Spatiotemporal behavior of the TIGGE medium-range ensemble forecasts

Using the recently-developed mean–variance of logarithms (MVL) diagram, together with the TIGGE archive of medium-range ensemble forecasts from nine different centres, an analysis is presented of the spatiotemporal dynamics of their perturbations, showing how the differences between models and perturbation techniques can explain the shape of their characteristic MVL curves. In particular, a divide is seen between ensembles based on singular vectors or empirical orthogonal functions, and those based on bred vector, Ensemble Transform with Rescaling or Ensemble Kalman Filter techniques. Consideration is also given to the use of the MVL diagram to compare the growth of perturbations within the ensemble with the growth of the forecast error, showing that there is a much closer correspondence for some models than others. Finally, the use of the MVL technique to assist in selecting models for inclusion in a multi-model ensemble is discussed, and an experiment suggested to test its potential in this context.

Low-order dynamical behavior in the martian atmosphere: Diagnosis of general circulation model results

The hypothesis of a low dimensional martian climate attractor is investigated by the application of the proper orthogonal decomposition (POD) to a simulation of martian atmospheric circulation using the UK Mars general circulation model (UK-MGCM). In this article we focus on a time series of the interval between autumn and winter in the northern hemisphere, when baroclinic activity is intense. The POD is a statistical technique that allows the attribution of total energy (TE) to particular structures embedded in the UK-MGCM time-evolving circulation. These structures are called empirical orthogonal functions (EOFs). Ordering the EOFs according to their associated energy content, we were able to determine the necessary number to account for a chosen amount of atmospheric TE. We show that for Mars a large fraction of TE is explained by just a few EOFs (with 90% TE in 23 EOFs), which apparently support the initial hypothesis. We also show that the resulting EOFs represent classical types of atmospheric motion, such as thermal tides and transient waves. Thus, POD is shown to be an efficient method for the identification of different classes of atmospheric modes. It also provides insight into the non-linear interaction of these modes.

A comparison of extreme value theory approaches for determining value at risk

This paper compares a number of different extreme value models for determining the value at risk (VaR) of three LIFFE futures contracts. A semi-nonparametric approach is also proposed, where the tail events are modeled using the generalised Pareto distribution, and normal market conditions are captured by the empirical distribution function. The value at risk estimates from this approach are compared with those of standard nonparametric extreme value tail estimation approaches, with a small sample bias-corrected extreme value approach, and with those calculated from bootstrapping the unconditional density and bootstrapping from a GARCH(1,1) model. The results indicate that, for a holdout sample, the proposed semi-nonparametric extreme value approach yields superior results to other methods, but the small sample tail index technique is also accurate.

An extreme value theory approach to calculating minimum capital risk requirements

This paper investigates the frequency of extreme events for three LIFFE futures contracts for the calculation of minimum capital risk requirements (MCRRs). We propose a semiparametric approach where the tails are modelled by the Generalized Pareto Distribution and smaller risks are captured by the empirical distribution function. We compare the capital requirements form this approach with those calculated from the unconditional density and from a conditional density - a GARCH(1,1) model. Our primary finding is that both in-sample and for a hold-out sample, our extreme value approach yields superior results than either of the other two models which do not explicitly model the tails of the return distribution. Since the use of these internal models will be permitted under the EC-CAD II, they could be widely adopted in the near future for determining capital adequacies. Hence, close scrutiny of competing models is required to avoid a potentially costly misallocation capital resources while at the same time ensuring the safety of the financial system.

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.

Influence of the quasi-biennial oscillation on the extratropical winter stratosphere in an atmospheric general circulation model and in reanalysis data

The interannual variability of the stratospheric polar vortex during winter in both hemispheres is observed to correlate strongly with the phase of the quasi-biennial oscillation (QBO) in tropical stratospheric winds. It follows that the lack of a spontaneously generated QBO in most atmospheric general circulation models (AGCMs) adversely affects the nature of polar variability in such models. This study examines QBO–vortex coupling in an AGCM in which a QBO is spontaneously induced by resolved and parameterized waves. The QBO–vortex coupling in the AGCM compares favorably to that seen in reanalysis data [from the 40-yr ECMWF Re-Analysis (ERA-40)], provided that careful attention is given to the definition of QBO phase. A phase angle representation of the QBO is employed that is based on the two leading empirical orthogonal functions of equatorial zonal wind vertical profiles. This yields a QBO phase that serves as a proxy for the vertical structure of equatorial winds over the whole depth of the stratosphere and thus provides a means of subsampling the data to select QBO phases with similar vertical profiles of equatorial zonal wind. Using this subsampling, it is found that the QBO phase that induces the strongest polar vortex response in early winter differs from that which induces the strongest late-winter vortex response. This is true in both hemispheres and for both the AGCM and ERA-40. It follows that the strength and timing of QBO influence on the vortex may be affected by the partial seasonal synchronization of QBO phase transitions that occurs both in observations and in the model. This provides a mechanism by which changes in the strength of QBO–vortex correlations may exhibit variability on decadal time scales. In the model, such behavior occurs in the absence of external forcings or interannual variations in sea surface temperatures.

Reduced-order dynamics of the Martian atmospheric dynamics

In this paper we explore the possibility of deriving low-dimensional models of the dynamics of the Martian atmosphere. The analysis consists of a Proper Orthogonal Decomposition (POD) of the atmospheric streamfunction after first decomposing the vertical structure with a set of eigenmodes. The vertical modes were obtained from the quasi-geostrophic vertical structure equation. The empirical orthogonal functions (EOFs) were optimized to represent the atmospheric total energy. The total energy was used as the criterion to retain those modes with large energy content and discard the rest. The principal components (PCs) were analysed by means of Fourier analysis, so that the dominant frequencies could be identified. It was possible to observe the strong influence of the diurnal cycle and to identify the motion and vacillation of baroclinic waves.

Extreme rainfall variability in Australia: Patterns, drivers and predictability

Leading patterns of observed monthly extreme rainfall variability in Australia are examined using an Empirical Orthogonal Teleconnection (EOT) method. Extreme rainfall variability is more closely related to mean rainfall variability during austral summer than in winter. The leading EOT patterns of extreme rainfall explain less variance in Australia-wide extreme rainfall than is the case for mean rainfall EOTs. We illustrate that, as with mean rainfall, the El Niño-Southern Oscillation (ENSO) has the strongest association with warm-season extreme rainfall variability, while in the cool-season the primary drivers are atmospheric blocking and the subtropical ridge. The Indian Ocean Dipole and Southern Annular Mode also have significant relationships with patterns of variability during austral winter and spring. Leading patterns of summer extreme rainfall variability have predictability several months ahead from Pacific sea surface temperatures (SSTs) and as much as a year in advance from Indian Ocean SSTs. Predictability from the Pacific is greater for wetter than average summer months than for months that are drier than average, whereas for the Indian Ocean the relationship has greater linearity. Several cool-season EOTs are associated with mid-latitude synoptic-scale patterns along the south and east coasts. These patterns have common atmospheric signatures denoting moist onshore flow and strong cyclonic anomalies often to the north of a blocking anti-cyclone. Tropical cyclone activity is observed to have significant relationships with some warm season EOTs. This analysis shows that extreme rainfall variability in Australia can be related to remote drivers and local synoptic-scale patterns throughout the year.

Identification of Mechanical Systems through Kautz Filter

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Parametric VaR with goodness-of-fit tests based on EDF statistics for extreme returns

Parametric VaR (Value-at-Risk) is widely used due to its simplicity and easy calculation. However, the normality assumption, often used in the estimation of the parametric VaR, does not provide satisfactory estimates for risk exposure. Therefore, this study suggests a method for computing the parametric VaR based on goodness-of-fit tests using the empirical distribution function (EDF) for extreme returns, and compares the feasibility of this method for the banking sector in an emerging market and in a developed one. The paper also discusses possible theoretical contributions in related fields like enterprise risk management (ERM). © 2013 Elsevier Ltd.

Eventos extremos da zona de convergência intertropical sobre o Atlântico durante o período chuvoso da Amazônia oriental

Este trabalho reporta uma investigação observacional sobre as características climatológicas (período de 1985 a 2007) associadas aos eventos extremos da ZCIT observados sobre o Oceano Atlântico equatorial, procurando estabelecer as influências na variabilidade pluviométrica da Amazônia oriental, durante os meses de fevereiro, março e abril. Tais eventos foram selecionados objetivamente através da análise de Funções Ortogonais Empíricas e os padrões oceano-atmosfera associados aos eventos da ZCIT, bem como seus impactos na precipitação da Amazônia oriental, foram investigados com base em composições mensais. Os resultados evidenciaram algumas diferenças mensais, principalmente no padrão da circulação atmosférica em 200 hPa e na configuração vertical da circulação troposférica meridional associada à célula de Hadley equatorial. Quanto à estrutura dinâmica dos padrões oceano-atmosfera observada nos meses de fevereiro, março e abril, basicamente evidenciou-se que a ZCIT forma-se sobre o Oceano Atlântico equatorial numa região de confluência dos ventos alísios de sudeste e nordeste, coincidente com áreas contendo TSM anomalamente quente, movimento vertical ascendente associado à célula de Hadley, com divergência do vento em altos níveis. Os impactos de tais eventos na variabilidade espacial da precipitação sobre a Amazônia oriental mostrou que os principais estados afetados pela ZCIT são: Amapá, Pará e Maranhão. Adicionalmente, relatam-se alguns impactos sócio-ambientais (enchentes, alagamentos, queda de árvores, proliferação de doenças, entre outros) que ocorreram na Região Metropolitana de Belém, associados a ocorrência dos eventos extremos da ZCIT selecionados neste trabalho.

The response of the Sao Paulo Continental Shelf, Brazil, to synoptic winds

The response of the Sao Paulo Continental Shelf (SPCS) to synoptic wind forcing has been analyzed. Two different methods are used for this purpose, one based on hydrographic data, bottom topography, and geographical characteristics, and a second on analyzing currentmeter data directly and using empirical orthogonal functions. Both methods show similar results for an essentially barotropic shelf. The SPCS response in the subinertial frequency band appears to be trapped on the continental shelf. Numerical experiments have also been carried out showing results that qualitatively agree with the observations, including the velocity component parallel to the coastline.

The Truncated Inflated Beta Distribution

The study of proportions is a common topic in many fields of study. The standard beta distribution or the inflated beta distribution may be a reasonable choice to fit a proportion in most situations. However, they do not fit well variables that do not assume values in the open interval (0, c), 0 < c < 1. For these variables, the authors introduce the truncated inflated beta distribution (TBEINF). This proposed distribution is a mixture of the beta distribution bounded in the open interval (c, 1) and the trinomial distribution. The authors present the moments of the distribution, its scoring vector, and Fisher information matrix, and discuss estimation of its parameters. The properties of the suggested estimators are studied using Monte Carlo simulation. In addition, the authors present an application of the TBEINF distribution for unemployment insurance data.

Refined Estimation of Earthquake Source Parameters: Methods, Applications and Scaling Relationships

The objective of this work of thesis is the refined estimations of source parameters. To such a purpose we used two different approaches, one in the frequency domain and the other in the time domain. In frequency domain, we analyzed the P- and S-wave displacement spectra to estimate spectral parameters, that is corner frequencies and low frequency spectral amplitudes. We used a parametric modeling approach which is combined with a multi-step, non-linear inversion strategy and includes the correction for attenuation and site effects. The iterative multi-step procedure was applied to about 700 microearthquakes in the moment range 1011-1014 N•m and recorded at the dense, wide-dynamic range, seismic networks operating in Southern Apennines (Italy). The analysis of the source parameters is often complicated when we are not able to model the propagation accurately. In this case the empirical Green function approach is a very useful tool to study the seismic source properties. In fact the Empirical Green Functions (EGFs) consent to represent the contribution of propagation and site effects to signal without using approximate velocity models. An EGF is a recorded three-component set of time-histories of a small earthquake whose source mechanism and propagation path are similar to those of the master event. Thus, in time domain, the deconvolution method of Vallée (2004) was applied to calculate the source time functions (RSTFs) and to accurately estimate source size and rupture velocity. This technique was applied to 1) large event, that is Mw=6.3 2009 L’Aquila mainshock (Central Italy), 2) moderate events, that is cluster of earthquakes of 2009 L’Aquila sequence with moment magnitude ranging between 3 and 5.6, 3) small event, i.e. Mw=2.9 Laviano mainshock (Southern Italy).