Daniel Vázquez-Tarrío
email: danielvazqueztarrio@gmail.com

Hervé Piegay

Rosana Menéndez-Duarte

Textural signatures of sediment supply in gravel-bed rivers: revisiting the armour ratio

Keywords: Gravel-bed rivers, Armour ratio, Sediment supply, Bedload

The surface of the streambed in gravel-bed rivers is commonly coarser than the underlying bed material. This surface coarsening, or 'armouring', is usually described by means of the ratio between surface and subsurface grain-size metrics (the 'armour ratio'). Such surface coarsening is typical of river reaches that are degrading due to a deficit in sediment supply (e.g. gravel-bed reaches below dams or lakes), but non-degrading gravel-bed streams may also exhibit some degree of armouring in relation to specific hydrological patterns. For instance, selective transport during the recession limbs of long lasting floods may coarsen the bed more significantly than flash floods. Consequently, regional differences in bed coarsening should exist, reflecting in turn the variability in sediment and water regimes. In this paper, we explore the trends linking armour ratios to sediment supply, taking into account the differences in hydrological context. We based our analysis on a large data set of bedload and grain size measurements from 49 natural gravelbed streams and four flume experiments compiled from the scientific literature. Our main outcome documents how the balances between sediment yields and transport capacities have a quantifiable reflection on the armour ratios measured in the field: we report strong and statistically significant correlations between bedload fluxes and surface grain-size, and an asymptotic rise in armour ratios with the decline of sediment supply. Hydrological controls are also observed, but they are small compared to the signal related to sediment supply. Additionally, the trends observed in the field data are comparable to those previously documented in flume experiments with varying sediment feed. In this regard, different kinds of bedforms and particle arrangements have been commonly described with progressive reductions in sediment inputs and the subsequent coarsening of the streambed. Hence, armour ratios serve as a proxy for the general organization of the streambed of gravel-bed streams, and our results quantify this streambed adjustment to the dominant sediment supply regime.

Introduction

A longstanding idea in fluvial geomorphology is that balances between sediment transport capacities, water discharge and sediment supply influence channel geometry [START_REF] Parker | Physical basis for quasi universal relations describing bankfull hydraulic geometry of single thread gravel bed rivers[END_REF][START_REF] Parker | Transport of Gravel and Sediment Mixtures[END_REF], bed slope (e.g. [START_REF] Lane | Design of stable channels[END_REF][START_REF] Borland | Stream Channel Stability[END_REF][START_REF] Wilcock | Sediment transport primer: estimating bed-material transport in gravel-bed rivers[END_REF], streambed texture [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF][START_REF] Nelson | Response of bed surface patchiness to reductions in sediment supply[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF] and planform morphology [START_REF] Church | Bed material transport and the morphology of alluvial river channels[END_REF]. Short-term fluctuations in sediment supply (e.g. hillslope processes, bank erosion, fine release from the bed after large floods) lead to local and temporary adjustments in streambed texture (e.g. [START_REF] Church | Stabilizing self organized structures in gravel bed stream channels: Field and experimental observations[END_REF][START_REF] Clayton | Persistence of the surface texture of a gravel-bed river during a large flood[END_REF][START_REF] Turowski | Start and end of bedload transport in gravel bed streams[END_REF] and channel morphology (Hassan and Zimmerman, 2012). In the long term, the balances between sediment and water yields seem to exert a conspicuous control on dominant channel styles [START_REF] Montgomery | Channel-reach morphology in mountain drainage basins[END_REF][START_REF] Buffington | Changes in channel morphology over human time scales[END_REF] and river metamorphosis [START_REF] Métivier | Alluvial landscape evolution: what do we know about metamorphosis of gravel bed meandering and braided streams?[END_REF].

Seminal flume experiments by [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF], and early field observations (e.g. [START_REF] Gessler | The Beginning of Bedload Movement of Mixtures Investigated as Natural Armoring in Channels[END_REF][START_REF] Willets | The simulation of streambed armouring and its consequences[END_REF], reported how reductions in sediment supply tend to promote active channel narrowing, surface coarsening, bedload fining and transport rate decrease in gravel-bed rivers. Coarsening and fine sediment depletion in the riverbed is driven by a combination of winnowing during low flows [START_REF] Gomez | Temporal variations in bedload transport rates: the effect of progressive bed armouring[END_REF][START_REF] Gomez | Roughness of stable, armored gravel beds[END_REF][START_REF] Gomez | Effects of particle shape and mobility on stable armor development[END_REF], infiltration of fine sediment [START_REF] Marion | Experimental investigation of mobile armoring development[END_REF][START_REF] Curran | The importance of bed sediment sand content for the structure of a static armor layer in a gravel bed river[END_REF][START_REF] Berni | Characteristic time of sediment transport decrease in static armour formation[END_REF] and kinematic sorting [START_REF] Wilcock | The flow, the bed, and the transport: interaction in flume and field[END_REF][START_REF] Bacchi | The effects of kinetic sorting on sediment mobility on steep slopes[END_REF]Ferdowski et al., 2017) during bed load transport. Substantial subsequent work documents the influence of sediment inputs on the spatial and vertical patterns of grain size sorting [START_REF] Nelson | Response of bed surface patchiness to reductions in sediment supply[END_REF][START_REF] Recking | A comparison between flume and field bed load transport data and consequences for surface based bed load transport prediction[END_REF], the development of particle arrangements (e.g. [START_REF] Church | Stabilizing self organized structures in gravel bed stream channels: Field and experimental observations[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF] and overall streambed mobility [START_REF] Richards | Fluvial geomorphology: structured beds in gravelly rivers[END_REF][START_REF] Pfeiffer | Regional variation in gravel riverbed mobility, controlled by hydrologic regime and sediment supply[END_REF].

According to all of the above, surface grain-size responds to decreases in bedload through the expansion of coarse fixed patches [START_REF] Nelson | Response of bed surface patchiness to reductions in sediment supply[END_REF][START_REF] Yager | Taking the river inside: Fundamental advances from laboratory experiments in measuring and understanding bedload transport processes[END_REF], resulting in a general coarsening of the streambed [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF]. Hence, the degree of the latter may provide an idea of the dominant sediment supply conditions of a given river reach [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF][START_REF] Sklar | Translation and dispersion of sediment pulses in flume experiments simulating gravel augmentation below dams[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]. For this reason, fluvial geomorphologists have often used the field observation of surface coarsening as a way to characterize streambed mobility and/or to diagnose the magnitude of bed degradation below dams, for example (see Rollet et al. 2013;Vázquez-Tarrio et al. 2019). However, disparities in the patterns of sediment supply variability (e.g. at the annual, seasonal, intra-flood scale) between different hydrological contexts complicate the interpretation of surface coarsening measured in the field and its application to river diagnosis.

For instance, rivers experiencing long-lasting and sustained floods tend to exhaust fine sediment from the riverbed, which in turn enhances the degree of coarsening compared to the situation expected in streams with comparable sediment supplies, but submitted to flash floods [START_REF] Laronne | The non-layering of gravel streambeds under ephemeral flood regimes[END_REF][START_REF] Hassan | Experiments on the effect of hydrograph characteristics on vertical grain sorting in gravel bed rivers[END_REF]. The hydrological regime is then a source of variability in the degree of surface coarsening that overlaps the signal related to the dominant sediment supply conditions. Moreover, sediment supply is difficult to quantify due to inherent complexities in bedload measurement [START_REF] Pitlick | Differences in sediment supply to braided and single thread channels: what do the data tell us?[END_REF]; therefore, the field assessment of streambed response to sediment supply fluctuations is not easy.

In this paper, we build on these ideas in order to quantify the relative weight of sediment supply versus hydrological controls in governing surface armouring. To accomplish this, we based our analysis on a large compilation of grain-size measurements and bedload discharge information extracted from the scientific literature for 49 natural gravel-bed rivers and four flume experiments.

We structured this analysis in two steps. First, we performed a wide review of the compiled grainsize data, from which metrics adequate for exploring the links between bed texture and sediment supply were identified. Then, we performed a meta-analysis of the compiled data (based on the metrics introduced in the review) in order to highlight the main trends in armour ratios, and their covariation with channel hydraulics and bedload fluxes. Understanding the linkages between streambed texture and sediment transport regime is a key question in fluvial geomorphology, river ecology, civil engineering and river restoration [START_REF] Pfeiffer | Sediment supply controls gravel river geometry[END_REF]. Consequently, our analysis may have interesting implications for near-future research on gravel-bed rivers.

Compiled data

The dataset used in the present paper consists of grain-size and bedload measurements collected at 49 river sites (summarized in Table 1). An important amount of the compiled data derives from the extensive campaign of sediment transport measurements carried out on Idaho, Nevada [START_REF] King | Sediment transport data and related information for selected gravel-bed streams and rivers in Idaho[END_REF], Colorado and Wyoming rivers (Ryan et al., 2002;2005), which probably represents some of the best available datasets on bedload in gravel-bed rivers to date. These data have previously been presented and analysed in several papers (Ryan et al., 2002;2005;[START_REF] King | Sediment transport data and related information for selected gravel-bed streams and rivers in Idaho[END_REF][START_REF] Barry | A general power equation for predicting bedload transport rates in gravel bed rivers[END_REF]Mueller et al., 2005;[START_REF] Muskatirovic | Analysis of bedload transport characteristics of Idaho streams and rivers[END_REF][START_REF] Pitlick | Differences in sediment supply to braided and single thread channels: what do the data tell us?[END_REF]. The remaining data come from comparable measurements in other gravel-bed streams [START_REF] Milhous | Sediment transport in a gravel bottomed stream[END_REF]Emmet and Seitz, 1974;[START_REF] Seitz | Suspended and bedload sediment transport in the Snake and Clearwater rivers in the vicinity of Lewiston, Idaho[END_REF][START_REF] Jones | Sediment transport in the Snake and Clearwater rivers in the vicinity of Lewiston, Idaho[END_REF][START_REF] Reid | Dynamics of bedload transport in Turkey Brook, a coarse grained alluvial channel[END_REF][START_REF] Lisle | Stabilization of a gravel channel by large streamside obstruction and bedrock bends, Jacoby Creek, northwestern California[END_REF]1989;Williams and Rosgen, 1986;[START_REF] Gomez | Two data sets describing channel wide temporal variations in bedload transport rates[END_REF]Kuhle, 1992;[START_REF] Lisle | Spatial variation in armouring in a channel with high sediment supply[END_REF][START_REF] Andrews | Marginal bed load transport in a gravel bed stream, Sagehen Creek, California[END_REF]Reid et al., 1995;[START_REF] Madej | Channel response to sediment wave propagation and movement, Redwood Creek, California, USA[END_REF][START_REF] Mclean | Sediment transport along lower Fraser River: 1. Measurements and hydraulic computations[END_REF]Almedej, 2002;[START_REF] Church | Mobility of bed material in Harris Creek[END_REF][START_REF] Wilcock | A two fraction model for the transport of sand/gravel mixtures[END_REF][START_REF] Erwin | Downstream effects of impounding a natural lake: the Snake River downstream from Jackson Lake Dam, Wyoming, USA[END_REF][START_REF] Mueller | Sediment supply and channel morphology in mountain river systems: 2. Single thread to braided transitions[END_REF].

Grain sizes (surface and substrate/subsurface) for each selected river were obtained from the graphical reading of grain-size curves extracted from the corresponding papers. When bed material was sampled at several locations or moments in the same river, we averaged the results to obtain a characteristic grain-size measure for each case study. Stream discharge information is available for 44 of the 49 selected case studies, together with width-averaged data on the main ow characteristics (velocity, active width). Using this information, we computed bed shear stress 1 for more details see the supplementary files). We also compiled, for each case study, values for the representative channel-forming or dominant discharge (Table 2), which were derived from the information provided in the original papers about the bankfull discharge (in single-thread channels) or the ~1 to 2-year return period discharge (in multi-thread channels) (Table 2). Information on bedload discharges was also available (Table 1); in this regard, we acknowledge the great work of data compilation carried out by [START_REF] Recking | A comparison between flume and field bed load transport data and consequences for surface based bed load transport prediction[END_REF][START_REF] Recking | An analysis of nonlinearity effects on bed load transport prediction[END_REF], who provided bedload information for these field sites as supporting files (ibid). We grouped the data following three different criteria. We made an initial classification according to dominant channel morphology, grouping the different case studies as riffle and pool, step-pool and plane-bed channels (after [START_REF] Montgomery | Channel-reach morphology in mountain drainage basins[END_REF]. Due to its geomorphological significance, we also defined a separate group for multi-thread rivers, in spite of the fact that each single thread of a braided river commonly shows a riffle and pool or bar-pool morphology. We also classified the different data according to the general sediment supply conditions at the catchment scale (Table 3). Following [START_REF] Recking | Influence of sediment supply on mountain streams bedload transport[END_REF], we defined three main groups of data: i.

low sediment supply, with channels draining highly vegetated watersheds and no clear active sediment sources and/or alluvial material; ii. moderate sediment supply, with rivers located in catchments in which significant bare land areas and/or sparse vegetation, and punctually distributed active sediment sources, are observed; and iii. high sediment supply, with channels well-coupled to landslides/slope deposits, or fed by strong bank erosion and/or bar-edge trimming (e.g. channels with braided morphology). We based this classification on the scarce information (study site description, photographs, etc.) provided by the original studies and our own inspection of the rivers through Google Earth. Finally, we also grouped the compiled data according to --onsnow----flood streams (Table 3). Apart from field data, we also benefited from the results of previous flume experiments that explored the role of sediment feed reductions on the surface texture [START_REF] Church | Stabilizing self organized structures in gravel bed stream channels: Field and experimental observations[END_REF][START_REF] Hassan | Experiments on surface structure and partial sediment transport[END_REF][START_REF] Nelson | Response of bed surface patchiness to reductions in sediment supply[END_REF]. Streambed surface is, in general, coarser than the underlying subsurface grain-size distribution (GSD) in the compiled dataset: the average D50 and D84 are both coarser on the surface than the subsurface GSD (Figure 1A). The degree of surface coarsening has usually been quantified in D * ): the ratio between a characteristic grain size (normally, the median size) on the surface GSD and the same characteristic grain size in the subsurface GSD [START_REF] Bunte | Sampling surface and subsurface particle-size distributions in wadable gravel-and cobble-bed streams for analyses in sediment transport, hydraulics, and streambed monitoring[END_REF]:

Eq. 1

where Di refers to the ith-percentile of the GSD. A value of D * equal to 1 means that the surface and subsurface GSD are very similar. When the surface is coarser than the subsurface GSD, then D * > 1; the coarser the surface is compared to the subsurface GSD, the larger the D * . Average armour ratios are larger in the compiled data if estimated using the median size rather than using the D84 (~3.1 against ~1.8, respectively) (Figure 2), outlining that differences between both GSD are more important towards finer size fractions. In addition, some different tendencies could be appreciated according to channel morphology (Figure 3).

Apart from surface coarsening, some other complementary trends can be identified and seem intimately related to the former (Figures 1C and1D). For instance, the percentages of fine sediment are, on average, larger in the subsurface (~15%) than on the surface GSD (~6%) (Figure 1D). Furthermore, patterns of grain-size sorting also show differences: D84/D50 sorting indexes are again larger in the subsurface (~3.6 on average) than on the surface GSD (~2.1 on average), suggesting that subsurface GSD is more poorly sorted (Figure 1C). All these differences are -test for unequal variances, p-value<0.05). It could initially be thought that methodological biases may explain a part of these trends.

Subsurface GSD is commonly determined by sieving dredged or excavated bulk volume samples [START_REF] Church | River Bed Gravels: Sampling and Analysis[END_REF]. Conversely, a wide diversity of methods have been proposed to approach the surface GSD, such as the classical [START_REF] Wolman | A method for sampling coarse river-bed material[END_REF] pebble-count method, the photosieving approach [START_REF] Ibbeken | Photo sieving: A method for grain size analysis of coarse grained, unconsolidated bedding surfaces[END_REF][START_REF] Butler | Automated extraction of grain-size data for gravel surfaces using digital image processing[END_REF][START_REF] Rubin | A simple autocorrelation algorithm for determining grain size from digital images of sediment[END_REF][START_REF] Graham | Automated sizing of coarse-grained sediments: image-processing procedures[END_REF][START_REF] Buscombe | Estimation of grain size distributions and associated parameters from digital images of sediment[END_REF], Detert and Weitbrecht, 2013) or the more recent protocols based on highresolution topography (e.g. [START_REF] Heritage | Terrestrial laser scanning of grain roughness in a gravel bed river[END_REF][START_REF] Brasington | Modeling river bed morphology, roughness, and surface sedimentology using high resolution terrestrial laser scanning[END_REF][START_REF] Vázquez-Tarrío | Using UAS optical imagery and SfM photogrammetry to characterize the surface grain size of gravel bars in a braided river (Vénéon River, French Alps)[END_REF][START_REF] Woodget | Subaerial gravel size measurement using topographic data derived from a UAV SfM approach[END_REF]. Grain sizes determined from area-by-weight sample methods (like the photosieving approach) are not directly equivalent to grain sizes determined from volume-by-weight sampling procedures (e.g. size sieving of bulk volume samples) [START_REF] Kellerhals | Sampling procedures for coarse fluvial sediment[END_REF][START_REF] Bunte | Sampling surface and subsurface particle-size distributions in wadable gravel-and cobble-bed streams for analyses in sediment transport, hydraulics, and streambed monitoring[END_REF]. However, in the study cases compiled here, surface GSD was generally sampled using a grid-by-number pebble count, while subsurface GSD was always obtained from one variant or another (dredging, digg sampling strategy (Table 1). Particle-size distributions determined from volume-by-weight (sizesieving of bulk volume samples) and grid-by-number (pebble count) samples are said to be equivalent [START_REF] Kellerhals | Sampling procedures for coarse fluvial sediment[END_REF][START_REF] Bunte | Sampling surface and subsurface particle-size distributions in wadable gravel-and cobble-bed streams for analyses in sediment transport, hydraulics, and streambed monitoring[END_REF][START_REF] Rice | A hybrid method for size characterization of coarse subsurface fluvial sediments[END_REF], and so surface coarsening seems to be a real trend in the compiled data, and not an artefact issuing from methodological biases.

Sediment supply vs. hydrologic controls on surface coarsening and s

The grain size of sediment inputs should exert an obvious control on the grain calibre of the available bed material within a specific river reach, which in turn may condition the sediment size

In this regard, we could consider subsurface GSD as a proxy for the GSD of the average annual sediment inputs [START_REF] Kuhnle | Mean size distribution of bed load on Goodwin Creek[END_REF][START_REF] Lisle | Particle size variations between bed load and bed material in natural gravel bed channels[END_REF][START_REF] Church | Upland gravel-bed rivers with low sediment transport[END_REF][START_REF] Recking | An analysis of nonlinearity effects on bed load transport prediction[END_REF][START_REF] Segura | Coupling fluvial hydraulic models to predict gravel transport in spatially variable flows[END_REF], i.e. the GSD available in the subsurface should condition the GSD of the streambed surface. Within the compiled data, we observe some statistically significant and moderate correlation between surface and subsurface GSD (Figure 4), which highlights this undeniable influence of the sediment supply GSD on the GSD of the However, it is interesting to notice how variance in grain-size data is larger for surface than subsurface GSD (see Figures 1A andB). This suggests that grain-size variability introduced by the sediment supplies is diluted by the variability in surface coarsening introduced by some other controls.

In this regard, the compiled data show some statistically significant differences (ANOVA test, pvalue < 0.05) in armour ratios according to the amounts of sediment supply at the catchment scale (Figure 5): rivers with high sediment supplies tend to show lower armour ratios than streams with low sediment feeds. Surface coarsening ) has been described in gravelbed settings for a long time (e.g. [START_REF] Gessler | The Beginning of Bedload Movement of Mixtures Investigated as Natural Armoring in Channels[END_REF], and already related to the higher or lower availability of upstream sediment inputs. Armouring has been, thereby, typically reported in degrading beds and river reaches with low or no sediment supply (e.g. gravel-bed reaches below dams or lakes) [START_REF] Gessler | The Beginning of Bedload Movement of Mixtures Investigated as Natural Armoring in Channels[END_REF][START_REF] Willets | The simulation of streambed armouring and its consequences[END_REF][START_REF] Chin | Streambed armouring[END_REF][START_REF] Gomez | Effects of particle shape and mobility on stable armor development[END_REF]Vericat et al., Bertin and transport episodes with large sand sediment supplies [START_REF] Laronne | Interrelationships between bed morphology and bed material transport for a small, gravel-bed channel[END_REF][START_REF] Gomez | Temporal variations in bedload transport rates: the effect of progressive bed armouring[END_REF]Klaasen, 1988;[START_REF] Chin | Streambed armouring[END_REF][START_REF] Venditti | Can coarse surface layers in gravel bedded rivers be mobilized by finer gravel bedload? Eos Trans[END_REF][START_REF] Vericat | Breakup and reestablishment of the armour layer in a large gravel-bed river below dams: the lower Ebro[END_REF][START_REF] Wang | The Breakup of Armor Layer in a Gravel Bed Stream with No Sediment Supply[END_REF][START_REF] Venditti | Mobilization of coarse surface layers in gravel-bedded rivers by finer gravel bed load[END_REF][START_REF] Spiller | Artificial reproduction of the surface structure in a gravel bed[END_REF][START_REF] Curran | The importance of bed sediment sand content for the structure of a static armor layer in a gravel bed river[END_REF][START_REF] Orrú | Armor breakup and reformation in a degradational laboratory experiment[END_REF]Bertin and Freidrich, 2018) and re-form during the falling limb of the flood hydrograph, together with a progressive reduction in sediment mobility and the winnowing of finer and more mobile particles [START_REF] Mao | The effect of hydrographs on bed load transport and bed sediment spatial arrangement[END_REF]. However, >1) can also be observed in rivers fed by significant sediment supplies (Figure 5). Therefore, nondegrading gravel-bed streams with considerable sediment inputs may also exhibit some armouring. In truth, bedload transport models [START_REF] Wilcock | Persistence of armor layers in gravel-bed streams[END_REF], tracer studies [START_REF] Haschenburger | Partial transport in a natural gravel bed channel[END_REF], flume experiments [START_REF] Hassan | Experiments on the effect of hydrograph characteristics on vertical grain sorting in gravel bed rivers[END_REF], and field observations (Andrews and Erdman, 1986;[START_REF] Clayton | Persistence of the surface texture of a gravel-bed river during a large flood[END_REF][START_REF] Haschenburger | Streambed Disturbance over a Long Flood Series[END_REF] support the occurrence of such their persistence even during large floods. The sheltering of small particles into pockets and interstices between coarse grains can contribute to the development of these coarsened surfaces in well-supplied rivers (Parker et al., 1982;Parker and Klingeman, 1982;[START_REF] Andrews | Persistence in the size distribution of surficial bed material during an extreme snowmelt flood[END_REF][START_REF] Andrews | Formation of a coarse surface layer as the response to gravel mobility[END_REF][START_REF] Berni | Characteristic time of sediment transport decrease in static armour formation[END_REF]. Surface coarsening represents in these cases an effective mechanism allowing for the transport of the coarse fractions in the gravel load at the same rate as those which are finer (Parker and Klingemann, 1982;[START_REF] Parker | Equal mobility of gravel in streams: The remains of the day[END_REF][START_REF] Parker | 1D Sediment Transport Morphodynamics with Applications to Rivers and Turbidity Currents[END_REF]. As such, it leads to a progressive equalization between the bedload and the subarmour GSDs (Parker and Klingemann, 1982;[START_REF] Marion | Experimental investigation of mobile armoring development[END_REF]Mario et al., 2003;[START_REF] Mao | Grain size and topographical differences between static and mobile armour layers[END_REF][START_REF] Powell | Structural properties of mobile armors formed at different flow strengths in gravel bed rivers[END_REF] Moreover, in gravel-bed rivers, the amount of entrained bed material and the grain size of the bedload increase as flow discharge rises [START_REF] Milhous | Sediment transport in a gravel bottomed stream[END_REF][START_REF] Jones | Sediment transport in the Snake and Clearwater rivers in the vicinity of Lewiston, Idaho[END_REF][START_REF] Kuhnle | Mean size distribution of bed load on Goodwin Creek[END_REF][START_REF] Andrews | Marginal bed load transport in a gravel bed stream, Sagehen Creek, California[END_REF][START_REF] Wathen | Unequal mobility of sand and gravel in weakly bimodal sediment[END_REF][START_REF] Powell | Evolution of bed load grain size distribution with increasing flow strength and the effect of flow duration on the caliber of bed load sediment yield in ephemeral gravel bed rivers[END_REF][START_REF] Ryan | The nature of flow and sediment movement in Little Granite Creek near Bondurant[END_REF][START_REF] Wilcock | The flow, the bed, and the transport: interaction in flume and field[END_REF]McArdell, 1993, 1997;[START_REF] Clayton | Persistence of the surface texture of a gravel-bed river during a large flood[END_REF][START_REF] Pitlick | Differences in sediment supply to braided and single thread channels: what do the data tell us?[END_REF][START_REF] Recking | A generalized threshold model for computing bed load grain size distribution[END_REF]. We could, thereby, expect differences in mobility between different grain-size classes with fluctuations in flow discharge. Therefore, selective transport and horizontal winnowing of fines during recession limbs and/or low flows may exhaust the fine sediment and favour the development of a cover of coarse material preventing further sediment transport [START_REF] Harrison | Report on special investigations of bed sediment segregation in a degrading bed[END_REF][START_REF] Gessler | Self stabilizing tendencies of alluvial channels[END_REF][START_REF] Little | The role of sediment gradation of channel armoring[END_REF][START_REF] Proffitt | Transport of non uniform sediments[END_REF][START_REF] Chin | Streambed armouring[END_REF]. In this regard, perennial and seasonal streams subjected to long-lasting floods and sustained receding limbs might have more chances of suffering a coarsening of their bed surfaces and thus become more armoured. In the opposite extreme, we could consider streams experiencing flashing-flood hydrology. A flash flood involves a sudden increase of peak flows, bed shear stresses and equal mobility for all the particle sizes represented in the streambed [START_REF] Laronne | Very high rates of bedload sediment transport by ephemeral desert rivers[END_REF][START_REF] Laronne | The non-layering of gravel streambeds under ephemeral flood regimes[END_REF]Reid and Laronne, 1995). In such cases, we should not expect large differences between the surface, subsurface and bedload GSDs [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF][START_REF] Chin | Streambed armouring[END_REF][START_REF] Powell | Evolution of bed load grain size distribution with increasing flow strength and the effect of flow duration on the caliber of bed load sediment yield in ephemeral gravel bed rivers[END_REF][START_REF] Parker | Transport of Gravel and Sediment Mixtures[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF][START_REF] Bertin | Effects of surface texture and structure on the development of stable fluvial armors[END_REF]. As a result, streams receiving comparable amounts of sediment inputs may exhibit different armour ratios depending on the dominant hydrological regime [START_REF] Hassan | Experiments on the effect of hydrograph characteristics on vertical grain sorting in gravel bed rivers[END_REF].

Unfortunately, the compiled data are mostly from mountain streams dominated by snowmelt flow regimes, probably because planning field-campaigns in order to measure bedload is easier in this kind of rivers compared to rainfall-dominated settings, where it is more difficult to know in advance when a channel-forming flow is going to occur (also to monitor within a fairly deep flow channel with long rising and falling limbs). Thus, it is not easy to explore in depth the influence of hydrological regime with the available data. In any case, snowmelt-dominated rivers, usually submitted to sustained floods during the melting season, tend to show larger armour ratios than rainfall or flash-flood dominated streams (see dotplot shown in Figure 6). Furthermore, the percentage of fine sediment also tends to be lower in these snowmelt-dominated streams (Figure 6B), indicating fine sediment depletion during the long and gradually declining limbs of typical snowmelt hydrographs. On the other hand, glacial-fed rivers, which normally have high-sediment supplies from glacial/periglacial sources (particularly the glacial flour transported from glaciated upland basins), show relatively low armour ratios (Figure 6B). The influx of fine sediments represented by the glacial flour may help the coarse grains composing the armour layer to become more mobile [START_REF] Cui | Sediment pulses in mountain rivers: 1. Experiments[END_REF]Venditti et al. 2010a, b;[START_REF] Yager | Taking the river inside: Fundamental advances from laboratory experiments in measuring and understanding bedload transport processes[END_REF]. In addition, the flow regime of glacial-fed rivers is often characterised by daily peaks of discharge, rising and falling successively, and these somewhat shorter, rapidly changing hydrographs are less prone to promote armouring [START_REF] Hassan | Experiments on the effect of hydrograph characteristics on vertical grain sorting in gravel bed rivers[END_REF]. Hence, in conjunction, both issues may determine the relatively low armour ratios documented here in the case of glacial-fed rivers.

To summarize, our review of field data shows how sediment supply, together with the shape of the dominant flood hydrographs, condition surface armouring in gravel-bed rivers. The hydrological regime controls the rate at which bedload and fine sediment are winnowed and exhausted during the course of transport events. For instance, we can expect a less armoured surface if a continuous replenishment of sediment exists during the transport episode, as we can reasonably expect for glacial fed streams. In the opposite extreme, we can anticipate a better developed armouring and a streambed surface more depleted in fines in cases where the bedload is exhausted, which is likely when streams are subjected to long-lasting snowmelt hydrographs.

This is in accordance with the set of flume experiments by [START_REF] Hassan | Experiments on the effect of hydrograph characteristics on vertical grain sorting in gravel bed rivers[END_REF] who investigated the influence of different hydrographs on surface armouring and observed varying textural responses to steady vs. gradually varying flows. Nevertheless, fine sediment depletion during floods may take more or less time depending on the amount of sediment supplied from upstream sources. Therefore, the rate at which bedload is supplied into the channel may modulate the effects of flow hydrographs and strongly determine the rate and degree of fine sediment depletion, and consequently the degree of armour development.

Surface armouring and streambed mobility

As stated above, surface coarsening is associated with fine sediment exhaustion from the streambed and the development of clast arrangements and imbrications [START_REF] Church | Stabilizing self organized structures in gravel bed stream channels: Field and experimental observations[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]. The increase of particle stability linked to surface structuration may involve a decrease in the frequency of clast mobility and streambed disorganization [START_REF] Church | Stabilizing self organized structures in gravel bed stream channels: Field and experimental observations[END_REF][START_REF] Church | Mobility of bed material in Harris Creek[END_REF]. To further explore this issue, we introduce a new metric: the transport stage ratio * c *

). This is defined as the ratio between the peak basal shear stress for a given flow discharge and its critical value for incipient sediment motion. Critical stresses for sediment D84 (see supplementary files

for more information about how we computed transport stage ratios). Values of this metric, estimated at the dominant channel-forming discharge, are close to the critical thresholds for entrainment of the coarser fraction of bed sediment in well-armoured streams (Figure 7A). However, in poorly armoured streams, Shields stresses are well above these critical values. These poorly armoured streams also show larger bedload fluxes (see the values for transport intensities in Fig. 7A). A turning point can be defined close to an armour ratio of ~2:

there are no channels with large transport intensities ( > 0.0001) and high transport stages at dominant discharge * c * > 2) for armour ratios larger than 2. These observations confirm that overall streambed mobility would be larger in poorly armoured streams, and document how wellarmoured streambed surfaces are seldom moved. Considering all of the above, the compiled data support the idea of surface armouring being conditioned by dominant sediment supply conditions (section 2.2) -characterised by larger armour -(Figure 7B).

Quantifying sediment supply conditions in gravel-bed rivers

Our review of the literature clearly shows how the GSD of a , at a given river reach, adjusts to the volume of sediment inputs and the ability of the channel to export the available sediment inputs (Figures 6 and7), an idea already outlined by previous field and flume studies [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]. Introducing metrics allowing the quantitative description of the sediment supply is then of interest as shown by [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF] who proposed their own metric (q * ) [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF][START_REF] Montgomery | Channel-reach morphology in mountain drainage basins[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]:

Eq. 2

where qs refers to the bedload transport rate per unit width and the subscripts s and ss to the surface p 2 is the ratio between the sediment transport capacity to mobilize the surface GSD and the capacity to recruit sediment from a hypothetical surface as fine as the subsurface. When actual bedload rates match the bedload transport capacity of the channel, q * should equal 1. Conversely, if sediment inputs into the channel are lower than transport capacities, then q * < 1. Here we computed the q * ratio, based on flow characteristics at the representative channel-forming discharge and on equation (details on q * calculation are explained in the supplementary information, Subsection S.3). The obtained values of q * are in good agreement with our initial classification of compiled data as high-, moderate-and low-sediment supplied channels (Figure 8A).

However, t

q * has the problem of estimating bedload transport capacity of a channel for a hypothetical situation where the GSD equals its subsurface GSD (qss, denominator in eq. 2). In the field cases compiled here, this required the application of a bedload equation for the estimation of qss, with all the uncertainties linked to choosing the right formula. For that reason, we propose a simpler metric to quantify the ratio between the flux of sediment entering a given river reach, and the capacity of the channel to transport that sediment downstream: the ratio between bedload fluxes (qs) and stream power ( ) at the representative or dominant channel-forming discharge. This metric quantifies the mass of sediment carried by a river with a given amount of hydraulic power. Values of this ratio are in good agreement with our initial classification of the compiled data as high-, moderate-and low-sediment supply channels (Figure 8B), confirming its usefulness for characterizing the dominant sediment supply conditions in gravel-bed rivers. Using Meyer-these authors described the links between surface armouring (D50s/D50ss) and sediment supply (q * ) as:

Eq. 3

where is the basal shear stress and css is the critical shear stress for the inception of motion in the subsurface sediment. At the time when [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF] published their work, using Meyercommon use in sediment transport studies. However, more sophisticated bedload transport formulas have been proposed since then (e.g. [START_REF] Wilcock | Surface-based models for mixed size sediment[END_REF][START_REF] Recking | An analysis of nonlinearity effects on bed load transport prediction[END_REF], which proved to perform well for 1D computations of bedload in natural gravel-bed streams (e g. [START_REF] Parker | 1D Sediment Transport Morphodynamics with Applications to Rivers and Turbidity Currents[END_REF][START_REF] Recking | A comparison between flume and field bed load transport data and consequences for surface based bed load transport prediction[END_REF][START_REF] Camenen | Assessment of Methods Used in 1D Models for Computing Bed-Load Transport in a Large River: The Danube River in Slovakia[END_REF][START_REF] Vázquez Tarrío | Assessment of bedload equations using data obtained with tracers in two coarse bed mountain streams (Narcea River basin, NW Spain)[END_REF][START_REF] Hinton | Comparison of Calibrated Empirical and Semi-Empirical Methods for Bedload Transport Rate Prediction in Gravel Bed Streams[END_REF]. In this paper, based on 3) (after [START_REF] Recking | Quantifying the morphological print of bedload transport[END_REF] bedload equation, the following expressions are obtained (see details in the supplementary information):

for partial-mobility conditions Eq. 4

for full-mobility conditions Eq. 5

where f in eq. 4 is a parameter relating D50 * to D84 * (~1.4, according to Figure 2). Eqs. 4 and 5 provide a simple mathematical description of how D * should correlate and change with q * . As opposed to eq. 3, eqs. 4 and 5 use D84 * rather than D50 * , 3) equation works with the 84-th percentile of the surface GSD as the reference bed sediment size.

In Figure 9 we have plotted D84 * against q * for the field data, the latter estimated from flow characteristics at the dominant channel-forming q * calculation are explained in the supplementary information). We have also incorporated into this plot data from flume experiments (extracted from [START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]; see supplementary information), which tend to overlap the field data: armour ratios change with bedload supply following a similar trend in flume and field data. Additionally, the obtained fit is very close to the curve defined by eq. 4 (low-transport stage conditions). This suggests that partial mobility conditions may dominate bedload motion at the dominant discharge in well-armoured streams.

We also plotted armour ratios against qs/ ratios (Figure 10A), and the data show a moderate but statistically significant correlation between the qs/ ratio and the armour ratios. As shown above (Figure 4), Ds is partially controlled by Dss. This covariation may be introducing some noise in the plot shown in Figure 10A. In order to remove this effect, we propose a new version of the armour ratio (D ** ):

Eq. 6

where is the parameter defining how surface grain-size scales to subsurface grain-size.

According to Figure 4, is ~ 0.62 and ~0.41 for D84 and D50, respectively.

of the armour ratio shows a stronger correlation to the qs/ ratio (Figure 10B). Similar to Figure 9, Figure 10 shows how streambed surface tends to coarsen with decreasing sediment supplies (proxied here by the qs/ ratios). Although the number of plots is not well balanced across the different groups of data, it is worth pointing out that in Figures 9 and 10 rainfall data tend to plot close to the regression line, while snowmelt data tend to show a larger scatter and broader range of armour ratios. Snowmelt systems are typically located in the upper parts of the catchment compared to rainfall streams, which are usually located downstream, further from the coarser sediment sources. Consequently, this implies that rainfall streams will be somewhat less prone to develop larger armour ratios even if their sediment supply is limited. In this regard, large armour ratios may have some dependence on the upstream/downstream location of the stream and its particular geological context, as already suggested by [START_REF] Pitlick | Differences in sediment supply to braided and single thread channels: what do the data tell us?[END_REF].

Hydrological controls on surface armouring

Figures 9 and 10 clearly show how streambed surface evolves and becomes progressively armoured with declining sediment supplies. Nevertheless, there is a certain amount of scatter in both plots, which highlights that some variability in armour ratios may exist with a given sediment supply. Indeed, data from snowmelt streams tend to plot in the upper envelope of the point cloud in Figure 9 and, conversely, data from glacial-fed and flash-flood dominated streams tend to fall in the lower envelope, while flume data project in the middle of the point cloud, together with rainfall dominated rivers. Similarly, in Figure 6 snowmelt dominated streams tend to show larger armour ratios and smaller qs/ ratios than rainfall, flash flood and glacial-fed dominated streams.

All these observations highlight the variability in surface armouring and sediment supply conditions and their interplay with different hydrological regimes.

However, we should also consider that adjustments of the streambed to shifts in sediment supply conditions are not always synchronous and there is potentially a lag between the two. For instance, surface coarsening slowly propagates downstream after widespread land cover changes in the upland basin or downstream from a dam (Rollet et al., 2013), so it can take several years before we observe riverbed coarsening following a significant upstream perturbation. Furthermore, in snowmelt systems, some hysteresis in bedload supplies can be observed over the hydrological year [START_REF] Moog | Annual hysteresis in bed load rating curves[END_REF]; for instance, there can be significant bedload transport for a given discharge in early spring, while bedload rates are reduced for similar flow discharges occurring at the end of the flood season (Misset et al., in press). We have not controlled for all these variables, so they probably introduce additional scatter in the relations between surface armouring and sediment supply reported here.

Quantifying the variability in armour ratios

Based on the analysis performed in Subsections 4.1 and 4.2, we can conclude that surface coarsening accommodates to the dominant sediment supply conditions, but the rate at which bedload is emptied during the course of transport episodes may modulate the streambed adjustment to sediment supply. This may complicate the use of armour ratio for river diagnosis, insofar as the dominant sediment supply conditions are not the only drivers of surface grain-size in gravel-bed rivers. The rate at which fine bedload exhausts during floods, the seasonal variability in sediment availability and the time lag before the riverbed starts to respond after a significant shift in the upstream bed material supplies also have a non-negligible impact on the armour ratios documented at a given river reach. All these constraints may be largely dependent on site-specific controls, such as the cross-sectional extent of armour break-up, the shape and duration of the flow hydrograph, and the local availability of loose and fine sediment coming from upstream reaches and bank toes.

In this regard, Figures 9 and 10 not only illustrate how surface coarsening scales with sediment supply, but also show the range of potential variability in armour ratios for a given sediment supply and observed within the compiled field data. That said, we could report rivers more or less armoured than the streambed conditions expected for with a given bedload input, reminiscent of [START_REF] Jain | Armor or Pavement[END_REF][START_REF] Parker | Fluvial armor[END_REF], so we refer to more (or less) mobile armour layers than the average mobility expected for a given sediment supply condition (defined by the best fit in Figures 9 and10). To handle this variability, we performed a quantile regression analysis and plotted the regression between the different percentiles of the D * distribution and the sediment supply metrics (q* and qs/ ), obtaining two diagrams that illustrate the likelihood of a given value of D * (Figure 11A) or D ** (Figure 11B) with a given sediment supply. Fluctuations from the 1-st to the 99-th percentiles are linked to a set of factors, which include differences in the hydrological regime, seasonal variability and time passed after significant shifts in upstream sediment inputs. Thus, Figures 11A and 11B can be easily combined with some available qualitative information on a specific study site in order to have an idea of the most probable values for the armour ratio with 406 a given sediment supply and hydrological regime. 407 exhibit a lower degree of surface armouring, while plane-bed and step-pool channels show higher armour ratios. Higher armour ratios in step-pool channels could be related to the existence of jammed stones and large immobile boulders that may contribute to larger armour ratios. In plane bed channels, large protruding grains and immobile stones defining transversal ribs and cells are also common [START_REF] Church | Stabilizing self organized structures in gravel bed stream channels: Field and experimental observations[END_REF], and may help define a surface coarser than in riffle and pool and braided channels. Following this, eq. 8 would provide a mathematical expression describing how the increase in bedload rates with flow discharge is modulated by the differences in sediment supply, which is parameterised through the armour ratio and the dummy variables (i.e. dominant macro-bedforms). In Figure 12, we compare the transport intensities estimated using eq. 8 to the true values measured in the field. Regression predictions plot close to the 1:1 line, with an average 0.9 ratio between predictions and truth-values and 43% of points showing a discrepancy lower than one order of magnitude. Riffle and pool and braided data show a larger scatter than planebed and step-pool morphologies; this is probably related to the larger cross-sectional variability in shear stress and sediment paths, typical of these channel settings [START_REF] Recking | Quantifying the morphological print of bedload transport[END_REF]Vázquez-Tarrío et al., 2018).

Discussion

Sediment supply accommodated through armouring in gravel-bed rivers

Our meta-analysis shows a decline in the armour ratio with increasing bedload supplies (quantified through the q * -metrics and qs/ dd ) in the compiled field data (Figures 7 and8), which is similar to the trends observed in previous flume experiments [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]. In this regard, plots shown in Figures 7 and8 quantify the important imprint of sediment supply over surface armouring in gravel-bed rivers. It should be noted that q * was computed based on subsurface GSD, using the common approach of equalling subsurface GSD to the average GSD of the bedload. However, bedload capacities would be more adequately computed based on the actual GSD of the bedload. There may be situations where shifts in sediment sources and catchment patterns of sediment production could lead to changes in the grain size of the sediment supplies; for instance, mountain watersheds submitted to massive afforestation (or forest clearance), or river reaches fed by largely managed (e.g. dammed, dredged) tributaries. In such situations, we would expect changes in the GSD of the bedload (fining or coarsening) that may derive in a change in bedload transport capacities; this would in turn influence surface GSD together with changes in the amount of sediment inputs.

There is a certain amount of unexplained scatter within the data in Figures 7 and8, so there should be other contributing and explanatory variables for data variance in them apart from bedload supply. We believe that the variability introduced by differences in the shape of the dominant competent flow hydrograph and flow duration [START_REF] Hassan | Experiments on the effect of hydrograph characteristics on vertical grain sorting in gravel bed rivers[END_REF][START_REF] Phillips | Effect of flood hydrograph duration, magnitude, and shape on bed load transport dynamics[END_REF] are the most probable candidates. These flow parameters would be largely variable amongst the selected study reaches and could not be described by a single q * or qs/ ratio based only on peak discharge. As pointed out above, gravel-bed streams submitted to long receding hydrograph limbs and experiencing several floods per year are likely to develop a higher degree of armouring than equivalent streams in terms of sediment supply, but experiencing less frequent flooding and a short falling limb [START_REF] Hassan | Experiments on the effect of hydrograph characteristics on vertical grain sorting in gravel bed rivers[END_REF]. Therefore, flood hydrograph may exert an important control on armouring, together with sediment supply. Although the available data do not let us explore this issue in much depth, in general they are in agreement with this general picture: snowmelt-dominated data tend to show larger armour than rainfall-dominated rivers in Figure 6, although the possibility of time lags between previous changes in upstream sediment inputs and streambed adjustment, or even some seasonal variability in sediment supply, should not be dismissed, since both may play a role in the variability documented in the compiled data. The influence on armouring of these time lags and seasonal variability in sediment inputs may be more important in those channel morphologies better coupled or connected with upstream sediment sources (e.g. braided channels), where one-shot observations of armour ratios may not detect well the average trends.

However, despite the scatter in the data, the overall picture shown by Figures 9 and 10 illustrates how the signal linked to differences in sediment yields is the dominant one, and it is globally wellrecorded through the surface grain size and the armour ratio in gravel-bed rivers. Our analysis suggests that sediment supply drives streambed surface GSD in gravel-bed rivers in two different ways: i. the GSD of the sediment supplied and introduced into the channel network exerts an obvious control, since it defines the range of grain sizes that are available in the bed material (Figure 4); ii. streambed surface represents the sediment layer in more intimate contact with fluid forces, so it adjusts to the balances between volumes of sediment supplied into the channel and the reach (Figures 9 and10). In principle, stream ability to convey sediment inputs downstream is size-selective (Paola and Seal, 1995), and this partially explains why the surface layer tends to coarsen. This influence of hydraulic conditions could be eventually more important and partially blur the primary influence of the GSD of the bedload.

Based on our data and quantile regression analysis, we have created two diagrams illustrating the likelihood of a certain armour ratio for a given sediment supply (Figure 11). We believe these diagrams provide a useful frame to interpret armour ratios measured in the field, and to characterize streambed state and mobility in a quick way. For many applied issues (channeldesign, river restoration), an adequate diagnosis of the hydro-morphological status of a given reach is fundamental. However, information of bedload fluxes is lacking in many cases. In such cases, armour ratios measured in the field may provide a quick characterization of the sediment supply conditions and streambed mobility of the considered river reach, by combining diagrams such as those shown in Figure 9 with some qualitative knowledge about the dominant hydrological regime.

Implications for equilibrium channel geometry

We observed how in most of the compiled data shear stresses at the dominant discharge are close to critical thresholds for sediment motion (Figure 10). These observations reflect surface adjustment to dominant hydraulic conditions. In this respect, theoretical work [START_REF] Parker | Self formed rivers with equilibrium banks and mobile bed: Part II. The gravel river[END_REF][START_REF] Parker | Hydraulic geometry of active gravel rivers[END_REF] and decades of observations in gravel-bed alluvial channels [START_REF] Parker | 1D Sediment Transport Morphodynamics with Applications to Rivers and Turbidity Currents[END_REF]Mueller and Pitlick, 2005;[START_REF] Parker | Physical basis for quasi universal relations describing bankfull hydraulic geometry of single thread gravel bed rivers[END_REF] supported the hypothesis of threshold or nearthreshold channels [START_REF] Parker | Physical basis for quasi universal relations describing bankfull hydraulic geometry of single thread gravel bed rivers[END_REF][START_REF] Phillips | Self-organization of river channels as a critical filter on climate signals[END_REF][START_REF] Métivier | threshold theory, and channel stability[END_REF].

According to this idea, alluvial channel dimensions adjust in such a way that the threshold for the motion of median-size grains occurs close to bankfull flows (e.g. [START_REF] Mackenzie | Breaking from the average: Why large grains matter in gravel bed streams[END_REF].

However, in our data Shields values at the dominant discharge are close to the critical thresholds for the entrainment of the coarser fraction of bed sediment only in well-armoured streams (Figure 10); otherwise, Shields stresses are well above these critical values in poorly armoured streams. [START_REF] Pfeiffer | Sediment supply controls gravel river geometry[END_REF] observed that only supply-limited streams meet the threshold channel condition, while in capacity-limited systems they reported Shields stresses at bankfull considerably over the critical levels. Based on these observations, these authors concluded that the common observation of channels adjusting to threshold conditions simply reflects the fact that the channels most commonly surveyed in the field are subject to modest sediment supplies.

Nevertheless, we propose an alternative interpretation for the trends shown in Figure 10 and [START_REF] Pfeiffer | Sediment supply controls gravel river geometry[END_REF]. According to the data analysed in this manuscript, high-sediment supply systems correspond mainly to multi-thread and riffle-pool streams (Figure 3). These kinds of settings are characterized by bar morphologies, which involve complex 3D flow structures [START_REF] Francalanci | Do alternate bars affect sediment transport and flow resistance in gravel bed rivers? Earth Surface Processes and Landforms[END_REF], specific patterns of grain size sorting [START_REF] Paola | Topographic sorting[END_REF]Lisle et al., 1992) and a great variability in shear stress distributions across their cross-section (Recking, 2009;[START_REF] Recking | Quantifying the morphological print of bedload transport[END_REF]. Furthermore, gravel dunes and bedload sheet propagation [START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF] represent an additional source of form roughness in these rivers. Consequently, we expect larger biases in bedload estimates when averaging shear stresses across the cross section of these streams [START_REF] Recking | An analysis of nonlinearity effects on bed load transport prediction[END_REF]. Therefore, it is possible that 1D averaged shear stresses are not an adequate proxy for the actual variability in shear stresses acting at the local and grain scales in riffle and pool and multi-thread settings. This may explain the observed deviation from nearthreshold conditions, which could be to a large degree an artefact resulting from the assumptions made when estimating cross-section averaged shear stresses [START_REF] Yager | The trouble with shear stress[END_REF].

Armour ratio: a proxy for the channel planform configuration

Our review outlined differences in armour ratios according to channel morphology (Figure 3), with multi-thread and riffle and pool rivers exhibiting, in general, a lower degree of surface armouring than plane-bed and step-pool channels. The scale of the roughness and protruding elements in step-pool channels is in general larger, with channel-spanning ribs (steps) composed by an accumulation of jammed cobbles and boulders transverse or oblique to the channel [START_REF] Zimmermann | Channel morphology, gradient profiles and bed stresses during flood in a step pool channel[END_REF][START_REF] Chin | Toward a theory for step pool in stream channels[END_REF], alternating with pools [START_REF] Church | Form and stability of step pool channels: research progress[END_REF][START_REF] Lamarre | The role of morphology on the displacement of particles in a step pool river system[END_REF].

Step-pool streams are normally close to headwater areas and are largely dependent on the accumulation of relatively fine colluvium inputs into pools and around protruding boulders [START_REF] Turowski | Start and end of bedload transport in gravel bed streams[END_REF][START_REF] Recking | Influence of sediment supply on mountain streams bedload transport[END_REF][START_REF] Recking | A field investigation of the influence of sediment supply on step pool morphology and stability[END_REF][START_REF] Piton | The concept of travelling bedload and its consequences for bedload computation in mountain streams[END_REF]. Accordingly, protruding cobbles and boulders can be found on the bed surface of step-pool channels, even with large sediment supplies and thick alluvial covers. This may explain the generally larger armour ratios observed for step-pool streams. Similarly, the data for braided rivers tend to show lower armour ratios (Figure 3), which results from the large sediment inputs typical of braided streams.

The trends in armour ratios with channel morphology documented here suggest that planform style, dominant macrobedforms, streambed mobility and grain size adjust together to dominant sediment supply conditions. In this regard, a typical sequence of reach types observed in many mountain basins corresponds to a downstream progression from step pool at headwaters, planebed (or forced pool-riffle) to pool-riffle and/or multithreaded channel morphologies at the piedmont valley (e.g. [START_REF] Warburton | Mountain Environments[END_REF]. In their seminal paper, [START_REF] Montgomery | Channel-reach morphology in mountain drainage basins[END_REF] suggested that this kind of longitudinal sequence describes opposing trends between sediment supply and transport capacities in the downstream direction. In this regard, [START_REF] Pitlick | Differences in sediment supply to braided and single thread channels: what do the data tell us?[END_REF] documented a downstream trend to lower armour ratios in rivers from Colorado and Utah.

The trends observed here are in good agreement with this general scheme.

Additionally, gravel-bed rivers exhibit a wide diversity of bed features that are larger than individual clasts and smaller than reach-scale patterns. Sediment supply plays a critical role in the development of one kind of bed structuration or another [START_REF] Buffington | A procedure for classifying textural facies in gravel-bed rivers[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]. Dominant bedforms in gravel bed rivers evolve from gravel dunes [START_REF] Carling | Subaqueous gravel dunes[END_REF] and bedload sheets in poorly armoured streams [START_REF] Whiting | Bedload sheets in heterogeneous sediment[END_REF][START_REF] Nelson | Response of bed surface patchiness to reductions in sediment supply[END_REF]Recking et al., 2009), to a sequence of pebble clusters [START_REF] Brayshaw | Characteristics and origin of cluster bedforms in coarse-grained alluvial channels[END_REF], transverse ribs [START_REF] Koster | Transverse ribs: their characteristics, origin, paleohydraulic significance[END_REF][START_REF] Allen | Sedimentary Structures, Their Character and Physical Basis[END_REF], stone lines [START_REF] Laronne | Interrelationships between bed morphology and bed material transport for a small, gravel-bed channel[END_REF] and reticulate stone cells [START_REF] Church | Stabilizing self organized structures in gravel bed stream channels: Field and experimental observations[END_REF][START_REF] Hassan | Experiments on surface structure and partial sediment transport[END_REF] with decreasing sediment supplies [START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]. Indeed, the stability of a gravel streambed is increased by the presence of particle arrangements and clusters (e.g., [START_REF] Reid | Particle interaction and its effect on the thresholds of initial and final bedload motion in coarse alluvial channels[END_REF][START_REF] Church | Stabilizing self organized structures in gravel bed stream channels: Field and experimental observations[END_REF][START_REF] Hassan | Experiments on surface structure and partial sediment transport[END_REF][START_REF] Piedra | The spatial distribution of coarse surface grains and the stability of gravel river beds[END_REF][START_REF] Ockelford | The impact of stress history on bed structure[END_REF][START_REF] Heays | Laboratory study of gravel-bed cluster formation and disintegration[END_REF]. Therefore, streambed textures adjust to sediment supply reductions not only through surface coarsening, but also through a decrease in streambed mobility and a different bed surface organization. [START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF] have proposed a phase diagram for bedforms in gravel bed rivers, relating q * to the armour ratio (Figures 16.5 and 16.9 in Venditti et al., 2017) that is in some way comparable to our Figure 7. If armour ratio varies in parallel to channel morphology, dominant macroforms, bed sediment mobility and streambed structures (as our analysis shows), then the armour ratio should be

Concluding Remarks

A large body of research in fluvial geomorphology has contributed to establishing the general idea that sediment supply, bedload fluxes, channel morphology, bankfull shear stresses and surface grain size are intimately related in gravel bed rivers. In this paper, we aimed to quantify the existing links between sediment supply and surface coarsening. Based on the re-analysis of a large database of bedload discharge information for gravel-bed streams, we have proposed semiempirical relations describing how surface grain-size and armour ratios evolve with the balances between bedload yields and channel sediment transport capacities. Armour ratios increase with decreasing sediment inputs, as inferred from the dimensional analysis of bedload equations and as already shown by previous flume experiments.

Accounting for armouring is important for many reasons, since it influences the local availability of bedload, hydraulic roughness, bed permeability, and physical conditions for aquatic organisms.

We believe that the empirical relationships found here between bedload yields and armour ratios have the potential to provide a quantitative frame for exploring the links between surface armouring, hydraulics and sediment availability in specific gravel-bed reaches and are a step towards predicting textural adjustments to changes in sediment supply (for example, downstream dams). Additionally, since armouring can provide important qualitative information about the bedload regime (e.g. partial mobility vs. full mobility, sediment supply) of a specific river reach, our results may potentially provide some interesting clues for palaeohydrological analysis.

Figure 1 .

 1 Figure 1. Comparison between surface and subsurface grain-size parameters in the compiled database. A: D50 (in mm); B: D84 (in mm). C: D84/D50 ratio. D: Percentage of fines (< 2mm) present in the sediment.

Figure 2 .

 2 Figure 2. Armour ratios based on D50 plotted versus the armour ratios based on D84.

Figure 3 .

 3 Figure 3. Differences in armour ratios according to channel morphology. A: Armour ratio based on the media size of the bed sediment (D50). B: Armour ratio based on the 84-th percentile (D84) of the grain-size distribution (GSD). N: Number of data.

Figure

  Figure 4. Surface grain-size parameters plotted versus subsurface parameters. A: D50. B: D84. C: Percentage of fine sediment (< 2 mm). We have segregated the data according to hydrological regime.

Figure 5 .

 5 Figure 5. Differences in armour ratios according to sediment-supply conditions at the catchment scale. See main text. A: D50 * . B: D84 * .

Figure 6 .

 6 Figure 6. Differences in armour ratios (A and B) and percentages of fine sediment (C) according to the dominant flow regime.

Figure

  Figure 7. A: Armour ratio (D84 * ) plotted versus the transport stage ( d

Figure 8 .

 8 Figure 8. Differences in sediment-supply metrics (q * and qs/ d) according to our initial classification of data as low-, moderate-or high-sediment supply streams (see the main text). A: sediment supply metrics proposed by Dietrich et al. (1989). B: our own sediment supply metrics (see main text).

Figure 9 .

 9 Figure 9.q * (see main text for more details).

Figure 10 .

 10 Figure 10. Armour ratio (A) and corrected armour ratio (B) plotted versus the ratio between bedload fluxes and streampower (qs/ d).

Figure 11 .

 11 Figure 11. Diagrams issued from quantile regression analysis of the compile data, defining the likelihood of a certain value of the armour ratio according to sediment supply metrics (see main text for more details).

Figure 12 .

 12 Figure 12. Bedload transport intensities estimated using eq. 8 plotted versus transport intensities measured in the field. MT: Multi-thread channels; PB: Plane-bed; RP: Riffle and pool; SP: step-pool streams.

Acknowledgements:

  The present work has been possible thanks to the financial support provided by the grant ACB17-44, co-funded by the post--FICYT (Government of the Principality of Asturias) and the Marie Curie Co-Fund. This work was also performed -17-EURE-0018) of Université de Lyon Investissements d'Avenir operated by the French National Research Agency (ANR). We would like to thank Pablo Turrero García and Daniel Grace for their review of the English version of the manuscript. percentile of the surface grain-size distribution Diss: i-th percentile of the subsurface grain-size distribution Di * : Armour ratio, or the ratio between the i-the percentiles of the surface and subsurface grain-size distributions Di ** : Corrected version of the armour ratio, i.e. armour ratio computed accounting for the inherent covariation between surface and subsurface grain sizes f: Ratio between the armour ratio estimated based on the 84-th percentiles (D84) and the armour ratio based on the median size (D50) of the grain size averaged) bed shear stress for sediment entrainment cs: Critical (section averaged) bed shear stress for the inception of motion of the surface sediment particles css: Critical (section averaged) bed shear stress for the inception of motion of the subsurface sediment particles ci * : Critical threshold Shields stress for entrainment particle with sizes corresponding to the i-th percentile of the grain-size distribution

Table 1 .

 1 Sources

	Sediment	sampling	method	HS 7.62 or 15.2	cm (0.25 mm	mesh)	HS 7.62 or 15.2	cm (0.25 mm	mesh)	HS 7.62 or 15.2	cm (0.25 mm	mesh)	HS (7.6 cm),	0.5 mm mesh		HS (7.62 cm)		HS (7.6 and 15	cm	HS 7.62 or 15.2	cm (0.25 mm	mesh)	Wadable	version of	Elwha	sampler,	HS (7.6 cm)	HS (7.6 cm)
		N		100				88			82			31			43		78	85	77	109	95
	Q Qb	(m 3 /s) (g/s•m)	6.0-0.0-	30.9 336.4		0.3-4.7 0.0-6.8		33.7-0.4-	291.7 633.5	0.0-0.3 56.2-837.0	212.0-213.0-	7104.0 2590.0	288.0-0.1-	3511.0 284.0	0.4-6.4 0.0-9.7	2.8-	13.8	0.1-0.0-	1.24 21.2	0.0-0.5 0.0-14.7
	Flow	depth	(m)		0.4-1.1			0.1-0.5			0.6-2.1			0.0-0.1			1.7-3.6			3.4-46.3	0.2-0.5	0.3-0.5	0.1-0.4	0.1-0.2
	Flow	width	(m)		12.8		4.94-	11.89	52.4-	61.0	0.3-	2.2	98.5-	309.0	125.0-	149.0	7.0-	11.9	15.0-	17.2	2.8-	3.0	1.7-	2.1
	GSD measuring method		Surface Subsurface	Pebble count Core and core sampling sampling	Pebble count Core and core sampling sampling	Pebble count Core sampling	Contact 10 kg-	sampling volumetric	technique sampling	Pebble count (?) Dredge sampling	Sieve	Pebble count analysis of	dug material	Pebble count Core and core sampling sampling	Pebble count Barrel method	Pebble count Barrel method	Pebble count Barrel method
	Subsurface	D84 (mm)		101			97			86			12			184			70	83	52	23	59
	Surface	D84	(mm)		250			220			141			19			52			70	145	112	142	100
		Slope			0.091			0.03			0.0038			0.03			0.0008			0.00037	0.0146	0.008	0.058	0.053
	Channel	style	Plane-	bed	Plane-	bed	Riffle	and pool	Step-	Pool		Braided		Riffle	and pool	Plane-	bed	Braided	Step-	Pool	Plane-	bed
		Source		King et al.	(2004)	King et al.	(2004)	King et al.	(2004)	Gomez	(1988)	Williams	and Rosgen	(1989)	Jones and	Seiz (1980)	King et al.	(2004)	Ryan et al.	(2005)	Ryan et al.	(2002)	Ryan et al.	(2002)
		River/Reach		Big Wood	River	Blackmare	Creek		Boise river		Borgne				Chulitnana	River	Clearwater	River	Dollar Creek	East Fork	San Juan	East Saint-	Louis Creek	Fool Creek

of field data and information compiled for this study. D84: 84-th percentile of the grain-size distribution (GSD). Q: Flow discharges. Qb: Bedload discharges. HS: Helley-Smith sampler. N: number of data.

Table 2 .

 2 Information on the dominant channel-forming discharge for the case study selected for the present meta-analysis. (

	Flow	regime		-		Snowmelt	Snowmelt	Snowmelt	Snowmelr	Snowmelt	Glacial	fed	Glacial	fed	Glacial	fed	Snowmelt	Snowmelt	Flahs-	floods	Snowmelt
	Sediment	supply		High		Low/Mod	erate	Low	Moderate	High	Moderate/	High		High		High	High	Moderate	Low	Low	Moderate
	River/Reach	Snake River	below Jackson	Lake	South Fork	Payette	South Fork Red	River	Squaw Creek	USGS	Sunlight Creek-4	Sunlight Creek-11	Susitna River near	Talkeetns	Susitna River at	Sunshine, Alaska	Talkeetna River	near Talkeetna	Thompson Creek	Trapper Creek	Turkey Brook	Valley Creek
	Sediment Flow regime supply		Low Rainfall		High Rainfall	Moderate Rain-on-snow/Snowmelt	High Rainfall	Low Snowmelt	Low Snowmelt		Low/Moderate Snowmelt		Moderate/High Snowmelt	Moderate Snowmelt	Moderate Rain-on-snow/Snowmelt	Moderate Rain-on-snow/Snowmelt	Moderate/High Impounded
	River/Reach		Oak Creek		Pacific creek	Rapid river	Redwood	Creek	Saint-Louis	Creek	Sagehen	Creek	Salmon River	below Yankee	Salmon River	near Obsidian	Salmon River	near Shoup	Selway River	Silver Creek	Snake River
	Sediment Flow regime supply	Rain-on-	Low snow/Snowme	lt	Low Rainfall	Low Snowmelt	Low Snowmelt	Low Snowmelt /Moderate	Low Snowmelt	Rain-on-	Moderate snow/Snowme	lt	Low/Moderate Snowmelt	Moderate/High Snowmelt	Rain-on-	Low snow/Snowme	lt	High Flash-floods	Rain-on-	Moderate snow/Snowme	lt
	River/Reach		Harris creek		Jacoby	Johns creek	Little Buckhorn	Creek	Little Granite Creek	Little Slate		Lochsa Creek		Lolo Creek	Middle Fork	Middle Fork Piedra	River	Nahal Yatir	Fork North	Clearwater
	River/Reach Sediment supply Flow regime	Big Wood Moderate Snowmelt River	Blackmare Low Creek Snowmelt	Boise river Moderate /High Snowmelt	Borgne High Glacial fed	Chulitnana High River Glacial fed	Clearwater Moderate Impounded River /High		Dollar Creek Low Snowmelt		East Fork High San Juan Rain-on-snow/Snowm elt	East Saint-Low Louis Creek Snowmelt	Fool Creek Low Snowmelt	Fraser River High Snowmelt	Goodwin Moderate Rainfall creek

*

) Bankfull discharge. ( ** ) Dominant discharge provided by

[START_REF] Mueller | Sediment supply and channel morphology in mountain river systems: 2. Single thread to braided transitions[END_REF]

. ( *** ) Reference discharge provided by

[START_REF] Church | Catalogue of alluvial river channel regime data[END_REF]

Table 3 .

 3 Information on sediment-supply at the catchment scale and dominant flow regime for the data compiled in the present work.

Table 4 .

 4 Sources of flume data compiled for this study.

	Flume	Source	S	W (m)	L (m)	h (cm)	D50s (mm)	Shields	Feed rate	r (h)
	Tsukuba	Nelson et al. (2009)	0.0035-0.0052	7.5	0.3	10.2-11.3	3.7-4.9	0.049-0.086	1.7-17.4g/min•cm	6-7.5
	Berkeley	Nelson et al. (2009)	0.0043-0.0055	28	0.9	21.8-22.8	10.1-11.8	0.045-0.061	0-23.3 g/min•cm	20.7-28.9
	UBC	Church et al. (1998)	0.001-0.012	0.5/0.8	6/10	0.5-7.4	1.9-5.1	0.003-0.117	No feed	-
	UBC	Hassan and Church (200)	0.006/0.007	0.8	10	0.1-6.7	2.4-4.5	-	1.2-0.644 kg/h	96

S: Flume slope. W: Flume width. L: Flume length. h: water depth. D50: 50-th percentile of sediment GSD. r: experiment duration.

  Table 4 describes the main characteristics of these experiments. Information for these flume investigations was extracted from graphical reading of figures presented in Venditti et al. (2017) (Figures 16.1, 16.2 and 16.5 in that paper).

	3. Review of the compiled data
	3.1. Surface coarsening in gravel-bed rivers

Streambed surfaces adjust to available bedload yields (Figures 9 and 10). Reciprocally, surface coarsening controls the frequency and magnitude of armour breakup and streambed disorganization during floods (Figure 7). Strongly armoured streambeds are more difficult to disorganize and more infrequently moved. Therefore, we could expect a lower degree of bed material recruitment into bedload during regular flows. With this in mind, we expected surface armouring to have some control over bedload rates. In order to explore this issue, we took the available information on bedload discharges (Table 1) and performed a multiple regression analysis linking bedload rates to flow magnitude and armour ratios: Eq. 7

where is bedload transport intensity (see supplementary information), and Q/Qd is the ratio between the peak discharge for the transport episode and the dominant discharge (hereinafter called flow ratio). However, the wide diversity of channel morphologies represented amongst the compiled data should be highlighted, since channel macroforms control flow and sediment transport patterns, which in turn may potentially affect bedload rates [START_REF] Ferguson | The missing dimension: effects of lateral variation on 1-D calculations of fluvial bedload transport[END_REF][START_REF] Francalanci | Do alternate bars affect sediment transport and flow resistance in gravel bed rivers? Earth Surface Processes and Landforms[END_REF][START_REF] Recking | Quantifying the morphological print of bedload transport[END_REF]Vázquez-Tarrío et al., 2018;[START_REF] Vázquez-Tarrío | Assessing Controls on the Displacement of Tracers in Gravel-Bed Rivers[END_REF].

For this reason, we introduced a set of three binary indicators into the regression analysis to incorporate into it the influence of channel morphology:

Eq. 8 where RP, SP and BR are the dummy variables taking a value of 1 in the cases of riffle and pool, step-pool and braided channels, respectively. In the case of plane-bed channels, the three dummy variables would be 0.

To test whether eqs. 7 and 8 fit the available bedload information, we used ordinary multiple regression in linearized form and stepwise procedures, after log transforming all the variables included in the equation. Both equations explain the variance in the compiled bedload data to a statistically significant degree, with all the variables included in the regression model being significant (Table 5). The R 2 values imply that eq. 8 is more robust than eq. 7 (R 2 = 0.60 vs. 0.34, respectively), which outlines the existence of some morphological imprint on bedload transport rates. According to the regression model, transport intensities increase with the 1.7 positive power of flow ratios. Conversely, bedload rates are negatively correlated to armour ratios, i.e. bedload rates tend to be considerably weaker in well-armoured channels. With the aim of assessing the relative importance of each of the independent variables incorporated into the regression model, we used the method proposed by [START_REF] Lindeman | Introduction to Bivariate and Multivariate Analysis[END_REF], often recommended for assigning shares of relative weight of predictors to the R 2 . According to this analysis, channel morphology is the variable that explains the largest amount of variability in bedload data (~53 % of R 2 ), followed by flow magnitude (23% of R 2 ) and armour ratios (21% of R 2 ). Differences in dominant channel morphology have a strong effect on the variability in bedload rates observed between the compiled data, but differences in surface armouring also have a large impact.

1 Variance Inflation Factor Table 5. Results from the multiple regression model based on eq. 8 (see main text).

Different channel morphologies and macro-bedforms result from the adjustment of channel macro-roughness to different balances between sediment supply and transport capacity [START_REF] Montgomery | Channel-reach morphology in mountain drainage basins[END_REF]; similarly, armouring is the consequence of the adjustments in roughness at the grain-scale to the same balances between sediment supply and capacity [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]. Consequently, both dominant channel morphology and armour ratios constitute a proxy of sediment supply and should be related. Interestingly enough, we have observed systematic differences in armour ratios between the different channel morphologies (see Figure 3). In general, multi-thread channels and rivers with riffles and pools Eq. S1 where g is the gravitational acceleration, S is the channel slope, D84 the 84 th percentile of the surface GSD and ql * the dimensionless specific discharge:

where ql is the flow discharge normalized by channel width. Then, we estimated the water depth (d) from:

Eq. S3

For the hydraulic radius (R), we assumed a rectangular cross-section:

Eq. S4 where w is channel width. Finally, we computed the cross-section averaged basal shear stresses from the hydraulic radius-slope product:

Eq. S5

S. 2. A simple model for armour ratios based on bedload formulae

As explained in the main text, [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF] developed a metric (q * ) quantifying the balances between the sediment supplied into a reach and its actual bedload transport capacities [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF][START_REF] Montgomery | Channel-reach morphology in mountain drainage basins[END_REF][START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]:

where qs refers to the bedload transport rate per unit width and the subscripts s and ss to the surface and subsurface sediment, respectively. Combining eq. 1 with the Meyer-(1948) bedload transport equation, Dietrich et al. (1999) suggested:

Eq. S7 where is the bed shear stresses and c the critical stress for incipient motion. Writing shear stresses in their non-dimensional form ( * ):

Eq. S8 [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF] finally arrived at:

Eq. S9

This expression quantifies the links between surface armouring (D50s/D50ss) and sediment supply (q * ), based on Meyerto any other bedload equation. In this paper, we decided to use Reckin [START_REF] Recking | Quantifying the morphological print of bedload transport[END_REF], since this equation has been tested and validated against bedload discharge information from natural gravel-bed rivers (e.g. [START_REF] Hinton | Comparison of Calibrated Empirical and Semi-Empirical Methods for Bedload Transport Rate Prediction in Gravel Bed Streams[END_REF]. [START_REF] Recking | Simple method for calculating reach-averaged bed-load transport[END_REF] proposed the following expression for bedload rates:

Eq. S10

where is the dimensionless transport rate, estimated using the Einstein parameter: Eq. S11

Coefficients A, and are three model parameters, for which values of 14, 2.5 and 4 were proposed, respectively [START_REF] Recking | Simple method for calculating reach-averaged bed-load transport[END_REF], Recking et al., 2016). * m is a mobility shear stress that allows to determine low transport conditions (with partial transport and bed clustering) apart from higher transport ones [START_REF] Recking | Quantifying the morphological print of bedload transport[END_REF]. [START_REF] Recking | Simple method for calculating reach-averaged bed-load transport[END_REF] estimates * m from:

Eq. S12

Eq. S10 is such that for low transport conditions ( * ref << * m):

Eq. S13

and for higher transport conditions ( * ref << * m):

Eq. S14

We can now combine equation S6 with the expression for the Einstein parameter (eq. S11): = Eq. S15

Incorporating now eq. S13 into eq. S15, we can deduce:

Eq. S16

for low transport conditions. Taking into account the expression for * m (eq. S12) and assuming a similar bed slope for the surface and subsurface case:

Eq. S17

We could now introduce the idea that the armour ratio based on the D50 is linearly related to the value based on the D84 (see Figure 2 in the main text of the paper):

Eq. S18

Incorporating this idea into eq. S17, then:

Eq. S19

Now, we can simplify eq. S16 based on eq. S19:

Eq. S20

Combining eq. S20 with that for the dimensionless Shields stress based on the D84 (eq. S8), then:

Eq. S21 at low transport conditions.

At high transport conditions (when, * ref >> * m,), we should combine eq. S14 with eq. S15, and we arrive at:

Eq. S22

Combining this expression with that for the dimensionless Shields stress:

Eq. S23 at full mobility conditions.

In Section 5 of the paper, we investigated and discussed whether available field measures of bedload fluxes may explain some trends in armour ratios (D * ) in the compiled data. More q * ) (at bankfull) could be correlated to the armour ratio in the available data and how well it adjusted to eq. S22 and/or S23 (as concluded in S. 2). According to [START_REF] Dietrich | Sediment supply and the development of the coarse surface layer in gravel-bedded rivers[END_REF], q * can be estimated from eq. S6. Estimating q* from eq. S6 needs two inputs: i. actual bedload rates (in the numerator); and ii. bedload capacities in the denominator. In this paper, the numerator was defined from the bedload rates measured at (close to) dominant flows for each compiled study case. Bedload rates at dominant discharges were calculated following these steps: i. for each case study we defined the best power fit relating bedload to water discharge (based on the available bedload discharge information, see Table 1 in the paper); ii. we applied the obtained regression equation to the bankfull discharge, and we computed the bedload discharge at dominant flows. Concerning the denominator qss in eq. S6, we approached channel transport capacities (for all the selected case studies) from the bedload rates estimated usin -S11), but based on subsurface GSD.

The approach followed when defining q* was obviously different in the case of flume data. As outlined in the main text of the paper, we also benefited from the results of some flume experiments that explored the role of sediment feed reductions on surface texture [START_REF] Church | Stabilizing self organized structures in gravel bed stream channels: Field and experimental observations[END_REF][START_REF] Hassan | Experiments on surface structure and partial sediment transport[END_REF][START_REF] Nelson | Response of bed surface patchiness to reductions in sediment supply[END_REF]. Data from these flume experiments was extracted from the graphical reading of figures presented in [START_REF] Venditti | Bedforms, structures, patches, and sediment supply in gravel bed rivers[END_REF]. Venditti et al.

(2017) estimated q * for these flume experiments as the ratio between the bedload transport rate after the bed has adjusted to a new sediment feed divided by the transport rate for an unarmoured bed, before any feed reduction.

S. 4. How did we compute transport-stage ratios for the compiled dataset?

In Figures 8 and 10, we worked with and analysed transport stage ratios, which are defined as the ratio between Shields stresses and the critical (or reference) Shields stresses for incipient sediment motion [START_REF] Wilcock | Sediment transport primer: estimating bed-material transport in gravel-bed rivers[END_REF]:

Eq. S24

Shields stresses are calculated for the 84 th percentile of GSD in this paper, since D84 provides a measure of the largest grains in the bed, which probably control hydraulic roughness and morphological stability [START_REF] Mackenzie | Breaking from the average: Why large grains matter in gravel bed streams[END_REF]. In eq. S24 (and Figures 8 and 10 in the paper), c * is the critical Shields stress below which no sediment transport is assumed to occur. This