Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions.

In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three others on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. We also propose a combined test procedure, whose level is again perfectly controlled through the Monte Carlo test technique and has better power properties than the individual tests that are combined. Finally, in a simulation experiment, we show that the technique suggested provides perfect control of test size and that the new tests proposed can yield sizeable power improvements.

Structures algébriques, systèmes superintégrables et polynômes orthogonaux

Cette thèse est divisée en cinq parties portant sur les thèmes suivants: l’interprétation physique et algébrique de familles de fonctions orthogonales multivariées et leurs applications, les systèmes quantiques superintégrables en deux et trois dimensions faisant intervenir des opérateurs de réflexion, la caractérisation de familles de polynômes orthogonaux appartenant au tableau de Bannai-Ito et l’examen des structures algébriques qui leurs sont associées, l’étude de la relation entre le recouplage de représentations irréductibles d’algèbres et de superalgèbres et les systèmes superintégrables, ainsi que l’interprétation algébrique de familles de polynômes multi-orthogonaux matriciels. Dans la première partie, on développe l’interprétation physico-algébrique des familles de polynômes orthogonaux multivariés de Krawtchouk, de Meixner et de Charlier en tant qu’éléments de matrice des représentations unitaires des groupes SO(d+1), SO(d,1) et E(d) sur les états d’oscillateurs. On détermine les amplitudes de transition entre les états de l’oscillateur singulier associés aux bases cartésienne et polysphérique en termes des polynômes multivariés de Hahn. On examine les coefficients 9j de su(1,1) par le biais du système superintégrable générique sur la 3-sphère. On caractérise les polynômes de q-Krawtchouk comme éléments de matrices des «q-rotations» de U_q(sl_2). On conçoit un réseau de spin bidimensionnel qui permet le transfert parfait d’états quantiques à l’aide des polynômes de Krawtchouk à deux variables et on construit un modèle discret de l’oscillateur quantique dans le plan à l’aide des polynômes de Meixner bivariés. Dans la seconde partie, on étudie les systèmes superintégrables de type Dunkl, qui font intervenir des opérateurs de réflexion. On examine l’oscillateur de Dunkl en deux et trois dimensions, l’oscillateur singulier de Dunkl dans le plan et le système générique sur la 2-sphère avec réflexions. On démontre la superintégrabilité de chacun de ces systèmes. On obtient leurs constantes du mouvement, on détermine leurs algèbres de symétrie et leurs représentations, on donne leurs solutions exactes et on détaille leurs liens avec les polynômes orthogonaux du tableau de Bannai-Ito. Dans la troisième partie, on caractérise deux familles de polynômes du tableau de Bannai-Ito: les polynômes de Bannai-Ito complémentaires et les polynômes de Chihara. On montre également que les polynômes de Bannai-Ito sont les coefficients de Racah de la superalgèbre osp(1,2). On détermine l’algèbre de symétrie des polynômes duaux -1 de Hahn dans le cadre du problème de Clebsch-Gordan de osp(1,2). On propose une q - généralisation des polynômes de Bannai-Ito en examinant le problème de Racah pour la superalgèbre quantique osp_q(1,2). Finalement, on montre que la q -algèbre de Bannai-Ito sert d’algèbre de covariance à osp_q(1,2). Dans la quatrième partie, on détermine le lien entre le recouplage de représentations des algèbres su(1,1) et osp(1,2) et les systèmes superintégrables du deuxième ordre avec ou sans réflexions. On étudie également les représentations des algèbres de Racah-Wilson et de Bannai-Ito. On montre aussi que l’algèbre de Racah-Wilson sert d’algèbre de covariance quadratique à l’algèbre de Lie sl(2). Dans la cinquième partie, on construit deux familles explicites de polynômes d-orthogonaux basées sur su(2). On étudie les états cohérents et comprimés de l’oscillateur fini et on caractérise une famille de polynômes multi-orthogonaux matriciels.

Multivariate Density Estimation: An SVM Approach

We formulate density estimation as an inverse operator problem. We then use convergence results of empirical distribution functions to true distribution functions to develop an algorithm for multivariate density estimation. The algorithm is based upon a Support Vector Machine (SVM) approach to solving inverse operator problems. The algorithm is implemented and tested on simulated data from different distributions and different dimensionalities, gaussians and laplacians in $R^2$ and $R^{12}$. A comparison in performance is made with Gaussian Mixture Models (GMMs). Our algorithm does as well or better than the GMMs for the simulations tested and has the added advantage of being automated with respect to parameters.

Equatorial Kelvin waves as revealed by EOS Microwave Limb Sounder observations and European Centre for Medium-Range Weather Forecasts analyses: Evidence for slow Kelvin waves of zonal wave number 3

[1] Temperature and ozone observations from the Microwave Limb Sounder (MLS) on the EOS Aura satellite are used to study equatorial wave activity in the autumn of 2005. In contrast to previous observations for the same season in other years, the temperature anomalies in the middle and lower tropical stratosphere are found to be characterized by a strong wave-like eastward progression with zonal wave number equal to 3. Extended empirical orthogonal function (EOF) analysis reveals that the wave 3 components detected in the temperature anomalies correspond to a slow Kelvin wave with a period of 8 days and a phase speed of 19 m/s. Fluctuations associated with this Kelvin wave mode are also apparent in ozone profiles. Moreover, as expected by linear theory, the ozone fluctuations observed in the lower stratosphere are in phase with the temperature perturbations, and peak around 20–30 hPa where the mean ozone mixing ratios have the steepest vertical gradient. A search for other Kelvin wave modes has also been made using both the MLS observations and the analyses from one experiment where MLS ozone profiles are assimilated into the European Centre for Medium-Range Weather Forecasts (ECMWF) data assimilation system via a 6-hourly 3D var scheme. Our results show that the characteristics of the wave activity detected in the ECMWF temperature and ozone analyses are in good agreement with MLS data.

On the Meridional Structure of Annular Modes

Using a simple stochastic model, the authors illustrate that the occurrence of a meridional dipole in the first empirical orthogonal function (EOF) of a time-dependent zonal jet is a simple consequence of the north–south excursion of the jet center, and this geometrical fact can be understood without appealing to fluid dynamical principles. From this it follows that one ought not, perhaps, be surprised at the fact that such dipoles, commonly referred to as the Arctic Oscillation (AO) or the Northern Annular Mode (NAM), have robustly been identified in many observational studies and appear to be ubiquitous in atmospheric models across a wide range of complexity.

MJO Simulation Diagnostics

The Madden–Julian oscillation (MJO) interacts with and influences a wide range of weather and climate phenomena (e.g., monsoons, ENSO, tropical storms, midlatitude weather), and represents an important, and as yet unexploited, source of predictability at the subseasonal time scale. Despite the important role of the MJO in climate and weather systems, current global circulation models (GCMs) exhibit considerable shortcomings in representing this phenomenon. These shortcomings have been documented in a number of multimodel comparison studies over the last decade. However, diagnosis of model performance has been challenging, and model progress has been difficult to track, because of the lack of a coherent and standardized set of MJO diagnostics. One of the chief objectives of the U.S. Climate Variability and Predictability (CLIVAR) MJO Working Group is the development of observation-based diagnostics for objectively evaluating global model simulations of the MJO in a consistent framework. Motivation for this activity is reviewed, and the intent and justification for a set of diagnostics is provided, along with specification for their calculation, and illustrations of their application. The diagnostics range from relatively simple analyses of variance and correlation to more sophisticated space–time spectral and empirical orthogonal function analyses. These diagnostic techniques are used to detect MJO signals, to construct composite life cycles, to identify associations of MJO activity with the mean state, and to describe interannual variability of the MJO.

Summertime precipitation variability over europe and its links to atmospheric dynamics and evaporation

Gridded monthly precipitation data for 1979-2006 from the Global Precipitation Climatology Project are used to investigate interannual summer precipitation variability over Europe and its links to regional atmospheric circulation and evaporation. The first empirical orthogonal function (EOF) mode of European precipitation, explaining 17.2%-22.8% of its total variance, is stable during the summer season and is associated with the North Atlantic Oscillation. The spatialtemporal structure of the second EOF mode is less stable and shows monthtomonth variations during the summer season. This mode is linked to the Scandinavian teleconnection pattern. Analysis of links between leading EOF modes of regional precipitation and evaporation has revealed a significant link between precipitation and evaporation from the European land surface, thus, indicating an important role of the local processes in summertime precipitation variability over Europe. Weaker, but statistically significant links have been found for evaporation from the surface of the Mediterranean and Baltic Seas. Finally, in contrast to winter, no significant links have been revealed between European precipitation and evaporation in the North Atlantic during the summer season.

Independent component analysis of climate data: A new look at EOF rotation

The complexity inherent in climate data makes it necessary to introduce more than one statistical tool to the researcher to gain insight into the climate system. Empirical orthogonal function (EOF) analysis is one of the most widely used methods to analyze weather/climate modes of variability and to reduce the dimensionality of the system. Simple structure rotation of EOFs can enhance interpretability of the obtained patterns but cannot provide anything more than temporal uncorrelatedness. In this paper, an alternative rotation method based on independent component analysis (ICA) is considered. The ICA is viewed here as a method of EOF rotation. Starting from an initial EOF solution rather than rotating the loadings toward simplicity, ICA seeks a rotation matrix that maximizes the independence between the components in the time domain. If the underlying climate signals have an independent forcing, one can expect to find loadings with interpretable patterns whose time coefficients have properties that go beyond simple noncorrelation observed in EOFs. The methodology is presented and an application to monthly means sea level pressure (SLP) field is discussed. Among the rotated (to independence) EOFs, the North Atlantic Oscillation (NAO) pattern, an Arctic Oscillation–like pattern, and a Scandinavian-like pattern have been identified. There is the suggestion that the NAO is an intrinsic mode of variability independent of the Pacific.

Using idealized snow forcing to test teleconnections with the Indian summer monsoon in the Hadley Centre GCM

Anomalous heavy snow during winter or spring has long been regarded as a possible precursor of deficient Indian monsoon rainfall during the subsequent summer. However previous work in this field is inconclusive, in terms of the mechanism that communicates snow anomalies to the monsoon summer, and even the region from which snow has the most impact. In this study we explore these issues in coupled and atmosphere-only versions of the Hadley Centre model. A 1050-year control integration of the HadCM3 coupled model, which well represents the seasonal cycle of snow cover over the Eurasian continent, is analysed and shows evidence for weakened monsoons being preceded by strong snow forcing (in the absence of ENSO) over either the Himalaya/Tibetan Plateau or north/west Eurasia regions. However, empirical orthogonal function (EOF) analysis of springtime interannual variability in snow depth shows the leading mode to have opposite signs between these two regions, suggesting that competing mechanisms may be possible. To determine the dominant region, ensemble integrations are carried out using HadAM3, the atmospheric component of HadCM3, and a variety of anomalous snow forcing initial conditions obtained from the control integration of the coupled model. Forcings are applied during spring in separate experiments over the Himalaya/Tibetan Plateau and north/west Eurasia regions, in conjunction with climatological SSTs in order to avoid the direct effects of ENSO. With the aid of idealized forcing conditions in sensitivity tests, we demonstrate that forcing from the Himalaya region is dominant in this model via a Blanford-type mechanism involving reduced surface sensible heat and longwave fluxes, reduced heating of the troposphere over the Tibetan Plateau and consequently a reduced meridional tropospheric temperature gradient which weakens the monsoon during early summer. Snow albedo is shown to be key to the mechanism, explaining around 50% of the perturbation in sensible heating over the Tibetan Plateau, and accounting for the majority of cooling through the troposphere.

Toward a combined seasonal weather and crop productivity forecasting system: Determination of the working spatial scale

A methodology is presented for the development of a combined seasonal weather and crop productivity forecasting system. The first stage of the methodology is the determination of the spatial scale(s) on which the system could operate; this determination has been made for the case of groundnut production in India. Rainfall is a dominant climatic determinant of groundnut yield in India. The relationship between yield and rainfall has been explored using data from 1966 to 1995. On the all-India scale, seasonal rainfall explains 52% of the variance in yield. On the subdivisional scale, correlations vary between variance r(2) = 0.62 (significance level p < 10(-4)) and a negative correlation with r(2) = 0.1 (p = 0.13). The spatial structure of the relationship between rainfall and groundnut yield has been explored using empirical orthogonal function (EOF) analysis. A coherent, large-scale pattern emerges for both rainfall and yield. On the subdivisional scale (similar to 300 km), the first principal component (PC) of rainfall is correlated well with the first PC of yield (r(2) = 0.53, p < 10(-4)), demonstrating that the large-scale patterns picked out by the EOFs are related. The physical significance of this result is demonstrated. Use of larger averaging areas for the EOF analysis resulted in lower and (over time) less robust correlations. Because of this loss of detail when using larger spatial scales, the subdivisional scale is suggested as an upper limit on the spatial scale for the proposed forecasting system. Further, district-level EOFs of the yield data demonstrate the validity of upscaling these data to the subdivisional scale. Similar patterns have been produced using data on both of these scales, and the first PCs are very highly correlated (r(2) = 0.96). Hence, a working spatial scale has been identified, typical of that used in seasonal weather forecasting, that can form the basis of crop modeling work for the case of groundnut production in India. Last, the change in correlation between yield and seasonal rainfall during the study period has been examined using seasonal totals and monthly EOFs. A further link between yield and subseasonal variability is demonstrated via analysis of dynamical data.

On the drivers of inter-annual and decadal rainfall variability in Queensland, Australia

Queensland experiences considerable inter-annual and decadal rainfall variability, which impacts water-resource management, agriculture and infrastructure. To understand the mechanisms by which large-scale atmospheric and coupled air–sea processes drive these variations, empirical orthogonal teleconnection (EOT) analysis is applied to 1900–2010 seasonal Queensland rainfall. Fields from observations and the 20th Century Reanalysis are regressed onto the EOT timeseries to associate the EOTs with large-scale drivers. In winter, spring and summer the leading, state-wide EOTs are highly correlated with the El Nino–Southern Oscillation (ENSO); the Inter-decadal Pacific Oscillation modulates the summer ENSO teleconnection. In autumn, the leading EOT is associated with locally driven, late-season monsoon variations, while ENSO affects only tropical northern Queensland. Examining EOTs beyond the first, southeastern Queensland and the Cape York peninsula emerge as regions of coherent rainfall variability. In the southeast, rainfall anomalies respond to the strength and moisture content of onshore easterlies, controlled by Tasman Sea blocking. The summer EOT associated with onshore flow and blocking has been negative since 1970, consistent with the observed decline in rainfall along the heavily populated coast. The southeastern Queensland EOTs show considerable multi-decadal variability, which is independent of large-scale drivers. Summer rainfall in Cape York is associated with tropical-cyclone activity.

A mechanism for Atlantic multidecadal variability in the Kiel Climate Model

Atlantic Multidecadal Variability (AMV) is investigated in a millennial control simulation with the Kiel Climate Model (KCM), a coupled atmosphere–ocean–sea ice model. An oscillatory mode with approximately 60 years period and characteristics similar to observations is identified with the aid of three-dimensional temperature and salinity joint empirical orthogonal function analysis. The mode explains 30 % of variability on centennial and shorter timescales in the upper 2,000 m of the North Atlantic. It is associated with changes in the Atlantic Meridional Overturning Circulation (AMOC) of ±1–2 Sv and Atlantic Sea Surface Temperature (SST) of ±0.2 °C. AMV in KCM results from an out-of-phase interaction between horizontal and vertical ocean circulation, coupled through Irminger Sea convection. Wintertime convection in this region is mainly controlled by salinity anomalies transported by the Subpolar Gyre (SPG). Increased (decreased) dense water formation in this region leads to a stronger (weaker) AMOC after 15 years, and this in turn leads to a weaker (stronger) SPG after another 15 years. The key role of salinity variations in the subpolar North Atlantic for AMV is confirmed in a 1,000 year long simulation with salinity restored to model climatology: No low frequency variations in convection are simulated, and the 60 year mode of variability is absent.

Isomap nonlinear dimensionality reduction and bimodality of Asian monsoon convection

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 dimensionality reduction, is applied to 1958–2001 ERA-40 sea-level pressure anomalies to study nonlinearity of the Asian summer monsoon intraseasonal variability. Using the leading two Isomap time series, the probability density function is shown to be bimodal. A two-dimensional bivariate Gaussian mixture model is then applied to identify the monsoon phases, the obtained regimes representing enhanced and suppressed phases, respectively. The relationship with the large-scale seasonal mean monsoon indicates that the frequency of monsoon regime occurrence is significantly perturbed in agreement with conceptual ideas, with preference for enhanced convection on intraseasonal time scales during large-scale strong monsoons. Trend analysis suggests a shift in concentration of monsoon convection, with less emphasis on South Asia and more on the East China Sea.

Surface water temperature observations of large lakes by optimal estimation

Optimal estimation (OE) and probabilistic cloud screening were developed to provide lake surface water temperature (LSWT) estimates from the series of (advanced) along-track scanning radiometers (ATSRs). Variations in physical properties such as elevation, salinity, and atmospheric conditions are accounted for through the forward modelling of observed radiances. Therefore, the OE retrieval scheme developed is generic (i.e., applicable to all lakes). LSWTs were obtained for 258 of Earth's largest lakes from ATSR-2 and AATSR imagery from 1995 to 2009. Comparison to in situ observations from several lakes yields satellite in situ differences of −0.2 ± 0.7 K for daytime and −0.1 ± 0.5 K for nighttime observations (mean ± standard deviation). This compares with −0.05 ± 0.8 K for daytime and −0.1 ± 0.9 K for nighttime observations for previous methods based on operational sea surface temperature algorithms. The new approach also increases coverage (reducing misclassification of clear sky as cloud) and exhibits greater consistency between retrievals using different channel–view combinations. Empirical orthogonal function (EOF) techniques were applied to the LSWT retrievals (which contain gaps due to cloud cover) to reconstruct spatially and temporally complete time series of LSWT. The new LSWT observations and the EOF-based reconstructions offer benefits to numerical weather prediction, lake model validation, and improve our knowledge of the climatology of lakes globally. Both observations and reconstructions are publically available from http://hdl.handle.net/10283/88.

20th century intraseasonal Asian monsoon dynamics viewed from Isomap

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 to 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 whereas 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.