Developments in Bias Correction for Reanalysis
Dick Dee1, Sakari Uppala1, Shinya Kobayashi1,2, Magnus Lindskog3, Adrian Simmons1
1

European Centre for Medium-Range Weather Forecasts, United Kingdom
2
Japan Meteorological Agency, Japan
3
Swedish Meteorological and Hydrological Institute, Sweden
Correspondence: Dick.Dee@ecmwf.int

INTRODUCTION
A major problem with the use of observations for climate analysis is the presence of biases, and the effect on theestimation of climate signals of changes in these biases, their sampling frequencies, and details of the analysis
techniques. This problem also exists in atmospheric reanalyses, which combine many different types of observations
together with information from sophisticated models in order to produce accurate and dynamically consistentestimates of global atmospheric parameters.
In spite of best efforts to remove all systematic errors at the source, some residual biases inevitably remain. Their
presence can be readily detected in a reanalysis system by monitoring the data against a common reference. The data
assimilation then provides a final opportunity to correct the biases in the data, and possibly in the model as well, basedon the consensus of all information presented to the analysis system. This idea, and the practical challenge of dealing
with a heterogeneous and evolving observing system, has led to the development of automated bias correction
schemes embedded in the analysis component of the data assimilation system.
In this paper we briefly review the use in ERA-Interim of a variational bias correction scheme for adaptively
correcting biases in satellite radiance data, and discuss practical aspects such as the need for constraining the system
where model biases are large and observations are sparse. We also discuss the extension of the variational approachfor correcting other types of observations, including ozone profile data. Finally we present some thoughts on using thedata assimilation to correct model biases, and show experimental results obtained with a weak-constraint formulationof the four-dimensional variational analysis method in use at ECMWF.
VARIATIONAL BIAS CORRECTION OF RADIANCE DATA
Bias correction of observations has always been a practical necessity both for NWP and reanalysis. Due to thegrowing complexity of the observing system and its evolution over long time periods, some kind of automated system
for handling the bias corrections is now indispensable. Variational bias correction of radiance data was first
implemented for at NCEP in their Statistical Spectral Interpolation analysis system (Derber and Wu 1998) and later at
ECMWF (Dee 2004) by extending the ECMWF 4D-Var analysis system.

Variational bias correction provides an automatic inter-calibration of the observing system in the context of theforecast model, producing bias corrections that improve the consistency of the information entering the analysis.
Figure 1 shows an example of bias corrections produced during the first 10 years of reanalysis in ERA-Interim, inthis case for radiance data from MSU channel 2 on NOAA-10, 11, 12, and 14. The corrections account forsystematic errors in the data (e.g. due to calibration issues) but also for errors in the fast radiative transfer model
used to simulate the data (e.g. due to inaccurate spectroscopy). The corrections may also falsely correct the datafor errors in the background which are due to forecast model bias, especially where observations are sparse (suchas in the stratosphere).

Figure 1: Global mean bias corrections for MSU channel 2 radiances in ERA-Interim
There are strong indications that variational bias correction of radiance data is beneficial to the quality of theERA-Interim reanalysis. For example, the vertical consistency of the temperature analysis, as well as the fit toradiosonde data in the polar regions, is much improved compared to ERA-40; see Figures 2 and 3.

Figure 2: Fit to radiosonde u-wind observations in the Arctic regions for ERA-40 (red) and ERA-Interim (black).

Figure 3: Aug 1993 zonal mean temperatures for ERA-Interim (left) and the difference relative to ERA-40 (right).
VARIATIONAL BIAS CORRECTION OF OZONE PROFILE DATA
The variational bias correction method is quite general and may be applied to data types other than radiances.
For the next-generation analysis system in development at the ECMWF we are considering the use of thisapproach to provide bias corrections for ozone data. Figure 4 shows a timeline for ozone observations used inERA-Interim during the period 1989-2002. The observing system is quite complex, consisting of retrieved total
column ozone together with ozone profile data from sensors with different vertical resolutions, and many gaps inthe data. Closer inspection reveals many systematic differences among the different sources of ozone informationentering the analysis.

Figure 4: Timeline of ozone data sources used in ERA-Interim between 1989 and 2002.
Figure 5 shows some results of an experiment using variational bias correction of ozone data. During the selectedperiod high-resolution ozone profile data from GOME on ERS-2 were re-introduced into the system (on 4 January1997). The plots show opposite bias corrections produced by the variational scheme for SBUV data (for the layer
between the surface and 16 hPa) and GOME data (for the layer between 32 and 18 hPa). Plots in Figure 6 show theimpact of the variational bias corrections (applied to all ozone data in the system) on the analysis increments.

Figure 5: Departure statistics for SBUV (top, layer between the surface and 16 hPa) and GOME ozone layer data(bottom, layer between 32 and 18 hPa) during January 1997. Shown are: global means (dashed) and standard
deviations (solid) of analysis (blue) and background (red) departures, and global mean bias corrections (black).

Figure 6: Globally averaged analysis increments for stratospheric ozone concentrations [mg/kg] for January 1997, for
an experiment with (bottom) and without (bottom) variational bias correction of ozone data. Model levels 10, 20, 30,
40 indicated along the vertical axes approximately correspond to pressure levels 1, 10, 50, and 100 hPa, respectively.

USE OF WEAK-CONSTRAINT 4D-VAR TO CONTROL STRATOSPHERIC MODEL BIAS
Systematic model errors in the upper stratosphere can be quite large, as can be seen for example by looking at
the average drift in the five-day forecast. Figure 7 shows the evolution of this drift in ERA-Interim
upper-stratospheric temperature forecasts for a one-year period over the Antarctic region. It is typically on theorder of 10K or more at model level 4, which corresponds to about 1 hPa in the ERA-Interim system. Althoughreasonably accurate observations for the upper stratosphere are provided by SSU and AMSU-A (but seeKobayashi et al., 2008) the standard 4D-Var analysis method is not designed to handle systematic model errors.

Figure 7: Evolution of the mean upper-stratospheric temperature [K] error (5-day forecast errors verified againstanalyses) over the Antarctic (south of 70S) during 1992. The vertical axis extends from about 40h to 0.1 hPa.
Trémolet (2007) shows how 4D-Var can be extended to account for model errors. This requires the use of themodel as a weak constraint in the variational analysis, in contrast to the usual requirement in 4D-Var that themodel equations be satisfied exactly during the analysis window:

Results of a preliminary experiment involving the addition to the ERA-Interim system of a weak constraint
applied in the stratosphere only are presented in Figure 8. We rely on the mean background departures withrespect to radiance data from SSU channel 3 as a good measure of systematic model error in a deep layer of theupper stratosphere, roughly extending from 5 hPa to the stratopause. The figure shows that the average departures
for August 1993, which clearly show the poor representation of the winter polar vortex, are in fact significantlyreduced by allowing for model error in the analysis.

Figure 8: Mean background departures for SSU channel 3 radiances for August 1993, from ERA-Interim (left panel)and from an experimental assimilation using weak-constraint 4D-Var (right panel).
REFERENCES
Dee, D. P., 2004: Variational bias correction of radiance data in the ECMWF system. Proceedings of the ECMWF
workshop on assimilation of high spectral resolution sounders in NWP. Reading, UK, 28 June-1 July 2004,
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Derber, J.C., and W.-S. Wu, 1998: The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system.
Mon. Wea. Rev., 126, 2287-2299.
Kobayashi, S., M. Matricardi, D. Dee, and S. Uppala, 2008: Use of the SSU and AMSU-A observations inreanalyses. This issue.
Trémolet, Y., 2007: Accounting for an imperfect model in 4D-Var. Quart. J. Roy. Meteor. Soc., 132, 2483-2504