Unimodality of wave amplitude in the northern Hemisphere

A novel statistic for local wave amplitude of the 500-hPa geopotential height field is introduced. The statistic uses a Hilbert transform to define a longitudinal wave envelope and dynamical latitude weighting to define the latitudes of interest. Here it is used to detect the existence, or otherwise, of multimodality in its distribution function. The empirical distribution function for the 1960-2000 period is close to a Weibull distribution with shape parameters between 2 and 3. There is substantial interdecadal variability but no apparent local multimodality or bimodality. The zonally averaged wave amplitude, akin to the more usual wave amplitude index, is close to being normally distributed. This is consistent with the central limit theorem, which applies to the construction of the wave amplitude index. For the period 1960-70 it is found that there is apparent bimodality in this index. However, the different amplitudes are realized at different longitudes, so there is no bimodality at any single longitude. As a corollary, it is found that many commonly used statistics to detect multimodality in atmospheric fields potentially satisfy the assumptions underlying the central limit theorem and therefore can only show approximately normal distributions. The author concludes that these techniques may therefore be suboptimal to detect any multimodality.

Wave height analysis from 10 years of observations in the Norwegian Sea

Large waves pose risks to ships, offshore structures, coastal infrastructure and ecosystems. This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. During the period 2000 to 2009, surface elevation was recorded every 0.59 s during sampling periods of 30 min. The Hmax observations scale linearly with Hs on average. A widely-used empirical Weibull distribution is found to estimate average values of Hmax/Hs and Hmax better than a Rayleigh distribution, but tends to underestimate both for all but the smallest waves. In this paper we propose a modified Rayleigh distribution which compensates for the heterogeneity of the observed dataset: the distribution is fitted to the whole dataset and improves the estimate of the largest waves. Over the 10-year period, the Weibull distribution approximates the observed Hs and Hmax well, and an exponential function can be used to predict the probability distribution function of the ratio Hmax/Hs. However, the Weibull distribution tends to underestimate the occurrence of extremely large values of Hs and Hmax. The persistence of Hs and Hmax in winter is also examined. Wave fields with Hs>12 m and Hmax>16 m do not last longer than 3 h. Low-to-moderate wave heights that persist for more than 12 h dominate the relationship of the wave field with the winter NAO index over 2000–2009. In contrast, the inter-annual variability of wave fields with Hs>5.5 m or Hmax>8.5 m and wave fields persisting over ~2.5 days is not associated with the winter NAO index.

Variability and trends in England and Wales precipitation

The England and Wales precipitation (EWP) dataset is a homogeneous time series of daily accumulations from 1931 to 2014, composed from rain gauge observations spanning the region. The daily regional-average precipitation statistics are shown to be well described by a Weibull distribution, which is used to define extremes in terms of percentiles. Computed trends in annual and seasonal precipitation are sensitive to the period chosen, due to large variability on interannual and decadal timescales. Atmospheric circulation patterns associated with seasonal precipitation variability are identified. These patterns project onto known leading modes of variability, all of which involve displacements of the jet stream and storm-track over the eastern Atlantic. The intensity of daily precipitation for each calendar season is investigated by partitioning all observations into eight intensity categories contributing equally to the total precipitation in the dataset. Contrary to previous results based on shorter periods, no significant trends of the most intense categories are found between 1931 and 2014. The regional-average precipitation is found to share statistical properties common to the majority of individual stations across England and Wales used in previous studies. Statistics of the EWP data are examined for multi-day accumulations up to 10 days, which are more relevant for river flooding. Four recent years (2000, 2007, 2008 and 2012) have a greater number of extreme events in the 3-and 5-day accumulations than any previous year in the record. It is the duration of precipitation events in these years that is remarkable, rather than the magnitude of the daily accumulations.

Effect of sequence distribution on the morphology, crystallization, melting, and biodegradation of poly(epsilon-caprolactone-co-epsilon-caprolactam) copolymers

Two types of poly(epsilon-caprolactone (CLo)-co-poly(epsilon-caprolactam (CLa)) copolymers were prepared by catalyzed hydrolytic ring-opening polymerization. Both cyclic comonomers were added simultaneously in the reaction medium for the First type or materials where copolymers have a random distribution of counits, as evidenced by H-1 and C-13 NMR. For the second type of copolymers, the cyclic comonomers were added sequentially, yielding diblock poly(ester-amides). The materials were characterized by differential scanning calorimetry (DSC), wide- and small-angle X-ray scattering (WAXS and SAXS), and transmission and scanning electron microscopies (TEM and SEM). Their biodegradation in compost was also studied. All copolymers were found to be miscible by the absence of structure in the melt. TEM revealed that all samples exhibited a crystalline lamellar morphology. DSC and WAXS showed that in a wide composition range (CLo contents from 6 to 55%) only the CLa units were capable of crystallization in the random copolymers. The block copolymer samples only experience a small reduction of crystallization and melting temperature with composition, and this was attributed to a dilution effect caused by the miscible noncrystalline CLo units. The comparison between block and random copolymers provided a unique opportunity to distinguish the dilution effect of the CLo units on the crystallization and melting of the polyamide phase from the chemical composition effect in the random copolymers case, where the CLa sequences are interrupted statistically by the CLo units, making the crystallization of the polyamide strongly composition dependent. Finally, the enzymatic degradation of the copolymers in composted soil indicate a synergistic behavior where much faster degradation was obtained for random copolymers witha CLo content larger than 30% than for neat PCL.

Controlled variation of monomer sequence-distribution in the synthesis of aromatic poly(ether ketone)s

The effects of varying the alkali metal cation in the high-temperature nucleophilic synthesis of a semi-crystalline, aromatic poly(ether ketone) have been systematically investigated, and striking variations in the sequence-distributions and thermal characteristics of the resulting polymers were found. Polycondensation of 4,4'-dihydroxybenzophenone with 1,3-bis(4-fluorobenzoyl)benzene in diphenylsulfone as solvent, in the presence of an alkali metal carbonate M2CO3 (M= Li, Na, K, or Rb) as base, affords a range of different polymers that vary in the distribution pattern of 2-ring and 3-ring monomer units along the chain. Lithium carbonate gives an essentially alternating and highly crystalline polymer, but the degree of sequence-randomisation increases progressively as the alkali metal series is descended, with rubidium carbonate giving a fully random and non-thermally-crystallisable polymer. Randomisation during polycondensation is shown to result from reversible cleavage of the ether linkages in the polymer by fluoride ions, and an isolated sample of alternating-sequence polymer is thus converted to a fully randomised material on heating with rubidium fluoride.

Detection of frailty in Weibull lifetime data using Outlier tests

Heterogeneity in lifetime data may be modelled by multiplying an individual's hazard by an unobserved frailty. We test for the presence of frailty of this kind in univariate and bivariate data with Weibull distributed lifetimes, using statistics based on the ordered Cox-Snell residuals from the null model of no frailty. The form of the statistics is suggested by outlier testing in the gamma distribution. We find through simulation that the sum of the k largest or k smallest order statistics, for suitably chosen k , provides a powerful test when the frailty distribution is assumed to be gamma or positive stable, respectively. We provide recommended values of k for sample sizes up to 100 and simple formulae for estimated critical values for tests at the 5% level.

Reversible, nondegradative conversion of crystalline aromatic poly(ether ketone)s into organo-soluble poly(ether dithioketal)s

Crystalline aromatic poly(ether ketone)s Such as PEEK and PEK may be cleanly and reversibly derivatized by dithioketalization of the carbonyl groups With 1,2-ethanedithiol or 1,3-propanedithiol under strong acid conditions. The resulting 1,3-dithiolane and 1,3-dithiane polymers are hydrolytically stable, amorphous, and readily soluble in organic solvents such as chloroform and THF and are thus (unlike their parent polymers) easily characterized by gel permeation chromatography (GPC). GPC analysis of a range of derivatized PEEK samples using light-scattering detection revealed, in some instances, a bimodal molecular weight distribution with a small but potentially significant (and previously undetected) very high-molecular-weight fraction.

Application of cylindrical distribution functions to wide-angle X-ray scattering from oriented polymers

A systematic approach is presented for obtaining cylindrical distribution functions (CDF's) of noncrystalline polymers which have been oriented by extension. The scattering patterns and CDF's are also sharpened by the method proposed by Deas and by Ruland. Data from atactic poly(methyl methacrylate) and polystyrene are analysed by these techniques. The methods could also be usefully applied to liquid crystals.

A detailed single chain model for molten poly(tetrafluoroethylene) from a novel structure refinement technique on neutron scattering data

We present a new methodology that couples neutron diffraction experiments over a wide Q range with single chain modelling in order to explore, in a quantitative manner, the intrachain organization of non-crystalline polymers. The technique is based on the assignment of parameters describing the chemical, geometric and conformational characteristics of the polymeric chain, and on the variation of these parameters to minimize the difference between the predicted and experimental diffraction patterns. The method is successfully applied to the study of molten poly(tetrafluoroethylene) at two different temperatures, and provides unambiguous information on the configuration of the chain and its degree of flexibility. From analysis of the experimental data a model is derived with CC and CF bond lengths of 1.58 and 1.36 Å, respectively, a backbone valence angle of 110° and a torsional angle distribution which is characterized by four isometric states, namely a split trans state at ± 18°, giving rise to a helical chain conformation, and two gauche states at ± 112°. The probability of trans conformers is 0.86 at T = 350°C, which decreases slightly to 0.84 at T = 400°C. Correspondingly, the chain segments are characterized by long all-trans sequences with random changes in sign, rather anisotropic in nature, which give rise to a rather stiff chain. We compare the results of this quantitative analysis of the experimental scattering data with the theoretical predictions of both force fields and molecular orbital conformation energy calculations.