We use the System Tool Kit (STK, available from AGI, http://www.agi.com/products/) to generate the S-5P orbit geometry and the geolocation of the edges of the swath as a function of time. Based on these characteristics, we generate the location of the individual observations with a spatial distance of 7 km. We apply time and longitude shifts to the STK-generated orbits to obtain the orbits for the 3 summer and 3 winter months of this study. Subsequently, we compute the solar and viewing geometries. Finally, we maintain segments of the orbits that have an overlap with the modeling domain.

We obtain cloud fields from the high-resolution operational weather forecast archive of the ECMWF. We retrieve meteorological fields of liquid water content, ice water content, specific humidity, and cloud fraction at a resolution of 0.25×0.25∘ for June–August and November 2003–January 2004. We convert these quantities to cloud optical properties. The optical properties determine the reflectance, and we use them to estimate effective cloud fractions and effective cloud top heights as retrieved from the satellite observations (Acarreta et al., 2004). We compare the distribution of effective cloud fractions with the distribution of effective cloud fractions obtained from OMI observations and find a reasonable agreement for summer and winter months. We derive the cloud fractions at the resolution of the ECMWF 0.25×0.25∘ grid. This is close to 30×30 km2 at the Equator and decreases as a function of latitude. The ground pixel of OMI UV-2 and visible channels is 13×24 km2 at nadir, increasing to 13×128 km2 at edges of the swath. We consider that the ECMWF grid cells and OMI pixels are of comparable size for comparing the cloud fraction distributions (close to 0.5 million pixels or cells in each distribution). We model clouds as simple Lambertian reflectors and ignore any wavelength dependency of cloud fraction.

We use these effective cloud fractions (and corresponding cloud radiance fractions) to provide weights to the cloud-free and cloud-covered fractions of the surface scene. We use the cloud altitude for the computation of the averaging kernel.

Because of the large number of observations that will become available from the S-5P instrument, full radiative transfer calculations for each observation separately are not feasible. We thus choose to build lookup tables for a set of geometries based on a radiative transfer code that employs the adding–doubling method in combination with optimal estimation (using the radiative transfer toolbox DISAMAR; de Haan, 2012). Lookup tables are set up for the averaging kernels (1-D vectors as a function of altitude) and the measurement uncertainty. Results are stored for a number of surface albedos, cloud–surface pressures, solar zenith angles, viewing zenith angles, and relative azimuth angles. We provide the lookup table details in Table 1. We provide the kernels on 21 pressure levels between 1050.0 and 0.1 hPa. We specify the uncertainties for clear-sky and cloudy-sky separately.

Each simulation with DISAMAR consists of a forward calculation of the satellite–observed spectrum, followed by a retrieval step based on the optimal estimation method (Rodgers, 2000). We convert instrument noise, listed in Table 1, into uncertainties for the retrieved CO column. We take a priori trace gas profiles from the CAMELOT study (Levelt et al., 2009). As indicated above, we assume that both the cloud and the surface are Lambertian reflectors. Kujanpää et al. (2015) provide further details of this procedure.

The albedo is a major influence on the uncertainty because it directly determines the signal observed by the instrument. We show this dependence in Fig. 3. Over land, albedo values are typically of the order of 0.1–0.2, with typical column errors of the order of 2 DU, or about 1017 molecules cm-2. Because typical CO columns over Europe are 2×1018 molecules cm-2, this is a relatively small error of the order of 5 %. These numbers are in good agreement with the results presented in the CO ATBD of TROPOMI (document available from https://sentinel.esa.int/web/sentinel/user-guides/sentinel-5p-tropomi/document-library). Over the ocean, the albedo is very low, and the noise dominates the signal. To simulate this behavior in a realistic way we have added the albedo values 0.005, 0.01, and 0.02 to the albedo list in the lookup tables.

We note that the uncertainties reported here are substantially lower than reported for SCIAMACHY (e.g., Gloudemans et al., 2008). This reflects a difference in specifications of the instruments, and the fact ice buildup on the detectors affected the SCIAMACHY observations. Real TROPOMI observations will show whether the result that these are relatively small errors is realistic.

The generation of the synthetic observations consists of the following steps:

Co-location of the nature run vertical profiles of CO to the locations of the observations.

We show the results of this process in Fig. 5. The figure demonstrates the high resolution of the NR (about 7 km) and the corresponding simulated amount of detail. The bottom panel shows the corresponding CO observations. Over land, the NR features are clearly present due to the relatively low uncertainty. Over the ocean and Mediterranean, noise dominates the signal. We observe an improved information content near Iceland, related to thick cloud cover, where the higher signal reduces the relative noise.

We perform two OSSEs. The first one includes all pixels in the OSSE domain, regardless of whether they are cloudy or clear-sky, and the second only includes clear-sky pixels. We consider a pixel to be clear when the cloud fraction is less than 10 %. Comparison of the ARs from these two OSSEs indicates that the impact of including all pixels is small. The largest differences between the respective ARs in relation to the NR are 4 % in regions over northern Europe (North Sea and Scandinavia), with the AR for clear-sky pixels closer to the NR (not shown). We can explain these results by the fact the summer generally has low amounts of cloud. Consequently, we only present the results from the OSSE with all pixels.

To evaluate the AR, we calculate the χ2 diagnostic associated with the observation minus forecast (OmF) differences (see, e.g., Lahoz et al., 2007a). Here, we normalize the OmF differences by the background error. We also calculate histograms of the observation minus analysis (OmA) differences, the observation and the simulation from the CR (observation minus control run, hereafter OmC) differences, and the OmF differences. We use the observational error to normalize the differences building the histograms of OmA, OmC, and OmF.

Figure 6 (top panel) shows the chi-squared time series for OmF and its associated autocorrelation function calculated over the 3-month period of the OSSE experiments, computed as daily averages. The chi-squared diagnostic starts with a maximum of about 1.56 and takes values down to 0.75, with a mean of 0.9 over the OSSE 3-month period. The chi-squared time series is nearly stable since it exhibits relatively small variability (a standard deviation of about 0.14). Furthermore, the autocorrelation of the chi-squared statistic drops to zero, with no correlation after a time delay of 20 days. The calculation of the autocorrelation shows that the chi-squared statistic is uncorrelated after a time lag of 20 days; this means that after this time the mathematical expectation E(χ2) is equal to the average of the chi-squared statistics. We find E(χ2) = 0.90, which is close to the theoretical value of 1 (see Lahoz et al., 2007a). This result indicates that the a priori error statistics as represented in the B matrix slightly overestimate the actual error statistics from the OmF differences.

To test whether the observations, forecast, and analysis fields, as well as their associated errors, are consistent with each other, we calculate the histograms of OmA, OmF, and OmC only over land (normalized by the observation error) over the 3-month period (Fig. 6, bottom panel). For a properly set up assimilation system, the OmF and OmA normalized histograms should be close to a Gaussian distribution with mean of 0 and standard deviation of 1. Figure 6 (bottom panel) shows that the OmA and OmF differences are close to a Gaussian distribution centered near to or at zero. The OmF has a mean and standard deviation of 0.10 and 1.73, respectively, whereas the OmA has nearly a 0 mean and a standard deviation of 1.05. This indicates that the center of the OmA histogram is closer to zero and more peaked than the histogram of OmF. We expect this, since the analyses should be closer to the observations than the forecasts. Furthermore, the histogram for OmA indicates that the errors in the R matrix, the observational counterpart of the B matrix, are a good representation of the analysis error.

Based on the above results, we conclude that the background error covariance matrix, B, and its observational counterpart, R, prescribed in our assimilation system are reasonably well characterized (see, e.g., Lahoz et al., 2007a, for a discussion of the specification of errors in a data assimilation system). Furthermore, the above results are consistent with the assumption that the errors in the observations and the forecasts are Gaussian.

The shape of the OmC normalized histogram, which has a mean and standard deviation of 2.36 and 5.60, respectively, indicates the presence of a relatively large bias between the S-5P observations and the CR. The assimilation reduces this bias, as shown by the analyses being significantly closer to the observations than the simulation from the CR. This shows that the assimilation of simulated S-5P CO total column observations has a significant impact on the CO forecasts and analyses.

To understand further the impact on the surface CO field of the simulated S-5P CO total column measurements, we calculate the analysis increment (δx) for a single analysis time at 14:00 UTC on 15 June 2003. We calculate this increment as the analysis minus the model first guess (1 h forecast). The analysis increment provides a quantitative diagnostic of the quality of the analysis (see, e.g., Fitzmaurice and Bras, 2008).

Figure 7 (top panel) shows the spatial distribution of δx at the model surface. One can see the spread of the impact of the simulated observations across large regions. This is due to S-5P having a wide swath allowing it to sample larger regions. The most substantial corrections are over land, where there are sufficient observations to have an impact. Over sea, the increments tend to be negligible, as any observations found there have relatively large errors. Thus, there will not be much difference between the model first guess and the analysis. Likewise, this is also true in the regions outside the satellite footprint.

To provide further insight into the impact of S-5P CO measurements, we calculate latitude–height and longitude–height cross sections at 48.8∘ N, 2.6∘ E, near Paris, for 15 June 2003. Figure 5 (bottom left and bottom right panels) shows a zoom of the zonal and meridional vertical slices of the analysis increment. We see significant corrections to the model first guess (identified by large increments) confined to a deep layer. These corrections are larger at the surface and exhibit a second maximum around 650 hPa. This vertical structure is mainly attributable to the forecast error standard deviation (given as a vertically varying fraction of the local CO mixing ratio), the square root of the diagonal entry of the B matrix, which is higher in the boundary layer (where the value of the S-5P CO averaging kernel is close to 1). The shape of the S-5P analysis increments also exhibits a second peak around 650 hPa. The increments for this particular day thus show a clear impact from the S-5P CO measurements in the PBL and the free troposphere.

The shape of the S-5P increments is similar to that of typical SCIAMACHY analysis increments, which also extend through a deep layer and have a maximum at the surface (Tangborn et al., 2009). The fact that both these analysis increments stretch out over a deep layer is due to similarities in the S-5P and SCIAMACHY averaging kernels – both are close to unity over cloud-free land (see Fig. 5). Note that the situation shown in Fig. 7 is a snapshot and depends on the particular conditions for this time. An average of the increments over the summer period would tend to show a uniform distribution in height.

Figure 8 shows the fields of surface CO from the CR, as well as the NR and the AR, averaged over the northern summer period. One can see the general change of CO over land between the CR (top left panel) and the AR (bottom panel). We can ascribe this to the contribution of simulated S-5P total column CO data sampled from the NR. This figure shows several differences between the CR and AR fields that indicate the superior behavior of the AR in capturing features in the NR. For example, over eastern Europe and Russia, the AR CO concentration values are closer to those in the NR (with a mean bias between -1.5 and +1.5 ppbv); in particular, the CR shows generally lower values than in the NR (mean bias around -6 ppbv). Nevertheless, over Portugal, where the NR shows the forest fires that occurred over the summer, the AR captures them only slightly better than the CR. We expect this relatively poor performance of the CR regarding fires, as the fires are not included in the CR setup (see Sect. 2.4). Although the AR, in the operational setup, captures the CO concentrations emitted by forest fires slightly better than the CR (through assimilation of CO measurements), the relatively poor temporal resolution of the S-5P ultimately limits its performance. However, the most important deficiency is due to the criterion used in the operational setup in which we activate a data-screening test to discard observations far away from the model (see Sect. 3.2.5). A geostationary satellite, given its relatively high temporal resolution, should be able to capture better the temporal variability of CO from these forest fires (Edwards et al., 2009).

In this section, we provide a quantitative assessment of the benefit from S-5P CO total column measurements on the CO surface analysis. For this, we perform a statistical analysis of the different OSSE experiments for northern summer 2003.

We calculate the mean bias (MB, in parts per billion by volume, ppbv), its magnitude reduction (MBMR, ppbv), and the root mean square error (RMSE, ppbv) and its reduction rate (RMSERR, %). Note that although recent papers have raised concerns over the use of the RMSE metric (Willmott and Matsuura, 2005; Willmott et al., 2009), Chai and Draxler (2014) discuss circumstances where the RMSE is more beneficial. We use the correlation coefficient, ρ, to measure the linear dependence between two datasets and the fraction of the true variability (i.e., variability represented by the NR) reproduced by the CR or AR.

For a single model grid box, we define the statistical metrics (MB, RMSE, ρ) with respect to the NR as MBMR=MB(CR)-MB(AR)RMSE(X)=1N∑(X-NR)2RMSERR=100×1-RMSE(AR)RMSE(CR)ρx=∑X-X¯NR-NR¯∑X-X¯2∑NR-NR¯2 where X denotes the CR or the AR; N is the number of data samples, the vertical bars denote the absolute value operator, and the overbar symbol represents the arithmetic mean operator. The MB metric gives the average value by which the CR or the AR differs from the NR over the entire dataset.

Figure 9 presents the zonal and meridional means of the difference between the CR and the AR averaged over the northern summer 2003 (1 June–31 August). We also plot the confidence interval representing the areas where the AR is not significantly different to the CR at the 99 % confidence limit (highlighted in grey). These two figures show that there is benefit from the S-5P CO total column data over the first few bottom levels of the troposphere, i.e., the lowermost troposphere. Between the surface and 800 hPa, a negative peak is present in the zonal difference field (over Scandinavia) and in the meridional difference field (over eastern Europe). Note that the zonal field shows two areas, one with positive values and the other with negative values, representing a CR greater than the AR and a CR smaller than the AR, respectively. The positive peak, at a slightly higher level (i.e., lower pressure) than the negative peak, is representative of the Mediterranean Sea, whereas the negative peak is more representative of the land areas (Scandinavia and eastern Europe). Figure 9 indicates that the S-5P CO corrects the model in the lower troposphere with a larger impact over land and with a smaller impact in the PBL. This is consistent with the behavior of the analysis increments shown in Fig. 7.

Figure 10 shows the performance of the biases between the CR and the NR, and the AR and the NR at the surface, as well as averaged over the northern summer of 2003 (1 June–31 August). The MBMR, which compares the magnitude of the CR vs. NR and AR vs. NR biases, indicates the geographical areas where the simulated S-5P CO total column data have the most impact. The MBMR shows that the AR is closer to the NR than the CR, almost everywhere in the domain (reflected by the prevalence of the red colors in the bottom left panel). This indicates that the simulated S-5P CO total column data generally provide a benefit at the surface, and especially over land areas where the CO sources are sparse. This suggests that due to the relatively small variability of CO over remote land regions, the S-5P data can provide a larger benefit compared to regions where the variability is relatively high.

We also calculate the RMSE as well as the reduction rate of the RMSE, RMSERR (Fig. 11), both keeping the systematic error (Fig. 11, top) and removing the systematic error (Fig. 11, bottom). We calculate the bias in the AR and CR by subtracting the NR field from each of them, producing an unbiased AR and CR. For the case where we remove the systematic error, we perform the statistics on the unbiased AR and CR. If we examine the RMSE statistics, Fig. 9 shows that the CR gets closer to the NR over the Atlantic Ocean and over the eastern domain, including Russia and Scandinavia, when we remove the systematic error. For example, over these areas we obtain ∼ 30 ppbv and ∼ 10 ppbv for the RMSE keeping and removing the systematic error, respectively. For the reduction of the RMSE, RMSERR, the behavior for the CR is similar overall, showing a reduction rate of 60 % and 30–45 % keeping and removing the systematic error, respectively. Note that over Scandinavia the reduction rate goes down from 60 % to about 10 % after removing the systematic error.

These results indicate that S-5P CO data show more benefit when keeping the systematic error in the calculation of the RMSE. Following our guiding principle of avoiding an overoptimistic OSSE, we consider only the values of RMSE obtained when we remove the systematic error. For this case, the average reduction rate for the AR is around 20–25 % over land (except Scandinavia) and close to 10 % over sea and over Scandinavia.

In Fig. 12, we show the correlation between the CR and the NR, as well as the correlation between the AR and the NR, at the surface for the 3 northern summer months (1 June–31 August). The AR is closer than the CR to the NR with the correlation coefficient reaching 0.9 over land. By contrast, the correlation coefficient between the CR and the NR is typically less than 0.5, with very low values over eastern Europe, where CO sources are sparse.

Figure 13 shows time series from the NR, the CR, and the AR over the three areas of the study domain represented by the squares shown in Figs. 10 (bottom panel) and 11 (right panels): (i) the Paris region (Fig. 13, top panel); (ii) a region over Portugal (5∘ W–40∘ N), where forest fires occur during the northern summer (Fig. 13, middle panel); and (iii) an area in the eastern part of the study domain (25∘ E–53∘ N), where the reduction of RMSE (i.e., RMSERR) is much larger than for other regions (Fig. 13, bottom panel). For all three areas, the AR is generally closer to the NR than the CR, showing the impact of the simulated observations. We calculate the biases between the AR and CR vs. the NR by computing the difference NR-X, where X is AR or CR, and normalizing by the number of observations over the northern summer period. The biases are (i) 48 ppbv for CR and 38 ppbv for AR in the Paris region, (ii) 101 ppbv for CR and 83 ppbv for AR in Portugal, and (iii) 21 ppbv for CR and 5 ppbv for AR in the eastern part of domain. Note that the AR and the CR capture the variability but not the values of the peaks. However, the LEO only samples at most twice a day over Paris and may not capture the peaks. In Fig. 13, we indicate the S-5P revisit time by the plus signs at the top of the panel and one can see that the peaks do not coincide with the time of the S-5P measurements. Another factor could also be that the emission inventory used in the AR has lower values than the one used in the NR.

Over Paris (top panel), the CR is already close to the NR and the impact of the S-5P CO simulated observations is small. Over Portugal (middle panel), the presence of fires is not seen in the CR (e.g., a maximum of CO at the beginning of the heat wave), as the fire emissions were not taken into account in the CR as they are not known a priori (see Sect. 2.4). In contrast, over this specific location we see the impact of the fires on the CO concentrations in the AR with, however, much lower values than for the NR. During the fires, the CO concentrations in the AR over Portugal are larger than 500 ppbv, whereas the CR remains relatively unchanged with concentrations less than 200 ppbv. Over the eastern part, where there are lower emissions compared for instance to Paris (bottom panel), the temporal variability is not high and the magnitude of the bias between the CR and the NR is small, but it is removed in the AR. Moreover, note that the operational screening test was still in force (see section below).

The assimilation system we use has a default criterion to discard CO column observations with values larger than 75 % of the MOCAGE value. This criterion is not appropriate to situations resulting in excessive values in the CO concentrations, as is the case for forest fires. To understand further the performance of the OSSE over the period of the Portugal forest fires we perform a second OSSE without this default criterion. This second OSSE covers the period of the forest fires (25 July–15 August). For this second OSSE, we compare the total column values and the surface values of the CO fields from the CR and the AR (Figs. 14 and 15, respectively).

Figure 14 shows the CO total column at 14:15 UTC on 4 August 2003 (during the period of the Portugal forest fires) from the NR (top left panel), the simulated S-5P observations (top right panel), the CR (bottom left panel), and the AR (bottom right panel). We can see that the AR captures the fire event, indicated by relatively high values of the CO total column over Portugal, whereas the CR does not. This confirms the results shown in Fig. 13, which highlight the benefit provided by the S-5P CO total column measurements, in particular regarding the capture of the signature of the Portugal forest fires. Note that the S-5P measurement is noise-dominated over the sea (top right panel). This accounts for the sharp edge in the CO total column field seen between the Iberian Peninsula and the Bay of Biscay for the AR (bottom right panel).

Figure 15 shows the time series of the surface CO concentrations over the period 25 July–15 August (that of the Portugal forest fires). In comparison to the original OSSE (see middle panel of Fig. 13), the AR is now closer to the NR, having now peak values of about 900 ppbv instead of peak values of about 550 ppbv. The CR still has peak values less than 200 ppbv. This indicates that the relatively low values in the AR (in comparison to the NR) for the original OSSE shown in the middle panel of Fig. 13 result from the application of the default criterion to discard CO column observations that are far away from MOCAGE values. The results from Fig. 15 confirm those shown in Fig. 14 and reinforce the benefit provided by the S-5P CO total column measurements, in particular regarding the capture of the signature of the Portugal forest fires. This sensitivity test also shows the limitations of using standard operational criteria.