Pure rotational-Raman channels of the Esrange lidar for temperature and particle extinction measurements in the troposphere and lower stratosphere

The Department of Meteorology at Stockholm University operates the Esrange Rayleigh/Raman lidar at Esrange (68° N, 21° E) near the Swedish city of Kiruna. This paper describes the design and first measurements of the new pure rotational-Raman channel of the Esrange lidar. The Esrange lidar uses a pulsed Nd:YAG solid-state laser operating at 532 nm as light source with a repetition rate of 20 Hz and a pulse energy of 350 mJ. The minimum vertical resolution is 150 m and the integration time for one profile is 5000 shots. The newly implemented channel allows for measurements of atmospheric temperature at altitudes below 35 km and is currently optimized for temperature measurements between 180 and 200 K. This corresponds to conditions in the lower Arctic stratosphere during winter. In addition to the temperature measurements, the aerosol extinction coefficient and the aerosol backscatter coefficient at 532 nm can be measured independently. Our filter-based design minimizes the systematic error in the obtained temperature profile to less than 0.51 K. By combining rotational-Raman measurements (5–35 km height) and the integration technique (30–80 km height), the Esrange lidar is now capable of measuring atmospheric temperature profiles from the upper troposphere up to the mesosphere. With the improved setup, the system can be used to validate current lidar-based polar stratospheric cloud classification schemes. The new capability of the instrument measuring temperature and aerosol extinction furthermore enables studies of the thermal structure and variability of the upper troposphere/lower stratosphere. Although several lidars are operated at polar latitudes, there are few instruments that are capable of measuring temperature profiles in the troposphere, stratosphere, and mesosphere, as well as aerosols extinction in the troposphere and lower stratosphere with daylight capability

Renormalization flow in extreme value statistics

The renormalization group transformation for extreme value statistics of independent, identically distributed variables, recently introduced to describe finite size effects, is presented here in terms of a partial differential equation (PDE). This yields a flow in function space and gives rise to the known family of Fisher-Tippett limit distributions as fixed points, together with the universal eigenfunctions around them. The PDE turns out to handle correctly distributions even having discontinuities. Remarkably, the PDE admits exact solutions in terms of eigenfunctions even farther from the fixed points. In particular, such are unstable manifolds emanating from and returning to the Gumbel fixed point, when the running eigenvalue and the perturbation strength parameter obey a pair of coupled ordinary differential equations. Exact renormalization trajectories corresponding to linear combinations of eigenfunctions can also be given, and it is shown that such are all solutions of the PDE. Explicit formulas for some invariant manifolds in the Fr\'echet and Weibull cases are also presented. Finally, the similarity between renormalization flows for extreme value statistics and the central limit problem is stressed, whence follows the equivalence of the formulas for Weibull distributions and the moment generating function of symmetric L\'evy stable distributions.Comment: 21 pages, 9 figures. Several typos and an upload error corrected. Accepted for publication in JSTA

Observations of the mesospheric semi-annual oscillation (MSAO) in water vapour by Odin/SMR

International audienceMesospheric water vapour measurements taken by the SMR instrument onboard the Odin satellite between 2002 and 2006 have been analysed with focus on the mesospheric semi-annual circulation in the tropical and subtropical region. This analysis provides the first complete picture of mesospheric SAO in water vapour, covering altitudes above 80 km where the only previous study based on UARS/HALOE data was limited. Our analysis shows a clear semi-annual variation in the water vapour distribution in the entire altitude range between 65 km and 100 km in the equatorial area. Maxima occur near the equinoxes below 75 km and around the solstices above 80 km. The phase reversal occurs in the small layer in-between, consistent with the downward propagation of the mesospheric SAO in the zonal wind in this altitude range. The SAO amplitude exhibits a double peak structure, with maxima at about 75 km and 81 km. The observed amplitudes show higher values than the UARS/HALOE amplitudes. The upper peak amplitude remains relatively constant with latitude. The lower peak amplitude decreases towards higher latitudes, but recovers in the Southern Hemisphere subtropics. On the other hand, the annual variation is much more prominent in the northern hemispheric subtropics. Furthermore, higher volume mixing ratios during summer and lower values during winter are observed in the Northern Hemisphere subtropics, as compared to the corresponding latitude range in the Southern Hemisphere

Extremal driving as a mechanism for generating long-term memory

It is argued that systems whose elements are renewed according to an extremal criterion can generally be expected to exhibit long-term memory. This is verified for the minimal extremally driven model, which is first defined and then solved for all system sizes N\geq2 and times t\geq0, yielding exact expressions for the persistence R(t)=[1+t/(N-1)]^{-1} and the two-time correlation function C(t_{\rm w}+t,t_{\rm w})=(1-1/N)(N+t_{\rm w})/(N+t_{\rm w}+t-1). The existence of long-term memory is inferred from the scaling of C(t_{\rm w}+t,t_{\rm w})\sim f(t/t_{\rm w}), denoting {\em aging}. Finally, we suggest ways of investigating the robustness of this mechanism when competing processes are present.Comment: 5 pages, no figures; requires IOP style files. To appear as a J. Phys. A. lette

Role of disorder in the size-scaling of material strength

We study the sample size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the fluctuations due to disorder and another controlled by stress-concentrations, ruled by continuum fracture mechanics. The results are formulated in terms of a scaling law involving a statistical fracture process zone. Its existence and scaling properties are only revealed by sampling over many configurations of the disorder. The scaling law is in good agreement with experimental results obtained from notched paper samples.Comment: 4 pages 5 figure

Maximum relative height of one-dimensional interfaces : from Rayleigh to Airy distribution

We introduce an alternative definition of the relative height h^\kappa(x) of a one-dimensional fluctuating interface indexed by a continuously varying real paramater 0 \leq \kappa \leq 1. It interpolates between the height relative to the initial value (i.e. in x=0) when \kappa = 0 and the height relative to the spatially averaged height for \kappa = 1. We compute exactly the distribution P^\kappa(h_m,L) of the maximum h_m of these relative heights for systems of finite size L and periodic boundary conditions. One finds that it takes the scaling form P^\kappa(h_m,L) = L^{-1/2} f^\kappa (h_m L^{-1/2}) where the scaling function f^\kappa(x) interpolates between the Rayleigh distribution for \kappa=0 and the Airy distribution for \kappa=1, the latter being the probability distribution of the area under a Brownian excursion over the unit interval. For arbitrary \kappa, one finds that it is related to, albeit different from, the distribution of the area restricted to the interval [0, \kappa] under a Brownian excursion over the unit interval.Comment: 25 pages, 4 figure

Generalised extreme value statistics and sum of correlated variables

We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and (generally) correlated random variables with a sum distributed according to one of the three (k-dependent) asymptotic distributions of extreme value statistics, namely the Gumbel, Frechet and Weibull distributions. These classes, as well as the limit distributions, are naturally extended to real values of k, thus providing a clear interpretation to the onset of Gumbel distributions with non-integer index k in the statistics of global observables. This is one of the very few known generalisations of the central limit theorem to non-independent random variables. Finally, in the context of a simple physical model, we relate the index k to the ratio of the correlation length to the system size, which remains finite in strongly correlated systems.Comment: To appear in J.Phys.

Statistics of leaders and lead changes in growing networks

We investigate various aspects of the statistics of leaders in growing network models defined by stochastic attachment rules. The leader is the node with highest degree at a given time (or the node which reached that degree first if there are co-leaders). This comprehensive study includes the full distribution of the degree of the leader, its identity, the number of co-leaders, as well as several observables characterizing the whole history of lead changes: number of lead changes, number of distinct leaders, lead persistence probability. We successively consider the following network models: uniform attachment, linear attachment (the Barabasi-Albert model), and generalized preferential attachment with initial attractiveness.Comment: 28 pages, 14 figures, 1 tabl

Extreme statistics for time series: Distribution of the maximum relative to the initial value

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/f^alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRH_I). The exact MRH_I distribution is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random acceleration), and alpha=infinity (single sinusoidal mode). For other, intermediate values of alpha, the distribution is determined from simulations. We find that the MRH_I distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all alpha. The two main distinguishing features of the MRH_I distribution are the much larger weight for small relative heights and the divergence at zero height for alpha>3. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some non-periodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the MRH_I distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.Comment: 29 pages, 4 figure

Extreme events driven glassy behaviour in granular media

Motivated by recent experiments on the approach to jamming of a weakly forced granular medium using an immersed torsion oscillator [Nature 413 (2001) 407], we propose a simple model which relates the microscopic dynamics to macroscopic rearrangements and accounts for the following experimental facts: (1) the control parameter is the spatial amplitude of the perturbation and not its reduced peak acceleration; (2) a Vogel-Fulcher-Tammann-like form for the relaxation time. The model draws a parallel between macroscopic rearrangements in the system and extreme events whose probability of occurrence (and thus the typical relaxation time) is estimated using extreme-value statistics. The range of validity of this description in terms of the control parameter is discussed as well as the existence of other regimes.Comment: 7 pages, to appear in Europhys. Let