Oxygen and sulfur mass-independent isotopic signatures in black crusts: the complementary negative ∆S-reservoir of sulfate aerosols?

Institut de physique du globe de Paris, Université de Paris, CNRS, F-75005 Paris, France. Sorbonne Université, CNRS-INSU, Institut des Sciences de la Terre de Paris, IsteP UMR7193 Paris, France. Department of Earth and Planetary Sciences, McGill University, Montréal, Canada. 10 LATMOS-IPSL Sorbonne Université Université Versailles St.-Quentin, Paris, France. GET, Université Paul Sabatier, Toulouse, France.


Introduction
The oxidation of sulfur dioxide emitted into the atmosphere (between 100 and 110 Tg(SO 2 ) yr −1 ; Klimont et al., 2013) can result in the formation of H 2 SO 4 that forms sulfate aerosols; having light-scattering properties that alter the radiative balance of the planet. Furthermore, they also modify the microphysical properties of clouds through the number and size of cloud condensation nuclei (CCN; e.g., Weber et al., 2001). Although quantified with large uncertainties, the formation of sulfate aerosols results in an Earth surface cooling (Forster et al., 2007), with a negative radiative forcing from −0.62 to −0.21 W m −2 (on average ∼ −0.41 W m −2 ). Overall, sulfate aerosols are the most efficient particles that counterbalance the greenhouse effect (Stocker, 2014). Uncertainties regarding the formation of sulfate aerosols relate to the large variety of oxidants and conditions (e.g., pH), but, in view of their major impact on climate, a more accurate understanding of the formation of these particles is necessary. Given that the oxidants have distinct δ 18 O and 17 O signatures, the SO 2 oxidation pathways are commonly constrained using oxygen multi-isotope ratios (δ 18 O, δ 17 O, and 17 O, defined in the following section) (Alexander et al., 2012;Bindeman et al., 2007;Jenkins and Bao, 2006;Lee and Thiemens, 2001;Savarino et al., 2000;Martin, 2018). Sulfur isotope fractionation during SO 2 oxidation by OH, O 2 TMI, H 2 O 2 , O 3 (Harris et al., 2012a(Harris et al., , b, 2013a, and NO 2 (Au Yang et al., 2018) have been determined, so additional constraints can also be brought by S multi-isotope compositions (δ 34 S, δ 33 S, δ 36 S, 33 S, and 36 S). At present, however, it is difficult to reach a consistent budget for tropospheric SO 2 oxidation (chemically and isotopically). Indeed, most of rural and urban sulfate aerosols have positive 33 S values (Au Yang et al., 2019;Guo et al., 2010;Han et al., 2017;Lin et al., 2018b;Romero and Thiemens, 2003;Shaheen et al., 2014), implying either a source of SO 2 with 33 S > 0 ‰ (which has not been identified yet as all known sources have 33 S ∼ 0 ‰; Lin et al., 2018b) or more likely processes such as SO 2 photolysis in the stratosphere (e.g., Farquhar et al., 2001), contributing to the 33 S-enriched tropospheric sulfate reservoir from initial SO 2 with 33 S = 0 ‰, which should be balanced by a 33 S-depleted reservoir but which remains scarce (see Shaheen et al., 2014;Han et al., 2017;Lin et al., 2018a). Negative 33 S values were suggested to result specifically from combustion (Lee et al., 2002) and/or OCS (carbonyl sulfide) photolysis (Lin et al., 2011). Still, the mass balance among positive and negative 33 S values is not consistent. As none of the most significant tropospheric SO 2 oxidation reactions can account for 33 S anomalies in sulfate aerosols (Au Yang et al., 2018;Guo et al., 2010;Han et al., 2017;Harris et al., 2013b;Lee et al., 2002;Lin et al., 2018a, b;Romero and Thiemens, 2003;Shaheen et al., 2014), this leads to the suggestion that either some reactions or SO 2 sources have been overlooked. Finally, a recent study highlights the possibility of SO 2 oxidation on mineral dust surfaces resulting in 33 S-depleted sulfate deposition in rural environments and subsequent 33 S enrichment of residual SO 2 transported to cities (Au Yang et al., 2019), but the negative 33 S values are still missing. In this respect, black crusts potentially represent new ways to sample the atmosphere in urban regions at a relatively global scale. They are generally formed by the sulfation of the underlying carbonate substrate resulting in a gypsum layer (Camuffo, 1995) (Fig. 1). Due to their degradation effects on monuments and buildings, in particular because the molar volume of CaSO 4 is larger than that of CaCO 3 , several studies investigated sources of sulfur in black crusts, using primarily the isotopic composition of sulfur (δ 34 S) and oxygen (δ 18 O) and microscopic and mineralogical aspects. Anthropogenic sulfur was found to be the major source contributing to monument degradation in several localities compared to marine or volcanic sulfate sources (Longinelli and Bartelloni, 1978;Montana et al., 2008Montana et al., , 2012Torfs et al., 1997). Sulfates from the host rock, i.e., plaster, mortar, or oxidized pyrite (defined as intrinsic in the literature; Klemm and Siedel, 2002;Kloppmann et al., 2011;Kramar et al., 2011;Vallet et al., 2006), and sulfates from aquifer rising by capillarity (Kloppmann et al., 2014) were also identified as sulfur sources in black crusts. Black crusts being sometimes the host of microbial activity (Gaylarde et al., 2007;Sáiz-Jiménez, 1995;Scheerer et al., 2009;Schiavon, 2002;Tiano, 2002), other studies investigated the role of bacteria in gypsum formation through sulfate reduction and/or SO 2 oxidation (Tiano, 2002;Tiano et al., 1975). Except the work of Šrámek (1980) measuring black crust sulfates δ 34 S that rule out the implication of micro-organisms in their formation, no further constraint has been brought so far. In this paper, we present new oxygen and sulfur isotopic composition measurements of sulfate extracted from black crusts and report significant 17 O, 33 S, and 36 S anomalies that help to discuss oxygen and sulfur isotopic variations both in term of source effects to elucidate their origin and in terms of fractionation processes leading to black crust formation in the Paris area. "mass-dependent", meaning the isotopic fractionation relies on the mass differences between the isotopes; this remains valid for most unidirectional (kinetic) and/or exchange (equilibrium) reactions. In a system with at least three isotopes, mass fractionation laws at equilibrium and high temperature can be derived from their partition function (Bigeleisen and Mayer, 1947;Dauphas and Schauble, 2016;Urey, 1947;Young et al., 2002)  O, m being the mass of each isotope, and 17/16 α SO 4 −SO 2 being the isotope fractionation factor between two phases (defined in the introduction). The same equations can be written for 33 S and 36 S.
Here, we will use 17 β, 33 β, and 36 β values (∼ 0.5305, 0.515 and 1.889, respectively) for the high-temperature limit, which has been shown to be applicable for a wide range of temperature phases (Dauphas and Schauble, 2016) and isotope systems (S, Fe, Mg, O, Si, etc.). Thus, the β exponent represents the slope in a δ-δ space, called the "massdependent fractionation line", which is actually approximated from a curve (this simplification is not used in this paper). Deviations from the reference "mass-dependent" curve do not imply necessarily isotopic variations that are independent from the isotope masses. These deviations are quantified with the parameter expressed by Eqs. (1), (2), and (3) (Farquhar and Wing, 2003;Thiemens, 1999): Small nonzero 17 O-33 S-36 S values (typically between −0.1 ‰ and +0.1 ‰) can result from mixing, massdependent processes such as Rayleigh distillation, or mass conservation effects and nonequilibrium processes (Farquhar et al., 2007a;Ono et al., 2006a), whereas large nonzero 17 O− 33 S-36 S values (higher than +0.2 ‰ or lower than −0.2 ‰) imply mass-independent fractionation (Cabral et al., 2013;Delavault et al., 2016;Farquhar et al., 2000Farquhar et al., , 2007bFarquhar et al., , 2002Ono et al., 2003). Oxidation reactions would then change δ 17 O and δ 18 O but not the 17 O, which would primarily vary through mixing of O reservoirs with variable 17 O. Possible mechanisms producing nonzero 17 O-33 S-36 S values recorded in sulfate aerosols are discussed in the following sections. In this paper, we investigate the different processes responsible for the 17 O, 33 S, and 36 S values recorded by black crust sulfates and what can be inferred in terms of black crust formation.

Sampling sites
To access sulfate aerosols from the Parisian region, black crusts were sampled following the prevailing winds according to a NW-SE cross section from Fécamp to Sens (Fig. 2b,  c). Therefore, the studied area covers rural, urban, and industrial zones including four power plants, major highways, and the large Paris metropolis.
A total of 27 samples were collected on the external faces of churches and monuments and on walls in the streets. The substrates were generally Lutetian and Cretaceous limestone, i.e., the typical building rocks in the Parisian basin. To ensure a representative sample of sulfate aerosols, the sampling was carried out preferentially oriented to NW or, if possible, not directly exposed to traffic emissions. Moreover, to avoid sulfate contamination from soils (i.e., salts by capillary action, water from runoff), black crusts were sampled at least at a height of 1.50 m above ground level. More details about the samples are summarized in Table 1.

Methods
An X-ray diffractometer (XRD D2 phaser BRUKER, ISTeP Sorbonne Université) was used to specify the mineralogical nature of each sample and therefore to demonstrate the nature of sulfur. Structural and chemical aspects were subsequently investigated using scanning electron microscopy (SEM, IS-TeP Sorbonne Université).
Sulfates were leached from 20 to 100 mg of black crusts and the conversion of gypsum into pure barite was performed according to the protocol developed at the Institut des Sciences de la Terre de Paris (ISTeP) as described by Le Gendre Table 1. Characteristics of black crust samples. Their name was given according to the city and the department where they are located and following the number of samples gathered at the same place (NA77-1: NA = Nangis; 77 = department; -1 = first sample collected).    . For two NBS127 measurements measured each day during 5 d (n = 10), we obtained a mean δ 18 O = −0.43 ± 0.54 (2σ ) and a mean I. Genot et al.: Oxygen and sulfur mass-independent isotopic signatures 17 O = 0.044 ± 0.020 (2σ ) within error of the recent value reported by Cowie and Johnston (2016). Bao (2006) reported up to 2 ‰ variation in the correction factor that would result from sample impurity, but, as our samples were purified with an ion-exchange resin and the mean variation of the duplicates is lower than for NBS127, we applied a correction factor of 9.03 to δ 18 O for all analyzed samples based on the certified value of NBS127.

Morphological and chemical aspects
After having confirmed the gypsum nature of the sample by X-ray diffraction, the structural and chemical aspects of black crusts from four different environments were investigated on the basis of SEM observations. In agreement with previous studies (Fronteau et al., 2010;Siegesmund et al., 2007), all samples display two distinct layers. An opaque layer (a few tens of micrometers thick) comprising massive and sparse gypsum crystals as well as aggregates of clay minerals and particulate matter was overlying a layer (∼ 100 µm) composed of more crystallized acicular and rosette-like crystal gypsum (tens of micrometers, Fig. 3a). As shown in Fig. 3b, soot is present in both urban and rural encrustations being consistent with previous observations (Guo et al., 2010). Moreover, fly ash particles resulting from coal or oil combustion are present in all environments. Parisian samples (PA13-2 and PA14-1) show many fly ashes of a diameter size < 10 µm (primarily composed of Fe) with small gypsum crystals (few micrometers) on their surfaces (Fig. 3c). This is consistent with the catalyzer effect of combustion particles released by diesel and gasoline vehicles, which increases the rate of SO 2 fixation as sulfate (Rodriguez-Navarro and Sebastian, 1996). Scarce fly ashes were also observed in samples from the city of Mantes-la-Jolie (northwest of Paris).
The sample MR27-1 shows isolated halite crystals (< 10 µm, Fig. 3e), which can result from marine aerosols, in agreement with its location near the sea, and numerous fly ashes (Fig. 3d), most likely from power plants and traffic roads. The dissolution of rhombohedral calcite and subsequent precipitation of gypsum crystals is also illustrated in Fig. 3f.
In summary, the presence of particulate matter and salts highlights several local or distant sources of S-bearing compounds and a prevailing anthropogenic source in the whole Parisian basin atmosphere, which may be distinguished and quantified with the isotopic composition of sulfate.

The δ 34 S-δ 18 O-17 O systematics
Sulfate in black crusts may have multiple origins that could be either primary or secondary. We refer to primary sulfates here as sulfates that are not formed in the atmosphere from SO 2 oxidation. They can originate from the host rock itself where sulfur occurs both as sulfide, such as pyrite that would be subsequently dissolved and oxidized as sulfate, and as carbonate-associated sulfates (CASs), which substitute for carbonate in the lattice. Sulfates in black crusts can also have been directly emitted into the atmosphere for instance by sea spay, resulting in sea-salt sulfate aerosols, or as products of combustion by refineries, vehicle exhaust, or biomass burning; these commonly correspond to "primary sulfates" in the literature. On the contrary, secondary sulfates result from the oxidation of tropospheric S-bearing gases (mainly SO 2 ) and other compounds including dimethyl sulfide (DMS, (CH 3 ) 2 S) by various oxidants (O 3 , H 2 O 2 , OH, O 2 TMI, and NO 2 ). As black crusts are mainly consisted of   (Janssen et al., 1999;Lyons, 2001;Mauersberger et al., 1999) with lower values in the troposphere of ∼ spectively, of their isotopic anomalies to the sulfate, thus resulting in mass-independent fractionation signatures ( 17 O = 8.75 ‰ and 0.65 ‰, respectively) (e.g., Bao et al., , 2001aBao et al., , b, 2010Jenkins and Bao, 2006;Lee et al., 2002;Lee and Thiemens, 2001;Li et al., 2013;Martin et al., 2014 Longinelli and Bartelloni, 1978;Torfs et al., 1997, Kramar et al., 2011, Vallet et al., 2006 and sulfate aerosols from the USA and China (Fig. 5;Bao et al., 2001a;Jenkins and Bao, 2006;Lee and Thiemens, 2001;Li et al., 2013;Romero and Thiemens, 2003). In particular, there is a positive correlation between δ 34 S and δ 18 O covering a large range of variation of ∼ 17 ‰ and ∼ 9 ‰, respectively (Fig. 4), which can be interpreted in two ways: either a process leads to a variable enrichment or depletion of 18 O and 34 S in the crusts or it reflects a mixing between at least one depleted (in both 18 O and 34 S) and one enriched end-member. In the following paragraphs, we discuss in detail the respective roles of several processes (e.g., partial SO 2 oxidation, mixing) that could lead to this correlation and overprint (or not) of the source signatures. As with previous studies, we will conclude that δ 34 S-δ 18 O-17 O values do record a mixing between different (natural and anthropogenic) sources, but addressing the role of processes is important (a prerequisite) to assess the consistency of the 33 S anomaly origin.

Processes affecting O and S isotopic compositions
Firstly, gypsum precipitation would fractionate both O and S isotopes following a slope of 0.67 ± 0.02 (Fig. 4) when considering fractionation factors for 18 O/ 16 O between the dissolved sulfate and the gypsum of ∼ 1.002 or 1.0036 (experimental and natural values, respectively) (Lloyd, 1968). For 34 S/ 32 S, the ranges would be between 1.000 and 1.0024 (Ault and Kulp, 1959;Nielsen, 1974;Raab and Spiro, 1991;Thode et al., 1961), and a Rayleigh-type process in which black crusts represents the cumulated (precipitated) product at different residual fraction F of dissolved sulfates that are leached. However, the slope defined by the samples is steeper, ∼ 1.52 (R 2 = 0.58), implying that the gypsum pre-  ing the black crusts would increase up to ∼ 9 ‰ at maximum when < 10 % SO 2 is oxidized, which cannot explain the ∼ 17 ‰ δ 34 S variation, especially since 40 % oxidized SO 2 is reported (Chin et al., 2000). To generate δ 34 S values as high as 17 ‰, O 3 and H 2 O 2 oxidation pathways should increase drastically (i.e., requiring the absence of an O 2 TMI pathway), predicting an increase of 17 O up to ∼ 6.5 ‰, which is not consistent with 17 O ∼ 0 ‰ associated with high δ 34 S (Fig. 5). Therefore, SO 2 partial oxidation can explain a part of the data but not the whole isotope variations. The large δ 34 S range could also reflect temporal variation, since in Greenland ice cores δ 34 S was > 10 ‰ before the industrial period (Patris et al., 2002), which is dominated by SO 2 from DMS (Sofen et al., 2011) and then decreased < 4 ‰ in the 1960s, which is dominated by anthropogenic SO 2 . Following this variation, black crusts on recently renovated churches should display low δ 34 S and those renovated before the industrial period should display higher δ 34 S. However, samples ME77-2 (δ 34 S = −0.54 ‰) and EV27-1 (δ 34 S = 6.60 ‰) compared to PY89-1 (δ 34 S = 0.46 ‰) gathered on churches restored after World War II and in 1772, respectively, present no significant temporal variation, which might be due to higher proportions of anthropogenic SO 2 emitted recently (0.5 Tg S yr −1 before the industrial period and up to 69 Tg S yr −1 for the present day; Sofen et al., 2011, and references therein). Thus, black crusts do not seem to record temporal isotopic variation, even if samples with δ 34 S = −2.66 ‰ and δ 34 S = 13.99 ‰ should be dated to confirm this assumption. Alternatively, with well-exposed surfaces to precipitation emphasizing wash-out and subsequent reprecipitation, black crusts could rather probe "recent" SO 2 oxidation. So far, no known processes seem to affect the isotopic compositions, which rather probe the source signatures.

Source effects
If δ 34 S-δ 18 O variation reflects mixing of sources, at least two end-members are required. Determined graphically in Figs. 4 and 5, a first one would be 18 O-34 S enriched both around 18 ‰ with a near-zero 17 O, which in view of the sampling cross section from NW to SE and west-dominating winds could correspond to the sea-spray isotopic signature, but available data usually display δ 18 O of ∼ 9 ‰ (Markovic et al., 2016) and δ 34 S ∼ 21 ‰ (Rees et al., 1978), ruling out the occurrence of sea-sprays. With the DMS produced by phytoplankton and oxidized in the atmosphere (1125 Tg S yr −1 ) being higher than sea-salt emissions (6-12 Tg S yr −1 (Alexander et al., 2005, and references therein), with δ 34 S of 15 ‰-20 ‰ (Calhoun et al., 1991), sulfate aerosols deriving from DMS oxidation could rather represent this 18 O-34 S-enriched end-member. However, the absence of a correlation between δ 34 S, δ 18 O, 17 O and the distance from coastline (Fig. S1) and near-zero 17 O for high δ 34 S values (Fig. 5) is not consistent with a signifi-  The depleted end-member is graphically characterized by δ 34 S < −3 ‰ with little constrained δ 18 O from 5 ‰ to 15 ‰ (Fig. 4, dashed box "An") and 17 O from ∼ 0 ‰ to 2.6 ‰ (Fig. 5, dashed box An). Sulfates from dissolved and oxidized sedimentary pyrites contained in the building carbonate stone are known to have δ 34 S < −12 ‰ (since at least the last 500 Myr; Canfield, 2004). Despite a sulfide content that can vary between a few tens to thousands of parts per million (Thomazo et al., 2018), our sampled carbonate stones are very whitish, suggesting a low sulfide content. Even if it would certainly not affect the mass balance, we took into account pyrite oxidation, as other studies did on black crusts (Kramar et al., 2011;Vallet et al., 2006). With the S isotope fractionation factor during pyrite oxidation being negligible (between 0.996 and 1; Thurston et al., 2010, and references therein) compared to O isotopes, we modeled the δ 18 O variation according to a Rayleigh distillation to represent the sulfide oxidation, commonly occurring via O 2 + H 2 O at the atmosphere-carbonate building stone interface. With an initial δ 18 O of ∼ −6 ‰ of rainwater in the Paris Basin and a mean 18 α water-sulfate of 1.010 (Gomes and Johnston, 2017), sulfates from pyrite oxidation would have δ 18 O of ∼ 4 ‰ and as low as −6 ‰ if water would be in limited amounts (i.e., residual fraction of water F ∼ 0). Very recently, pyrite oxidation was hypothesized to occur via O 3 (Hemingway et al., 2019), which would lead to positive 17 O of sulfates with low δ 34 S, explaining the depleted end-member. However, our data are strikingly higher than for black crusts from Ljubljana (Slovenia; Kramar et al., 2011), which show δ 34 S as low as −20 ‰ and δ 18 O between −2 ‰ and 5 ‰ (Fig. 4) that would be typical for pyrite oxidation. Besides, there is so far no evidence for a higher oxidation flux of pyrite via O 3 than major constituents as H 2 O and O 2 . This means that another source should have negative δ 34 S. Anthropogenic sulfur represents ∼ 60 % of the total sulfur released worldwide and includes primary sulfates as oil, coal, and biomass combustion products as well as SO 2 emission that can be oxidized into secondary sulfates. When considering coal and oil combustion, δ 34 S can vary largely between −30 ‰ and 32 ‰ (e.g., Faure, 1986). More locally, a recent study reported a narrow range from −0.57 ‰ to 11.33 ‰ for sulfur emitted by transport and industries in Paris (Au Yang et al., 2020). Lee et al. (2002) (Lee and Thiemens, 2001), corresponding to secondary sulfate aerosols (named An in Figs. 4 and 5). As the distinction between primary and secondary sulfate aerosols having near-zero 17 O is not possible, we assume a mixing with only two end-members, CAS/Plaster and anthropogenic sulfur (primary and secondary). Furthermore, in view of the O isotope variability caused by the oxidation, mixing proportions were calculated based only on δ 34 S values. We chose the end-members graphically and in agreement with the literature, i.e., a CAS/PL δ 34 S value of 18 ‰, in the range from 11 ‰ to 24 ‰ (Kloppmann et al., 2011;Rennie and Turchyn, 2014;Turchyn et al., 2009) (Fig. 4) and an An δ 34 S value of −3 ‰, similar to Montana et al. (2008) as well the closest to sulfates measured in Paris. CAS/PL proportions range from 2 % to 81 % with an average of ∼ 32 %. With an extreme δ 34 S of −10 ‰ for the An end-member, encompassing black crusts from Antwerp, the CAS/PL proportion averaged 49 %. This highlights that host-rock sulfate is on average not the main S provider, and that black crusts record atmospheric sulfate aerosols. Excluding the most "contaminated" samples by CAS/PL and assuming that those having 17 O > 0.65 ‰ obviously represent SO 2 oxidized by O 3 and H 2 O 2 , the minimum proportion of MIF-bearing sulfates, and hence secondary sulfates, can be estimated at ∼ 63 %, which is close to estimations by Lee and Thiemens (2001) and Sofen et al. (2011). In summary, black crusts sample significant amounts of atmospheric SO 2 and complement existing sampling such as aerosols, which allow us to address the origin of the 33 S anomaly.  (Table 2). These values are quite unusual compared with anthropogenic and natural aerosols. As illustrated by Fig. 6, black crust sulfate 33 S values are all negative, and it is worth noting that this depletion occurs with near-constant 36 S values. This is somewhat distinct from most aerosols, which display almost exclusively positive 33 S values up to ∼ 0.5 ‰ and both positive and negative 36 S values (Au Yang et al., 2019;Guo et al., 2010;Lin et al., 2018b;Romero and Thiemens, 2003;Shaheen et al., 2014). So far, the only negative 33 S values down to −0.6 ‰ were measured in sulfate aerosols from Beijing (China) during winter months (Han et al., 2017) (no 36 S values provided), and these values were assumed to result from incomplete combustion of coal. This assumption ultimately relies on the work of Lee et al. (2002), which showed that primary anthropogenic aerosols formed by high-temperature combustion (e.g., diesel) result in near-zero 33 S-36 S values, whereas those formed by low-temperature combustion (e.g., biomass burning) result in 33 S down to −0.2 ‰ and 36 S values varying between −1.9 ‰ and 0.2 ‰ (data recalculated with 36 β = 1.9). Negative 36 S values well correlated with biomass burning proxies are also reported in East China (Lin et al., 2018b), although 33 S was ∼ 0 ‰. As in many other cities, Paris has long been affected by coal and wood burning, we can hypothesize that 33 S-36 S variations result from high-and/or low-temperature combustion processes. Some black crust sulfates with near-zero 33 S-36 S values could result from high-temperature combustion, but this would not explain negative 33 S-36 S values. Furthermore, according to Lin et al. (2018b), low-temperature combustion would preferentially fractionate 36 S over 33 S, which should result in a steep slope in 33 S-36 S space. The trend defined by our black crust samples shows higher 33 S fractionation than 36 S with 33 S values lower than those obtained by available low-temperature combustion experiments (< −0.2 ‰; Lee et al., 2002) and with 36 S values in the range of aerosols. Furthermore, no 33 S evolution is observed in black crusts sampled on churches with different ages of renovation (see Sect. 5.1; ME77-2 33 S = −0.21 ‰; EV27-1 33 S = −0.05 ‰; and PY89-1 33 S = −0.21 ‰), whereas we would expect a 33 S increase in black crusts from −0.2 ‰ to 0 ‰ due to the reduction of sulfur emission from low-temperature replaced by high-temperature combustion processes. Therefore, available data highlight that neither high-nor low-temperature combustion processes are responsible for low 33 S measured in black crusts.
With a part of black crust sulfates being atmospheric in origin, isotopic effects during SO 2 oxidation could be responsible for 33 S-36 S variations. To better address this issue, we calculated the 33 S-36 S values of sulfates predicted by each of the main SO 2 oxidation pathways and by a mixing of them in the proportions given by Sofen et al. (2011). We  Romero and Thiemens (2003); and Shaheen et al. (2014), while the combustion process reflects samples from Lee et al. (2002). Modeled 33 S-36 S values of cumulated black crusts (BC) sulfates -formed by SO 2 wet and dry deposition with a magnetic isotope effect (MIE; 33 S depletion compared to initial SO 2 with constant negative 36 S) and of cumulated secondary aerosols formed by SO 2 oxidation by O 3 , O 2 TMI, OH, and H 2 O 2 ( 33 S enrichment compared to initial SO 2 ) from an initial SO 2 with 33 S-36 S = 0 ‰ -are reported with corresponding β exponents (see Sect. 5.2.2 for model explanation). Residual SO 2 and global cumulated BC plus secondary aerosol isotopic compositions were not reported for better readability. Percentages indicate the fraction of produced cumulated BC and secondary aerosols.
(see caption text). We also used NO 2 values (Au Yang et al., 2018) and T -dependent equations determined by Harris et al. (2013b) to calculate each 34 α with initial sulfur dioxide 33 S and 36 S of 0 ‰ (Lin et al., 2018b). As mentioned earlier (Au Yang et al., 2018;Harris et al., 2013b), none of these models can account for anomalous 33 S-36 S values in either aerosols or in black crusts (Fig. 6). Although oxidation with O 2 TMI at T = 50 • C could produce negative 33 S down to −0.37 ‰, which would account for the lowest 33 S observed in black crusts, this oxidation pathway would also produce larger 36 S down to −1.50 ‰ at odds with the 36 S reported in the black crust. Their potential combination cannot account for sulfate aerosol data from the literature (Au Yang et al., 2019;Guo et al., 2010;Lin et al., 2018b;Romero and Thiemens, 2003;Shaheen et al., 2014) or for the black crust as it would result in slightly negative 33 S-36 S values that could not explain the 33 S as low as −0.34 ‰ (yellow frames in Fig. 6). Available literature data are therefore not consistent with the anomalous 33 S-36 S values recorded in black crust sulfates.
Mass-dependent processes can also result in small 33 S-36 S variations, depending on the magnitude of the 34 S fractionation (Ono et al., 2006a). As mentioned in Sect. 5.1.2, a mixing between a 33,34 S-depleted end-member (An) consisting of anthropogenic sulfur (δ 34 S = −3 ‰, 33 S = 0 ‰) and a 33,34 S-enriched sulfates end-member (CAS/PL) from plaster or CAS (δ 34 S = 18 ‰, 33 S = 0 ‰) would result in small 33 S values of −0.01 ‰ for 50 % mixing, which is far from the maximum measured 33 S of ∼ −0.34. Moreover, the slope between 33 S-36 S would be about −7, which is at odds with our observations. Therefore, we conclude that mixing cannot account for the black crust 33 S-36 S variations.

A new oxidation pathway implying magnetic isotope effect
Several studies proposed that positive 33 S measured in sulfate aerosols, with 33 S up to 0.5 ‰, from, for example, East China and California could result from stratospheric fallout of SO 2 (with 33 S potentially up to 10 ‰ higher; Ono et al., 2013), which underwent UV photolysis by short-wavelength radiation (Romero and Thiemens, 2003;Lin et al., 2018a, b). This suggestion primarily relies on the similarities between 33 S-36 S values of sulfate aerosols and laboratory experiments of SO 2 photolysis conducted at different wavelengths (Romero and Thiemens, 2003) and on the correlation between 35 S-specific activity and 33 S values (Lin et al., 2018b). However, these studies never addressed the absence of the complementary negative 33 S reservoir, which is required to balance the positive 33 S reservoir (see Au Yang et al., 2019). In this respect, it is worth mentioning that volcanic and stratospheric aerosols trapped in Antarctic ice cores (see Gautier et al., 2018, and references therein) show both positive 33 S (up to ∼ 2 ‰) and complementary negative 33 S values (down to −1 ‰) and weighed average 33 S = 0 ‰ explained by prior partial deposition. Stratospheric fluxes are actually too low to account for 33 S > 0.1 ‰ (Lin et al., 2016;Au Yang et al., 2019). Accordingly, some other authors rather tried to explain the positive anomalies of most aerosols with "tropospheric" chemical reactions, which are SO 2 oxidation by the main oxidant including NO 2 , H 2 O 2 , OH, O 3 , and O 2 TMI, but experimental data result in a maximum 33 S values of ∼ 0.2 ‰ for all studied reactions (Au Yang et al., 2018;Harris et al., 2013b). Isotope effects associated with SO 2 oxidation by minor species, such as Criegee radicals, remains to be investigated (Au Yang et al., 2018). In summary, whatever the stratospheric vs. tropospheric origin of positive 33 S values recorded by most aerosols, there is a 33 S isotope imbalance and a missing reservoir with negative 33 S that must exist. Han et al. (2017) reported 33 S values down to −0.6 ‰ in sulfate aerosols from Beijing. As discussed above, the authors' suggestion calling for lowtemperature combustion is little supported by available data, and clearly the very restricted location and time interval, over a month, where these anomalies occurred cannot counterbalance, both spatially and temporally, the common positive 33 S values of most aerosols; the missing reaction or reservoir requires, instead, to be ubiquitous worldwide.
In this study, black crust sulfates display negative 33 S values (from ∼ 0 ‰ down to −0.34 ‰). These values are certainly produced by tropospheric chemical reactions. Otherwise, they would have, according to the stratospheric origin model, the same sign as those measured among aerosols. Furthermore, the chemical reactions (or reaction) involved in the formation of black crusts must be distinct compared to those leading to the formation of tropospheric aerosols. As developed thoroughly, black crusts could well represent the missing sulfur reservoir.
An additional observation is that negative 33 S values occur with near-constant 36 S (from −0.76 ‰ to −0.22 ± 0.20 ‰; Fig. 6). This signature is typical of the magnetic isotope effect (MIE), which involve a radical pair, where coupling between the nuclear magnetic moment of the nucleus of odd isotopes and the electron occurs, allowing for electron spin transition from singlet to triplet (or vice versa) (Buchachenko et al., 1976). This leads to distinct half-lives between odd and even isotopes, resulting in specific odd over even isotope enrichment (or depletion). MIE has been so far reported for various reactions occurring on a surface (Buchachenko, 2001(Buchachenko, , 2000Turro, 1983) such as sulfate thermochemical reduction (Oduro et al., 2011) or Fe reduction in magneto-tactic bacteria (Amor et al., 2016), which are the most geologically relevant. It is worth pointing out that MIE could also be responsible for positive 17 O values measured in black crusts, i.e., as opposed to the 17 O anomaly being inherited from SO 2 oxidants. However, Lee et al. (2002) also measured the O multi-isotope compositions of sulfate aerosols (i.e., from the atmosphere as opposed to reaction on a solid substrate) from Paris and obtained 17 O = 0.2 and 0.8 ‰ for the Paris highway and in the 13th zone, respectively, which is in good agreement with our three samples collected in Paris (from 0.17 ‰ to 0.89 ‰). Thus, this is consistent with black crust formation recording mostly an atmospheric signal and no significant magnetic isotope effect on 17 O.
The magnetic effect could occur on a surface such as on mineral dust suspended in the atmosphere during aerosol formation, leading to residual 33 S-depleted atmospheric SO 2 from which black crusts would subsequently form. This model would, however, predict that some sulfate aerosols subsequently formed to display negative 33 S values: such values are extremely uncommon, being primarily restricted to the Beijing winter months (Han et al., 2017). Instead, the magnetic effect could occur during black crust formation, on the carbonate building stone, leading to residual 33 Senriched atmospheric SO 2 from which tropospheric aerosols would subsequently be formed, which is consistent with available observations. This model would, however, predict some black crust subsequently formed to display positive 33 S: such values have not been found yet and this may well reflect sample bias, with our data being the first reported for such samples. Both scenarios imply nonzero 33 S values of residual atmospheric SO 2 , which contrast with the data by Lin et al. (2018b) showing 33 S of ∼ 0 ‰ (n = 5, 33 S varying from −0.04 ‰ to 0.01 ± 0.01 ‰). Given that, in the study of Lin et al. (2018b), SO 2 was sampled close to the third largest Chinese megacity, such nonzero 33 S values may thus be rather symptomatic of emitted (i.e., anthropogenic) SO 2 rather than residual or background (i.e., after significant black crust and aerosols formation). SO 2 in the Paris Basin still has to be measured to confirm this assumption, but, so far, this could be consistent with the interpretation that nonzero 33 S values of residual or background atmospheric SO 2 are erased by anthropogenic SO 2 having zero 33 S values (Au Yang et al., 2019) moving towards the local source(s) of anthropogenic SO 2 .
In the absence of additional observations, proposing a chemical reaction, and hence a radical pair that breaks and recombines, would be very speculative, but our data clearly point towards the occurrence of a magnetic effect during the formation of black crusts, involving ubiquitous heterogeneous chemical reactions. This is supported by previous recognition of sulfur radicals such as SO − x (Herrmann, 2003) or S-S (see Babikov, 2017. But note that their 36 S/ 33 S slope is distinct from ours). Clearly, the reaction does not occur after sulfate formation such as during dissolutionprecipitation mechanisms, which do not involve any radical species. As mentioned above, magneto-tactic bacteria can produce MIE when reducing Fe (Amor et al., 2016). With microbial activity being sometimes present on black crusts (Gaylarde et al., 2007;Sáiz-Jiménez, 1995;Scheerer et al., 2009;Schiavon, 2002;Tiano, 2002), the involvement of microorganisms, affecting only the sulfur isotopes as the most negative 33 S, does not correspond to the most negative 17 O, which represents another possibility to investigate. Another implication that can be tested in future work is that the kinetics of heterogeneous reactions leading to sulfate and black crust formation should be comparable or faster than those leading to aerosol formation. So far, Li et al. (2006) showed comparable loss of atmospheric SO 2 by heteroge- Figure 7. Modeled δ 34 S and 33 S values of black crust (BC) sulfates (instantaneous and cumulated) formed by SO 2 wet and dry deposition with a MIE ( 33 S depletion compared to initial SO 2 ) and of secondary aerosols (instantaneous and cumulated) formed by SO 2 oxidation by O 3 , O 2 TMI, OH, and H 2 O 2 ( 33 S enrichment compared to initial SO 2 ) from an initial SO 2 with δ 34 S =1 ‰ and 33 S = 0 ‰ (red point). 33 S enrichment of residual SO 2 and global cumulated BC plus secondary aerosol isotopic compositions are also reported. Percentages indicate the fraction of produced cumulated BC and secondary aerosols (see Sect. 5.2.2 for model explanation). Black crust sulfate isotopic compositions (dark gray points) can be explained by a mixing (red triangle) between sulfates from CAS/plaster (dashed square, δ 34 S = 18 ‰ and 33 S = 0 ‰; see Sect. 5.1), primary anthropogenic sulfates (dashed square, δ 34 S = −3 ‰ and 33 S = 0 ‰), and sulfates formed by wet and dry deposition of SO 2 undergoing a MIE and oxidized SO 2 forming secondary aerosols (cumulated BC sulfates and cumulated BC neous oxidation on calcium carbonate substrates and by gasphase oxidation. Our conclusions show a strong analogy with the model of Au Yang et al. (2019), who suggest that SO 2 photooxidation on mineral dust could form sulfate aerosols depleted in 33 S that would then be deposited. The residual SO 2 would be subsequently enriched in 33 S, then be oxidized by common O 3 , H 2 O 2 , O 2 , or OH oxidants. Their 33 Sdepletion mechanism was not further constrained, except that it was speculated to be photochemical in origin.
If correct, this view requires reassessing the overall S isotope fractionation during SO 2 atmospheric reaction. So far, previous studies assumed that the overall sulfur isotopic fractionation between the wet and dry deposit and oxidized SO 2 was equal to 1 (i.e., no isotope effect), but negative 33 S in black crusts is inconsistent with such an assumption.
Starting with an SO 2 33 S value of 0 ‰ (Au Yang et al., 2018;Lin et al., 2018b) and forming oxidized (sampled by secondary aerosols) and wet and dry deposit (sampled by black crusts) reservoirs with 33 S values up to 0.50 ‰ down to −0.34 ‰, respectively, mass balance implies that SO 2 dry and wet depositions and secondary sulfate aerosols represent ∼ 60 % and 40 %, respectively. This is in good agreement with proportions obtained by Chin et al. (2000) and quoted by Harris et al. (2013b). Therefore, we conclude that MIE happening during SO 2 dry and wet depositions could be a viable mechanism responsible for 33 S enrichment of secondary sulfate aerosols and that black crusts could represent the 33 Snegative complementary reservoir.
In order to better apprehend the aerosols and black crust complementarity, we modeled the S isotopic fractionation of both black crusts and aerosols during SO 2 oxidation (Figs. 6 and 7). We assumed a Rayleigh distillation model to represent the atmosphere-building-stone interface open system. The global fractionation factor between residual SO 2 and oxidized (secondary aerosols) plus deposited (black crusts) SO 2 is defined as with A and B being the proportions of SO 2 deposited and oxidized, being equal to 60 % and 40 %, respectively. This allows us to deduce the 33,34,36 α BC-SO 2 and the associated 33,36 β factors. A δ 34 S of 1 ‰ for the initial SO 2 was considered to obtain black crusts of at least −3 ‰ (see Sect. 5.1.2) and 33 S-36 S = 0 ‰; 34 α aerosols-SO 2 was taken as 1.0097 as calculated using the different oxidation channel proportions of Sofen et al. (2011). With the oxidation being mass dependent, we chose 33,36 β aerosols-SO 2 values of 0.515 and 1.9, respectively (Harris et al., 2012b). The best fit is obtained for 34 α BC-SO 2 = 0.9985, 33 α BC-SO 2 = 0.9986, and 36 α BC-SO 2 = 0.9972 with 33,36 β = 0.9 and 1.9, respectively. The 33 S enrichment in secondary sulfate aerosols is well represented by this parameterization (instantaneous and cumulated products; Figs. 6 and 7). The concomitant 33 S depletion in modeled cumulated deposit is also well represented. The 33 S isotopic fractionation occurring during the MIE is higher than the one observed in black crusts. To a first-order approximation, this model works, predicting the total cumulated products of black crusts and aerosols to have 33 S values of −0.23 ‰ and 0.35 ‰, respectively. The match is not perfect, which does not entirely capture the black crust isotopic compositions. But remember that black crusts are produced from anthropogenic Parisian SO 2 , whereas aerosols formed in other locations possibly formed from distinct anthropogenic SO 2 δ 34 S values. In addition, we are aware that our model strongly depends on oxidation pathways estimated by Sofen et al. (2011), which vary spatially and temporally. The main weakness is the poorly constrained estimate of intrinsic S-bearing compounds (CAS/plaster end-member) in Figure 8. Scheme summarizing the sulfur sources and processes that lead to black crust formation. Sulfur dioxide releases by anthropogenic activities can either be oxidized in the atmosphere by H 2 O 2 , O 3 , OH, O 2 TMI and formed secondary sulfate aerosols that will react with the carbonate building stone to produce 33 S-enriched black crust sulfates or be deposited, as dry and wet deposit, on the carbonate substrate where its oxidation into SO − x then sulfates through MIE will produce 33 S-depleted black crust sulfates and a 33 S-enriched residual SO 2 (source 3). Primary sulfates emitted by anthropogenic activities (source 2) or carbonate-associated sulfates and/or plaster of the host rock (source 1) are also likely sources contributing to black crust formation.
the host rock as well as sulfate aerosols ( 33 S > 0 ‰), which dilutes the 33 S anomaly, lowering the overall black crust 33 S. Ultimately, black crusts result mainly from the deposition followed by oxidation of SO 2 on the building stone rather than aerosol accumulation. The δ 34 S value of initial anthropogenic SO 2 is another poorly constrained parameter whose variability might be difficult to estimate both spatially and temporally.
In conclusion, black crusts could represent the complementary sulfur end-member to sulfate aerosols. Its fractionation factor is relatively restricted (−1.5 ‰) and is thus likely identifiable from its negative 33 S values. Our model is actually consistent with the assumption that the global SO 2 oxidation occurs with little fractionation ( 34 α global = 1.00298) as commonly done in the literature. Finally, Fig. 8 summarizes the different sulfur sources involved in the black crusts as well as the processes leading to their formation. Black crust isotopic compositions could thus be explained by a mixing between sulfates from CAS/plaster (δ 34 S ∼ 18 ‰ and 33 S = 0 ‰; see Sect. 5.1 and 1 in Fig. 8), primary anthropogenic sulfates (δ 34 S ∼ −3 ‰ and 33 S = 0 ‰; see 2 in Fig. 8), and wet and dry deposition of SO 2 undergoing MIE during its oxidation on the building stone combined with secondary aerosols (see red triangle in Fig. 7 and process 3 in Fig. 8).

Conclusions
Our study shows that black crusts do preserve an atmospheric signal of SO 2 oxidation, inferred from the nonzero 17 O. Part of the sulfate originates from the surrounding plaster and/or from the stone itself, but overall > 60 % originates from anthropogenic activities. We also discovered negative 33 S values with near-constant 36 S signatures, which probably reflect the magnetic isotope effect involving a new oxidation pathway. The magnetic isotope effect is supposed to occur during the deposition of SO 2 on the building stone surface (most likely carbonate), where SO 2 is oxidized to sulfate, leading to a 33 S depletion in black crust sulfates. Therefore, the resulting 33 S enrichment of residual SO 2 could account for positive 33 S values of sulfate aerosols observed worldwide, making black crust sulfates their complementary 33 S reservoir.
Data availability. All data needed to draw the conclusions in the present study are shown in Table 2 and/or the Supplement. For additional data related to this study, please contact the corresponding author (genot@ipgp.fr).
Author contributions. IG conducted oxygen isotope measurements under the supervision of EM and ELG at IPGP. DAY conducted sulfur isotope measurements at McGill University. IG and EM collected the samples. IG, PC, EM, and DAY interpreted the data. IG wrote the paper with contributions from all coauthors. EM and MR conceived the project.