Detection and correction of the misplacement error in THz Spectroscopy by application of singly subtractive Kramers-Kronig relations

In THz reflection spectroscopy the complex permittivity of an opaque medium is determined on the basis of the amplitude and of the phase of the reflected wave. There is usually a problem of phase error due to misplacement of the reference sample. Such experimental error brings inconsistency between phase and amplitude invoked by the causality principle. We propose a rigorous method to solve this relevant experimental problem by using an optimization method based upon singly subtractive Kramers-Kronig relations. The applicability of the method is demonstrated for measured data on an n-type undoped (100) InAs wafer in the spectral range from 0.5 up to 2.5 THz.Comment: 16 pages, 5 figure

Lyapunov analysis of multiscale dynamics: the slow bundle of the two-scale Lorenz 96 model

We investigate the geometrical structure of instabilities in the two-scale Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a slow bundle in tangent space, composed by a set of vectors with a significant projection onto the slow degrees of freedom; they correspond to the smallest (in absolute value) Lyapunov exponents and thereby to the longer timescales. We show that the dimension of the slow bundle is extensive in the number of both slow and fast degrees of freedom and discuss its relationship with the results of a finite-size analysis of instabilities, supporting the conjecture that the slow-variable behavior is effectively determined by a nontrivial subset of degrees of freedom. More precisely, we show that the slow bundle corresponds to the Lyapunov spectrum region where fast and slow instability rates overlap, “mixing” their evolution into a set of vectors which simultaneously carry information on both scales. We suggest that these results may pave the way for future applications to ensemble forecasting and data assimilations in weather and climate models

Return levels of temperature extremes in southern Pakistan

Southern Pakistan (Sindh) is one of the hottest regions in the world and is highly vulnerable to temperature extremes. In order to improve rural and urban planning, it is useful to gather information about the recurrence of temperature extremes. In this work, return levels of the daily maximum temperature Tmax are estimated, as well as the daily maximum wet-bulb temperature TWmax extremes. We adopt the peaks over threshold (POT) method, which has not yet been used for similar studies in this region. Two main datasets are analyzed: temperatures observed at nine meteorological stations in southern Pakistan from 1980 to 2013, and the ERA-Interim (ECMWF reanalysis) data for the nearest corresponding locations. The analysis provides the 2-, 5-, 10-, 25-, 50-, and 100-year return levels (RLs) of temperature extremes. The 90 % quantile is found to be a suitable threshold for all stations. We find that the RLs of the observed Tmax are above 50 °C at northern stations and above 45 °C at the southern stations. The RLs of the observed TWmax exceed 35 °C in the region, which is considered as a limit of survivability. The RLs estimated from the ERA-Interim data are lower by 3 to 5 °C than the RLs assessed for the nine meteorological stations. A simple bias correction applied to ERA-Interim data improves the RLs remarkably, yet discrepancies are still present. The results have potential implications for the risk assessment of extreme temperatures in Sindh

Testing the validity of THz reflection spectra by dispersion relations

Complex response function obtained in reflection spectroscopy at terahertz range is examined with algorithms based on dispersion relations for integer powers of complex reflection coefficient, which emerge as a powerful and yet uncommon tools in examining the consistency of the spectroscopic data. It is shown that these algorithms can be used in particular for checking the success of correction of the spectra by the methods of Vartiainen et al [1] and Lucarini et al [2] to remove the negative misplacement error in the terahertz time-domain spectroscopy.Comment: 17 pages, 4 figure

Accessing extremes of mid-latitudinal wave activity: methodology and application

A statistical methodology is proposed and tested for the analysis of extreme values of atmospheric wave activity at mid-latitudes. The adopted methods are the classical block-maximum and peak over threshold, respectively based on the generalized extreme value (GEV) distribution and the generalized Pareto distribution (GPD). Time-series of the ‘Wave Activity Index’ (WAI) and the ‘Baroclinic Activity Index’ (BAI) are computed from simulations of the General Circulation Model ECHAM4.6, which is run under perpetual January conditions. Both the GEV and the GPD analyses indicate that the extremes ofWAI and BAI areWeibull distributed, this corresponds to distributions with an upper bound. However, a remarkably large variability is found in the tails of such distributions; distinct simulations carried out under the same experimental setup provide sensibly different estimates of the 200-yr WAI return level. The consequences of this phenomenon in applications of the methodology to climate change studies are discussed. The atmospheric configurations characteristic of the maxima and minima of WAI and BAI are also examined

Bistable systems with stochastic noise: Virtues and limits of effective one-dimensional Langevin equations

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power

Effects of stochastic parametrization on extreme value statistics

Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations are computational tools used in the Earth system models, which are aimed at reproducing the impact of unresolved scales on resolved scales. The performance of parametrizations has usually been examined on typical events rather than on extreme events. In this paper, we consider a modified version of the two-level Lorenz’96 model and investigate how two parametrizations of the fast degrees of freedom perform in terms of the representation of extreme events. One parametrization is constructed following Wilks [Q. J. R. Meteorol. Soc. 131, 389–407 (2005)] and is constructed through an empirical fitting procedure; the other parametrization is constructed through the statistical mechanical approach proposed by Wouters and Lucarini [J. Stat. Mech. Theory Exp. 2012, P03003 (2012); J. Stat. Phys. 151, 850–860 (2013)]. The two strategies show different advantages and disadvantages. We discover that the agreement between parametrized models and true model is in general worse when looking at extremes rather than at the bulk of the statistics. The results suggest that stochastic parametrizations should be accurately and specifically tested against their performance on extreme events, as usual optimization procedures might neglect them. The provision of accurate parametrizations is a task of paramount importance in many scientific areas and specifically in weather and climate modeling. Parametrizations are needed for representing accurately and efficiently the impact of the scales of motions and of the processes that cannot be explicitly represented by the numerical model. Parametrizations are usually constructed in order to optimize the overall performance of the model, thus aiming at an accurate representation of the bulk of the statistics. Nonetheless, numerical models are key to estimating, anticipating, and predicting extreme events. Here, we analyze critically in a simple yet illustrative example the performance of parametrizations in describing extreme events, and we conclude that good performance on typical conditions cannot be in any way extrapolated for rare conditions, which could, nonetheless, be of great practical relevance