Quarterly Journal of the Royal Meteorological Society

ERA‐Interim is the latest global atmospheric reanalysis produced by the European Centre for Medium‐Range Weather Forecasts (ECMWF). The ERA‐Interim project was conducted in part to prepare for a new atmospheric reanalysis to replace ERA‐40, which will extend back to the early part of the twentieth century. This article describes the forecast model, data assimilation method, and input datasets used to produce ERA‐Interim, and discusses the performance of the system. Special emphasis is placed on various difficulties encountered in the production of ERA‐40, including the representation of the hydrological cycle, the quality of the stratospheric circulation, and the consistency in time of the reanalysed fields. We provide evidence for substantial improvements in each of these aspects. We also identify areas where further work is needed and describe opportunities and objectives for future reanalysis projects at ECMWF. Copyright © 2011 Royal Meteorological Society

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 set‐up 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% to 77%. In general, low‐frequency variability is found to be well represented and from 10 hPa downwards general patterns of anomalies in temperature match those from the ERA‐Interim, MERRA‐2 and JRA‐55 reanalyses.

ERA‐40 is a re‐analysis of meteorological observations from September 1957 to August 2002 produced by the European Centre for Medium‐Range Weather Forecasts (ECMWF) in collaboration with many institutions. The observing system changed considerably over this re‐analysis period, with assimilable data provided by a succession of satellite‐borne instruments from the 1970s onwards, supplemented by increasing numbers of observations from aircraft, ocean‐buoys and other surface platforms, but with a declining number of radiosonde ascents since the late 1980s. The observations used in ERA‐40 were accumulated from many sources. The first part of this paper describes the data acquisition and the principal changes in data type and coverage over the period. It also describes the data assimilation system used for ERA‐40. This benefited from many of the changes introduced into operational forecasting since the mid‐1990s, when the systems used for the 15‐year ECMWF re‐analysis (ERA‐15) and the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) re‐analysis were implemented. Several of the improvements are discussed. General aspects of the production of the analyses are also summarized.

A number of results indicative of the overall performance of the data assimilation system, and implicitly of the observing system, are presented and discussed. The comparison of background (short‐range) forecasts and analyses with observations, the consistency of the global mass budget, the magnitude of differences between analysis and background fields and the accuracy of medium‐range forecasts run from the ERA‐40 analyses are illustrated. Several results demonstrate the marked improvement that was made to the observing system for the southern hemisphere in the 1970s, particularly towards the end of the decade. In contrast, the synoptic quality of the analysis for the northern hemisphere is sufficient to provide forecasts that remain skilful well into the medium range for all years. Two particular problems are also examined: excessive precipitation over tropical oceans and a too strong Brewer‐Dobson circulation, both of which are pronounced in later years. Several other aspects of the quality of the re‐analyses revealed by monitoring and validation studies are summarized. Expectations that the ‘second‐generation’ ERA‐40 re‐analysis would provide products that are better than those from the firstgeneration ERA‐15 and NCEP/NCAR re‐analyses are found to have been met in most cases. © Royal Meteorological Society, 2005. The contributions of N. A. Rayner and R. W. Saunders are Crown copyright.

When the atmospheric turbulent flux of a minor constituent such as CO2 (or of water vapour as a special case) is measured by either the eddy covariance or the mean gradient technique, account may need to be taken of variations of the constituent's density due to the presence of a flux of heat and/or water vapour. In this paper the basic relationships are discussed in the context of vertical transfer in the lower atmosphere, and the required corrections to the measured flux are derived.

If the measurement involves sensing of the fluctuations or mean gradient of the constituent's mixing ratio relative to the dry air component, then no correction is required; while with sensing of the constituent's specific mass content relative to the total moist air, a correction arising from the water vapour flux only is required. Correspondingly, if in mean gradient measurements the constituent's density is measured in air from different heights which has been pre‐dried and brought to a common temperature, then again no correction is required; while if the original (moist) air itself is brought to a common temperature, then only a correction arising from the water vapour flux is required.

If the constituent's density fluctuations or mean gradients are measured directly in the air in situ, then corrections arising from both heat and water vapour fluxes are required.

These corrections will often be very important. That due to the heat flux is about five times as great as that due to an equal latent heat (water vapour) flux. In CO2 flux measurements the magnitude of the correction will commonly exceed that of the flux itself. The correction to measurements of water vapour flux will often be only a few per cent but will sometimes exceed 10 per cent.

A simple analytic model is constructed to elucidate some basic features of the response of the tropical atmosphere to diabatic heating. In particular, there is considerable east‐west asymmetry which can be illustrated by solutions for heating concentrated in an area of finite extent. This is of more than academic interest because heating in practice tends to be concentrated in specific areas. For instance, a model with heating symmetric about the equator at Indonesian longitudes produces low‐level easterly flow over the Pacific through propagation of Kelvin waves into the region. It also produces low‐level westerly inflow over the Indian Ocean (but in a smaller region) because planetary waves propagate there. In the heating region itself the low‐level flow is away from the equator as required by the vorticity equation. The return flow toward the equator is farther west because of planetary wave propagation, and so cyclonic flow is obtained around lows which form on the western margins of the heating zone. Another model solution with the heating displaced north of the equator provides a flow similar to the monsoon circulation of July and a simple model solution can also be found for heating concentrated along an inter‐tropical convergence line.

The Twentieth Century Reanalysis (20CR) project is an international effort to produce a comprehensive global atmospheric circulation dataset spanning the twentieth century, assimilating only surface pressure reports and using observed monthly sea‐surface temperature and sea‐ice distributions as boundary conditions. It is chiefly motivated by a need to provide an observational dataset with quantified uncertainties for validations of climate model simulations of the twentieth century on all time‐scales, with emphasis on the statistics of daily weather. It uses an Ensemble Kalman Filter data assimilation method with background ‘first guess’ fields supplied by an ensemble of forecasts from a global numerical weather prediction model. This directly yields a global analysis every 6 hours as the most likely state of the atmosphere, and also an uncertainty estimate of that analysis.

The 20CR dataset provides the first estimates of global tropospheric variability, and of the dataset's time‐varying quality, from 1871 to the present at 6‐hourly temporal and 2° spatial resolutions. Intercomparisons with independent radiosonde data indicate that the reanalyses are generally of high quality. The quality in the extratropical Northern Hemisphere throughout the century is similar to that of current three‐day operational NWP forecasts. Intercomparisons over the second half‐century of these surface‐based reanalyses with other reanalyses that also make use of upper‐air and satellite data are equally encouraging.

It is anticipated that the 20CR dataset will be a valuable resource to the climate research community for both model validations and diagnostic studies. Some surprising results are already evident. For instance, the long‐term trends of indices representing the North Atlantic Oscillation, the tropical Pacific Walker Circulation, and the Pacific–North American pattern are weak or non‐existent over the full period of record. The long‐term trends of zonally averaged precipitation minus evaporation also differ in character from those in climate model simulations of the twentieth century. Copyright © 2011 Royal Meteorological Society and Crown Copyright.

The two main principles underlying the use of isentropic maps of potential vorticity to represent dynamical processes in the atmosphere are reviewed, including the extension of those principles to take the lower boundary condition into account. the first is the familiar Lagrangian conservation principle, for potential vorticity (PV) and potential temperature, which holds approximately when advective processes dominate frictional and diabatic ones. the second is the principle of ‘invertibility’ of the PV distribution, which holds whether or not diabatic and frictional processes are important. the invertibility principle states that if the total mass under each isentropic surface is specified, then a knowledge of the global distribution of PV on each isentropic surface and of potential temperature at the lower boundary (which within certain limitations can be considered to be part of the PV distribution) is sufficient to deduce, diagnostically, all the other dynamical fields, such as winds, temperatures, geopotential heights, static stabilities, and vertical velocities, under a suitable balance condition. the statement that vertical velocities can be deduced is related to the well‐known omega equation principle, and depends on having sufficient information about diabatic and frictional processes. Quasi‐geostrophic, semigeostrophic, and ‘nonlinear normal mode initialization’ realizations of the balance condition are discussed. an important constraint on the mass‐weighted integral of PV over a material volume and on its possible diabatic and frictional change is noted.

Some basic examples are given, both from operational weather analyses and from idealized theoretical models, to illustrate the insights that can be gained from this approach and to indicate its relation to classical synoptic and air‐mass concepts. Included are discussions of (a) the structure, origin and persistence of cutoff cyclones and blocking anticyclones, (b) the physical mechanisms of Rossby wave propagation, baroclinic instability, and barotropic instability, and (c) the spatially and temporally nonuniform way in which such waves and instabilities may become strongly nonlinear, as in an occluding cyclone or in the formation of an upper air shear line. Connections with principles derived from synoptic experience are indicated, such as the ‘PVA rule’ concerning positive vorticity advection on upper air charts, and the role of disturbances of upper air origin, in combination with low‐level warm advection, in triggering latent heat release to produce explosive cyclonic development. In all cases it is found that time sequences of isentropic potential vorticity and surface potential temperature charts—which succinctly summarize the combined effects of vorticity advection, thermal advection, and vertical motion without requiring explicit knowledge of the vertical motion field—lead to a very clear and complete picture of the dynamics. This picture is remarkably simple in many cases of real meteorological interest. It involves, in principle, no sacrifices in quantitative accuracy beyond what is inherent in theconceptof balance, as used for instance in the initialization of numerical weather forecasts.

The vertical distribution of horizontal mean wind in the lowest 8 metres over a reservoir (1·6 km × 1 km) has been measured using sensitive anemometers freely exposed from a fixed mast in water 16 m deep, the fetch being more than 1 km. The resulting profiles are closely logarithmic, the small differences being systematic and possibly due to the thermal instability which existed when the measurements were made.

The usual law for wind profiles in neutral stability is where u is the wind speed at height z, k is von Kármán's constant, log z (0) the intercept on the log z axis, and u_* the so‐called friction velocity defined by τ₀ = pu, τ₀ being the surface drag and rH the density of the air.

To characterize the profiles u_*/k, their slope, was plotted in relation to z (0), their intercept; this allowed a direct comparison with other profiles, in particular those recently measured in a laboratory channel by Sibul. The agreement was better than expected and indicated that z (0) was comparatively independent of fetch and stability but was largely determined by u_*. The relation between u_* and z (0) agreed roughly with the simplest non‐dimensional relation between them, gz (0)/u = constant, so that one is led to a generalized wind profile for flow over a water surface which specifies the drag, given the wind at one known height. An approximate value of the constant is 12·5.

This expression can be compared with earlier work. The better wind‐profile observations show rough agreement; the experimental scatter is necessarily large since a water surface is aerodynamically much smoother than most land surfaces, precision anemometry in difficult circumstances being required to provide sufficiently precise values. Oceanographic measurements of the tilt of water surfaces are in fair agreement at high wind speeds but at low wind speeds the data are conflicting. The early results which imply that the drag‐coefficient (u/u²) increases with decreasing wind speed in light winds are thought to be in error; some support for this belief comes from recent estimates of drag using a modified ageostrophic technique, which agree roughly among themselves and with the general expression.

The probable importance of NO and NO₂ in controlling the ozone concentrations and production rates in the stratosphere is pointed out. Observations on and determinations of nitric acid concentrations in the stratosphere by Murcray, Kyle, Murcray and Williams (1968) and Rhine, Tubbs and Dudley Williams (1969) support the high NO and NO₂ concentrations indicated by Bates and Hays (1967).

Some processes which may lead to production of nitric acid are discussed.

The importance of O (¹S), possibly produced in the ozone photolysis below 2340 Å, on the ozone photochemistry is mentioned.

A one‐dimensional model is adopted to describe the energy partition of sparse crops. Theoretical development of this model yields a combination equation which describes evaporation in terms of controlling resistances associated with the plants, and with the soil or water in which they are growing. the equation provides a simple but physically plausible description of the transition between bare substrate and a closed canopy. Although the aerodynamic transfer resistances for incomplete canopies have, as yet, no experimental justification, typical values, appropriate to a specimen agricultural crop and soil, are shown to have limited sensitivity in the model. Processes which require further study if the equation is to be used to calculate evaporation throughout a crop season are also discussed.