Different geomorphic processes control suspended sediment and bedload export from glaciers

Domain: earth_science
Published: 2025-07-01
Editorial outcome: major_revision

Abstract
Ongoing cryospheric change has modified sediment export from glacierized catchments substantially, with significant implications for ecosystems and downstream users, notably hydropower companies. Sediment is exported either as finer sediment in suspension or as coarser bedload with intermittent contact between sediment and the bed. To date, the difficulty in observing subglacial bedload transport limits the understanding of the physical processes associated with evacuating bedload compared with suspended load. We elucidate the factors controlling sediment export by inverting a physically-based numerical model of subglacial sediment production and sediment transport with suspended sediment and continuous bedload discharge records from an Alpine glacier. Comparable quantities of suspended sediment and bedload are exported, and model results suggest that both rely on the availability of sediment for transport. Yet, bedload export in subglacial channels also depends on particular hydraulic conditions, notably channel shape and hydraulic roughness. This makes exporting bedload-sized particles inefficient compared to fine-grained sediment. As a result, subglacial hydraulics should be explicitly considered when examining bedload export processes, and suspended and bedload transport should be considered separately. Inefficient bedload evacuation by meltwater implies that glacial erosion may only continue when non-fluvial mechanisms evacuate sediment, such as sediment entrainment into the ice.

Introduction
Establishing the processes driving subglacial erosion and sediment export from glaciers is key as glaciers are extremely effective erosive agents as compared with other mechanisms1–3, shaping mountain landscapes e.g. 4–7 and driving sediment delivery that impacts hydropower and ecosystems e.g. 8–10. Underneath glaciers, sediment export responds to the availability of sediment, controlled by glacial erosion processes such as abrasion of bedrock by sliding, debris-laden ice and quarrying of bedrock1,2,11,12. Additionally, sediment export responds to subglacial fluvial transport conditions, controlled by the shear stress of water flowing through a subglacial channel with changing size13–16.

Sediment is exported fluvially either as finer sediment in suspension or as coarser bedload with intermittent contact between sediment clasts and the channel’s bed. These two mechanisms have been extensively evaluated in river systems17,18, where sediment discharge by both processes is a function of sediment supply, sediment size, sediment sorting, and flow conditions. Yet, the sediment supply and transport processes controlling bedload and suspended sediment export in subglacial fluvial systems remain highly uncertain19. Continuous high-resolution records of suspended sediment export from glaciers have been extensively collected e.g. 20–23. Some mechanisms by which glaciers evacuate suspended sediment are reasonably well established from observations20,24–30. However, this is not the case for bedload, with the few records available commonly collected distanced downstream from the glacier31,32, where they are impacted by subaerial hydraulic conditions and proglacial processes that modify significantly the glacier export signal33,34. Recent advances in environmental seismology e.g. 35 however, allow researchers to measure bedload below glaciers and at their termini, quantifying the role of bedload transport in a glacier’s total sediment export33. This means we can now quantify both suspended load and bedload export continuously from glaciers, isolating subglacial sediment transport processes.

Observations show that bedload can comprise up to 50% of total sediment export from a glacier during a melt season24,33, and models suggest that glacier quarrying creates bedload-sized material in amounts comparable to the suspended sediment produced by glacier abrasion36. The current assumption is that subglacial rivers have the excess capacity necessary to evacuate most of the sediment produced by erosion e.g. 2,19. However, research has yet to establish the differing hydraulic and geomorphic conditions leading to the fluvial mobilization of quarried-bedload material and abraded-suspended material. It appears that subglacial water can easily mobilize suspended sediment2,22. As a result, the mobilization of sediment can depend largely on sediment production and access of subglacial meltwater to abraded sediment27,30,37,38. Transporting larger bedload clasts, on the other hand, requires high shear stresses between subglacial water and the conduit bed, and this competence needs to be maintained along the full length of the channel2,19,39. As access to glacier beds is limited, subglacial sediment transport processes remains poorly evaluated, including their variability in time and space40,41. This knowledge gap inhibits a better understanding of landscape evolution and forecasting sediment discharge from glacierized catchments as they respond to changing climate with differing hydrology and glacial conditions.

Here, we demonstrate quantitatively that different processes control bedload and suspended load export from glaciers, using records collected directly at the glacier terminus. We apply a lumped-element model of glacial erosion and sediment transport in subglacial pressurized flow conditions to topography and continuous hydrology records from the Otemma glacier in Switzerland for the melt seasons of 2020 and 2021 (Fig. 1; see Methods). Otemma glacier is a 6 km long glacier with unknown hard or soft bed characteristics, in an Alpine climate. The model setup is identical for both suspended load (SSL) and bedload (BL), except for the sediment grain size D (SSL: 0.2 cm; BL: 7.8 cm 33) and sediment transport relationship (SSL: sand-sized sediment transport formula from Engelund and Hansen, 196742 and BL: bedload transport formula Wilcock and Crowe, 200343). Comparing some model outputs to observed sediment transport records in a Monte Carlo framework allows us to evaluate the different parameters controlling sediment availability and subglacial sediment transport conditions. The model application first demonstrates that different subglacial sediment availability and hydraulic processes control suspended and bedload export. Using both forward model outputs and the posterior parameter distributions, we then infer the specific processes controlling bedload and suspended load export. Lastly, we discuss the impact of the different sediment transport processes on landscape evolution in glaciated terrain and on sediment export under current climate warming and glacier retreat.

Results
Model outputs show that different processes control SSL and BL export from Otemma glacier (Fig. 2). As substantial quantities of SSL and BL are exported from the glacier33, this suggests that different parameterizations of the two processes are needed to fully capture subglacial sediment export. The mismatch in processes occurs despite the model being able to successfully represent SSL process interactions consistently in 2020 and 2021, along with capturing SSL and BL variations (Fig. 3).

To evaluate the processes that control SSL and BL, the model was run with a large number of randomly selected parameter values using inversion to identify values that best represented each transport mode. Parameters control the sediment production rate during the model run (ε_), the sediment stored below the glacier before the model initialization (H0), the channel shape (β), and channel roughness (fi; Fig. 1). Both the observations and resultant model outputs were averaged over 5 day periods and compared to the SSL and BL data using their relative error (see Methods; Fig. 2). Following the inversion, no parameter combinations successfully captured the observed variations in both BL and SSL (Fig. 2). The failure of the model to reconcile SSL and BL export together strongly suggests that different physical processes control these two transport modes.

While no single set of parameters accurately represents both SSL and BL simultaneously (Fig. 2), the model adequately represents SSL and BL individually (Fig. 3), with specific parameter combinations. We ran the model 2, 000, 000 times and retained the top performing 0.05% of model runs (1000) for bedload (BL) and suspended load (SSL) over the years 2020 and 2021, resulting in four different parameter sets. Results from the inversion show that, with optimum parameter combinations, the model’s mean relative error is between 8% and 20% for both BL and SSL cases. Furthermore, the model captures observed variations in sediment transport from the glacier (Fig. 3).

The variance of the optimum parameter combinations amongst the experiments further highlights the different processes that control BL and SSL export (Fig. 4). These distributions are significantly different across all four experiments. Yet, with the exception of sediment production (ε_) and friction factor (fi) each parameter correlation that is positively or negatively correlated, or insignificant, in SSL 2020 remains so in 2021 (Fig. 4a, c). This trend between years suggests that similar hydro-geomorphic processes controls SSL export. For instance, sediment production (ε_) and initial till thickness condition (H0) are negatively correlated in both years, as are channel shape factor (β) and initial till thickness condition (H0). Fewer such parameter interactions occur amongst the other three cases (Fig. 4). This agreement between 2020 and 2021 highlights consistency in SSL export processes between the 2 years and the model’s ability to represent them.

In the BL case, the hydraulic parameters channel shape factor (β) and friction factor (fi) are negatively correlated in both 2020 and 2021. However, other similar interactions between the 2 years do not emerge. This absence could be due in part to the relatively short study period in 2020 that reduced the sensitivity of the sediment availability parameters, sediment production (ε_) and initial till thickness condition (H0).

Forward model outputs and inverted parameters demonstrate the different sediment availability and mobilization processes driving SSL and BL export (Figs. 2, 4). To establish the particular processes controlling sediment export, we examine SSL and BL results from both years. However, we note that the 2020 model runs cover a substantially shorter time period, because the model is not able to capture a severe reduction in BL export observed this season33,44 (see Methods; Figs. S4–S5). Forward model outputs show that sediment discharge capacity far exceeds sediment discharge in the SSL cases (Fig. 3b, h). Excess SSL sediment transport capacity (i.e. suspended sediment load sediment transport capacity) suggests that SSL operates in a supply-limited regime. However, a transport-limited regime controls BL export at times, with small differences between sediment discharge capacity and sediment discharge (Fig. 3k). Due to the supply-limited SSL regime, the parameters controlling subglacial sediment availability develop narrow posterior parameter distributions (sediment production rates ε_) and initial sediment thickness conditions (H0; Fig. 4a, c).

A negative correlation occurs between sediment production rate (ε_) and initial sediment thickness condition (H0) for SSL in both years (Fig. 4). The relationship develops as lower erosion rates must compensate for higher initial sediment thickness to produce the observed quantity of SSL45. In the SSL case, the posterior distributions for variables driving sediment transport capacity, β and fi, do not interact with the erosion rate (ε_; Fig. 4a). β and fi values span the parameter space, resulting in viable subglacial water pressure and water velocity conditions (see Methods; Fig. 5). As a result, they do not represent particular water velocity and channel growth conditions that control sediment transport capacity, which would control SSL export in a transport-limited regime (Fig. 6).

Sediment availability controls BL export as well in both years, although optimum parameter combinations for BL in 2021 are narrower than in 2020. This suggests less influence on sediment availability in 2020, likely due to the significantly shorter study period that year which limits the influence of sediment availability. Here, sediment production rate (ε_) and initial sediment thickness condition (H0) develop optimum parameter distributions that deviate significantly from their prior ones (Fig. 4a, c). During the longer study period 2021, the negative correlation between sediment production rate (ε_) and initial sediment thickness condition (H0) shows that a specific quantity of sediment must be available for an optimum model run. Despite the dependence on sediment availability, in BL for both 2020 and 2021 a strong negative relationship occurs between the two hydraulic parameters, channel shape (β) and roughness (fi). This relationship lies contrary to the positive relationship between the β and fi parameters in the SSL cases (see Methods, Fig. 5). Here, the optimum hydraulic parameters for BL are a subset of those resulting in feasible subglacial hydraulic conditions for Otemma glacier (Figs. 4d, 5). Therefore, the optimum parameter distributions reflect the specific hydrological conditions to capture the observed BL export, not possible subglacial hydraulic conditions.

Our model parameterizes SSL and BL with different relationships (SSL: Engelund and Hansen, 196742 and BL: Wilcock and Crowe, 200343). In turn, we compare hydraulic factors such as water velocity and shear stress to examine the different hydraulic conditions between the SSL and BL optimum parameter combinations. For 2021, the longer study period with more BL variations (Fig. 3d), the subset of optimum hydraulic parameters for the BL numerical experiments does not result in a specific mean sediment transport capacity over the season. In BL, parameter combinations of channel shapes (β) and roughness (fi) result in mean seasonal shear stress integrated across the channel bed width, spanning 87% of the viable hydraulic conditions (Fig. 6d, h). Furthermore, the BL parameters result in seasonal mean channel width and water velocities covering a substantial range of viable subglacial hydraulic conditions as well (37 % and 70 % of the viable range, respectively).

The relationship between the channel shape (β) and roughness (fi) parameters in the BL cases for 2021, instead, result in a narrow seasonal mean unit shear stress, encompassing only 11% of the viable subglacial hydraulic conditions (Fig. 6b, f). Increasing channel shear stress would cause both the unit sediment transport capacity to increase and the channel’s growth rate to accelerate e.g. 34,46–48. Over short timescales (i.e. less than a day), increases in water discharge will result in rapid increases in shear stress and thus sediment transport capacity34,49. However, at longer timescales, increased shear stress has a counteracting effect on sediment transport capacity. At timescales longer than days, elevated shear stress causes the subglacial channel size to grow, reducing water velocity and sediment transport capacity34,49. In turn, these channel size-water velocity adjustments likely filter high BL events in response to high sediment transport conditions. Similar processes occur in subaerial channels50, but likely over longer periods than the continuous channel size evolution here34. Feedbacks between channel growth and sediment transport capacity appear to heavily impact the evolution of sediment discharge in response to water discharge variations and peak discharge events (Fig. 6). As a result, further observations that evaluate subglacial channel shape or water velocity51 might yield more rigorous parameterizations of both subglacial hydrology and bedload transport. The model outputs from 2020 exhibit a similar trend in these hydraulic factors as compared to 2021, with higher sensitivity to shear stress compared to other factors (Fig. 6a–h).

Methods
Datasets
The model requires inputs of water discharge and glacier topography to be compared with bedload and suspended sediment discharge from the glacier.

We use water discharge, bedload discharge, and suspended sediment discharge data collected from Otemma glacier (45°57'03"N, 7°27'02"E) during summers of 2020 and 2021 at a 2 min resolution33. The continuous record of suspended sediment export was evaluated using a turbidity probe calibrated to a turbidity-suspended sediment relationship. The flux of suspended sediment was established by multiplying the suspended sediment concentration by the coincident water discharge, also measured at the site using a stage height-water discharge relationship. Bedload transport flux was monitored using seismic data. To quantify the bedload flux, seismic data was post-processed using a geophysical inversion model71 in the open source R package seis (version 0.5.0). Field tests were used to establish model parameters and the model was calibrated using coincident water stage measurements as no direct measurements of bedload transport were available33. We also note, that temporal changes in bedload export also correspond to changing behavior of the proglacial river identified through imagery analysis44. These datasets are introduced to the model using a linear interpolated spline, and timestamps with no data were omitted from the analysis.

Ice thickness in the main trunk of Otemma glacier was estimated to be 150 m using available data72. The glacier is estimated to be 6 km long and on average 1 km wide based upon 2020 aerial photographs from SwissTopo (https://map.geo.admin.ch). Otemma glacier’s terminus is at 2496 m a.s.l., while we consider its maximum elevation of the main glacier at Col de Charmotane 3016 m a.s.l.

Subglacial sediment transport model
We use a lumped-element model that evolves the thickness of a subglacial sediment layer in response to transport and supply-limited sediment transport conditions and erosional processes45. A lumped subglacial hydraulics model was used to establish sediment transport capacity34.

A lumped-element model simulates the evolution of the thickness of a subglacial till layer H45. Sediment production, or bedrock erosion, adds sediment to the layer. Fluvial sediment transport in supply- and transport-limited regimes mobilizes or deposits sediment, thus removing or adding material to the till layer, respectively16,73. The model uses the Exner Equation74–76, a mass conservation relationship, to evolve the till layer height

∂H/∂t = (Qs + m_)/lw (1)

where H is the till layer height, l(w) is the glaciers’ length (width), m_ is a sediment production rate. Qs represents fluvial sediment flux underneath the glacier

Qs = Qb if Qb ≤ m_ lw (2a)
Qs = Qbσ(H) + m_ w(1 - σ(H)) otherwise (2b)

Qb is the sediment discharge capacity (see equations (9) and (10)), σ is a sigmoidal function, smoothing the transition from transport to supply-limited conditions when H is small, effectively reducing sediment availability16.

The source term m_ is defined as,

m_ = ε_ max(0, 1 - H/Hmax) (3)

where Hmax denotes the maximum height of till beyond which sediment production ceases and ε_ represents the rate of bedrock erosion that depends on glacier sliding or shear stress.

We leverage a lumped R-channel model34 to parameterize the subglacial hydraulics and sediment transport capacity needed to establish Qs (Equation (1)). This model assumes that water flows through a subglacial channel with length l, underneath a glacier with ice thickness h_ice. Channel size evolves with flow and creep from ice creep

∂S/∂t = C1 Qw Δh/l - C2 h_n S (4)

where t represents time, C1 = (1 - ρw cp c t) ρw i L g and C2 = 2A (ρw n g)^n are constants (refer to Table S1), g denotes gravitational acceleration, Qw is the water discharge, h = 1/2(h_ice + h_p) is the mean hydraulic head, with h_p as the water pressure head, ρw and ρ_ice are the densities of water and ice, respectively, and n is Glen’s parameter, typically n = 377. The head drop Δh is

Δh = l f_i v^2 / 2g D_h (5)

where f_i is a friction factor, D_h is the hydraulic diameter, l is the glacier length, and v = Qw/S is the water velocity. Channel area S comes from the hydraulic diameter D_h with

S = D_h^2 (β - sin β) / 8 sin^2(β/2) (6)

where β is the central angle of the circular segment of the channel boundary (Hooke angle)78. The width of the channel floor w_b is represented as

w_b = 2 sin(β/2) S / (β - sin β) (7)

Shear stress τ, needed in most sediment transport relationships, is established through the Darcy-Weisbach formulation

τ = 1/8 f_i ρ_w v^2 (8)

where f_i is the Darcy-Weisbach friction factor and velocity v = Qw/S. In applying the model to measurements of SSL, we implement the total sediment transport relationship of Engelund and Hansen42

Q_bs = 0.1 f_i D_50 (ρ_b/ρ_w - 1)^2 g^2 ρ_w τ^2.5 w_b (9)

where ρ_b and ρ_w are the density of the bedrock or sediment, f_i is the friction factor above, D_50 is median sediment size, τ is the shear stress evaluated in Equation (8), and w_b denotes the width of the channel floor that integrates the sediment transport rate across the width of the subglacial channel (Equation (7); Table S1).

To evaluate volumetric bedload transport when comparing model outputs to the BL record, we implement the Wilcock and Crow43 sediment transport relationship

Qb = ρ_b W* g (g (ρ_b/ρ_w - 1) D_50^3)^0.5 w_b (10)

where R_h is the hydraulic radius of the channel (R_h = D_h/4), and W* is the dimensionless transport rate, and Ψ is the hydraulic gradient Δh/l

W* = 0.002 τ*^6.1 if τ* ≤ 1.143 (11a)
W* = 14 (1 - 0.894/τ*^0.5)^4.5 otherwise (11b)

where ψ* is the ratio between the dimensionless bed shear stress and the dimensionless reference bed shear stress, given as

Ψ* = τ* / (0.05 (ρ_b/ρ_w - 1) D_50^3)^0.5 (12)

Note that this relationship is valid for values of D_50 > 4 mm.

Numerical experiments
We apply the model to records of suspended sediment load (SSL) and bedload (BL) discharge from the Otemma glacier (Section), using the respective sediment transport relationship (Eqs. (9) and (10)).

We run the model a large number of times with different parameter values and test model outputs against the observed records of sediment discharge in a Monte Carlo framework45,79. Parameter values are selected randomly so that they do not depend on the model outcomes of a previous set of parameter. We selected parameter ranges such that distributions formed within their boundaries across all four ensembles (SSL and BL with 2020 and 2021; Fig. 4). This way parameters from all four ensembles were sampled from the same prior distributions. To implement this scheme, for each model run we create a vector of randomly selected parameter values θ to run in the forward model

θ = [ε_, H0, β, f_i] (13)

ε_ is the sediment production rate to produce sediment over the model run used to evaluate the till source m_ in ref. 45. H0 is the initial till height condition used to evaluate the amount of sediment stored below the glacier before the model initialization. β is the Hooke angle, controlling the shape and thus the width of the subglacial channel78. f_i is the Darcy-Weisbach friction factor used to evaluate the water velocity and hydraulic potential to calculate shear stress and evolution of channel size (see ref. 34). The range of possible values and their sampling distribution are given in Table S1.

When running the model forward, we apply a spin-up to establish the initial channel cross-sectional area by applying maximum water discharge over the first 3 days of the study period until the change in cross-sectional area is negligible.

Model outputs (Q) with different parameters (θ) are compared against the observed sediment discharge records (Qo) from the BL or SSL datasets using relative error (ξ)

ξ(θ) = 1/n Σ |Q(θ) - Qo| / Qo (14)

n is the number of data points. Q and Qo are values averaged over 5 day periods, to reduce the impact of sediment transport times compared to water discharge within the glacier, which is not accounted for in the model e.g. Ref. 80.

For the year 2020, model runs commenced for on June 26, 2020 and ceased on August 31, 2020. For 2021, model runs commenced on June 15, 2021 and ceased on August 1, 2021. These periods coincides with available bedload and suspended load data. In 2021, data were collected until August 22, 2021. However, a substantial reduction in sediment export from Otemma glacier occurred between August 1 to 3, 2021. The possibility that this resulted from instrument error is minimal as imagery shows that proglacial forefield morphodynamics were tightly coupled to the reduced sediment input44. The lumped element model here do not able to capture this transition to reduced sediment export (Fig. S4–S5). Therefore, we only model the beginning of the season in 2020.

We cull model runs if they experience a flotation fraction of > 1.2 or if their hydraulic head exceeds the maximum glacier elevation for > 1% of the study period. Additionally, we remove model runs experiencing water velocity > 1.5 m s-1.

To test the viability of similar processes to capture SSL and BL, the model is first run with 500,000 identical parameter values for SSL and BL cases over both 2020 and 2021. The comparison is done using Equation (14), with physically infeasible runs being culled.

Additionally, we identify optimum parameter combinations using inversion a Monte Carlo inversion. We run the model with 2 × 10^6 randomly selected parameter values and quantify the relative error for each viable one (ξ; Equation (14)). For the analysis of both the posterior parameter combinations and their resultant forward model behavior, we utilize the top performing 0.05% (1000) of all runs.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper entitled “Different geomorphic processes control suspended sediment and bedload export from glaciers” deals with subglacial erosion and sediment export from glaciers. It is based on a subglacial erosion and sediment transport model that has been compared with high-frequency and continuous records of suspended and bedload fluxes collected during two melt seasons in a glacier (Otemma Glacier, Switzerland). Main results show that suspended sediment exports are mainly controlled by sediment supply, while bedload exports are governed by subglacial hydraulic conditions. This allows the authors to emphasize the importance of separating suspended and bedload transport in subglacial sediment export studies. My general feeling about this paper is mixed. On one side, I find that the idea of applying a lumped modelling approach to the unique sediment transport dataset collected in the Otemma glacier is quite original, and it allows the authors to bring new insights about processes controlling sediment exports. On the other side, I do not find that the authors are quite convincing in showing how the modelling approach allow them to provide good evidences of these controlling factors. This may be partly due to my low level of expertise in erosion and sediment transport modelling. However, I still believe that the manuscript needs a substantial improvement to better explain how geomorphic processes have been inferred from modelling results. I notably think that the section entitled “Processes controlling the export of bedload and suspended load” is a key part of the paper that has been poorly written, and that fails to provide clear evidences supporting conclusions about controlling factors. The analytical approach must be better explained and justified here. Another major concern is about sediment transport capacity. This has been computed with the Engelund-Hansen formulae for suspended sediment, and with the Wilcock-Crowe formulae for bedload. It would have been interesting to provide rationales for these choices, because many equations are available, and none of them is considered as optimal in any circumstances. I am notably wondering if similar conclusions would have been obtained if other equations would have been used. Other comments Fig. 1a: I do not find these cartoons of subglacial processes graphically efficient. It is particularly true for the parameters represented in the cross-section sketch, which are quite difficult to figure out. A better drawing work would be quite useful for improving the theoretical and graphical impact of this figure. Symbols that appear in these sketchs must be explained in the caption. Fig. 2: cost of parameter combinations that is represented here is unclear to me. This needs to be mathematically explained in the supplementary material. “As comparable quantities of SSL and BL are exported from the glacier, this suggests that different parameterizations of the two processes are needed”: I do not understand this argument that should be better explained. “posterior parameter distributions”: needs to be explained in the main text. Does this correspond to model outputs, or to the optimum combination or parameters for BL and SSL? Typo and wording: see annoted pdf files (article and supplements) The lack of line numbers does not facilitate the review work…", "reviewer_2": "The authors examine the distinct geomorphic processes governing fluvial sediment transport from glaciers, distinguishing between fine-grained suspended sediment and coarser bedload transport. They invert a physically based numerical model for sediment production and transport using a continuous record of bedload and suspended sediment flux. Since both the model architecture and observational data stem from prior work, the primary contribution here lies in synthesizing the two to identify specific controls on each transport mode. Their findings show that while both suspended sediment and bedload export are influenced by sediment availability, bedload transport is further constrained by hydraulic factors such as channel shape and roughness. This highlights that subglacial fluvial systems are more efficient at evacuating suspended sediments, whereas bedload transport requires higher shear stress for mobilization. The authors conclude that hydraulics should be explicitly considered when examining bedload transport processes and emphasize the need to treat suspended and bedload transport separately in glacial sediment export models. Overall, I find this paper to be generally well-written and of sufficiently broad interest to the community to warrant publication in Nature Communications. Notably, while many previous studies have inferred erosion rates through parameterizations linking suspended sediment in proglacial rivers to glacier dynamics, this study conclusively demonstrates that such an approach captures only a fraction of the total picture. Below, I present my thoughts, first outlining my primary issues, followed by minor concerns and a few grammatical suggestions and rewordings. Primary issues My main concern with this work is its heavy reliance on prior publications for key details, making aspects of the study difficult to interpret in isolation. This project builds upon previous papers that explore both the model development and the SSL/BL dataset. I had to search through the referenced papers to locate essential details needed to fully understand the authors' interpretations. For example, of the four main parameters used for the inversion—ε˙ (bedrock erosion potential), H0 (initial till height condition), β (Hooke angle), and fi (Darcy-Weisbach friction factor)—none are explicitly found in the equations provided in the methods section, making the analysis feel somewhat opaque. While I appreciate the need for brevity, including a summary of key model elements in the supplementary materials or fleshing out the methods could significantly improve clarity. • What the justifications are for the range in parameter values? For instance, in Delaney et al. 2024, the range for Hg0 and Hf0 is ~10-4 m to 5 cm, whereas in this paper study H0 ranges from 10-4 to 2 mm. Why the order of magnitude difference here? Similarly, is the increase in ε˙ compared to Delaney et al., 2024 meant to capture the production from abrasion and quarrying versus simply abrasion/SSL, or is there another motivation? • The study relies on bedload measurements from seismic techniques and suspended sediment from direct measurements, acquired in a previous study. While these methods are reasonable, a more explicit statement of their respective uncertainties and potential biases could be added in this paper, given the poor performance of the BL inversion in 2020. • “We elucidate the factors controlling sediment export by inverting a physically based numerical model of subglacial sediment production and sediment transport with suspended sediment and the first continuous bedload discharge records from an Alpine glacier.” It is not clear to me how the sediment production component in this model is “physically based”. Going back to Delaney et al., 2019, I see erosion rate is parameterized as a linear relation with slip speed, with reference to Herman et al., 2015 season (empirical relationship rather than based on first principals). However, this dataset focused on SSL in a proglacial river over a short melt season. Is bedrock erosion rate in this current study just held to a constant sediment production determined through inversion, or does it vary in time with slip speed, etc. ? The bedload component of 2020 performs poorly with the inversion which the authors attribute to “the lumped-element model’s limited ability to capture decreasing BL availability observed from August in the 2020.” Additional clarification would be useful here. First, is there speculation as to why this drop-off occurs? The bedload flux is itself the product of an inversion. Are there potential issues with the source data? Further, if the inversion is not designed to capture the decrease, could the analysis be successfully conducted on the data prior to August 2020 instead of the full season to provide at least a partial baseline for comparison against the other BL and SSL parameters? There is no discussion of how well the best fit parameters found through inversion align with physical expectations for this glacier. Minor points “from the Otemma glacier in Switzerland” It would be helpful to briefly state what is known about the bed conditions here. Hard, soft, mixed, unknown, etc. “Sediment is exported fluvially either as finer sediment in suspension or as coarser bedload with intermittent contact between sediment and the bed.” “Here, we are able for the first time to show that different processes control bedload and suspended load export from glaciers.” Perhaps “show quantitively” or “show how.” Other studies have reported similar results suggesting that BL and SSL operate differently with discharge and drainage system evolution (e.g. reference 31) “The disparity in SSL and BL performance (Figure 2) occurs despite the model’s ability to represent SSL and BL well, individually in three out of four datasets. (Figure 3).” “…suggesting that similar hydrogeomorphic processes controls SSL export in the two years.” Is the assumption that hydrogeomorphic controls on BL differed between the two years or that the poor performance of the inversion in 2020 precludes a comparison? “SSL experiments here suggest that sediment is evacuated with relative ease once produced, independent of subglacial sediment transport conditions... BL is evacuated less efficiently (Figure 3), potentially leaving substantial sediment available at the glacier bed.” I have difficulty reconciling this statement with myriad observations of recently exposed or in-siu poorly sorted till deposits. While SSL may be easily mobilized along one section of the bed or in a channel, there are many glaciers with full or partial till cover, which contain an abundance of fines, implying sand-sized and smaller particles are regularly created through comminution and stored in the subglacial environment intermixed with BL-sized particles. Perhaps specify: can be evacuated with relative ease once produced through abrasion. Minor suggested rewordings: “To date, the difficulty in observing subglacial bedload transport resulted in limited understanding of the physical processes associated with evacuating bedload compared with suspended load.” Underneath Beneath glaciers, sediment export Water transports sediment fluvially either in suspension, composed largely of sand and finer particles, or as bedload, where clasts roll, slide, or saltate over the channel’s bed. …models suggest that glacier quarrying creates bedload-sized material in amounts comparable to the suspended sediment produced by glacier abrasion. SSL sediment transport capacity (i.e. suspended sediment load sediment transport capacity) instead of particular subglacial hydraulic conditions that partially impact BL transport As a result of the number of subglacial channels and their non-linear effect on transport capacity, BL dependence on sediment transport capacity could be even less than suggested by the analysis here. Figure 5 y-axis: pa Pa Methods: Parameter values are selected randomly so that they do not depend dependent on the model outcomes of a previous set of parameter"}, "author_response": "Dear Editor, We thank Reviewer 1 for their detailed and constructive comments. Their work, we believe, has provided feedback that has greatly improved the manuscript. The reviewer’s comments are in gray, our response is in black and quotations from the new text are in bold font. Best regards, Ian Delaney on behalf of all authors General Comments • My general feeling about this paper is mixed. On one side, I find that the idea of apply- ing a lumped modelling approach to the unique sediment transport dataset collected in the Otemma glacier is quite original, and it allows the authors to bring new insights about processes controlling sediment exports. On the other side, I do not find that the authors are quite convincing in showing how the modelling approach allow them to provide good evidences of these controlling factors. This may be partly due to my low level of expertise in erosion and sediment transport modelling. However, I still believe that the manuscript needs a substantial improvement to better explain how geomorphic processes have been inferred from modelling results. I notably think that the section entitled “Processes controlling the export of bedload and suspended load” is a key part of the paper that has beenpoorlywritten,andthatfailstoprovideclearevidencessupportingconclusionsabout controlling factors. The analytical approach must be better explained and justified here. We thank the reviewer for the careful and balanced consideration of our work. While the reviewer points to several positive points, we also take seriously the comments of uncer- taintyinthemodelingapproachandtheneedtobetterdescribethe“Processescontrolling the export of bedload and suspended load.” Following comments from R2, we believe that part of the uncertainty is due to a streamlined and minimal methods explanation. Rather than referencing the models used, as in the previous version, we have summarized the models and datasets. Furthermore, we have referenced these materials in the main text. We have carefully considered the ways to improve the “Processes controlling the export of bedload and suspended load” section. Figure S4, formally in the supplement, is now in the text. With the as new model runs have been added, the text has been updated substantially. Additionally, the recommendations made in the attached pdf file have been integrated. We believe that these changes have improved this section. • Another major concern is about sediment transport capacity. This has been computed withtheEngelund-Hansenformulaeforsuspendedsediment,andwiththeWilcock-Crowe formulaeforbedload. Itwouldhavebeeninterestingtoproviderationalesforthesechoices, because many equations are available, and none of them is considered as optimal in any circumstances. I am notably wondering if similar conclusions would have been obtained if other equations would have been used. We thank the reviewers for these comments. Engelund and Hansen (1967) is an equation thatiscommonlyacceptedfortransportofsandtogravelsizedsediment. Ithasbeenused extensivelyandcitedover2500times(GoogleScholar). Wehavechosenthisformulagiven its validation over sand size particles that are characteristic of subglacial and proglacial streams. 1 Wilcock and Crowe (2003) is a commonly accepted bedload transport parameterization that has been used extensively as well (1100 citations; Google Scholar). We are aware of no other transport formula that is more commonly accepted for large bedload sized material. Excess shear stress approaches can be traced back to the 1930s (Shields, 1936) were generalized to gravel in the classic work of Meyer-Peter Mu¨ller in the 1940s and then havedevelopedintooneofthetwomainapproachesforsedimenttransportmodelling(the otheronebeingstreampowerbased). Wemightexpectthedetailedpredictionstochange if different models were used but not the general patterns. We note that both formulas respond to shear stress in the subglacial channel (now described in the supplementary material)andthatincreasedshearstressisneededtomobilizelargersediment,regardless of the transport equation itself. As a result, we see no reason why the general choice of sedimenttransportrelationshipwouldsubstantiallyimpacttheoutcomeofthestudy. When the hydraulic or sediment transport conditions are compared to each other (i.e. Figure 5, now Figure 6), we use shear stress, or shear stress across the channel bed. This way the hydraulic conditions can be compared, regardless of the choice in sediment transport formula. WehaveaddedthefollowingsentencestothetextinSection3. Ourmodelparameterizes SSLandBLwithdifferentrelationships(SSL:EngelundandHansen,1967(Engelund andHansen,1967)andBL:WilcockandCrowe,2003(WilcockandCrowe,2003)). In turn,wecomparehydraulicfactorssuchaswatervelocityandshearstresstoexam- ine the different hydraulic conditions between the SSL and BL optimum parameter combinations. Specific Comments • Fig. 1a: I do not find these cartoons of subglacial processes graphically efficient. It is particularly true for the parameters represented in the cross-section sketch, which are quite difficult to figure out. A better drawing work would be quite useful for improving the theoretical and graphical impact of this figure. Symbols that appear in these sketchs must be explained in the caption. Wethankthereviewerforthiscomment. Afterspeakingwithcolleaguesweareuncertainof ways to substantially improve the figure. However, we have added the following text to the caption to clarify the different parameters. (sediment production rate (ε˙), the sediment height initial condition (H ), the channel shape (β), and channel roughness (f ). 0 i • Fig. 2: cost of parameter combinations that is represented here is unclear to me. This needs to be mathematically explained in the supplementary material. Excellent comment. The details are described in the “Methods” section. However, we have added the following text to the figure caption: Cost is defined as relative error (cid:12) (cid:12) or ξ(θ) = 1 (cid:80)(cid:12)Q(θ)−Qo(cid:12), where θ is a parameter set, Q(θ) is model output and Q is nr (cid:12) Qo (cid:12) o observations. • “As comparable quantities of SSL and BL are exported from the glacier, this suggests that different parameterizations of the two processes are needed”: I do not understand this argument that should be better explained. This point should have been more clearly stated. We have slightly modified the sentence and nowbelieve theintended meaningis clearer. As substantial quantities ofSSLand BL are exported from the glacier(Mancini et al., 2023), this suggests that different parameterizations of the two processes are needed to fully capture subglacial sedi- ment export. 2 • “posterior parameter distributions”: needs to be explained in the main text. Does this correspond to model outputs, or to the optimum combination or parameters for BL and SSL? We have reworded the text to: optimum parameter combinations for consistency with the paragraph above it . • Typo and wording: see annoted pdf files (article and supplements) We thank the reviewer for carefully reading and editing the manuscript. The corrections proposed in these comments have greatly improved the manuscript. References Engelund, F. and Hansen, E. (1967). A monograph on sediment transport in alluvial streams. Technical report, TechnicalUniversityofDenmark,Copenhagen,Denmark. Mancini, D., Dietze, M., Mu¨ller, T., Jenkin, M., Miesen, F., Roncoroni, M., Nicholas, A., andLane, S.(2023). Filter- ing of the Signal of Sediment Export From a Glacier by Its Proglacial Forefield. Geophysical Research Letters, 50(21):e2023GL106082. e2023GL1060822023GL106082. Shields,A.(1936).AnwendungderAehnlichkeitsmechanikundderTurbulenzforschungaufdieGeschiebebewegung. PhDThesisTechnicalUniversityBerlin. Wilcock, P. and Crowe, J. (2003). Surface-based transport model for mixed-size sediment. Journal of Hydraulic Engineering,129(2):120–128. 3 Dear Editor, We thank Reviewer 2 for their detailed and constructive comments. Their work, we believe, has provided feedback that has greatly improved the manuscript. Thereviewer’scommentsareinbold,ourresponseisinitalicsandquotationsfromthenewtext are in normal font. Best regards, Ian Delaney on behalf of all authors General Comments Reviewer comment: My main concern with this work is its heavy reliance on prior publica- tions for key details, making aspects of the study difficult to interpret in isolation. This project builds upon previous papers that explore both the model development and the SSL/BL dataset. I had to search through the referenced papers to locate essential details needed to fully un- derstand the authors’ interpretations. For example, of the four main parameters used for the inversion—ε˙ (bedrock erosion potential), H0 (initial till height condition), β (Hooke angle), and fi (Darcy-Weisbach friction factor)—none are explicitly found in the equations provided in the methods section, making the analysis feel somewhat opaque. While I appreciate the need for brevity, including a summary of key model elements in the supplementary materials or fleshing out the methods could significantly improve clarity. Authors’ response: We thank the reviewer for bringing these issues to light. Along with com- ments from Reviewer 1, it is clear that our methodology should be better described and this should significantly strengthen the manuscript. We have addressed the itemized issues below. Additionally, we have included a more detailed summary of the bedload flux evaluation (Mancini et al., 2023), along with summarizing the sediment transport modeling components (Delaney et al., 2024b) and sediment capacity and hydraulics variations (Delaney et al., 2024a). • Reviewer comment: What the justifications are for the range in parameter values? For instance, in Delaney et al. 2024, the range for Hg0 and Hf0 is 10-4 m to 5 cm, whereas in this paper study H0 ranges from 10-4 to 2 mm. Why the order of magnitude difference here? Similarly,istheincreaseinε˙comparedtoDelaneyetal.,2024meanttocapturethe production from abrasion and quarrying versus simply abrasion/SSL, or is there another motivation? Authors’ response: We should have been clearer about this in the original manuscript. Thetextbelowstatestheconditionsforevaluatingtheparameterranges. Withrespectthe comparison with Delaney et al. (2024b), we note that in this case values of H could be f0 quitelargeastheproglacialareacomprisedarelativelysmallproportionofthecatchment. As a result, large variation in this parameter could still result in an adequate volume of sediment being expelled from the catchment. We anticipate that in a catchment with a proportionally larger proglacial area, H would be smaller or at least more narrowly de- f0 fined. With respect to the H parameter in Delaney et al. (2024b), this could be larger for g0 several reasons. First, would be variations between catchments and glaciers. However, anotherimportantreasonisthattheinversiontherespannedsevenyearscontinuously. As a result, there is more freedom in the inversion for large stocks of sediment to be present at the beginning of the model run and depleted throughout. In the application here, H is g0 roughly1−2mm,comparedto5mminDelaneyetal.(2024b). Thislikelybetterreflectsthe 1 potentialamountofsedimentavailableoverasingleseasonaspresentedhere. Duetothe lack of water discharge measurements in the spring, fall and winter at Glacier d’Otemma, a continuous inversion was not possible. In the application here, we discuss how ε˙ could represent both abrasion in the SSL case and quarrying in the BL case. As Delaney et al. (2024b) was published prior to this work here, we propose that the ε˙ value in that manuscript would represent abrasion, not quar- rying. We note, however, that the multi year inversion presented in Delaney et al. (2024b) likelymeansthatalowervalueofε˙wouldbefoundasthisratewouldbemaintainedthrough lowtransporttimeperiods(i.e. winter),whereasthevalueε˙herewouldbeforthesummer period where higher abrasion (and to a lesser extent quarrying) rates can persist (Ugelvig et al., 2018). The implications of the multi-seasonal runs and the lack of knowledge about sediment production in low melt conditions is discussed in Section 5.3 of Delaney et al. (2024b). In response to this comment, the following text has been added to the methods section: We selected parameter ranges such that distributions formed within their bound- aries across all four ensembles (SSL and BL with 2020 and 2021; Figure 4). This wayparametersfromallfourensemblesweresampledfromthesamepriordistribu- tions. • Reviewer comment: The study relies on bedload measurements from seismic tech- niques and suspended sediment from direct measurements, acquired in a previous study. While these methods are reasonable, a more explicit statement of their respective uncertainties and potential biases could be added in this paper, given the poor performance of the BL inversion in 2020. Authors’response: Wehaveincludedthefollowingtextinthemethodssection: Thecon- tinuous record of suspended sediment export was evaluated using turbidity probes calibratedtoturbidity-suspendedsedimentrelationship. Thefluxofsuspendedsed- imentwasestablishedbymultiplyingthesuspendedsedimentconcentrationbythe coincident water discharge, also measured at the site using a stage high-water dis- charge relationship. Bedload transport flux was monitored using seismic data. To quantify the flux, seismic data was post-processed using a geophysical inversion model (Dietze et al., 2019) in the open source R package eseis (version 0.5.0). Field tests were used to establish model parameters and the model was calibrated using coincidentwaterstagemeasurementsasnodirectmeasurementsofbedloadtrans- port were available (Mancini et al., 2023). These datasets were introduced to the model using a linear interpolated spline, and timestamps with no data were omitted from the analysis. We also discuss the robustness of the measurements below in response to another com- ment below. • Reviewer comment: “We elucidate the factors controlling sediment export by inverting a physically based numerical model of subglacial sediment production and sediment trans- portwithsuspendedsedimentandthefirstcontinuousbedloaddischargerecordsfroman Alpineglacier.”Itisnotcleartomehowthesedimentproductioncomponentinthismodelis “physicallybased”. GoingbacktoDelaneyetal.,2019,Iseeerosionrateisparameterized asalinearrelationwithslipspeed,withreferencetoHermanetal.,2015season(empirical relationship rather than based on first principals). However, this dataset focused on SSL in a proglacial river over a short melt season. Is bedrock erosion rate in this current study just held to a constant sediment production determined through inversion, or does it vary in time with slip speed, etc. ? 2 Authors’ response: This is an important point that demands clarification. With a more developedmethodssectionwebelievethatthispointwillbeclearer. Here,wehavechosen erosion rate to be a steady value. In previous work, it was necessary for glacier erosion to be dependent on slip speed as we would expect different parts of the glacier to produce different amounts of sediment, hence the value of a spatially distributed model (Delaney et al., 2019, 2023). However, in this case, because conditions are averaged over the bed of the glacier, we believe that a single value of erosion rate is appropriate. This is discussed fully in Section 5.3 of Delaney et al. (2024b). We believe the term physically based is appropriate here given the representation of physical processes, however, we wouldwelcomesuggestsforanotherterminologyproposedbythereviewer. Thetextinthe methods has also been adjusted to read: ε˙ represents the rate of bedrock erosion held steady through the model run...Here, erosion rate is a parameter, unlike previous work(Delaney et al., 2019, 2023), where erosion depended on glacier sliding or shear stress. • Reviewercomment: Thebedloadcomponentof2020performspoorlywiththeinversion which the authors attribute to “the lumped-element model’s limited ability to capture de- creasing BL availability observed from August in the 2020.” Additional clarification would be useful here. First, is there speculation as to why this drop-off occurs? The bedload flux is itself the product of an inversion. Are there potential issues with the source data? Further,iftheinversionisnotdesignedtocapturethedecrease,couldtheanalysisbesuc- cessfully conducted on the data prior to August 2020 instead of the full season to provide at least a partial baseline for comparison against the other BL and SSL parameters? Authors’response: Thisisanexcellentcomment. Wehavediscussedseveralreasonsfor apotentialdropoffinbedloadexportfromtheglacier. Possiblereasonsincludebehaviorof an overdeepening or simply sediment exhaustion in the main channel. However, following the drop off in sediment export from the glacier, the proglacial river transitions from braid- ing behavior to incision on the basis aerial imagery analysis (Mancini et al., 2024). This behavior of the proglacial river is expected given a reduction in sediment supply from the river. Asaresult,thereisstrongevidencefrombothseismicdataandimagerythatsucha drop off occurred, and that it was not the result of measurement error. We also thank the reviewer for the recommendation to include the inversion for the first part of the season. This has been done and the results are presented in the updated manuscript. The following text has been added to the “Methods” to explain the updated modeling procedure. Fortheyear2020,modelrunscommencedforonJune26,2020andceasedonAugust 31, 2020. For 2021, model runs commenced on June 15, 2021 and ceased on August 1, 2021. These periods coincides with available bedload and suspended load data. In 2021, data were collected until August 22, 2021. However, a substantial drop off in sediment export from Otemma glacier occurred between August 1 to 3, 2021. The possibilitythatthisresultedfrominstrumenterrorisminimalasimageryalsoshows the proglacial river response to the reduced sediment input (Mancini et al., 2024). The lumped element model here was not able to capture this transition to reduced sediment export (Figure S4-S5). Therefore, we only modeled the beginning of the season. • Reviewer comment: There is no discussion of how well the best fit parameters found through inversion align with physical expectations for this glacier. 3 Authors’ response: We thank the review for this comment. The following paragraph has been added to the section “Divergent impact on landscape evolution due to different sensitivities to hydraulic conditions and sediment availability”: TheaboveresultsdemonstratethatdifferentprocessescontrolBLandSSLexport, with BL being partially controlled by hydraulic factors and SSL fully responding to sediment availability at Otemma glacier. Interplay between hydraulic parameters values for channel shape (β) and roughness (f ) can result in viable subglacial hy- i draulic conditions (Figure S4)(Werder and Funk, 2009; Pohle et al., 2022). However, results here suggest that only a narrow range of parameter combinations can re- sult in the sediment transport capacity variations needed to capture the observed sedimentexport(Figure4). Otherglaciersmayexhibitdifferentdependenceonsed- imentproductionrate(ε˙)andinitialsedimentthicknesscondition(H ). Forinstance, 0 thestrongdependenceofSSLexportonglacierslidingforarelativelysteepglacier may suggest reduced sediment storage and greater dependence on sediment pro- ductionrate(ε˙)(Hermanetal.,2015). Conversely,thicksedimenthasbeenobserved below the Greenland Ice Sheet(Walter et al., 2014), suggesting greater initial sed- iment thickness condition (H ) there. Additionally, values of sediment production 0 rate (ε˙) and initial sediment thickness condition (H ) could depend on the time pe- 0 riod of the inversion. For instance, longer study periods may result in larger initial sediment thickness conditions (H ) to account for the continuity of sediment avail- 0 ability across the inversion period (Delaney et al., 2024b). Specific Comments • Reviewer comment: “from the Otemma glacier in Switzerland” It would be helpful to briefly state what is known about the bed conditions here. Hard, soft, mixed, unknown, etc. Authors’ response: Text now reads: Otemma glacier is a 6km long glacier with unknown hard or soft bed characteristics, in an Alpine climate. • Reviewer comment: “Sediment is exported fluvially either as finer sediment in suspension or as coarser bedload with intermittent contact between sediment and the bed.” Authors’ response: Text now reads: Sediment is exported fluvially either as finer sediment in suspension or as coarser bedload with intermittent contact between sediment clasts and the channel’s bed. • Reviewercomment: “Here,weareableforthefirsttimetoshowthatdifferentprocesses control bedload and suspended load export from glaciers.” Perhaps “show quantitively” or “show how.” Other studies have reported similar results suggesting that BL and SSL operate differently with discharge and drainage system evolution (e.g. reference 31) Authors’ response: The reviewer is correct that this should be clarified. The text now reads: Here, we are able for first time to quantitatively that different processes control bedload and suspended load export from glaciers, using records collected directly at the glacier terminus. We note that Mao et al. (2014), e.g. reference 31, collected these records some distance downstream of a glacier as discussed earlier in our manuscript. As a result, the signal measured by them is likely not a glacial signal (Mancini et al., 2023). We believe that this new phrasing better captures the novelty of the study, 4 • Reviewercomment: “ThedisparityinSSLandBLperformance(Figure2)occursdespite the model’s ability to represent SSL and BL well, individually in three out of four datasets. (Figure 3).” Authors’ response: We believe that this phrasing is clearer: No single set of param- eters accurately represents both SSL and BL simultaneously (Figure 2). However, with specific parameter combinations, the model adequately represents SSL and BL individually (Figure 3). • Reviewer comment: “...suggesting that similar hydrogeomorphic processes controls SSL export in the two years.” Is the assumption that hydrogeomorphic controls on BL differed between the two years or that the poor performance of the inversion in 2020 precludes a comparison? Authors’ response: The reviewer is correct. We have added the following paragraph to the text. In the BL case, the hydraulic parameters channel shape factor (β) and friction factor (f ) are negatively correlated in both 2020 and 2021. However, other i similar interactions between the two years do not emerge. This absence could be due in part to the relatively short study period in 2020 that reduced the sensitivity of the sediment availability parameters, sediment production (ε˙) and initial till thick- ness condition (H ). 0 • Reviewercomment: “SSLexperimentsheresuggestthatsedimentisevacuatedwithrel- ative ease once produced, independent of subglacial sediment transport conditions... BL is evacuated less efficiently (Figure 3), potentially leaving substantial sediment available at the glacier bed.” I have difficulty reconciling this statement with myriad observations of recently exposed or in-siu poorly sorted till deposits. While SSL may be easily mobilized along one section of the bed or in a channel, there are many glaciers with full or partial till cover, which contain an abundance of fines, implying sand-sized and smaller particles are regularly created through comminution and stored in the subglacial environment intermixed with BL-sized particles. Perhaps specify: can be evacuated with relative ease once produced through abrasion. Authors’ response: Excellent comment. The text now reads: SSL experiments here suggest that sediment is evacuated with relative ease once produced by abrasion and accessed by a subglacial channel, independent of subglacial sediment trans- port conditions... Minor suggested rewordings: • Reviewer comment: “To date, the difficulty in observing subglacial bedload transport resulted in limited understanding of the physical processes associated with evacuating bedload compared with suspended load.” Authors’ response: Text now reads: To date, the difficulty in observing subglacial bedload transport limits the understanding of the physical processes associated with evacuating bedload compared with suspended load. • Reviewer comment: Underneath Beneath glaciers, sediment export Authors’ response: Done. • Reviewercomment: Watertransportssedimentfluviallyeitherinsuspension,composed largely of sand and finer particles, or as bedload, where clasts roll, slide, or saltate over the channel’s bed. 5 Authors’ response: Done. • Reviewer comment: ...models suggest that glacier quarrying creates bedload-sized materialinamountscomparabletothesuspendedsedimentproducedbyglacierabrasion. Authors’ response: Done. • Reviewer comment: SSL sediment transport capacity (i.e. suspended sediment load sediment transport capacity) Authors’ response: Done. • Reviewer comment: instead of particular subglacial hydraulic conditions that partially impact BL transport Authors’ response: Done. • Reviewercomment: Asaresultofthenumberofsubglacialchannelsandtheirnon-linear effectontransportcapacity,BLdependenceonsedimenttransportcapacitycouldbeeven less than suggested by the analysis here. Authors’ response: We thank the reviewer for the careful read. • Reviewer comment: Figure 5 y-axis: pa to Pa Authors’ response: Fixed • Reviewer comment: Methods: Parameter values are selected randomly so that they do not depend dependent on the model outcomes of a previous set of parameter Authors’ response: Done. References Delaney, I., Anderson, L., and Herman, F. (2023). Modeling the spatially distributed nature of subglacial sediment transportanderosion. EarthSurfaceDynamics,11(4):663–680. Delaney,I.,Tedstone,A.,Werder,M.A.,andFarinotti,D.(2024a).Subglacialandsubaerialfluvialsedimenttransport capacityresponddifferentlytowaterdischargevariations. EGUsphere,pages1–25. Delaney, I., Werder, M., Felix, D., Albayrak, I., Boes, R., andFarinotti, D.(2024b). ControlsonSedimentTransport FromaGlacierizedCatchmentintheSwissAlpsEstablishedThroughInverseModelingofGeomorphicProcesses. WaterResourcesResearch,60(4):e2023WR035589. Delaney,I.,Werder,M.A.,andFarinotti,D.(2019). ANumericalModelforFluvialTransportofSubglacialSediment. JournalofGeophysicalResearch: EarthSurface,124(8):2197–2223. Dietze,M.,Lagarde,S.,Halfi,E.,Laronne,J.,andTurowski,J.(2019). Jointsensingofbedloadfluxandwaterdepth byseismicdatainversion. WaterResourcesResearch,55(11):9892–9904. Herman,F.,Beyssac,O.,Brughelli,M.,Lane,S.,Leprince,S.,Adatte,T.,Lin,J.Y.Y.,Avouac,J.P.,andCox,S.C. (2015). Erosionbyanalpineglacier. Science,350(6257):193–195. Mancini, D., Dietze, M., Mu¨ller, T., Jenkin, M., Miesen, F., Roncoroni, M., Nicholas, A., andLane, S.(2023). Filter- ing of the Signal of Sediment Export From a Glacier by Its Proglacial Forefield. Geophysical Research Letters, 50(21):e2023GL106082. e2023GL1060822023GL106082. Mancini,D.,Roncoroni,M.,Dietze,M.,Jenkin,M.,Mu¨ller,T.,Ouvry,B.,Miesen,F.,Pythoud,Q.,Hofmann,M.,Lardet, F., Nicholas, A., and Lane, S. (2024). Rates of evacuation of bedload sediment from an alpine glacier control proglacial stream morphodynamics. Journal of Geophysical Research: Earth Surface, 129(8):e2024JF007727. e2024JF0077272024JF007727. 6 Mao,L.,Dell’Agnese,A.,Huincache,C.,Penna,D.,Engel,M.,Niedrist,G.,andComiti,F.(2014). Bedloadhysteresis inaglacier-fedmountainriver. EarthSurfaceProcessesandLandforms,39(7):964–976. Pohle, A., Werder, M. A., Gra¨ff, D., and Farinotti, D. (2022). Characterising englacial R-channels using artificial moulins. JournalofGlaciology,68(271):879–890. Ugelvig, S. V., Egholm, D. L., Anderson, R. S., and Iverson, N. R. (2018). Glacial Erosion Driven by Variations in MeltwaterDrainage. JournalofGeophysicalResearch: EarthSurface,123(0):2863–2877. Walter,F.,Chaput,J.,andLu¨thi,M.(2014). ThicksedimentsbeneathGreenland’sablationzoneandtheirpotential roleinfutureicesheetdynamics. Geology,42(6):487–490. Werder, M. A. and Funk, M. (2009). Dye tracing a jo¨kulhlaup: II. testing a jo¨kulhlaup model against flow speeds inferredfrommeasurements. JournalofGlaciology,55(193):899–908. 7"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The revised version of the manuscript is of excellent quality, and the authors have very well addressed all my comments. They also have provided clear and convincing arguments about the changes made to the manuscript. I would therefore recommend acceptance of publication. After a careful reading of the manuscipt and supplementary material, only few typos have been noticed: L171: delete “this” L218-219: unclear sentence Fig. 3: the thick black line separating the two years could be removed Congratulations to the authors for this very impressive work that should be of great interest to scientists working on glacier erosion and sediment transport", "reviewer_2": "It is my opinion that the authors have addressed the revisions satisfactorily, and I no longer have any outstanding concerns regarding this manuscript. I recognize and appreciate the thoughtful attention they gave to the reviewer feedback and fully support its publication in Nature Communications. During my readthrough I noticed a few small issues, which I detail below: • Line 57: we are able for first time à for the first time • Line 81: parameter values combinations à value • Line 171: model outputs from 2020 does not exhibit à do not exhibit • Extra spaces throughout and would be worth double checking: e.g. o Line 80: and BL , the model was à BL, the o Line 92: bedload (BL ) and suspended load (SSL ) à (BL) …(SSL) o Line 121: (Figure 3 k) à (Figure 3k) o Line 158: (Figure 6 b, f). à (Figure 6b, f) o Line 211: BL , à BL, o Line 212: BL ’s à BL’s o Line 219: ice e.g. 62 or sediment deformation e.g. 63. Line 202 “Similarly, sediment availability’s role in representing SSL export could support using empirical “erosion rules” in parameterizing glacier abrasion and suspended sediment export. “Erosion rules” could well represent sediment production through abrasion, itself heavily dependent on glacier sliding.” Small point, but a power-based abrasion rule has a stronger physical basis than rules that depend solely on slip speed ( eg Hallet, 2011; Hansen et al, 2023 doi: 10.1130/G50673.1)"}, "author_response": "Dear Editor, Again, we wish to express our gratitude for your work in editing this manuscript and accepting it for publication. The reviewer comments are in gray, response to the reviewer’s comments is in normal font, and quotes from the text are in bold. Best regards, Ian Delaney, on behalf of all authors Reviewer 1 The revised version of the manuscript is of excellent quality, and the authors have very well addressed all my comments. They also have provided clear and convincing arguments about the changes made to the manuscript. I would therefore recommend acceptance of publication. After a careful reading of the manuscipt and supplementary material, only few typos have been noticed: Congratulations to the authors for this very impressive work that should be of great interest to scientists working on glacier erosion and sediment transport Specific Comments • L171: delete “this” Done. • L218-219: unclear sentence Text now reads: Therefore, glacial erosion of bedrock may only occur if sediment is evacuated by non-fluvial means such as entrainment by the ice e.g.(Iverson, 1993) or sediment deformation e.g.(Hansen and Zoet, 2022). • Fig. 3: the thick black line separating the two years could be removed Done. Reviewer 2 Specific Comments • Line 57: we are able for first time to: for the first time Changed to: Here, first time we demonstrate • Line 81: parameter values combinations to: value Changed to: parameter values using inversion • Line 171: model outputs from 2020 does not exhibit to: do not exhibit Done. • Extra spaces throughout and would be worth double checking: e.g. – Line 80: and BL , the model was to: BL, the Done. – Line 92: bedload (BL ) and suspended load (SSL ) to: (BL) ...(SSL) Done. – Line 121: (Figure 3 k) to: (Figure 3k) Done. – Line 158: (Figure 6 b, f). to: (Figure 6b, f) Done. – Line 211: BL , to: BL, Done. – Line 212: BL ’s to: BL’s Done. – Line 219: ice e.g. 62 or sediment deformation e.g. 63 Done. • Line 202 “Similarly, sediment availability’s role in representing SSL export could support usingempirical“erosionrules”inparameterizingglacierabrasionandsuspendedsediment export. “Erosion rules” could well represent sediment production through abrasion, itself heavily dependent on glacier sliding.” Small point, but a power-based abrasion rule has a stronger physical basis than rules that depend solely on slip speed ( eg Hallet, 2011; Hansen et al, 2023 doi: 10.1130/G50673.1) Excellent comment. We have changed the text to read: “Erosion rules” could well represent sediment production through abrasion, itself heavily dependent on glacier sliding, particularly abrasive power at the glacier bed (Hallet,1979;Alleyetal.,1997;Hermanetal.,2015;Koppesetal.,2015;Hansenetal., 2023). References Alley, R. B., Cuffey, K. M., Evenson, E. B., Strasser, J. C., Lawson, D. E., and Larson, G. J. (1997). How glaciers entrainandtransportbasalsediment: physicalconstraints. QuaternaryScienceReviews,16(9):1017–1038. Hallet,B.(1979). Atheoreticalmodelofglacialabrasion. JournalofGlaciology,23(89):39–50. Hansen, D.D., Brooks, J.P., Zoet, L.K., Stevens, N.T., Smith, L., Bate, C.E., andJahnke, B.J.(2023). Apower- basedabrasionlawforuseinlandscapeevolutionmodels. Geology,51(3):273–277. Hansen,D.D.andZoet,L.K.(2022).Characterizingsedimentfluxofdeformingglacierbeds.JournalofGeophysical Research: EarthSurface,pagee2021JF006544. Herman,F.,Beyssac,O.,Brughelli,M.,Lane,S.,Leprince,S.,Adatte,T.,Lin,J.Y.Y.,Avouac,J.P.,andCox,S.C. (2015). Erosionbyanalpineglacier. Science,350(6257):193–195. Iverson,N.R.(1993). Regelationoficethroughdebrisatglacierbeds: Implicationsforsedimenttransport. Geology, 21(6):559–562. Koppes,M.,Hallet,B.,Rignot,E.,Mouginot,J.,Wellner,J.S.,andBoldt,K.(2015). Observedlatitudinalvariationsin erosionasafunctionofglacierdynamics. Nature,526(7571):100–103. 2"}]

Decision letter