Possible threshold controls on sediment grain properties of 1 Peruvian coastal river basins

10 Twenty-one coastal rivers located along the entire western Peruvian margin were analyzed to 11 determine possible controls on sediment grain properties. This represents one of the largest grain 12 size dataset that has been collected over a large area. Modern gravel beds were sampled along a 13 north-south transect on the western side of the Peruvian Andes where the rivers cross the tip of 14 the mountain range, and at each site the long a -axis and the intermediate b -axis of about 500 15 pebbles were measured. Morphometric properties of each drainage basin, sediment and water 16 discharge together with flow shear stresses were determined and compared against measured 17 grain properties. Grain size data show that the values for the D 50 are nearly constant and range 18 between 2-3 cm, while the values of the D 96 range between 6 and 12 cm. The ratios between the 19 intermediate and the long axis range from 0.67 to 0.74. Linear correlations between all grain size 20 percentiles and water shear stresses, mean basin denudation rates, mean basin slopes and basin 21 sizes are small to non-existent. However exceptionally large D 50 values of 4-6 cm were measured 22 for basins situated between 11-12°S and 16-17°S latitude where hillslope gradients are steeper 23


INTRODUCTION
The size and shape of gravels bear crucial information about (i) the transport dynamics of mountain rivers (Hjulström, 1935;Shields, 1936;Blissenbach, 1952;Koiter et al., 2013;Whittaker et al., 2007;Duller et al., 2012;Attal et al., 2015), (ii) the mechanisms of sediment supply and provenance (Parker, 1991;Paola et al., 1992a, b;Attal and Lavé, 2006), and (iii) environmental conditions such as uplift and precipitation (Heller and Paola, 1992;Robinson and Slingerland, 1998;Foreman et al., 2012;Allen et al., 2013;Foreman, 2014).The mechanisms by which grain size and shape change from source to sink have often been studied with flume experiments (e.g.McLaren and Bowles, 1985;Lisle et al., 1993) and numerical models (Hoey and Ferguson, 1994).These studies have mainly been directed towards exploring the controls on the downstream reduction in grain size of gravel beds (Schumm and Stevens, 1973;Hoey and Fergusson, 1994;Surian, 2002;Fedele and Paola, 2007;Allen et al., 2016).In addition, it has been proposed that the grain size distribution particularly of mountainous rivers mainly depends on: (i) tectonic uplift resulting in steepening of the entire landscape (Dadson et al., 2003;Wittmann et al., 2007;Ouimet et al., 2009), (ii) earthquakes and seismicity causing the release of large volumes of landslides (Dadson et al., 2003;McPhillips et al., 2014); (iii) precipitation rates and patterns controlling river discharge and shear stresses (D'Arcy et al., 2017;Litty et al., 2017); and (iv) bedrock lithology where low erodibilty lithologies are sources of larger volumes of material (Korup andSchlunegger, 2009, Allen et al., 2015).Accordingly, the sediment caliber in these rivers could either reflect the nature of erosional processes in the headwaters and conditions thereof (such as lithology, slope angles, seismicity releasing landslides), which then corresponds to supply-limited conditions.Alternatively, if enough material is supplied to the streams, then the grain size pattern mainly depends on the runoff and related shear stresses in these rivers, which in turn corresponds to transport-limited conditions.
The western margin of the Peruvian Andes represents a prime example where these mechanisms and related controls on the grain size distribution of river sediments can be explored.In particular, this mountain belt experiences intense and frequent earthquakes (Nocquet et al., 2014) in response to subduction of the oceanic Nazca plate beneath the continental South American plate at least since late Jurassic times (Isacks, 1988).Therefore, it is not surprising that erosion and the transfer of material from the hillslopes to the rivers has been considered to strongly depend on the occurrence of earthquakes (McPhilipps et al., 2014).On the other hand, it has also been proposed that denudation in this part of the Andes is controlled by distinct precipitation rate gradients.These inferences have been made based on concentrations of in-situ cosmogenic 10 Be measured in river-born quartz (Abbühl et al., 2011;Carretier et al., 2015;Reber et al., 2017), and on morphometric analyses of the western Andean landscape (Montgomery et al., 2001).
Accordingly, erosion along the western Peruvian Andes has been related to either the occurrence of earthquakes and thus to tectonic processes (McPhillips et al., 2014) or rainfall rates (Abbühl et al., 2011;Carretier et al., 2015) and thus to the stream's mean annual runoff (Reber et al., 2017).
Therefore, we hypothesize that hillslope erosion paired with the streams runoff are likely to have a measurable impact on the grain size pattern in the Peruvian streams.
Here we present data on sediment grain properties from rivers situated on the western margin of the Peruvian Andes (Figure 1A) in order to elucidate the possible effects of intrinsic factors such as morphometric properties of the drainage basins (mean slope, drainage area, stream lengths), and extrinsic properties (runoff and seismic activity) on sediment grain properties.To this extent, we collected grain size data from gravel bars of each stream along the entire western Andean margin of Peru that are derived from 21, over 700-km 2 -large basins.Sampling sites were situated at the outlets of valleys close to the Pacific Coast.This represents one of the largest grain size datasets that have ever been collected over areas which have experienced different tectonic and climatic conditions.

Geologic and tectonic setting
The study area is located at the transition from the Peruvian Andes to the coastal lowlands along a transect from the cities of Trujillo in the north (8°S) to Tacna in the south (18°S).In northern and central Peru, a flat, up-to 100 km wide, broad coastal forearc plain with Paleogene-Neogene and Quaternary sediments connects to the western Cordillera.This part of the western Cordillera consists of Cretaceous to late Miocene plutons of various compositions (diorite, but also tonalite, granite and granodiorite) that crop out over an almost continuous, 1600-km long arc that is referred to as the Coastal Batholith (e.g.Atherton, 1984;Mukasa, 1986;Haederle and Atherton, 2002; Figure 1B).In southern Peru, the coastal plain gives way to the Coastal Cordillera that extends far into Chile.The western Cordillera comprises the central volcanic arc region of the Peruvian Andes with altitudes of up to 6768 m.a.s.l., where currently active volcanoes south of 14°S of latitude are related to a steep slab subduction.On the other hand, Cenozoic volcanoes in the central and northern Peruvian arc have been extinct since c. 11 Ma due to a flat slab subduction, which inhibited magma upwelling from the asthenosphere (Ramos, 2010).
The bedrock of the Western Cordillera is dominated by Paleogene, Neogene and Quaternary volcanic rocks (mainly andesitic or dacitic tuffs, and ignimbrites) originating from distinct phases of Cenozoic volcanic activity (Vidal, 1993).These rocks rest on Mesozoic and Early Paleogene sedimentary rocks (Figure 1B).
The tectonic conditions of the western Andes are characterized by strong N-S gradients in Quaternary uplift, seismicity and long-term subduction processes, which in turn seem controlled by a plethora of tectonic processes.The northern segment of the coastal Peruvian margin (i.e. to the north of 13°S latitude), hosts a coastal plain that shows little evidence for uplift, and the Nazca plate subducts at a low angle.Also in this region, the occurrence of large historical earthquakes at least along the coastal segment has been much less (Figure 2c).Only in northernmost Peru (4° to 6° S latitude) uplift of the coastal area is associated with subduction earthquakes (Bourgois et al., 2007).Further south, in the Cordillera Blanca area (around 12° S latitude) may have been uplifted due to upwelling of magma (McNulty and Farber, 2002).In particular, the coastal segment south of 13°S hosts raised Quaternary marine terraces (Regard et al., 2010), suggesting the occurrence of surface uplift at least during Quaternary times.Since the number and altitude of the terraces increases closer to the area where currently the Nazca ridge subducts, uplift of the coastal area in a radius of approximately 200 km around the ridge (roughly 12° to 14° S latitude) is attributed to ridge subduction (Sébrier et al., 1988;Macharé and Ortlieb, 1992).Between 15° and 18° S latitude, uplift is associated with bending of the Bolivian orocline (Noury et al., 2016).The area south of 12° S latitude is also the segment of the Andes where the number of earthquakes with magnitudes > 4 has been large relative to the segment farther north (Figures 1 and 2c).In contrast, the northern segment of the coastal Peruvian margin (i.e., to the north of 13°S latitude), hosts a coastal plain that has been subsiding and the Nazca plate subducts at a low angle.Also in this region, the frequency of large historical earthquakes at least along the coastal segment has been much less (Figure 2c)

Morphology
The local relief along the western Cordillera has been formed by deeply incising rivers that flow perpendicular to the strike of the Andes (Schildgen et al., 2007).The morphology of the longitudinal stream profiles is characterized by two segments separated by a distinct knickzone (Trauerstein et al., 2013).These geomorphic features have formed through headward retreat in response to a phase of enhanced surface uplift during the late Miocene (e.g., Schildgen et al., 2007).Upstream of these knickzones, the streams are mainly underlain by Cenozoic volcanoclastic rocks, while farther downstream incision has disclosed the Coastal Batholith and older meta-sedimentary units (Trauerstein et al. 2013).The upstream edges of these knickzones also delineate the upper boundaries of the major sediment sources (Litty et al., 2017).Little to nearly zero clastic material has been derived from the headwater reaches on the Altiplano, where the flat landscape has experienced nearly zero erosion, as 10Be-based denudation rate estimates (Abbühl et al., 2011) and provenance tracing have shown (Litty et al., 2017).
The pattern of mean slopes per drainage basin reveals a distinct N-S trend (Table 1).The corresponding values increase from 20° to 25° going from 6°S to 10°S latitude (where they reach maximum values between 0.4 to 0.45 m/m) after which they decrease by nearly 50% to values ranging between 10° and 15°.These relationships have not been explored yet, but most likely reflect the extent to which streams have crossed the western escarpment and sourced their waters in the relatively flat plateau of the Puna region.Indeed, most of the western Peruvian streams have their water sources on this flat area and then cross the western escarpment, which yields relatively low mean basin slopes particularly for basins south of 12°S.Contrariwise, the basins around 11°-12°S latitudes (which are characterized by the steep slopes) have their sources in the relatively steep Cordillera Negra (Figure 1A), which is a relatively dry mountain range situated on the steep escarpment.Along these latitudes, the high Andes are constituted by the high and heavily glaciated Cordillera Blanca situated farther to the east (Figure 1A).This mountain range is drained by the Rio Santa, which flows parallel to the Andes strike within the valley of the Rio Santa , and then crosses the Cordillera Negra at a right angle (Figure 1A).

Climatic setting and runoff of streams
The Peruvian western margin shows an E-W contrasting precipitation pattern with high annual precipitation rates up to 800 mm on the Altiplano and c. 0 mm per year on the coast ( (Huffman et al., 2007;Figure 1C).This precipitation gradient in the western Andes is related to the position of the Intertropical Convergence Zone (ITCZ, inset of Figure 1C) associated with an orographic effect on the eastern side of the Andes (Bookhagen and Strecker, 2008).During austral summer (January) the center of the ITCZ is located farther south, transferring the moisture from the Amazon tropical basin to the Altiplano (Garreaud et al., 2009) and leading to a wet climate on the Altiplano with high precipitation rates.During austral winter, the Altiplano is under the influence of dry air masses from the subsiding branch of the Hadley cell that result in a more equatorial position of the ITCZ and in a dry persistent westerly wind with almost no precipitation on the Altiplano.Additionally, the Andes form an orogenic barrier preventing Atlantic winds and moisture from reaching the coast.In addition, every 2 to 10 years, near to the Equator, the Pacific coast is subjected to strong precipitation resulting in high flood variability, related to the El Niño weather phenomenon (DeVries, 1987).
Mean annual discharge of streams along the western Peruvian margin has been reported by Reber et al. (2017).These authors calculated mean annual discharge values using the TRMM-V6.3B43.2precipitation database by Huffman et al. (2007) as a basis.Reber et al. (2017, see their Table 3) corrected the theoretical values for water losses due to evaporation and irrigation using the gauging record of a minimum of 12 basins situated close to the Pacific ocean.For these areas hydrological data has been reported by the Sistema Nacional de Información de Recursos Hídricos (SNIRH).The hydrological data thus cover a time span of c. 12 years.The results show a pattern where mean annual ruonff of these streams ranges between c. 10-40 m 3 /s.Rivers where mean annual runoff values are nearly 80 m 3 /s comprise the Rio Santa at c. 9°S latitude (Figure 1A), which derives its water from glaciers in the Cordillera Blanca.Two other streams with high discharge values are situated at 16°-17°S (Rio Ocoña and Rio Camaña, Figure 1A) where the corresponding headwaters spread over a relatively large area across the Altiplano, thereby collecting more rain than the other basins.

SITE SELECTION AND METHODS
Sampling sites are situated in the main river valleys in the western Cordillera between 8°S and 18°S latitude just before it gives way to the coastal margin.Only the 21 main river basins were selected, which were generally larger than 700 km 2 .We selected the downstream end of these rivers for simplicity because this yields comparable conditions as the base level is the same for all streams.Sampling sites are all accessible along the Pan-American Highway (see Table 1 for the coordinates of the sampling sites).Additionally, the Majes basin (marked with red color on Figure 1A) has been sampled at five sites from upstream to downstream to explore the effects related to the sediment transport processes for a section across the mountain belt, but along the stream (Figure 3; Table 2).The Majes basin has been chosen because of its easy accessibility in the upstream direction and because the morphology of this basin has been analyzed in a previous study (Steffen et al., 2010).
We randomly selected five longitudinal bars where we collected our grain size dataset.It has been shown that using a standard frame with fixed dimensions to assist gravel sampling reduces user-biased selections of gravels (Marcus et al., 1995;Bunte and Abt, 2001a).In order to reduce this bias, we substituted the frame by shooting an equal number of photos at a fixed distance (c. 1 m) from the ground surface at each longitudinal bar.Ten photos were taken from an approximately 10 m 2 -large area to take potential spatial variabilities among the gravel bars into account.From those photos, the intermediate b-axes and the ratio of the b-axes and the long aaxis of around 500 randomly chosen pebbles were manually measured (Bunte and Abt, 2001b) and processed using the software program ImageJ (Rasband, 1997).Our sample population exceeds the minimum number of samples needed for statistically reliable estimations of grain size distributions in gravel bars (Howard, 1993;Rice and Church, 1998).
The pebbles were characterized on the basis of their median (D 50 ), the D 84 and the coarse (D 96 ) fractions.This means that 50%, 84% and 96% of the sampled fraction is finer grained than the 50 th , 84 th and 96 th percentiles of the samples.On a gravel bar, pebbles tend to lie with their short axis perpendicular to the surface, thus exposing their section that contains the a-and b-axes (Bunte and Abt, 2001b).However, the principal limitation is the inability to accurately measure the fine particles < 3 mm (see also Whittaker et al., 2010).While we cannot resolve this problem with the techniques available, we do not expect that this adds a substantial bias in the grain size distributions reported here as their relative contributions to the point count results are minor (i.e.

< 5%, based on visual inspection of the digital images).
Catchment-scale morphometric parameters and characteristics, including drainage area, mean slope angle for each catchment, slope angle of the stream channel at the sampling site and distances from the sample sites to the upper edge of the Western Escarpment were extracted from the 90-m-resolution digital elevation model (DEM) Shuttle Radar Topography Mission (SRTM; Reuter et al., 2007).
Because grain size patterns largely depend on water shear stresses, we explored where such correlations might exist.We thus computed water shear stresses  following Hancock and Anderson (2002) and Litty et al. (2016), where: (1).
Here, ρ=1000 kg/m 3 is the water density, g the gravitational acceleration, Q (m 3 /s) is mean annual water discharge that we have taken from Reber et al. ( 2017), W (m) the channel width, and S (m/m) is the channel gradient.Stream channel widths with an estimated error of 2 m were measured on satellite images where available, and on photos taken during the field campaign.
We were also interested in exploring whether sediment flux has a measurable impact on the grain size pattern because higher denudation rates could be associated with the supply of more coarsegrained material to the trunk stream This in turn could result in larger clasts in these streams and this could potentially cause gravel fronts to shift towards more distal sites (Dingle et al., 2017), thereby coarsening the sediment caliber at our sampling sites.These basins have recently been analyzed for 10 Be-based catchment averaged denudation rates and mean annual water fluxes (please see Reber et al., 2017, and information presented above).This allows us to explore whether sediment flux, which equals the product between 10 Be-based denudation rates and basin size, has a measurable impact on the grain size pattern.We have considered the 10 Be-based basin mean denudation rates (Reber et al., 2017; Table 1) as variable because higher denudation rates could be associated with the supply of more coarse-grained material to the trunk stream, which in turn could result in larger clasts in these streams.Furthermore, we also calculated mean basin sediment fluxes as a product between 10 Be-based denudation rates and basin size.We considered this variable because Possible covariations and correlations between grain size and/or morphometric parameters and basin characteristics were evaluated using Pearson correlation coefficients, thus providing corresponding r-values (Table 3).The r-values measure the linear correlations between variables.

Grain size
The results of the grain size measurements reveal a large variation for the b-axis where the values of the D 50 range from 1.3 cm to 5.5 cm (Figure 2h; Table 1).Likewise, D 84 values vary between 3 cm and 10.5 cm.The sizes for the D 96 reveal the largest spread, ranging from 6 cm to 31 cm.The ratio between the lengths of the b-axis and a-axis (sphericity ratio) is nearly constant and varies between 0.67 and 0.74 (Figure 2i).Note that between 15.6°S and 13.7°S, no gravel bars are encountered in the rivers where they leave the mountain range, and only sand bars can be found.Therefore no results are exhibited for these latitudes (Figure 2h and 2i).

The Majes basin
The D 50 percentile of the b-axis decreases from 6.2 cm to a value of 5.2 cm c. 80 km farther downstream (Figures 3 and 4 and Table 2).Likewise, the D 84 decreases from 19 cm to 8.7 cm, and the D 96 decreases from 31 cm to 11.6 cm (Figure 4).Geomorphologists widely accept the notion that the downstream hydraulic geometry of alluvial channels reflects the decrease of particle size within an equilibrated system involving stream flow, channel gradient, sediment supply and transport (Hoey and Ferguson, 1994;Fedele and Paola, 2007;Attal and Lavé, 2009).Sternberg (1875) formalized these relations and predicted an exponential decline in particle size in gravel-bed rivers as a consequence of abrasion and selective transport where the gravel is transported downstream.The relation follows the form: D x = D 0 e -αx (Sternberg, 1875).Here, the exponent α decreases from 0.3 for the D 96 to 0.1 for the D 50 (Figure 4).

Correlations between grain sizes and morphometric properties
Table 3 shows the Pearson correlation coefficients (r-value) between the grain sizes, the morphometric parameters and the characteristics of the basins.As was expected, the D 50 , D 84 and D 96 all strongly correlate with each other (0.73 < r-value < 0.93), but the b/a ratios do not correlate with any of the three percentiles (-0.1 < r-value < 0.1).Likewise, inter-correlation relationships also exist among other variables such as catchment area, distance from the western escarpment, sediment flux and water discharge (Table 3).The D 50 values positively but weakly correlate with the sizes of the catchment area (r-value = 0.31), the distances from the Western Escarpment (r-value = 0.35), the mean annual shear stress at the sampling site (r-value = 0.23), the denudation rates (r-value = 0.34) and the sediment fluxes (r-value = 0.42; Table 3).The D 84 and the D 96 values correlate positively with the mean annual shear stress exerted by the water flux with a r-value of 0.33 and 0.39 (Table 3).However, we note that these correlations are weak, and some might break apart if the largest values for e.g.shear stresses (Table 3) are removed.
At a broader scale, values of the D 50 are nearly constant between 2 and 3 cm (Table 3).The largest D 50 with values of up to 6 cm are encountered in streams that are either sourced in the Cordillera Negra where mean basin slope angles are larger than 20°, or in the Rio Ocoña and Rio Camaña rivers located at 16°-17°S, which have the largest mean annual discharge as they capture their waters from a broad area on the Altiplano.
The ratio of the intermediate axis over the long axis negatively correlates with the distance from the Western Escarpment (r-value = -0.33),albeit with a poor correlation, but a strong and positive correlation is found with the mean slope angles of the basins (r-value = 0.63; Table 3).

SLOPE ANGLE CONTROLS ON SPHERICITY
The poor negative correlation of -0.33 between the sphericity of the pebbles and distance from the escarpment edge (Table 3) prevents us from inferring a distinct control of this variable.On the other hand, the positive Pearson correlation of 0.63 between the sphericity of the pebbles and the mean basin slope is quite high (Table 3), thus pointing towards a significant control.This suggests that basins with steeper slopes produce rounder pebbles.We do not consider that this pattern is due to differences in exposed bedrock in the hinterland because the litho-tectonic architecture is fairly constant along the entire Peruvian margin (Figure 1).We tentatively infer that time scales of transport and evacuation of material are likely to be shorter in steeper basins compared to shallower ones.This might influence the shape of pebbles as they tend to flatten as effects of abrasion and 3D heterogeneities of bedrock that becomes more obvious with time and transport distance (Sneed and Folk, 1958).We thus see the positive correlation between mean hillslope angle and the sphericity of pebbles as a very likely consequence of shorter transport times in steeper basins, but we note that this hypothesis needs to be confirmed by detailed realtime surveys of material transport from sources down to the end of these rivers.

Downstream fining trends in the Majes basin indicate fluvial controls
In fluvial environments, the sorting of the sediment depends on the downstream distance from its source (Hoey and Ferguson, 1994;Kodoma, 1994;Paola and Seal, 1995).This is particularly the case for the Majes river, where we see an exponential, downstream fining trend (Figure 4).This is somewhat surprising because sufficiently voluminous sediment input from other sources may perturb any downstream fining trends in the grain size distribution (Rice and Church, 1998).
Likewise, in the Majes basin, the sediment supply from the hillslopes to the trunk stream has occurred mainly through debris flow processes and landsliding (Steffen et al., 2010;Margirier et al., 2015).So, while the supply of hillslope-dervied material is likely to have been accomplished by mass wasting processes, the evacuation and transport of this sediment down to the Pacific Ocean has occurred mainly through fluvial transport.

Grain size and earthquake impact
Landslides and debris flows represent the main processes of hillslope erosion and the main source of sediment in tectonically active orogens (Hovius et al., 1997;Korup et al., 2011).They are generally associated with triggers such as earthquakes or intense rainfall and generally supply coarse and voluminous sediments to the trunk rivers (Dadson et al., 2003;McPhillips et al., 2014).In that sense, we would expect a positive correlation between the frequency of large earthquakes and the grain size where an increase in earthquake frequency would induce an increase in landslide occurrence, thereby supplying coarser grained sediment from the hillslopes to the rivers.These relationships have been elaborated in multiples studies where positive relationships between landslide occurrence and the size of earthquakes have been documented (e.g., Keefer, 1984;1994;Parker et al., 2011).We note here that a global-scale correlation between earthquake magnitudes and areas affected by landslides suggests that mass movements are triggered by earthquakes if a threshold magnitude of 5.5 is exceeded (Keefer, 1984).Here, we consider earthquakes with magnitudes >4.5 because Figure 1 by Keefer (1984) suggests that earthquakes with magnitudes as low as 4.5 are theoretically able to release landslides over an area larger than 10 km 2 , which is already a large area.However, we do not see correlation between the number of recorded historical earthquakes larger than 4.5 Mw and the grain size data (Figure 2c).We then expect that the frequency of earthquakes larger than 4.5 Mw, and related to this, the subduction mechanisms, do not exert a measurable control on the grain size in the rivers of the western Peruvian Andes.

Possible threshold limits as controls on the grain size pattern
We consider the correlations between the grain size data and the basins scale properties (basin area, mean basin denudation rates, water shear stresses, sediment fluxes) as weak and unconvincing (Table 3).However, we recall that the D 50 records a nearly uniform pattern with values that range between 2-3 cm along the studied western Peruvian margin.However, higher values of up to 6 cm are either measured in streams where mean slope angles of the bordering hillslopes in the upstream basin exceed 20° (between 11° and 12°S) or where water runoff values are nearly twice as large as the mean of all Peruvian streams (ranging between 10-40 m 3 /s between 16° and 17°S; see Figure 3 and Table 3).Based on these observations, we tentatively interpret a supply control on the median grain size for the Cordillera Negra streams where slopes are mediating grain size through a threshold effect.In this case, these thresholds on the hillslopes are likely to be conditioned by the at-yield mechanical states of bedrock (Montgomery, 2001;Ouimet et al., 2009), where hillslopes with dip angles up to 20-25° can be sustained.Under these conditions, mass failure processes are likely to dominate the supply of material to the trunk stream, thereby increasing the caliber of the supplied material and causing the bedload material to coarsen.In the same sense, a threshold response to steeper slopes has been interpreted for the pattern of 10 Be-based denudation rates in the Andes (Reber et al., 2017) and in the Himalayas (Ouimet et al., 2009).In both cases, the relationships between denudation rates and mean basin slopes was considered to follow a non-linear diffusive mass transport model where denudation rates are proportional to mean basin slopes for low gradients, while these relationships become non-linear for slopes approaching a critical value.Reber et al. (2017) set this critical value to 27.5°, but the linear relationship of their dataset breaks apart for gradients larger than 0.4, which corresponds to an angle of c. 21°.At these conditions, hillslopes approach a threshold where slope angles are limited by the mechanical strength of bedrock (Montgomery, 2001;Schlunegger et al., 2013).Hillslope erosion is then mainly accomplished through mass failure processes, which in turn, is likely to supply more coarse-grained material to the trunk stream (see above), as modern examples have shown (Bekaddour et al., 2013).We note, however, that a confirmation of this hypothesis requires data about the spatial density and frequency of landslide occurrence along the western Peruvian Andes.This dataset, however, is not available yet, and its establishment warrants further investigations.
In basins situated between 16°-17°S, mean basin slopes are clearly below threshold conditions, but the D 50 is twice as large as in neighboring rivers.Interestingly, these streams have mean annual discharge values that are twice as large as the western Peruvian streams on the average.Similar to the Cordillera Negra, we relate the relationships at 16°-17°S to threshold controls.In this case, however, they are likely to be conditioned by transport.The mechanisms by which grain size can be mediated through a threshold effect upon transport are less well understood, but it has been known at least since the engineering work by Shields (1936), and particularly by Peter Meyer Müller (1948) that threshold conditions have to be exceeded and have a control on transport of grains in fluvial streams.As a consequence, at transport-limited conditions, sediment flux, and most likely also the caliber of the transported material, depends on the frequency and the magnitudes at which these thresholds are exceeded rather than on a mean value of water discharge (Dadson et al., 2003).This might be the reason why values of water shear stresses, that are calculated based on the annual mean of water flux, are not sufficiently strongly correlated with the D 50 values to invoke a strong controls thereof (Table 3).However, the lack of information about discharge patterns prevents us from calculating the magnitude-frequency distribution of runoff.Nevertheless, we consider the occurrence of larger peak floods for streams that capture a large portion of their waters on the Altiplano Plateau.This might indeed be the case for the Rio Ocoña and Rio Camaña.We thus tentatively assign large peak floods for these streams, which might explain the larger D 50 values encountered in their gravel bars.Although highly speculative, we support our statement by the highly seasonal character of preciptation occurrence particularly on the eastern Andean margin and the Altiplano Plateau, which is largely conditioned by the monsoonal Andean jet (see above).We note, however, that this statement warrants a high resolution hydrological dataset for the western Peruvian sreams, which is not available.
An exception from these relationships is presented by the Rio Santa (Figure 1A) where mean annual water discharge reaches a value of almost 80 m 3 /s, but where the size of the D 50 is low.
We relate this to the possible supply-limited state of this stream, conditioned by the orogenparallel valley of the Rio Santa between the Cordillera Blanca and the Cordillera Negra, which has acted as a subsiding graben since the past 5.4 Ma (Giovanni et al., 2010;Margirier et al., 2015) and which might thus have operated as a sediment trap.This interpretation is also consistent with the low 10 Be-based catchment averaged denudation rates measured for the Rio Santa basin, as noted by Reber et al. (2017).
Note that our inferences are largely based on the pattern of the D 50 , and that the consideration of the larger percentiles might add alternative views on our interpretations.However, since all percentiles are inter-correlated, as the pattern of the Pearson correlation coefficients suggests (Table 3), we think that our general conclusions about the occurrence of thresholds upon the supply and transport of sediment will not change.Note also that either transport or supply control and related thresholds were identified by Reber et al. (2017) for their explanation of the 10Bebased datasets on basin-averaged denudation rates on the western Peruvian Andes.We tentatively interpret that the grain size pattern of the Peruvian streams follows these lines.

Conclusion
We present a complete dataset about grain sizes for all major rivers that are situated on the western Andean margin of Peru.We did not find any correlations to the current seismic regimes, where a larger occurrence of earthquakes with magnitudes larger than 4.5 Mw is expected to increase the supply of coarse-grained material.However, we found that the values for the D 50 are nearly constant and range between 2 and 3 cm.Exceptionally larger D 50 values of 4-6 cm were measured for basins situated between 11-12°S and 16-17°S where hillslope gradients are steeper than average (i.e., 20-22°), and where mean annual stream flows exceed the average values of the western Peruvian streams (10-40 m 3 /s) by a factor of 2. We suggest that the generally uniform grain size pattern has been perturbed where either mean basin slopes, or water fluxes exceed threshold conditions upon the supply and the transport of material.This might have implications for our understanding of the controls on the grain size distribution of gravelly-based streams.The ta le also displays grain size results together ith the ri ers' and asins' properties and hydrologi al properties.
Morphometric dataset for the sampled drainage basins.All calculations are based on the 90 m resolution DEM (NASA) The precipitation, water discharge data and the denudation rates are from Reber et al., in review

Figure 1 :
Figure 1: A: Map of the studied basins showing the sampling sites and the western escarpment

Figure 2 :
Figure 2: Topography of subducting Nazca plate, where slab depth data has been extracted from

Figure 3 :
Figure 3: Geological map of the Majes basin overlain by the precipitation pattern (Precipitation

Figure 4 :
Figure 4: Grain size results along the Majes River.

Figure 4 :
Figure 4: Grain size results along the Majes River.

Table 1 :
Location of the sampling sites with the altitude in meters above sea level.The table also displays grain size results together with the rivers' and basins' properties and hydrological properties.

Table 2 :
Location of the sampling sites in the Majes basin and grain size results in the Majes basin.

Table 3 :
Results of the statistical investigations, illustrated here as correlation matrix of the rvalues.The valuess in bold show significant correlation between the grain size data and the different catchment scale properties.

Table 1 :
Location of the sampling sites with the altitude in meters above sea level.