A Global Assessment of the Controls on the Fractionation of Arc Magmas

During the differentiation of arc magmas, fractionating liquids follow a series of cotectics, where the co‐crystallization of multiple minerals control the melt compositional trajectories, commonly referred to as liquid lines of descent (LLD). These cotectics are sensitive to intensive properties, including fractionation pressure and melt H2O concentration, and changes in these variables produce systematic differences in the LLDs of arc lavas. Based on a compilation of experimental studies, we develop two major element proxies that exploit differences in LLDs to constrain the fractionation conditions of arc magmas. Near‐primary fractionating magmas evolve along the olivine‐clinopyroxene cotectic, which is pressure‐sensitive. We use this sensitivity to develop a proxy for early fractionation pressure based on the normative mineral compositions of melts with 8 ± 1 wt.% MgO. Fractionation in more evolved magmas is controlled by the clinopyroxene‐plagioclase cotectic, which is strongly sensitive to magmatic H2O contents. We use this relationship to develop an H2O proxy that is calibrated to the normative mineral components of melts with 2–4 wt.% MgO. These two proxies provide new tools for estimating the variations in pressure and temperature between magmatic systems. We applied these proxies to compiled major element data and phenocryst assemblages from modern volcanic arcs and show that in island arcs early fractionation is relatively shallow and magmas are dominantly H2O‐poor, while continental arcs are characterized by more hydrous and deeper early fractionation. These differences likely reflect variations in the relative contributions of decompression and flux melting in combination with distinct upper plate controls on arc melt generation.

During crystallization, the removal of cumulate minerals from differentiating magmas produces distinct compositional trends that are commonly referred to as liquid lines of descent (LLD). Critically, with progressive fractionation, all melt compositions converge to cotectics where the fractionating mineral assemblages do not vary. The locations and trajectories of these cotectics do not chiefly depend on the initial melt bulk composition but on intensive properties such as pressure, H 2 O concentration and oxygen fugacity. Therefore, the major element LLDs along which arc magmas evolve do not primarily depend on the parental melt composition but on the conditions under which the magmas fractionate. Variations in fractionation conditions can therefore be inferred from the distinct compositional trends generated along LLDs (e.g., Parman et al., 2010;Zimmer et al., 2010). In this study, we develop two proxies that relate differences in major element LLDs to melt H 2 O contents and fractionation pressure. We then apply these proxies to a global compilation of arc lava compositions to identify first order differences in fractionation conditions among active arcs.

Existing Methods to Estimate Magma H 2 O Contents and Fractionation Pressure
Several techniques exist to estimate pre-eruption magmatic H 2 O contents and fractionation pressures. These methods can broadly be divided into three groups: (a) direct measurements, typically of melt inclusions; (b) mineral-melt equilibria, based on either the partitioning of hydrogen in nominally anhydrous minerals, or on H 2 O-sensitive mineral-liquid exchange reactions; and (c) experimentally constrained liquid lines of descent. We will discuss existing LLD-based methods in the context of our new proxies below, but first offer a brief summary of the other approaches.
The most direct technique to constrain pre-eruptive H 2 O contents is to measure the H 2 O contents of melt inclusions trapped in phenocrysts (e.g., Portnyagin et al., 2007;Ruscitto et al., 2012;Sisson & Layne, 1993). If the melt inclusion H 2 O content is not modified post-entrapment, this approach can directly constrain the original H 2 O contents of the magma. Further, when H 2 O and CO 2 are both present in melt-inclusions, minimum entrapment and hence fractionation pressures can also be constrained (Newman & Lowenstern, 2002). Primary limitations to this technique are that vapor-saturated melts may degas prior to melt inclusion formation, and melt inclusions are susceptible to rapid post-entrapment diffusive re-equilibration, especially of hydrogen (Bucholz et al., 2013;Gaetani et al., 2012), which modifies the apparent melt H 2 O contents and oxidation state. To minimize the effects of diffusive re-equilibration, melt inclusion studies are often restricted to relatively recently erupted ash and scoria (Lloyd et al., 2013).
Mineral-melt partitioning-based hygrometers and barometers provide valuable information on the conditions of magmatic differentiation. The plagioclase-melt hygrometer (Lange et al., 2009;Waters & Lange, 2015), based on the strongly H 2 O-dependent distribution of the anorthite component between plagioclase and melt, is the most commonly used mineral-melt hygrometer. A range of mineral-melt barometers have also been developed, many of which are derived from the pressure sensitivity of Al-rich components in pyroxenes (e.g., Neave & Putirka, 2017;Putirka, 2008Putirka, , 2016. The primary limitation of all mineral-melt approaches lies in the evaluation of primary equilibrium as well as the need for independent temperature estimates. Alternatively, melt H 2 O contents can be constrained by directly measuring the hydrogen contents of nominally anhydrous minerals (NAMs, e.g., Mitchell et al., 2017;Urann et al., 2022). For minerals with experimentally constrained hydrogen partition coefficients (i.e., garnet, olivine, clinopyroxene), this method expands our ability to estimate primary H 2 O contents to systems that are otherwise difficult to constrain. However, the H 2 O contents of NAMs are difficult to measure and re-equilibration due to rapid hydrogen diffusion frequently destroys the record of primary H 2 O contents (e.g., Demouchy et al., 2006).
While both melt-inclusion and mineral melt-based estimates of magmatic H 2 O contents and pressures provide valuable constraints, their application is restricted by the availability of appropriate samples, that is, lavas containing the necessary phenocrysts and a glassy matrix or melt inclusions. A complementary approach for investigating global arc magma systematics is to use the whole rock compositions of erupted magmas to locate pressure-and H 2 O-sensitive cotectics in compositional space.

Major Element Proxies for Variations in Liquid Lines of Descent
In this study, we develop two proxies that relate variations in major element liquid lines of descent in arc magmas to differences in their fractionation conditions. We rely on the large number of experimental studies investigating liquid lines of descent in tholeiitic and calc-alkaline systems to infer the relationships between conditions of fractionation and LLD compositional trajectories (experimental studies summarized in Table S1 of the Supporting Information S1). Many of these studies provide clear examples of how LLDs change in response to different fractionation pressures vs. Ulmer et al., 2018Villiger et al., 2004vs. Villiger, Ulmer, & Müntener, 2007 and magmatic H 2 O contents (Alonso-Perez et al., 2009;Melekhova et al., 2015;Nandedkar et al., 2014vs. Villiger, Ulmer, & Müntener, 2007. Based on these experiments, a representative simplified fractionation sequence can be defined for arc basalts across a range of experimental conditions: Most primitive arc magmas last equilibrate with the sub-arc mantle at conditions where they are multiply saturated in olivine, orthopyroxene and clinopyroxene, typically at 10-18 kbars and 1,220-1,350°C (for recent compilations of multiple saturation points see Till, 2017). At pressures greater than this multiple saturation point, clinopyroxene becomes the liquidus phase, while olivine is the liquidus phase at lower pressures. Concomitantly, the temperature difference between the olivine-liquidus and clinopyroxene-in increases with decreasing pressure: at pressures just below the multiple saturation point, clinopyroxene is rapidly added to the fractionating assemblage, while at lower pressures, the olivine liquidus field expands resulting in prolonged olivine-only fractionation prior to clinopyroxene-in. By contrast, in dry magmas fractionating at low pressures (as is typical at many mid-ocean ridges), plagioclase may stabilize before clinopyroxene but only after extensive olivine-only fractionation. Thus, during fractionation at relatively high pressures, the liquid line of descent exhibits only a limited initial enrichment in clinopyroxene-forming oxide components (e.g., CaO), while at lower pressures a much larger CaO-enrichment interval is observed, and this difference persists during differentiation following the olivine-clinopyroxene cotectic ( Figure 1a).
As melts continue to evolve along the LLD, plagioclase joins the fractionating assemblage. Continuing silica enrichment during differentiation makes the melts lose olivine-saturation, either by olivine-consuming peritectic reactions that produce orthopyroxene or through fractional crystallization. Numerous prior studies have established that increases in melt H 2 O contents cause a decrease in plagioclase stability (Eggler, 1972;Gaetani et al., 1993;Sisson & Grove, 1993a), and that the first appearance of plagioclase is strongly controlled by H 2 O contents but is relatively pressure insensitive at crustal pressures (Eggler, 1972). Therefore, plagioclase-forming components such as Al 2 O 3 passively increase in fractionating melts until plagioclase joins the crystallizing assemblage ( Figure 1b). Consequently, a delay in plagioclase-in will increase the maximum observed Al 2 O 3 contents along any liquid line of descent, an observation previously used to constrain melt H 2 O contents (Parman et al., 2010;Pichavant & Macdonald, 2007;Sisson & Grove, 1993b). Continuing fractionation proceeds along the clinopyroxene-plagioclase (±amphibole) cotectic for an extended interval, typically until the system reaches at least intermediate SiO 2 contents at temperatures below ∼1,050°C in H 2 O-poor systems and below ∼900°C in H 2 O-rich systems.
Additional phases may also be stable during arc magma fractionation: at elevated pressures (>8-10 kbars), garnet may become a fractionating phase, particularly in more evolved compositions (Alonso-Perez et al., 2009;Ulmer et al., 2018). Hornblende plays an important role in the fractionation sequence of hydrous magmas , but rarely appears before the melt has cooled below 1,050°C (Melekhova et al., 2015;Nandedkar et al., 2014;Ulmer et al., 2018); amphibole appears as a near-liquidus phase only in H 2 O-saturated basaltic magmas (Krawczynski et al., 2012;Stern et al., 1975). Orthopyroxene occurs mostly in minor abundances but can become a more important phase in systems with SiO 2 -rich primitive compositions (e.g., Grove et al., 2003;Ulmer et al., 2018). Finally, FeTi-oxides are present in evolved arc sequences and stabilize earlier on wet than on dry LLDs (Sisson & Grove, 1993a). Despite potential complications from these additional phases, the early portions of the LLDs of most arc magmas can be readily understood from the fractionation systematics of olivine, clinopyroxene and plagioclase.
The pressure dependency of CaO-enrichment was previously described in dry MORB systems (Langmuir et al., 1992), and the systematics of the olivine-clinopyroxene cotectic form the basis of multiple barometers applied to MORB LLDs (Danyushevsky et al., 1996;Herzberg, 2004;Michael & Cornell, 1998;. Melekhova et al. (2015) also used the pressure sensitivity of the olivine-clinopyroxene cotectic in variably hydrated parental magmas from the Lesser Antilles to deduce their pressures of fractionation. Similarly, the suppression of plagioclase crystallization by H 2 O has been leveraged to infer magmatic H 2 O contents using the relations between melt H 2 O contents and either the maximum Al 2 O 3 recorded in lavas sampling a common LLD (Parman et al., 2010) or the Al 2 O 3 content in melts multiply saturated with olivine, 4 of 36 plagioclase, and clinopyroxene or hornblende (Pichavant & Macdonald, 2007;Sisson & Grove, 1993b). Each of these hygrometers is restricted to a relatively narrow range of basaltic to basaltic-andesite compositions where plagioclase first stabilizes. In the following sections we develop proxies for fractionation pressure and melt H 2 O contents based on the olivine-clinopyroxene and clinopyroxene-plagioclase cotectics respectively and show that these proxies are robust for a range of arc magma compositions. We begin by first describing the compiled database of experimental liquids and our approach to developing the H 2 O and pressure proxies.

Experimental Liquid Database
A total of 1,248 experimental liquids were compiled from 54 publications (summary of compiled experimental publications available in Table S1 of the Supporting Information S1). Publications with experiments conducted Figure 1. Illustration of liquid lines of descent (LLD) determined from fractional crystallization experiments for basaltic starting compositions at different pressures and initial water contents. In each panel, symbols denote phenocryst assemblage, and color and symbol are used to distinguish experimental pressures and hydration states. (a) The LLD of magmas shown in MgO-CaO space. Three segments are observed in these LLDs, corresponding to olivine only, olivine + clinopyroxene and clinopyroxene + plagioclase ± amphibole cotectics. The gray vertical bar centered on 8 wt. % MgO shows the region sampled by P ol-cpx . (b) LLD of magmas shown in MgO-Al 2 O 3 space. The same three fractionation segments are again observable, and the hydrous and dry clinopyroxene-plagioclase cotectics are well-distinguished. Horizontal bar centered on 3 wt. % MgO shows the primary compositional criteria used to identify samples for calculating H 2 O cpx-pl . (c) The same experimental series as in a and b projected into the normative plagioclase-clinopyroxene-olivine pseudo-ternary. Here large symbols are used to identify experiments with appropriate compositions for calculating H 2 O cpx-pl . (d) Phenocryst mineral compositions from the same experimental series plotted in the plagioclase-clinopyroxene-olivine pseudo-ternary space. Symbols represent different phases and are labeled in the figure. Plotted experimental data in all panels from Nandedkar (2014), Nandedkar et al. (2014), Ulmer et al. (2018), Villiger et al. (2004),  at ≤20 kbars and with tholeiitic to relatively K-rich calc-alkaline and mafic to intermediate starting compositions were prioritized. The compilation includes 528 anhydrous experiments, of which 324 were conducted at 1 atm and 204 at elevated pressures. The remaining 720 experiments were conducted with hydrous bulk compositions, including 333 experiments that were fluid-saturated (either H 2 O or a mixed C-O-H fluid) and 387 that were fluid-undersaturated. For each experiment, the melt composition, phenocryst assemblage, and melt fraction were compiled. For nearly all experiments, melt fractions are reported in the original publications and were calculated using mass balance or less commonly by point counting and/or image processing techniques. For a small subset of experiments that do not report melt fractions, we calculated melt fractions assuming that K 2 O is perfectly incompatible.
We also compiled the H 2 O concentrations of all hydrous melts. Where available, we relied on published directly measured H 2 O contents, which included measurements made using various techniques including Raman and Fourier transform infrared spectroscopy, ion microprobe, calibrated electron microprobe measurements and Karl-Fischer titration. When not directly measured, we calculated melt H 2 O contents based on mass balance for H 2 O-undersaturated experiments and using VESIcal (Iacovino et al., 2021) for fluid-saturated experiments after calculating melt Fe 2 O 3 contents from the reported experimental fO 2 using the calibration of Kress and Carmichael (1991). As some biases may be introduced by combining these methods, we used the same approach to calculate H 2 O contents in experiments with direct measurements and additionally calculated H 2 O contents using the plagioclase-melt hygrometer (Waters & Lange, 2015). Comparisons of all three methods show acceptable agreement given the generally large uncertainties for many of these approaches ( Figure S1 in Supporting Information S1), consistent with previous studies (Devine et al., 1995).
In principle, thermodynamic phase equilibria modeling can complement our experimental compilation and help to further refine models for how fractionation pressure and melt H 2 O contents control liquid lines of descent. However, when comparing liquid lines of descent calculated with rhyoliteMELTS (Gualda et al., 2012) to representative series of experiments, we found that rhyoliteMELTS consistently fails to accurately reproduce the location of both the olivine-clinopyroxene and clinopyroxene-plagioclase cotectics in both hydrous and anhydrous experiments conducted at pressures above 2 kbars (Text S1 in Supporting Information S1). This is consistent with results from previous experimental studies (e.g., Nandedkar et al., 2014;Villiger et al., 2004) that compared their results to MELTS and shows that both more experiments and better solution models are needed before phase equilibria models can be relied on to model liquid lines of descent at a range of pressures and volatile contents.

Development of Pressure and H 2 O Proxies Based on Mineral Projections
Two requirements must be satisfied before leveraging the compositions of melts crystallizing on cotectics as proxies for fractionation pressure and magmatic H 2 O contents: (a) melts in equilibrium with the cotectic mineral assemblages must be identifiable; and (b) the proxies must rely only on melt components buffered by the cotectic assemblages. The first criterium is trivial to evaluate with the experimental data set. However, satisfying this requirement is more challenging in natural lavas, where the crystalline cargoes of erupted lavas may not correspond to the equilibrium fractionating assemblages (see Section 6.1). Therefore, instead of relying on phenocryst assemblages to identify suitable lavas, we used the reported phase assemblages of experimental liquids to identify ranges of magma compositions that are most often in equilibrium with a given cotectic assemblage. By using these same criteria to filter the experimental calibration data set, we incorporate into our proxies the uncertainties that result from including some liquids that are not on the cotectic. We additionally exclude from our calibration experiments where iron or alkali loss was observed, and those with melt fractions below 0.2, where identification and analysis of equilibrium melt becomes difficult, or above 0.95, where the melt composition may still be sensitive to the starting composition. The experimental data used to calibrate the two proxies are provided in Tables S2 and S3. To satisfy the second requirement, we follow previous workers studying magmatic fractionation (e.g., Grove et al., 1992;Herzberg, 2004;Merzbacher & Eggler, 1984;Yang et al., 1996) and use normative mineral components (Tormey et al., 1987) to isolate the melt components most sensitive to the systematics of the olivine-clinopyroxene and clinopyroxene-plagioclase cotectics. This projection recalculates the bulk composition of a liquid as mineral components, which then can be readily identified as enriching or fractionating. The sensitivity of these normative mineral components to cotectic fractionation is enhanced by projecting the normative mineral components into the olivine-clinopyroxene-plagioclase pseudo-ternary space that includes both cotectic assemblages (Figure 1c).
Following projection, the relationship between normative mineral components and P or H 2 O was quantified by fitting a piecewise-planar surface defined by equations with the form: where X and Y are projected normative mineral components, a, b, and c are fitted coefficients, and max(i, j) is a function that returns the greater of the two values i and j. This equation defines two portions of the model, a positive planar surface with a gradient determined by a and b, and a constant zero-valued component, and ensures continuity between these components. Given the limited experimental data set, we did not use separate training and test data, but estimated the model uncertainty by repeating this fitting procedure using 10-fold cross validation and calculating the average RMSE of the test fraction from each cross validation. Implementations of both proxies as Excel worksheets are available for download as Tables S4 and S5.

P ol-cpx : An Early Fractionation Barometer Based on the Olivine-Clinopyroxene Cotectic
As described above, clinopyroxene crystallization begins in most systems after an interval of olivine-only fractionation. However, melts often evolve on the olivine-clinopyroxene cotectic for a relatively limited interval prior to the stabilization of plagioclase. As plagioclase fractionation can obscure the olivine-clinopyroxene systematics, it is essential to restrict the calibration data set for this proxy to a range of melts that maximizes the percentage of compositions in equilibrium with olivine and clinopyroxene while minimizing the number of plagioclase-crystallizing lavas. We found that melts with ∼8 wt. % MgO best balanced these two objectives as the experimental compilation shows a dramatic increase in the number of melts crystallizing clinopyroxene at this MgO content (Figure 2a), suggesting that melts with this composition are typically near the onset of clinopyroxene-olivine fractionation. To optimize the calibration of this pressure proxy, we used experimental melt compositions linearly interpolated to 8 wt. % MgO, and only included experimental series where the two bracketing experiments with the nearest MgO contents contained between 6 and 10 wt. % MgO. We observe that nearly all experimental series conducted at pressures >4 kbars are on the olivine-clinopyroxene cotectic at 8 wt. % MgO, while several lower pressure experiments had not yet stabilized clinopyroxene but are close to clinopyroxene saturation ( Figure 2c). Some anhydrous experiments begin crystallizing plagioclase prior to ∼8 wt. % MgO, particularly at low pressure, but these experiments have melt compositions consistent with the trend defined by plagioclase-free experiments. This is indicative of limited fractionation immediately upon plagioclase-saturation. Finally, none of the melts with ∼8 wt. % MgO are saturated in amphibole.
We fit Equation 4 to these data to find the relationship between normative clinopyroxene and olivine contents and pressure ( Figure 2b; Equation 5): Pol−cpx(kbars) ± 1.8 = max(7.66Ol − 77.07Cpx + 19.43, 0) This equation defines the clinopyroxene-olivine cotectic barometer (which we refer to as P ol-cpx ) and reflects the expected relationship between fractionation pressure and the olivine-clinopyroxene cotectic: pressure is negatively correlated with clinopyroxene content and is ∼10X more sensitive to changes in normative clinopyroxene contents than olivine contents. P ol-cpx has an uncertainty of 1.8 kbars estimated based on the average RMSE calculated from 10-fold cross validation. The overall systematics supports a semi-quantitative relationship where normative clinopyroxene content in early fractionating melts correlates with early fractionation pressure. Arc magmas with lower normative clinopyroxene can be inferred to crystallize at shallow pressures, while higher normative clinopyroxene indicates early fractionation at higher pressures. This pressure proxy should only be applied to natural whole rock data with 8.0 ± 1.0 wt. % MgO that fall within the field defined by the experimental calibration data set in the olivine-clinopyroxene-plagioclase pseudoternary.
We note that the approach behind estimating P ol-cpx shares some similarities to the Ca 6.0 metrics developed in previous studies of arc magmas (Plank & Langmuir, 1988;Turner & Langmuir, 2015) as CaO contents are buffered during fractionation on the olivine-clinopyroxene cotectic. However, the distinction between using melt compositions at 8 versus 6 wt. % MgO is critical. In experiments with liquids with ∼6 wt. % MgO, nearly all anhydrous compositions crystallize plagioclase, while many H 2 O-bearing experiments are still plagioclase free ( Figure S2 in Supporting Information S1). This sensitivity to the strongly H 2 O-dependent plagioclase stability (see Section 3.4) causes the correlation between fractionation pressure and normative clinopyroxene contents to weaken significantly for melts with 6 wt.% MgO.

H 2 O cpx-pl : A Hygrometer Based on the Clinopyroxene-Plagioclase Cotectic
Melts typically evolve along the clinopyroxene-plagioclase (±hornblende) cotectic for an extended temperature interval ( Figure 3a) and within this interval the difference in plagioclase-forming oxide components between hydrous and dry melts is broadly constant (Figures 1b and 1c). Therefore, a proxy for magmatic H 2 O contents based on this cotectic could potentially be applied to a wide range of melt compositions. Nevertheless, H 2 O is continuously enriched during fractionation until reaching fluid-saturation, at which point initial differences in H 2 O content converge to (pressure-dependent) saturation values. To isolate differences in magmatic H 2 O contents independent of the extent of differentiation, we focus on developing a clinopyroxene-plagioclase cotectic H 2 O proxy for melts with 2-4 wt. % MgO, which typically includes andesitic to dacitic compositions. In addition, we restrict the calibration data set to SiO 2 contents between 52 and 65 wt.%, and X Mg below 0.65. The first of these criteria helps to avoid any melts that have evolved past clinopyroxene and/or hornblende stability, while the second ensures that no melts in (near-) equilibrium with mantle olivine are included.
Applying these criteria yields melts from 146 experiments that range in pressure from 1 atm to 12 kbar including 26 anhydrous experiments. To calibrate the H 2 O proxy (which we refer to as H 2 O cpx-pl ), we fit Equation 4  The modeled relationship has an RMSE of 1.4 wt. % H 2 O (Figure 3c), indicating relatively strong predictive power. The proxy has stronger sensitivity to the normative clinopyroxene component than the plagioclase component. However, as the normative olivine component remains roughly constant throughout the calibration data set (Figure 3b), the plagioclase and clinopyroxene components must be inversely correlated. Thus, the H 2 O cpx-pl is consistent with the hypothesis that normative plagioclase contents and H 2 O are correlated, and moreover shows that there is a complimentary inverse correlation between normative clinopyroxene contents and H 2 O.
Finally, we also note that the barometer and hygrometer both define relatively similar trends in the olivine-clinopyroxene-plagioclase pseudo-ternary space. It has been observed in past studies that increasing pressure may also inhibit plagioclase crystallization (e.g., Bartels et al., 1991;Bender et al., 1978), raising the possibility that the effects due to changes in pressure and H 2 O contents are conflated in our two proxies. However, we are confident that P ol-cpx and H 2 O cpx-pl successfully isolate the effects of pressure and H 2 O: we found that attempting to model the experimental pressures of the H 2 O cpx-pl data set results in a much worse fit compared to the H 2 O cpx-pl , and more importantly, the modeled pressure surface is nearly orthogonal to the hygrometer calibration ( Figure S3 in Supporting Information S1), showing that the H 2 O cpx-pl proxy is insensitive to differences in fractionation pressure. Further, there is essentially no overlap between the compositional fields of the two calibration data sets (Figure 3b), and melts have necessarily undergone significant differentiation from ∼8 wt. % to 2-4 wt. % MgO between the two proxies.

Fe-Mg Systematics: The Tholeiitic Index (THI)
Lastly, an alternative LLD-based proxy for magmatic H 2 O contents is the Tholeiitic Index (Zimmer et al., 2010). The Tholeiitic Index leverages the observation that LLDs characterized by Fe-enrichment (tholeiitic) trends are generated in magmas with low H 2 O contents, while Fe-depletion (calc-alkaline) LLDs are characteristic of high H 2 O contents (Sisson & Grove, 1993a to X ± 0.5 wt. %., and second, we calculate the median Fe4 and Fe8 rather than the mean to better represent the dominant population in each arc. To note this difference, we subsequently refer to this modified index as THI m .

The Significance of Other Fractionating Phases
As described above, the motivation for the P ol-cpx and H 2 O cpx-pl is based on the displacements in the compositional space of the olivine-clinopyroxene and clinopyroxene-plagioclase cotectics with changes in magmatic H 2 O contents and pressure. However, orthopyroxene, amphibole and garnet are also observed in some of the compiled experiments. Fractionation of these phases influences the normative olivine, clinopyroxene and plagioclase melt components, yet the LLDs that include fractionation of any of these additional phases are similar to those that only fractionate olivine, clinopyroxene and plagioclase.
This insensitivity is in part because orthopyroxene plots similarly in the olivine-clinopyroxene-plagioclase pseudo-ternary space to olivine-rich cumulates, while amphibole and garnet are compositionally like clinopyroxene-and plagioclase-bearing cumulates (Figure 1d). While orthopyroxene fractionation may moderate SiO 2 -enrichment, its effect on the clinopyroxene and plagioclase components remains similar to that of olivine. Orthopyroxene has appreciable CaO and Al 2 O 3 and therefore does not plot exactly at the olivine vertex ( Figure 1d). However, the fractionation of minor amounts of orthopyroxene with low CaO and Al 2 O 3 does not meaningfully hinder normative plagioclase enrichments in the magma. Similarly, the fractionation of amphibole and garnet from arc magmas drives rapid SiO 2 -enrichment. Yet, typical amphibole and garnet compositions from arc magmas plot centrally in the olivine-clinopyroxene-plagioclase pseudo-ternary in a similar location to clinopyroxene-plagioclase cumulates ( Figure 1d). Therefore, additionally fractionating these phases has a relatively minor impact on the evolution of magmas along the clinopyroxene-plagioclase cotectic. In fact, the amphibole-plagioclase cotectic is often a direct extension of the clinopyroxene-plagioclase cotectic (Grove & Donnelly-Nolan, 1986).
In contrast, crystallization of either hornblende or garnet prior to the melt reaching the clinopyroxene-plagioclase cotectic will have greater impact on the LLD. However, hornblende stability requires ≥4 wt. % H 2 O in the melt and, more importantly, temperatures below ∼1,050°C (Blatter et al., 2013;Melekhova et al., 2015). Only very H 2 O-rich magmas cool below this temperature prior to reaching the clinopyroxene-plagioclase cotectic and most arc magmas will not stabilize amphibole prior to reaching this cotectic (see also Section 6.1). Similarly, early garnet fractionation occurs only above at least 12 kbars in hydrous magmas (Klein & Müntener, 2023;Müntener et al., 2001), and at even higher pressures in anhydrous systems. While fractionation at these pressures may be important in the thickest arcs, they likely do not represent the dominant fractionation conditions of typical arc magmas. We caution against applying the proxies to locations where significant early garnet fractionation could be expected.

Global Arc Geochemical Data Set
We compiled whole rock major element compositions of arc volcanic rocks using the precompiled arc and arc seamount data sets from Georoc (http://georoc.mpch-mainz.gwdg.de/georoc/) ( Figure 4; Table 1). We subdivided some of the Georoc arc data sets, separating the Alaskan Peninsula from the Aleutians data set and dividing the Andes data into Northern, Central, Southern and Austral Volcanic Zones. We filtered all data to include only analyses that were published after 1970 with anhydrous totals between 98 and 102 wt. %, and excluded samples described as altered or with a loss of ignition greater than 5 wt. %. We further restricted the data to volcanic systems that were primarily active in the Pliocene and later. This time window was necessary for arcs with relatively few analyses, yet in all arcs most samples are Pleistocene or younger, allowing comparison of the compiled data to modern arc physical parameters. Additionally, we excluded analyses of fore-arc lavas and of samples from actively spreading back-arcs. Finally, alkaline silica-undersaturated magmas are separated from calc-alkaline and tholeiitic magmas by a thermal divide and thus evolve along a distinct LLD (Schmidt & Weidendorfer, 2018). We therefore excluded the small populations of strongly peralkaline arc volcanics. Our compiled filtered data sets are available as Data Set S1.  Table 1. Colors correspond to arc type: continental arcs are shown in blue, oceanic arcs are shown in red, and arcs that transition between continental and oceanic basements are shown in orange.

Compilation of Phenocryst Assemblages for Selected Arcs
An assumption critical to our approach is that melt compositions are controlled by cotectics sensitive to fractionation pressure and H 2 O contents. Consequently, the samples used in calculating P ol-cpx and H 2 O cpx-pl could be expected to contain the phenocryst assemblages olivine + clinopyroxene(±orthopyroxene) and clinopyroxene + plagioclase (±amphibole), respectively. We thus compiled the reported phenocryst assemblages for the Central America, Cascadia, the Aleutians and Alaskan Peninsula, Izu-Bonin, Marianas, and Sunda arcs from the original publications (Table S6). For each sample, this data set lists the minerals observed and distinguishes between phases that are explicitly documented as opposed to descriptions that are more ambiguous (e.g., a sample described as olivine + plagioclase ± clinopyroxene phyric would be recorded as definitely containing olivine and plagioclase and possibly containing clinopyroxene). Here, we focus on the explicitly described phenocryst assemblages, which yield a data set significantly smaller than the complete geochemical data set.

Arc Physical Parameters
In discussing the significance of the new LLD proxies, we compare the results with various subduction zone physical parameters (Table 1). For these parameters, we rely on the data of Syracuse et al. (2010) when their arc definitions align geographically with the geochemical data sets compiled here. Otherwise, we manually recalculate the subduction zone parameters from Syracuse and Abers (2006) and Syracuse et al. (2010) for geographically appropriate regions, which are noted in Table 1. We also compare the proxy values to the average crustal thickness of each arc, which we compiled from local seismic studies at all arcs, except for the Scotia Arc, for which no local seismic studies exist and where we instead rely on constraints from gravity modeling (Larter et al., 2003). In most arcs the seismic data from multiple independent studies are consistent with relatively invariant crustal thicknesses, but for arcs where there is evidence for trench-parallel variation or significant differences between studies representative average crustal thicknesses were estimated from the available data. Crustal thickness values and consulted references are listed in Table 1 and references for all consulted studies are listed in Table S7.

Pressures of Early Fractionation
The systematics of fractionation on the olivine-clinopyroxene cotectic and of P ol-cpx are illustrated for representative arcs in Figure 5 (plots of all proxies for each arc are provided in Data Set S2). In the early fractionation interval sampled by P ol-cpx , most continental arcs show constant to slightly decreasing CaO with a decrease in MgO (Figure 5a), consistent with fractionation on the olivine-clinopyroxene cotectic. The relatively low CaO contents (<10 wt. % at 8 wt. % MgO) correspond to lower normative clinopyroxene (Figure 5d). As a result, calculated pressures for continental arcs are consistently higher than 8 kbars and extend up to ∼14 kbars (Figure 7a). Island arcs have a less pronounced CaO/MgO slope near 8 wt. % MgO (Figures 5b and 5c) and higher CaO contents corresponding to elevated normative clinopyroxene, suggesting more limited clinopyroxene fractionation in this interval (Figures 5e and 5f). Calculated early fractionation pressures in island arcs are variable, but median values are mostly less than ∼7 kbars (Figure 7a). These elevated early fractionation pressures, and the wide variation observed in some arcs are consistent with polybaric fractionation, which may play an important role in arc crust formation Melekhova et al., 2015).
These results indicate that there is a clear difference between early fractionation depths in continental and island arcs. Two arcs, Central America and the Aleutians, exhibit more complex behavior: both are characterized by a strongly bimodal distribution of calculated pressures (Figures 5e and 7a). Within the Central American Arc, we observe a primary population of samples that yield P ol-cpx estimates above ∼8 kbars, comparable to other continental arcs, and a second population with calculated P ol-cpx below 5 kbars. Low pressure samples are exclusively produced in a small number of volcanoes erupting tholeiitic basalts in Nicaragua (Walker, 1984). These samples likely represent a LLD that fractionates at lower pressures within the crust, distinct from the broader Central American LLD. As the median P ol-cpx in Central America falls between these two distinct populations, we use the median of the higher pressure population to represent the typical early fractionation pressure dominant in the Central American arc. Similarly, the high pressure (>12 kbars) population in the Aleutians is exclusively from seafloor samples dredged west of the westernmost emergent volcano, where the plate boundary transitions to a nearly strike-slip orientation. These samples may contain significant slab melt components that are not observed elsewhere in the Aleutians (Yogodzinski et al., 2015). We therefore exclude these atypical samples from the calculated Aleutian median pressure. Figure 6 illustrates the data used to calculate H 2 O cpx-pl for representative arcs. Al 2 O 3 contents as a function of MgO are plotted for arcs with LLDs consistent with fractionation of dominantly H 2 O-rich (Cascades), intermediate (Aleutians) and relatively dry (Izu Bonin) magmas. In each case, a wide range of Al 2 O 3 concentrations is observed at >4 wt. % MgO. Many of these relatively mafic compositions are likely not yet fractionating on the clinopyroxene-plagioclase cotectic, and thus the spread reflects varying extents of olivine ± clinopyroxene fractionation and variations in the parental melt compositions. As MgO decreases to below ∼4 wt. %, maximum Al 2 O 3 contents are reached, and Al 2 O 3 concentrations subsequently decrease for each arc (Figures 6a-6c). As MgO contents decrease to below 2 wt. %, the range of values observed in each arc narrows significantly and most arcs converge toward a single trend, suggesting that the magmas have reached relatively shallow, fluid-saturated conditions by this stage. Consistent with the experimental LLDs (Figure 1c), most arc magmas evolving on the clinopyroxene-plagioclase cotectic follow similar trajectories in the olivine-clinopyroxene-plagioclase pseudo-ternary space. However, magmas with comparable MgO contents from different arcs plot at distinct points along the cotectic LLD due to varying extents of prior plagioclase fractionation and indicative of differing H 2 O contents. At 2-4 wt. % MgO, Cascades lavas are relatively Al 2 O 3 -rich, corresponding to elevated normative plagioclase contents and calculated H 2 O contents are dominantly above 4 wt. % (Figure 6d). In contrast, samples from Izu Bonin show a wide range in Al 2 O 3 contents, but the dominant population has less than 15 wt.% Al 2 O 3 and comparatively little normative plagioclase (Figures 6c and 6f). These samples are consistent with greater extents of plagioclase fractionation and yield-calculated H 2 O contents below 2 wt.% (Figure 6f) Figures 6b and 6e).

H 2 O in Fractionating Arc Magmas
We find that all arcs are characterized by a broad, but typically unimodal distribution of H 2 O contents, and that there are well-resolved differences between arcs (Figures 6 and 7b). Continental arcs generally show elevated H 2 O contents (i.e., >4 wt. %; Figure 6a), while several island arcs are dominated by magmas with notably lower calculated H 2 O contents (<3 wt.%), including the Aleutians, Izu Bonin, Kermadec, and Marianas (Figure 7b).
To complement H 2 O cpx-pl , we examine the Tholeiitic Index (THI m ; Figure 8). While variations in the Tholeiitic Index exist between individual volcanoes within a single arc (Zimmer et al., 2010), large systematic differences are also resolvable between arcs. Some arcs, such as the Cascades (Figure 8a (Figure 8d).

Liquid Lines of Descent and Phenocryst Populations
The above results are interpreted in terms of cotectic crystallization. Based on this rationale, one might expect that the erupted lavas contain phenocryst assemblages consistent with these cotectics. To evaluate this inference, we compiled a database of reported phenocryst assemblages for six representative arcs.  (Table 1) and colored corresponding to arc type as in Figure 4. Median P ol-cpx pressures and H 2 O cpx-pl contents are marked with small black triangles. Central America and Aleutians have strongly bi-modal P ol-cpx distributions. As discussed in the main text, in both instances, one of these populations is geographically limited and not taken to be representative of the typical LLD. These populations are shown here in lighter colors and are excluded from the calculated median pressures. Scatter plots and histograms for all arcs are available in Data Set S2. Figure 9 shows plots of MgO and CaO contents for the six arcs with phenocryst data, colored by phenocryst assemblage. We find that there is only a sparse record of samples that are olivine(-only) and olivine + clinopyroxene(-only) phyric, and there is no obvious evolution from olivine phyric to olivine + clinopyroxene bearing samples. Instead, plagioclase phenocrysts are reported in most samples even at MgO contents above 8 wt. % (Figure 9). Samples with 7-9 wt.% MgO, as used to calculate the pressure proxy, dominantly contain olivine + clinopyroxene + plagioclase phenocrysts in Central America, Sunda, and the Aleutians, while Izu-Bonin, the Marianas, and the Cascades have more variable phenocryst assemblages of olivine, olivine + plagioclase or olivine + clinopyroxene + plagioclase (Figure 9 and Figure S4a in Supporting Information S1). Although the samples used for P ol-cpx chemically lie on the experimentally derived olivine-clinopyroxene cotectic, they rarely exhibit olivine + clinopyroxene   Figure S5 of the Supporting Information S1.

Olivine + Clinopyroxene Cotectic
phenocryst assemblages. This difference shows that fractionation depth and depth of final equilibration within the arc crust are rarely congruent for deeply fractionated erupted magmas. While direct transport from the lower crust to the surface would likely preserve the lower crustal fractionating assemblage, intermittent storage at shallower pressures appears to replace the higher pressure phenocrysts assemblage in favor of a shallower pressure assemblage. With decreasing pressure, the clinopyroxene-stability field shrinks strongly, while the plagioclase and olivine fields expand (Presnall et al., 1978). Consequently, during transport to the surface, intermittent stor age and eruption, plagioclase is stabilized at the expense of clinopyroxene.
Critically, while most samples have a low pressure phenocryst assemblage, we suggest that these phases are rarely fractionated. In our phenocryst data set, there is no observable shift in P ol-cpx between populations with olivine ± clinopyroxene phenocrysts and samples that also contain plagioclase phenocrysts ( Figure S4a in Supporting Information S1), requiring that the plagioclase-bearing shallow pressure assemblage does not appreciably fractionate. Limited fractionation of arc magmas at shallow pressures is also consistent with the observation that mafic cumulates are rare at upper crustal levels in exposed arc sections Jagoutz, 2014;, suggesting that most crystal fractionation occurs at high pressures prior to transport to shallower levels. This apparent discrepancy between LLD and phenocryst assemblage is directly analogous to the "pyroxene paradox" in the MORB system (e.g., Dungan & Rhodes, 1978), where clinopyroxene fractionation is inferred from MORB liquid lines of descent but clinopyroxene-bearing MORB samples are rare. This is explained through the same mechanism, with clinopyroxene fractionation at higher pressures and subsequent resorption of clinopyroxene and crystallization of plagioclase upon transport to shallower levels .

Clinopyroxene-Plagioclase Cotectic
The phenocryst assemblages of samples near the experimentally defined clinopyroxene-plagioclase cotectic generally contain phenocrysts consistent with this cotectic (Figure 10 and Figure S4b in Supporting Information S1). Nearly all samples with less than ∼5 wt. % MgO contain phenocrysts of both plagioclase and clinopyroxene ( Figure 10). Additional phases include orthopyroxene or olivine, and amphibole, which are not expected to significantly alter the clinopyroxene-plagioclase systematics.
In detail, more than 95% of the samples used to calculate H 2 O cpx-pl in Central America, the Aleutians, and Sunda, as well as over 80% of samples from the Marianas and Izu-Bonin contain (at least) the expected plagioclase + clinopyroxene cotectic phenocryst assemblage. The Cascades are an apparent exception, as 280 out of the 406 Cascade samples have assemblages consistent with the clinopyroxene-plagioclase cotectic, but 88 samples (>20%) contain plagioclase without clinopyroxene. As this plagioclase-only sample population is skewed to slightly higher Al 2 O 3 contents compared to the clinopyroxene + plagioclase samples ( Figure S4b in Supporting Information S1) this may be evidence for plagioclase accumulation in some Cascade magmas. Nevertheless, the near-primitive high-Al 2 O 3 and high-CaO lavas in the Cascades have been shown to represent true melt compositions (Baker et al., 1994;Grove et al., 2002).
Finally, in Figure S5 of Supporting Information S1 we identify samples that also contain amphibole phenocrysts. Amphibole is rare in compositions near the olivine-clinopyroxene cotectic due to the elevated temperatures and/or lower H 2 O contents below 4 wt. % during the early stages of fractionation. The subsequent appearance of amphibole is strongly correlated with calculated H 2 O cpx-pl : lavas erupted at arcs with higher H 2 O are more frequently amphibole-phyric, while amphibole is rarely observed at the Marianas and Izu-Bonin, the two arcs with the lowest calculated H 2 O contents in the phenocryst compilation. Further, amphibole is rarely observed in samples with less than 3-4 wt. % H 2 O cpx-pl , consistent with a minimum H 2 O content of ∼4 wt. % required for amphibole stability (Prouteau & Scaillet, 2003;Sisson & Grove, 1993a). Finally, the samples with amphibole in addition to clinopyroxene + plagioclase still follow the clinopyroxene-plagioclase cotectic ( Figure S5 in Supporting Information S1).

Sensitivity of P ol-cpx to Primitive Magma Compositions
Several previous studies examined the Ca-Mg systematics in arc magmas (Plank & Langmuir, 1988;Turner & Langmuir, 2015), which in near-primary mafic magmas is primarily controlled by the olivine-clinopyroxene cotectic. In contrast to our approach that focuses on magmas with ∼8 wt. % MgO, these studies focused on variations in CaO contents at MgO 6 wt. % (Ca 6.0 ) and interpreted these variations as reflective of differences in primary melt compositions rather than fractionation conditions. Primitive arc basalts have ∼9-13 wt. % MgO (Schmidt Phenocryst assemblages are colored as in Figure 9. Amphibole-bearing samples are plotted in Figure S5 of the Supporting Information S1.  shown in individual arc plots in Data Set S2). Thus, basaltic samples with ∼6 wt. % MgO have undergone significant fractionation relative to primitive basalt compositions. Moreover, the LLD at 6 wt. % MgO is increasingly sensitive to H 2 O contents in addition to pressure, as most dry magmas at 6 wt. % MgO are already crystallizing plagioclase (Figures 1b and 3a and Figure S2 in Supporting Information S1). Basaltic compositions with 6 wt. % MgO will therefore have CaO values modified by (unaccounted) fractionation of variable proportions of olivine, clinopyroxene and plagioclase. Consequently, Ca 6.0 values (and other components normalized to 6 wt. % MgO) are neither robust indicators of primary compositions nor of fractionation pressure. In contrast, the correlation between experimental melt composition at 8 wt. % MgO and pressure is strong, despite a wide range of starting compositions and H 2 O contents in the compiled experiments (Figures 3b and 3c), showing that P ol-cpx is a more robust indicator of fractionation pressure for basaltic melts.
In contrast to primitive arc basalts, primitive andesites frequently have MgO contents near 8 wt. % (e.g., Baker et al., 1994;Kelemen, Hanghøj, & Greene, 2003; for a compilation see Schmidt & Jagoutz, 2017) and thus will be included in the population used to calculate P ol-cpx . Although these primitive melts have undergone little crustal differentiation, we argue that their melt compositions are still consistent with olivine-clinopyroxene cotectic control, only that this control is exerted in the mantle. Reaction of primitive basalts with lherzolite in the shallow mantle can produce high-magnesium andesites in equilibrium with a wehrlitic residue (Mitchell & Grove, 2016). These melts are thus effectively controlled by the olivine-clinopyroxene(+orthopyroxene) cotectic while their Mg# remains buffered in equilibrium with mantle olivine. Based on this interpretation, anomalously high P ol-cpx values from locations such as the westernmost Aleutians may be a result of differentiation or reequilibration on the olivine-clinopyroxene(+orthopyroxene) cotectic at mantle pressures.

Evidence for Multiple Liquid Lines of Descent at Individual Arcs
This contribution focuses on the systematic differences in the dominant LLDs between arcs, but parental melts within a single arc may differ in their H 2 O contents and may fractionate at different pressures. Indeed, a large body of work has shown significant variations in LLDs within single arcs (e.g., Jagoutz et al., 2011;Kay & Kay, 1985;Rezeau et al., 2021;Turner et al., 2016), a difference that is already present in the primitive melts (Schmidt & Jagoutz, 2017) and is evident in single volcanoes (Baker et al., 1994;Fujinawa, 1988;Grove et al., 2002;Hunter, 1998;Le Voyer et al., 2010). Similarly, there is significant dispersion within the populations used to calculate each of the proxies utilized here (Figures 7 and 8d), consistent with varying LLDs in most arcs.
To further illustrate the evidence for multiple LLDs, we compare P ol-cpx , H 2 O cpx-pl and THI m to their Q statistics (Figure 11), which is a robust estimate of the dispersion (scale) for non-Gaussian and asymmetric data samples (Rousseeuw & Croux, 1991). We used this statistic as many of the arcs have long-tailed distributions, and distributions for arcs with low pressures or H 2 O contents are strongly asymmetric. Most arcs exhibit 2-4 kbars of variability in P ol-cpx (Figure 11a) regardless of median value or arc type. A different systematic is present in the two hydration proxies: island arcs that are characterized by the lowest H 2 O contents show only limited dispersion (low Q statistic values) indicative of a single (relatively dry) LLD. In contrast, most arcs with higher median H 2 O contents show greater dispersion and are dominated by magmas that evolve along H 2 O-rich LLDs, but also contain magmas that follow less hydrous fractionation paths.

Correlations Between Proxies
The preceding discussion shows that the new proxies as well as the Tholeiitic Index show resolvable differences between the dominant LLDs at the arc scale. Next, we examine these systematic differences and explore how these proxies relate to arc parameters to constrain the mechanisms and processes that produce the observed range of LLDs. We observe a strong negative correlation between Fe-enrichment and H 2 O contents (Figure 12a), consistent with the traditional interpretation that drier magmas evolve on a tholeiitic Fe-enrichment trend, while the calc-alkaline Fe-depletion trend is intimately linked to its hydrous character (Sisson & Grove, 1993a;Zimmer et al., 2010). This strong correlation shows that both the Tholeiitic Index and H 2 O cpx-pl constrain the hydration state of differentiating arc magmas. The observed scatter results from the proxies being calculated from different major elements and at different stages of the LLD. Further, calculated THI m and median H 2 O cpx-pl both correlate with median P ol-cpx values (Figures 12b and 12c): arcs with high H 2 O contents and calc-alkaline differentiation trends have higher calculated fractionation pressures, while relatively dry tholeiitic arcs show lower fractionation pressures, suggesting that more calc-alkaline and hydrous magmas begin to differentiate at comparatively higher pressures.
An additional relationship is evident from Figure 12: continental arcs are dominantly characterized by high H 2 O cpx-pl and low THI m values consistent with wet LLDs, as well as by higher P ol-cpx indicative of deeper early fractionation. In comparison, the high THI m index and low H 2 O cpx-pl, relatively dry LLDs are mostly observed at island arcs, which also define the shallower early fractionation arc population.
In Figure 13 and Figure S6 in Supporting Information S1, we also compare the three proxies to a range of arc physical parameters. Similar to the comparisons between proxies, in many instances we observe both moderately strong linear correlations between multiple arc parameters and LLD proxies (e.g., crustal thickness and wedge height with most proxies; Figure 13) and also find systematic differences in the systematics of island and continental arcs. In contrast, some proxies show little to no correlation with any of the LLD proxies (e.g., convergence velocity, Figure  S6 in Supporting Information S1). In the following sections, we discuss the significance of these relationships.

The Correlation Between Crustal Thickness and P ol-cpx
The seismically defined crustal thickness (Moho) corresponds in most arcs to the transition from plagioclase-bearing gabbroic cumulates to plagioclase-free ultramafic cumulates (Christensen & Mooney, 1995;Tatsumi et al., 2008), a boundary that is well documented in arc sections where the Moho is exposed (Behn & Kelemen, 2006;. P ol-cpx samples the LLD of arc magmas prior to plagioclase fractionation (Figures 2a and 3a) and thus should reflect fractionation pressures below this boundary. However, at pressures below 10-12 kbars, plagioclase first appears in both hydrous and anhydrous experimental LLDs less than 50°C below the experimental temperatures of melts with 8 wt. % MgO ( Figure S7a in Supporting Information S1). Thus, while P ol-cpx does not directly reflect the plagioclase-in boundary, given the typically steep thermal gradients in the lower arc crust , magmas differentiating in all but the thickest continental arcs reach plagioclase stability shortly after evolving to 8 wt. % MgO, and we expect that calculated P ol-cpx pressure should closely correlate with Moho depth.
In evaluating this hypothesis, we find that the P ol-cpx values calculated at most well-studied arcs agree closely with local seismic Moho observations (as indicated by the dashed 1:1 line in Figure 13c), while three arcs have significantly deeper seismic Mohos compared to P ol-cpx : the Central Volcanic Zone (CVZ) in the Andes, the Aleutians and Vanuatu. The CVZ has the thickest crust of any modern arc (>65 km; Yuan et al., 2002), and thus if early fractionation occurs near the seismic Moho, P ol-cpx should be >18 kbars. These high pressures extend beyond the calibration data set used for P ol-cpx and at these pressures it is possible that significant garnet fractionation occurs during early fractionation of CVZ magmas, which would interfere with reliable P ol-cpx estimates. The disagreement in the Aleutians is well-explained by the seismic studies conducted there: the lower crust of the Aleutians is inferred to be dominated by pyroxenites based on high P-wave velocities (Vp) and low Vp/Vs ratios , and thus the Moho depth in these studies corresponds to the petrologic Moho and not the typically measured seismic Moho. An Aleutian seismic Moho assumed to be the boundary between the mid-crust and this pyroxenite-rich lower crust at ∼20 km agrees within error with the P ol-cpx estimate of 4.7 kbars. Finally, the cause of the disagreement at Vanuatu is less clear. While there is a lack of recent detailed seismic studies of this arc, it is also possible that the elevated crustal thickness here is reflective of recent tectonic processes (Meffre & Crawford, 2001) or a relict continental basement in Vanuatu (Buys et al., 2014). If these three arcs are excluded, all 16 of the remaining well-studied arcs show excellent agreement between P ol-cpx and the seismic Moho within the P ol-cpx uncertainty.
As noted above, the temperature decrease necessary for melts with ∼8 wt. % MgO to subsequently reach plagioclase-in is relatively small in both anhydrous and hydrous LLDs at pressures below 10-12 kbars. However, the absolute temperatures of these melts can vary significantly, primarily as a function of H 2 O contents: plagioclase appears in H 2 O-poor LLDs at temperatures more than 200°C higher than in H 2 O-rich systems ( Figure S7b   Figure 11. Estimates of the intra-arc variability in the calculated median P ol-cpx , H 2 O cpx-pl , and Tholeiitic Index. Population dispersion is represented using the Q statistic (Rousseeuw & Croux, 1991). For a population of samples, the Q statistic represents an estimate of the scale of a variable that is robust to outliers and asymmetric distributions. Q values are scaled so as to be comparable to the scale of the standard deviation scale of a normal distribution. Systematics in P ol-cpx (a) show that most arcs exhibit 2-4 kbar variability in early fractionation pressures, while both H 2 O cpx-pl (b), and the Tholeiitic Index (c) show that H 2 O-poor arcs often have very restricted populations, while significant dispersion, suggesting a range of hydration states, is observed in most H 2 O-rich systems. In each panel, symbol colors represent island (red), transitional (orange) and continental (blue) arcs. Arcs are labeled with a two-letter code, which are listed in Table 1. Proxy values calculated from arcs with less than 15 samples are shown with empty symbols. in Supporting Information S1). As there are large variations in the hydration state of magmas within individual arcs (Figures 11b and 11c), the temperatures of magmas corresponding to plagioclase-in and P ol-cpx must vary strongly within single arcs. These differences in LLDs likely contribute to the broad, poorly resolved Moho in many arcs (e.g., Shillington et al., 2004;Takahashi et al., 2008), and are consistent with the observed variability in P ol-cpx values within individual arcs ( Figure 11a). As most arcs erupt a range of variably hydrated magmas (d-f) Comparisons with mantle wedge height, calculated as the difference between sub-arc slab depth and crustal thickness. (g-i) Comparisons with arc thermal parameters. Linear best-fit lines are shown in black and r 2 values are given for all fits. All proxies are well correlated with crustal thickness, and THI m and P ol-cpx are also well correlated with wedge heights. While the linear fit between wedge height and H 2 O cpx-pl is comparatively poor, there is a clear systematic clustering of these data for wedge heights above and below ∼100 km. Similar clustering is also present in comparisons between crustal thickness and H 2 O cpx-pl , as well as between both wedge height and crustal thickness and THI m . In comparison, poor correlations with no evident systematics are observed between all three proxies and the arc thermal parameter. Arc symbols and labels as in Figure 11. Tonga (marked with a triangle) has an extreme thermal parameter value (∼160) and is omitted from the plots for visibility and also excluded from the calculated fits.
including at least some H 2 O-poor magmas (Figures 7 and 11), the base of this broadly defined Moho likely corresponds to the earliest plagioclase-in boundary at temperatures of 1,150-1,200°C ( Figure S7b in Supporting Information S1).

The Relationship Between H 2 O Proxies and Physical Arc Parameters
The  (Newman & Lowenstern, 2002; see also Plank et al., 2013). Although we cannot exclude that some arc magmas reach fluid-saturation relatively early, we contend that the systematic differences in H 2 O cpx-pl and THI m distributions between relatively H 2 O-poor and H 2 O-rich arcs ( Figure 11) argue against fluid-saturation as a primary control on magmatic H 2 O contents. Similarly, the observed correlations between hydration proxies, crustal thickness and early fractionation pressure (Figures 12b, 12c, 13a, and 13b) seem difficult to explain if the hydration proxies are simply reflective of relatively evolved magmas reaching fluid-saturation at shallow pressures.
If fluid-saturation is not a primary control, the dichotomy between continental and island arcs raises a question: what is the fundamental mechanism that leads to these different behaviors? Is the range of H 2 O contents in arc magmas dominantly controlled by processes during magma generation such as variable contributions of H 2 O-rich slab material (Grove et al., 2002;Ruscitto et al., 2012) or variations in mantle wedge melting (Plank & Langmuir, 1988;Turner et al., 2016)? Alternatively, in what ways does arc crust itself influence these variations?
The correlations between magma hydration proxies and arc physical parameters allow for two distinct interpretations, (1) one that results from considering all arcs together, and (2) one motivated by considering continental and islands arcs as distinct populations. These two interpretations suggest somewhat contrasting answers to the above questions.
1. If all arcs are considered together, H 2 O cpx-pl and THI m are only modestly correlated with the thermal state of the slab as characterized by the thermal parameter (Figures 13g and 13h), suggesting that this is not a primary control on the hydration state of arc magmas. In contrast, a strong correlation is observed between mantle wedge height and THI m (Figure 13e). While the correlation between H 2 O cpx-pl and wedge height is weak (Figure 13d), there are pronounced clusters in the data: arcs with primarily low H 2 O content magmas (<4 wt.%) are dominantly observed in arcs with mantle wedge heights greater than 100 km, while arcs with wedge heights below 100 km have median H 2 O cpx-pl values of at least 4 wt. %. Similarly, both hydration proxies exhibit weak to moderate linear correlations with crustal thickness and a similar threshold is present, where H 2 O-poor LLDs are only found when crustal thickness is less than ∼25 km, and H 2 O-rich LLDs are restricted to crust thicker than 20 km (Figures 13a and 13b). These observations suggest that there is a significant control between either wedge height or upper plate thickness and the hydration state of arc magmas. 2. Alternatively, if continental and island arcs are examined separately, two distinct relationships are apparent ( Figure 13)

Mechanisms for the Generation of H 2 O-Rich and H 2 O-Poor Arc Magmas
The above two interpretations of the hydration proxy data require distinct mechanisms to generate the observed range of arc magmas. Similar to previous studies (Chin et al., 2018;Plank & Langmuir, 1988;Turner et al., 2016), one explanation consistent with the combined global systematics relates the observed range of arc magmas to differences in the relative contributions of decompression (dry) and flux (wet) melting. In these models, the amount of decompression melting is positively correlated with melting column height. Greater extents of decompression melting in the mantle wedge dilute the slab-derived flux of H 2 O, yielding on average lower H 2 O arc melts. The decompression melting component may include a large contribution from adiabatic decompression melting (e.g., Conder et al., 2002) or from initially H 2 O-fluxed melts ascending into the hot core of the mantle wedge where the extent of melting increases to maintain equilibrium with the surrounding mantle (Grove et al., 2002). This process could produce the observed spectrum of arcs ranging from thin-crusted island arcs associated with dominantly low-H 2 O magmas to thick-crusted continental arcs fluxed with more hydrous magmas.
This wedge-height dependent model predicts a continuum of LLDs with primary H 2 O contents varying inversely with mantle wedge melting column heights but cannot explain the dichotomy between continental and island arcs. While several properties differ between these settings, we focus here on three possible mechanisms: (a) The shallowest slab dips are exclusively observed at continental arcs and may be a direct result of either enhanced slab suction or plate coupling as crustal thickness increases (Sharples et al., 2014;Tovish et al., 1978). Although shallow slab dips are not necessarily correlated with shorter mantle wedge melting columns, they may hinder corner flow and limit the contribution of decompression melting to arc magmas (England & Wilkins, 2004); (b) Continental arcs likely subduct significantly more crustal material than island arcs. Crustal recycling at subduction zones is primarily estimated using sedimentary sections sampled by oceanic drill cores, which do not show a systematic difference between continental and island arcs (Plank & Langmuir, 1998). However, these drill cores are typically located hundreds of kilometers from trenches, and therefore underestimate near-trench additions of crustal material. These contributions are important for continental arcs, where enhanced subaerial erosion from coastal cordilleras deposits terrigenous sediments in the trench (e.g., Collinet & Jagoutz, 2017; but are essentially absent in intra-oceanic arcs. The greater crustal thicknesses at continental arcs may also lead to enhanced subduction erosion (e.g., Heuret et al., 2012;Straub et al., 2020). These terrigenous materials can carry a significant volume of H 2 O to sub-arc depths (Hacker, 2008) and may contribute to differences in the amounts of slab-derived fluids supplied to continental arcs compared to island arcs, independent of slab thermal parameter.
(c) Finally, lower crustal fractionation within thick arcs may allow for a greater role of deep magmatic recharge . Models have shown that this process can introduce additional feedbacks that lead to greater enrichments in incompatible elements (including H 2 O) in melts that are eventually extracted from these deep crustal magma systems .

Implications for the Growth of Arc Crust and Continental Crust Formation
The discussion to this point has focused on modern physical parameters of arcs, which implies a relatively static view of arc systems. In this view, the differentiation in arcs with more hydrous magmas begins deeper than in arcs dominated by drier magmas and more hydrous arcs follow calc-alkaline, Fe-depletion trends typical of continental crust. Moreover, high pressure differentiation in hydrous arcs will produce garnet and amphibole-rich, silica-poor cumulates (Alonso-Perez et al., 2009;Müntener et al., 2001) that are density-unstable and readily removed by delamination (Jagoutz et al., 2011;Jull & Kelemen, 2001;Müntener et al., 2001), leaving a more evolved bulk arc crust composition that is similar to estimates of bulk continental crust (Jagoutz & Kelemen, 2015;Rudnick & Gao, 2003). Thus, more hydrous, thicker arcs appear well-suited to create new continental crust, while thin crusted, dominantly tholeiitic, island arcs would seem inefficient. Yet, subduction geometry and arc crustal thickness evolve over the lifespan of an arc (e.g., Kay et al., 2005) and long-lived island arcs can generate new continental crust (Jagoutz & Schmidt, 2012;. How do H 2 O-poor island arcs with a thin oceanic upper plate such as Tonga or Scotia evolve to generate continental crust, or do some island arcs never generate continental crust? As discussed above, the upper plate thermal structure and specifically the depth to the temperatures at which magmas cool sufficiently to crystallize plagioclase fundamentally controls arc crustal thickness. We suggest that the flux of magma itself exerts a strong control on the temperature structure of arc crust. While the geotherm that magmas are exposed to is a function of the pre-existing upper plate thickness and thermal structure (e.g., Kelemen, Rilling, et al., 2003), the upper plate thermal structure is also strongly influenced by the sensible and latent heat advected by magmas (England & Katz, 2010;Rees Jones et al., 2018). Thus, a decrease in magma flux should result in cooler temperatures and enhanced fractionation at depth, leading to deeper early fractionation pressures, deeper plagioclase stability, and thus increased seismic Moho depths. In this model, the flux of magma to arc crust is inversely correlated with Moho depth and exerts a strong control on the petrologic and thermal structure of the arc crust (cf., Till et al., 2019). Long-term estimates of magmatic fluxes in modern arcs appear to broadly support this inverse relationship between magma flux and crustal thickness: in comparison to continental arcs, island arcs are characterized by both thinner crust and also elevated average (felsic) magmatic fluxes of at least 60-80 km 3 /km/Myr (Jicha & Jagoutz, 2015)-rates that are matched in continental arcs only during magmatic flare-up events (Ducea et al., 2017;Paterson & Ducea, 2015).
Tectonic processes may also help to maintain the continental and island arc dichotomy. Most modern island arcs are extensional (due to slab pull and trench retreat; Lallemand et al., 2005), which serves to maintain high arc crust temperatures, and may directly reduce crustal thicknesses, in some cases resulting in intra-arc rifting and arc-relocation. A prime example of extensional arc failure is the Marianas, where the construction of the third iteration of arc crust is currently underway (the first two resulting in the Kyushu-Palau and West Mariana Ridges; Beccaluva et al., 1980). Tectonic processes may similarly be important in generating the thickest arcs today. Cumulates produced at pressures above 10-12 kbars are garnet-rich (Ducea et al., 2021;Jagoutz et al., 2011;Lee & Anderson, 2015) and have high densities and fast seismic velocities. These cumulates may delaminate and will also have seismic velocities comparable to mantle peridotite Müntener & Ulmer, 2006), and thus arc magmatism alone should struggle to produce seismically observable arc crust thicker than ∼42 km. Instead, tectonic shortening and underplating must play an important role in producing the thickest continental arcs observed today.
Distinct mechanisms may counteract both factors to improve the efficiency of continental crust construction at island arcs. As in thick continental arcs, if island arcs transition to compressional settings, tectonic overthickening or underplating could increase crustal thickness and depress upper plate temperature profiles. This newly thickened and cooler crust would cause future magmas to differentiate deeper, generating a durable increase in crustal thickness. However, as most modern island arcs are extensional, tectonic shortening may mostly become relevant during island arc collision events (Niu et al., 2013). Alternatively, if island arcs transition to more continent-like magmatism, that is, lower magmatic fluxes and more H 2 O-rich magmas, crustal thickening may also occur. Factors otherwise characteristic of continental arcs that promote more hydrous magmas are shallowing slab dips or trench-ward arc migration. Both reduce the mantle wedge melting column beneath the arcs and thus reduce the decompression melting productivity, which should in turn increase H 2 O contents in parental magmas.
The Aleutian Arc provides a compelling example of how these processes can interact to produce continent-like crust at an island arc. Among island arcs the Aleutian arc has an unusually shallow sub-arc slab depth ( Figure 13) and as discussed above, may have thicker than typical island arc crust and is well-known for producing continental crust-like calc-alkaline magmas (e.g., Kay & Kay, 1985). The Aleutian arc is also unusual in that it is a comparatively long-lived island arc that has never undergone intra-arc rifting (Jicha et al., 2006). It has been shown that subduction zone age correlates with slab dip (Hu & Gurnis, 2020), and thus the unusual long-term survival of the Aleutian arc may have primed it to evolve to a more hydrous, thicker arc. Finally, if the flux of subducted crustal material is a critical factor in continental arc magmatism, island arcs proximal to continents may subduct larger volumes of terrigenous sediments, as is currently occurring in the southern Lesser Antilles.

Conclusion
Our new proxies show that for arc magmas, the olivine-clinopyroxene and clinopyroxene-plagioclase cotectics are dominantly controlled by (early) fractionation pressure and H 2 O content, respectively. These proxies reveal that arcs with hydrous, deeper fractionating melts evolve toward the calc-alkaline compositions characteristic of continental crust as opposed to drier, shallower fractionating arc systems that typically follow Fe-enrichment trends in island arcs. Governing factors appear to relate to the upper plate crustal thickness and to a lesser extent mantle wedge height.
The strong correlation between early fractionation pressure and arc crustal thickness points to strong control of the plagioclase-in boundary and highlights the importance of the upper plate temperature in controlling the differentiation pressures of arc magmas. The relationships between hydration proxies and subduction zone physical parameters allow for two opposing interpretations: (a) when all arcs are taken together, an apparent inverse relationship between mantle wedge height and magma hydration state indicates that the relative contribution of decompression melting to arc magmatism decreases with decreasing melting column height; or (b) when continental and island arcs are considered separately, continental and island arcs are quite distinct. Specifically, continental arcs have restricted proxy values consistent with H 2 O-rich LLDs but span a range of mantle wedge heights and crustal thicknesses, while island arcs have a wide range of hydration states but quite limited ranges of mantle wedge heights and crustal thicknesses. This dichotomy suggests that fundamental differences exist in magma generation processes between continental and island arcs. Finally, these distinct models suggest contrasting processes by which thick, calc-alkaline continental crust can be generated at initially thin and dominantly tholeiitic island arcs.

Data Availability Statement
No new data were produced during this project. All data compiled as part of this research are available on figshare at https://dx.doi.org/10.6084/m9.figshare.22621027. Detailed comments on a previous version of this manuscript by editor Jane Blichert-Toft, Tom Sisson and an anonymous reviewer helped to significantly refine this work. BZK and OJ were supported by NSF Grant EAR-1552202, and BZK acknowledges additional funding from the University of Lausanne.