A three-dimensional global ozone distribution has been derived from
assimilation of ozone profiles that were observed by satellites. By
simultaneous assimilation of ozone profiles retrieved from the nadir
looking satellite instruments Global Ozone Monitoring Experiment 2
(GOME-2) and Ozone Monitoring Instrument (OMI), which measure the
atmosphere at different times of the day, the quality of the derived
atmospheric ozone field has been improved. The assimilation is using
an extended Kalman filter in which chemical transport model TM5 has
been used for the forecast. The combined assimilation of both GOME-2
and OMI improves upon the assimilation results of a single
sensor. The new assimilation system has been demonstrated by
processing 4 years of data from 2008 to 2011. Validation of the
assimilation output by comparison with sondes shows that biases vary
between

Depending on the altitude, ozone in the Earth's atmosphere has different effects. In the stratosphere, ozone filters the harmful ultraviolet part from the incoming solar radiation, preventing it from reaching the surface. Near to the surface, ozone is a pollutant, which has negative effects on human health and can reduce crop yields. At the same time, ozone is a greenhouse gas with an important role in the temperature of the atmosphere.

Because of the important role ozone has in climate change, it has
been designated as an essential climate variable (ECV) by the Global
Climate Observing System (GCOS) of the World Meteorological
Organization

The European Space Agency (ESA) has initiated the Climate Change
Initiative (CCI) programme, which aims at long-term time series of
satellite observations of the ECVs
(

Vertical ozone measurements from space-based ultraviolet (UV)
instruments started with the Solar Backscatter Ultraviolet (SBUV)
instruments from 1970 onwards on different satellites

Two commonly used types of data assimilation are 4DVAR and
(ensemble) Kalman filtering. For example, ozone profiles and total
columns from different instruments (such as GOME) were assimilated
using a 4DVAR assimilation scheme in the production of the
ECMWF ERA-Interim reanalysis

The model covariance matrix is an integral and essential part of
a Kalman filter, but it is difficult to derive and computationally
expensive in the analysis calculation. Therefore, most Kalman
filter implementations try to approximate the model covariance
matrix. In the ensemble Kalman filter, a selection of the ensemble
members can be used to approximate the model covariance

In this research, we follow the Kalman filter approach described
in

In Sect.

Data from the UV-VIS satellite instruments GOME-2 and OMI are available for the last 10 years.

GOME-2

OMI

The algorithms used to retrieve the ozone profiles from GOME-2 and
OMI are both based on an optimal estimation technique. The state
of the atmosphere is given by the state vector

The averaging kernel can also be written as

Because the sensitivity of the retrieval to the vertical ozone
distribution is represented by the averaging kernel, it is
important to include the averaging kernel in the assimilation
algorithm. Together, the retrieved state vector, the averaging kernel
and error covariance matrices represent all information gained from
the retrieval

The model used in the assimilation is a global chemistry transport
model called TM5 (Tracer Model, version 5), see

In the current model setup used for the assimilation of the ozone
profiles, TM5 runs globally with grid cells of 3

Above 230

The assimilation algorithm uses a Kalman filter, and is described
in

The observation operator interpolates the model field to the
observation location, converts the model units to the retrieval
units and takes the smoothing of the satellite instruments into
account by incorporating the averaging kernel. The model grid cells
are

In general, the number of elements in an ozone profile is much larger than the
degrees of freedom (about 5 to 6). We can therefore reduce the number of data
points per profile by taking the singular value decomposition of the

The computational cost of the assimilation algorithm can be further reduced
by minimizing the size of the model covariance matrix

Unfortunately, the

For the numerical stability of the assimilation algorithm, the difference
between the observation and the model should not be too large. A filter is
implemented that rejects the observation when the absolute difference between
the observation and the model forecast is larger than 3 times the square
root of the sum of the variance in the observation and the variance in the forecast:

Not all available ozone profiles can be assimilated into TM5 because the
computational cost would be too high. Averaging retrievals on the model grid
(sometimes called superobservations) was not possible because the
assimilation algorithm described in this paper requires
AKs and averaging AKs is not straightforward. Therefore 1 out of 3
GOME-2 profiles and 1 out of 31 OMI profiles are used. These numbers are
chosen such that more or less the same number of observations are assimilated
for each instrument, taking into account the decrease in available pixels due
to the row anomaly in OMI. For OMI, the outermost pixels on each side of the
swath are neglected, because of the large area of these pixels. Of the
resulting retrievals, only cloud-free scenes (cloud fraction

The first version of our assimilation algorithm was described in

The covariance matrix of the observations that is used in the assimilation is composed of two components, the error on the spectral observations and the error of the a priori information. Since the spectral errors affect the assimilation results, they are first verified using the following method.

For a given wavelength, two adjacent detector pixels may have a radiance or
reflectance difference that depends on the slope of the spectrum. Given enough
samples, the standard deviation of the mean difference is a good indication of
the noise at that particular wavelength. The relative difference

For GOME-2, we checked 4 days in 2008: 15 March, 25 June, 26 September and
25 December. On 10 December 2008 the band 1A/1B boundary was shifted from approximately 307 to 283

GOME-2 Metop-A radiance spectra calculated by OPERA: before

OMI radiance spectrum used in the retrieval, the area around
310

Figure

The wavelength grid for OMI varies with the location across the detector, so
the error verification has been performed with a dependence on the cross-track
position. An example radiance spectrum along with the uncertainties is shown in
the left panel of Fig.

On 1 February 2010, a L0 to L1b processor update was implemented for OMI.
The new processor version includes more detailed information on the row anomaly
and a new noise calculation for the three channels UV1, UV2 and VIS. More
information can be found on the following website:

In general, the spectral uncertainties for GOME-2 show a good agreement with
our fitted uncertainties and therefore we simply use the uncertainties provided
with the observations. The spectral uncertainties for OMI show a good agreement
with our fitted uncertainties before the processor update, but are too small
afterwards. The consequences of these smaller uncertainties will be shown in
Sect.

In Sect.

In the previous version of the assimilation algorithm, the error growth for
the total column was modelled by the function

Therefore, we use the following function

Maximum relative model error (

In order to calculate the time independent correlation field, we
follow the National Meteorological Center's method (NMC-method) to
determine the correlation in the model

We use a slightly different approach as

Determination of the TM5 correlation field. The solid line is an assimilation model run, the dashed lines are 10 day free model runs. After 10 days, there are 11 ozone fields for each given day which can be used to determine the correlations.

Calculated

Global validation results for 2008–2011 for GOME-2

The difference between the assimilation and free model runs is used
to determine the correlations between all pairs of grid cells in
the vertical direction (constant location), in the East–West
direction (constant latitude and altitude), and in the North–South
direction (constant longitude and altitude). The correlations are
determined as a function of the distance. Since the East–West
distance between two grid cells is larger at the equator than near
the poles, the East–West correlation also depends on the
latitude. The calculated correlations as a function of distance are
fitted with a Gaussian distribution (with correlations less than
0.01 set to zero). Both the calculated and fitted correlations are
shown in Fig.

The biases between two instruments should be as small as possible for a stable assimilation. Therefore, a bias correction as a function of solar zenith angle (SZA), viewing angle (VA) and time has been developed based on the results of the comparison with sondes. The bias correction factor is one minus the median of the relative deviation based on all collocated data in a given year. All observations in a given year are multiplied by this correction factor.

Figure

Stations used for the validation and bias correction of GOME-2 and OMI.

The bias of GOME-2 with respect to sondes varies between

GOME-2 OmF (blue) and OmA (red) for the surface layer

We have assimilated GOME-2 (on Metop-A) and OMI ozone profiles for a period of 4 years between 2008 and 2011 using the Kalman filter algorithm described in the previous sections. In total, four model runs were performed: a “free” model run without assimilation, a model run with assimilation of GOME-2 ozone profiles only, a model run with assimilation of OMI ozone profiles only and a model run with simultaneous assimilation of GOME-2 and OMI ozone profiles.

OMI OmF (blue) and OmA (red) for the surface layer

An important diagnostic of any assimilation system is the difference between
the observations and the model (also known as innovations). In the following,
we define the relative observation minus forecast (OmF) for layer

In Fig.

OMI OmF (blue) and OmA (red) for the layer around 0.3

Both OmF and OmA for the GOME-2 assimilation run show regular
decreases with a period of about 1 month. These decreases are caused
by GOME-2 being operated in “narrow-swath mode”, when the swath is
320

Sudden changes in the OmF and OmA are visible for some altitudes for both
instruments at the start of some years. One example is in the layer just above
the 10

Closer inspection of the OMI OmF and OmA change at the start of 2010 (see the
lower left panel of Fig.

Comparison of Figs.

Lower uncertainties in the spectra lead to lower uncertainties in the
observations, which in its turn changes the balance between model and
observations in the Kalman filter and affects the innovations. Because
the variance in the observation is lower, more pixels will be rejected
by the OmF filter (see Sect.

Number of assimilated observations from GOME-2

Mean OmF

In order to show the geographical distribution of the OmF and OmA, the absolute
values for each layer were quadratically added and the square root was taken
from the result. These column-integrated OmF and OmA values were averaged on
a daily basis for latitude bins with a size of

The OmF of the results should be consistent with the uncertainties of the
observations and the model forecast. The expected OmF is based on the
observation error and the forecast error and is the mean of the square
root term in the right-hand side of Eq. (

Observed vs. expected OmF.

Note that the pressure levels are those from the observations, not the regridded
levels used in the calculation of the OmF and OmA above. The expected and
observed OmF are close to the 1-to-1 line, which shows that the model error

Validation of the model runs with ozone sondes for 2008–2011.

The model output was validated against ozone sondes that were
obtained from the World Ozone and Ultraviolet Radiation Data
Centre (

In the troposphere, the assimilation also improves, but not as much
as in the stratosphere. Note that in the troposphere the chemistry
scheme is different than in the stratosphere (see
Sect.

Two meridional cross sections over the Tibetan Plateau, located
at

To demonstrate the performance of the assimilation algorithm we
analysed the results for a day above the Tibetan Plateau (located
between 30 and 40

When two instruments are assimilated simultaneously, their differences should
be taken into account. For example, the algorithms used for the retrieval of
GOME-2 and OMI ozone profiles both produce partial columns. However, the number
of layers in the retrievals differ and the sensitivity of the retrieval is
expressed by the averaging kernel. Both the different vertical resolution
and the averaging kernel are incorporated into the observation operator

Two different instruments can be biased with respect to each other. In order to
minimize the bias, a bias correction scheme has been implemented with respect to
ozone sondes. We used cloud-free observations (max. cloud fraction 0.20) for the
bias correction in order to get a maximum amount of information from the
troposphere. As a consequence, we could not use all available sondes in deriving
the bias correction. Sudden changes in the bias correction parameters are
visible at the start of the year, when the parameters are changed. To minimize
these changes, it might be worthwhile to implement an interpolation scheme for
the bias correction parameters similar as for the MSR data

The model can run a full chemistry scheme, but instead a parameterized chemistry
scheme has been used in favour of speed. Another possibility to increase the
accuracy of the model is to increase the horizontal resolution from the current

The model covariance matrix is also an expensive step in the assimilation algorithm. We have reduced the calculation cost by parameterizing it into a time-dependent error field and a time-independent correlation field. The data from April 2008 was used to derive the correlations, which were then used for the whole assimilation period. The assumption that the derived correlations are constant throughout time has not been tested.

An algorithm for the simultaneous assimilation of GOME-2 and OMI ozone profiles has been described. The algorithm uses a Kalman filter to assimilate the ozone profiles into the TM5 chemical transport model. Compared to previous versions, the algorithm is significantly updated. The observational error has been characterized using a newly developed in-flight calibration method. Since the Kalman filter equations are too expensive to calculate directly for the current setup, the model covariance matrix is divided into a time-dependent error field and a time independent correlation field. The time evolution is applied to the error field only, while the correlation is assumed to be constant. The model error growth is modelled by a new function that prevents the error from increasing indefinitely, and the correlation field has been newly derived using the NMC method. Large biases between retrievals of the two instruments might destabilize the assimilation. To avoid this, a bias correction using global ozone sonde observations has been applied to the retrieved ozone profiles before assimilation.

Four model runs were performed spanning the years between 2008 and 2011:
without assimilation, with assimilation of GOME-2 only, with assimilation of
OMI profiles only and with simultaneous assimilation of both GOME-2 and OMI
profiles. Depending on the altitude, the OmF and OmA for one instrument might
be larger than the other, which might change in the course of time.
Assimilating the observations from these instruments simultaneously increases
the overall sensitivity of the assimilation. Two notable instrumental effects
are the band 1A/1B wavelength shift for GOME-2, which causes a significant
decrease in OmF and OmA. For OMI, after the L0 to L1b processor update on
1 February 2010, the uncertainty in the observations is too small with
respect to the method of in-flight validation of the uncertainties presented
in this paper. This caused a decrease in the number of assimilated
observations for both GOME-2 and OMI. The expected and observed OmF and OmA
are more similar for the combined assimilation than for the separate
assimilations. Validation with sondes from the WOUDC shows that the combined
assimilation performs better than the single sensor assimilation in the
region between 100 and 10

OMI L2 ozone profiles are operationally retrieved and can
be obtained from NASA's Goddard Earth Sciences (GES) Data and Information
Services Center (DISC) on-line archive at

The authors declare that they have no conflict of interest.

The authors acknowledge all scientists and institutes who contributed their
ozone sonde data to the World Ozone and Ultraviolet Radiation Data Centre