Within the Copernicus Climate Change Service (C3S), ECMWF is producing the ERA5 reanalysis which, once completed, will embody a detailed record of the global atmosphere, land surface and ocean waves from 1950 onwards. This new reanalysis replaces the ERA-Interim reanalysis (spanning 1979 onwards) which was started in 2006. ERA5 is based on the Integrated Forecasting System (IFS) Cy41r2 which was operational in 2016. ERA5 thus benefits from a decade of developments in model physics, core dynamics and data assimilation. In addition to a significantly enhanced horizontal resolution of 31 km, compared to 80 km for ERA-Interim, ERA5 has hourly output throughout, and an uncertainty estimate from an ensemble (3-hourly at half the horizontal resolution). This paper describes the general setup of ERA5, as well as a basic evaluation of characteristics and performance, with a focus on the dataset from 1979 onwards which is currently publicly available. Re-forecasts from ERA5 analyses show a gain of up to one day in skill with respect to ERA-Interim. Comparison with radiosonde and PILOT data prior to assimilation shows an improved fit for temperature, wind and humidity in the troposphere, but not the stratosphere. A comparison with independent buoy data shows a much improved fit for ocean wave height. The uncertainty estimate reflects the evolution of the observing systems used in ERA5. The enhanced temporal and spatial resolution allows for a detailed evolution of weather systems. For precipitation, global-mean correlation with monthly-mean GPCP data is increased from 67% This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

The extension of the ERA5 reanalysis back to 1950 supplements the previously published segment covering 1979 to the present. It features the assimilation of additional conventional observations, as well as improved use of early satellite data. The number of observations assimilated increases from 53,000 per day in early 1950 to 570,000 per day by the end of 1978. Accordingly, the quality of the reanalysis improves throughout the period, generally joining seamlessly with the segment covering 1979 to the present. The fidelity of the extension is illustrated by the accurate depiction of the North Sea storm of 1953, and the events leading to the first discovery of sudden stratospheric warmings in 1952. Time series of ERA5 global surface temperature anomalies show temperatures to be relatively stable from 1950 until the late 1970s, in agreement with the other contemporary full-input reanalysis covering this period and with independent data sets, although there are significant differences in the accuracy of representing specific regions, Europe being well represented in the early period but Australia less so. The variability of ERA5 precipitation from month to month agrees well with observations for all continents, with correlations above 90% for most of Europe and generally in excess of 70% for North America, Asia and Australia. The evolution of upper air temperatures, humidities and winds shows smoothly varying behaviour, including tropospheric warming and stratospheric cooling, modulated by volcanic eruptions. The Quasi-Biennial Oscillation is well represented throughout. Aspects to be improved upon in future reanalyses include the assimilation of tropical cyclone data, the spin-up of soil moisture and stratospheric humidity, and the representation of surface temperatures over Australia.

The pi contribution to the electron localization function (ELF) is used to compare 4npi- and (4n+2)pi-electron annulenes, with particular focus on the aromaticity of 4npi-electron annulenes in their lowest triplet state. The analysis is performed on the electron density obtained at the level of OLYP density functional theory, as well as at the CCSD and CASSCF ab initio levels. Two criteria for aromaticity of all-carbon annulenes are set up: the span in the bifurcation values DeltaBV(ELF(pi)) should be small, ideally zero, and the bifurcation value for ring closure of the pi basin RCBV(ELF(pi)) should be high (> or = 0.7). On the basis of these criteria, nearly all 4npi-electron annulenes are aromatic in their lowest triplet states, similar to (4n+2)pi-electron annulenes in their singlet ground states. For singlet biradical cyclobutadiene and cyclooctatetraene constrained to D4h and D8h symmetry, respectively, the RCBV(ELF(pi)) at the CASSCF level is lower (0.531 and 0.745) than for benzene (0.853), even though they have equal proportions of alpha- and beta-electrons.

An algorithm for the solution of the linear response equation in the random phase approximation is presented. All entities including frequency arguments, matrices, and vectors, are assumed to be complex, and it represents the core equation solver needed in complex polarization propagator approaches where nonstimulated relaxation channels are taken into account. Stability and robustness of the algorithm are demonstrated in applications regarding visible, ultraviolet, and x-ray spectroscopies. An implementation of the algorithm at the level of four-component relativistic, noncollinear, density functional theory for imaginary (but not complex) frequency arguments has been achieved and is used to determine the electric dipole dispersion interaction coefficients for the rubidium and cesium dimers. Our best estimates for the C(6) coefficients of Rb(2) and Cs(2) are equal to 14.0x10(3) and 21.9x10(3) a.u., respectively.

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