Impacts of Plant Roots on Debris-Flow Bed Erosion in Laboratory Experiments

–1– 1 Impacts of Plant Roots on Debris-Flow Bed Erosion in 2 Laboratory Experiments 3 Anna J. van den Broek1, Dagmar T. Mennes1, Maarten G. Kleinhans1, 4 Lonneke Roelofs1, Jana Eichel1, Daniel Draebing1, Tjalling de Haas1 5 1Department of Physical Geography, Utrecht University, Utrecht, 3584 CB, The Netherlands 6 Corresponding author: Anna J. van den Broek, [email protected] –2– 7 Abstract 8 Debris flows often increase in size due to bed erosion and entrainment, enhancing 9 their hazardous potential. However, the effects of plant rooting on debris-flow erosion 10 on ubiquitous vegetated slopes remain unknown, which hinders debris-flow hazard as11 sessment. Here, we investigated the effects of roots on debris-flow bed erosion using scaled 12 experiments in a 5 m long, 0.3 m wide laboratory flume with an erodible bed. Roots of 13 fast-growing Sorghum bicolor (Sudan grass) seedlings were used as proxies for tree roots 14 to quantify the effect of varying rooting characteristics on erosion. Our results indicate 15 that erosion decreases non-linearly with increasing Root Length Density (RLD) and Root 16 Area Ratio (RAR). Increases in either parameter enhance root–soil contact, thereby im17 proving soil stability and reducing erosion. Among the two, RLD, and thus the combined 18 effect of root length and root density, appears most influential, as RAR does not cap19 ture the three-dimensional structure of the root system. Our experimental results sug20 gest that increasing root-soil contact at the debris-flow bed reduces erosion, decreasing 21 or even preventing debris-flow volume growth. These findings imply that alterations in 22 vegetation characteristics, such as those resulting from forest fires or reforestation, af23 fect debris-flow erosion and open up possibilities for biogeomorphic scale experiments 24 for slope processes. 25 Keywords: debris flow, erosion, vegetation roots, Root Length Density, Root Area Ra26 tio, hazard mitigation 27 Highlights 28 • Experiments show that rooting enhances soil stability and reduces debris-flow ero29 sion. 30 • Root Length Density has a strong non-linear effect in reducing bed erosion. 31 • Seedlings offer potential for studying root effects on debris flows in experiments. 32 Graphical Abstract –3– 33 1 Introduction 34 Debris flows are powerful and destructive mass movements that annually cost thou35 sands of lives and billions of euros worldwide (Prakash et al., 2024). The number of ca36 sualties has been directly linked to debris-flow volume (Dowling & Santi, 2014), which 37 may grow several orders of magnitude by bed and bank erosion during transport (e.g. 38 Iverson et al., 2011; Jakob & Hungr, 2005). Therefore, understanding debris-flow ero39 sion is important for effective hazard assessment and mitigation. Previous laboratory, 40 modeling, and fieldwork studies have shown that debris-flow bed erosion depends on com41 plex interactions between debris-flow forces and bed strength. Many flow properties have 42 been correlated to bed erosion rates including volume (De Haas et al., 2022; Chen et 43 al., 2005), depth (Sc h u ¨ rc h et al., 2011; McDougall & Hungr, 2005), velocity (Iverson, 2012; 44 McDougall & Hungr, 2005), and basal, shear and impact forces (Roelofs et al., 2022; 45 Li et al., 2020; Jakob & Hungr, 2005), where an increase in either of these factors gen46 erally enhances erosion. The resistance of the bed against erosion, or bed shear strength, 47 has been found to depend strongly on the pore-pressure of the bed at the bed-flow in48 terface. An increase in pore-pressure reduces intergranular friction and therefore weak49 ens the bed shear strength (Zheng et al., 2023; Roelofs et al., 2023; Zheng et al., 2021; 50 McCoy et al., 2012; Iverson, 2012). Vegetation roots are known to play a crucial role in 51 improving bed, bank, and soil strength in both fluvial environments (Pollen, 2007; Pollen 52 & Simon, 2005) and soil stability processes in mountainous environments (Draebing et 53 al., 2023; Roering et al., 2003; Schmidt et al., 2001). By strengthening the soil matrix, 54 they help resist erosion, reduce sediment transport, and mitigate the risk of slope fail55 ures. Roots resist tension forces and dissipate shear stresses through the soil using their 56 tensile strength (Ghestem et al., 2014), increase shear strength by anchoring the soil (Poirier 57 et al., 2018; Kaspar & Singer, 2011), and bind soil particles through adhesive secretions 58 and chemical reactions with clay (Galloway et al., 2020; Poirier et al., 2018). 59 While previous studies documented debris flows interaction with plants in many 60 mountain regions (Figure 1; Booth et al., 2020; Bollschweiler et al., 2008; Wilford et al., 61 2005; Bunn & Montgomery, 2004; Johnson et al., 2000), we have surprisingly little 62 quantitative understanding of how roots affect debris-flow erosion. Field observations 63 indicate that roots can reduce debris-flow erosion (Cui et al., 2024; Wilford et al., 2005). 64 Months to years after wildfires, where the above-ground biomass is destroyed, erosion 65 by debris flows peaks due to weakened soil strength as a result of root decay (Thomas 66 et al., 2021; de Graff, 2018; Meyer et al., 2001). In industrial forests, debris flows often 67 scour channels down to bedrock, whereas in old-growth forests with well-developed root 68 structures, such scouring is rare (Schmidt et al., 2001; Bunn & Montgomery, 2004). On 69 debris-flow fans, root webs are observed to offer resistance to debris-flow erosion (Figure 70 1b and d; Wilford et al., 2005). Combined with the well-documented role of plant roots 71 in soil stability (e.g. Vannoppen et al., 2015; Ghestem et al., 2014; De Baets et al., 2007), 72 these findings suggest that roots may play a vital role in reducing erosion caused by de73 bris flows (Figure 2). Despite the significance, our understanding of the effect of roots 74 on debris-flow erosion remains limited, mainly because of a lack of quantitative data. This 75 lack results from the infrequent and destructive character of debris flows, making it hard 76 to measure flow properties, root characteristics, bed strength, and interactions between 77 debris flow and bed in the field (Iverson, 1997). As data on debris-flow forces and of root 78 characteristics are limited, their combined influence on erosion dynamics remains even 79 more poorly constrained. 80 To improve our insight into this poorly understood process, we aim to (1) unravel 81 the impacts of plant roots on debris-flow erosion and (2) test the applicability of fast82 growing seedlings to study debris flow—plant interactions in scaled laboratory exper83 iments. Here, we present novel experiments in a small-scale debris-flow flume with an 84 erodible sediment bed, in which we grow live seedlings to form beds with a wide range 85 of root traits. Laboratory experiments enable systematic and quantitative exploration –4– Figure 1. Examples of interactions between debris flows and vegetation. (a) Post-wildfire debris flow in Jamestown, Colorado, November 2013 (White, 2013), (b) The root network in a forest stand strengthens the soil, enhancing its resistance to the development of new channels on a debris-flow fan; British Columbia, Canada (Wilford et al., 2005), (c) Debris flow running through a forested fan; Keze gully, China (Cui et al., 2024), (d) A debris flow gully formed after a forest fire, exposing roots protruding from the gully banks; Glenwood Canyon, Colorado, USA (with courtesy of Francis Rengers), (e) A scour hole formed by a debris flow after a forest fire; Glenwood Canyon, Colorado, USA (with courtesy of Francis Rengers) (f) Exposed roots after severe debris-flow erosion of a debris-flow fan; British Columbia, Canada (Wilford et al., 2005). –5– Figure 2. Sketch of (a) the primary forces driving debris flow erosion in the absence of vegetation, and (b) the additional mechanical effects of vegetation roots on debris-flow erosion reduction by increased soil cohesion and shear stress distribution through tensile strength. 86 of the effects of plant roots on debris-flow erosion under controlled conditions. In exper87 iments, initial and boundary conditions can be precisely controlled, allowing for the iso88 lation of individual variables. Debris flows have been successfully scaled in previous ex89 periments, which, for example, increased our understanding of the effects of bed and debris90 flow composition on erosion (Roelofs et al., 2023; Zheng et al., 2021), the seismic vibra91 tions and normal-force fluctuations of debris flows (De Haas et al., 2021), and sediment 92 trapping by vegetation (He et al., 2023). However, scant debris-flow experiments have 93 been conducted with plant roots. Fast-growing seedlings have already been successfully 94 used in other geomorphic experiments to study various earth surface processes (e.g. Lokhorst 95 et al., 2019; De Baets et al., 2007), but their potential remains largely unexplored in debris96 flow research. Such species offer several advantages, including the development of nat97 ural root-soil contacts, a relatively short cultivation period, and the ability to alter root 98 traits systematically. We conducted controlled laboratory experiments to quantify the 99 effect of roots on debris-flow erosion. In this paper we do not test effects of above-ground 100 biomass, which we removed, but focus on systematically varied root traits across exper101 iments to identify key factors governing erosion reduction. The data generated could pro102 vide insights into the effects of wildfires and deforestation on debris-flow erosion, par103 ticularly when above-ground biomass is lost and remaining roots play a key role (Thomas 104 et al., 2021; de Graff, 2018; Meyer et al., 2001). A better understanding of these processes 105 would also contribute to more accurate debris-flow models and foster the development 106 of strategies to reduce debris-flow erosion and mitigate its hazards. 107 2 Methods 108 To study the effect of roots on debris-flow erosion, we conducted 38 experiments 109 in a flume with an erodible bed penetrated by natural roots. Each experiment’s seed110 ing densities and vegetation ages differed to vary root traits while keeping the bed and 111 debris-flow composition constant. For each density, an experiment was conducted with 112 5-day-old and 8-day-old vegetation to vary root length and diameter (see Table S1 for 113 conditions of each experiment). The initial set of experiments was meant to determine 114 the best experimental setup and to verify the applicability of the method. Therefore, each 115 experimental setup was repeated once. The outcomes of these experiments are not in116 cluded in the results. Once consistency and applicability were confirmed, subsequent ex117 periments were conducted only once. –6– Figure 3. Schematic overview of the debris flow flume, with images showing the flume and the grown plants of 5 and 8 days old. All lengths are in centimeters. 118 2.1 Flume setup 119 The experiments were conducted in a debris-flow flume consisting of a 5.4 m long 120 and 0.3 m wide channel inclined at 34◦, a mixing tank with a forced-action mixer and 121 custom-made release gate (set-up is similar to Roelofs et al. (2023) and De Haas et al. 122 (2021); Figure 3). Five laser sensors captured flow hydrographs and velocities through 123 time-distance measurements. Force fluctuations at the bed were measured using a Geospace 124 GS-20DX geophone force plate (0.14 m wide, 0.06 m long), installed at 2.90 m and 2.98 125 m downstream of the release gate, recording seismic movement (vertical and horizontal) 126 with a 10–1000 Hz response. The shear stress exerted by the debris flow on the bed was 127 calculated as: 128 τ = ρgH sin(S) (1) 129 where τ is the shear stress (Pa), ρ is the density of the flow (kg/m3), g is the gravita130 tional acceleration (m/s2), H is the flow depth (m), and S is the channel bed slope. In 131 the lower 2.5 m of the channel, a vegetated erodible bed of 0.07 m thick was placed in 132 a depression in the channel floor, of which the age and number of planted seeds were var133 ied for each experiment. Bed elevation of the erodible bed was quantified before and af134 ter each experiment at sub-mm resolution with a Vialux z-Snapper three-dimensional 135 scanner. From the measurements, the erosion volumes of the erodible bed were quan136 tified by obtaining the difference in bed elevation before and after each experiment. The 137 erosion rate was calculated by dividing the erosion volume by 1.5 seconds, as most ero138 sion occurs within this time range under the influence of the boulder-rich debris flow front 139 (Roelofs et al., 2023; De Haas et al., 2022; Zheng et al., 2021). At 46 cm downstream 140 of the start of the erodible bed, pore water pressures were measured at 3 and 4 cm be141 low the surface (custom-made with Keller Pressure PR-23SY, with an accuracy of ±0.25 142 %FS). Using a needle, water was inserted into the bed surrounding the pore-pressure mea143 surement instruments to ensure saturated conditions. –7– 144 For all experiments, debris-flow and bed compositions were kept constant (Table 145 S2). Debris flows consisted of 75% sand, 5% clay (kaolin), 20% gravel, and a water frac146 tion of 20% by weight (Figure 4a and b). The erodible bed was loosely packed and con147 sisted of 96% sand and 4% clay (Figure 4c and d). The bed had a water fraction of 13% 148 by weight (Table S2). Figure 4. Grain size distributions used in the experiments. (a) Grain size distribution of the debris flow and erodible bed used for the experiments, (b) the cumulative grain size distribution of the debris flow and the erodible bed. 149 2.2 Describing flow characteristics 150 To compare the scaled debris flows with natural ones, the Bagnold, Savage, and 151 friction numbers were calculated for each experiment. These numbers describe the re152 lationship between the forces that resist motion in debris flows, comprising collisional, 153 frictional, and viscous forces (Iverson, 1997). The Bagnold number compares collisional 154 and viscous forces (Iverson, 1997): vsρsδ2γ 155 N b = (2) v f µ 156 where Nb is the Bagnold number (-), vs is the volumetric solids fraction, ρs is the den157 sity of the flow (kg/m3), δ is the mean grain size (m), v f is the volumetric fraction of 158 fines, γ is the flow shear rate (1/s): 159 u γ = (3) H 160 where u is the debris flow frontal velocity (m/s), and H is the maximum flow depth (m). 161 The interstitial fluid viscosity µ is estimated as (De Haas et al., 2015; Iverson, 1997): 162 = 1 + 2.5vf + 10.05vf 2 w + 0 . 00273 16 . 6 v f (4) 163 where µw is the dynamic viscosity of pure water (0.001002 Pa s). For Nb > 200, the col164 lisional forces dominate the viscous forces (Iverson, 1997). The Savage number compares 165 collisional and frictional forces: ρsδ2γ2 166 N s = ( ρ (5) − ρf )gH tan ϕ′ µ µ s –8– s 167 where ρ f is the fluid density (kg/m3), and ϕ ′ is the angle of internal friction, estimated 168 at 42˚ (De Haas et al., 2015). The collisional forces dominate the viscous forces when 169 Ns > 0.1 (Iverson, 1997). Finally, frictional and viscous forces are compared with the 170 friction number: 171 N f = vs(ρs − ρf )gH tan ϕ′ (1 − v )γµ (6) 172 For Nf > 2000, frictional forces dominate viscous forces (Iverson, 1997). 173 2.3 Plant growth and quantification of root characteristics 174 To simulate natural root-soil contact as present in the field, live seedlings of Sorghum 175 bicolor were grown in the erodible bed. S. bicolor is a fast-growing seedling with a high 176 germination rate and straight tap roots penetrating deep into the bed. Although the root 177 architecture of S. bicolor is less complex than those of mature trees, it provides a prac178 tical and scalable proxy for studying root–soil interactions. Its roots exhibit similar me179 chanical effects in reinforcing soil and resisting erosion at small experimental scales (Lokhorst 180 et al., 2019), enabling us to approximate the stabilizing effect of roots in a controlled set181 ting. The tap root systems present in S. bicolor allow unambiguous data collection, pro182 cessing, and interpretation. The seed density was based on Lokhorst et al. (2019), who 183 showed that a density of 2 seeds/cm2 is a typical density with measurable effects in small184 scale geomorphic experiments of channel bank collapse and erosion by flow. Our seed 185 density ranged from 0.4 to 6 seeds/cm2. The average germination rate was 70%, grad186 ually declining to approximately 50% throughout the experiments, likely due to the de187 crease in light caused by shorter daylight. This resulted in root densities ranging from 188 0.3 to 4 roots/cm2, assuming one root per seedling. Each sowing density was tested twice: 189 once with plants grown for 5 days and once with plants grown for 8 days, which allowed 190 for variation in root length and diameter. Before the start of each experiment, the above191 ground biomass was cut off without disturbing the soil to isolate the effects of the roots 192 on debris-flow erosion. 193 Before every experiment, we measured root length, root diameter, root density, root 194 length density (RLD), root area ratio (RAR), and root tensile strength (RTS), consid195 ering that these root traits have been identified as most important for stabilizing soils 196 and controlling erosion by overland flow (Vannoppen et al., 2015; Ghestem et al., 2014; 197 Bischetti et al., 2009; De Baets et al., 2008; Ali & Osman, 2008; De Baets et al., 2007; 198 Pollen, 2007). Root lengths and diameters were averaged over ten roots and measured 199 using an electronic caliper with an accuracy of 0.01 mm. Root density was determined 200 by counting the number of plants per unit of surface area. As we used tap roots in our 201 experiments, the number of plants corresponds to the number of roots. RLD is used to 202 quantify root distribution in soil, and was calculated as the root length per unit volume 203 of soil (Figure 5a; Vannoppen et al., 2015; Ghestem et al., 2014; De Baets et al., 2007): 204 RLD = Root Length soil Volume (7) 205 where the RLD is the Root Length Density (cm/cm3), the sum of the root lengths refers 206 to the length of the total root system (cm) within the soil volume sampled (cm3), which 207 translates to the volume of the erodible bed. For our experiments, the measured root 208 lengths were scaled up based on the total number of counted roots. The RAR is defined 209 as the fraction of a plane of soil occupied by roots per unit area (Figure 5b; Bierman & 210 Montgomery, 2014; De Baets et al., 2008; Stokes et al., 2009): –9– 211 RAR d = I A r (8) A 212 where RARd is the Root Area Ratio (-), Ar is the root area per root (m2), and A the 213 area measured (m2). The measured area is the width times the depth of the soil in the 214 flume. The root area is calculated by: 215 π 2 A r = 4 d (9) 216 where d is the root diameter (m). A different function to calculate RAR uses the RLD 217 (De Baets et al., 2006): 218 RAR RLD = RLD × A r (10) Figure 5. Illustration of the calculations of the concepts (a) RLD and (b) RAR, where W is the width, H is the height, and L is the length of the soil sample. 219 The apparent cohesion with roots (henceforth ’root cohesion’) was calculated to 220 assess the additional shear strength to the soil provided by roots. Root cohesion quan221 tifies the effect of root traits on debris-flow erosion and allows for a comparison to the 222 shear stress exerted by debris flows. Root cohesion was calculated using the Wu and Wal223 dron model (Waldron, 1977; Alam et al., 2018; Wu, 1984), with both RARd and RAR RLD 224 as input. As our roots grow perpendicular to the soil and barely change position dur225 ing shearing (Schmidt et al., 2001), root cohesion (Cr) is calculated as: 226 C r = RTS × RAR (11) 227 The WWM model assumes that all roots break simultaneously, which we assume valid 228 for fast-flowing debris flows. The RTS provides a measure of the roots’ resistance to break229 ing as a result of shear and is calculated as: 230 RTS = F max A r (12) 231 where Fmax is the maximum force that is exerted on a root before breaking (N), and Ar 232 the root area (mm2) (De Baets et al., 2008). For 26 roots, the diameter was measured –16– 388 ford et al., 2005; Bunn & Montgomery, 2004; Schmidt et al., 2001). Erosion was observed 389 between patches of roots, where root density was lower. This pattern agrees with field 390 observations, as root networks spread outward from trees, leading to lower root cohe391 sion and consequently more erosion (De Baets et al., 2007; Roering et al., 2003). 392 Table 4.3 presents the shear stresses and root traits measured during the exper393 iments, alongside values reported from the field. This comparison provides insight into 394 the relative magnitudes of forces governing debris-flow erosion. RTS in natural environ395 ments is often some order of magnitude greater than the shear stresses exerted by de396 bris flows, although the range is large. While RTS also exceeds shear stresses in our tests, 397 the difference in magnitude is less pronounced. Additionally, root cohesion in our exper398 iments is considerably lower than in field conditions. This discrepancy is expected, as 399 our setup features taproots distributed over a large area, whereas natural conditions are 400 often calculated per individual tree with a large root system. To compensate, we cre401 ated high root densities. However, root cohesion remains on the lower end, possibly due 402 to the experimental root simplicity. These deviations suggest that in our experiments, 403 the erosion may be higher than expected in natural settings. Nonetheless, this discrep404 ancy does not undermine the value of our experiments, as our primary goal is not to recre405 ate real-world conditions, but to isolate and study the interactions between debris flows 406 and plant roots. Despite the scaling differences, the combination of scaled debris flow 407 experiments and scaled roots enables a systematic study of debris flow-root interactions. 408 Our findings offer insight into how roots reinforce the soil and affect bed erosion, with 409 fundamental mechanisms and morphological features that are consistent between the lab410 oratory and the field. 411 4.4 Small-scale, big impact: lab versus field observations 412 Our research shows that there is high potential for using scaled live plants in debris413 flow experiments. This enables us to study the effects of plants on debris flows with a 414 degree of control that is not attainable in the field, and enables systematic exploration 415 of changes in boundary conditions and materials. Both modelling (e.g. Liu et al., 2021) 416 and field research (e.g. Tang et al., 2018; Michelini et al., 2017; Johnson et al., 2000) 417 have been done on plant—debris flow interactions, but these studies remain primarily 418 qualitative due to the lack of quantitative information regarding debris-flow forces and 419 plant traits. Our experimental study, for the first time, contributes quantitative knowl420 edge because we can control the root conditions. 421 Our pioneering tests offer many options for future expansion and improvement. Our 422 experiments were conducted using S. bicolor seedlings as a proxy for tree roots. Tree root 423 systems are typically characterized by extensive and hierarchical branching structures, 424 with roots varying in diameter, orientation, and length, and often interconnecting to form 425 complex networks (Ghestem et al., 2014; Bischetti et al., 2009). Moreover, natural en426 vironments host diverse tree species of varying ages, further increasing heterogeneity in 427 root architecture and mechanical behavior (Pohl et al., 2011; Stokes et al., 2009). Where 428 the simple root systems in our setup likely result in an underestimation of erosion re429 sistance, future experiments could employ plant species with more complex, multi-scale 430 root systems. Improving measurement of pore-pressure and water content could enhance 431 our understanding of how roots affect loading conditions and pore water transfer between 432 debris flow and bed, which is crucial for debris-flow erosion (Roelofs et al., 2023; Zheng 433 et al., 2023). Roots may reduce erosion by increasing permeability and enhancing drained 434 conditions (Liu et al., 2021; Kaspar & Singer, 2011; De Baets et al., 2011; Reubens et 435 al., 2007). Under these drained conditions, water and air can diffuse through the soil pores 436 without increasing pore-pressure, which helps maintain intergranular friction. However, 437 increased permeability could also facilitate the transfer of moisture and pore-pressure 438 from the debris flow to the bed, thereby increasing pore-pressure in the bed and poten439 tially enhancing erosion (Zheng et al., 2023). Furthermore, our experiments lacked above- –17– Table 1. Debris flow shear stresses measured during the experiments and during debris flow events in the field, along with root traits measured in the experiments and the field. The root cohesion from our experiments was calculated using RAR RLD . The root traits given by Vergani et al. (2012) are measured in the Swiss Alps, the traits given by Bischetti et al. (2009) in the Italian Alps. Shear stress RTS Root cohesion KPa N/mm 2 KPa Our experiments 0.47–0.59 0.85–1.8 1.9 × 10 −4 –4.3 × 10 −3 . . . . . . . . . . . . . . . . . . . . . . . . Illgraben a, b 0.37–5.1 Roßbichelbach (modeled) c 4 –15 Montecito, USA d 1.6 . . . . . . . . . . . . . . . . . . . . . . . . Acer pseudoplatanus e 3.68–31.48 Castanea sativa e,f 0.81–45 8.1–19.6 Fagus sylvatica e,f 3.38–75.22 14.4–86 Fraxinus excelsior e 3.89–24.91 Larix decidua e,f 1.03–110 17.4–38.3 Ostrya carpinifolia e,f 1.8–30.17 5.4–30 Picea abies e,f 2.84–95 13.8–35.4 a de Haas et al. (2022) b Berger et al. (2011) c Dietrich & Krautblatter (2019) d Kostynick et al. (2025) e Vergani et al. (2012) f Bischetti et al. (2009) 440 ground biomass, which could reduce debris flow energy and size through obstructions 441 (Liu et al., 2021; Michelini et al., 2017). However, above-ground biomass simultaneously 442 increases the chances of root pullout, decreasing the soil strength and increasing erosion 443 (Chen et al., 2024; Stokes et al., 2009). Further research could improve our under444 standing of the combined effect of above and below-ground biomass on debris-flow in445 duced erosion. 446 Our findings suggest that preventing cuttings or even planting trees on debris-flow 447 fans and catchments can serve as effective strategies for mitigating debris-flow hazards, 448 as an increase in RLD and RAR decreases erosion and therefore diminishes the volume 449 and impact of a debris flow. Further experiments, modeling that represents the rooting 450 density and structure, and additional field data will be essential for deepening our un451 derstanding and the predictability of these processes. 452 5 Conclusions 453 We experimentally investigated the effects of plant roots on debris-flow erosion to 454 gain a better understanding of the interaction between debris flows and trees. By com455 bining measurements of debris-flow characteristics, erosion, and root traits, we were able 456 to quantify the reduction of debris-flow induced erosion by roots compared to rootless 457 beds. While our setup simplifies natural root structures and conditions and isolates ef- –18– 458 fects of below-ground biomass from effects of above-ground biomass, it enables a con459 trolled study of fundamental erosion mechanisms. 460 Our experiments showed a clear non-linear relationship between RLD and debris461 flow bed erosion, with minimal difference between 5-day-old and 8-day-old roots. RAR 462 and root cohesion followed the same non-linear trend when calculated from RLD, in463 dicating that the combined effect of root length and root density is an important fac464 tor for reducing debris-flow bed erosion. These results imply a potential application: veg465 etating debris-flow-prone slopes could reduce erosion and flow volume growth, thereby 466 lessening their hazardous impact. The results also offer insight needed for hazard assess467 ment: after wildfires, root decay may weaken root cohesion, increasing susceptibility to 468 erosion and enhancing debris-flow volume and hazards. 469 Our results demonstrate that small-scale debris-flow experiments with live seedlings 470 can provide valuable insights into the effects of plants on debris-flow erosion that are chal471 lenging to investigate in the field. Further experimental exploration can provide a sci472 entific basis for the mitigation of debris-flow hazards using nature-based solutions and 473 give insights into the effects of changing vegetation due to wildfires and deforestation on 474 debris-flow hazards. Our findings point to a new pathway towards incorporating root char475 acteristics into erosion models, and show the importance of vegetation in debris-flow-prone 476 areas. 477 Open Research 478 Experimental data, including preand post-flow DEMs, flow measurements, and 479 the root trait measurements are available via Yoda (online repository of Utrecht Uni480 versity) under this link: https://public.yoda.uu.nl/geo/UU01/NYY5H3.html. DOI: 481 10.24416/UU01-NYY5H3. 482 Acknowledgements 483 This work was supported by the Dutch Research Council (NWO) (grant VI.Vidi.233.008 484 to TdH). The authors gratefully acknowledge the help of Arjan van Eijk, Bas van Dam, 485 Marcel van Maarseveen, and Henk Markies in designing and constructing the flume and 486 measurement set-ups, as well as their assistance during the experiments. We would also 487 like to thank Caitlin Amels en Jelle Posthuma for helping out with the pre-experiments. 488 Sample CRediT author statement 489 Anna J. van den Broek: Conceptualization, Investigation, Writing - Original 490 Draft, Formal analysis, Visualization. Dagmar T. Mennes: Investigation, Writing - 491 Review & Editing. Maarten G. Kleinhans: Conceptualization, Writing - Review & 492 Editing, Supervision. Lonneke Roelofs: Writing - Review & Editing. Jana Eichel: 493 Conceptualization, Writing - Review & Editing, Supervision. Daniel Draebing: Con494 ceptualization, Writing - Review & Editing, Supervision. Tjalling de Haas: Concep495 tualization, Writing - Review & Editing, Supervision, Funding acquisition. 496 References 497 Alam, S., Banjara, A., Wang, J., Patterson, W., & Baral, S. (2018). Novel ap498 proach in sampling and tensile strength evaluation of roots to enhance soil 499 for preventing erosion. 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Exp nmbr Age roots Sowed density Root density RLD RAR d C r RAR RLD C r with RLD days seeds/cm3 roots/cm3 cm/cm3 − ×10−5 MPa ×10−2 − ×10−4 MPa ×10−3 1 - - - - - - - - 2 - - - - - - - - 3a 5 0.4 0.28 0.10 0.647 0.79 1.55 0.189 3b 8 0.4 0.26 0.16 0.721 0.771 3.16 0.338 4a 5 0.5 0.41 0.13 1.31 1.12 3.03 0.259 4b 8 0.5 0.33 0.21 0.981 0.981 4.30 0.430 5a 5 0.76 0.60 0.20 1.92 1.82 4.47 0.422 5b 8 0.76 0.46 0.28 1.26 1.33 5.40 0.569 6a 5 1 0.83 0.48 2.08 2.14 8.48 0.874 6b 8 1 0.75 0.59 1.61 1.85 8.91 1.02 7a 5 1.4 1.1 0.36 3.91 3.37 9.28 0.799 7b 8 1.4 0.87 0.65 1.15 2.10 5.99 1.09 8a 5 2 1.3 0.53 4.03 3.93 11.4 1.11 8b 8 2 1.5 1.21 3.57 4.11 20.6 2.37 9a 5 3 2.3 0.88 6.99 6.80 18.9 1.83 9b 8 3 2.0 1.46 3.61 5.25 18.4 2.67 10a 5 4 2.1 0.42 7.46 6.64 10.3 0.913 10b 8 4 2.0 1.27 4.98 5.65 22.4 2.55 11a 5 6 3.6 0.98 12.9 11.3 24.9 2.19 11b 8 6 3.3 2.14 8.44 9.47 38.4 4.31 Table S2. Key characteristics of the experimental settings of the flume experiments, including the varied root densities and the debris flow composition and characteristics. Debris flow components Unit Values Clay (kaolin) dry weight fraction 0.05 kg 2.4 Sand dry weight fraction 0.75 kg 36 Gravel dry weight fraction 0.2 kg 9.6 Water dry weight fraction 0.2 kg 12 Flume settings Unit Value Flume angle degrees 34 ◦ Bed components Unit Values Clay (kaolin) dry weight fraction 0.04 Sand dry weight fraction 0.96 Water dry weight fraction 0.13 Number of seeds Unit Tested range Seed density seeds/cm 2 0.4 – 6 manuscript submitted to Engineering Geology –2– Table S3. Results of the regression analysis for the correlation between the net bed change and the variables calculated from the measured traits. The logarithmic regression is described as bedchange = a log(variable) + b plant age Constant a Constant b R 2 p-value Root density 5day 2079 - 3717 0.878 1.96 × 10−4 8day 2376 - 1838 0.948 2.29 × 10− 6 Root length density 5day 2254 - 1300 0.936 1.97 × 10−5 8day 2278 - 998.3 0.963 2.89 × 10−6 Root area ratio (RAR d ) 5day 1774 14720 0.817 8.29 × 10−4 8day 2299 22710 0.814 8.62 × 10− 4 Root area ratio (RAR RLD ) 5day 2022 10860 0.917 4.97 × 10−5 8day 2298 13790 0.868 2.59 × 10− 4 Root cohesion calculated with (RARd) 5day 1938 - 16510 0.8531 3.75 × 10−4 8day 2368 23030 0.916 5.18 × 10− 5 Root cohesion calculated with (RAR RLD ) 5day 2169 12020 0.9339 1.59 × 10−5 8day 2305 13420 0.9452 1 . 15 × 10 − 5