Estimating interchannel observation-error correlations for IASI radiance data in the Met Office system

The optimal utilisation of hyper-spectral satellite observations in numerical weather prediction is often inhibited by incorrectly assuming independent interchannel observation errors. However, in order to represent these observation-error covariance structures, an accurate knowledge of the true variances and correlations is needed. This structure is likely to vary with observation type and assimilation system. The work in this article presents the initial results for the estimation of IASI interchannel observation-error correlations when the data are processed in the Met Office one-dimensional (1D-Var) and four-dimensional (4D-Var) variational assimilation systems. The method used to calculate the observation errors is a post-analysis diagnostic which utilises the background and analysis departures from the two systems. The results show significant differences in the source and structure of the observation errors when processed in the two different assimilation systems, but also highlight some common features. When the observations are processed in 1D-Var, the diagnosed error variances are approximately half the size of the error variances used in the current operational system and are very close in size to the instrument noise, suggesting that this is the main source of error. The errors contain no consistent correlations, with the exception of a handful of spectrally close channels. When the observations are processed in 4D-Var, we again find that the observation errors are being overestimated operationally, but the overestimation is significantly larger for many channels. In contrast to 1D-Var, the diagnosed error variances are often larger than the instrument noise in 4D-Var. It is postulated that horizontal errors of representation, not seen in 1D-Var, are a significant contributor to the overall error here. Finally, observation errors diagnosed from 4D-Var are found to contain strong, consistent correlation structures for channels sensitive to water vapour and surface properties

Filtering properties of wavelets for local background-error correlations

International audienceBackground-error covariances can be estimated from an ensemble of forecast differences. The finite size of the ensemble induces a sampling noise in the calculated statistics. It is shown formally that a wavelet diagonal approach amounts to locally averaging the correlations, and its ability to spatially filter this sampling noise is thus investigated experimentally. This is first studied in a simple analytical one-dimensional framework. The capacity of a wavelet diagonal approach to model the scale variations over the domain is illustrated. Moreover, the sampling noise appears to be better filtered than when only using a Schur filter, in particular for small ensembles. The filtering properties are then illustrated for an ensemble of Meteo-France Arpege forecasts. This is done both for the ‘time-averaged correlations', and for the ‘correlations of the day'. It is shown that the wavelets are able to extract some length-scale variations that are related to the meteorological situation

The error of representation: basic understanding

Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation where the distributions on the true attractor and the forecast attractors are separately Gaussian and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model

ESG Reputation Risk Matters: An Event Study Based on Social Media Data

We investigate the response of shareholders to Environmental, Social, and Governance-related reputational risk (ESG-risk), focusing exclusively on the impact of social media. Using a dataset of 114 million tweets about firms listed on the S&P100 index between 2016 and 2022, we extract conversations discussing ESG matters. In an event study design, we define events as unusual spikes in message posting activity linked to ESG-risk, and we then examine the corresponding changes in the returns of related assets. By focusing on social media, we gain insight into public opinion and investor sentiment, an aspect not captured through ESG controversies news alone. To the best of our knowledge, our approach is the first to distinctly separate the reputational impact on social media from the physical costs associated with negative ESG controversy news. Our results show that the occurrence of an ESG-risk event leads to a statistically significant average reduction of 0.29% in abnormal returns. Furthermore, our study suggests this effect is predominantly driven by Social and Governance categories, along with the "Environmental Opportunities" subcategory. Our research highlights the considerable impact of social media on financial markets, particularly in shaping shareholders' perception of ESG reputation. We formulate several policy implications based on our findings

Simulation of Laser Beam Propagation With a Paraxial Model in a Tilted Frame

We study the Schr\"odinger equation which comes from the paraxial approximation of the Helmholtz equation in the case where the direction of propagation is tilted with respect to the boundary of the domain. In a first part, a mathematical analysis is made which leads to an analytical formula of the solution in the simple case where the refraction index and the absorption coefficients are constant. Afterwards, we propose a numerical method for solving the initial problem which uses the previous analytical expression. Numerical results are presented. We also sketch an extension to a time dependant model which is relevant for laser plasma interaction

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

Simulation of Laser Propagation in a Plasma with a Frequency Wave Equation

The aim of this work is to perform numerical simulations of the propagation of a laser in a plasma. At each time step, one has to solve a Helmholtz equation in a domain which consists in some hundreds of millions of cells. To solve this huge linear system, one uses a iterative Krylov method with a preconditioning by a separable matrix. The corresponding linear system is solved with a block cyclic reduction method. Some enlightments on the parallel implementation are also given. Lastly, numerical results are presented including some features concerning the scalability of the numerical method on a parallel architecture

A Priori Error Estimate of a Multiscale Finite Element Method for Transport Modeling

International audienceThis work proposes an \textit{a priori} error estimate of a multiscale finite element method to solve convection-diffusion problems where both velocity and diffusion coefficient exhibit strong variations at a scale which is much smaller than the domain of resolution. In that case, classical discretization methods, used at the scale of the heterogeneities, turn out to be too costly. Our method, introduced in~\cite{ECCOMAS}, aims at solving this kind of problems on coarser grids with respect to the size of the heterogeneities by means of particular basis functions. These basis functions are defined using cell problems and are designed to reproduce the variations of the solution on an underlying fine grid. Since all cell problems are independent from each other, these problems can be solved in parallel, which makes the method very efficient when used on parallel architectures. This article focuses on the proof of an \textit{a priori} error estimate of this method

Female sexual behavior in mice is controlled by kisspeptin neurons.

Sexual behavior is essential for the survival of many species. In female rodents, mate preference and copulatory behavior depend on pheromones and are synchronized with ovulation to ensure reproductive success. The neural circuits driving this orchestration in the brain have, however, remained elusive. Here, we demonstrate that neurons controlling ovulation in the mammalian brain are at the core of a branching neural circuit governing both mate preference and copulatory behavior. We show that male odors detected in the vomeronasal organ activate kisspeptin neurons in female mice. Classical kisspeptin/Kiss1R signaling subsequently triggers olfactory-driven mate preference. In contrast, copulatory behavior is elicited by kisspeptin neurons in a parallel circuit independent of Kiss1R involving nitric oxide signaling. Consistent with this, we find that kisspeptin neurons impinge onto nitric oxide-synthesizing neurons in the ventromedial hypothalamus. Our data establish kisspeptin neurons as a central regulatory hub orchestrating sexual behavior in the female mouse brain