A seismic signature of river bedload transport during storm events

Leslie Hsu,1,2 Noah J. Finnegan,1 and Emily E. Brodsky1

Received 12 April 2011; revised 3 June 2011; accepted 3 June 2011; published 14 July 2011.

[1] Seasonal patterns in high frequency seismic waves nearrivers can record energy transmitted to the river bed fromparticle impacts during bedload transport. Here we showthat single storm events in a river can also be observedseismically. We analyzed the high frequency seismic noisein a reach of the Cho‐Shui (Zhuóshuı̌) River in centralTaiwan and made detailed observations during individualstorm events. Discharge, derived from a water level gage4.25 km from the seismometer, is highly variable due totyphoons. We found a correlation between seismic amplitudeand discharge that differs on the rising and falling limbs ofthree storms. During each storm, for a given discharge theamplitude of seismic waves are on average two times greateron the rising limb of the storm than on the falling limb, inboth aggradational and erosional events. Clockwisehysteresis in both aggradational and erosional events impliesthat water turbulence, alone, is not the source of the seismicwaves. If seismic wave amplitude correlates linearly with theflux of bedload, this implies a roughly two‐fold decrease intransport efficiency over the time‐scale of days duringindividual storms. The observed change in transportefficiency can plausibly be explained by the disturbance ofbed armor during storms and subsequent reformation duringthe waning stages. This data highlights the potential forfluvial seismology to reveal the dynamics of bedloadtransport. Citation: Hsu, L., N. J. Finnegan, and E. E. Brodsky(2011), A seismic signature of river bedload transport during stormevents,Geophys. Res. Lett., 38, L13407, doi:10.1029/2011GL047759.

1. Introduction

[2] Gravel and cobble transport by rivers governs channelchange, and is therefore of great importance to geomor-phologists and river engineers. The most commonly usedapproaches to estimating bedload transport rates are empir-ically calibrated relationships based on flume experiments[e.g., Meyer‐Peter and Müller, 1948; Wilcock and Crowe,2003]. However, it is difficult to assess how effectivelysuch relationships predict transport rates during extremeevents in large rivers because quantitative measures of bed-load transport are labor intensive and, at high flows, oftendangerous to obtain. For logistical reasons, most bedloadstudies have been carried out in small mountain streams.[3] Particle impacts on the river bed transfer momentum,

which in turn generates elastic (seismic) waves. Therefore,seismology can potentially constrain bedload transport ratesin rivers. High frequency (>1 Hz) seismic waves have been

used to study earth surface processes such as ocean waves[Adams et al., 2002], landslides [Favreau et al., 2010],rockfalls [Deparis et al., 2008], debris flows [LaHusen,2005; Suwa et al., 2003; Burtin et al., 2009], and snowavalanches [Vilajosana et al., 2007; Cole et al., 2009]. In allof these cases, remote monitoring is possible because geo-phones or seismometers capture ground vibrations causedby the surface process. A few studies have used seismo-logical data to study fluvial processes [e.g., Govi et al.,1993], and recent work showed that high frequency seis-mic waves may provide a way to monitor bedload sedimenttransport in inaccessible rivers in the Himalaya. Burtin et al.[2008] showed that seismic wave amplitude along the TrisuliRiver in Nepal correlated well with hydrological processessuch as daily precipitation and river discharge cycles. Inaddition, over the year of available data, the seismic ampli-tude was greater for a given river stage at the start of theIndian Monsoon than at the end. This was interpreted asevidence for a bedload source for seismic waves, as opposedto water turbulence, because significant hysteresis is notexpected in the relationship between stage and turbulence,whereas hysteresis is common in sediment rating curves.However, in addition to sediment supply, many other factors(e.g., bed armoring, channel geometry) might influence therelationship between river stage and the amplitude of groundvibrations.[4] In this paper we move closer to a direct connection

between bedload transport and seismic wave amplitude bystudying one site on the Cho‐Shui River in Taiwan thathas experienced repeated, short‐lived, and quantitatively‐documented typhoons. This dataset combines nearby waterlevel, channel cross‐section, discharge, and seismic ampli-tude measurements from existing infrastructure. A major goalof our work is to determine if a consistent, time‐varyingrelationship between the amplitude of ground vibrations andriver flux holds during multiple events. By examining severalevents with different durations and intensities, we show thatduring each storm there is a clear distinction between theseismic amplitudes generated for a given water discharge asthe water rises compared to when it falls. Whether the eventis aggradational or erosional, there is a greater amplitudeof seismic noise at the beginning of the storm in all threetyphoon events. This key observation combined with acontrasting observation for smaller subevents and simplehydraulic arguments suggests that bedload transport controlsthe seismic wave generation. Furthermore, the observedhysteresis is consistent with an increase in the threshold stressfor sediment entrainment during each event caused bypacking and/or coarsening of the alluvial bed.

2. Site and Methods

[5] The study site on the Cho‐Shui River in Taiwan wasselected because it has highly variable water discharge, high

1Department of Earth and Planetary Sciences, University ofCalifornia, Santa Cruz, California, USA.

2Now at Lamont-Doherty Earth Observatory, Palisades, NewYork, USA.

Copyright 2011 by the American Geophysical Union.0094‐8276/11/2011GL047759

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sediment supply, available high frequency seismic wavemeasurements from a broadband seismometer, and availablewater level and discharge data derived from a gaging station.At the site, the river is gravel‐bedded within a bedrockcanyon. The local channel width is 200 m and the local reachbed slope is 0.005 (Figure S1 of the auxiliary material).1

[6] The seismic station SUANG‐LONG (SSLB of theBroadband Array in Taiwan for Seismology, 23.7875N,120.9540E) is located ∼50 meters from the edge of the river.It includes an STS‐2 sensor that collects broadband data at20 Hz sampling frequency. The water station (1510H075,Bao‐shih Bridge, 23.7942N, 120.9142E) is 4.25 kmdownstream of the seismometer, and records hourly waterlevel. Water discharge is calculated from river stage com-bined with measured cross sections [Water ResourcesPlanning Commission, 2008, 2009]. The channel bed hereis dynamic; the channel elevation at a specific point in thecross sectional profile may change by meters from storm tostorm (Figure S2). The variable channel geometry leads tocomplexities in the rating curves, which relate water level

and discharge (Figure S3). While the water level value is araw measurement without any interpretation, if aggradationor erosion has occurred, its unit of meters above sea level(m.a.s.l.) does not necessarily translate directly to localwater depth. In contrast, the derived discharge measurementis calculated with a rating curve and should account for bedelevation change, however the accuracy of the rating curveis uncertain in highly dynamic reaches. Consequently, weuse both the water level and discharge datasets accordinglyin our analysis.[7] We examined the high frequency content of the seis-

mic noise, which was previously shown to link to riverprocesses [Burtin et al., 2008]. We extracted the 1–9 Hzband, then calculated the envelope with a Hilbert transform.Figure 1 shows the distinctions between the raw signal, thebandpassed signal, and the envelope function. We used anhourly average of the envelope function to compare with thehourly water data. We analyzed seismic amplitude and waterdata from the entire year 2008, which had several stormevents, and the one large storm in 2009, Typhoon Morakot.

3. Results: Hysteresis in the RelationshipsBetween Seismic Amplitude Versus Water Leveland Seismic Amplitude Versus Discharge

[8] The time series for seismic wave amplitude and waterlevel closely track each other on the rising limb, butdecrease at different rates on the falling limb. Figures 2a–2cshow this close relationship for the three storms with com-plete seismic records, Events 2008a, 2008b, and 2009a(Morakot), respectively. (A fourth storm, Event 2008c,shows the same patterns but has a significant gap in theseismic record. It is shown in Figure S4.) At the beginningof the flood hydrograph, the increase in seismic amplitudeoccurs immediately, within one hour (one timestep) of theincrease in water level. However, the relationship betweenseismic amplitude and water level differs on the rising andfalling limbs of the storms. After the peak water level, theseismic noise decays at a faster rate, reaching the initial baselevel values before the water level returns to base level. Thiscreates a clockwise hysteresis effect in seismic amplitude asa function of water level (Figures 2d–2f).[9] The same patterns are observed in the time series of seis-

mic wave amplitude and water discharge. They closely followeach other on the rising limb of storms, with both dischargeand seismic amplitude increasing sharply (Figures 2g–2i). Onthe falling limb, the seismic amplitude decreases faster thanthe water discharge. For a given discharge, the ratio of theseismic amplitude on the rising limb to the amplitude on thefalling limb is about two (see auxiliary material for moredetails). Note that the two smaller discharge peaks (one on thefalling limb of Event 2008b in Figure 2b, and one on the risinglimb of Event 2009a in Figure 2c) do not exhibit the clockwisehysteresis. The peak on the falling limb of Event 2008bactually displays counter‐clockwise hysteresis (Figure 2e, 2k,insets). These subevents are smaller both in magnitude (thepeak discharge is much lower, by almost an order of magni-tude) and duration (they last for a day or less, instead of a weekor more). Also, for the subevent on the falling limb, the initialcondition of the bed is different from the condition for largeevents because the pre‐subevent discharge is not as lowas pre‐storm base level. The entire dataset, which shows the

Figure 1. Illustration of the seismic processing steps,showing the difference between raw, filtered, and envelopevalues for storm and non‐storm data. (a) Raw seismic veloc-ity data (m/s) recorded at station SSLB for two differentconditions: Black line: during the peak of Typhoon Morakot(10 August 2009) and gray line: base level flow one weekbefore the storm (3 August 2009). (b) 1–9 Hz band filtereddata for the same time period, showing the high frequencycomponent of the signal linked to river processes. (c) Theenvelope (Hilbert function – a measure of the power inthe signal over time) is shown by the red lines, (storm: thickred line; base level: thin red line, which covers the grey lineat this resolution.) Note that the amplitude of the seismicvelocity is much larger during the storm than during thebackground base level flow.

1Auxiliary materials are available in the HTML. doi:10.1029/2011GL047759.

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events in the context of preceding and subsequent data, isshown in Figure S5.

4. The Source of Seismic Waves

[10] We are measuring energy transferred from the river tothe bed due to either fluid turbulence or impacting bedloadparticles. In order to link the seismic signal to sedimenttransport processes, it is necessary to first determine whichof these scenarios is more likely. Towards this end, we useour data to test end‐member hypotheses for the source of theseismic noise by exploring each of their predictions of thehysteresis.

[11] Hysteresis could occur in the absence of bedload‐generated seismic waves by two distinct processes. First,hysteresis can result from the fact that on the rising limb ofa flood, the flood wave drives a pressure gradient in thedirection of the river flow, whereas on the falling limb thewater surface generates a pressure gradient that opposesthe river flow. This means that for the same stage, a highervelocity (and therefore discharge) is observed on the risinglimb than on the falling limb. Second, hysteresis can begenerated by a change in bed shape due to erosion oraggradation that causes a change in stage‐discharge rela-tionships during a storm. Alternatively, if sediment transportgenerates the seismic waves, hysteresis can be linked to either

Figure 2. Relationships between seismic wave amplitude, water level, and discharge. We show the three events with acomplete seismic record, (a) Event 2008a, (b) Event 2008b, (c) Event 2009a (Typhoon Morakot) – each entire column cor-responds to the same event. (a–c) Seismic wave amplitude (m/s, left axis, gray‐gradient dots becoming lighter with time)and water level (meters above sea level, blue line) versus time (date). The water level curves suggest channel aggradation inFigures 2a and 2b, but erosion in Figure 2c. (d–f) Seismic wave amplitude vs. water level corresponding to events 2008a,2008b, and 2009a, respectively. Gray gradient showing temporal evolution matches that in Figures 2a–2c. Arrows indicatethe clockwise hysteresis. (e) The inset shows that the small peak on the falling limb of 2008b exhibits counter‐clockwisehysteresis. The inset scale is the same as in the main panel – the subset is simply translated – but the inset shading wasrescaled to the sub‐period to better show the sense of the hysteresis. (f) The abnormally high values in Event 2009a aredue to seismicity from earthquakes. (g–l) Same as (a–f ) but for discharge (m3/s) instead of water level.

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supply limitation during the event [e.g., Leopold and Emmett,1977] or bed armor destruction and reformation [e.g., Reidet al., 1985]. These distinct predictions of the source ofhysteresis provide a tool to distinguish between the sourcesof the seismic waves.[12] If turbulent dissipation is the source of seismic

amplitude, we expect a linear scaling between shaking anddischarge [e.g., Burtin et al., 2008]. This is because turbu-lence should depend most directly on the rate of dissipationof potential energy via turbulence, or in other words, riverpower. River power, for a given slope and cross‐section,depends linearly on discharge under steady and uniformflow. Thus if the observed hysteresis is related to the watersurface pressure gradient effect articulated above, then the2‐fold reduction in seismic amplitude on the falling limbcompared to the rising limb should correspond to a 2‐foldreduction in discharge on the falling limb compared to therising limb. For the most clearly resolved rising hydro-graph limbs in the observed storms, stage changes by ∼5 mover a time‐scale, t, of ∼8 hours. Assuming this rise occursfrom the downstream translation of a flood wave of heighth at velocity u, the slope of the wave front, Sw, can becomputed by:

Sw ¼ h= u�ð Þ ð1Þ

For a conservatively low estimate of the average flowvelocity during a flood (2 m/s), the downstream water sur-face slope, Sw, needed to explain the magnitude of waterrise during a storm is approximately 9 × 10−5 m/m, orroughly 1/60 the bed slope for the reach examined. This∼2% increase in the driving stress of a river from the floodwave is insufficient to explain the 2‐fold higher magnitudeof the seismic amplitude (and thus inferred discharge) on therising limb. Thus, water surface pressure gradients are notlikely to be the source of the hysteresis.[13] To explain the sign of the observed hysteresis in all of

typhoons examined, net channel bed aggradation would berequired during each storm so that more water would beconveyed for a given water surface elevation on the risinglimb as compared to the falling limb. Between 2008 and2009, however, we observe significant incision of thechannel (Figure S2). During Event 2009a, roughly 0.7 m ofbed incision occurred at the gage (Figures 2c and S5b).Nevertheless, the sense of hysteresis in the relationshipbetween seismic wave amplitude and discharge is the samefor this event as in net aggradational events 2008a and2008b. Since the data supports neither of the potentialhysteresis effects associated with turbulence in the watercolumn being the sole source of seismic waves, we concludethat bedload transport must be a contributor to seismic wavegeneration.[14] Source limitation is a documented cause of hysteresis

in bedload transport during events in nature [e.g., Leopoldand Emmett, 1977; Moog and Whiting, 1998]. At a givenreach during the course of an event, the sediment fractionmobilized by the shear stress of the flow may be depleted.The supply is built up again during low flows. At this site inthe Cho‐Shui river, source limitation is unlikely due to theabundant sediment supply. In addition, the storms we ana-lyzed in 2008 follow each other immediately, leaving littletime to replenish the sediment. Therefore source limitationcannot be the explanation for the hysteresis in all events. In

addition, because the gravel transport distances for a stormare typically small relative to the length of a river [e.g., Goffand Ashmore, 1994], we focus on local (as opposed tosource) effects as an explanation for the inferred reduction intransport efficiency.[15] The second mechanism for hysteresis caused by bed-

load transport involves bed armor destruction and refor-mation. The state of the bed, for example grain size andpacking density, can change over the course of a stormevent. For a given bed stress, coarsening or packing of thebed should translate directly into a reduction in transportefficiency [e.g., Reid et al., 1985;Wilcock and Crowe, 2003;Gran and Montgomery, 2005; Turowski et al., 2011]. Thuschanges in the packing density or grain size of the bed mightprovide a simple explanation for the observed hysteresis.[16] The conceptual picture is a pre‐storm bed that is

armored, but this densely‐packed state is destroyed duringthe early part of the rising limb, exposing an un‐armoredbed that will mobilize more readily at a given shear stress.As the flood peak wanes, the armor reforms (due to selectivetransport of finer grains or progressive packing of the bed)bringing the bed back to a more stable arrangement. Herewe make a simplifying assumption that bedload flux islinearly related to the amplitude of seismic shaking, and weconsider only saltating particles that achieve terminalvelocity before impact. Then for the characteristic grain sizesampled by our signal, impact energy should scale with thenumber of impacting particles, i.e., the bedload flux. Sincethe amplitude of seismic waves is linearly proportional tothe impact force at the source [Aki and Richards, 2002,equation 4.26], it follows that seismic amplitude shouldscale linearly with transport rate under the simplifyingconditions described above. The observed hysteresis thusimplies, on average, a two‐fold reduction in transport ratefor a given discharge during each storm. Rolling or draggingcontacts between particles are expected to have a smallercontribution to seismic noise (less energy transfer) thancollisions, so if these interactions make up some fraction ofthe moving bedload, the same seismic wave amplitudewould be caused by a larger flux of bedload than weassume. If the fraction of total bedload that is rolling ordragging is the same on the rising and falling limbs, thenthere is no change to the two‐fold reduction in transport rate.If bedload transport has a greater fraction of these less‐energetic rolling or dragging contacts on the falling limb,then a greater bedload flux occurs for the same seismicenergy level, and the reduction in transport rate would be anoverestimate.[17] Both experiments [Charru et al., 2004] and ob-

servations [Reid et al., 1985] show substantial changes intransport rates for a given stage simply due to changes in thepacking and/or grain size of the bed. Thus the observedhysteresis is consistent with a bedload source for seismicamplitude. Moreover, our results indicate that on the Cho‐Shui River, changes in the efficiency of bedload transportfollow a similar trajectory from large storm to large storm,regardless of whether there is net aggradation or erosion.Although it is possible that both water and bedload con-tribute to the observed shaking, our results indicate thatbedload is the dominant component of the seismic source.[18] A possible explanation for why the smaller subevents

do not exhibit the same hysteresis as the typhoons is that theseevents have different initial conditions compared to the large

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events. For example, Reid et al. [1985] demonstrated thatthe delay between the hydrograph peak and the bedloadtransport peak on a creek in England was controlled pri-marily by how consolidated the bed was. Transport eventsthat took place when the bed was consolidated resulted inpeaks in gravel transport on the recessional limb of thehydrograph, which would generate counter‐clockwise hys-teresis. In our results, the one clear example of counter‐clockwise hysteresis on the falling limb of event 2008b(Figures 2e and 2k, insert) occurs ∼ten days after the peakground vibrations in a typhoon, during an interval, asexplained above, when armoring is inferred to have occurred.The peak discharge of the subevent is much smaller than thelarge typhoons and has less energy to completely destroy thearmor on the rising limb. Thus, whereas on the scale of anentire typhoon, net bed armoring may occur, high frequencysubevents may introduce complexity that interrupts this trendover shorter timescales.[19] Other factors may also affect the amplitude of the

high frequency seismic noise observed at this site. Althoughthe seismometer is most sensitive to the seismic wavesgenerated proximally, signals are also generated from themore distant reaches. We have adopted the most naturalexplanation based on observed stage changes locally, but anexhaustive analysis would require data from the entire riversystem together with the spatial pattern of the river inrelation to the seismometer. Also, tributary inputs of finersediment, including that from debris flows, may affect theseismic signal. Investigating the influence of tributary inputsis beyond the scope of this paper, but we note that to be theexplanatory factor for the observed hysteresis in all of ourstorms, the tributary input timing and characteristics wouldneed to be relatively similar for all events, and additionallywould need to affect the seismic wave amplitude over theduration of the falling limb, which we find unlikely.[20] Lastly, we note that the river gage is 4.25 km

downstream of the seismometer. Because flood wavespropagate downstream, this means that peak flows areexperienced by the seismometer before the river gage.Additionally, at any time on the rising limb of a flood theseismometer will always experience slightly higher flowsthan the river gage. On the falling limb, the opposite will bethe case. Thus the offset between the seismic and hydro-logical stations provides another possible explanation forhysteresis. However, at 4.25 km apart and using a possibleflood flow velocity of 2–5 m/s, the temporal lag between theseismic and hydrologic data would be between 2125 and850 seconds (35–14 minutes), which is well below ourtimestep of one hour. This indicates that hysteresis is alsoprobably not due to the spatial offset between the seismicstation and the river gage. Moreover, we note that theduration of the seismically observed peak is shorter than thewidth of the peak of the discharge, which further suggeststhat the hysteresis is not due to a simple temporal offset ofthe signals.

5. Conclusions

[21] We have demonstrated that the event‐scale timeseries of high frequency seismic amplitude, a measure ofenergy from a river available for geomorphic work, isconsistent with a bedload source. Using hourly stage anddischarge measurements on a gravel‐rich mountain stream,

we tested hypotheses to explain the measured high fre-quency seismic noise by water turbulence or bedloadtransport. We observed clockwise hysteresis in the seismicamplitude‐stage and seismic amplitude‐discharge relation-ships for both aggradational and erosional events, consistentwith a bedload sediment source for the seismic noise thatis dependent on evolving bed packing conditions. Thedestruction and reformation of armor over the course of thestorm is a natural explanation for the observations. The dataare inconsistent with hysteresis driven entirely by turbulentpressure fluctuations. These observations demonstrate thepotential of fluvial seismology as a method to detect riverbed evolution over storm timescales.

[22] Acknowledgments. We thank Hui‐Hsuan Kate Chen for helpwith data and translation for the hydrology data, and acknowledge theBATS (Broadband Array in Taiwan for Seismology) for making their dataavailable through the IRIS Data Management Center. The paper benefitedfrom discussions with Colin Stark.[23] The Editor thanks the two anonymous reviewers for their assis-

tance in evaluating this paper.

ReferencesAdams, P. N., R. S. Anderson, and J. Revenaugh (2002), Microseismic mea-

surement of wave‐energy delivery to a rocky coast, Geology, 30(10),895–898, doi:10.1130/0091-7613(2002)030<0895:MMOWED>2.0.CO;2.

Aki, K., and P. Richards (2002), Quantitative Seismology, Univ. Sci.,Sausalito, Calif.

Burtin, A., L. Bollinger, J. Vergne, R. Cattin, and J. L. Nabelek (2008),Spectral analysis of seismic noise induced by rivers: A new tool to mon-itor spatiotemporal changes in stream hydrodynamics, J. Geophys. Res.,113, B05301, doi:10.1029/2007JB005034.

Burtin, A., L. Bollinger, R. Cattin, J. Vergne, and J. L. Nabelek (2009),Spatiotemporal sequence of Himalayan debris flow from analysis ofhigh‐frequency seismic noise, J. Geophys. Res., 114, F04009,doi:10.1029/2008JF001198.

Charru, F., H. Mouilleron, and O. Eiff (2004), Erosion and deposition ofparticles on a bed sheared by a viscous flow, J. Fluid Mech., 519,55–80, doi:10.1017/S0022112004001028.

Cole, S. E., S. J. Cronin, S. Sherburn, and V. Manville (2009), Seismic sig-nals of snow‐slurry lahars in motion: 25 September 2007, Mt Ruapehu,New Zealand, Geophys. Res. Lett. , 36, L09405, doi:10.1029/2009GL038030.

Deparis, J., D. Jongmans, F. Cotton, L. Baillet, F. Thouvenot, and D. Hantz(2008), Analysis of rock‐fall and rock‐fall avalanche seismograms in theFrench Alps, Bull. Seismol. Soc. Am., 98(4), 1781–1796, doi:10.1785/0120070082.

Favreau, P., A. Mangeney, A. Lucas, G. Crosta, and F. Bouchut (2010),Numerical modeling of landquakes, Geophys. Res. Lett., 37, L15305,doi:10.1029/2010GL043512.

Goff, J. R., and P. Ashmore (1994), Gravel transport and morphologicalchange in braided Sunwapta River, Alberta, Canada, Earth Surf. Pro-cesses Landforms, 19(3), 195–212, doi:10.1002/esp.3290190302.

Govi, M., F. Maraga, and F. Moia (1993), Seismic detectors for continuousbed‐load monitoring in a gravel stream, Hydrol. Sci. J., 38(2), 123–132,doi:10.1080/02626669309492650.

Gran, K. B., and D. R. Montgomery (2005), Spatial and temporal patternsin fluvial recovery following volcanic eruptions: Channel response tobasin‐wide sediment loading at Mount Pinatubo, Philippines, Geol.Soc. Am. Bull., 117(1–2), 195–211, doi:10.1130/B25528.1.

LaHusen, R. (2005), Acoustic Flow Monitor System—User Manual, U.S.Geol. Surv. Open File Rep., 02‐429.

Leopold, L. B., and W. W. Emmett (1977), 1976 bedload measurements,East Fork River, Wyoming, Proc. Natl. Acad. Sci. U. S. A., 74(7),2644–2648, doi:10.1073/pnas.74.7.2644.

Meyer‐Peter, E., and R. Müller (1948), Formulas for bed‐load transport, inProceedings of the 2nd Meeting of the International Association forHydraulic Structures Research, pp. 39–64, Delft, Netherlands.

Moog, D. B., and P. J. Whiting (1998), Annual hysteresis in bed load ratingcurves, Water Resour. Res. , 34(9), 2393–2399, doi:10.1029/98WR01658.

Reid, I., L. E. Frostick, and J. T. Layman (1985), The incidence andnature of bedload transport during flood flows in coarse‐grained alluvial

HSU ET AL.: SEISMIC SIGNATURE OF RIVER BEDLOAD L13407L13407

5 of 6

channels, Earth Surf. Processes Landforms, 10(1), 33–44, doi:10.1002/esp.3290100107.

Suwa, H., J. Akamatsu, and Y. Nagai (2003), Energy radiation by elasticwaves from debris flows, in Proceedings of the 3rd International Con-ference on Debris‐Flow Hazards Mitigation: Mechanics, Prediction,and Assessment, edited by D. Rickenmann and G. F. Wieczorek,pp. 895–904, Millpress, Rotterdam, Netherlands.

Turowski, J. M., A. Badoux, and D. Rickenmann (2011), Start and end ofbedload transport in gravel‐bed streams, Geophys. Res. Lett., 38,L04401, doi:10.1029/2010GL046558.

Vilajosana, I., E. Surinach, G. Khazaradze, and P. Gauer (2007), Snow ava-lanche energy estimation from seismic signal analysis, Cold Reg. Sci.Technol., 50(1–3), 72–85, doi:10.1016/j.coldregions.2007.03.007.

Water Resources Planning Commission (2008), Hydrological year bookof Taiwan, Republic of China, technical report, Minist. of Econ. Aff.,Taipei.

Water Resources Planning Commission (2009), Hydrological year bookof Taiwan, Republic of China, technical report, Minist. of Econ. Aff.,Taipei.

Wilcock, P. R., and J. C. Crowe (2003), Surface‐based transport model formixed‐size sediment, J. Hydraul. Eng., 129(2), 120–128, doi:10.1061/(ASCE)0733-9429(2003)129:2(120).

E. E. Brodsky and N. J. Finnegan, Department of Earth and PlanetarySciences, University of California, Santa Cruz, CA 95064, USA.L. Hsu, Lamont‐Doherty Earth Observatory, 61 Rte. 9W, Palisades, NY

10964, USA. (hsu.leslie@gmail.com)

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2011GL047759-supplement Hsu et al., 2011 S1

Supporting nonprint material

Auxiliary materials

Figure S1. Locations of the seismometer station (red star, SUANG-LONG, SSLB of the

Broadband Array in Taiwan for Seismology 23.7875N, 120.9540E) and the water gaging station

(blue star, Station 1510H075, Bao-shih Bridge of the WRA, 23.7942N, 120.9142E), in the

mountainous area of central Taiwan. The water station is ~4250 meters downstream of the

seismic station.

2011GL047759-supplement Hsu et al., 2011 S2

Figure S2. Cross sections at the water gaging station 1510H075, Bao-shih Bridge, 23.7942N,

120.9142E, from 2007-2010, showing large changes in bed geometry [Water Resources Planning

Commission]. The 2008 cross section is net aggradational relative to 2007 while the 2009 and

2010 cross sections are net erosional relative to the previous years.

2011GL047759-supplement Hsu et al., 2011 S3

Figure S3. Discharge vs. water level (rating curves) for the three storms in Figure 2 of the main

text. (a) Event 2008a, (b) Event 2008b, and (c) Event 2009a. The rating curve is different for the

rising and falling limbs of the storms.

2011GL047759-supplement Hsu et al., 2011 S4

Figure S4. Event 2008c, which is not in the main body of the paper because a significant portion

of the seismic recording is missing (the gap immediately after the peak). This storm has the same

rating curve for the rising and falling limb, but it still exhibits hysteresis with approximately two

times lower seismicity on the falling limb for the data that exists.

2011GL047759-supplement Hsu et al., 2011 S5

Figure S5. Time series of discharge and water level measured at the water gaging station at Bao-

shih bridge and seismic amplitude from the station SSLB for 2008 (blue line) and 2009 (red line).

(a) Water discharge (m3/s) with the events analyzed in the paper labeled – 2008a, 2008b, 2008c,

2009a. The unlabeled event in July 2008 was missing a large portion of seismic data and was not

presented. Event 2009a is Typhoon Morakot.. (b) Water level (meters above sea level). Changes

in base flow elevation before and after typhoon events reflect changes in bed elevation. For

example, in Event 2009a there is net lowering of the channel (−0.7 m from the beginning of

August until the end of September), as shown by the zoom-in inset, whereas in Event 2008b

there is net aggradation. (c) Seismic wave amplitude (m/s): Hourly averaged values of the

envelope function of the 1-9 Hz seismic data - representing the power of the seismic signal over

time. There are several periods of missing data when the seismometer was not operating.

2011GL047759-supplement Hsu et al., 2011 S6

Supplemental Material

1. Comparison between the rising and falling limbs of storms: Constant discharge

To compare the seismic amplitude on the rising and falling limbs of the storms, we calculated the

ratio of the two values (one-hour average of the seismic wave envelope) at a given discharge

(Table S1). We used discharge values on the fast-changing rising limb, avoiding sub-event

anomalies and the peak flow. We avoided the events that were missing data from the rising limb.

The tables below show the points that were used to obtain the average difference in magnitude

between rising and falling limb seismic wave amplitude at a given discharge. The ratios range

between 1 and 3, with an average of 2.

Table S1. Comparison between the rising and falling limbs of storms: Constant discharge

Event 2008a

rising limb falling limb

discharge seismic

amplitude discharge seismic

amplitude ratio

m3/s *10^-7 m/s m

3/s *10^-7 m/s (-)

176 0.41 174 0.33 1.2

194 0.51 194 0.28 1.8

246 0.65 252 0.44 1.5

335 1.48 581 0.54 2.8

730 1.91 760 0.90 2.1

1087 2.04 1125 1.10 1.9

1373 2.33 1397 1.19 2.0

1894 2.88 1862 2.34 1.2

Event 2008b

rising limb falling limb

discharge seismic

amplitude discharge seismic

amplitude ratio

m3/s *10^-7 m/s m

3/s *10^-7 m/s (-)

97 0.46 100 0.45 1.0

104 0.46 105 0.38 1.2

106 0.50 106 0.37 1.3

130 0.49 139 0.36 1.4

2011GL047759-supplement Hsu et al., 2011 S7

142 0.53 145 0.32 1.7

164 0.73 164 0.37 1.9

201 0.87 211 0.46 1.9

232 1.00 234 0.45 2.2

277 1.01 279 0.46 2.2

326 0.92 327 0.42 2.2

355 1.06 359 0.52 2.0

429 1.53 427 0.67 2.3

510 1.84 506 0.66 2.8

635 1.76 634 1.05 1.7

642 1.71 643 0.92 1.9

659 1.82 660 0.97 1.9

709 2.41 722 1.08 2.2

Event 2009a

rising limb falling limb

discharge seismic

amplitude discharge seismic

amplitude ratio

m3/s *10^-7 m/s m

3/s *10^-7 m/s (-)

403 1.14 397 0.38 3.0

443 1.31 455 0.38 3.4

517 1.48 517 0.41 3.6

493 1.21 496 0.40 3.0

594 1.24 592 0.45 2.8

639 1.37 688 0.51 2.7

663 1.45 692 0.56 2.6

929 1.68 925 0.69 2.4

1260 1.78 1264 1.11 1.6

1229 1.93 1228 1.06 1.8

1454 1.97 1490 1.31 1.5

1293 1.97 1264 1.08 1.8

1537 2.34 1581 1.46 1.6

1726 3.03 1763 1.53 2.0

2063 3.94 2141 1.82 2.2

2389 4.49 2408 2.03 2.2

2841 4.28 2828 3.14 1.4

Event 2008c (Supplemental Material Only)

rising limb falling limb

discharge seismic

amplitude discharge seismic

amplitude ratio

m3/s *10^-7 m/s m

3/s *10^-7 m/s (-)

163 0.60 162 0.32 1.9

221 0.93 220 0.39 2.4

247 0.98 252 0.41 2.4

258 0.96 259 0.40 2.4

263 1.03 267 0.43 2.4

462 1.96 462 0.57 3.4

639 2.19 631 0.71 3.1