A new set of orthogonal patterns in weather and climate: Optimally interpolated patterns.

A new spectral-based approach is presented to find orthogonal patterns from gridded weather/climate data. The method is based on optimizing the interpolation error variance. The optimally interpolated patterns (OIP) are then given by the eigenvectors of the interpolation error covariance matrix, obtained using the cross-spectral matrix. The formulation of the approach is presented, and the application to low-dimension stochastic toy models and to various reanalyses datasets is performed. In particular, it is found that the lowest-frequency patterns correspond to largest eigenvalues, that is, variances, of the interpolation error matrix. The approach has been applied to the Northern Hemispheric (NH) and tropical sea level pressure (SLP) and to the Indian Ocean sea surface temperature (SST). Two main OIP patterns are found for the NH SLP representing respectively the North Atlantic Oscillation and the North Pacific pattern. The leading tropical SLP OIP represents the Southern Oscillation. For the Indian Ocean SST, the leading OIP pattern shows a tripole-like structure having one sign over the eastern and north- and southwestern parts and an opposite sign in the remaining parts of the basin. The pattern is also found to have a high lagged correlation with the Niño-3 index with 6-months lag.

Independent component analysis of climate data: A new look at EOF rotation

The complexity inherent in climate data makes it necessary to introduce more than one statistical tool to the researcher to gain insight into the climate system. Empirical orthogonal function (EOF) analysis is one of the most widely used methods to analyze weather/climate modes of variability and to reduce the dimensionality of the system. Simple structure rotation of EOFs can enhance interpretability of the obtained patterns but cannot provide anything more than temporal uncorrelatedness. In this paper, an alternative rotation method based on independent component analysis (ICA) is considered. The ICA is viewed here as a method of EOF rotation. Starting from an initial EOF solution rather than rotating the loadings toward simplicity, ICA seeks a rotation matrix that maximizes the independence between the components in the time domain. If the underlying climate signals have an independent forcing, one can expect to find loadings with interpretable patterns whose time coefficients have properties that go beyond simple noncorrelation observed in EOFs. The methodology is presented and an application to monthly means sea level pressure (SLP) field is discussed. Among the rotated (to independence) EOFs, the North Atlantic Oscillation (NAO) pattern, an Arctic Oscillation–like pattern, and a Scandinavian-like pattern have been identified. There is the suggestion that the NAO is an intrinsic mode of variability independent of the Pacific.

Effects of patch size and density on flower visitation and seed set of wild plants: a pan-European approach

1. Habitat fragmentation can affect pollinator and plant population structure in terms of species composition, abundance, area covered and density of flowering plants. This, in turn, may affect pollinator visitation frequency, pollen deposition, seed set and plant fitness. 2. A reduction in the quantity of flower visits can be coupled with a reduction in the quality of pollination service and hence the plants’ overall reproductive success and long-term survival. Understanding the relationship between plant population size and⁄ or isolation and pollination limitation is of fundamental importance for plant conservation. 3. Weexamined flower visitation and seed set of 10 different plant species fromfive European countries to investigate the general effects of plant populations size and density, both within (patch level) and between populations (population level), on seed set and pollination limitation. 4. Wefound evidence that the effects of area and density of flowering plant assemblages were generally more pronounced at the patch level than at the population level. We also found that patch and population level together influenced flower visitation and seed set, and the latter increased with increasing patch area and density, but this effect was only apparent in small populations. 5. Synthesis. By using an extensive pan-European data set on flower visitation and seed set we have identified a general pattern in the interplay between the attractiveness of flowering plant patches for pollinators and density dependence of flower visitation, and also a strong plant species-specific response to habitat fragmentation effects. This can guide efforts to conserve plant–pollinator interactions, ecosystem functioning and plant fitness in fragmented habitats.

Notations and conventions in molecular spectroscopy: part 1. General spectroscopic notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part I in a series, establishes the notations and conventions used for general spectroscopic notations and deals with quantum mechanics, quantum numbers (vibrational states, angular momentum and energy levels), spectroscopic transitions, and miscellaneous notations (e.g. spectroscopic terms). Further parts will follow, dealing inter alia with symmetry notation, permutation and permutation-inversion symmetry notation, vibration-rotation spectroscopy and electronic spectroscopy.

Notations and conventions in molecular spectroscopy: part 2. Symmetry notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part 2 in a series, establishes the notations and conventions used for the description of symmetry in rigid molecules, using the Schoenflies notation. It deals firstly with the symmetry operators of the molecular point groups (also drawing attention to the difference between symmetry operators and elements). The conventions and notations of the molecular point groups are then established, followed by those of the representations of these groups as used in molecular spectroscopy. Further parts will follow, dealing inter alia with permutation and permutation-inversion symmetry notation, vibration-rotation spectroscopy and electronic spectroscopy.

Notations and conventions in molecular spectroscopy: part 3. Permutation and permutation-inversion symmetry notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part 3 in a series, deals with symmetry notation referring to groups that involve nuclear permutations and the inversion operation. Further parts will follow, dealing inter alia with vibration-rotation spectroscopy and electronic spectroscopy.

Force constants and dipole moment derivatives of molecules from perturbed Hartree-Fock calculations II. Applications to limited basis set SCF-MO wavefunctions

The perturbed Hartree–Fock theory developed in the preceding paper is applied to LiH, BH, and HF, using limited basis‐set SCF–MO wavefunctions derived by previous workers. The calculated values for the force constant ke and the dipole‐moment derivative μ(1) are (experimental values in parentheses): LiH, ke  =  1.618(1.026)mdyn/Å,μ(1)  =  −18.77(−2.0±0.3)D/ÅBH,ke  =  5.199(3.032)mdyn/Å,μ(1)  =  −1.03(−)D/Å;HF,ke  =  12.90(9.651)mdyn/Å,μ(1)  =  −2.15(+1.50)D/Å. The values of the force on the proton were calculated exactly and according to the Hellmann–Feynman theorem in each case, and the discrepancies show that none of the wavefunctions used are close to the Hartree–Fock limit, so that the large errors in ke and μ(1) are not surprising. However no difficulties arose in the perturbed Hartree–Fock calculation, so that the application of the theory to more accurate wavefunctions appears quite feasible.

Vibration-rotation spectra of CH3F

Rotational structure has been resolved and analyzed in the 1049-cm−1 parallel fundamental and the 1182 cm−1 perpendicular fundamental bands in the infrared spectrum of the CH3F molecule. Combination bands at 2223 cm−1 and around 2650 cm−1 have also been studied. The effective resolving power of the spectrometer was 0.25 cm−1 for all these bands. The two long-wavelength fundamentals have been analyzed in much greater detail than in previous work, and a complete analysis of the perpendicular band has been made, including the J-structure in the P and R branches of the sub-bands. Rotational constants of CH3F determined in this work and elsewhere are summarized in Table XIII of the text. Some anomalous intensity perturbations in the rotation lines of the 1182-cm−1 fundamental have been observed, and are discussed.

Vibration-rotation spectra of monofluoroacetylene: 1700 to 7500 cm−1

High-resolution vibration-rotation spectra of monofluoroacetylene are reported for many bands in the region 1700 to 7500 cm−1. The spectra were observed on Nicolet 7199 and Bruker IFS 120 Fourier spectrometers, with resolutions of about 0.06 and 0.003 cm−1, respectively. About 130 bands have been observed in this region, of which about 80 have been rotationally analyzed. The assignment of vibrational labels to the higher energy levels is complicated by the effects of strong Fermi resonances, and many weak localized rotational resonances are observed.

Raman selection rules for vibration-rotation transitions in symmetric top molecules

Symmetry restrictions on Raman selection rules can be obtained, quite generally, by considering a Raman allowed transition as the result of two successive dipole allowed transitions, and imposing the usual symmetry restrictions on the dipole transitions. This leads to the same results as the more familiar polarizability theory, but the vibration-rotation selection rules are easier to obtain by this argument. The selection rules for symmetric top molecules involving the (+l) and (-l) components of a degenerate vibrational level with first-order Coriolis splitting are derived in this paper. It is shown that these selection rules depend on the order of the highest-fold symmetry axis Cn, being different for molecules with n=3, n=4, or n ≧ 5; moreover the selection rules are different again for molecules belonging to the point groups Dnd with n even, and Sm with 1/2m even, for which the highest-fold symmetry axes Cn and Sm are related by m=2n. Finally it is shown that an apparent anomaly between the observed Raman and infra-red vibration-rotation spectra of the allene molecule is resolved when the correct selection rules are used, and a value for the A rotational constant of allene is derived without making use of the zeta sum rule.