular, that the strengthening of northward moisture transport over the Arabian Sea is a likely reason for the significant positive trend of rainfall in the core monsoon region of Pakistan. In contrast, over the central-north India region, the rainfall trends are significantly decreasing due to the weakening of northward moisture transport over the Bay of Bengal. The leading empirical orthogonal functions clearly show the strengthening (weakening) patterns of vertically integrated moisture transport over the Arabian Sea (Bay of Bengal) in seasonal and monthly interannual time scales. The regression analysis between the principal components and rainfall confirm the dipole pattern over the region. Our results also suggest that the extra-tropical phenomena could influence the mean monsoon rainfall trends over Pakistan by enhancing the cross-equatorial flow of moisture into the Arabian Sea.

The Asian summer monsoon is a high-dimensional and highly nonlinear phenomenon involving considerable moisture transport towards land from the ocean, and is critical for the whole region. We have used daily ECMWF reanalysis (ERA-40) sea-level pressure (SLP) anomalies on the seasonal cycle, over the region 50–145° E, 20° S–35° N, to study the nonlinearity of the Asian monsoon using Isomap. We have focused on the two-dimensional embedding of the SLP anomalies for ease of interpretation. Unlike the unimodality obtained from tests performed in empirical orthogonal function space, the probability density function, within the two-dimensional Isomap space, turns out to be bimodal. But a clustering procedure applied to the SLP data reveals support for three clusters, which are identified using a three-component bivariate Gaussian mixture model. The modes are found to appear similar to active and break phases of the monsoon over South Asia in addition to a third phase, which shows active conditions over the western North Pacific. Using the low-level wind field anomalies, the active phase over South Asia is found to be characterised by a strengthening and an eastward extension of the Somali jet. However during the break phase, the Somali jet is weakened near southern India, while the monsoon trough in northern India also weakens. Interpretation is aided using the APHRODITE gridded land precipitation product for monsoon Asia. The effect of large-scale seasonal mean monsoon and lower boundary forcing, in the form of ENSO, is also investigated and discussed. The outcome here is that ENSO is shown to perturb the intraseasonal regimes, in agreement with conceptual ideas.

The extra-tropical atmosphere is characterized by robust circulations which have time scales longer than that associated with developing baroclinic systems but shorter than a season. Such low frequency variability is governed to a large extent by non-linear dynamics, and hence is chaotic. A useful aspect of this low-frequency circulation is that it can often be described by just a few quasi-stationary regime states, broadly defined as recurrent or persistent large scale structures, that exert a significant impact on the probability of experiencing extreme surface weather conditions. We review a variety of techniques for identifying circulation regimes from reanalysis and numerical model output. While various techniques often yield similar regime circulation patterns, they offer different perspectives on the regimes. The regimes themselves are manifest in planetary scale patterns. They affect the structure of synoptic scale patterns. Extra-tropical flow regimes have been identified in simplified atmospheric models and comprehensive coupled climate models and in reanalysis data sets. It is an ongoing challenge to accurately model these regime states and high horizontal resolutions are often needed to accurately reproduce them. The regime paradigm helps to understand the response to external forcing on a variety of time scales, has been helpful in categorizing a large number of weather types and their effect on local conditions, and is useful in downscaling. Despite their usefulness, there is a debate on the \non-equivocal" and systematic existence of these nonlinear circulation regimes. We review our current understanding of the nonlinear and regime paradigms and suggest future research.

It is known that the empirical orthogonal function method is unable to detect possible nonlinear structure in climate data. Here, isometric feature mapping (Isomap), as a tool for nonlinear dimensi ...

Three methods are utilized in this paper to assist in the groundwater clustering, in an arid region aquifer, into similar zones according to its quality. A multiple regression is first applied in order to assess the importance of the different chemical constituents in the amount of total dissolved salt, which shows the dominance of chlorine and sodium. A multivariate analysis based on empirical orthogonal functions and hierarchical clustering (EOFs) is applied to assist in water quality clustering in the studied aquifer. The clustering has produced five distinguished categories of groundwater quality, which agree well with World Health Organisation criteria and limits for water usage. Based on these categories, spatial distribution maps of groundwater quality are produced by Kriging and GIS software.

We propose an expansion of multivariate time-series data into maximally independent source subspaces. The search is made among rotations of prewhitened data which maximize non-Gaussianity of candidate sources. We use a tensorial invariant approximation of the multivariate negentropy in terms of a linear combination of squared coskewness and cokurtosis. By solving a high-order singular value decomposition problem, we extract the axes associated with most non-Gaussianity. Moreover, an estimate of the Gaussian subspace is provided by the trailing singular vectors. The independent subspaces are obtained through the search of “quasi-independent” components within the estimated non-Gaussian subspace, followed by the identification of groups with significant joint negentropies. Sources result essentially from the coherency of extremes of the data components. The method is then applied to the global sea surface temperature anomalies, equatorward of 65°, after being tested with non-Gaussian surrogates consistent with the data anomalies. The main emerging independent components and subspaces, supposedly generated by independent forcing, include different variability modes, namely, The East-Pacific, the Central Pacific, and the Atlantic Niños, the Atlantic Multidecadal Oscillation, along with the subtropical dipoles in the Indian, South Pacific, and South-Atlantic oceans. Benefits and usefulness of independent subspaces are then discussed.

A systematic analysis of the winter North Atlantic eddy-driven jet stream latitude and wind speed from 52 model integrations, taken from the coupled model intercomparison project phase 3, is carried out and compared to results obtained from the ERA-40 reanalyses. We consider here a control simulation, twentieth century simulation, and two time periods (2046-2065 and 2081-2100) from a twenty-first century, high-emission A2 forced simulation. The jet wind speed seasonality is found to be similar between the twentieth century simulations and the ERA-40 reanalyses and also between the control and forced simulations although nearly half of the models overestimate the amplitude of the seasonal cycle. A systematic equatorward bias of the models jet latitude seasonality, by up to 7°, is observed, and models additionally overestimate the seasonal cycle of jet latitude about the mean, with the majority of the models showing equatorward and poleward biases during the cold and warm seasons respectively. A main finding of this work is that no GCM under any forcing scenario considered here is able to simulate the trimodal behaviour of the observed jet latitude distribution. The models suffer from serious problems in the structure of jet variability, rather than just quantitiative errors in the statistical moments. © 2012 Springer-Verlag Berlin Heidelberg.

Daily precipitation is investigated in this study in terms of simple first order autoregressive models. The methodology is based on combining theory from censored processes with continuous autoregressive models to model intermittent phenomena. The choice of short-memory autoregressive models is corroborated further by recent findings on scaling properties of daily precipitation records. The theory and application to synthetic models are presented. The methodology is then applied to Northern Ireland Armagh Observatory daily precipitation for the period 1950–2001 for each month. Both zero- and non zero-mean processes are considered. The analysis indicates that the model parameters do capture seasonality where, for example, the autocorrelation co-efficient is larger in winter, compared to in the summer. This is arguably a reflection of the stronger effect of large-scale processes on rainfall in winter compared to summer. Interestingly, the parameters of the zero- and non zero-mean processes are found to be quite similar, reflecting the symmetric nature of the truncated processes in the midlatitude and extratropics. It is suggested, in particular, that the process mean can be used as a measure to quantify dryness or wetness of a given region. Ways of model improvement, including power transformation, based on the square root, to represent extremes using exploratory quantile–quantile plots better are also discussed. Copyright © 2012 Royal Meteorological Society

Preferred jet stream positions and their link to regional circulation patterns over the winter North Atlantic/European sector are investigated to corroborate findings of multimodal behaviour of the ...

The polar winter stratospheric vortex is a coherent structure that undergoes different types of deformation that can be revealed by the geometric invariant moments. Three moments are used—the aspect ratio, the centroid latitude, and the area of the vortex based on stratospheric data from the 40-yr ECMWF Re-Analysis (ERA-40) project—to study sudden stratospheric warmings. Hierarchical clustering combined with data image visualization techniques is used as well. Using the gap statistic, three optimal clusters are obtained based on the three geometric moments considered here. The 850-K potential vorticity field, as well as the vertical profiles of polar temperature and zonal wind, provides evidence that the clusters represent, respectively, the undisturbed (U), displaced (D), and split (S) states of the polar vortex. This systematic method for identifying and characterizing the state of the polar vortex using objective methods is useful as a tool for analyzing observations and as a test for climate models to simulate the observations. The method correctly identifies all previously identified major warmings and also identifies significant minor warmings where the atmosphere is substantially disturbed but does not quite meet the criteria to qualify as a major stratospheric warming.

Spring Saharan cyclones constitute a dominant feature of the not-well-explored Saharan region. In this manuscript, a climatological analysis and classification of Saharan cyclone tracks are presented using 6-hourly NCEP/NCAR sea level pressure (SLP) reanalyses over the Sahara (10°W–50°E, 20°N–50°N) for the Spring (March–April–May) season over the period 1958–2006. A simple tracking procedure based on following SLP minima is used to construct around 640 Spring Saharan cyclone tracks. Saharan cyclones are found to be short-lived compared to their extratropical counterparts with an e-folding time of about 3 days. The lee side of the west Atlas mountain is found to be the main cyclogenetic region for Spring Saharan cyclones. Central Iraq is identified as the main cyclolytic area. A subjective procedure is used next to classify the cyclone tracks where six clusters are identified. Among these clusters the Western Atlas–Asia Minor is the largest and most stretched, whereas Algerian Sahara–Asia Minor is composed of the most long-lived tracks. Upper level flow associated with the tracks has also been examined and the role of large scale baroclinicity in the growth of Saharan cyclones is discussed.

Sectorial and planetary-scale winter circulation regimes are studied and the relationship between them is investigated in order to find how much the simultaneous occurrence of sectorial regimes contributes to the occurrence of hemispheric regimes. The strategy is based on the multivariate Gaussian mixture model. The number of components in the model is estimated using two approaches. The first one is based on arguments from order statistics of the mixture proportions and the second uses a more severe test based on reproducibility. The procedure is applied next to the 500-hPa height field over the North Pacific, the North Atlantic, and the Northern Hemisphere using the empirical orthogonal function state space. Two highly significant regimes are found in each case, namely, the Pacific–North America (pattern) (±PNA)–North Atlantic Oscillation (±NAO) for the hemisphere—±PNA for the Pacific sector and ±NAO for the Atlantic sector. The sectorial regimes reflect mainly blocking and no-blocking flows. The results are tested further by applying a spatial clustering algorithm and are found to be consistent, particularly along the regime axes in the system state space. The relationship between hemispheric and sectorial circulation regimes is investigated. The data in each sector are first classified and then the times of simultaneous occurrence of sectorial regimes are identified. A new hemispheric dataset is then obtained by discarding maps corresponding to those co-occurrence times, and a new regime analysis is conducted. The results show that the hemispheric regime behavior has significantly decreased, suggesting that synchronization between sectorial circulation regimes could play an important role in the occurrence of planetary circulation regimes. The interannual variability of regime events is also discussed.

Whereas the predominance of El Nino Southern Oscillation (ENSO) mode in the tropical Pacific sea surface temperature (SST) variability is well established, no such consensus seems to have been reached by climate scientists regarding the Indian Ocean. While a number of researchers think that the Indian Ocean SST variability is dominated by an active dipolar-type mode of variability, similar to ENSO, others suggest that the variability is mostly passive and behaves like an autocorrelated noise. For example, it is suggested recently that the Indian Ocean SST variability is consistent with the null hypothesis of a homogeneous diffusion process. However, the existence of the basin-wide warming trend represents a deviation from a homogeneous diffusion process, which needs to be considered. An efficient way of detrending, based on differencing, is introduced and applied to the Hadley Centre ice and SST. The filtered SST anomalies over the basin (23.5N-29.5S, 30.5E-119.5E) are then analysed and found to be inconsistent with the null hypothesis on intraseasonal and interannual timescales. The same differencing method is then applied to the smaller tropical Indian Ocean domain. This smaller domain is also inconsistent with the null hypothesis on intraseasonal and interannual timescales. In particular, it is found that the leading mode of variability yields the Indian Ocean dipole, and departs significantly from the null hypothesis only in the autumn season.

Preferred structures in the surface pressure variability are investigated in and compared between two 100-year simulations of the Hadley Centre climate model HadCM3. In the first (control) simulation, the model is forced with pre-industrial carbon dioxide concentration (1×CO2) and in the second simulation the model is forced with doubled CO2 concentration (2×CO2). Daily winter (December-January-February) surface pressures over the Northern Hemisphere are analysed. The identification of preferred patterns is addressed using multivariate mixture models. For the control simulation, two significant flow regimes are obtained at 5% and 2.5% significance levels within the state space spanned by the leading two principal components. They show a high pressure centre over the North Pacific/Aleutian Islands associated with a low pressure centre over the North Atlantic, and its reverse. For the 2×CO2 simulation, no such behaviour is obtained. At higher-dimensional state space, flow patterns are obtained from both simulations. They are found to be significant at the 1% level for the control simulation and at the 2.5% level for the 2×CO2 simulation. Hence under CO2 doubling, regime behaviour in the large-scale wave dynamics weakens. Doubling greenhouse gas concentration affects both the frequency of occurrence of regimes and also the pattern structures. The less frequent regime becomes amplified and the more frequent regime weakens. The largest change is observed over the Pacific where a significant deepening of the Aleutian low is obtained under CO2 doubling.

Investigation of preferred structures of planetary wave dynamics is addressed using multivariate Gaussian mixture models. The number of components in the mixture is obtained using order statistics of the mixing proportions, hence avoiding previous difficulties related to sample sizes and independence issues. The method is first applied to a few low-order stochastic dynamical systems and data from a general circulation model. The method is next applied to winter daily 500-hPa heights from 1949 to 2003 over the Northern Hemisphere. A spatial clustering algorithm is first applied to the leading two principal components (PCs) and shows significant clustering. The clustering is particularly robust for the first half of the record and less for the second half. The mixture model is then used to identify the clusters. Two highly significant extratropical planetary-scale preferred structures are obtained within the first two to four EOF state space. The first pattern shows a Pacific–North American (PNA) pattern and a negative North Atlantic Oscillation (NAO), and the second pattern is nearly opposite to the first one. It is also observed that some subspaces show multivariate Gaussianity, compatible with linearity, whereas others show multivariate non-Gaussianity. The same analysis is also applied to two subperiods, before and after 1978, and shows a similar regime behavior, with a slight stronger support for the first subperiod. In addition a significant regime shift is also observed between the two periods as well as a change in the shape of the distribution. The patterns associated with the regime shifts reflect essentially a PNA pattern and an NAO pattern consistent with the observed global warming effect on climate and the observed shift in sea surface temperature around the mid-1970s.

Robust tools are presented in this manuscript to assess changes in probability density function (pdf) of climate variables. The approach is based on order statistics and aims at computing, along with their standard errors, changes in various quantiles and related statistics. The technique, which is nonparametric and simple to compute, is developed for both independent and dependent data. For autocorrelated data, serial correlation is addressed via Monte Carlo simulations using various autoregressive models. The ratio between the average standard errors, over several quantiles, of quantile estimates for correlated and independent data, is then computed. A simple scaling-law type relationship is found to hold between this ratio and the lag-1 autocorrelation. The approach has been applied to winter monthly Central England Temperature (CET) and North Atlantic Oscillation (NAO) time series from 1659 to 1999 to assess/quantify changes in various parameters of their pdf. For the CET, significant changes in median (or scale) and also in low and high quantiles are observed between various time slices, in particular between the pre- and post-industrial revolution. Observed changes in spread and also quartile skewness of the pdf, however, are not statistically significant (at 95% confidence level). For the NAO index we find mainly large significant changes in variance (or scale), yielding significant changes in low/high quantiles. Finally, the performance of the method compared to few conventional approaches is discussed.

Empirical orthogonal functions (EOFs) are widely used in climate research to identify dominant patterns of variability and to reduce the dimensionality of climate data. EOFs, however, can be difficult to interpret. Rotated empirical orthogonal functions (REOFs) have been proposed as more physical entities with simpler patterns than EOFs. This study presents a new approach for finding climate patterns with simple structures that overcomes the problems encountered with rotation. The method achieves simplicity of the patterns by using the main properties of EOFs and REOFs simultaneously. Orthogonal patterns that maximise variance subject to a constraint that induces a form of simplicity are found. The simplified empirical orthogonal function (SEOF) patterns, being more 'local'. are constrained to have zero loadings outside the main centre of action. The method is applied to winter Northern Hemisphere (NH) monthly mean sea level pressure (SLP) reanalyses over the period 1948-2000. The 'simplified' leading patterns of variability are identified and compared to the leading patterns obtained from EOFs and REOFs. Copyright (C) 2005 Royal Meteorological Society.

Trends are very important in climate research and are ubiquitous in the climate system. Trends are usually estimated using simple linear regression. Given the complexity of the system, trends are expected to have various features such as global and local characters. It is therefore important to develop methods that permit a systematic decomposition of climate data into different trend patterns and remaining no-trend patterns. Empirical orthogonal functions and closely related methods, widely used in atmospheric science, are unable in general to capture trends because they are not devised for that purpose. The present paper presents a novel method capable of systematically capturing trend patterns from gridded data. The method is based on an eigenanalysis of the covariance/correlation matrix obtained using correlations between time positions of the sorted data, and trends are associated with the leading nondegenerate eigenvalues. Application to simple low-dimensional time series models and reanalyses data are presented and discussed. Copyright © 2006 Royal Meteorological Society.

This study investigates variability in the intensity of the wintertime Siberian high (SH) by defining a robust SH index (SHI) and correlating it with selected meteorological fields and teleconnection indices. A dramatic trend of –2.5 hPa decade−1 has been found in the SHI between 1978 and 2001 with unprecedented (since 1871) low values of the SHI. The weakening of the SH has been confirmed by analyzing different historical gridded analyses and individual station observations of sea level pressure (SLP) and excluding possible effects from the conversion of surface pressure to SLP. SHI correlation maps with various meteorological fields show that SH impacts on circulation and temperature patterns extend far outside the SH source area extending from the Arctic to the tropical Pacific. Advection of warm air from eastern Europe has been identified as the main mechanism causing milder than normal conditions over the Kara and Laptev Seas in association with a strong SH. Despite the strong impacts of the variability in the SH on climatic variability across the Northern Hemisphere, correlations between the SHI and the main teleconnection indices of the Northern Hemisphere are weak. Regression analysis has shown that teleconnection indices are not able to reproduce the interannual variability and trends in the SH. The inclusion of regional surface temperature in the regression model provides closer agreement between the original and reconstructed SHI.

Seasons are the complex nonlinear response of the physical climate system to regular annual solar forcing. There is no a priori reason why they should remain fixed/invariant from year to year, as is often assumed in climate studies when extracting the seasonal component. The widely used econometric variant of Census Method II Seasonal Adjustment Program (X-11), which allows for year-to-year variations in seasonal shape, is shown here to have some advantages for diagnosing climate variability. The X-11 procedure is applied to the monthly mean Niño-3.4 sea surface temperature (SST) index and global gridded NCEP–NCAR reanalyses of 2-m surface air temperature. The resulting seasonal component shows statistically significant interannual variations over many parts of the globe. By taking these variations in seasonality into account, it is shown that one can define less ambiguous ENSO indices. Furthermore, using the X-11 seasonal adjustment approach, it is shown that the three cold ENSO episodes after 1998 are due to an increase in amplitude of seasonality rather than being three distinct La Niña events. Globally, variations in the seasonal component represent a substantial fraction of the year-to-year variability in monthly mean temperatures. In addition, strong teleconnections can be discerned between the magnitude of seasonal variations across the globe. It might be possible to exploit such relationships to improve the skill of seasonal climate forecasts.

Robust statistical tools have been used to investigate non-normality and nonlinearity of the El Nino Southern Oscillation (ENSO) in observations and coupled model simulations. The analysis confirms previous suggestions that the observed Nino-3 sea surface temperature (SST) anomalies are positively skewed. The non-linearity is estimated using a simple nonlinear stochastic model, which relates the sea surface temperature anomalies to the observed thermocline depth anomalies in the Nino-3 region. There is evidence that saturation of SST only occurs when the thermocline is deep. The nonlinearity has also been estimated for the Nino-3 SST indices from twenty four different coupled models participating in the El Nino Simulation Intercomparison Project (ENSIP). Large differences are found between models and observations. In particular, the majority of the coupled models underestimate the nonlinearity seen in the observed Nino-3 sea surface temperature index. More than half of the models have Nino-3 SST indices that are normally distributed at 99% confidence level. Only a few models exhibit significant nonlinearity yet this tends to be rather different in character from the nonlinearity seen in the observations. Furthermore, no significant association is found between the means and the spread nor between the spread and the skewness for the different coupled model Nino-3 SST indices.

[1] Mixture model techniques are applied to a daily index of monsoon convection from ERA-40 reanalysis to show regime behavior. The result is the existence of two significant regimes showing preferred locations of convection within the Asia/Western-North Pacific domain, with some resemblance to active-break events over India. Simple trend analysis over 1958-2001 shows that the first regime has become less frequent while the second becomes much more dominant. Both undergo a change in structure contributing to the total OLR trend over the ERA-40 period. Stratifying the data according to a large-scale dynamical index of monsoon interannual variability, we show the regime occurrence to be strongly perturbed by the seasonal condition, in agreement with conceptual ideas. This technique could be used to further examine predictability issues relating the seasonal mean and intraseasonal monsoon variability or to explore changes in monsoon behavior in centennial-scale model integrations.