Across-strike asymmetry of the Andes orogen linked to the age and geometry of the Nazca plate

The spine of Andes – the trace of the highest mountain topography – weaves back and 15 forth, in places near the coastline, in others farther inland. Its position is thought to be partially influenced by the asymmetric distribution of rainfall causing the migration of the topographic divide (i.e. mountain peaks) in favor of the more erosive (wetter) side and consuming the less erosive (drier) side. Here, we demonstrate that erosion rates in the Andes are not controlled by rainfall and conclude that the position of this mountain chain is better described by the age and 20 radius of curvature of the subducting Nazca plate. Our results suggest that mountain range migration might be a common component of orogenesis but for reasons different than those predicted by coupled climate-tectonic models. Cyclical variations in Andean orogeny might also accompany lateral migrations of mountain ranges.

We also observe a relationship between rainfall ratio and orogen asymmetry that is weak when compared to slab age, yet statistically significant (Fig. 3C). To test the relative dependence of 95 asymmetry on slab age and rainfall, we use an added variable analysis by adding slab age and rainfall ratio as independent predictors, one at a time in a multilinear model composed of the two. This analysis shows that the correlation is reduced to a small range in asymmetry after correcting for slab age (Fig. 3D), which is not the case after correcting for rainfall ratio (Fig. 3E).
To test if rainfall ratio correlates with the orogen's deviation from symmetry, we invert the 100 asymmetry metric (i.e. 1 -Wp/Wt), normalize it by 0.5 (maximum asymmetry), and take the absolute rainfall ratio for cases of higher rainfall in the retro-wedge, thus making both rainfall ratio and asymmetry metrics unidirectional. This shows no relationship between asymmetry and rainfall ratio (Fig. 3F), which is in line with the added variable analysis (Fig. 3E). The highest asymmetries are located where it rains two to three times on one said compared to the other, 105 suggesting that the highest rainfall ratios observed for moderate asymmetries could be coincidental (Fig. 3C, F). Normalizing rainfall ratio by the height of mountains does not change these results, further supporting the latter statement (Fig. S4). Thus, orographic rainfall does not control the position of the mountain range divide despite being a consequence of it. 110 We maintain that just as the subducting plate age and geometry control mountain building, they also significantly control the asymmetry of orogenic wedges. Low-angle subduction increases plate coupling (15,23) and stress propagation into the overriding plate (24,25). Also, as slab angles decrease, the position of melting in the mantle wedge is pushed farther away from the trench and underneath the overriding arc (22). Consequently, slab angles also control the position of magmatic production and therefore accretion to the orogen unlike collisional orogens. Moreover, the Nazca slab age and thickness in concert with the crustal thickness in the Andes have been used to explain the variations in shear force at the plate interface and ultimately the vertical and horizontal stress distributions in the Andes, with older slabs and thicker overriding plates associated with high vertical stresses near the trench (16), consistent with our results (Fig.   120 3A, B). By extension, this suggests that orographic precipitation cannot create asymmetric mass fluxes capable of offsetting the primary controls by subduction zone dynamics in the Andes, which is in line with previous studies (9) and is further explored in the next section. 125 Rainfall can modulate the relationship between hillslope gradient and river channel steepness across different climatic regimes in the Andes ( However, these distinctions need not require changes in erosion rates as these are most strongly controlled by hillslope gradients irrespective of rainfall rates ( Fig. 4D-F). If anything, precipitation rates are important at the transition from arid to semi-arid climates, where a 250 mm/a rainfall-rate threshold might be enough to achieve high erosion rates (Fig. 4E, F). Further 135 increases in rainfall rates are not associated with systematic changes in erosion rates (Fig. 4F) just as orogenic asymmetry is insensitive to high rainfall ratios (Fig. 3F). The variability in erosion rates decreases with increasing rainfall rates (Fig. 4E), consistent with observations in This manuscript has not been peer-reviewed.

Similar erosion rate but different landscape form
Submitted to Science Advances 8 the Andes and Himalaya (27,28). Similarly eroding landscapes have a wide range of river steepnesses, hillslope gradients, and rainfall rates but are much more dependent on hillslope gradient (Fig. 4D, E). These results are in line with global and regional studies (2,7,9,10,13) That rainfall rates are imprinted in landscape form does not mean it can move mountains.
Erosion rates on either side of a mountain range need to follow the rainfall trends for summits to systematically migrate laterally over the timescale of tectonic accretion. Such a pattern would 145 require that hillslope transport and erosional efficiencies were controlled by rainfall as has been previously proposed (29)(30)(31). However, these predictions might be more complex due to the influence of vegetation for climates with greater than 250 mm/a rainfall rates (28). In the southern Central Andes, erosional efficiency in semi-arid landscapes is equivalent to that of temperate landscapes (2,9). Thus, assuming erosion rates are equivalent to rock uplift rates in 150 our dataset, how landscapes respond to differences in tectonic regimes does not seem to be primarily a function of climate. This result is in line with the small or inexistent role of rainfall on orogen asymmetry (Fig. 3). These observations also reinforce previous notions from the literature that while rainfall modulates landscape form, it does not modulate the pace of erosion (26,32). 155

Lateral migration of mountain ranges
Our data suggests that the mountain range may change position within the orogenic wedge over time as a function of the subducting slab age and geometry. This result is a natural conclusion given the correlations we documented and inferences that the geometry of the subducting Nazca plate changed systematically over at least the last 40 Ma (33). A change in the mountain range axis position does not require a change in the width of the orogenic wedge as has been demonstrated in numerical models (34) and agrees with observed variations of the loci of Andean mountain building in the northern Central Andes (35). In fact, it has been proposed that these relationships are all part of an Andean cycle of mountain building, magmatic production, 165 and deformation (36,37).
Andean cyclicity has now been suggested based on geochemical (36)  across-strike lines depict swaths used in the analysis of orogen asymmetry. Each swath profile is 100 km wide and goes from the trench out to the deformation front (solid red line). Two northernmost points (marked by "x") were 195 excluded from geometry analyses as they might experience slab edge effects(50). Elevation of the Andes from 30 arc-second data colored according to the bottom color scale. Ridges on the Nazca plate (gray traces) coincide with outliers (faint numbered centerlines) in the asymmetry analysis (see Fig. 3): 1 -Orocline/Iquique ridge (-21°), 2 -Orocline (-19°), 3 -Nazca Ridge, 4 -Carnegie Ridge.

Fig. 3.
Age and radius of curvature respectively explain 67% and 45% of the variance in orogenic asymmetry.
Correlations between orogen asymmetry and (A) slab age at trench (R 2 = 0.67; p-value < 0.001; F-statistic = 37.3), 205 (B) equivalent radius of curvature for a plastic plate (R 2 = 0.45; p-value < 0.01; F-statistic = 11.6), and (C) prowedge (Rp) to retro-wedge (Rr) rainfall ratio (R 2 = 0.45; p < 0.01; F-statistic = 11.5). Outliers (gray circles) noncoincidentally correspond to key features in the Nazca plate (shown in Figure 2) and were excluded from this regression but not from the others. (D) Added variable plot showing that accounting for slab age removes most of the variance in orogen asymmetry (R 2 = 0.19; p = 0.05; F-statistic = 4.3). (E) Added variable plot showing that 210 accounting for rainfall ratio does not remove the variance in orogen asymmetry, which can still be accounted for using slab age (R 2 = 0.57; p < 0.01; F-statistic = 23.8). (F) Absolute rainfall ratios and orogen asymmetries normalized by 0.5 (0 is symmetric and 1 is 100% asymmetric) show no relationship with the absolute rainfall ratio (i.e. corrected for the expected direction of range migration) (R 2 = 0.04; p = 0.4; F-statistic = 0.7). The lower the Fstatistic, the closer to the null-hypothesis that variables are uncorrelated. Based on these plots we interpret that 215 asymmetric rainfall does not explain topographic asymmetry in the Andes. The viscous plate equivalent radius of curvature, Rvs(20), yields similar results as the one in Fig. 3B while a minimum radius of curvature used for simple slab geometries, Rmin(20), does not (Fig. S1). All regressions were performed using the Matlab's fitlm function with the robust routine which minimizes the effects of outliers. The same analysis using mean centered data is presented in the Supplementary Figure S5 along with regression coefficients for slope comparison (Supplementary Table S1). 220 basin-wide erosion rate data points in the Andes. Panel A shows relationships between hillslope gradient and river steepness colored by rainfall rates, with shaded bands indicating subsampled examples, B and C. For given hillslope 225 gradient (B) and river steepness (C) classes (bands in panel A), increases in rainfall are associated with shallower rivers (B, R 2 = 0.19; p < 0.01; F-statistic = 14) and steeper hillslopes (C, R 2 = 0.24; p < 0.01; F-statistic = 16).
Rainfall rates are well correlated with erosion rates in arid to semiarid (0 -250 mm/a) landscapes as indicated by an 230 R 2 of ~0.4 but these metrics are poorly correlated in wetter landscapes (F). R 2 values were computed in intervals of This manuscript has not been peer-reviewed.
Submitted to Science Advances 14 250 mm/a up to 1000 mm/a, and in intervals of 500 mm/a up to 3000 mm/a rainfall rates.

Other Supplementary Materials for this manuscript include the following: 385
Data Table S1 to S3 Data Table S1: Orogen data: Radius of curvature, slab age, asymmetry, and precipitation ratio. 390 Data Table S2: Erosion rate and topographic data.
Data Table S3: Excluded erosion rate data.

Materials and Methods
Orogen asymmetry, slab age and radius of curvature, and rainfall ratio Orogenic asymmetries were calculated as the ratio of distances between trench to peak mean topography and trench to retro arc deformation front (based on the published maps (15, 37)), thus ranging from 0 to 1, the latter being close to the retro arc deformation front (Fig. S2). 400 We acknowledge that the pro arc deformation fronts sometimes are not directly on the trench but somewhere between the trench and prowedge; however, the location of this prowedge front is not always well defined, unlike the trench. Furthermore, the subduction zone interface is where the ultimate megathrust is located and defines the western limit of the Andes orogen (37). 405 We chose the peak mean topography as an approximation of the greatest mass within the mountain range. Peak mean topography was identified in 100 km wide swath topographic profiles computed using Topotoolbox (41). A gaussian curve was fit to the mean topography, after which a tallest point was identified. Swath center lines follow the trench-normal azimuths (19) starting at the Nazca trench outline (Supplementary Dataset). Radius of curvature (19) and Rainfall ratio is calculated as the ratio between prowedge and retrowedge average rainfall. To do this, we averaged the rainfall rates west of the peak mean topography and divided those by the 415 average east of it. We used the 29-year average rainfall rates from the global dataset reanalyzed by the Climate Research Unit (20) and extends south of 35°S, unlike TRMM 2b31 (42). Rainfall ratios greater than one denote orographic effects with greater rainfall in the pro-wedge side. Ratios smaller than one were inverted and multiplied by -1 to preserve the scale of rainfall ratio on both sides. These ratios were then compared to the orogen asymmetry metric.

Morphometric indices and erosion rates
Erosion rates and basin morphometrics were paired in order to compare landscape morphometry and erosion rates (see Supplementary Dataset). The latter was obtained from the Octopus 2018 database (13). The entire Andean database contains 477 basins and we added 9 425 more from the Southern Central Andes yet not included to the dataset (9) for a total of 486 basins. Erosion rates from the latter were recalculated to the same production rate scaling method (43) used in the Octopus database. We excluded 65 replicates but do not have information on grain sizes, so those were not distinguished in the dataset. We also removed basins with drainage areas greater than 10 4 km 2 (39 basins) as these contain large alluvial areas and do not drain 430 predominantly one uplifting block. This way, all of the included basins have outlets west of the Andean deformation front (Fig. 2). One basin from ~49°S Latitude was excluded as its morphometry would not be comparable to the rest of the dataset given glacial activity. Lastly, we excluded 9 basins from the Bolivian Sub-Andean thrust fronts as these thrusts uplift exceptionally erodible sedimentary rocks that produce high erosion rates that are outliers in the 435 original dataset (44). All of the data, including excluded ones, are provided in Supplementary Dataset. It is worth noting that this dataset uses topographic shielding calculations which can bias erosion rates low (45) in the steepest basins. Therefore, not accounting for topographic shielding would potentially increase the dependence of erosion rates on hillslope gradient shown in Fig. 4D. For more information on cosmogenic nuclides and erosion rate calculations, see For the same basins, we extracted morphometric data from Shuttle Radar Topographic Mission (SRTM) 90 m dataset (46) using Topotoolbox (41) and the Topographic Analysis Kit (47) with default settings. We used 30 m SRTM data (46) for basins with drainage area smaller than 5 445 square kilometers. In the former, basin morphometrics were calculated using a threshold drainage area of 10 6 m 2 and in the latter, 5 x 10 5 m 2 . Both hillslope gradient and river steepness data are basin-wide averages. Hillslope gradient was first calculated as the steepest slope (m/m) in an eight-cell neighborhood around each pixel and then averaged over the area of the analyzed basins. River steepness (ksn) is first calculated for distinct river stretches using a concavity index 450 of 0.5 for all rivers with drainage area greater than the threshold area (quick method in TAK (47)). Basin-wide rainfall rates were obtained from the 11-year average Topographic Rainfall Measurement Mission 2b31 dataset (42), which is the most widely used in basin-wide erosion rate analyses.   The figures depict mean (red line), minimum (lower cyan line), maximum (upper cyan line) and standard deviation (blue lines) for elevations along a 100 km wide swath about a centerline (red line in map immediately below each swath). A gaussian fit to the average elevation to smooth out noises along the profile is shown in green along which the highest altitude is marked by a red diamond. The position of the diamond informs the asymmetry of the orogen. Here, rainfall ratio data were normalized by the maximum elevation (scaled 0 to 1, the latter being the maximum in the dataset) in the swath profile and subsequently multiplied by 0.5 to reduce spread 490 in the data. This slightly improves the relationship in Panel C but does not remove the dominance of slab age over the regression. (A) R 2 = 0.67; p-value < 0.001; F-statistic = 37.3, (B) R 2 = 0.31; p-value < 0.02; F-statistic = 7.92, (C) R 2 = 0.42; p-value < 0.005; F-statistic = 12.9, (D) R 2 = 0.35; p-value < 0.01; F-statistic = 9.56, (E) R 2 = 0.66; p-value < 0.001; F-statistic = 34.3, (F) R 2 = 0.14; p-value = 0.1; F-statistic = 2.95.

Fig S5: Mean-centered regression analyses show higher slope dependence of orogen asymmetry on tectonic metrics.
Here we performed the same analysis as in Figure 3 of the 500 main text but independent variables (slab age, radius of curvature, rainfall ratio) had the mean value subtracted and normalized by the standard deviation. Regression statistics and coefficients are presented in the Supplementary Table S1. Table S1: Summary statistics of mean-centered regressions to the data presented in Fig S5  and Fig. 3  P r e p r i n t ( V a l a n d W i l l e n b r i n g ) Dataset for Val and Willenbring (not peer reviewed) Data P r e p r i n t ( V a l a n d W i l l e n b r i n g )

505
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