An empirical linear mixed-effects model approach to compare TROPOMI/Sentinel 5 Precursor NO2 observations with ground-based measurement in the Iberian Peninsula *

Urban air quality is an essential aspect of environmental monitoring, as atmospheric pollution is increasingly perceived to be responsible for substantial degradation of the quality of life, worldwide (World Health Organization, 2016, 2015). While atmospheric pollutants can have devasting effects on human health, documented effects are mostly attributable to long-term/continuous exposure, causing chronic and acute conditions such as cancer and cardiovascular malfunctions (World Health Organization, 2003; Cede et al., 2006; Bechle, Millet and Marshall, 2013; Cersosimo, Serio and Masiello, 2020a; Tack et al., 2021a). 

In the present case study, the tropospheric NO₂ (NO₂^CT) is studied, by comparing satellite data observations with in situ measurements, to disclose their correlation and investigate its seasonal cycle. 

The aim of this analysis is to recognize: (i) which are the typical and exceptional conditions of NO₂^CT concentrations that occurred in 2020 (taking into the account the global pandemic that led to widespread confinement form March to June 2020); (ii) what is the relation between NO₂^CT concentrations (satellite data) and in-situ NO₂ concentrations in each and across the cities; and (iii) describe the seasonal cycle of NO2 concentrations in each of the case study cities.

Two sets of NO₂ observation data were used in this study: satellite-acquired remote sensing observations and in-situ measurements.

The methodology used comprises the following steps:

• Processing and quality assessment (QA) of the satellite data - data from the TROPOMI (the TROPOspheric Monitoring Instrument) satellite on board of the Sentinel-5 Precursor (S5P) was used; Level 2 outputs from S5P include automated quality assurance parameters; S5P data was retrieved from the corresponding Pre-Operations Data Hub (https://s5phub.copernicus.eu/) in  Feb of 2021, including only offline processing mode (OFFL). The temporal coverage includes the period from 2020-01-01 to 2020-12-31. The geographic domain considered was a box with the following coordinates: 35° N/10° W and 44° N/5° E.
• In-situ data observations - data was retrieved from European Environment Agency (EEA) database (https://www.eea.europa.eu/); the stations included in the data collection correspond to the major Functional Urban Areas (FUAs) of the Iberian Peninsula – Lisbon and Oporto (in Portugal), and Madrid and Barcelona (in Spain) – and the same temporal coverage was considered. The crucial step used on this in-situ dataset was the aggregation of the Weekdays (Wd) and Weekend days (WEd) averages (separately), using only values from 11h to 14h, which corresponds to the overpass of the TROPOMI Satellite (this was done to have the best correlation possible with the performance of Sentinel-5P).
• Complementary meteorological observations - to better understand the seasonality of NO₂ concentrations, this data was retrieved from the European Climate Assessment & Dataset project (ECA&D, https://www.ecad.eu/). 

Before proceeding to the linear mixed model, outliers were identified and removed through the Mahalanobis Distance (MD) method.

Results from the LMM show that a significant (p-value < 0.01) and strong (R² > 0.88) correlation exists between satellite and in-situ observations across all cities and most in-situ stations while controlling for the intra-site autocorrelation (see Table 1).

Table 1. Linear Mixed-Effects Model LMMb estimates (level =0).

Through this method, it was possible to reach an overall level 0 equation to convert the satellite-based NO₂^CT data (µg/mol) into the in-situ NO₂ measurements (µg/m³) - see Equation 1, where the β_{0, j,k} is the level 1/2 intercept estimates and the β_{1, j,k} is the level 1/2 slope estimates. In addition, the level 1 equations allow to predict NO₂ in-situ concentrations from satellite data information at each city level (see black lines in Figure 1). Finally, at level 2, linear correlations correspond to the model estimates at the stations' level - these correlations are observed as coloured lines in Figure 1.

As per the level 0 estimates the NO₂^CT conversion to NO₂ in-situ is 0.1815, varying between 0.1557 and 0.2156 (at the 95% confidence interval). At the city level (level 1), the conversion factor estimates vary between 0.1616 (Oporto) and 0.1993 (Lisbon), while the intercept ranges between 37.0848 (Oporto) and 7.2242 (Lisbon). Finally, at the stations level (level 2), greater inter-stations variance is found in Oporto, where two stations have noticeable contrasting intercept in slope estimates.

To illustrate the LMM conversion estimates from satellite NO₂^CT observations to NO₂ in situ measurements, Figure 2 shows the first week of 2020 before (a) and after (b) conversion.

Figure 2. Representation of the differences between (a) converted tropospheric nitrogen dioxide (considering SI units of µmol/m²), and (b) converted in-situ nitrogen dioxide (considering SI units µg/m³) for the same weekday (Wd 1).

Major sources of NO₂ emission are known to be industrial plants and vehicles exhaust, which have a huge impact on the spatial pattern of the concentrations of this particular gas. Nonetheless, seasonal differences are known to occur in response to air temperature changes - maximum amounts are typical during the winter, while greater temperatures reduce NO₂ concentrations (Velders et al., 2001; Petritoli et al., 2004; Cede et al., 2006; Ordóñez et al., 2006). 

These seasonal differences occur because of the air density changes - air density is lower in the summer (when the temperature is higher) leading to NO₂ expansion. The opposite occurs in winter weeks/days, when colder temperatures raise air density, which leads to greater NO₂ concentrations. 

In Figure 3, winter and summer examples of NO₂ concentration levels are shown to highlight these seasonal aspects - while major FUAs can be noticed in both Figure 3.a and Figure 3.b (particularly Madrid, Barcelona, Lisbon or Oporto), estimates of weekly mean in-situ concentrations are circa 50% lower in the summer. 

Figure 3. Confrontation between (a) Winter week (3^rd weekday of 2020 - 10 to 17 of January of 2020) versus (b) Summer week (32^nd weekday of 2020 - 7 to 14 of August of 2020), considering NO₂^CT converted into µg/m³. 

In addition, considering the fact that 2020 was an abnormal year (due to the World pandemic Covid-19), major differences were observed pos- and pre- Covid in the Iberian Peninsula - these are shown in the next figure. It should be mentioned that Spain (specifically Madrid) was more affected by this virus, and consequently led to a lockdown long before Portugal. It is also important to have into account the relationship between NO₂ concentrations (considering the 4 cities in the study) with near-surface wind direction patterns. In the following figure (Figure 4), these facts can be observed, where the wind roses are representative of Weekday 2 and Weekday 10 for the city of Madrid (which shows a higher concentration of the pollutant compared with other regions), showing maps of NO₂ concentrations before and after lockdown. 

As can be observed in this figure, the wind has an impact on the dispersion of NO₂ - the impact of the wind can be clearly observed, affecting the dispersion of this pollutant. On weekday 10, the impact of the wind on NO₂ concentrations is more difficult to observe because of the low concentrations of this pollutant in all of the cities, more specificly in Madrid.

Figure 4. Confrontation of NO₂ concentration maps with the respective wind roses (considering only Madrid Station) between (a) Pre-Lockdown week/days (Weekday 2 – corresponds to 10-17 of January of 2020) versus (b) Pos-Lockdown week/days (Weekday 10 – corresponds to 6-13 of March of 2020), considering NO₂^CT converted into µg/m³. 

To complement the analysis in Lisbon, Porto, Barcelona and Madrid, Figure 5 shows the weekly concentrations of NO₂ average per country, as measured in-situ (i.e., retrieved from EEA).

The figure highlights similar seasonal patterns in both countries although greater mean values are found in Spain in the first weeks of 2020. However, around week number 14, Portugal showed higher values of concentrations - this can be explained by the earlier lockdown implemented in Spain. Lower concentration values of this pollutant are found from week 12 to week 37, which match not only the lockdown of both cities but also the temperature increase.

To conclude, Figure 6 shows a mosaic of the 4 cities in this study, depicting the corresponding metropolitan plumes to highlight the differences in terms of values and spatial pattern, in greater detail - week number 3 is shown since similar NO₂^CT concentrations and low cloud cover is found in all the cities. Results show not only greater values in Spain's FUAs but also wider plumes, as expected due to the greater size of these metropolis.

• In the present study, 4 Iberian Cities (Lisbon, Oporto, Madrid and Barcelona) are analysed by comparing tropospheric and in-situ measurements of NO₂.
• An LMM was developed to convert tropospheric into near-surface NO₂ measurements, with significant results across all cities and most stations (R² > 0.88, p-value < 0.01), while controlling for intra-station autocorrelation.
• NO₂ concentration was found to be greater in the city of Madrid considering the first weeks of 2020; however, when considering all the time range, this city shows earlier NO₂ levels reduction, a fact that can be explained due to the world pandemic, which led Madrid into an earlier lockdown, compared to other Iberian Peninsula cities. In Madrid, these low values are attributable to the lockdown because this region has a higher population density and generally presents greater amounts of NO₂ concentrations.
• In Portugal, Lisbon shows a similar seasonal pattern as in Madrid, although later lockdown-related NO₂ concentration reduction.
• In future work, the temporal scale of the analysis shall be extended to include more years and the spatial coverage expanded to other European FUAs - for example, in central Europe, where greater concentrations of NO₂ are typically found.
• In addition, data fusion techniques shall be explored with the aim of raising the spatial resolution, namely considering machine learning models based on satellite and in-situ observations, as well as data related with activities that are known to contribute to the emission of this gas (e.g., traffic, industrial plants).