Covariance analysis of the Coulomb explosion of ammonia induced by intense nanosecond laser at 532 nm

The Coulomb explosion of ammonia clusters induced by nanosecond laser at 532 not with an intensity of similar to 10(12) Wcm(-2) has been studied by time of flight mass spectrometry. The dominant multiply charged ions are N3+ and N2+ with kinetic energies of 110 and 50 eV respectively. The electrons generated from the multiphoton ionization are heated through inverse bremsstrahlung by the laser field when colliding with neutral or ionic particles. When their energies surpass the corresponding ionization potentials of the molecules or ions, the subsequent electron impact ionization may take place thus resulting in multi-charged nitrogen ions. Covariance analysis is made to study the possible pathways of the Coulomb explosion.

Measurements of OVOC fluxes by eddy covariance using a proton-transfer-reaction mass spectrometer – method development at a coastal site

We present here vertical fluxes of oxygenated volatile organic compounds (OVOCs) measured with eddy covariance (EC) during the period of March to July 2012 near the southwest coast of the United Kingdom. The performance of the proton-transfer-reaction mass spectrometer (PTR-MS) for flux measurement is characterized, with additional considerations given to the homogeneity and stationarity assumptions required by EC. Observed mixing ratios and fluxes of OVOCs (specifically methanol, acetaldehyde, and acetone) vary significantly with time of day and wind direction. Higher mixing ratios and fluxes of acetaldehyde and acetone are found in the daytime and from the direction of a forested park, most likely due to light-driven emissions from terrestrial plants. Methanol mixing ratio and flux do not demonstrate consistent diel variability, suggesting sources in addition to plants. We estimate air-sea exchange and photochemical rates of these compounds, which are compared to measured vertical fluxes. For acetaldehyde, the mean (1 sigma) mixing ratio of 0.13 (0.02) ppb at night may be maintained by oceanic emission, while photochemical destruction out-paces production during the day. Air-sea exchange and photochemistry are probably net sinks of methanol and acetone in this region. Their nighttime mixing ratios of 0.46 (0.20) and 0.39 (0.08) ppb appear to be affected more by terrestrial emissions and long-distance transport, respectively.

Covariance among North Sea ecosystem state indicators during the past 50 years - contrasts between coastal and open waters

Regime shift and principal component analysis of a spatially disaggregated database capturing time-series of climatic, nutrient and plankton variables in the North Sea revealed considerable covariance between groups of ecosystem indicators. Plankton and climate time-series span the period 1958–2003, those of nutrients start in 1980. In both regions, the period from 1989 to 2001 identified in principal component 1 had warmer surface waters, higher Atlantic inflow and stronger winds, than the periods before or after. However, it was preceded by a regime shift in both open (PC2) and coastal (PC3) waters during 1977 towards more hours of sunlight and higher water temperature, which lasted until 1997. The relative influence of nutrient availability and climatic forcing differed between open and coastal North Sea regions. Inter-annual variability in phytoplankton dynamics of the open North Sea was primarily regulated by climatic forcing, specifically by sea surface temperature, Atlantic inflow and co-varying wind stress and NAO. Coastal phytoplankton variability, however, was regulated by insolation and sea surface temperature, as well as Si availability, but not by N or P. Regime shifts in principal components of hydrographic and climatic variables (explaining 55 and 61% of the variance in coastal and open water variables) were detected using Rodionov's sequential t-test. These shifts in hydroclimatic variables which occurred around 1977, 1989, 1997 and 2001, were synchronized in open and coastal waters, and were tracked by open water chlorophyll and copepods, but not by coastal plankton. North–central–south or open-coastal spatial breakdowns of the North Sea explained similar amounts of variability in most ecosystem indicators with the exception of diatom abundance and chlorophyll concentration, which were clearly better explained using the open-coastal configuration.

Covariance Averaging for Improved Estimation and Portfolio Allocation

We propose a new method for estimating the covariance matrix of a multivariate time series of nancial returns. The method is based on estimating sample covariances from overlapping windows of observations which are then appropriately weighted to obtain the nal covariance estimate. We extend the idea of (model) covariance averaging o ered in the covariance shrinkage approach by means of greater ease of use, exibility and robustness in averaging information over different data segments. The suggested approach does not su er from the curse of dimensionality and can be used without problems of either approximation or any demand for numerical optimization.

Small area estimation using linear mixed models with heterogeneous covariance structures of random effects

The problem of Small Area Estimation is about how to produce reliable estimates of domain characteristics when the sample sizes within the domain is very small ou even zero.

Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

Covariance, correlations, and r squared

lecture slides for COMP6235

A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances