Comparison of source apportionment approaches and analysis of 1 non-linearity in a real case model application 2

The response of particulate matter (PM) concentrations to emission reductions was analysed by assessing 11 the results obtained with two different source apportionment approaches. The brute force (BF) method source impacts, 12 computed at various emission reduction levels using two chemical transport models (CAMx and FARM), were 13 compared with the contributions obtained with the tagged species (TS) approach (CAMx with PSAT module). The 14 study focused on the main sources of secondary inorganic aerosol precursors in the Po Valley (Northern Italy): 15 agriculture, road transport, industry and residential combustion. The interaction terms between different sources 16 obtained from a factor decomposition analysis were used as indicators of non-linear PM10 concentration responses to 17 individual source emission reductions. Moreover, such interaction terms were analysed in the light of the free ammonia 18 / total nitrate gas ratio to determine the relationships between the chemical regime and the non-linearity at selected 19 sites. The impacts of the different sources were not proportional to the emission reductions and such non-linearity was 20 most relevant for 100% emission reduction levels compared with smaller reduction levels (50% and 20%). Such 21 differences between emission reduction levels were connected to the extent to which they modify the chemical regime 22 in the base case. Non-linearity was mainly associated with agriculture and the interaction of this source with road 23 transport and, to a lesser extent, with industry. Actually, the mass concentration of PM10 allocated to agriculture by 24 TS and BF approaches were significantly different when a 100% emission reduction was applied. However, in many 25 situations the non-linearity in PM10 annual average source allocation was negligible and the TS and the BF approaches 26 provided comparable results. PM mass concentrations attributed to the same sources by TS and BF were highly 27 comparable in terms of spatial patterns and quantification of the source allocation for industry, transport and residential 28 combustion. The conclusions obtained in this study for PM10 are also applicable to PM2.5. 29 30


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Air pollution is the main environmental cause of premature death. Ambient air pollution caused 4.2 million deaths involves the quantification of the influence of different human activities (e.g. transport, domestic heating, industry, 38 agriculture) and geographical areas (e.g. local, urban, metropolitan areas, countries) to air pollution at a given location.

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SA modelling studies involving secondary inorganic pollutants are generally based on chemistry transport models

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Even though these approaches are often considered as two alternative SA methods, they actually pursue different circumstances; for instance, the intensity of the emission reduction, which imposes the need to quantify it for different 76 emission reduction levels (ERLs) (see Section 3.2). Thunis et al. (2015) showed that for yearly average relationships 77 between emission and concentration changes, linearity is often a realistic assumption and consequently, TS and BF 78 methods are expected to provide comparable results, as reported by Belis et al. (2020). The abovementioned 79 considerations suggest the need to monitor whether non-linearity is significant for a given study area and time window.

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The objective of this study is to identify and quantify the factors leading to non-linear response of PM concentrations 81 to source emission reductions in a real-world situation with significant PM concentrations. To that end, the influence 82 on PM 10 concentration of various sources with different chemical profiles were calculated using both the BF approach 83 with two different chemical transport models (CAMx and FARM) and the TS approach using one of these chemical-84 transport models (CAMx).

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The results of the simulations were then used to:

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The application of such CTMs required the implementation of a comprehensive modelling system (e.g. Pepe et al.,

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In CAMx, homogenous gas phase reactions of nitrogen compounds and organic species were reproduced through the 120 CB05 mechanism (Yarwood et al., 2005). The aerosol scheme was based on two static modes (coarse and fine).

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Secondary inorganic compounds evolution were described by the thermodynamic model ISORROPIA ( Manager pre-processing system (ARIA Technologies and ARIANET, 2013).

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Initial and boundary conditions were taken from a parent CAMx simulation covering the whole Italy and driven by 145 MACC-II system (http://www.gmes-atmosphere.eu/services/aqac/) that provides 3D global concentrations fields.  Table 2.

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In this study, are mainly analysed the interactions between sources AGR, TRA and IND are mainly analysed.

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Additional runs were executed using FARM at 50% and 20% ERLs to test also the impacts and interactions of RES

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with the previous ones. 160

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The annual average impacts of AGR, TRA and IND on PM 10 derived by BF approach with CAMx and FARM for 173 different emission reduction levels (ERLs) are shown in Figure 2 while those of RES are shown in Figure S3. In a 174 linear situation the impacts allocated to each source decrease proportionally to the intensity of the emission reduction

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(C 100% = 2 C 50% = 5 C 20% ). For that reason, the impacts at the 100% ERL can be compared directly with TS 176 contributions while those of 50% and 20% must be multiplied by factor 2 and 5, respectively. The linearity between 177 different ERLs is discussed in Section 3.2. To facilitate the comparison between different models, impacts are 178 expressed as percentage of the base case in these figures. In Figure 2, the highest impacts are those of AGR followed respectively). Such non-linear behaviour is associated with a situation near to double counting, which results in 203 negative interaction terms, and for nitrate, also to the NH 4 NO 3 equilibrium, since both effects lead to BF impacts 204 higher than TS contributions (Appendix A).

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Despite the comparable range of BF impacts and TS contributions of AGR on PM 10 at 50% and 20% ERLSs ( Figure   206 3), there is a considerable dispersion around the regression line (R 2 between 0.65 and 0.

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The non-linearity between TS and BF source apportionment of PM 10 secondary inorganic constituents observed in  The analysis of the impacts reported in this section clearly points out AGR as the source mostly associated with the 257 non-linear response of BF impacts with respect to TS.

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In this section the connection between the magnitude of the emission reduction and the BF source impacts on PM 10 is 260 analysed more in detail. The scatter plots in Figure 4 depict the relationships between BF impacts at different ERLs

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for every source and model. IND is the source for which the similarity between the different ERLs is the highest with 262 regression slopes and R 2 between impacts calculated for the three ERLs of CAMx and the two of FARM near unity.

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Although also the regressions between TRA impacts are linear, the 50% ERL impacts are ca. 8% lower and the 20% 264 ERL ca. 12% lower than those obtained with 100% ERL using the same model. The impacts at 50% and 20% ERLs 265 are well correlated, and the latter are less than 5% below the former for both CAMx and FARM values. For AGR the 266 relationship between the impacts calculated for both 50% and 20% ERLs are clearly non-linear when compared to 267 100% ERL. In the latter impacts are 3 or 4 times higher than the former two, especially for mid to high impacts. By 268 comparison, the relationship between impacts at 50% and 20% ERLs is closer to linearity (R² = 0.99), with the latter 269 leading to 18% -20% lower impacts than the former. The results shown in Figure 4 confirm that AGR is the source 270 presenting the most serious non-linearity among those emitting SIA precursors (see Section 3.1). In addition, the 271 analysis indicates that also for TRA the impacts of the different ERLs are not fully equivalent.

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The large differences in AGR impacts on PM 10 between 100% and the other ERLs are likely explained by two reasons.

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Firstly, turning off AGR 100% systematically shifts the system into a different chemical regime, while this is not the 274 case for the other sources, and secondly, the influence of limiting precursors (leading to less than double counting and 275 consequently less BF overestimation with respect to TS) is not expressed at 100% ERL (Appendix A Section A2.2).

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The differences between 50% and 20% ERLs could be explained by the way in which limited chemical regimes 277 interact with the reduction of emissions. Since the non-linearity associated with limited chemical regimes appears only 278 when the emission reduction causes a drop of concentrations higher than the excess of the non-limiting precursor

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(Appendix A), the chance of such non-linearity to influence source impacts is proportional to the emission reduction.

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However, the relatively small differences observed between 50% and 20% ERLs are likely due to the smoothing effect 281 of the NH 4 NO 3 equilibrium with respect to the non-linearity caused by a limited chemical regime because such 282 equilibrium leads PM 10 concentrations to change even when the non-limiting precursor emission reduction is lower 283 than the excess (Appendix A Figure A1).

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A similar analysis was carried with FARM at 50% ERLs for residential heating ( Figure S10) and the resulting 302 interaction terms were very low compared with those the other sources at the same ERL. The explanation is that 303 despite the considerable contribution of this source to PM 10 its origin is mainly primary with a high non-reactive 304 carbonaceous fraction (Piazzalunga et al., 2011) and therefore the impact on the secondary inorganic aerosol is limited.

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The values of the interaction terms depend on the pollutant concentration. In order to define when ĉ is significantly 306 different from zero, and consequently when the non-linearity is not negligible, the absolute value |0.5| % BC is 307 proposed. Such arbitrary threshold was defined to highlight the interactions that according to the analysis of the 308 impacts presented in the previous sections are associated with evident non-linear situations (e.g. AGR-TRA). In

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Figures S11 and S12 are reported the maps of the interaction terms expressed as % of the base case for 100% and 50%

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A common feature of all three sites is that the higher the ERL the higher the difference between the GR of the scenarios 342 and the one of the base case providing evidence about the extent to which the emission reductions alter the original 343 conditions. The points representing simulations in which AGR is reduced sit to the left of their respective base case.

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The scenarios with 100% ERL often lead to changes in the chemical regime and to the highest absolute interaction industry) which is an example of compensation process (Appendix A Section A2.5). Figure 6a shows that for 50% behaviours as those at 50%.

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In MI the base case simulations correspond to a chemical regime where NH 4 NO 3 is limited by NH 3 (Figure 6b). The

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inhibition of NH 4 NO 3 formation by H 2 SO 4 is unclear since the GR values calculated from both models are close to interaction terms (data points at the bottom left of Figure 6b). However, unlike the previous site, the combined 100%

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(data points to the right of the corresponding base case) while the inhibition by H 2 SO 4 is uncertain since data points 380 remain close to the boundary between the two regimes.

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In RA_P, both base cases are in a regime of NH 4 NO 3 formation limited by NH 3 . However, for CAMx base case where NH 4 NO 3 formation is limited by NH 3 (data points to the right of the corresponding base case) and not inhibited 396 by H 2 SO 4 (with some data points close to the boundary between the two regimes).

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Among the scenarios at 50% and 20% ERLs, those involving AGR and IND lead to the highest absolute interaction 398 terms, of which some (C5AI, F2AI) are negative and clearly different from zero (non-linearity) with the exception of 399 F5AI that presents a negligible interaction term. The higher interaction terms for the AGR-IND scenarios with respect 400 to the other sites may be related to the greater importance of IND compared to TRA in this particular region.

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The numerical relationship between the interaction terms and the gas ratio delta (i.e. the difference between the gas 402 ratio in one run and the corresponding base case) varies from site to site and, therefore, it is not possible to define 403 acceptability thresholds valid for the entire domain.

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The factors that trigger differences in SA between the TS and the BF approaches also lead to non-linearity among 427 different levels of emission reduction. For PM 10 , this non-linearity is higher between 100% and the other reduction It was also observed that in the majority of the tested scenarios at 50% and 20% ERLs, interaction terms are either 435 negligible or remain low (a few percent of the base case concentrations). In these conditions, the TS and the BF 436 approaches provide comparable results. Such findings were confirmed in this study by the direct comparison between 437 these two approaches that provided highly comparable spatial patterns and quantification of the role (contribution or 438 impact) of IND, TRA and RES sources.

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Due to its high emission levels and stagnation of air masses, the situations potentially leading to non-linear responses to stronger ERL (e.g. greater than 50%, as shown in figure 4) is discouraged too. Likewise, in such situations, the use

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of TS results to derive information about emission reduction impact can be totally misleading.

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The findings of the present work about PM 10 are also valid for the behaviour of PM2.5. In the runs used for this study 451 these two size fractions present the same geographical patterns and values because the difference between them (the 452 coarse fraction) is mainly primary and thus expected to respond linearly to emissions reduction. with high AGR emissions reduction (e.g. 100%) lead to a shift of the NH 4 NO 3 formation chemical regime. One of the 465 implications of these findings is that when there is a strong non-linear response (e.g. 100% reduction of AGR) it is 466 not appropriate to sum the impacts obtained with single source reductions to estimate the combined effect of more 467 than one source.

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Finally, it is important to stress the complementarity of the BF and TS are different but complementary techniques.

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Understanding how they work is necessary to adopt the one which is most suitable for the purposes of the work. On 470 the one hand, BF is the best choice to assess the response of the air quality system to changes in the emission rates.

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For instance, this approach emphasises better the key role of agriculture and is then most suitable for planning 472 purposes. On the other hand, TS is most valuable when the focus is on the actual mass transferred from sources to 473 receptors in the situation described in the base case, . It is, therefore, most appropriate for studying the health impact

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One of the main outcomes of this study is that in most situations (linear response) the two approaches provide similar shorter time windows (daily, seasonal averages or pollution episodes) the non-linearities are likely be more prominent.

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If there is a clear non-linear response, precaution is needed in the interpretation of the results from both approaches:

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-in BF it is not appropriate to sum of the impact of the sources obtained by single source reduction because

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The methodology proposed in this study provides the means to identify non-linear responses to promote a more    Since near the stoichiometric ratio a is similar to b, the actual interaction term is close to but less negative than the 663 double counting interaction term.

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Most commonly, the concentrations of the precursors significantly differ from the stoichiometric ratio and 666 consequently one of them acts as limiting factor or limiting precursor (in the example below the one emitted by source

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A, which implies C A > C B ). In this case, the emission reduction can lead to two different situations: 668 2.2a) the reduction of the emissions causes a decrease of the non-limiting precursor () concentration lower or 669 equal to the its excess with respect to the limiting precursor () leading to an interaction equal to zero because 670 C B is zero and C AB = C A . 671 In this case the potential interaction does not take place 673 2.2b) the reduction of the emissions of source B is enough to reduce the concentration of precursor  by more 674 than its excess with respect to  leading to a negative ĉ AB with lower absolute value than the double counting. In the real world, situations where NH 4 NO 3 formation is limited by free NH 3 availability (GR<1) or total nitrate 683 availability (GR>1) are common. However, due to feedback processes, the impact of reducing the emissions of a non-684 limiting precursor is small but not null, while the one of reducing the emissions of a limiting precursor may be 685 smoothed by the NH 4 NO 3 equilibrium (see Section A2.4).

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The interaction between two sources A and B can be affected by a third one C when the precursors emitted by the two 688 sources B and C compete to react with the one emitted by source A (See eqs. A2 and A3). In the formation of SIA,

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there is competition between HNO 3 and H 2 SO 4 to react with NH 3 to produce ammonium nitrate and ammonium 690 sulfate, respectively. HNO 3 derives from NOx emissions emitted i.a. by road transport (there are other sources), H 2 SO 4 691 mainly comes from SO 2 emitted by industry, and NH 3 is mainly emitted from agriculture.

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In situations where the formation of SIA is not limited neither by H 2 SO 4 nor by HNO 3 availability (and conditions are 693 favourable to the formation of (NH 4 ) 2 SO 4 ), the reaction H 2 SO 4 + NH 3 produces 1 mol of (NH 4 ) 2 SO 4 every 2 mols of 694 NH 3 while the reaction HNO 3 + NH 3 produces 1 mol of NH 4 NO 3 for every mol of NH 3 . The yield of aerosol in terms 695 of mols of the second reaction is twice the one of the first reaction. The difference of mass in µg/m -3 is as follows:

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Consequently, when the SO 2 emissions are reduced in an NH 3 -limited regime and HNO 3 replaces H 2 SO 4 to react with 699 NH 3 there is an increase in the PM concentration.

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In order to quantify the abovementioned competition it is necessary to compute the interaction between at least three 701 sources at once (eq. A5).

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The competition in a three-source system may lead to negative C (= increase in PM 10 ) for the single IND reduction  718 In case only the source of ammonia (A) is reduced, C=C A with K= (b+C A ) (a/q+C A ) (A12)

719
In case only the source of nitric acid precursors (B) is reduced, C=C B with K= (b/q+C B ) (a +C B ) (A13) Solving these second order equations for different emission reductions (represented by q in eq. A 12-14) shows that 722 the inequality C AB < C A +C B (i.e. ĉ AB < 0) is always observed ( Figure A1). Moreover, the interaction terms vary 723 in a non-linear way with respect to the emission reduction becoming less negative when the system moves away from 724 stoichiometric conditions ( Figure A1).

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In addition to the determinants described in the previous sections, which are mainly associated with the modellistic 731 approaches used to estimate source impacts and with atmospheric chemistry, there are other factors that may alter the 732 linearity of the relationship between the emission reductions ΔE and the response ΔC. In this section, we generically 733 refer to such alterations as compensation.

734
Compensation are all the processes taking place in real world conditions which alter the ΔC expected to result from a 735 given ΔE in a theoretical exercise (either at the single cell or at the entire grid level), leading to interaction terms 736 different from those expected only on the basis of applied emission reduction.

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Compensation of precursor emissions: the actual emission reduction (E) of one precursor is lower than the 738 expected E in a system with few sources because in a complex system, like the one analysed in this study, there are 739 other sources of the same precursor in the grid. Consequently, the reduction of its concentration (C) may not be