Analogs of atmospheric circulation (Yiou et al., 2013; Lorenz, 1969; Van Den Dool, 1994; Zorita and Storch, 1999; Cattiaux et al., 2012) have been widely used for different climatological purposes, notably for atmospheric reconstructions and in the characterization of the role of synoptic circulation in extreme meteorological events (Yiou et al., 2013; Vautard et al., 2018). Circulation analogs are generally computed from daily pressure spatial distributions. Here, we built the analogy based on three successive layers:

Synoptic. Circulation analogs are computed similarly to previous studies. We used daily sea-level pressure (SLP) data to better characterize near-surface atmospheric circulation as our study covers near-surface pollutants. The SLP data are extracted from NCEP/NCAR reanalysis data (Kalnay et al., 1996) along the historical period that covers 2012 to 2019. The SLP fields considered here have a horizontal resolution of 2.5×2.5∘ and cover a spatial domain ranging -20∘ W to +15∘ E in longitude and +40 to +60∘ N in latitude. This region is chosen because it includes atmospheric pressure patterns that influence near-surface wind (Raynaud et al., 2017) in our area of study. For each day of the study period, the 50 best circulation analogs (minimum spatial correlation of 0.5) are sought, using the spatial correlation as a way to measure similarity between SLP fields. The calendar distance between the day in the study period and days in the historic period is a maximum of 30 d. Out of 50 potential days with analog atmospheric circulation, only those with a spatial correlation higher than 0.6 (representing 97.8 % of all analog days, 23.2 analogs/day on average) were kept.

Regional. The air mass trajectory (AMT) of each synoptic analog was compared to the AMT of the corresponding lockdown day. For each day, trajectory density (log of the occurrence of trajectory endpoints) was calculated over a 0.5∘ × 0.5∘ grid covering western Europe. The distribution of spatial correlation values between each day of LP and each analog day is presented in Fig. S4. Since this distribution is rather spread out, a low threshold at 0.2 (representing 70 % of analog days, 16.3 analogs/day on average) was selected in order to remove the worst analog AMT but also to keep sufficient variability. An example of satisfactory and unsatisfactory analogs is shown in Fig. S5.

Local. A specific constraint on local ambient temperature and relative humidity (RH) was implemented. Indeed, both variables are key drivers of the partitioning of semi-volatile material, such as ammonium nitrate. Therefore, a satisfactory representation of local meteorological conditions by the analogs is needed in order to robustly capture and characterize any change of concentration. Over the study period, the analog performance regarding temperature and RH respectively ranges from -15 to +15 ∘C and from -36 % to +64 %. Concretely, analogs that are much colder and wetter (higher RH) than the observation day may be associated with enhanced condensation of semi-volatile and/or hygroscopic compounds, which would lead to an overestimation of the estimated decrease of, e.g., nitrate. This specifically occurred on 21, 22 and 23 April 2020. To avoid that issue, we excluded the analogs having the 5 % worst performance from the list. Acceptable ranges were therefore between the 5th and 95th percentiles (excluded) of ΔT and ΔRH values, which were respectively ]-9.3, 6[ and ]-19, 35[. Despite these relatively wide ranges, the A3Q methodology allows us to efficiently reconstruct meteorological conditions during the lockdown period. Indeed, Fig. S11 presents, for the January–May 2020 period, the temporal variations of observed and estimated temperature, RH and pressure. It shows low mean bias values, as well as satisfactory correlation coefficients (r value of 0.78, 0.82 and 0.63, respectively), which indicates a satisfactory analogy. Sensitivity tests presented below also demonstrate that stricter ranges do not significantly change the analog results.

Daily absolute concentration change (DAC) and median relative change (MRC) for each species are defined as 2DACij=Obsij-Analogij3MRCj=Mjobs-MjanalogMjanalog, where Obsij and Analogij are the daily concentration at ti of species j, measured and calculated from A3Q, respectively. Mjobs and Mjanalog are the median concentration during lockdown, measured and calculated from A3Q, respectively.

Daily averages have been computed for each variable. A valid average is considered if at least 75 % of the day is covered.

Because the dataset consists in multi-year observations, long-term trends may impact the estimated concentration change due to lockdown. To that end, a seasonal Mann–Kendall (MK) test was performed on each variable for the January 2012–February 2020 period. The Mann–Kendall R package was used (Bigi and Vogt, 2020; Collaud Coen et al., 2020), which includes three pre-whitening approaches in order to reduce the weight of autocorrelation. Results are summarized in Table 1. From this analysis, NOx, OA, HOA, OOA, O3 and BCff concentrations (2012–2020, including lockdown) were linearly corrected on a daily basis.

In order to limit the unwanted weight of positive outliers which have poor statistical representativity, the 1 % highest daily concentrations of each variable were removed.

The results presented here primarily depend on the list of analog days that are calculated. The overall analog number is at first determined by the strictness of the correlation coefficients of atmospheric circulation and air mass origin. Selection of best analogy leads to poor statistical representativeness (Fig. S6), with a low number of analog days. It is instead preferable to remove analog days associated with the worst trajectory correlation (Fig. S4). It is noteworthy that little change in the correlation coefficients (Table 2, Scenario 1–4) has little impact on the results (for all variables) presented in this paper (Fig. S7). This can mainly be related to the reasonable change in the number of analog days.

Similarly, the impact of subsequent filtering with temperature and relative humidity was also investigated. To this end, two additional scenarios were considered (Scenario 5–6, Table 2). Scenario 5 and Scenario 6 have limited impact on traffic-related variables (Fig. S7), as opposed to wood-burning tracers and secondary compounds. This especially highlights the essential role of meteorological representativeness in order to characterize the changes of secondary pollution. Indeed, when no temperature and RH filtering is performed (Scenario 5), the highest decrease of NO3 is linked to analog days that are associated with higher RH (Fig. S8a) and lower temperature (Fig. S8b), which favor the partitioning of nitrate in the particulate phase. Scenario 6 has a stricter filtering than the base one and exhibits very good performance regarding the reconstruction of meteorological conditions (Table 3). However, we show that both scenarios have very similar daily NO3 concentration change despite slight discrepancies in meteorological performance. This underlines that the thresholds used in the base scenario are sufficient to provide robust results.

Furthermore, the performance of the analog methodology has been evaluated on a business-as-usual period, from 1 January 2020 to 1 March 2020, similarly to the work of Petetin et al. (2020) and Grange et al. (2021) The construction of the analog list went through the same steps, with the same thresholds. The acceptability range for ΔT and ΔRH moved to ]-5, 4[ and ]-16, 19[, respectively. This can primarily be related to the less extreme climatological conditions of January–February 2020. Mean bias (MB), normalized mean bias (NMB), Pearson's correlation coefficient (r) and the fraction of data within a ratio of 2 (FAC2) have been used for the evaluation.

Scatter plots and metric values are respectively presented in Fig. 3 and Table 4. Results indicate satisfactory performance of all variables during the evaluation period, although the range of observed concentrations remains rather low.

The lower performance of BBOA in terms of co-variations (r=0.45) may be related to the absence of 2019 data, where fewer analog days could lead to higher dispersion but also to the fickleness of the wood-burning source. Still, as presented in the Results section, BBOA variations are consistent with BCwb.

Nitrogen oxides play a central role within the atmospheric reactor, enabling the formation of secondary pollutants (Kroll et al., 2020) such as tropospheric ozone and secondary organic and inorganic aerosols (SOAs and SIAs, respectively). Ozone is found to increase by 20 % (Fig. 4). This negative feedback, due to the titration effect of NO, is already well characterized (Reis et al., 2000), and the magnitude of the change inversely follows the one of NOx well (Fig. 7a). A sharp enough decrease of NOx shall tip over ozone formation to a NOx-limited system (Markakis et al., 2014), which may be seen from this relationship, where ozone concentration change stabilizes at +20 µg/m3 for ΔNOx below -10 µg/m3 at SIRTA. Nevertheless, it is worth highlighting that the climatological extreme of spring 2020, with strong positive temperature anomalies, should have also contributed to increased O3 concentrations, as previously emphasized for Europe (Meleux et al., 2007). Even though meteorology is taken into account by the A3Q method, the unique character of this springtime heatwave inherently blurs the discrimination between ambient temperature and NOx impacts on ozone formation. This limitation would also occur for any other statistical approaches, such as machine learning. Figure 7b shows indeed that some of the highest ΔO3 values are associated with high temperatures (daily average >18 ∘C), concomitantly with substantial decrease of NOx concentrations. On the other hand, positive ΔO3 values are also obtained for rather low temperature (<10 ∘C) and highest decreases of NOx, which means that in this case the increase of O3 is only NOx-related.

Springtime in the Paris region is usually associated with PM pollution episodes that are mainly triggered by particulate ammonium nitrate (Beekmann et al., 2015) (NH4NO3), resulting from the reaction between HNO3 (NOx oxidation) and ammonia (NH3). For that matter, agricultural activities (the major source of NH3 in western Europe; Fortems-Cheiney et al., 2016) were neither stopped nor restrained during lockdown. Therefore, business-as-usual ammonia concentrations can reasonably be assumed, and since the formation regime of nitrate in Paris has previously been found to be NOx-limited (Petetin et al., 2016), a change of regime to NH3-limited is highly unlikely (Viatte et al., 2021). Nitrate exhibits a median decrease of 45 %. The decrease linearly follows the one of NOx (Fig. 8), although both compounds differ in terms of reactivity and footprint. A similar relationship is shown when using urban and peri-urban NOx concentrations (Fig. S10), which is consistent with the temporal correlation of ΔNOx throughout the Paris region (Fig. 5). However, a slight shouldering of the decrease for urban NOx can be noticed, which implies that this efficiency regarding NO3 is related to the amplitude of NOx reduction.

This result suggests the importance of rapid ammonium nitrate formation at a rather local scale (Petit et al., 2015; Wang et al., 2020) but shall not eclipse continental advection that can occur in Paris, especially during springtime (e.g., Beekmann et al., 2015). To that end, sulfate shows little change (-8 %) with no clear statistical significance (p>0.05), which indicates a similar influence of long-range pollution advection and that SO2 sources in eastern Europe (Pay et al., 2012) may not have experienced a significant decrease. Consistent information on that matter is unfortunately still rather scarce at the European scale. Filonchyk et al. (2020) recently showed an increase of SO2 in several Polish urban areas, although their methodology does not take meteorology into account. The Carbon Monitor initiative (Z. Liu et al., 2020) also records a decrease of 11.5 % of the power sector in Europe during 2020 compared to 2019. On specific days, positive peaks of ΔNO3 are concomitant with higher SO4 concentrations (Fig. 9). Since SO4 has been previously found to be mainly advected in northern France (e.g., Favez et al., 2021), also supported by the cluster analysis in Fig. S3b, this means that nitrate was, in these cases, mainly advected from long-range transport, despite a decrease of NOx. It is also concomitant with higher nitrogen oxidation ratio (NOR = NO3 / (NO2 + NO3)) values and the highest positive change (top panel of Fig. 9), suggesting a higher efficiency of HNO3 formation. Given the NOx / NO3 relationship (Fig. 8a), and hypothesizing that a decrease of locally formed NO3 is always associated with a decrease of NOx concentration at the measurement site, long-range-transported NO3 can be assumed to overcompensate for the regional decrease (Eq. 4). 4ΔNO3total=ΔNO3advected+ΔNO3local, where ΔNO3total is the daily concentration change at ti, calculated from A3Q. ΔNO3local is calculated from the relationship with ΔNOx (Fig. 8).

For instance, on 28 March and 19 April, the total ΔNO3 respectively of 11.7 and 6.7 µg/m3 could be apportioned into a regional decrease of -5.5 and -3.7 µg/m3, with an advected contribution of 17.2 and 10.4 µg/m3, respectively. This result would need to be further investigated and confirmed by, e.g., chemistry transport model simulations, but it still underlines the deleterious impact of long-range transport.

Secondary organic aerosols, proxied by OOA concentrations, exhibit a decrease of 25 % compared to business-as-usual conditions. Given the multitude of SOA precursors and formation pathways, this decrease can be linked to numerous factors. Indeed, Srivastava et al. (2019) recently highlighted the complexity of the SOA fractions in the Paris region during springtime. The lack of specific organic tracers prevents us from thoroughly apportioning SOA over the long-term analysis period of 2012–2020. As a consequence, the apparent decrease of 25 % may derive from several compensatory feedbacks, which cannot be individually characterized here. Although SOA in Paris can not only be related to traffic (Crippa et al., 2013; Srivastava et al., 2019), the decrease of OOA seems to be also correlated with ΔNOx (Fig. 8b). NOx steps in SOA formation notably when reacting with peroxy radicals (R-O2), resulting from volatile organic compound (VOC) oxidation with the hydroxyl radical. The exceptional amount of sunshine during lockdown may have positively influenced the availability of OH⚫ for the initialization of SOA formation. However, no direct observations available at SIRTA can support this assumption directly. The odd oxygen Ox (=O3+NO2), a conservative tracer of photochemical chemistry (Sun et al., 2020), shows a slight increase (+9 %). But unlike the findings of Herndon et al. (2008) in Mexico City during spring, only a moderate correlation is found with OOA (r2=0.4, slope = 0.068, following the recommendation of removing wood-burning- and long-range-transport-related episodes). This may be linked to the rather low Ox concentrations (60–110 µg/m3) during the lockdown period.

Despite very limited change on average (<1 %), daily OScSOA is found to differ from business-as-usual conditions, adopting a comma-like shape, as a function of ΔNOx (Fig. 8c). Indeed, although ΔOScSOA decreases until ΔNOx>-7 µg/m3, it increases back for higher NOx decreases, reaching a median of +0.05. Despite being moderate, this behavior may reflect some changes in SOA chemistry, notably regarding gas-phase oxidation of anthropogenic precursors, as highlighted in Herndon et al. (2008). But at this stage, the whole equation comprises too many unknown variables (from VOC precursors to particulate end products) in order to fully describe the impacts of lockdown measures on the numerous SOA formation mechanisms; this remains arduously apprehensible.