Bedload transport measurements with impact plate geophones in two 1 Austrian mountain streams ( Fischbach and Ruetz ) : system 2 calibration , grain size estimation , and environmental signal pick-up 3

7 The Swiss plate geophone system is a bedload surrogate measuring technique that has been installed in more than 20 8 streams, primarily in the European Alps. Here we report about calibration measurements performed in two mountain streams 9 in Austria. The Fischbach and Ruetz gravel–bed streams are characterized by important runoff and bedload transport during 10 the snowmelt season. A total of 31 (Fischbach) and 21 (Ruetz) direct bedload samples were obtained during a six year 11 period. Using the number of geophone impulses and total transported bedload mass for each measurement to derive a 12 calibration function, results in a strong linear relation for the Fischbach, whereas there is only a poor linear calibration 13 relation for the Ruetz measurements. Instead, using geophone impulse rates and bedload transport rates indicates that two 14 power law relations best represent the Fischbach data, depending on transport intensity; for lower transport intensities, the 15 same power law relation is also in reasonable agreement with the Ruetz data. These results are compared with data and 16 findings from other field sites and flume studies. We further show that the observed coarsening of the grain size distribution 17 with increasing bedload flux can be qualitatively reproduced from the geophone signal, when using the impulse counts along 18 with amplitude information. Finally, we discuss implausible geophone impulse counts that were recorded during periods 19 with smaller discharges without any bedload transport, and that are likely caused by vehicle movement very near to the 20 measuring sites. 21


Introduction 22
In the past decade or so, an increasing number of studies were undertaken on bedload surrogate acoustic measuring 23 techniques which were tested both in flume experiments and in field settings. A review of such indirect bedload transport 24 measuring techniques was recently published by Rickenmann (2017aRickenmann ( , 2017b. Examples of measuring systems include the 25 Japanese pipe microphone (Mizuyama et al., 2010a(Mizuyama et al., , 2010bUchida et al. 2013;Goto et al. 2014), the Swiss plate geophone 26 (Rickenmann and Fritschi, 2010, Rickenmann et al. 2012, 2014, other impact plate systems (Krein et al., 2008(Krein et al., , 2016Møen 27 et al. 2010;Reid et al. 2007;Beylich and Laute 2014;Taskiris et al. 2014), and hydrophones, i.e. underwater microphones 28 (Barton et al. 2010;Camenen et al. 2012;Rigby et al. 2015). It is well known that bedload transport rates often show very 29 2 large variability for given flow conditions (Gomez, 1991;Leopold and Emmett, 1997;Ryan and Dixon, 2008;Recking, 30 2010), and that prediction of (mean) bedload transport rates is still very challenging, particularly for steep and coarse-31 bedded streams (Bathurst et al., 1987;Nitsche et al., 2011;Schneider et al. 2015Schneider et al. , 2016. For such conditions, direct bedload 32 transport measurements are typically difficult to obtain, or may be impossible to make during high flow conditions (Gray et 33 al., 2010). In contrast, indirect bedload transport measuring methods have the advantage of providing continuous monitoring 34 data both in time and over a cross-sections, even during difficult flow conditions, and are therefore expected to increase our 35 understanding of bedload transport. 36 A fair number of these measuring techniques have been successfully calibrated for total bedload flux, which generally 37 requires contemporaneous direct bedload transport measurements in the field (Thorne, 1985(Thorne, , 1986Voulgaris et al., 1995;38 Rickenmann andMcArdell, 2007, 2008;Mizuyama et al. 2010b;Rickenmann et al. 2014;Mao et al., 2016;Habersack et al., 39 2017;Kreisler et al., 2017). Essentially, linear or power law relations were established between a simple metric 40 characterizing the acoustic signal and bedload mass. In some studies further calibration relations were established to identify 41 particle size, either based on signal amplitude (Mao et al., 2016;Wyss et al., 2016a) and/or on characteristic frequency of 42 that part of the signal which is associated with a single impact of a particle (e.g. for impact plate systems; Wyss et al., 2016b) 43 or by determining a characteristic frequency for an entire grain size mixture (for the hydrophone system; Barrière et al., 44 2015a). A few of the acoustic measuring techniques were used to determine bedload transport by grain size classes (Mao et 45 al., 2016;Wyss et al., 2016a). Finally, some studies examined to what extent findings from flume experiments can be 46 quantitatively transferred and applied to field sites for which independent, direct calibration measurements exist (Mao et al.,47 6 Eq. 2), while Eq. (3) represents a mean, linear calibration coefficient based on the total mass and the total number of 157 impulses for all calibration measurements taken together. The resulting coefficients (k lin , k pow , k tot ), exponents (e) and 158 statistical properties of the calibration relations are reported in Table 3. The squared correlation coefficient r 2 was 159 determined between the measured masses M and the estimated masses M reg (using eq. 1, 2, or k tot in eq. 2). The relative 160 standard deviation s e,r is determined for the ratios (M reg /M), using the regression relation to determine M reg from the recorded 161 impulses IMP. 162 For the Fischbach, the calibration relations in the form of Eqs. (1) and (2) show a rather high correlation coefficient (Fig. 163 5, Table 3), which is also characteristic for similar calibration relations determined for the Erlenbach (Rickenmann et al., 164 2012, 2014. For the Ruetz, the calibration relations in the form of Eqs. (1) and (2) are less well defined (Fig. 6, Table 3). 165 Due to the inclusion of four additional calibration measurements obtained in 2012 and 2013, the correlation coefficient for 166 the Ruetz is lower than in an earlier analysis that used only 17 measurements from the period 2008 to 2011 (Rickenmann et 167 al., 2014). This level of correlation is similar to calibration measurements obtained for the Navisence stream in Switzerland 168 (Wyss et al., 2016c) for which most measured bedload masses were smaller than 20 kg; for the Ruetz, 15 out of 21 169 calibration measurements also have bedload masses smaller than 20 kg. Using the k tot coefficient from Eq. (3) in Eq. (1)  170 results in very similar statistical properties as compared to using k lin in Eq. (1); while the relative standard deviation s e,r is 171 very similar for the Fischbach in both cases, it is about 25% larger for the Ruetz when using the k tot coefficient as compared 172 to using the k lin coefficient (Table 3). 173 Systematic flume experiments were performed for different grain size classes to investigate the dependence of a linear 174 calibration coefficient, defined as k bj = IMP/M, on grain size D (Wyss et al., 2016b). This study used bedload particles from 175 four streams including the Ruetz and Fischbach, and it was found that k bj values showed a local maximum at a grain size D 176 of around 40 mm, in agreement with earlier flume experiments using quartz spheres of different diameters (Rickenmann et 177 al., 2014). Therefore, we analysed the field calibration measurements from the Ruetz and Fischbach in a similar way (Fig. 7), 178 and these data essentially confirmed the findings from the flume experiments. The bedload samples from the Ruetz and 179 Fischbach show a general tendency for D 84 to increase with increasing unit bedload transport rate q b (Fig. 8), where D 84 is 180 the grain size for which 84 % of material by weight are finer (determined for particles with D > 10 mm). It is therefore not 181 surprising that k bj values also exhibit a local maximum when plotted against the impulse rate, IMPT (Fig. 9), which is a 182 proxy for transport rate, and where IMPT = IMP/(T s w p ), with the plate width w p = 0.5 m. Finally this lead us to determine 183 alternative calibrations in terms of unit bedload transport rate per plate width q b,p as a function of impulse rate, IMPT (Fig.  184 10), with a limiting value of around 0.5 to 1 (0.5 -1 m -1 s -1 ) to separate the two ranges with a different power law function: 185 qb,p = a1 IMPT b1 for IMPT < 0.48 (0.5 -1 m -1 s -1 ) (4) 186 qb,p = a2 IMPT b2 for IMPT > 0.48 (0.5 -1 m -1 s -1 ) where the units for q b,p are in (kg 0.5 -1 m -1 s -1 ) and for IMPT in (0.5 -1 m -1 s -1 ), and the coefficients and exponents are given in 188 Table 3. Here, we determined q b,p and IMPT deliberately per unit width of one plate since using the traditional 1 m unit 189 7 width would result in different coefficients a 1 and a 2 (and a different threshold value IMPT separating the application range 190 of Eq. 4 and Eq. 5), which would entail the risk of erroneous transformations of measured IMPT values into q b,p values for 191 each plate. In Table 3 we used the same coefficients and exponents (a 1 , b 1 , and a 2 , b 2 , respectively) for both stream sites. The 192 reason for this is evident from Figure 9. For the lower bedload transport or impulse rates (range of validity of Eq. 4), the 193 calibration measurements from the two streams show a very similar trend. For the higher bedload transport or impulse rates 194 (range of validity of Eq. 5), there are only calibration measurements from the Fischbach. The basic assumption hereby is that 195 Equations (4) and (5)  Ruetz data, resulting in the statistical properties of the calibration relations (4) and (5) as reported in Table 3. It appears that 201 the data from both channel sites can be described reasonably well with these calibrations relations, the relative standard 202 deviation se,r being about 98% for the higher impulse rates and about 110% for the higher impulse rates (Table 3). If Eqs. 203 (4) and (5) are applied to all calibration measurements of each stream separately, the clearly better statistical properties result 204 for the Fischbach (r 2 = 0.97, s e,r = 61 %) than for the Ruetz (r 2 = 0.50, s e,r = 145 %). In comparison to the calibration relation 205 determined with Eq. (2) for the Fischbach, Eqs. (4) and (5) will predict larger bedload transport rates for very small or very 206 large IMPT values (Fig. 10). 207

Coarsening of grain sizes with increasing bedload flux reflected in geophone signal 208
The amplitude histograms (AH data) for each calibration measurement were used to estimate grain size distributions (GSD) 209 for the basket sampler measurements, which were then compared with the sieve analyses of the bedload samples. For the 210 analysis of the AH data, the lowest class with impulses for A max < 0.056 V was excluded, as this class represents 211 predominantly signal noise. For the remaining 16 classes the sum of the impulses per amplitude class was determined for all 212 1 min time steps for the duration T s . This resulted in the proportion of impulses per amplitude class per calibration 213 measurement, not yet weighted for grain size. The impulses per class were weighted by the geometric mean diameter of each 214 class (Table 2) to the 2 nd power, D m 2 , to estimate the cumulative distribution of AH-values; this weighting procedure 215 corresponds essentially to the method of Wyss et al. (2016), which is summarized in Appendix A. It is also noted that the 216 start (and end) time of the bedload sampling does not exactly correspond to the start (and end) time of the recorded AH data, 217 which introduced a further (generally minor) uncertainty when interpolating AH data for the first and last recording time step 218 of each bedload sampling period. For the results shown in Figures 10 and 11, the GSD was averaged for given classes of unit 219 bedload transport rates q b , assigning the same weight to each measurement in a given q b class. Bedload transport classes and 220 corresponding abbreviation names are defined in Fig. 11 and 12. 221 8 For the bedload samples from both Fischbach and Ruetz a general coarsening trend of the grain size distribution (GSD) 222 with increasing unit bedload transport rate q b can be observed, in agreement with general bedload transport theory (Parker, 223 2008). However, GSDs from individual calibration measurements are quite variable within given classes of q b , both for the 224 bedload samples and for the estimated GSD from the AH values, and do not necessarily follow the general trend. The GSDs 225 estimated from the AH values generally show a qualitatively similar trend as the GSDs from the direct bedload samples, but 226 with a limited quantitative agreement between the two methods. 227 For the Fischbach (Fig. 11) it is noted that only 2 calibration samples were available for the class Fi1, and these had the 2 228 smallest bedload masses (with 19 and 8 kg, respectively); this may be a reason for the poor agreement between estimated 229 and measured GSDs. Similarly, the largest q b class Fi4 for the Fischbach includes only 1 bedload sample. For the Ruetz (Fig.  230 12) we note that for the classes Ru1 and Ru3 the bedload masses were relatively small, including only 5 to 6 kg. Together 231 with a small number of bedload samples (3 and 2, respectively), this may again be one reason for the relatively poor 232 agreement between estimated and measured GSDs. In contrast, the bedload masses for the Ruetz for the class Ru2 (11 to 23 233 kg) and Ru4 (15 to 129 kg) were clearly larger. 234

Environmental noise pick-up of the geophone signal 235
Both measuring stations are situated at a relatively high elevation, and the stream catchments include mountain peaks with 236 elevations above 3000 m a.s.l. Therefore the runoff during the winter period is very low, with a base flow below 0.6 m 3 s -1 at 237 the Fischbach and below 0.3 m 3 s -1 at the Ruetz. During such flow conditions, only about half or two thirds of the sill with 238 the steel plates is submerged under water (Fig. 2, Fig. S2). However, during winter geophone impulses are regularly 239 recorded at all the geophone sensors in both streams (Fig. 13, Fig. 14). According to hydraulic calculations and observations 240 the sill becomes fully submerged for flows of about 2.5 m 3 s -1 at the Fischbach and about 2.0 m 3 s -1 at the Ruetz. Therefore it 241 is unlikely that these geophone impulses are the result of bedload transport. 242 For the Fischbach and the discharge classes smaller than 3 m 3 s -1 the mean IMP values per 15 minutes (IMP 15 ) vary 243 between about 0.3 and 2.0. A similar analysis as in Fig. 13 but with a finer discharge resolution (classes of 0.25 m 3 s -1 ) is 244 presented in Fig. S3. It is also obvious that plates (sensors) no. 1 to 3 generally recorded more impulses than the other plates 245 no. 4 to 8 (Fig. 13, Fig. S3), which is unlikely a result of bedload transport. For discharges up to about 3 m 3 s -1 traffic noise 246 appears to be a likely source of the geophone impulses, since the local road passes on the river right side very close to the 247 plates no. 1 to 3 (Fig. 2). For discharge classes larger than 4 m 3 s -1 the plates no. 4 to 8 (which have a larger water depth than 248 plates no. 1 to 3) start to record more impulses on average (IMP 15 ) than plates no. 1 to 3; in addition the IMP 15 values start to 249 increase with increasing discharge (Fig. 13, Fig. S3). This behaviour is more in line with expectations from bedload-250 transport induced signals. 251 For the Ruetz and the discharge classes smaller than 1.0 m 3 s -1 the mean IMP 15 values vary between about 0.2 and 2.0. 252 Plates no. 5 to 8 generally recorded more impulses than the other plates no. 1 to 4 (Fig. 14, Fig. S4). The plates no. 1 to 3 are 253 typically not submerged during these flow conditions, and no signal is to be expected from bedload transport. Again, traffic 254 9 noise appears to be a likely source of the measured geophone impulses. The plates on the river left side (5 to 8) tend to 255 register more impulses on average because the access road to the parking lot passes on this side, hence more parking traffic 256 is to be expected. A clearer dominance of the plates no. 5 to 8 (which have a larger water depth than plates no. 1 to 4) 257 becomes apparent for discharge classes larger than about 1.5 m 3 s -1 at the Ruetz (Fig. 14, Fig. S4), which is in line with 258 expectations from bedload-transport induced signals. The mean value of IMP 15 averaged over all eight plates becomes larger 259 than about 2 for discharges larger than roughly 2.0 m 3 s -1 , and above this discharge level the IMP 15 values start to increase in 260 general with increasing discharge. 261 To further investigate the potential source of the implausible geophone recordings, we classified the measured IMP 15 262 values into 15 minute intervals during each day-time (Figs. S5, S6). For both streams and low flows, there is a clear daily 263 cycle of geophone impulse activity although discharge remains rather constant during the entire day. This pattern clearly is 264 present for the Fischbach for discharges Q smaller than about 3 m 3 s -1 and for the Ruetz for Q smaller than about 1.5 m 3 s -1 . 265 Geophone activity is higher during the afternoon and the first half of the night at the Fischbach, and primarily during day 266 time at the Ruetz. A clear absence of this or a similar daily pattern is evident for the Fischbach for Q larger than about 6 m 3 s -267 1 and for the Ruetz for Q larger than about 3.5 m 3 s -1 (Fig. S5, S6). This is a further indication that the geophone impulses at 268 smaller discharges are mainly traffic induced. Taken together, the above analysis and interpretation suggests that bedload 269 transport may be the dominant source of producing geophone impulses above a critical discharge Q c of about 3.5 m 3 s -1 at the 270 Fischbach, and above a Q c of about 1.5 m 3 s -1 at the Ruetz.

Calibration relations for the Swiss plate geophone system and grain size determination 281
For a system such as the Swiss plate geophone it is known that the signal response depends on factors such as grain size, 282 fluid or particle velocity, particle shape and mode of transport (i.e. sliding, rolling, saltating), and impact angle and impact 283 location on the steel plate (e.g. Wyss et al., 2016b;Rickenmann, 2017b). For a given stream we may assume that the most of 284 these factors vary within a given range, and the linear calibration coefficients primarily vary with flow conditions. Therefore, 285 we expect that the mean signal response from a given particle size traveling over the plate becomes more stable the larger is 286 the total number of particles that have been transported over the plate. This is the main reason why we have primarily 287 considered the summed geophone summary values in the past (e.g. Rickenmann et al., 2012Rickenmann et al., , 2014. Calibration 288 measurements from various sites confirmed the expectation that random factors influencing the signal response tend to be 289 more averaged out for longer integration periods (Rickenmann andMcArdell, 2007, 2008;Rickenmann et al., 2012Rickenmann et al., , 2014290 Wyss et al., 2016a290 Wyss et al., , 2016c. 291 However, it may also be interesting to consider calibration relations for example between bedload rates and impulse 292 rates. If a linear calibration relation in the form of Eq. (1) is generally valid, a division of M and IMP by the sampling 293 duration T s to determine rates will typically result in similar values for the linear calibration coefficient. Having performed 294 this alternative analysis in terms of bedload rates and impulse rates for the data of this study, two distinctly different ranges 295 of geophone signal response were found based on the data from the Fischbach (Fig. 10). These calibration measurements 296 suggest that two power law calibration relations in terms of rates provide a better fit than a single linear calibration relation 297 for the entire domain. The existence of two different ranges is likely a result of a changing GSD with increasing bedload 298 transport rates. We therefore also plotted data from calibration measurements at many other sites (Fig. 15), but no clear trend 299 for a similar pattern can be observed for most of these sites. The only exception is the Urslau stream in Austria; the 300 individual calibration measurements for this stream indicate a trend for a power law relation between q b and IMPT with an 301 exponent b < 1 for smaller q b values and with an exponent b > 1 for lager q b values (Kreisler et al., 2017). These calibration 302 measurements cover a range of about three orders of magnitude of q b values; however different methods were used to obtain 303 the bedload samples for smaller and larger bedload transport intensities, and for the smaller range of q b values the number of 304 measurements is limited. 305 For extreme flow conditions and very high bedload transport rates, there may be some limitations to extrapolating 306 calibration relations for the SPG system from the typical range of conditions investigated so far. Using the same steel impact 307 plates, we had installed piezoelectric bedload impact sensors (PBIS) in an earlier study to make bedload measurements at a 308 water intake of the Pitzbach mountain stream in Austria during two summer periods (Rickenmann and McArdell, 2008). 309 Impulses were counted in a similar way as for the Swiss plate geophone system. At the Tyrolean weir a total of 12 steel 310 plates with sensors were installed, with a natural gravel-bed surface upstream of the sill of 6 m width. Pressure sensors in the 311 settling basin downstream of the Tyrolean weir provided direct measurements of bedload volumes for calibration. 312 Downstream of the settling basin there is a flushing canal, where 3 steel plates with sensors were installed at the end of a 1.5 313 m wide and relatively smooth concrete channel. Flushing of sediment from the settling basin occurred over relatively short 314 time periods and thus produced high velocity flows and much higher bedload concentrations in the flow than at the (natural) 315 approach flow to the Tyrolean weir. While a reasonably well defined calibration relation could be obtained for the 316 measurements at the Tyrolean weir (Rickenmann and McArdell, 2008), a very large scatter was observed for the calibration 317 data of the flushing canal, for bedload volumes smaller than 100 m 3 (Fig. S9). This observation indicates that there are 318 limitations for the SPG system for extreme flow conditions. There is also evidence from debris-flow observations at the 319 Illgraben torrent in Switzerland with a geophone sensor mounted underneath a large steel plate (McArdell et al., 2007) that 320 the calibration relations for the SPG system obtained for bedload transport cannot be directly applied to estimate the mass of 321 debris flows. A somewhat similar limitation was observed for the Japanese pipe microphone system, for which signal 322 "saturation" may occur for high bedload transport rates, probably because this system is more sensitive to particle sizes 323 smaller than 10 mm as compared to the SPG system (Wyss et al, 2016a;Rickenmann, 2017aRickenmann, , 2017b. 324 We used the AH data recorded during the calibration measurements at the Fischbach and Ruetz to estimate the 325 transported bedload mass for each calibration measurement, M est , by applying the procedure presented by Wyss et al. 326 (2016a). This method is summarized in Appendix A, and it was specifically developed for the measuring conditions at the 327 Erlenbach stream in Switzerland. Here, we used Eq. (A3) with the coefficient and exponent determined from the Erlenbach 328 measurements; the relation of Eq. (A3) is expected to vary somewhat from site to site, and its application here is therefore 329 associated with uncertainty. To assess the performance of this procedure when applied to the Fischbach and Ruetz, we 330 plotted the ratio of estimated to observed bedload mass, M est /M, as a function of bedload transport rate per plate q b,p and of 331 observed mass M (Fig. 16). There is generally an over-estimation of bedload mass, up to a factor of about 10. Interestingly, 332 the over-estimation decreases with increasing bedload transport rate (Fig. 16a). This result is in agreement with Fig. 15, 333 which suggests that site-specific differences for calibration relations in terms of bedload transport rates and impulse rates 334 tend to be relatively smaller for higher values of q b . The degree of over-estimation of bedload mass as well as the scatter 335 around a mean trend line for both streams appears to decrease also with increasing bedload mass for the data of the 336 Fischbach and Ruetz (Fig. 16b), but this trend is somewhat less pronounced. Concerning grain size estimation from bedload 337 surrogate measuring techniques, it may be noted that only a few other acoustic measuring techniques were (partly) successful 338 in determining bedload transport by grain size classes from field measurements (Barrière et al., 2015b, using an impact plate 339 hydrophone system; Mao et al., 2016, using a Japanese impact pipe microphone system). 340 To illustrate the uncertainty associated with using different calibration relations, we determined the yearly bedload (YBL) 341 for 2010, which represents the year with the largest peak discharges and the largest YBL values (Table 4) (Table 4). The between-stream comparison shows a 347 much larger YBL for the Fischbach than for the Ruetz, which is due to more frequent peak discharges in the Fischbach 348 exceeding about 10 m 3 s -1 during the year 2010 (Fig. S7, S8). 349 Based on the analysis of the GSD of all bedload samples we found on average a coarsening of the GSD with increasing 350 bedload transport intensity (Figures 8, 11). However, GSDs from individual bedload samples are quite variable within given 351 classes of bedload transport rates. The same is true if GSDs of the bedload samples are analysed in terms of changing 352 discharge. The bedload samples were taken too randomly in time and too infrequently over the six years study period as to 353 allow to examine whether there is any hysteresis trend for daily discharge cycles or over the entire summer season. In a 354 12 follow-up study, possible hysteresis trends were investigated based on the continuous geophone data which were converted 355 into bedload fluxes using equations (4) and (5), and the related findings are discussed in a forthcoming paper. 356

Environmental noise pick-up of the geophone signal 357
Hydrophones (underwater microphones) have been used to monitor bedload transport both in riverine and in coastal 358 environments (e.g. Thorne, 1990;Camenen et al. 2012;Basset et al., 2013). The objective of using such a system is to record 359 self-generated noise produced by collisions of moving bedload particles against each other or against the bed. The 360 application of this bedload surrogate measuring system can be impaired by other sources of noise, which may be caused by 361 vessel traffic, marine seismic exploration, or underwater military operations. If the main interest is in the acoustic signal due 362 to bedload transport, discounting for other sources of noise may be challenging and will also depend for example on the 363 spatial distance and the dominant frequencies of the different acoustic sources (Hildebrand, 2009;Etter, 2012;Basset et al., 364 2013). 365 For the application of impact plates with acoustic sensors installed in a streambed there is very few experience with non-366 bedload transport related sources of noise that may compromise their usefulness. We have shown in section 3.3 that road 367 traffic is a likely source of environmental noise producing a similarly strong signal at the SPG system as low-intensity 368 bedload transport during periods with moderate discharges. This observation was made for our two study streams Fischbach 369 and Ruetz, where in both cases the stream bed runs very close-by to roads, which are located only about half the stream-370 width away from the edge of the bed. We have checked the impulse counts recorded for SPG systems installed at mountain 371 streams in Switzerland, particularly for low flow periods during winter time. There were generally very few impulses 372 recorded at these sites, indicating that road traffic is not an important source of noise. At these sites roads with regular traffic 373 are situated clearly farther away from the channel profile than at the two Austrian sites of this study: at the Navisence stream 374 period, and it was hypothesized that ice transport or break-up may be mainly responsible for the impulse counts. Impulses 386 may be typically as high as between 1 and 100 impulses for all seven plates and for 10 minute recording intervals. 387 13 Calculating a mean impulse value per plate for Q < 0.3 m 3 s -1 and including also zero values, this results in an average 388 duration of about 5 hours for one impulse to be registered at the Riedbach by one of the seven steel plates. This relatively 389 low occurrence frequency does not contradict the ice transport or break-up hypothesis. 390

Conclusions 391
The Fischbach and Ruetz gravel-bed streams are characterized by important runoff and bedload transport during the 392 snowmelt season. As a bedload surrogate measuring technique, the Swiss plate geophone (SPG) system has been installed in 393 2007 in both streams. During the six year period 2008 -2013, 31(Fischbach) and 21 (Ruetz) direct bedload samples were 394 obtained in the two streams, and these measurements were analysed to obtain calibration relations for the SPG system at the 395 two sites. 396 As applied at many other SPG sites in the past, we first established calibration relations using total transported bedload 397 mass and the number of geophone impulses. A second way of analysing the geophone calibration measurements consisted in 398 using bedload transport rates and geophone impulse rates. For the Fischbach the second approach resulted in two power law 399 calibration relations, with different coefficients and exponents for small and large transport rates. The exponent was smaller 400 than one for small transport rates, and larger than one for larger transport rates. For the Ruetz data with essentially only 401 lower transport intensities, the power law relation derived from the Fischbach is also in reasonable agreement with the Ruetz 402 calibration measurements. The non-linear power law calibration relations are in qualitative agreement with the observed 403 coarsening of the bedload with increasing transport rates. According to findings from flume studies the signal response per 404 unit bedload mass increases for small grains up to grain size of approximately 40 mm, and decreases again for larger grains 405 with increasing particle size (Wyss et al., 2016b); this provides qualitative support for the existence of the two power law 406 relations. A similar behaviour could be observed only for the calibration measurements at the Urslau stream in Austria 407 (Kreisler et al., 2017). In contrast, calibration measurements from six other sites, including the Ruetz stream, do not show 408 evidence for the existence of similar two-range power law calibration relations. 409 Amplitude information from the geophone signal was recorded in minute intervals at the Fischbach and Ruetz by 410 summing impulse counts separately for different amplitude classes (so-called AH data). Since signal amplitude correlates 411 with grain size at several SPG sites (Wyss et al., 2016a(Wyss et al., , 2016b(Wyss et al., , 2016c, this information was used to estimate the grain size 412 distribution for the bedload samples from the Fischbach and Ruetz. It was found that the observed coarsening of the grain 413 size distribution with increasing bedload flux could be qualitatively reproduced from the geophone signal using the AH data. 414 For smaller discharges at the Fischbach and Ruetz, in particular during the winter time, it was found that many 415 implausible geophone impulse counts were recorded. Both SPG measuring sites are situated very close to local roads with 416 regular traffic. The roads are only about half the stream width away from the steel plates, and we therefore identified vehicle 417 traffic as a likely source for the implausible geophone impulses. This is indirectly supported by a comparison with other SPG 418 sites in Switzerland. At most of these sites only very few implausible geophone impulse counts were recorded in the past, 419 14 which is probably due to the fact that the local roads are farther away from the steel plates, generally at least once or twice 420 the stream width. 421

Data availability 422
The data cannot be made publicly available for the time being since it is used by the Tyrolean Hydropower Company 423 TIWAG, the owner and provider of the data, in an ongoing hydropower project authorisation procedure.    Table 3. Coefficients, exponents and statistical properties for the calibration relations according to eq. 1, 2, 3, 4, 5. All 606 calibration relations refer to bedload mass with D > 10 mm, or unit bedload transport rate q b,p for D > 10 mm. In 607 the equations, the units are: M in (kg), q b,p in (kg 0.5 -1 m -1 s -1 ) and IMPT in (1 0.5 -1 m -1 s -1 ). Here r 2 is the 608 correlation coefficient between values calculated with the regression relation and the recorded bedload masses. 609 Similarly, in all figures, r 2 is determined between the predicted y-value and the observed y-value (in the linear 610 domain). The relative standard deviation s e,r is determined for the ratios (M est /M) of estimated bedload mass M est 611 calculated with the regression relation and the recorded impulses IMP, divided by the recorded bedload mass M. 612 For the first three relations, the number of calibration measurements (n) are given in Table1, for the other two  613 relations they are listed in this        Fischbach: data points marked "high" and "low" refer to impulse rates higher and lower than 1 (0.5 -1 m -1 s -1 ), respectively. The dashed lines are meant to guide the eye. Figure 8. Characteristic grain size D 84 (determined for particles with D > 10 mm) versus bedload flux q b , derived from the calibration bedload samples (for D > 10 mm). Fischbach: data points marked "high" and "low" refer to impulse rates higher and lower than 1 (0.5 -1 m -1 s -1 ), respectively. The regression line is based on both the Fischbach and Ruetz data. . Linear calibration coefficient k bj (for D > 10 mm) versus impulse rate IMPT. Fischbach: data points marked "high" and "low" refer to impulse rates higher and lower than 1 (0.5 -1 m -1 s -1 ), respectively. The regression lines are based on the Fischbach data only.