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1 In the format provided by the authors and unedited. DOI: /NGEO3005 Rapid post-seismic landslide evacuation boosted by dynamic river width Thomas Croissant 1,*, Dimitri Lague 1, Philippe Steer 1 and Philippe Davy 1 1 Géosciences Rennes, OSUR, CNRS, Université de Rennes 1, Campus de Beaulieu, Rennes 1. Supplementary figures Figure S1 Documentation of natural landslide removal in a bedrock river context. Aerial images showing (a) before and (b) after the occurrence of a landslide in the Clarence river, New Zealand. The image shows the river narrowing associated to the incision of the deposit, as the river width inside the deposit is ~3 times narrower than the initial bedrock valley. (Source: Google Earth). NATURE GEOSCIENCE 1

2 Figure S2 River transport capacity as a function of river width. Theoretical plot showing alluvial river transport capacity (QT) as a function of river width, for different channel slope (S). The river transport capacity is computed with a Meyer-Peter and Müller, [1948] bedload transport law similar to the one used in the 2D simulations. The input water discharge (Qw) and the critical shear stress (ττ cc ) are fixed and the slope ranges from 1 to 5%. NATURE GEOSCIENCE 2

3 Figure S3 Quantification of the river morphodynamic evolution. Temporal evolution of the alluvial channel width, W, slope, S and transport capacity (QT) for 2 end-member cases differing by their bedrock valley slopes (Sval). The alluvial channel properties (index ch) are normalized by their bedrock valley equivalent (index val). On the left panel (a, b, c: Sval = 1.2%), the case of a channel presenting a high ratio between the landslide volume (Vls) and river transport capacity. On the right panel (d, e, f: Sval = 7%), the case of a low ratio Vls/QT. The measurements are made at different locations in the bedrock channel: at the landslide location (in red) and 1 km downstream of the landslide (in black). Note the different time scales. These 2 cases illustrate well the influence of river narrowing on transport capacity increase and the temporal persistence of this process. The case with Sval = 1.2% shows that (a.) the alluvial river width can be reduced by a factor of four during vertical incision of the landslide deposit, leading in turn to (c.) a five time increase of river transport capacity. On the contrary, the case with Sval = 7 % shows that (d., e.) in the absence of significant river morphologic modification, (f.) the transport capacity remains the same throughout the simulation. NATURE GEOSCIENCE 3

4 Figure S4 Influence of landslide volume and bedrock transport capacity on export times. Landslide export time as a function of a. the landslide volume (Vls) and b. the bedrock river transport capacity (QT). For each plot, the dot color corresponds to one single parameter being varied, namely the landslide volume Vls, the bedrock valley slope S, the water discharge Qw, the median grain size D50, the bedrock valley width Wval, and the upstream sediment supply Qs,in. These plots show that the landslide export times cannot be expressed as a scaling relationship of river transport capacity nor landslide volume only. A single relationship is only obtained when the landslide export time is expressed as a function of the ratio between landslide volume and river transport capacity (Figure 3). c. Export time as a function of Vls / QT for different proportion of removed landslide volume. The line plots represent the fit obtained using equation 1: blue line: 50% of the initial landslide volume is exported; red line; 70% and black line: 90%. NATURE GEOSCIENCE 4

5 Figure S5 Influence of upstream sediment supply on landslide export times. a. Numerical experiments with an upstream sediment supply (Qs,in). The bedrock initial transport capacity (QT) is similar for all the simulation (S = 3%, W = 50 m, Qw = 160 m 3.s -1 and D50 = 0.20 m). The system response is studied for 3 different landslide volumes (Vls) with Qs,in ranging from 0 to 99% of the bedrock transport capacity (see dot colors). The export time is computed when a volume equal to 50% of the landslide volume is evacuated out of the deposit area. This volume is computed by adding the sediment exported from the landslide and the input sediment volume and by subtracting the sediment volume stored upstream of the landslide. The export times are plotted against the ratio between the landslide volume on the excess transport capacity (QT - Qs,in) to visually separate the results of the different simulations. b. Snapshots of a simulation with Qs,in/QT = The upstream sediment supply leads to the formation of a sediment delta that progrades downstream to reach the landslide deposit. Concurrently, the river incises vertically the landslide with a narrow channel as observed in the simulation without sediment supply. As the river incises the landslide, its transport capacity becomes greater than pre-landslide bedrock initial transport capacity because of the width reduction. During this phase, the upstream sediment supply only represents 26% of the alluvial river transport capacity. Therefore, the river efficiently copes with this additional upstream sediment supply which results in landslide export times similar than without this additional input sediment flux. In other words, an increase of sediment supply due to the removal of an upstream landslide would not affect the transport rate of the downstream landslide, considering the evacuation of the first 50% of the landslide. This forms the basis for assuming that landslides can be treated independently in the Monte-Carlo approach exploring the mean residence time of a population of landslides. NATURE GEOSCIENCE 5

6 Figure S6 Probability density function of river transport capacity, landslide volume and export time. a. Probability density function (pdf) of the transport capacity computed using Eq. 6 for the whole mountainous areas of Taiwan using a SRTM90 Digital Elevation Model. A power law function with an exponent equal to -2 (Eq. 7) fits well the data (R 2 = 0.99). The Taiwan DEM is used here as an example of the pdf. b. Probability density function of landslide volume obtained by combining a pdf of landslide area (Malamud and Turcotte, [2004]) and the landslide volume/area scaling relationship (eq. 10) obtained by Larsen et al., [2010]. The pdf of landslide area is parameterized with values found in Parker et al., [2011]. c. Probability density function of landslide export time. The colors represent the pdf obtained for different percentage of removed landslide volume: 50% (blue), 70% (red) and 90% (black).the pdf exhibits a right tail following a power law which exponent increases with the percentage of exported landslide volume. The pdf at 50% or 70% of exported landslide volume are light-tailed with power law exponent of -9 and -6, respectively. In these cases, the mean residence time of a landslide population is controlled by the mean export time of the individual landslides. The pdf at 90% of exported landslide volume is heavy-tailed with a power law exponent of -1. This implies that the mean residence time of a landslide population is controlled by the individual landslides with greater export times. NATURE GEOSCIENCE 6

7 Figure S7 Sensitivity Analysis of the mean residence of a population of co-seismic landslides. The mean residence time sensitivity is tested against the parameters that controls the river transport capacity such as catchment geometry, climatic context and median grain size. a. minimum drainage, b. maximum drainage area, c. normalized width index (kwn) and d. normalized steepness index (ksn). e. the discharge variability (k). f. the mean annual runoff (rr ). g. the median grain size (D50). Inside their realistic range of values, the parameters that most influence the mean residence time are first the channel steepness and mean annual runoff, secondly the discharge variability, median grain size and minimum drainage area. Finally, the bedrock valley width and the maximum drainage area only exert a weak control on mean residence time. NATURE GEOSCIENCE 7

8 Figure S8 Mean residence time of earthquake-derived landslides in active mountain ranges. Mean residence time computed for different catchments by accounting for their individual properties (see suppl. Table S3) and for a fixed median grain size set to D50 = 0.1 m. The errors bars shows the computations for D50 = m (lower limit) and D50 = 0.3 m (upper limit). NATURE GEOSCIENCE 8

9 Figure S9 Self-emergent river width at equilibrium as a function of water discharge. Dimensionless width (WW = WW/DD 50 ) as function of dimensionless discharge (QQ = QQ/ ggdd 5 50 ) for a set of 12 Eros simulations, with WW the river width, QQ the water discharge, gg the gravitational constant and DD 50 the median grain size. The red line displays the theoretical scaling law WW QQ,0.5 predicted for a river in near-threshold conditions for the incipient motion of bedload [Métivier et al, 2017]. Gray dots are natural rivers data from Li et al., [2014]. The light red area and dashed lines indicates uncertainties in the parameters of the threshold theory as defined in [Métivier et al, 2017]. NATURE GEOSCIENCE 9

10 2. Supplementary tables Table S1 List of parameters values range used in Eros for the different simulations. Parameters Units min. Value max. Value Discharge m 3.s Slope m.m Grain Size m Width m Landslide Volume m NATURE GEOSCIENCE 10

11 Table S2 List of the parameters used for catchment transport capacity calculations: kwn: width index, ksn: steepness index and k: discharge variability. Data from Bookhagen and Strecker, [2012]; Kritikos, [2013]; Lague, [2014]. Catchment k wn k sn mean runoff (m.yr -1 ) k Peikang Liwu Bagmati Bakeya San Gabriels Whataroa Poerua South Central Andes / ~ NATURE GEOSCIENCE 11

12 Table S3 Eros model parameterization. Parameters Notation Values Units Manning coefficient n m.s water density ρ w 1000 kg.m- 3 sediment density ρ s 2700 kg.m -3 gravitational constant g 9.81 m.s -2 critical Shields number ττ cc 0.03 / transport length ξ 2 m sediment erodability E / lateral erosion coefficient k e 0.01 / lateral deposition coefficient k d 0.5 / NATURE GEOSCIENCE 12

13 3. Supplementary Movies 3.1 Movie S1 Width Enhanced Removal (WER) simulation. This video shows the morphodynamic evolution of a landslide evacuation in the Width Enhanced Removal regime (i.e. high landslide volume to river transport capacity ratio, Fig. 1a). The simulation shows the significant river narrowing at the pulse location and throughout the bedrock valley. This mechanism allows for the acceleration of the landslide evacuation. River flows from top to bottom. 3.2 Movie S2 Constant Width Removal (CWR) simulation. This video shows the morphodynamic evolution of a landslide evacuation in the Constant Width Removal regime (i.e. low landslide volume to river transport capacity ratio, Fig. 1b). The simulation shows the fast evacuation of the landslide deposit without significant river morphology modifications. River flows from top to bottom. NATURE GEOSCIENCE 13

14 4. Supplementary discussion 4.1 Reduced influence of bedrock valley width. It may seem counter-intuitive that the valley width (measured as the width index) has a weak impact on the mean residence time of a population of landslides (Fig. 3a) given the dominant role played by dynamic channel narrowing in increasing total channel transport capacity. Yet, it is this very mechanism that makes the export time barely increase with the width index. For the largest landslides in the population, a single thread alluvial channel emerges in the landslide deposits and increases the river transport capacity. In that case the transport capacity at which the sediment is exported is independent of the bedrock valley width. Because the self-emergent channel quickly incises down to the bedrock slope, the bedrock steepness does impact significantly the export time during the second phase of landslide export. Only in the case of a narrow bedrock valley (e.g., gorges) does the alluvial width equal the bedrock valley width such that the transport capacity is dependent on valley width. Yet, the initial most rapid phase of landslide evacuation will still be independent of the valley width because the alluvial deposit, for a given landslide volume, are higher when the channel is narrow. Only when the phase of lateral erosion begins does bedrock valley width matters, but it does not contribute significantly to the evacuation of the first 50 % of landslide material. 4.2 Dam stability and landslide connectivity to the river network. Here, we discuss the role of several parameters that can affect the export time of landslides and govern the ensemble evacuation behavior of the population of landslides triggered by large magnitude earthquakes. - In our numerical experiments, the export time is counted from the onset of landslide incision, meaning that the time spanning from the landslide deposition to its destabilization is not accounted for. However, in half of natural cases, the dam fails rather quickly in about 10 days after the landslide deposition and the large majority of landslides (~85%) are destabilized within a year [Costa and Schuster, 1988]. Persistent dams only represent a small fraction of the total population of earthquake-triggered landslides and thus don't affect significantly the overall mean residence time of landslides. - Another aspect that needs to be considered is the timescale for the landslide material to enter the river network. Generally, we expect the transfer speed to be enhanced by hillslope steepness, rainfall intensity and the frequency of extreme events. For instance, in the case of the Wenchuan earthquake, ~50% of the landslides material was transferred from hillslopes to channels in 8 years [Zhang et al., 2016]. We note that the mountain ranges considered in this study are "fluvial" landscapes characterized by steep hillslopes and confined bedrock river channels. These geometrical characteristics promote landslide connectivity of large landslides with long runouts [Li et al., 2016]. Small landslides tend to be poorly connected to the drainage network [Li et al., 2016]and to stay longer on hillslopes. However, they have little influence on the mean residence time of a landslide population. NATURE GEOSCIENCE 14

15 4.3 Eros ability to reproduce empirical scaling between river width and discharge It is important that the model used in this study reproduces the empirical Lacey's law, WW QQ 0.5, between the river width (W) and the water discharge (Q) [Parker et al., 2007; Métivier et al., 2017]. We perform morphodynamic simulations with Eros using a simple initial topography and boundary conditions considering the case of a constant river flow (also referred as channel-forming discharge) on a tilted sediment plane without any input sediment flux. Different combinations of river discharge and median grain size (D50) are explored to sample the normalized discharge (QQ = QQ/ ggdd 5 50 ) values on two orders of magnitude. All the other parameters are kept identical to the ones used in the numerical experiments of the main paper (see Table S2). Each simulation is performed until the river geometry (width, slope and water depth) reaches a near-threshold configuration associated with a basal shear stress slightly below the incipient threshold of sediment motion. A precise morphodynamic evolution of such single thread channels is described in Davy et al., [2017]. Figure S9 shows that the self-emergent river width predicted by Eros is similar to natural rivers once the normalization by grain size is accounted for, and obey a similar scaling with discharge (W Q 0.5. ). This demonstrates that Eros contains the necessary physical ingredients to reproduce this empirical scaling relationship, which in turn gives us confidence in the modeled river morphological evolution and in the associated feedbacks between transport capacity, river width and river flow. NATURE GEOSCIENCE 15

16 5. Supplementary references Bookhagen, B., and M. R. Strecker (2012), Spatiotemporal trends in erosion rates across a pronounced rainfall gradient: Examples from the southern Central Andes, Earth Planet. Sci. Lett., , , doi: /j.epsl Costa, J. E., and R. L. Schuster (1988), The formation and failure of natural dams, Geol. Soc. Am. Bull., 100(7), , doi: / (1988)100<1054:tfafon>2.3.co;2. Davy, P., T. Croissant, and D. Lague (2017), A precipiton method to calculate river hydrodynamics, with applications to flood prediction, landscape evolution models and braiding instabilities, J. Geophys. Res. Earth Surf., accepted. Hancox, G. T., M. J. McSaveney, V. R. Manville, and T. R. Davies (2005), The October 1999 Mt Adams rock avalanche and subsequent landslide dam break flood and effects in Poerua river, Westland, New Zealand, New Zeal. J. Geol. Geophys., 48(4), , doi: / Korup, O. (2004), Landslide-induced river channel avulsions in mountain catchments of southwest New Zealand, Geomorphology, 63(1 2), 57 80, doi: /j.geomorph Kritikos, T. (2013), Geomorphic Hazard Analyses in Tectonically-Active Mountains : Application to the Western Southern Alps, New Zealand, University of Canterbury. Lague, D. (2014), The stream power river incision model: evidence, theory and beyond, Earth Surf. Process. Landforms, 39(1), 38 61, doi: /esp Larsen, I. J., D. R. Montgomery, and O. Korup (2010), Landslide erosion controlled by hillslope material, Nat. Geosci., 3(4), , doi: /ngeo776. Li, C., M. J. Czapiga, E. C. Eke, E. Viparelli, and G. Parker (2014), Variable Shields number model for river bankfull geometry: bankfull shear velocity is viscosity-dependent but grain sizeindependent, J. Hydraul. Res., 1686(January), 1 13, doi: / Li, G., A. J. West, A. L. Densmore, D. E. Hammond, Z. Jin, F. Zhang, J. Wang, and R. G. Hilton (2016), Connectivity of earthquake-triggered landslides with the fluvial network: Implications for landslide sediment transport after the 2008 Wenchuan earthquake, J. Geophys. Res. Earth Surf., 121(4), , doi: /2015jf Malamud, B., and D. Turcotte (2004), Landslides, earthquakes, and erosion, Earth Planet.. Métivier, F., E. Lajeunesse, and O. Devauchelle (2017), Laboratory rivers: Lacey s law, threshold theory, and channel stability, Earth Surf. Dyn., 5(1), , doi: /esurf Meyer-Peter, E., and R. Müller (1948), Formulas for Bed-Load Transport, Int. Assoc. Hydraul. Struct. Researach - Zweite Tagung - Second Meet. - Deuxième réunion. Parker, G., P. R. Wilcock, C. Paola, W. E. Dietrich, and J. Pitlick (2007), Physical basis for quasiuniversal relations describing bankfull hydraulic geometry of single-thread gravel bed rivers, J. Geophys. Res. Earth Surf., 112(May 2006), 1 21, doi: /2006jf Parker, R. N., A. L. Densmore, N. J. Rosser, M. de Michele, Y. Li, R. Huang, S. Whadcoat, and D. N. Petley (2011), Mass wasting triggered by the 2008 Wenchuan earthquake is greater than orogenic growth, Nat. Geosci., 4(7), , doi: /ngeo1154. Zhang, S., L. Zhang, S. Lacasse, and F. Nadim (2016), Evolution of Mass Movements near Epicentre of Wenchuan Earthquake, the First Eight Years, Sci. Rep., 6(October), 36154, doi: /srep NATURE GEOSCIENCE 16