# Comparison and evaluation of modelled and GOME measurement derived tropospheric NO2 columns over Western and Eastern Europe

I. B. Konovalov, Matthias Beekmann, R. Vautard, J. P. Burrows, A. Richter, H. Nüss, N. Elansky

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► To cite this version:

I. B. Konovalov, Matthias Beekmann, R. Vautard, J. P. Burrows, A. Richter, et al.. Comparison and evaluation of modelled and GOME measurement derived tropospheric NO2 columns over Western and Eastern Europe. Atmospheric Chemistry and Physics, 2005, 5 (1), pp.190. 10.5194/acp-5-169-2005. [https://hal.science/hal-00328378v1](https://hal.science/hal-00328378v1)
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# Comparison and evaluation of modelled and GOME measurement derived tropospheric NO₂ columns over Western and Eastern Europe

I. B. Konovalov<fnref n="1" />,<fnref n="2" />, M. Beekmann<fnref n="2" />, R. Vautard<fnref n="3" />, J. P. Burrows<fnref n="4" />, A. Richter<fnref n="4" />, H. Nüß<fnref n="4" />, and N. Elansky<fnref n="5" />

Received: 8 September 2004 – Published in Atmos. Chem. Phys. Discuss.: 13 October 2004

Revised: 4 January 2005 – Accepted: 21 January 2005 – Published: 24 January 2005

**Abstract.** We present the results of a first comparison of the tropospheric NO₂ column amounts derived from the measurements of the Global Ozone Monitoring Experiment (GOME) with the simulated data from a European scale chemistry transport model (CTM) which is distinct from existing global scale CTMs in higher horizontal resolution and more detailed description of the boundary layer processes and emissions. We employ, on the one hand, the newly developed extended version of the CHIMERE CTM, which covers both Western and Eastern Europe, and, on the other hand, the most recent version (Version 2) of GOME measurement based data-products, developed at the University of Bremen. We evaluate our model with the data from ground based monitoring of ozone and verify that it has a sufficiently high level of performance, which is expected for a state-of-the-art continental scale CTM. The major focus of the study is on a systematic statistical analysis and a comparison of spatial variability of the tropospheric NO₂ columns simulated with CHIMERE and derived from GOME measurements. The analysis is performed separately for Western and Eastern Europe using the data for summer months of 1997 and 2001. In this way, we obtain useful information on the nature and magnitudes of uncertainties of spatial distributions of the considered data. Specifically, for Western Europe, it is found that the uncertainties of NO₂ columns from GOME and CHIMERE are predominantly of the multiplicative character, and that the mean relative random (multiplicative) errors of the GOME measurement derived and simulated data averaged over the summer seasons considered do not exceed 23% and 32%, respectively. The mean absolute (additive) errors of both kinds of the data are estimated to be less than

3×10¹<fnref n="4" /> mol/cm<fnref n="2" />. In Eastern Europe, the uncertainties have more complex character, and the separation between their multiplicative and additive parts is not sufficiently unambiguous. It is found, however, that the total random errors of NO₂ columns from both GOME and CHIMERE over Eastern Europe are not, on the average, larger than the errors of the NO₂ columns with similar magnitudes over Western Europe.

## 1 Introduction

It is well known that in many instances air pollution by photo-oxidants has a non-local origin and that polluted air may be transported within the atmosphere over hundreds and even thousand of kilometres. The recognition of such a fact has fostered development of chemistry transport models (CTM) of the continental scale with the horizontal resolution of several tenths of kilometres, such as EMEP (see, e.g. Simpson et al., 2003), DEM (Zlatev et al., 1992), LOTOS (Builtjes, 1992), EURAD (Hass et al., 1995), CHIMERE (Schmidt et al., 2001), and others (see, e.g. Byun and Ching, 1999 for more references). Most of the existing European continental scale CTMs are focused on Western Europe, although some of them (e.g. EMEP and LOTOS) take into account also a part of Eastern Europe. It is obvious that a model with a larger domain, but nevertheless a good horizontal resolution, may not only be used to study transport processes on a larger scale but, besides, it may enable a broader insight into regularities and climatological features of atmospheric processes in different environments. Moreover, taking into account that continental scale CTMs are designed to simulate the fate of air pollution within the boundary layer more accurately than the global models, the development of continental

<footnote n="1">¹Institute of Applied Physics, Russian Academy of Sciences, Nizhniy Novgorod, Russia</footnote>

<footnote n="2">²Service d'Aéronomie, Institut Pierre Simon Laplace, Paris, France</footnote>

<footnote n="3">³Laboratoire de Météorologie Dynamique, Institut Pierre Simon Laplace, Paris, France</footnote>

<footnote n="4">⁴Institute of Environmental Physics and Remote Sensing, IUP/IFE, University of Bremen, Bremen, Germany</footnote>

<footnote n="5">⁵Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia</footnote>

<footnote>*Correspondence to:* I. B. Konovalov
(konov@appl.sci-nnov.ru)</footnote>
scale models for major populated regions contributes even-
tually to validation of available emission data and, conse-
quently, to better understanding of the chemical balance of
the troposphere and the atmosphere in general. However, the
extension of European CTMs beyond the Western Europe
presents rather serious difficulties, because the amount of
available observational data needed to specify model param-
eters, and, especially, to validate model results outside West-
ern Europe is rather limited. For example, only two stations
out of more than 100 ones in the EMEP ground based ozone
monitoring network are operating in Russia, and some other
former USSR countries, e.g. Ukrainia and Byelorussia have
no ozone measuring EMEP stations at all. The situation with
measurements of ozone precursors in the mentioned coun-
tries is even worse. Therefore, as far as modelling photo-
oxidant air pollution over Eastern Europe is concerned, the
traditional way of validation of continental scale CTMs via
comparison of simulations with ground based observations
of the key species (see, e.g. Fagerli et al., 2003) turns out to
be of very limited utility.

Meanwhile, a significant source of global observational
information concerning the atmospheric pollution, namely,
satellite measurements of trace gases in the troposphere,
has become available in recent years. It has been shown,
in particular, that measurements performed by the satellite
borne instrument of Global Ozone Monitoring Experiment
(GOME) (Burrows et al., 1999) can be used to retrieve the
tropospheric column amounts of nitrogen dioxide and sev-
eral other trace gases (see, e.g., Velders et al., 2001; Richter
and Burrows, 2002; Martin et al., 2002). More recently, the
data retrieved from the measurements of the Scanning Imag-
ing Absorption Spectrometer for Atmospheric Chartogra-
phy (SCIAMACHY) featuring higher spatial resolution than
GOME instrument have also become available (e.g. Buch-
witz et al., 2004), but these data still have a preliminary and
fragmentary character.

Although it is obvious, that comparison with NO₂ columns
cannot provide enough information about the overall model
performance (concerning, e.g. predictions of ozone concen-
trations), it may shed some light on the degree of uncertainty
of input NOₓ emission data and of the quality of representa-
tion of major oxidation and transport processes which play
an important part in variability of other important photo-
oxidants and their precursors. Besides, modelling of nitro-
gen dioxide is important by itself, taking into account that
NO₂ plays an important part in the photochemistry of both
the boundary layer and free troposphere (see, e.g. Kley et
al., 1999; Bradshaw et al., 2000) and contributes to radiative
forcing of the climate (Solomon et al., 1999; Velders et al.,
2001). Finally, comparison of simulated NO₂ columns and
those derived from satellite measurements may be helpful,
in turn, for evaluation of the satellite measurement derived
data, taking into account that the procedure of retrieval of
tropospheric NO₂ columns from satellite measurements al-
ways involves some a priori assumptions which are difficult

to validate, such as the shape of vertical profiles of tropo-
spheric NO₂, or the amount of scattering on aerosols.

The comparison performed within the framework of this
study may be especially interesting from the last point of
view particularly because we are the first to compare the
latest version (Version 2) of the GOME measurement based
data product for tropospheric NO₂ columns from the Bremen
University (http://www.doas-bremen.de/) with a CTM which
was not used in the stage of retrieval of these data. The main
difference between Version 2 and earlier Version 1 data is
that Version 2 data were derived using tropospheric NO₂ ver-
tical profiles from the global CTM MOZART (Horowitz et
al., 2003) while the constant profile with all NO₂ in a 1.5 km
boundary layer was assumed for Version 1 data. That is, on
the one hand, it is reasonable to expect that Version 2 data
are less uncertain than Version 1 data, but on the other hand,
they are more dependent on performance of a certain model
(MOZART). Therefore, a comparison of Version 2 data with
corresponding data from another model is believed to be a
really very useful step for evaluation of that new version of
the satellite measurement based data.

This study addresses the following issues. First, we
present the newly developed extended version of CHIMERE
CTM, which covers the whole Europe and some neighbour-
ing regions, and evaluate its performance over the whole do-
main. In doing so, we present, to the best of our knowledge,
first comparison of satellite measurement based data for tro-
pospheric NO₂ columns with calculations performed by a
continental scale CTM designed to study air quality issues.
The advantages of our model over the global CTMs, with
which the tropospheric NO₂ columns derived from GOME
measurements were compared earlier (Velders et al., 2001;
Lauer et al., 2002; Martin et al., 2003; Savage et al., 2004),
are higher spatial resolution that matches well the resolution
of GOME measurements in the South-to-North direction and
more detailed parameterisation of the boundary layer pro-
cesses. Our analysis is focused on statistical characteriza-
tion and comparison of “fine” structure of spatial distribu-
tions of the simulated and GOME measurement derived tro-
pospheric fields of NO₂. The comparison of model results
with satellite measurement data is supplemented by the com-
parison of the simulated ground based ozone concentrations
with those measured by the EMEP network and two stations
of scientific atmospheric monitoring in Russia. On the one
hand, the comparison of the simulated and observed ground
based ozone concentrations allows us to demonstrate that
CHIMERE features a sufficiently high level of performance
expected for state-of-the-art continental scale models. And
on the other hand, it is important in view of possible future
applications of CHIMERE to study photo-oxidant pollution
in Eastern Europe.

Second, we estimate the upper limits of spatially average
random uncertainties (as distinct from systematic uncertain-
ties equally applicable to all pixel considered) for both NO₂
columns simulated by CHIMERE and those derived from
GOME measurements. Moreover, we make an attempt to characterise these uncertainties in terms of absolute (additive) and relative (multiplicative) errors. This issue seems to be especially important from the point of view possible application of satellite measurements for inverse modelling of emissions, because simulated NO₂ columns are closely linked to NOₓ emission data.

Finally, we pay special attention to the analysis of differences in statistical characteristics and uncertainties of the GOME derived and simulated NO₂ columns between Western and Eastern Europe. Such an analysis is very useful. Indeed, while emissions inventories for Western Europe have been extensively exploited and independently validated in numerous studies comparing results of continental and regional scale CTMs with observations (although in most cases not directly to NOₓ or NOᵧ), the number and extent of similar studies concerning Eastern European countries is incomparably smaller, because of a severe deficit of both models and observations. Recent comparisons of tropospheric NO₂ columns derived from GOME measurements and those calculated by global models did not pay much attention to Eastern Europe, probably because the emission sources there are spread over vast territories, and, correspondingly, the average level of NO₂ pollution is much lower in Eastern Europe than over such densely populated regions as Western Europe or South Asia. Nevertheless, it would be useful to note that, for example, total anthropogenic NOₓ emissions in Russia are estimated to be considerably larger than those in any of the Western European countries taken alone (Vestreng, 2003).

The paper is organized as follows. The brief description of our version of the CHIMERE CTM is given in section 2, and its evaluation with data from the EMEP ground based ozone monitoring network is discussed in Sect. 3. Section 4 provides a description of the methods used to derive data for tropospheric NO₂ columns both from GOME measurements and calculations by CHIMERE. Section 5 is devoted to comparison of the satellite measurement derived tropospheric NO₂ columns with the corresponding simulated data, and Sect. 6 discusses the uncertainties of the analysed data. Finally, results of our study are summarised in Sect. 7.

## 2 Model description

This study is based on the use of the chemistry transport model CHIMERE which is an Eulerian multi-scale model designed for analysis of various air pollution related issues on urban and continental scales and for routine forecasting air pollution (http://prevair.ineris.fr). A description of basic features of the earlier version of the model can be found in the papers by Schmidt et al. (2001) and Vautard et al. (2001), and important recent updates are presented by Bessagnet et al. (2004). In DETAIL description of the model, the technical documentation and the source codes are available also on the web (http://euler.lmd.polytechnique.fr/chimere/). Therefore,

only those features which are the most important in the context of the given study or specific to our extended version of CHIMERE are mentioned below.

CHIMERE has been thoroughly evaluated both on the urban scale for the Ile-de-France region (Vautard et al., 2001, 2003) and continental scale for Western Europe (Schmidt et al., 2001; Bessagnet et al., 2004). Although CHIMERE enables modelling of both gases and aerosols, this paper focuses on gas-phase processes only.

The continental version of CHIMERE uses a rectangular grid with horizontal resolution of 0.5×0.5 degrees. The new CHIMERE domain used in this study is significantly larger (up to seven times) than any of the domains with which the model was used earlier. Specifically, it covers the region from 15° W to 70° E and from 25° N to 70° N, which includes the whole Europe, Middle East, and a part of Northern Africa.

Meteorological input data for the CTM have been obtained from simulations with the non-hydrostatic mesoscale model MM5 (http://www.mmm.ucar.edu/mm5/) that has been run on a regular grid with horizontal resolution of 100×100 km. MM5 is initialised and driven with NCEP ReAnalysis data available on the web (http://wesley.ncep.noaa.gov/ncep_data/) with a temporal resolution of 6 h and a spatial resolution varying from 1.8 to 2.5 degrees for different variables. MM5 is employed in order to compensate for this too low temporal and spatial resolution of NCEP data. Note that all previous studies with CHIMERE referenced above used ECMWF data with a horizontal resolution of about 50 km. Some "coarsening" of the standard configuration of CHIMERE proved to be inevitable in order to enable efficient simulations for the new larger domain.

In the vertical, the model has 8 layers whose heights are fixed using hybrid coordinates. The top of the upper layer is fixed at the 500 hPa pressure level. The fact that CHIMERE does not enable simulations of most of the free troposphere presents some limitation for our comparison of model calculations with tropospheric NO₂ columns derived from GOME measurements. However, this issue is not crucial, because, as is argued in Sect. 5, the spatial variability of tropospheric NO₂ columns is determined mostly by lower tropospheric NO₂. Vertical diffusion is calculated within CHIMERE itself using the parameterisation suggested by Troen and Mahrt (1986). Photolysis rates are calculated using the tabulated outputs from the Troposphere Ultraviolet and Visible model (TUV, Madronich and Flocke, 1998) and depend on altitude and zenith angle. The attenuation of radiation due to clouds is taken into account, based on the simplified assumption that the processes considered in the model take place below the top of the cloud layer. Correspondingly, the clear sky photolysis rates $J_c$ are scaled with a radiation attenuation coefficient A which is calculated as a function of cloud optical depth; the actual photolysis rates are defined as a product A and $J_c$.

The chemical scheme used (Derognat, 2002) is the same as the one presented in Schmidt et al. (2001), but with updated
reaction rates. It includes 44 species and about 120 reactions and was derived from the more complete MELCHIOR chemical mechanism (Latuatti, 1997) using the concept of chemical operators (Carter, 1990; Aumont et al., 1997). Laternal boundary conditions are prescribed using monthly average values of the climatological simulations by the second generation MOZART model (Horowitz et al., 2003).

The anthropogenic emissions are prescribed in essentially the same way as in the earlier studies with CHIMERE. Specifically, the annual EMEP data (Vestreng, 2003) for NOₓ, SO₂, CO, and non-methane volatile organic compounds (NMVOC) distributed to 11 SNAP sectors and grided with horizontal resolution of 50×50 km are used to specify emissions of corresponding model species for the most part of the new domain. But because dimensions of the new domain exceed sizes of the EMEP grid, the data from EDGAR V3.2 database (Olivier and Berdowski, 2001) are used to prescribe emissions for some territories (mainly, in Asia). These territories constitute only a minor part of the whole domain and are not the focus of this study. Daily, weekly, and seasonal variations of emissions were prescribed using data provided by the IER, University of Stuttgart (GENEMIS, 1994). As the new domain covers several time zones, the local administrative times were taken into account. The annual NMVOC emissions were split first into emissions of 227 real individual hydrocarbons using typical NMVOC profiles (Passant, 2002), and then emissions of these real species were aggregated into emissions of 10 NMVOC model species.

The land use data needed to parameterise biogenic emissions and dry deposition are obtained with a 1 km resolution from the GLCF database (Global Land Cover Facility, Hansen et al., 2000, http://glcf.umiacs.umd.edu) and aggregated to the CHIMERE grid. Biogenic emissions of isoprene, pinene and NO are parameterised in accordance to methodology suggested by Simpson et al. (1999), using distributions of tree species on a country basis provided in their work and the inventory of NO soil emissions by Stohl et al. (1996). The biogenic emissions for African and Asian countries (except Turkey and Kazakhstan) which are not covered in the cited inventories, are not taken into account, because they cannot be adequately described using the above mentioned methodologies designed for temperate regions. Simulations for these countries are anyway not the focus of this study and the paper's conclusions are not affected by this omission.

# 3 Model evaluation with ground based observations

## 3.1 Observational data

While the main aim of this paper is comparison of model results with data derived from satellite measurements, the comparison with ground based measurements presented in this section plays a complimentary role and is intended, mainly,

to demonstrate that our version of CHIMERE performs reasonably well in a “classical” way of evaluation of continental scale CTMs. Correspondingly, we do not consider here all available measurement data (that would be hardly possible to do within a single paper anyway), but use mainly the data of ozone measurements from EMEP ground based monitoring network (http://www-nilu.no/projects/ccc/emepdata.html) for the years 1997 and 2001, and the data from two Russian ozone monitoring stations situated in remote regions and supervised by Institute of Atmospheric Physics (Moscow). These measurements are best suited to our goals, because, on the one hand, predictions of ozone concentration, which, in the real atmosphere, depends on numerous physical and chemical processes, provide indeed a very serious test for the model performance. And on the other hand, as the EMEP network is intended to reflect regional background conditions relatively unaffected by local emissions of ozone precursors, the model resolution should be adequate at least for ozone.

Note that the measurements of other pollutants are less appropriate for comparison with our model. For example, insufficient resolution of the model's grid is the most likely reason for a rather large disagreement between NO₂ monitoring data and continental scale models (see, e.g. Schmidt et al., 2001; Fagerli et al., 2003; Bessagnet et al., 2004). Such disagreement reflects, in particular, the well-known fact of a large spatial and temporal variability of that relatively short-lived species. Besides, the measurement and representativeness errors are also considerable in the case of NO₂ (Aas et al., 2000). Consequently, although along with the comparison with ozone measurements we have also performed the similar comparison with the ground based measurements of nitrogen dioxide, the results of that comparison are discussed in this paper only very briefly.

The EMEP ozone-measuring network includes 151 stations. Normally, the hourly continuous measurements are reported. However, for some stations, the data were absent or incomplete for the periods that are considered in our study. Therefore, some selection criteria were needed. Specifically, only these days have been taken into account, for which the number of hourly measurements exceeded 18, and the stations with data gaps for more than 30% of days in the periods considered have been excluded from the analysis. As a result, for the summer period of 2001 considered below, we have selected 121 stations. Note that data from the major part of excluded stations (27 out of 30) are missing entirely for this period.

As it has been already pointed out in the introduction section, the EMEP monitoring network is extremely sparse over Eastern Europe. Correspondingly, an effort was made to include relevant data from other sources for this area. Specifically, we used data from ozone measurement stations situated at Kola Peninsula (Lovozero site, 250 m a.s.l., 68.0° N, 35.1° E) and in the Russian Caucasian region (Kislovodsk High-Mountain station, 2070 m a.s.l., 43.7° N,
42.7° E). Taking into account that data from only two ozone measuring EMEP stations in Russia are available for the periods considered in this study, the data from even two more ozone monitors provide very substantial additional contribution to available observational information concerning Eastern Europe. To the best of our knowledge, no publications are available in which the data from these stations are compared with CTM simulations.

When ground based observations are compared with model results, it is necessary to define which model level corresponds to a given station. The choice of the surface layer may be inappropriate for mountain sites where the model's grid cannot resolve details of a relief. In this study, we chose an appropriate model level by considering the difference between the actual height of a site (a.s.l.) and its height in the MM5 model topography (with resolution 100×100 km). Such a procedure is believed to be the most unambiguous, although it does not provide a general solution for the problem of low resolution of a model in mountainous areas where the performance of the model may be worse than over plains.

## 3.2 Results

Figure 1 presents a simulated distribution of mean daily maximums of ozone concentrations over model domain in comparison with the corresponding observed data. Note that simulated ozone concentrations are given for the lowest CHIMERE level, and only these stations are shown which, in accordance to the criterion discussed above, correspond to this level. Although it is difficult to judge about adequacy of the simulated ozone distribution based on comparison with the given very fragmentary observational picture, it is useful to note that both observations and measurements manifest the pronounced north-to-south gradient of ozone concentration. Such gradient appears to be quite a reasonable feature of the simulated ozone field taking into account that the stronger insolation and higher temperatures facilitate faster ozone production in densely populated regions in Southern Europe when compared with the similar regions in Northern Europe. Considering variability of ozone concentrations in the West to East direction, it can be noticed that both the model and observation show larger concentration over Germany and Italy than over England, Spain and Portugal in the West and Poland and Slovakia in the East. The high level of simulated ozone concentration over Mediterranean Sea and Persian Gulf is, probably, a result of a combination of large emissions of ozone precursors from surrounding coastal areas, strong radiation, and a low rate of ozone deposition on a water surface. Note also that the mean level of modelled ozone pollution is generally lower over Eastern than Western Europe in agreement with the lower population density and associated emissions of ozone precursors in Eastern Europe. In order to quantify the model performance in capturing spatial structure of the measured mean ozone concentrations, we have evaluated the correlation coefficient between the mean

<figure><img src="image_3.png" /><figcaption>Fig. 1. Spatial distributions of daily maximum average ozone concentrations calculated by CHIMERE and observed at stations of the EMEP monitoring network.</figcaption></figure>

observed and measured ozone concentrations for all sites. It equals 0.70.

Let us further consider several classical statistics used for evaluating air quality models. These are the standard correlation coefficient, R, the normalized root mean square error,

$$NRMSE = \frac{\left( \frac{1}{N} \sum_{i=1}^{N} (C_{i}^{m} - C_{i}^{o})^{2} \right)^{1/2}}{\bar{C}^{o}}, \quad (1)$$

and the mean normalized bias,

$$BIAS = \frac{\bar{C}^{m} - \bar{C}^{o}}{\bar{C}^{o}}. \quad (2)$$

Here, C^o and C^m are observed and modelled daily maximum concentrations at a given location, and C^o and C^m are their averages over the considered periods.

The statistics for all the measurement sites considered in our analysis are mapped in Fig. 2. The correlation coefficient is higher than 60% for the majority of sites (73 out of 121 considered), and higher than 80% for 15 sites, with an
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Comparison statistics for daily maximums of ozone concentrations simulated by CHIMERE and measured by ground based ozone monitors.</figcaption></figure>

average of 62%. Persistently high correlations are typical for Germany, Belgium, and the Netherlands, and generally smaller ones are found for the sites in Eastern and Northern Europe. This may be indicative of the fact that CHIMERE works best for the sites situated in relatively polluted environments where ozone behaviour is determined by photochemical processes rather than the long-range transport.

However, it is important to note that even when the model performs badly in terms of correlation coefficient, it still may

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Time series of daily maximums of ozone concentrations (mixing ratios) for summer season 2001. Solid lines and crosses show model results and observations, respectively. Note that the data are presented in original units of measurements for a given station.</figcaption></figure>

perform quite satisfactory with regard to normalized RMSE. For example, a very small correlation coefficient (29%) and a rather low NRMSE (18%) co-exist for the Kislovodsk high-mountain station. A similar behaviour is observed also for many other remote stations both in North and South of Europe. As the day-to-day variability of ozone concentration is relatively small at these sites, the errors of model predictions, which may be large when compared with the variance of the measured data, look small when compared with the mean value of ozone concentration. Taken on the average for all the sites, the NRMSE is found to be about 24 percent.

Biases are in the range from -20 to 20 percent for most of the sites. Their absolute magnitudes are less than 10% for 53 out of 121 sites considered, and less than 15% for 84 sites. When averaged over all the sites, the mean bias is slightly positive (about 7 percents).

When comparing model performances for Western and Eastern Europe, it becomes clear that CHIMERE performs better for Western Europe in terms of correlations but that differences are small in terms of NRMSE and mean biases. Specifically, for the sites located to West (East) of 18° E, the average values of the correlation coefficient, the normalised
RMSE, and the mean bias are found to be 65, 25, and 6 (44, 22, and 7) percent, respectively. As it has already been noted above, the relatively high correlations are typical for the sites located within highly urbanized regions, which are characteristic of Western Europe rather than of Eastern Europe. Correspondingly, the differences in the model performances with respect to the correlation coefficients cannot be considered as sufficiently strong evidence in favour of better quality of ozone simulations by CHIMERE for Western Europe when compared to those for Eastern Europe. It should be emphasised also that the statistics reported above for Eastern Europe are likely not quite representative of the whole of Eastern Europe because they are based on a very limited number of stations.

Figure 3 presents examples of simulated and observed time series of ozone daily maximums for several sites in Western Europe and Eastern Europe (Russia). It is interesting to note that the largest differences are observed during the episodes of elevated ozone concentrations, even if they are generally well pronounced in simulations, too. Among the sites presented in Fig. 3, the model performs worst at Lovozero. However, on the one hand, the typical ozone mixing ratio observed at this remote site is very low, and so the absolute errors of model predictions are not very large when compared with the other sites. On the other hand, Lovozero is situated almost on the edge of the model domain and thus the simulated results may depend strongly on the boundary conditions.

The statistics considered above, when taken alone, do not enable conclusions about model performance to be drawn in qualitative terms such as “good” or “bad”. Therefore, it would be useful to compare our results with the corresponding results of other European continental scale models. For such a purpose, we consider here the results of model evaluations presented in the Special Report to EUROTRAC (Roemer et al., 2003). Table 1 lists the comparison statistics for daily maximums of ozone concentration, obtained with several continental scale models for different measurements sites. Note that while not all of the sites considered in the Special Report belong to EMEP monitoring network, only EMEP sites are considered here. All the models, including ours, were run for the period from 1 May to 31 August 1997. It seems to be evident that although the performance of our version of CHIMERE is, to some degree, worse than the performance of the “standard” CHIMERE, it still equals on the average the performances of the other models.

The comparison statistics defined above were evaluated also using NO₂ near-ground daily mean concentrations simulated by CHIMERE and those measured at EMEP stations for three summer months of 1997. The values of the correlation coefficient, the normalised RMSE, and the mean bias averaged over 53 stations selected using the same criteria as in the case of ozone measurements are found to be 20, 80, and –19 percent, respectively. Although these results look significantly worse than similar results for ozone, the large

discrepancies between observations and simulations in this case are caused, most probably, by the reasons mentioned in the previous section (insufficient spatial resolution of the model in case of such a short-lived species as NO₂ and significant measurement errors) and do not mean that NO₂ data from CHIMERE are indeed of very low quality. In fact, the output data from CHIMERE represent NO₂ concentrations averaged over a grid cell and, therefore, it would be best to compare them to measurement data representing the similar scales. Such kind of data can be provided by satellite measurements, which, for that reason, seems to be much more suitable for evaluation of CHIMERE and other similar models than in situ measurements of NO₂. On the other hand, the disagreement with NO₂ ground based measurements does not look so large if we consider spatial correlation between simulations and measurements averaged over several months. Specifically, we have found that for the period indicated above, the respective correlation coefficient equals 0.82.

Finally, considering all the results presented in this section, we can conclude that our extended version of CHIMERE is a state-of-the-art continental scale model which simulates spatial-temporal evolution of near-ground ozone concentrations satisfactorily in Western, Central, and Northern Europe. However, the available ozone measurements do obviously not enable correct evaluation of the model performance for the major part of Eastern Europe, nor for Northern Africa and Middle East, for which no surface observations were available in this work. The comparison of the model results with the data derived from the GOME measurements, which is discussed in the next sections, provides substantial additional information on model performance in Eastern, as well as in Western Europe.

# 4 Description of tropospheric NO₂ data

## 4.1 Tropospheric NO₂ columns retrieved from GOME measurements

We use the most recent version (Version 2) of tropospheric NO₂ column data products that were created at the Institute of Environmental Physics (IUP), University of Bremen in the framework of European project POET (http://nadirnilu.no/poet/). These data were derived from the measurements performed by the Global Ozone Monitoring Experiment (GOME) spectrometer on a board of the second European Research Satellite (ERS-2). The GOME instrument is a grating pseudo double monochromator covering the wavelength range from 280 to 790 nm with the spectral resolution of 0.2–0.4 nm (Burrows et al., 1999); it is designed to detect radiation reflected from the ground and scattered back by the atmosphere, as well as the extraterrestrial solar radiance. Although the main target of GOME is observation of ozone fields, its data are used also to retrieve the column amounts
<table><caption>**Table 1.** Comparison statistics calculated for daily maximums of ozone concentrations observed at EMEP stations and simulated by European scale chemistry transport models for the period from 1 May to 31 August, 1997. The results for the standard version of CHIMERE and other models are listed in accordance to Roemer et al., 2003.</caption><thead><tr><th rowspan="2"></th><th colspan="3">R, %</th><th colspan="3">NRMSE, %</th><th colspan="3">BIAS (%)</th></tr><tr><th>chimere<fnref n="1" /></th><th>chimere<fnref n="2" /></th><th>other models avg.<fnref n="3" /></th><th>chimere<fnref n="1" /></th><th>chimere<fnref n="2" /></th><th>other models avg.<fnref n="3" /></th><th>chimere<fnref n="1" /></th><th>chimere<fnref n="2" /></th><th>other models avg.<fnref n="3" />,<fnref n="6" /></th></tr></thead><tbody><tr><td>vredepeel nl</td><td>84</td><td>81</td><td>72</td><td>20</td><td>35</td><td>31</td><td>20</td><td>20</td><td>10</td></tr><tr><td>eupen be</td><td>80</td><td>80</td><td>70</td><td>29</td><td>29</td><td>28</td><td>17</td><td>13</td><td>5</td></tr><tr><td>deuselbach de</td><td>85</td><td>84</td><td>67</td><td>15</td><td>18</td><td>23</td><td>6</td><td>2</td><td>11</td></tr><tr><td>brotjacklriegel de</td><td>77</td><td>81</td><td>51</td><td>23</td><td>12</td><td>23</td><td>-2</td><td>1</td><td>14</td></tr><tr><td>payerne ch</td><td>79</td><td>68</td><td>67</td><td>15</td><td>29</td><td>19</td><td>4</td><td>18</td><td>8</td></tr><tr><td>illmitz at</td><td>68</td><td>62</td><td>55</td><td>14</td><td>17</td><td>22</td><td>-4</td><td>0</td><td>12</td></tr><tr><td>ispra it</td><td>56</td><td>43</td><td>39</td><td>25</td><td>29</td><td>33</td><td>-13</td><td>11</td><td>18</td></tr><tr><td>aston hill uk</td><td>64</td><td>62</td><td>47</td><td>49</td><td>36</td><td>46</td><td>39</td><td>12</td><td>22</td></tr><tr><td>harwell uk</td><td>70</td><td>78</td><td>66</td><td>28</td><td>26</td><td>32</td><td>13</td><td>-3</td><td>10</td></tr><tr><td>sibton uk</td><td>69</td><td>86</td><td>60</td><td>31</td><td>20</td><td>33</td><td>2</td><td>1</td><td>12</td></tr><tr><td>yarner wood uk</td><td>68</td><td>71</td><td>58</td><td>33</td><td>26</td><td>38</td><td>23</td><td>4</td><td>20</td></tr><tr><td>eskdalemuir uk</td><td>71</td><td>79</td><td>62</td><td>42</td><td>23</td><td>31</td><td>33</td><td>3</td><td>14</td></tr><tr><td>mace head ie</td><td>68</td><td>68</td><td>60</td><td>15</td><td>27</td><td>27</td><td>2</td><td>-15</td><td>7</td></tr><tr><td>average<fnref n="4" />,<fnref n="6" /></td><td><strong>72</strong></td><td><strong>73</strong></td><td><strong>60</strong></td><td><strong>26</strong></td><td><strong>25</strong></td><td><strong>30</strong></td><td><strong>14</strong></td><td><strong>8</strong></td><td><strong>13</strong></td></tr><tr><td>birkenes no</td><td>51</td><td>nd</td><td>38</td><td>23</td><td>nd</td><td>27</td><td>10</td><td>nd</td><td>9</td></tr><tr><td>jeløya no</td><td>52</td><td>nd</td><td>45</td><td>19</td><td>nd</td><td>23</td><td>3</td><td>nd</td><td>10</td></tr><tr><td>rörvik se</td><td>63</td><td>nd</td><td>47</td><td>18</td><td>nd</td><td>23</td><td>10</td><td>nd</td><td>10</td></tr><tr><td>utö fi</td><td>36</td><td>nd</td><td>39</td><td>18</td><td>nd</td><td>26</td><td>3</td><td>nd</td><td>14</td></tr><tr><td>vindeln se</td><td>51</td><td>nd</td><td>42</td><td>25</td><td>nd</td><td>28</td><td>2</td><td>nd</td><td>10</td></tr><tr><td>esrange se</td><td>45</td><td>nd</td><td>45</td><td>23</td><td>nd</td><td>33</td><td>-8</td><td>nd</td><td>23</td></tr><tr><td>aliartos gr</td><td>20</td><td>14</td><td>10</td><td>20</td><td>nd</td><td>27</td><td>5</td><td>nd</td><td>12</td></tr><tr><td>noia es</td><td>69</td><td>65</td><td>44</td><td>16</td><td>24</td><td>31</td><td>3</td><td>-19</td><td>14</td></tr><tr><td>san pablo es</td><td>61</td><td>nd</td><td>34</td><td>14</td><td>nd</td><td>24</td><td>-9</td><td>nd</td><td>15</td></tr><tr><td>preila lt</td><td>52</td><td>44</td><td>47</td><td>24</td><td>21</td><td>27</td><td>14</td><td>6</td><td>14</td></tr><tr><td>starina sk</td><td>48</td><td>47</td><td>36</td><td>20</td><td>31</td><td>25</td><td>6</td><td>25</td><td>6</td></tr><tr><td>kosetice cs</td><td>73</td><td>65</td><td>52</td><td>13</td><td>16</td><td>24</td><td>-2</td><td>0</td><td>13</td></tr><tr><td>k-puszta hu</td><td>-23</td><td>-26</td><td>-21</td><td>31</td><td>28</td><td>34</td><td>-21</td><td>-15</td><td>25</td></tr><tr><td>average<fnref n="5" />,<fnref n="6" /></td><td><strong>46</strong></td><td><strong>nd</strong><fnref n="7" /></td><td><strong>35</strong></td><td><strong>20</strong></td><td><strong>nd</strong><fnref n="7" /></td><td><strong>27</strong></td><td><strong>7</strong></td><td><strong>nd</strong><fnref n="7" /></td><td><strong>13</strong></td></tr></tbody></table>

of some other gases, including NO₂, by means of the Differential Optical Absorption Spectroscopy (DOAS) method (Richter, 1997, see also http://www.doas-bremen.de/). ERS-2 has a sun-synchronous near-polar orbit with an equator crossing time of 10:30 LT in the descending node. The typical ground pixel size is 320 km across the track (i.e. in West-East direction), and 40 km along the track. The nearly global coverage is reached in 3 days.

It is important to note that the information provided by GOME measurements is sufficient for retrieval of only to-

tal atmospheric NO₂ slant columns. In earlier version (Version 1) of data products of the Bremen University group, the tropospheric NO₂ columns were evaluated further using the tropospheric excess method introduced by Richter and Burrows (2002). That method was based on the estimation of stratospheric NO₂ slant columns using total atmospheric NO₂ columns in remote parts of the oceans and the assumption of homogeneity of longitudinal distribution of stratospheric NO₂. In Version 2 data, a longitudinal variability of stratospheric NO₂ is estimated more accurately based on

<footnote n="1">¹ the current version of CHIMERE,</footnote>

<footnote n="2">² the standard Western European version of CHIMERE participated in the study by Roemer et al. (2003),</footnote>

<footnote n="3">³ the average over other European models (NILU-CTM, EUROS, MATCH, LOTOS, EURAD, REM3/CALGRID, DEM, STOCHEM, DNMI) participated in the study by Roemer et al. (2003),</footnote>

<footnote n="4">⁴ average over stations from Vredepeel to Mace Head,</footnote>

<footnote n="5">⁵ average over stations from Birkenes to K-puszta,</footnote>

<footnote n="6">⁶ for biases, the averages over their absolute values are given,</footnote>

<footnote n="7">⁷ not enough data</footnote>
simulations with the global CTM SLIMCAT (Chipperfield et al., 1999) sampled in the time of GOME overpass.

The tropospheric NO₂ columns are then derived from the tropospheric slant columns by applying the pre-calculated air mass factors (AMF) which prescribe an effective path of light in the troposphere and depend, in particular, on vertical distribution of the absorbing gas, aerosol and clouds in the troposphere, and on solar zenith angle and surface albedo. Different approaches and assumptions to evaluate air mass factors were used in different versions of data products of IUP. In particular, Version 1 data (see, e.g. Richter and Burrows, 2002; Lauer et al., 2002) were derived under simplified assumptions that all tropospheric NO₂ is homogeneously distributed (in vertical) below 1.5 km. The retrieval of Version 2 data is based on the use of monthly averaged AMF evaluated with NO₂ profiles from the global model MOZART for the year 1997 (Horowitz et al., 2003, see also http://www.mpimet.mpg.de/en/extra/models/mozart/).

Other major improvements concern the evaluations of cloud parameters and surface albedo, which are obtained from GOME measurements using the algorithms discussed by Koelemeijer et al. (2001) and Koelemeijer et al. (2003). Note that cloud parameters are needed to select the pixels with low cloud cover; a cloud cover threshold equal 0.2 is used in the retrieval of Version 2 data, and no further correction of AMF due to clouds is performed. Version 1 data will not be further discussed in this paper, although it seems worthwhile to note that the comparison of NO₂ columns simulated with CHIMERE with these data were also performed in the preliminary stage of our study. A disagreement between model results and Version 1 data was found to be significantly larger than in the case with Version 2 data that may be indicative of larger uncertainty of Version 1 data.

## 4.2 Simulated NO₂ columns

We use the model data corresponding to summer seasons of 1997 and 2001. The choice of the year 1997 has been almost obvious, taking into account that evaluation of AMF used for the retrieval of tropospheric NO₂ columns from GOME measurements were based on MOZART run for this year and, consequently, the respective GOME data are expected to be more consistent than the data for any other year. The year 2001 is considered mainly in order to get an idea of a degree to which our estimations may be sensitive to inter-annual variability of tropospheric NO₂. The choice of summer months has been pre-determined by the fact that CHIMERE is designed, primarily, for simulating photo-oxidant pollution that is usually strongest during the warm season. Besides, the uncertainty of GOME data may be larger for other seasons due to larger cloud cover and possible strong reflection from ice and snow.

In order to be consistent with GOME derived data, the modelled NO₂ columns for each model grid cell are taken in local solar time between 10 and 11 h and only on days

with insignificant cloud cover. Because the total cloud cover is not considered in CHIMERE, we use a selection criteria based on a 0.7 threshold value of the radiation attenuation coefficient, which corresponds to 30% reduction of solar radiation due to clouds. We tested the sensitivity of simulated monthly average NO₂ columns to the radiation attenuation coefficient threshold value and found that it is very insignificant. Note also, that whatever a criterion was used, the selection of “good” days and pixels out from the simulated data could not be done quite consistently with the procedure employed for retrieval of GOME data because of the use of different meteorological data.

The daily data for simulated NO₂ columns are combined in order to obtain monthly averaged distributions that can be used for comparison with the data-products for monthly mean NO₂ columns derived from GOME measurements. Also, in order to provide better similarity of horizontal resolution of simulated and GOME derived data, CHIMERE data has been preliminary averaged for each 7 consecutive grid cells in West-East direction. Note that CHIMERE grid used in this study is exactly the same as the grid used in Version 2 NO₂ data-products. Note also that although our version of CHIMERE is capable of simulating only lower tropospheric NO₂ columns (up to 500 hPa pressure level), we use evaluations of tropospheric NO₂ columns above 500 hPa, obtained using the same output database of the global CTM MOZART that is used to prescribe boundary and initial conditions for CHIMERE (see Sect. 2).

# 5 Overview and comparison of GOME retrieved and simulated NO₂ distributions over the model domain

Figure 4 presents distributions of tropospheric NO₂ columns derived from GOME measurements, lower and upper tropospheric NO₂ column amounts simulated with CHIMERE (below 500 hPa) and MOZART (above 500 hPa), respectively, and combined (CHIMERE plus MOZART) total tropospheric NO₂ columns; all the data shown are averages of June to August monthly means. Seasonally averaged distributions rather than data for individual months not only enable more concise presentation and discussion of our results, but it is also very reasonable to consider them from the point of view of potential applications of our results for inverse modelling of emissions. Indeed, averaging of modelled and observational data over summer period enables a drastic reduction of the “random” errors of the data, and, consequently, obtaining more consistent relationships between emission fields and NO₂ columns. Note that the data from MOZART are not quite consistent with the other data considered here, particularly because they correspond to another year. Therefore, we use these data for qualitative characterization of possible contribution of the upper tropospheric NO₂, rather than for exact quantitative estimations.
<figure><img src="image_6.png" /></figure>

**Fig. 4.** Distributions of tropospheric NO₂ columns derived from GOME measurements in comparison with lower tropospheric NO₂ columns (above 500 hPa pressure level) simulated with CHIMERE, upper tropospheric NO₂ columns evaluated with MOZART, and composed (CHIMERE plus MOZART) total tropospheric NO₂ columns. The GOME and CHIMERE data represent the averages over the summer months of 1997. Upper tropospheric NO₂ were evaluated by averaging monthly NO₂ MOZART data corresponding to the summer of 1996. Note differences in scales of the plots.

It is seen in Fig. 4 that many similarities exist between GOME measurements and simulated lower and total tropospheric NO₂ columns. In particular, both kinds of data exhibit the strongly enhanced NO₂ columns over the Great Britain, Belgium, Netherlands, and North-western Germany; some other polluted areas, such as Po Valley in Italy and Moscow region in Russia, are well pronounced. Both CHIMERE and GOME data indicate much lower level of air pollution in Eastern Europe compared to Western Europe. However, along with similarities, there are a number of differences. For example, GOME measurements give significantly larger values of NO₂ columns over Israel and Persian Gulf region than predicted by the models, but the reverse situation is observed, in particular, over areas at Southern Poland and around Moscow.

It is very important to note that, as evidenced by the MOZART data, the contribution of upper tropospheric NO₂

to the total tropospheric NO₂ columns is rather small over the most part of Western Europe. The relative contribution of the upper troposphere is more significant over Eastern Europe; nevertheless, as it can be seen in Fig. 4, spatial variations of both NO₂ columns derived from GOME measurement and those simulated by CHIMERE are generally much stronger than spatial variations of the upper tropospheric NO₂.

Figure 5 presents distributions of NO₂ columns derived from GOME and simulated by CHIMERE for summer of 2001. A comparison of Figs. 4 and 5 indicates that inter-annual variability of NO₂ columns is not large, although it can hardly be neglected completely. More careful examination of differences between 1997 and 2001 in the modelled and GOME measurement derived NO₂ columns reveals that they correlate very badly (R<0.2) and that the average (over the whole model domain) decrease of NO₂ column amounts is much larger in the CHIMERE (11%) than in the GOME
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Distributions of the tropospheric NO₂ columns derived from GOME measurements in comparison with the lower tropospheric NO₂ columns simulated by CHIMERE. The data shown represent the averages over summer months of 2001.</figcaption></figure>

data (0.1%). The last observation indicates that the EMEP emission database may overestimate an actual reduction of the anthropogenic NOₓ emissions. However, this supposition needs further careful analysis that is beyond the scope of this paper.

In order to enable a statistical analysis of differences between Western and Eastern Europe, we define two regions, one of which is restricted between 10° W, 18° E, 35° N and 60° N, and another between 18° E, 65° E, 40° N and 65° N. These regions will be referred to in the following as to Western and Eastern Europe, respectively. Although such a definition does not follow exactly any political boundaries, nevertheless, such defined regions seem to be well representative of more densely populated industrial regions in Western and Central Europe on the one hand, and less urbanized countries in Eastern Europe on the other hand.

Figure 6 presents the scatter-plots of simulated and GOME measurement derived NO₂ columns for Western and Eastern Europe. It is seen that the correlations are rather significant, although the scatter is also substantial. The agreement is apparently better for Western Europe; however, it is necessary to take into account the differences in scales of variability of the data for the two regions. The better correlations for Western Europe may stem simply from the fact that the range of possible magnitudes of NO₂ columns at Western Europe is much larger when compared to Eastern Europe. The differences between the considered regions are discussed in more details in the next section.

It is noteworthy that the slopes of the linear fits are considerably less than unity in all cases shown in Fig. 6. It is indicative of significant systematic errors in, at least, one of the considered datasets, whose magnitudes are dependent on the amplitude of the NO₂ columns. It is interesting to note also that a few points corresponding to values above 3×10¹⁵ mol/cm² in Eastern Europe look as if they were outliers, especially in the case of 1997. They correspond to the

areas about Krakow in Poland and Moscow in Russia. This observation may be indicative of overestimated NOₓ emissions prescribed in CHIMERE for these two areas. This overestimation is, probably, much stronger in the EMEP emission database for 1997 than for 2001. Anyway, our suggestion concerning overestimated NOₓ emissions about Krakow and Moscow is the hypothesis that yet needs to be proved in a further special research.

Table 2 lists the basic statistical characteristics of the discussed data for different months and years. Estimates of contributions of upper tropospheric NO₂ are given in Table 3. It is easy to see that the means of CHIMERE and GOME data agree for Western Europe within less than 32% of uncertainty (relative to the mean of the GOME retrievals) for all months considered in 1997. The negative difference between the means of the CHIMERE and GOME NO₂ columns is larger in 2001 and reaches 41% in August. The larger difference in 2001 is, mainly, due to the reduction of NO₂ column amounts in CHIMERE data in that year (compared to 1997), which is not found in GOME data. The consideration of the results given in Table 2 together with the estimates provided in Table 3 reveals that a considerable part of the noted discrepancies can be explained by the unaccounted contribution of the upper tropospheric NO₂ in CHIMERE NO₂ columns. But even without account of the upper troposphere, the obtained agreement between the model and GOME seems to be rather satisfactory. Indeed, the strong positive difference (more than 150% for Western Europe in summer months) between simulations performed with a global CTM and Version 1 GOME measurement derived data has been found by Lauer et al. (2002). Savage et al. (2004) have also found a strong positive difference (about 120%) between their simulations and GOME retrievals in June of 1997, although smaller differences (about 60%) have been found in July and August. Note, however, that Savage et al. (2004) compare their simulations with the GOME retrievals that are based on the same
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Scatter plots of the simulated and GOME derived NO₂ columns for Western and Eastern Europe.</figcaption></figure>

modelled NO₂ vertical profiles that have been used to calculate the modelled NO₂ columns, while the vertical NO₂ profiles that have been used to elaborate Version 2 data-products considered here are different from those obtained from CHIMERE. In our case, there is therefore a greater chance that systematic errors of the modelled and GOME measurement derived NO₂ columns have the same sign and similar magnitude. Nonetheless, an important advantage of our approach is that the random errors of the NO₂ columns from CHIMERE and GOME can be assumed to be statistically independent. This advantage is exploited in the next section.

As to Eastern Europe, CHIMERE gives about a factor two lower mean values than those derived from GOME measurements. However, it is easy to see that accounting for a contribution of the upper troposphere would again enable considerable improvement.

As it was already discussed above and is evidenced by the results presented in Tables 2 and 3, an expected contribution of the upper troposphere to variability of the total tropospheric NO₂ columns is rather small for both Western and Eastern Europe. Thus, the standard deviations ($\sigma$) of the data derived from GOME measurements and simulated with CHIMERE are compared directly. It is seen that the standard deviations of the seasonally averaged data agree within less than 20% of uncertainty for both years in Western Europe. But the differences are larger in monthly data, especially in August of both 1997 and 2001. In Eastern Europe, the difference is especially strong in 2001. It is particularly noteworthy that NO₂ columns from GOME show persistently stronger spatial variability than those from CHIMERE.

The disagreement of the standard deviations is not easy to interpret unambiguously because they bear information not only on variability of “true” values of the analysed
<table><caption>**Table 2.** Basic statistical characteristics of spatial distributions of GOME measurement derived and simulated tropospheric NO₂ columns for Western Europe (WE) and Eastern Europe (EE).</caption><thead><tr><th rowspan="3">year</th><th rowspan="3">period</th><th colspan="4">mean (mol×10<sup>15</sup>/cm<sup>2</sup>)</th><th colspan="4">σ (mol×10<sup>15</sup>/cm<sup>2</sup>)</th><th colspan="2">R</th></tr><tr><th colspan="2">WE</th><th colspan="2">EE</th><th colspan="2">WE</th><th colspan="2">EE</th><th rowspan="2">WE</th><th rowspan="2">EE</th></tr><tr><th>GOME</th><th>CHIMERE</th><th>GOME</th><th>CHIMERE</th><th>GOME</th><th>CHIMERE</th><th>GOME</th><th>CHIMERE</th></tr></thead><tbody><tr><td rowspan="4">1997</td><td>June</td><td>1.94</td><td>1.72</td><td>1.20</td><td>0.69</td><td>1.96</td><td>1.67</td><td>0.50</td><td>0.44</td><td>0.80</td><td>0.58</td></tr><tr><td>July</td><td>2.41</td><td>1.84</td><td>1.27</td><td>0.69</td><td>2.00</td><td>1.99</td><td>0.63</td><td>0.54</td><td>0.86</td><td>0.69</td></tr><tr><td>August</td><td>2.39</td><td>1.64</td><td>1.27</td><td>0.65</td><td>2.35</td><td>1.34</td><td>0.64</td><td>0.45</td><td>0.87</td><td>0.67</td></tr><tr><td>average</td><td>2.25</td><td>1.73</td><td>1.24</td><td>0.68</td><td>2.10</td><td>1.66</td><td>0.59</td><td>0.48</td><td>0.84</td><td>0.65</td></tr><tr><td></td><td><strong>summer</strong></td><td><strong>2.26</strong></td><td><strong>1.75</strong></td><td><strong>1.25</strong></td><td><strong>0.68</strong></td><td><strong>2.00</strong></td><td><strong>1.66</strong></td><td><strong>0.51</strong></td><td><strong>0.47</strong></td><td><strong>0.91</strong></td><td><strong>0.76</strong></td></tr><tr><td rowspan="4">2001</td><td>June</td><td>1.94</td><td>1.51</td><td>0.85</td><td>0.56</td><td>1.78</td><td>1.57</td><td>0.56</td><td>0.34</td><td>0.78</td><td>0.66</td></tr><tr><td>July</td><td>2.39</td><td>1.57</td><td>1.35</td><td>0.66</td><td>1.81</td><td>1.66</td><td>0.60</td><td>0.35</td><td>0.87</td><td>0.76</td></tr><tr><td>August</td><td>2.44</td><td>1.44</td><td>1.50</td><td>0.58</td><td>2.28</td><td>1.30</td><td>0.82</td><td>0.34</td><td>0.87</td><td>0.68</td></tr><tr><td>average</td><td>2.25</td><td>1.50</td><td>1.23</td><td>0.60</td><td>1.95</td><td>1.51</td><td>0.58</td><td>0.34</td><td>0.84</td><td>0.70</td></tr><tr><td></td><td><strong>summer</strong></td><td><strong>2.26</strong></td><td><strong>1.51</strong></td><td><strong>1.24</strong></td><td><strong>0.60</strong></td><td><strong>1.85</strong></td><td><strong>1.50</strong></td><td><strong>0.58</strong></td><td><strong>0.34</strong></td><td><strong>0.89</strong></td><td><strong>0.80</strong></td></tr></tbody></table>

characteristics and a contribution of random errors, but also on systematic errors that covariate with the true values. For example, our situation with the larger standard deviations of GOME data than that of CHIMERE data could be explained by larger random errors (noise) in the data from GOME. But on the other hand, we could expect the similar result if the data from GOME or CHIMERE were scaled with a nearly constant factors that are less or greater than unity, respectively. Those factors would represent systematic multiplicative (geometric) errors of the respective data.

The potential sources of systematic errors in NO₂ columns from a CTM and GOME are quite numerous and have already been discussed in details by Savage et al. (2004) and Boersma et al. (2004). It is important that the most likely errors both in models and in the GOME retrieval procedure are indeed of a multiplicative character, as they are associated, on the one hand, with miscalculation of NO₂ lifetime (due to errors in vertical transport, chemistry and deposition) and, on the other hand, with uncertainties of the air mass factor (due, e.g. systematic errors in input vertical profiles of tropospheric NO₂ or scattering on aerosols).

Regarding the differences in statistics for Western and Eastern Europe, it is useful to note that while values of both the mean and the standard deviation are significantly smaller for Eastern Europe, the relative differences are much larger in the standard deviations than in the means. Consequently, the ratios of the standard deviation to the means of both GOME derived and simulated data for Western Europe are considerably larger than the corresponding ratios for Eastern Europe. Specifically, these ratios are 37% and 75% higher for Western than for Eastern Europe in the case of CHIMERE data for 1997 and 2001, respectively. The differences are even much larger with the GOME data, because of more significant con-

<table><caption>**Table 3.** Statistical characteristics of upper tropospheric (below 500 hPa pressure level) NO₂ columns estimated using MOZART output database.</caption><thead><tr><th rowspan="2">period</th><th colspan="2">mean (mol×10<sup>15</sup>/cm<sup>2</sup>)</th><th colspan="2">σ (mol×10<sup>15</sup>/cm<sup>2</sup>)</th></tr><tr><th>WE</th><th>EE</th><th>WE</th><th>EE</th></tr></thead><tbody><tr><td>June</td><td>0.48</td><td>0.57</td><td>0.07</td><td>0.06</td></tr><tr><td>July</td><td>0.51</td><td>0.56</td><td>0.10</td><td>0.08</td></tr><tr><td>August</td><td>0.55</td><td>0.55</td><td>0.14</td><td>0.09</td></tr><tr><td>average</td><td>0.51</td><td>0.56</td><td>0.10</td><td>0.08</td></tr><tr><td><strong>summer</strong></td><td><strong>0.51</strong></td><td><strong>0.56</strong></td><td><strong>0.10</strong></td><td><strong>0.07</strong></td></tr></tbody></table>

tribution of the free tropospheric NO₂ to GOME data over Eastern Europe. These results mean, in particular, that if values of NO₂ columns for Eastern Europe were linearly scaled to obtain the same means for the both regions, the variance of such scaled values for Eastern Europe would be considerably less than that of the data for Western Europe. This substantial difference in distributions of NO₂ columns over Western and Eastern Europe seriously hinders the direct comparison of their uncertainties. In particular, in such a situation the smaller coefficient of correlation for Eastern Europe than for Western Europe can be explained not only by larger uncertainty of the data for Eastern Europe but by less variability of “true” NO₂ columns as well.
# 6 Analysis of “random” (non-systematic) uncertainties of modelled and GOME measurement derived distributions of tropospheric NO₂

## 6.1 Evaluation of the upper limit for the uncertainties

Let us consider the following variance of the difference,

$$E = \frac{1}{N} \sum_{i=1}^{N} (z_{g}^{i} - z_{c}^{i} - \bar{z}_{g} + \bar{z}_{c})^{2}, \qquad (3)$$

where $z_{g}^{i}$ and $z_{c}^{i}$ are values of NO₂ columns derived from GOME measurements and those simulated by CHIMERE for an i-th grid cell, respectively, while $\bar{z}_{g}$ and $\bar{z}_{c}$ are their mean values.

The meaning of E becomes easier to interpret if we write the following formal equalities,

$$\begin{gathered} z_{g}^{i} = z_{t}^{i} + \varepsilon_{g}^{i} + \theta_{g}, \\ z_{c}^{i} = z_{t}^{i} + \varepsilon_{c}^{i} + \theta_{c}, \end{gathered} \qquad (4)$$

where $z_{t}^{i}$ is a true (unknown) value of tropospheric NO₂ column, $\varepsilon_{g}^{i}$ and $\varepsilon_{c}^{i}$ are random errors (with the zero means) of GOME derived and simulated NO₂ columns, and

$$\theta_{g,c} = \frac{1}{N} \sum_{i=1}^{N} (z_{g,c}^{i} - z_{t}^{i}) \qquad (5)$$

are the systematic part of errors.

After substitution (4) into (3), E is expressed as follows,

$$E = \frac{1}{N} \sum_{i=1}^{N} (\varepsilon_{g}^{i} - \varepsilon_{c}^{i})^{2} \qquad (6)$$

That is, E is simply the mean squared difference of “random” (non-systematic) errors. If we assume further that these errors are almost independent, that is,

$$\overline{\varepsilon_{g}\varepsilon_{c}} \ll \overline{\varepsilon_{g}^{2}}, \qquad (7)$$

then we find that

$$E \approx \overline{\varepsilon_{g}^{2}} + \overline{\varepsilon_{c}^{2}}. \qquad (8)$$

So, under the given assumption, E represents the total mean squared error associated with both GOME derived and simulated NO₂ columns. In other words, the evaluation of E allows us to estimate the upper limit of random component of the uncertainty of either of the two datasets considered. The assumption (7) seems to be very reasonable considering the principal differences in methods used to obtain the data that we compare. Even if a strong covariance existed between uncertainties of NO₂ columns simulated by CHIMERE and MOZART, it could cause much smaller covariance between uncertainties of NO₂ columns simulated by CHIMERE and those derived from GOME, because the latter are sensitive to vertical profiles of NO₂ rather than to their column amounts. Possible reasons for a non-zero covariance between the uncertainties of CHIMERE and MOZART might be the use

of MOZART data for prescribing boundary conditions for CHIMERE and correlations of errors of anthropogenic emissions prescribed in the models. But it seems very unlikely that this covariance may be strong, taking into account that CHIMERE and MOZART use different chemical schemes, different gridded emission databases (EMEP and EDGAR, respectively), meteorological data, and, besides, have very different horizontal resolution.

The squared roots of E (that is, RMSE with respect to random errors) and their normalized values are listed in Table 4. It is seen that the errors are rather significant for both regions, and that they are larger when compared with the standard deviations than with the means of GOME derived data, especially for Eastern Europe. The ratio of RMSE to the standard deviation (it is sometimes referred to as the root relative squared error) characterizes, in our case, uncertainties in spatial variability of NO₂ columns. The uncertainties of the data averaged over three months are less than the uncertainties of the monthly datasets, but it is easy to see that their reductions are smaller than it could be expected if the errors for different months were independent (that is, the reductions are smaller than the square root of 3). Hence, we can conclude that a significant part of the error is persistent beyond the monthly time scale.

It is noteworthy that while the ratios of RMSE to the mean are larger for Western Europe, the ratios of RMSE to the standard deviation are much larger for Eastern Europe. Therefore, based on these results it seems impossible to conclude unambiguously whether the agreement between simulated and GOME derived data is better for one or the other part of Europe. The reason has already been discussed in the previous section. Nevertheless, as it is shown below, the picture will become clearer when analysing uncertainties as a function of magnitudes of the NO₂ columns.

## 6.2 The random error as a function of amplitude of NO₂ columns

As a preliminary step to further analysis, we would like to introduce the following simplified model of errors. Let us assume that values of tropospheric NO₂ columns derived from GOME measurements, $z_g$, relate to their true values, $z_t$, as follows:

$$z_g = z_t(1 + \delta_{s,g} + \delta_{r,g}) + \Delta_{s,g} + \Delta_{r,g}, \qquad (9)$$

where $\delta_{s,g}$, $\delta_{r,g}$, $\Delta_{s,g}$ and $\Delta_{r,g}$ are systematic and random parts of multiplicative and additive errors, respectively. It is assumed that $\delta_{s,g}$ and $\Delta_{s,g}$ are constants, while $\delta_{r,g}$ and $\Delta_{r,g}$ are random variables independent of $z_t$ and having zero means. Such assumptions are hardly satisfied exactly in any real situation, but they still may be a reasonable and useful approximation. The same kind of an error model is used below for NO₂ columns from CHIMERE, after the replacement of the index “g” with the index “c”. We further apply this
<table><caption>**Table 4.** Statistics for the total random errors of tropospheric NO₂ columns derived from GOME measurements and those calculated by CHIMERE.</caption><thead><tr><th rowspan="2">year</th><th rowspan="2">period</th><th colspan="2">RMSE(mol×10<sup>15</sup>/cm<sup>2</sup>)</th><th colspan="2"><u>RMSE</u><br>mean[gome]</th><th colspan="2"><u>RMSE</u><br>sigma[gome]</th></tr><tr><th>WE</th><th>EE</th><th>WE</th><th>EE</th><th>WE</th><th>EE</th></tr></thead><tbody><tr><td rowspan="5">1997</td><td>June</td><td>1.19</td><td>0.44</td><td>0.61</td><td>0.36</td><td>0.61</td><td>0.87</td></tr><tr><td>July</td><td>1.05</td><td>0.47</td><td>0.43</td><td>0.37</td><td>0.52</td><td>0.75</td></tr><tr><td>August</td><td>1.34</td><td>0.47</td><td>0.56</td><td>0.37</td><td>0.57</td><td>0.74</td></tr><tr><td>average</td><td>1.19</td><td>0.46</td><td>0.53</td><td>0.37</td><td>0.57</td><td>0.79</td></tr><tr><td><strong>summer</strong></td><td><strong>0.85</strong></td><td><strong>0.34</strong></td><td><strong>0.38</strong></td><td><strong>0.28</strong></td><td><strong>0.43</strong></td><td><strong>0.67</strong></td></tr><tr><td rowspan="5">2001</td><td>June</td><td>1.13</td><td>0.43</td><td>0.58</td><td>0.50</td><td>0.64</td><td>0.75</td></tr><tr><td>July</td><td>0.89</td><td>0.41</td><td>0.37</td><td>0.30</td><td>0.49</td><td>0.68</td></tr><tr><td>August</td><td>1.31</td><td>0.64</td><td>0.54</td><td>0.43</td><td>0.57</td><td>0.78</td></tr><tr><td>average</td><td>1.11</td><td>0.49</td><td>0.50</td><td>0.41</td><td>0.57</td><td>0.74</td></tr><tr><td><strong>summer</strong></td><td><strong>0.84</strong></td><td><strong>0.37</strong></td><td><strong>0.38</strong></td><td><strong>0.30</strong></td><td><strong>0.46</strong></td><td><strong>0.64</strong></td></tr></tbody></table>

model to our data in order to try to estimate their multiplicative and absolute errors independently.

The idea of the following analysis is to obtain information on the additive and multiplicative parts of the error, by repeating error analysis in a similar way as in the previous section, but separately for subsets of data with similar magnitudes. More specifically, we will have to evaluate the variance *E* given in (3) for each of the subsets. The selection of the subsets is based on the procedure of a “running window” applied to data preliminary arranged with growing amplitude.

Let us consider which kind of information we can get from such a procedure. For definiteness, we consider a case when the selection procedure is applied to GOME data, but same reasoning also holds for CHIMERE data. In such a case, a “local” version of the variance (3) after substitution of $z_g$ and $z_c$ from (9) takes the form:

$$E_g = \frac{1}{N_w} \sum_{j=1}^{N_w} \left( (z_t^{i(j)} - \bar{z}_t)(\delta_{s,g} - \delta_{s,c}) + z_t^{i(j)}(\delta_{r,g}^{i(j)} - \delta_{r,c}^{i(j)}) - \overline{z_t \delta_{r,g}} + \Delta_{r,g}^{i(j)} - \Delta_{r,c}^{i(j)} \right)^2, \quad (10)$$

where $N_w$ is the number of datapoints in the window, and the averaging is performed over the set of the selected data. Let us assume that the total ensemble of the data is sufficiently large, so that the variance of the GOME data within the “window” can be neglected when compared to their errors. Assume also that typical scales of all systematic and random multiplicative errors are much less than unity. Then, after substitution of $z_t$ from (9) to (10) and having performed Taylor’s expansion of $E_g$ up to quadratic terms with respect

to all $\delta_s$ and $\delta_r$, we obtain the following:

$$E_g \approx \frac{(\overline{\delta_{r,g}^2} + \overline{\delta_{r,c}^2})}{(1 + \delta_{s,g})^2} (\overline{z_g} - \Delta_{s,g})^2 + \overline{\Delta_{r,g}^2} + \overline{\Delta_{r,c}^2} \\ + \frac{(\overline{\delta_{r,g}^2} + \overline{\delta_{r,c}^2})}{(1 + \delta_{s,g})^2} \overline{\Delta_{r,g}^2} - \frac{2(\delta_{s,g} - \delta_{s,c})}{(1 + \delta_{s,g})} \overline{\Delta_{r,g}^2} \quad (11)$$

It is easy to see that if the approximation (11) is valid and the magnitudes of $\overline{z_g}$ are sufficiently large, we should expect a quasi-linear growth of $(E_g)^{1/2}$ with the increase of $\overline{z_g}$. The squared rate of such a growth can give an estimate of the upper limit of the random part of the mean squared relative error (MSRE) associated with multiplicative errors. Indeed, by definition we have:

$$MSRE_g = \left( \frac{\overline{z_g} - z_t}{z_g} \right)^2. \quad (12)$$

Using (9), assuming that $z_t(\delta_s+\delta_r) \gg \Delta_s$, $\Delta_r$, and performing Taylor’s expansion of the denominator, we find that

$$MSRE_g \approx \frac{\overline{\delta_{r,g}^2}}{(1 + \delta_{s,g})^2} + \frac{\delta_{s,g}^2}{(1 + \delta_{s,g})^2}. \quad (13)$$

The first term in the right hand side of (13), which corresponds to the random part of the multiplicative errors, is always less or equal to the rate of growth of $E_g$ determined by the fraction in the first term on the right-hand side of Eq. (11). For convenience, we report below our estimations in terms of the squared root of the random part of MSRE, that is RM-SRE.

It follows also from (11) that for the limiting case of $z_g$ near zero, the evaluations of *E* allow us to estimate the upper limit for random additive errors. Indeed, it is easy to see that

$$\overline{\Delta_{r,g}^2} \le \max[E_g(\overline{z_g} = \overline{z_g \min}); E_c(\overline{z_c} = \overline{z_c \min})] \quad (14)$$
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Running averages of squared differences between the deviations of the simulated and GOME measurement derived tropospheric NO₂ columns from their running mean values versus the running averages of the indicated data for Western Europe. The averaging procedure using a running window covering 100 data points is applied to the gridded data for the seasonally averaged tropospheric NO₂ columns from GOME or CHIMERE (as indicated in the figures) arranged with growing amplitude. The points on the curves are depicted with a frequency of 1/100.</figcaption></figure>

Figure 7 presents the dependences of the “running” evaluations of $E^{1/2}$, as a function of the corresponding running averages of the GOME or CHIMERE NO₂ columns for Western Europe. The running averages and statistics were calculated using a window consisting of 100 consecutive data points after the arrangement of all pixels in a growing order (with respect of GOME derived or simulated NO₂ columns.) Such a window was chosen as a reasonable compromise between poorer statistics and higher resolution that could be obtained with a narrower window and richer statistics but lower resolution with a wider window. We have found, however, that even the use of very different windows (covering, for example, 50 or 200 points) would not lead to serious changes in our results.

It is seen that along with random fluctuations, there is a well-pronounced quasi-linear positive trend in magnitudes of uncertainties. The largest deviation from the linear law takes place for the biggest NO₂ columns in the case of the dependencies on the running averages of CHIMERE data. This exception concerns, however, only a small part (less than 8 %) of the total number of data points. In accordance to (11), these trends are indicative of predominant role of multiplicative errors in total uncertainties of both GOME and CHIMERE data. As argued above, the root of the random part of the mean squared relative (multiplicative) errors can be estimated using the slopes of the linear fits of dependence of $E^{1/2}$ on the magnitude of respective data. It is noteworthy that the slopes of the best linear fits are significantly different in the cases of CHIMERE and GOME data. The difference in the slopes can be caused by difference in the systematic errors $\delta_{s,g}$ and $\delta_{s,c}$ (see Eq. 11).

In order to get an idea of possible uncertainties of our procedure, we have performed a special numerical exper-

iment using the data for 1997 as example. Specifically, we have preliminarily defined two pairs of the datasets, the first of which includes the original and specially transformed datasets for NO₂ columns from GOME, and the second one includes the original and specially transformed datasets for NO₂ columns from CHIMERE. The transformations are performed by adding artificial systematic and random multiplicative errors to the original data. The idea is to estimate a priori known errors using the procedure described above. The artificial errors have been prescribed based on the evaluations of real errors of the original data. Specifically, in the case with GOME data, we have applied a systematic error $\delta_s=-0.25$, based on the value of a slope (0.75) of the corresponding best linear fit in Fig. 6, and random multiplicative errors $\delta_r$ with the standard deviation of $\sigma_r=0.22$, in accordance to the slope of the corresponding fit in Fig. 7. Such transformed data were used as a substitute for the CHIMERE data. Similarly, in the case with the CHIMERE data, we have prescribed $\delta_s=0.33$ (0.75⁻¹⁻¹) and $\sigma_r=0.32$ and used such transformed data as a substitute for the GOME data. The random errors have been sampled from the lognormal distribution. Afterwards, we have applied our “running window” analysis to each of the two pairs datasets independently. The results of the analysis of such artificial errors are presented in Fig. 8.

The slopes of the linear fits shown in Fig. 8 are very close to those shown in Fig. 7. Thus we can indeed conclude that the behaviour of the curves shown in Fig. 7 can be mainly explained by the presence of multiplicative errors. The obtained values of the slopes for the transformed data (0.34 and 0.20) are different, to some degree, from the corresponding theoretical estimations that can be made using directly (11) (0.29 and 0.24, respectively). Based on these results, we
<figure><img src="image_10.png" /><figcaption>**Fig. 8.** The interpretation of the results presented in Fig. 7. The plots show the results of the same error analysis as in Fig. 7, but aimed at retrieving the known “errors” of the artificially transformed dataset. The “running window” analysis was applied to two pairs of the original and transformed datasets indicated in the figures, and the “running” RMSEs are plotted against the running averages of the indicated data.</figcaption></figure>

can expect that our estimations of the upper limit of multi-
plicative errors of the real data for Western Europe may be
uncertain within about 20%. However, taking into account
that both CHIMERE and GOME data are not quite perfect
and that their partial errors are therefore significantly smaller
than the total errors, it seems to be indeed safe to conclude
that the random part of the mean squared relative error of
NO₂ columns from CHIMERE and GOME for Western Eu-
rope is, on the average, less than 32 and 23 percent, respec-
tively. The contribution of the additive errors is not well pro-
nounced, but it is evident that they are, on the average, less
than 3×10¹⁴ mol/cm² (see Eq. 14 and Fig. 7).

Figure 9 presents the results of similar analysis for Eastern Europe. In order to facilitate a comparison between the results for Western and Eastern Europe, this figure reproduces also the corresponding section of the curves for Western Europe. The most surprising result is that the uncertainties for Eastern Europe are substantially lower than the uncertainties for Western Europe for the major part of the range of magnitudes of NO₂ columns for Eastern Europe, especially when the uncertainties are considered versus the data from GOME. Indeed, it seemed to be reasonable to expect that the potential uncertainties of input information used in CHIMERE and for retrieval of GOME NO₂ columns are larger for Eastern Europe than for Western Europe. Probably, this result is, mainly, due to the fact that Western European regions with relatively low levels of NO₂ pollution are usually situated in the vicinity of much more polluted regions, whereas for Eastern Europe they are more homogeneous and wide spread. As a consequence, the uncertainties of the NO₂ transport simulated by CHIMERE, on the one hand, and a low resolution of MOZART data used to evaluate AMF, on the other hand, may play much more significant role under considered conditions in Western Europe than in Eastern Europe.

It is evident that the uncertainties for Eastern Europe have
more complex character than those for Western Europe with
a less clear correlation between uncertainties and absolute
NO₂ columns. However, they also demonstrate positive
trends with the increase of the magnitudes of NO₂ columns,
which are indicative of multiplicative errors. The estimates
for multiplicative and additive errors can be obtained in the
same way as in the case of Western Europe. However, the
considerable scattering of the fitted uncertainties indicates
that the error model (9) is less relevant in this case, and the
error estimates are much less accurate than those in the case
of Western Europe. Note also that because of significant con-
tribution of additive errors, the slopes of the fits for E¹/²
given in Fig. 9 may underestimate actual values of the root of
the random part of MSRE. Therefore, any error estimates for
Eastern Europe that can be obtained using results presented
in Fig. 9 should be used with much care.

The analysis with a running window has been repeated for
each of the summer months of 1997 and 2001, and corre-
sponding estimations of the relative errors are listed in Ta-
ble 5. As it could be expected, the errors of the monthly
mean data are, on the average, larger than the errors of the
seasonally averaged datasets. The monthly estimates are
rather divergent, but have some common features in different
years. For example, the difference between the estimates for
CHIMERE and GOME data are largest for Western and East-
ern Europe in August of both 1997 and 2001. This and some
other similarities between our results for 1997 and 2001 may
be due to some regular differences in quality of the data from
CHIMERE and GOME in different months of a year.

6.3 Discussion

We now discuss results obtained in the previous section in
relation to independent estimates of uncertainties of tropo-
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** The same as in Fig. 7, but for Eastern Europe. For convenience, the plots reproduce also a subsection of the dependences for Western Europe.</figcaption></figure>

<table><caption>**Table 5.** Estimations of the upper limits of the mean random relative (multiplicative) error (%) of tropospheric NO₂ columns retrieved from GOME measurements and those calculated by CHIMERE.</caption><thead><tr><th rowspan="2">year</th><th rowspan="2">period</th><th colspan="2">WE</th><th colspan="2">EE</th></tr><tr><th>GOME</th><th>CHIMERE</th><th>GOME</th><th>CHIMERE</th></tr></thead><tbody><tr><td rowspan="4">1997</td><td>June</td><td>33</td><td>49</td><td>14</td><td>30</td></tr><tr><td>July</td><td>36</td><td>29</td><td>26</td><td>28</td></tr><tr><td>August</td><td>17</td><td>59</td><td>19</td><td>37</td></tr><tr><td>average</td><td>29</td><td>46</td><td>20</td><td>32</td></tr><tr><td></td><td><strong>summer</strong></td><td><strong>22</strong></td><td><strong>32</strong></td><td><strong>15</strong></td><td><strong>24</strong></td></tr><tr><td rowspan="4">2001</td><td>June</td><td>31</td><td>39</td><td>10</td><td>14</td></tr><tr><td>July</td><td>26</td><td>30</td><td>7</td><td>21</td></tr><tr><td>August</td><td>16</td><td>52</td><td>7</td><td>41</td></tr><tr><td>average</td><td>24</td><td>40</td><td>11</td><td>25</td></tr><tr><td></td><td><strong>summer</strong></td><td><strong>23</strong></td><td><strong>32</strong></td><td><strong>6</strong></td><td><strong>24</strong></td></tr></tbody></table>

spheric NO₂ columns derived from GOME measurement and those simulated by the models. As pointed out before, the multiplicative and additive errors defined above represent upper limits of random errors both in the GOME derived and simulated NO₂ column.

The main sources of errors in the GOME NO₂ columns are (i) the fit of NO₂ column from the spectrum, (ii) separation of stratospheric and tropospheric NO₂, and (iii) evaluation of tropospheric light path (including uncertainties associated with the surface albedo, AMFs, and cloud effects). For the Bremen V1 dataset, Richter and Burrows (2002) estimated the random (both in time and space) uncertainties associated with each individual NO₂ fit to be in the range of 2–4×10¹⁴ mol/cm². Obviously, the random uncertainties are significantly smaller (up to a factor of 3) in monthly averages of the retrieved data and, therefore, they can hardly contribute significantly to discrepancies between the simulations and GOME retrievals in our case. The upper limit for uncertainties associated with separation of stratospheric and tropospheric slant columns was estimated to be also about 10¹⁵, and is, probably, much lower in case of Version 2 data as result of the use of the SLIMCAT output and the restriction
to summer months. Finally, the uncertainties of Version 1 data, associated with the evaluation of tropospheric light path have been estimated to be in the wide range of ±200%. The tropospheric light path is evaluated much more consistently in Version 2 data and, also restriction to summer months reduces problems with clouds, snow and low sun. Therefore, it is reasonable to expect that the corresponding uncertainties should be significantly lower than 200%, as evidenced also by our results.

Martin et al. (2003) have reported estimates for uncertainties of their own version of data for tropospheric NO₂ columns derived from GOME measurements. Specifically, they estimated the absolute error of their data to be about 10¹⁵ mol/cm² and derived the total relative error to be of 42% for each scene and suggested that the monthly mean errors can be up to a factor of five less. Similar to Version 2 data used in our study, the data by Martin et al. (2003) are based on AMF factors evaluated with data from a global CTM. However, along with this and some other similarities, there are also some methodological differences, which might lead to some differences in uncertainties of the retrieved data.

Boersma et al. (2004) have recently published a detailed error analysis of their GOME NO₂ product and discussed the impact of different error sources on the final product. Although the exact numbers depend strongly on the location, season and assumptions made, they give relative uncertainties of 35–60% over polluted regions such as Western Europe and a lower limit for detectable columns of 3×10¹⁴ mol/cm². Again, the retrieval method used in this study differs from that of Boersma et al. (2004) in several points, but the overall errors should be comparable.

While the independent estimations discussed above concern the total mean relative error (which includes both systematic and random multiplicative errors), we have estimated here only its random (in space) part. Besides, our estimations include the unknown contribution of errors of NO₂ columns from CHIMERE. Meanwhile, it seems reasonable to expect that the systematic part of the errors of GOME data is not larger than their random part, because a contribution of different sources of errors may strongly vary in space. If it is so, the total mean (RMS) relative error of the Version 2 Bremen dataset for Western Europe is less than 50%, and the total mean additive error is less than 3×10¹⁴ mol/cm². Such limits are consistent with the independent estimates discussed above. Note that estimations of the random part of the errors of the GOME data (in contrast to estimations of total errors that include both systematic and random parts) can be especially useful for their potential applications to inverse modelling of emissions, as the standard methods of inverse modelling usually require a priori specification of the probability distribution function for errors of observations (see, e.g. Enting, 2002).

Although independent direct estimates of the uncertainty of NO₂ columns simulated by CHIMERE are not yet available, it seems reasonable to assume that it cannot be much

lower than the uncertainty of the employed NOₓ emission data. The uncertainty of available emission data is, most probably, in the range from 20 to 40 percent for Western Europe (see, e.g. Hanna et al., 1998; Kühlwein and Friedrich, 2000; Kühlwein et al., 2002; Beekmann and Derognat, 2003), but essentially unknown for Eastern Europe. Our estimations of the upper limit of the mean relative errors of the simulated NO₂ columns averaged over summer months (32% for Western Europe and 24% for Eastern Europe) is in line with common understanding of uncertainty of emission data. Note that it would be inappropriate to conclude that the uncertainty of emission data is greater for Western Europe than for Eastern Europe, since the difference in our estimates for Western and Eastern Europe may be due to the difference in the uncertainty of the GOME data.

## 7 Summary and conclusions

The main objectives of this study were (i) evaluation of the newly developed extended version of the CHIMERE CTM over its new large domain with a particular focus on Eastern Europe and (ii) evaluation of the new version (Version 2) data-products for tropospheric NO₂ column amounts derived from GOME measurement over Europe. In order to achieve these objectives, we have first compared the daily maxima of ground ozone concentrations simulated by CHIMERE for summer months of 1997 and 2001 with the corresponding data of ground based ozone measurements performed at more than 100 sites situated, mainly, in Western and Central Europe. We have found, in particular, that the average (over all the station considered) values of the correlation coefficient, the normalised RMSE, and the mean relative bias for daily maximums of ozone concentrations in 2001 are about 62, 24, and 7 percents, respectively. Values of the correlation coefficient are lower for available Eastern European sites when compared to those for Western European sites (44% versus 65%, on average), but, the biases and the normalised RMSE are higher (although very insignificantly) for Western European sites (6% versus 7%, and 22% versus 25% on the average, respectively). It has been argued that differences in correlation coefficients may be, in part, attributed to differences in environments of typical sites in Western and Eastern Europe. These results allow us to make a tentative conclusion that the overall model performance with regard to simulations of ground ozone is similar both for Eastern and Western Europe. However, this conclusion is indeed tentative because of severe deficit of ozone measurement data for Eastern Europe. On the whole, the results of the comparison of the simulated and observed ozone concentrations show that CHIMERE demonstrates a rather satisfactory performance similar to or better than other state-of-the-art European continental scale models.

We have compared next the tropospheric NO₂ columns derived from GOME measurements and NO₂ column amounts
calculated by CHIMERE. Specifically, we have considered the summer seasons of 1997 and 2001, and the main attention has been paid to the seasonally average spatial distributions of the tropospheric NO₂ columns. Because the model enables simulations only in the lower troposphere (below 500 hPa pressure level), the focus of our analysis was put on spatial variability of tropospheric NO₂ columns, as, indeed, the upper tropospheric part, as simulated with MOZART model, shows only little spatial variability.

The consideration of spatial correlations between the grid-
ded data for measured and simulated NO₂ columns has re-
vealed a rather close agreement between them over Western
Europe, where correlation coefficients for seasonally average
data are found to be equal to 0.91 in 1997 and 0.89 in 2001.
For Eastern Europe, the correlation coefficients are smaller
(0.76 and 0.80 in 1997 and 2001, respectively). However, it is
argued that a conclusion about relative quality of the data for
Western and Eastern Europe based on correlation and other
standard comparison statistics may be misleading because of
the considerable difference between statistical distributions
of the data for these two regions.

The reasonable assumption of independent error sources for GOME derived and simulated NO₂ columns has allowed us to estimate the upper limits of such errors. It has been found, in particular, that maximum RMSE of both simulated and measurement based NO₂ columns for summer seasons of 1997 and 2001 constitutes less than 38% of the corresponding mean values of tropospheric NO₂ columns derived from GOME measurements for Western Europe, and less than 30% for Eastern Europe.

Finally, we have considered the dependences (in statisti-
cal sense) of the uncertainty estimations on magnitude of
the simulated and GOME measurement derived tropospheric
NO2 columns. We have found that a dominant component of
the total errors for Western Europe has a multiplicative char-
acter, and the corresponding relative random error of the sea-
sonally averaged GOME and CHIMERE NO2 data has been
estimated to be less than 23% and 32%. As to Eastern Eu-
rope, our results suggest that the additive component of the
total uncertainty of the simulated and GOME measurement
derived NO2 columns is more substantial (compared to the
multiplicative component), especially over less polluted (pre-
dominantly rural) regions. The most interesting (and even
surprising) result is that the agreement between the simulated
and measurement based tropospheric NO2 columns has been
found to be generally better over Eastern Europe than over
Western Europe for low NO2 columns. Therefore, in a con-
trast to our initial expectation, we have found no evidences,
that either the performance of CHIMERE or the quality of
the NO2 columns derived from GOME measurements is un-
ambiguously worse for Eastern than for Western Europe.

On the whole, our study demonstrated a rather close
agreement between tropospheric NO₂ columns derived from
GOME measurements and those modelled by the extended
version of CHIMERE. The use of a continental scale model

has made possible comparison using the true resolution of the
GOME measurement derived data, in contrast to earlier com-
parisons performed with global models. No doubt, that the
use of state-of-the-art continental scale models featuring in
relatively high spatial and temporal resolution will be espe-
cially advantageous when model results will be considered in
parallel with the data retrieved from the satellite instruments
of the latest generation, SCIAMACHY and OMI, which pro-
vides considerably higher resolution of measurements than
the GOME instrument. Given the good agreement in spatial
structures displayed both by GOME derived and simulated
tropospheric NO2 columns, and given the expected rather lin-
ear relationship between NOx emissions and NO2 columns,
another interesting perspective of this work is to derive re-
gional scale emissions from satellite data by means of inverse
modelling.

*Acknowledgements.* Support for this study was provided by Russian Academy of Sciences in the framework of the Programme for Basic Research “Physics of Atmosphere; Electrical Processes, Radiophysical Methods of Research” (Project No. 4.1). I. B. Konovalov was supported by a grant from NATO Science Fellowships Sub-Programme. The authors thank Max-Planck Institute (Hamburg, Germany), M. Schultz, C. Granier, G. Brasseur and D. Niehl for graciously providing us with MOZART data. GOME raw data were provided by ESA through DFD/DLR. Analysis of the GOME data was supported by the European union under contract EVk2-CF1999-00011 (POET) and the University of Bremen.

Edited by: F. J. Dentener

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