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# Global chemical weathering dominated by continental arcs since the mid-Palaeozoic

## Abstract

Earth’s plate-tectonic activity regulates the carbon cycle and, hence, climate, via volcanic outgassing and silicate-rock weathering. Mountain building, arc–continent collisions and clustering of continents in the tropics have all been invoked as controlling the weathering flux, with arcs also acting as a major contributor of carbon dioxide to the atmosphere. However, these processes have largely been considered in isolation when in reality they are all tightly coupled. To properly account for interactions among these processes, and the inherent multi-million-year time lags at play in the Earth system, we need to characterize their complex interdependencies. Here we analyse these interdependencies over the past 400 million years using a Bayesian network to identify primary relationships, time lags and drivers of the global chemical weathering signal. We find that the length of continental volcanic arcs—the fastest-eroding surface features on Earth—exerts the strongest control on global chemical weathering fluxes. We propose that the rapid drawdown of carbon dioxide tied to arc weathering stabilizes surface temperatures over geological time, contrary to the widely held view that this stability is achieved mainly by a delicate balance between weathering of the seafloor and the continental interiors.

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## Data availability

All data generated or analysed during this study are provided in the online version of this article (Supplementary Data 13) and in Extended Data Tables 1 and 2. These data are also available via FigShare at https://doi.org/10.6084/m9.figshare.14877099 (Supplementary Data 1), https://doi.org/10.6084/m9.figshare.14877132 (Supplementary Data 2) and https://doi.org/10.6084/m9.figshare.14877162 (Supplementary Data 3). Source data are provided with this paper.

## Code availability

More details on the computational methods and tools used for this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank N. R. McKenzie and H. Jiang for comments that improved the manuscript. This study was supported by a Natural Environment Research Council (NERC) grant (NE/R004978/1) to T.M.G., which also supported T.K.H. and M.R.P. T.M.G. and T.K.H. were supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. R.D.M. was supported by the AuScope Simulation and Modelling National Research Infrastructure. A.S.M. was supported by the Deep Carbon Observatory, Richard Lounsbery Foundation and MCSA Fellowship NEOEARTH, project 893615. C.P.B. was supported by the National Sciences and Engineering Research Council of Canada (Discovery Grant RGPIN-2019-05709).

## Author information

Authors

### Contributions

T.M.G. conceived the idea, led the study, interpreted the data and prepared the manuscript and figures. T.K.H. performed the modelling, designed the network and carried out the analysis, with input from T.M.G. A.S.M. calculated the seafloor production rates, and both A.S.M. and R.D.M. provided support with GPlates and pyGPlates. M.R.P. and C.P.B. provided support with Sr isotope interpretation, and C.P.B. provided normalized Sr data. G.L.F. provided CO2 data, and both G.L.F. and E.J.R. assisted with palaeoclimate interpretation. T.M.G. wrote the manuscript with input from all co-authors.

### Corresponding author

Correspondence to Thomas M. Gernon.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review informationNature Geoscience thanks N. Ryan McKenzie, Hehe Jiang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Rebecca Neely, in collaboration with the Nature Geoscience team.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Relationship between seawater Sr composition and atmospheric CO2 since 410 Ma.

Bar plots showing the empirical rank correlation (Spearman’s rank correlation, in dark grey), BN rank correlation (modelled, light grey), and BN conditional rank correlation (modelled, red) for pCO2, and (87Sr/86Sr)sw, at lags from 0 to 50 Myr (that is, showing where pCO2 lags Sr). We present results for (a) the best estimate input time series (most probable values for pCO2 from Foster et al.12), and (b) using a set of 1,000 individual time series that captures the uncertainty in pCO2 and (87Sr/86Sr)sw. Here, the conditional rank correlation is the correlation between the two variables at a given lag, accounting for the effects of all shorter lags—similar in principle to the multivariate partial autocorrelation. The horizontal dashed lines denote 99% confidence intervals (t = 0.096). Note that the relationship between (87Sr/86Sr)sw and atmospheric CO2 is strongest at short (that is, zero) time lags (conditional correlation = -0.48), suggesting that the processes controlling seawater Sr influence atmospheric CO2 predominantly on short (<1 Myr) timescales. The conditional rank correlation of seawater Sr and CO2 at a lag of 20-25 Myr (albeit relatively weak) could either be due to some delayed Earth system response, or a correlation between Sr and another process driving CO2 variation on a different timescale. Note the reduction in the strength of the empirical and conditional correlations with the addition of input uncertainty.

### Extended Data Fig. 2 All tectonic, volcanic, geochemical and climate time series used in the network, and their uncertainty estimates.

See the Methods for full details of the uncertainties for each variable. The black line denotes the original input time series (mean values or ‘best estimates’ from both our analysis and prior studies). The shaded envelopes represent minimum and maximum values (light grey) and 90th and 10th percentiles (dark grey). The blue and green lines are examples of single realizations from the simulated input data set; that is, individual time-series that form part of the alternative data set used to investigate the effect of input uncertainty on the strength of correlations with (87Sr/86Sr)sw.

### Extended Data Fig. 3 The correlations of geologic processes with (87Sr/86Sr)sw and their time lags.

The plots show the empirical rank correlations (CEmp), Bayesian Network correlations (CBN), and BN conditional rank correlations (CCond), at time lags from 0 to 50 Myr in 2.5 Myr intervals, using the original, best estimate input data (Supplementary Data File S1). The values shown in dark grey on the plots are the highest absolute values of CEmp, and those in red are the highest absolute CCond. Horizontal dashed lines denote the confidence intervals for each node (t, light grey text), estimated based on the resolution of the original input data (before interpolation).

### Extended Data Fig. 4 The correlations of geologic processes with (87Sr/86Sr)sw and their time lags, using simulated input time series incorporating uncertainty estimates.

Similar to Extended Data Fig. 3, the plots show the empirical rank correlations (CEmp), Bayesian Network correlations (CBN), and BN conditional rank correlations (CCond), at time lags from 0 to 50 Myr in 2.5 Myr intervals. The difference here is that the model incorporates all the input uncertainty distributions (shown in Extended Data Fig. 2, and Supplementary Data File S2). Note that including these uncertainty distributions does not cause any major changes in the strength of correlations, or the apparent response timescales. The main changes (those above the confidence interval [CI] threshold) are shown by the vertical dashed lines (red for gain, blue for loss of Ccond); this includes an apparent weakening of the effects of atmospheric CO2 (likely due to the large uncertainty in this variable; Extended Data Fig. 2). We note however that this is replaced by ‘ice latitude’—a related proxy for climate state—at similar time lags. CI thresholds (dashed line, denoted t) are unchanged as these are estimates based on the resolution of the original input data.

### Extended Data Fig. 5 Present-day global distribution of continental volcanic arcs, and their Sr isotope compositions.

Map of continental volcanic arcs identified by Cao et al.15. The labels (a-h) correspond to the density histograms, which show the relative frequency of 87Sr/86Sr points for each arc from the EarthChem Library (earthchem.org). The mean and mode of the dataset (total N=5498) are represented by vertical dashed lines. Note that the relatively high 87Sr/86Sr compositions of the Central Zone of the Andean Belt can be explained by the presence of extremely thick crust in this region (>70 km) and a higher degree of crustal assimilation66.

### Extended Data Fig. 6 Effects of suture zones and seafloor production rates on the strontium isotopic composition of seawater.

Probability density for a, suture zone length9, identifying short (<5,180 km), intermediate (5,180-9,730 km), and long (=9,730 km) suture zones (note that these divisions are approximately equal quantiles); and b, seafloor production rates, discriminating low (<3.96 km2 yr−1), moderate (3.96-4.95 km2 yr−1) and high (>4.95 km2 yr−1) production rates.

### Extended Data Fig. 7 Clustering of continents within the tropics since 400 Ma.

Solid lines show the continental area within 20 (black) and 10 (red) of the equator through time, using the paleomagnetic reference frame of Domeier and Torsvik67, as extracted from Matthews et al.11. The dashed lines show the fractional area (that is, area within the belt divided by the total crustal area) through time. The source data are provided in Supplementary Data File S1.

### Extended Data Fig. 8 Calculation of seafloor production at mid-ocean ridges.

Diagram explaining the formal quantification of seafloor production rates (Methods). In GPlates, mid-ocean ridges contain both spreading and transform segments. a, and b, show how we distinguish these segments. Each mid-ocean ridge line is broken into separate segments. We take the mid-point of each segment and draw the tangent to it. In some cases this matches the segment quite well (for example, a) and in other cases the segment is more curved (for example, b). We then draw a great circle from the stage pole that describes the motion of one ridge flank from the other, to the mid-point of the segment. We then calculate the deviation angle between these two lines. As transform segments should form small circles around the stage pole, their deviation angle should be large, whilst the deviation angle for spreading segments should be small. We found 70 was a reasonable cut off, though in some locations where spreading is poorly constrained or very oblique, it does not work completely. Once we distinguished the spreading and transform segments, we extract the full spreading velocity of each segment c, and multiply this by the length of the ridge segment to calculate the crustal production.

### Extended Data Table 1 Correlations for all nodes in our final Bayesian Network with (87Sr/86Sr)sw.

Note that CEmp = Empirical Rank Correlation; CBN = BN Rank Correlation; CCond = Conditional Rank Correlation; Av = Average value over a 2.5 Myr window, up to the given lag (in Myr); for example, LIP eruptive area Av 7.5 Myr is the correlation between Sr and the average LIP eruptive area over time ≥(t-7.5) Ma to time <(t-5) Myr (note that if this is not specified the interval is 0 Myr; that is no lag). Nodes with CCond greater than the 99 percent confidence interval threshold (CIthresh, see the Methods for further details) were retained in the BN and are shown here. The reader is directed to Supplementary Data File S3 for the full table of correlations that includes nodes that were subsequently eliminated from the BN. Correlations calculated using (a) original inputs, and (b) simulated inputs (incorporating uncertainty distributions) are shown for comparison. To investigate how input uncertainty might affect the estimated correlations, we took the BN structure obtained using our original ‘best estimate’ data and recalculated all the network parameters using our new simulated data set. The resulting CEmp, CBN and CCond are shown in the last three columns. This shows that the dominant processes, that is, those nodes with the strongest influence (rows in bold), do not change significantly; and all nodes with the highest CCond remain highest within the simulated output.

### Extended Data Table 2 Empirical rank correlations (CEmp) for (87Sr/86Sr)sw, normalized (87Sr/86Sr)sw, and 87Sr/86Sr of igneous (ign.) rocks20, with all unlagged observables.

Note that the data used to calculate the correlations CEmp in this table span the interval from 1-360 Ma (that is, to allow a direct comparison with Extended Data Table 1), and that no time lags are included here.

## Source data

### Supplementary Data File S1

Time-series compilation of all data used in our network, spanning the period from 410–0 Ma. This includes (a) the predictor variables, which are: continental arc length15, suture zone length9, latitudinal extent of continental ice sheets9, continental area within 20 of the tropics (this study), continental area within 10 of the tropics (this study), plate tectonic fragmentation index (this study), subduction zone length11,60, seafloor production rates (this study), atmospheric pCO2 (ref. 12), area of LIPs within 15 of the tropics16, eruptive area of LIPs16, 87Sr/86Sr of continental igneous lithologies20; and (b) the node of interest, (87Sr/86Sr)sw (ref. 17), as well as a normalized version accounting for radioactive decay of 87Rb in the crust through geological time20. The records were interpolated to obtain a regular (1 Myr interval) time-series, and in cases where multiple values occurred within a single time stamp we used a moving average with a 1 Myr window.

### Supplementary Data File S2

Summary of the simulated time series (capturing uncertainty) for all input parameters, including the mean, median, 10th and 90th percentiles, and minimum and maximum values at 0.5 Ma time steps (see Methods for details). The full input file with all simulated inputs is 3 GB in size.

### Supplementary Data File S3

S3 tabulates the empirical rank correlations (CEmp) and BN correlations (CBN) for all individual input parameters and lagged parameters (the predictor nodes) with (87Sr/86Sr)sw (the node of interest). These were calculated by generating a saturated Bayesian Network with all 254 nodes (including lags), and computing CEmp and CBN for all predictor nodes with (87Sr/86Sr)sw. Correlations have been calculated using both the original (‘best estimate’) input data set and also the simulated data set, to evaluate the effect of input uncertainty (see Extended Data Fig. 2).

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Gernon, T.M., Hincks, T.K., Merdith, A.S. et al. Global chemical weathering dominated by continental arcs since the mid-Palaeozoic. Nat. Geosci. 14, 690–696 (2021). https://doi.org/10.1038/s41561-021-00806-0

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• DOI: https://doi.org/10.1038/s41561-021-00806-0

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