Theoretical insight into diagnosing observation error correlations using observation-minus-background and observation-minus-analysis statistics

To improve the quantity and impact of observations used in data assimilation it is necessary to take into account the full, potentially correlated, observation error statistics. A number of methods for estimating correlated observation errors exist, but a popular method is a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. The accuracy of the results it yields is unknown as the diagnostic is sensitive to the difference between the exact background and exact observation error covariances and those that are chosen for use within the assimilation. It has often been stated in the literature that the results using this diagnostic are only valid when the background and observation error correlation length scales are well separated. Here we develop new theory relating to the diagnostic. For observations on a 1D periodic domain we are able to the show the effect of changes in the assumed error statistics used in the assimilation on the estimated observation error covariance matrix. We also provide bounds for the estimated observation error variance and eigenvalues of the estimated observation error correlation matrix. We demonstrate that it is still possible to obtain useful results from the diagnostic when the background and observation error length scales are similar. In general, our results suggest that when correlated observation errors are treated as uncorrelated in the assimilation, the diagnostic will underestimate the correlation length scale. We support our theoretical results with simple illustrative examples. These results have potential use for interpreting the derived covariances estimated using an operational system.

Dynamical properties of S-gap shifts and other shift spaces

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified shift is both BSM and balanced, and any balanced shift is BSM. However, as we will demonstrate, there are examples of shifts which are BSM but not balanced. We also study the measure theoretic properties of balanced shifts. We show that a shift space admits a Gibbs state if and only if it is balanced. Restricting ourselves to S-gap shifts, we relate certain dynamical properties of an S-gap shift to combinatorial properties from expansions in non-integer bases. This identification allows us to use the machinery from expansions in non-integer bases to give straightforward constructions of S -gap shifts with certain desirable properties. We show that for any q∈(0,1) there is an S-gap shift which has the specification property and entropy q . We also use this identification to address the question, for a given q∈(0,1), how many S-gap shifts exist with entropy q? For certain exceptional values of q there is a unique S-gap shift with this entropy.

A new calibrated sunspot group series since 1749: statistics of active day fractions

Although the sunspot-number series have existed since the mid-19th century, they are still the subject of intense debate, with the largest uncertainty being related to the "calibration" of the visual acuity of individual observers in the past. Daisy-chain regression methods are applied to inter-calibrate the observers which may lead to significant bias and error accumulation. Here we present a novel method to calibrate the visual acuity of the key observers to the reference data set of Royal Greenwich Observatory sunspot groups for the period 1900-1976, using the statistics of the active-day fraction. For each observer we independently evaluate their observational thresholds [S_S] defined such that the observer is assumed to miss all of the groups with an area smaller than S_S and report all the groups larger than S_S. Next, using a Monte-Carlo method we construct, from the reference data set, a correction matrix for each observer. The correction matrices are significantly non-linear and cannot be approximated by a linear regression or proportionality. We emphasize that corrections based on a linear proportionality between annually averaged data lead to serious biases and distortions of the data. The correction matrices are applied to the original sunspot group records for each day, and finally the composite corrected series is produced for the period since 1748. The corrected series displays secular minima around 1800 (Dalton minimum) and 1900 (Gleissberg minimum), as well as the Modern grand maximum of activity in the second half of the 20th century. The uniqueness of the grand maximum is confirmed for the last 250 years. It is shown that the adoption of a linear relationship between the data of Wolf and Wolfer results in grossly inflated group numbers in the 18th and 19th centuries in some reconstructions.

Diagnosing observation error correlations for Doppler radar radial winds in the Met Office UKV model using observation-minus-background and observation-minus-analysis statistics

With the development of convection-permitting numerical weather prediction the efficient use of high resolution observations in data assimilation is becoming increasingly important. The operational assimilation of these observations, such as Dopplerradar radial winds, is now common, though to avoid violating the assumption of un- correlated observation errors the observation density is severely reduced. To improve the quantity of observations used and the impact that they have on the forecast will require the introduction of the full, potentially correlated, error statistics. In this work, observation error statistics are calculated for the Doppler radar radial winds that are assimilated into the Met Office high resolution UK model using a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. This is the first in-depth study using the diagnostic to estimate both horizontal and along-beam correlated observation errors. By considering the new results obtained it is found that the Doppler radar radial wind error standard deviations are similar to those used operationally and increase as the observation height increases. Surprisingly the estimated observation error correlation length scales are longer than the operational thinning distance. They are dependent on both the height of the observation and on the distance of the observation away from the radar. Further tests show that the long correlations cannot be attributed to the use of superobservations or the background error covariance matrix used in the assimilation. The large horizontal correlation length scales are, however, in part, a result of using a simplified observation operator.

Biases in comparative analyses of extinction risk: mind the gap

1. Comparative analyses are used to address the key question of what makes a species more prone to extinction by exploring the links between vulnerability and intrinsic species’ traits and/or extrinsic factors. This approach requires comprehensive species data but information is rarely available for all species of interest. As a result comparative analyses often rely on subsets of relatively few species that are assumed to be representative samples of the overall studied group. 2. Our study challenges this assumption and quantifies the taxonomic, spatial, and data type biases associated with the quantity of data available for 5415 mammalian species using the freely available life-history database PanTHERIA. 3. Moreover, we explore how existing biases influence results of comparative analyses of extinction risk by using subsets of data that attempt to correct for detected biases. In particular, we focus on links between four species’ traits commonly linked to vulnerability (distribution range area, adult body mass, population density and gestation length) and conduct univariate and multivariate analyses to understand how biases affect model predictions. 4. Our results show important biases in data availability with c.22% of mammals completely lacking data. Missing data, which appear to be not missing at random, occur frequently in all traits (14–99% of cases missing). Data availability is explained by intrinsic traits, with larger mammals occupying bigger range areas being the best studied. Importantly, we find that existing biases affect the results of comparative analyses by overestimating the risk of extinction and changing which traits are identified as important predictors. 5. Our results raise concerns over our ability to draw general conclusions regarding what makes a species more prone to extinction. Missing data represent a prevalent problem in comparative analyses, and unfortunately, because data are not missing at random, conventional approaches to fill data gaps, are not valid or present important challenges. These results show the importance of making appropriate inferences from comparative analyses by focusing on the subset of species for which data are available. Ultimately, addressing the data bias problem requires greater investment in data collection and dissemination, as well as the development of methodological approaches to effectively correct existing biases.

Conservative force fields in non-Gaussian statistics

In this Letter, we determine the kappa-distribution function for a gas in the presence of an external field of force described by a potential U(r). In the case of a dilute gas, we show that the kappa-power law distribution including the potential energy factor term can rigorously be deduced in the framework of kinetic theory with basis on the Vlasov equation. Such a result is significant as a preliminary to the discussion on the role of long range interactions in the Kaniadakis thermostatistics and the underlying kinetic theory. (C) 2008 Elsevier B.V. All rights reserved.

The corotation gap in the Galactic H i distribution

We used the H i data from the LAB Survey to map the ring-shaped gap in H i density that lies slightly outside the solar circle. Adopting R(0) = 7.5 kpc, we find an average gap radius of 8.3 kpc and an average gap width of 0.8 kpc. The characteristics of the H i gap correspond closely to the expected ones, as predicted by theory and by numerical simulations of the gas flow near the corotation resonance.

Using gap-crossing capacity to evaluate functional connectivity of two Atlantic rainforest birds and their response to fragmentation

One of the main consequences of habitat loss and fragmentation is the increase in patch isolation and the consequent decrease in landscape connectivity. In this context, species persistence depends on their responses to this new landscape configuration, particularly on their capacity to move through the interhabitat matrix. Here, we aimed first to determine gap-crossing probabilities related to different gap widths for two forest birds (Thamnophilus caerulescens, Thamnophilidae, and Basileuterus culicivorus, Parulidae) from the Brazilian Atlantic rainforest. These values were defined with a playback technique and then used in analyses based on graph theory to determine functional connections among forest patches. Both species were capable of crossing forest gaps between patches, and these movements were related to gap width. The probability of crossing 40 m gaps was 50% for both species. This probability falls to 10% when the gaps are 60 m (for B. culicivorus) or 80 m (for T caerulescens). Actually, birds responded to stimulation about two times more distant inside forest trials (control) than in gap-crossing trials. Models that included gap-crossing capacity improved the explanatory power of species abundance variation in comparison to strictly structural models based merely on patch area and distance measurements. These results highlighted that even very simple functional connectivity measurements related to gap-crossing capacity can improve the understanding of the effect of habitat fragmentation on bird occurrence and abundance.

MAGNETIC FIELD INDUCED NEAR-BAND-GAP OPTICAL PROPERTIES IN EuTe LAYERS

The magnetic response of the near-band-edge optical properties is studied in EuTe layers. In several magneto-optical experiments, the absorption and emission are described as well as the related Stokes shift. Specifically, we present the first experimental report of the photoluminescence excitation (PLE) spectrum in Faraday configuration. The PLE spectra shows to be related with the absorption spectra through the observation of resonance between the excitation light and the zero-field band-gap. A new emission line appears at 1.6 eV at a moderate magnetic field in the photoluminescence (PL) spectra. Furthermore, we examine the absorption and PL red-shift induced by the magnetic field in the light of the d-f exchange interaction energy involved in these processes. Whereas the absorption red-shift shows a quadratic dependence on the field, the PL red-shift shows a linear dependence which is explained by spin relaxation of the excited state.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Developing and Facilitating a Successful Hybrid Statistics Course

This presentation will outline an effective model for a Hybrid Statistics course. The course continues to be very successful, incorporating on-line instruction, testing, blogs, and above all, a data analysis project driven trajectory motivating students to engage more aggressively in the class and rise up to the challenge of writing an original research paper. Obstacles, benefits and successes of this endeavor will be addressed.

Gender Equality a case study of Sweden : Gender Equality Gender Equity and policies of combating inequality at workplace to make the society equal.

The paper analyses Gender Equality, Gender Equity and policies of combating inequality at workplace to make the society equal as a case study of Sweden. The aim of paper is see the gender equality, gender equity, discrimination against women at workplace and to describe the policies combating inequality in the welfare state of Sweden. This work highlights the gender equality in terms of institutionalizing gender equality, gender equity, gender and pay gap, parental leave, gender and the pension system and sexual behavior directed towards women and policies combating inequality to bring equality in society. For my research I used the secondary data the fact sheets, scientific literature, statistics from eurostate of Sweden and case studies about Swedish society and the theoretical explanation to explain the phenomena. To achieve my aim I used the combination of both qualitative and quantitative methods of research. I showed the empirical evidences of these phenomena from the Swedish society and theoretical analysis about equality and equity of gender in different wakes of life. I found an interesting conclusion that there are good policies and legislation to combat inequality to bring society but there are no policies to change the perception of society about male and female role.