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.

The ERA‐40 re‐analysis

This article describes the performance of the variational bias correction system for satellite radiance data in ERA-Interim, and considers implications for the representation of climate signals in reanalysis. We briefly review the formulation of the method and its ability to automatically develop bias estimates when radiance measurements from newly available satellite sensors are first introduced in the reanalysis. We then present several results obtained from the first 19 years (1989–2007) of ERA-Interim. These include the identification of Microwave Sounding Unit (MSU) instrument calibration errors, the response of the system to the Pinatubo eruption in 1991, and the detection of a long-term drift in biases of tropospheric AMSU-A data. We find that our results support the notion that global reanalysis provides an appropriate framework for climate monitoring. Copyright © 2009 Royal Meteorological Society

Variational bias correction of satellite radiance data in the ERA‐Interim reanalysis

All data assimilation systems are affected by biases, caused by problems with the data, by approximations in the observation operators used to simulate the data, by limitations of the assimilating model, or by the assimilation methodology itself. A clear symptom of bias in the assimilation is the presence of systematic features in the analysis increments, such as large persistent mean values or regularly recurring spatial structures. Bias can also be detected by monitoring statistics of observed-minus-background residuals for different instruments. Bias-aware assimilation methods are designed to estimate and correct systematic errors jointly with the model state variables. Such methods require attribution of a bias to a particular source, and its characterization in terms of some well-defined set of parameters. They can be formulated either in a variational or sequential estimation framework by augmenting the system state with the bias parameters.

http://climateknowledge.org/reanalysis/Dee_Bias_Data_Assimilation_QJRMS_2005.pdf

Bias and data assimilation

Recent verification statistics show a considerable improvement in the accuracy of forecasts from three global numerical weather prediction systems. The improvement amounts to about a 1-day gain in predictability of mean-sea-level pressure and 500 hPa height over the last decade in the northern hemisphere, with a similar gain over the last 3 years in the southern hemisphere. Differences between the initial analyses from the three systems have been substantially reduced.

Detailed study of the European Centre for Medium-Range Weather Forecasts verifications shows that identifiable improvements in the data assimilation, model and observing systems have significantly increased the accuracy of both short- and medium-range forecasts, although interannual (flow-dependent) variations in error-growth characteristics complicate the picture. The implied r.m.s. error of 500 hPa height analyses has fallen well below the 10 m level typical of radiosonde measurement error. Intrinsic error-doubling times, computed from the divergence of northern hemisphere forecasts started 1 day apart, exhibit a small overall reduction over the past 10 years at day two and beyond, and a much larger reduction at day one. Error-doubling times for the southern hemisphere have become generally shorter and are now similar to those for the northern hemisphere. One-day forecast errors have been reduced so much in the southern hemisphere that medium-range forecasts for the region have become almost as skilful as those for the northern hemisphere.

The approach to saturation of forecast error beyond the 10-day range has been examined for sets of 21-day forecasts. When the systematic (sample-mean) component of the error is subtracted, forecast errors and the differences between successive forecasts both appear to level out near the end of the 21-day range at values close to the limit set by the natural level of variance of the atmosphere for the northern hemisphere. A number of features of the model 500 hPa height fields remain quite realistic at the three-week range. The most obvious discrepancy in mean climate is in the Pacific/North-American sector, and variance is too high in the southern hemisphere. Copyright © 2002 Royal Meteorological Society

https://www.ecmwf.int/sites/default/files/elibrary/2001/12238-some-aspects-improvement-skill-numerical-weather-prediction.pdf

Some aspects of the improvement in skill of numerical weather prediction

Data assimilation is the process by which observations are combined with short-range NWP model output to produce an analysis of the state of the atmosphere at a specified time. Since its inception in the late 1990s, the multiagency Weather Research and Forecasting (WRF) model effort has had a strong data assimilation component, dedicating two working groups to the subject. This article documents the history of the WRF data assimilation effort, and discusses the challenges associated with balancing academic, research, and operational data assimilation requirements in the context of the WRF effort to date. The WRF Model's Community Variational/Ensemble Data Assimilation System (WRFDA) has evolved over the past 10 years, and has resulted in over 30 refereed publications to date, as well as implementation in a wide range of real-time and operational NWP systems. This paper provides an overview of the scientific capabilities of WRFDA, and together with results from sample operation implementations at the U.S. ...

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The Weather Research and Forecasting Model's Community Variational/Ensemble Data Assimilation System: WRFDA

Recently, much progress has been made in the direct assimilation of satellite radiance measurements in numerical weather-prediction systems. In order to use radiances from the TIROS Operational Vertical Sounder (TOVS), biases between the observed radiances and those simulated from the model first guess must be corrected. The original scheme for TOVS radiance-bias correction at the European Centre for Medium-Range Weather Forecasts utilized a global scan correction, and a linear air-mass correction, with the observed radiances from the Microwave Sounding Unit channels 2, 3 and 4 as predictors. The new scheme differs in two fundamental ways. Analysis of radiance data shows a significant residual scan bias which depends strongly on latitude for some channels. The new scheme applies a latitudinally dependent scan correction to take this into account. The air-mass predictors are now computed from the background field, since the background field contains a more consistent representation of the air mass and surface characteristics than the observed microwave radiances. Four new predictors are used, 1000–300 hPa thickness, 200–50 hPa thickness, model surface skin temperature and total precipitable water. In particular, the skin-temperature predictor is able to differentiate between ocean and sea-ice, performing much better than the old scheme in the winter hemisphere. The use of model predictors is a change in philosophy away from correction of the observations to correction of the computed forward radiances. This leads to a natural extension where the gradient of the bias correction can be taken into account in variational retrieval schemes.

B. A. Harris

Papers

A satellite radiance-bias correction scheme for data assimilation