Dear Author,
Please, note that changes made to the HTML content will be added to the article before publication, but are not reflected in this PDF.
Note also that this file should not be used for submitting
corrections.
AUTHOR QUERY FORM
Journal: GEOMOR Please e-mail or fax your responses and any corrections to:
Narasimhan, Karuna
E-mail: [email protected] Fax: +1 619 699 6721
Article Number: 4748
Dear Author,
Please check your proof carefully and mark all corrections at the appropriate place in the proof (e.g., by using on-screen annotation in the PDF file) or compile them in a separate list. Note: if you opt to annotate the file with software other than Adobe Reader then please also highlight the appropriate place in the PDF file. To ensure fast publication of your paper please return your corrections within 48 hours.
For correction or revision of any artwork, please consult http://www.elsevier.com/artworkinstructions.
Any queries or remarks that have arisen during the processing of your manuscript are listed below and highlighted by flags in the proof. Click on the ‘Q’ link to go to the location in the proof.
Location in article Query / Remark: click on the Q link to go
Please insert your reply or correction at the corresponding line in the proof
Q1 Please confirm that given names and surnames have been identified correctly.
Q2 Citation “D'Agostino and Lenzi (1999)” has not been found in the reference list. Please supply full details for this reference.
Q3 Citation “Church y Hassan (1991)” has not been found in the reference list. Please supply full details for this reference.
Q4, Q5, Q8 The citation “Batalla and Martin Vide, 2005” has been changed to match the author name/date in the reference list. Please check here and in subsequent occurrences, and correct if necessary.
Q6 Citation “Hassan and Church, 2002” has not been found in the reference list. Please supply full details for this reference.
Q7 The citation “Schick and Sharon (1976)” has been changed to match the author name/date in the reference list. Please check here and in subsequent occurrences, and correct if necessary.
Q9, Q10, Q11 Please supply the name of the publisher.
Q12 “G. Mathias” was captured as author's given name. Please check.
Please check this box if you have no corrections to make to the PDF file. □
Thank you for your assistance.
Our reference: GEOMOR 4748 P-authorquery-v11
Page 1 of 1
UNCORRECTED PR
OOF
1
Bedload transport rates for coarse-bed streams in an Atlantic region
2
(Narcea River, NW Iberian Peninsula)
3Q1
Daniel Vázquez-Tarrío ⁎ , Rosana Menéndez-Duarte
4 INDUROT (Universidad de Oviedo), Edificio de Investigación, c/Gonzalo Gutiérrez de Quirós, s/n, Campus de Mieres, 33600, Mieres, Spain
a b s t r a c t
5 a r t i c l e i n f o
6 Article history:
7 Received 17 June 2013
8 Received in revised form 7 April 2014 9 Accepted 8 April 2014
10 Available online xxxx 11 Keywords:
12 Bedload
13 Fluvial sediment transport 14 Coarse-bed streams
15 Tracers
16 Mountain rivers
17 Rivers from northern Cantabrian Mountain Range (NW Spain) are emplaced in an Atlantic region, draining to the
18 Bay of Biscay and saving 2000 m in a short path. Thus, high gradient streams normally develop with coarse-bed
19 sediment and a strong importance of bedload transport processes in their morphosedimentary dynamics. In the
20 present work, tagged clasts (painted and with inserted magnets) were used as tracers in order to estimate
21 bedload transport rates in two of those coarse bed streams (River Pigüeña and River Coto) belonging to
22 River Narcea drainage basin. Four methodological steps were followed: (1) grain size analysis of bed sediment;
23 (2) preparing tracer clasts in the laboratory; (3) seeding the studied reaches with the tracers, measuring their
24 displacements afterflood events; and (4) analysis of data. Ten flood episodes with the ability to disturb tracer
25 position were registered along two hydrological years (2009–2010 and 2010–2011); bedload transport rates
26 were estimated for six of these episodes. Values ranging from 1.1 to 4.1 kg/s were obtained for Pigüeña, and
27 values ranging from 0.20 to 0.28kg/s were obtained for Coto. Also, an attempt at analysis of threshold conditions
28 was tried, and a regression model between bedload transport rates and shear stress was built.
29 © 2014 Published by Elsevier B.V.
30 31 32 33
34 1. Introduction
35 Bedload transport accounts of an important fraction of the total clas- 36 tic load transported byfluvial systems. Estimation of bedload transport 37 rates has been revealed as a very difficult task because bedload trans- 38 port depends on processes that stronglyfluctuate in time and in space 39 (Gomez, 1983, 1991). Several approaches have been developed in 40 order to estimate bedload transport rates. These approaches can be 41 grouped in three different strategies.
42 On the one hand, one approach consists of the development of com- 43 plex theoretical or semiempirical relations between the hydraulic 44 parameters of theflow and the transport conditions (Meyer Peter and 45 Müller, 1948; Einstein, 1950; Parker et al., 1982; Wilcock and Crowe, 46 2003).
47 On the other hand, another approach consists in the execution of 48 field measurements during flood events. Four principal field methods 49 have been described in the scientific literature: the use of samplers 50 (Helley and Smith, 1971; Sterling and Church, 2002; Vericat et al., 51 2006); installation of sediment traps on the channel (Laronne et al., 52 1992; Reid et al., 1995; García et al., 2000; Bergman et al., 2007); the in- 53 stallation of very expensive and complex structures on a channel, such
54 as the conveyor belt ofLeopold and Emmet (1976)in East Fork River;
55 andfinally, the use of tagged clasts as“bedload transport tracers”
56 (Haschenburger, 1996; Haschenburger and Church, 1998; Hassan and
57 Ergenzinger, 2003).
58 The aforementioned methods could be grouped under the label of
59 the forward approach to the sediment transport problem; the last way
60 to accomplish transport rate estimations is the morphological or inverse
61 approach. This approach is based on the existent relationships between
62 changes in channel morphology and sediment transport (Martin
63 and Church, 1995; Ham, 1996; Ashmore and Church, 1998; Ham and
64 Church, 2000). Aerial photographs, terrestrial LIDAR models, and/or sat-
65 ellite imagery could be employed with geomorphological purposes;
66 particularly, they could be used in order to identify changes influvial
67 environments (Lewin and Hughes, 1976; Surian, 1999; O'Connor et al.,
68 2003; Hughes et al., 2006) and then to explore sediment transport
69 behavior in gravel-bed rivers (Martin and Church, 1995; Ham, 1996;
70 Ham and Church, 2000).
71 The“tracer method” constitutes a cheap and relatively easy method
72 (Hassan and Ergenzinger, 2003). Furthermore, observing and measur-
73 ing tracer displacements afterflood episodes can reveal information
74 about sediment travel distances (Hassan et al., 1991), bedload transport
75 rates (Haschenburger and Church, 1998), or even about threshold con-
76 ditions (Church and Hassan, 2002; Hassan and Ergenzinger, 2003). A lot
77 of ways to tag clasts have been employed: they go from simply painting
78 the clasts (Laronne and Carson, 1976) to inserting magnets or radio-
79 tracers (Hassan et al., 1984; Ergenzinger and Schmidt, 1995) inside Geomorphology xxx (2014) xxx–xxx
⁎ Corresponding author. Tel.: +34 984082158.
E-mail address:[email protected](D. Vázquez-Tarrío).
http://dx.doi.org/10.1016/j.geomorph.2014.04.015 0169-555X/© 2014 Published by Elsevier B.V.
Contents lists available atScienceDirect
Geomorphology
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / g e o m o r p h
UNCORRECTED PR
OOF
80 them. The main problem of this technique relies on its limitation to nar- 81 row channels (0–20 m). When channel width gets much wider, tracer 82 recovery drops down dramatically and then the method efficiency 83 (Hassan and Ergenzinger, 2003); also, safety conditions are not good 84 enough in wide channels.
85 Despite considering the foregoing limitations, in this work bedload 86 transport rates are measured using the tracer technique. The studied 87 rivers are located in the northern watershed of Cantabrian Mountain 88 Range, belonging to the River Narcea drainage basin. They constitute 89 narrow gravel-bed channels, with conditions that make adequate use 90 of the tracer method. Then, several populations of clasts were tagged 91 (painting and/or inserting magnets) and seeded over the bed surface 92 offive gravel- and cobble-bed streams; the aim was the estimation of 93 bedload transport rates for thoseflood episodes capable of triggering 94 tracer movement.
95 Bedload sediment transport is important when considering the geo- 96 morphological function of channels in the River Narcea basin and other 97 river basins from the Cantabrian Mountain Range, and this at different 98 scales (Temporal and spatial).
99 During the last decades, the working life of several hydraulic works 100 built in the lower Narcea has been reduced because of local aggradation 101 phenomena and bank erosion processes. That observation should there- 102 fore be extended to other drainage basins placed in the Atlantic Iberian 103 Peninsula (Fernández-Iglesias et al., 2006; Vázquez-Tarrio et al., 2011).
104 Particularly in lower River Narcea channel, geomorphological evolution 105 had interacted with the effects of strongfloods (Fernández-Iglesias 106 et al., 2006). Related to this,flood risk mapping (in the context of the 107 EU framework) and management requires a proper understanding of 108 sediment transport. Also, salmon species constitute an importantfish- 109 ery resource in this region, and its spawning habitat is strongly con- 110 trolled by bedload. Future interventions in order to restore or preserve 111 salmon habitats should require a proper understanding of bedload 112 transport into these channels.
113 Furthermore, in 1955–1965 two major dams have been installed in 114 the River Narcea basin for the purpose of energy supply. Comparison be- 115 tween aerial photographs from 1956 and aerial photographs taken 116 nowadays shows important geomorphological changes. For example, 117 geomorphological plan view of these channels has changed from a 118 braided channel to a single channel; also,flood dynamics seem to 119 have concentrated along a narrow corridor withinfloodplains. These 120 sorts of changes could be related to the“hungry waters” phenomena 121 (Kondolf, 1997), or otherwise, they could be linked to the general evo- 122 lution of Atlantic rivers during historical times. Both phenomena prob- 123 ably are contributing. Explaining in what degree and elucidating this 124 question requires a proper understanding of sediment budgets in 125 those basins. Bedload transport rates are a key question to consider in 126 these sediment budgets; particularly, in that geomorphological context, 127 where coarse-bed rivers and steep channel slopes are ubiquitous.
128 In this sense, a strong source of evidence exists in template latitudes 129 suggesting an important decrease of sediment supply from headwater 130 areas during the last century. That decrease in sediment supply has 131 been linked to land use changes during the twentieth century 132 (Trimble, 1977; Descroix and Gautier, 2002; Piégay et al., 2004; Batalla 133 et al., 2005). Atlantic river basins from the Iberian Peninsula are not 134 any different to the aforementioned conditions. They constitute strong- 135 ly forested basins, which had experienced an increase in its vegetal 136 cover during the last century. Slope phenomena are dispersed and, 137 in general, occur far from the higher order channels. At short to 138 medium-term timescales, the river channel conveyor belt seems to be 139 the main driver of landscape changes. Bedload transfers are again a 140 key question in order to understand recent landscape dynamics in 141 these regions.
142 Despite all of the above stated reasons, there is a complete lack of 143 quantitative data about sediment transport rates and bedload condi- 144 tions in Atlantic rivers in European climates. Previous works on bedload 145 sediment transport in rivers located in the Iberian Peninsula have been
146 carried out by authors such asGarcía et al. (1999),Batalla and Martín
147 Vide (2001), orVericat et al. (2006), but they worked with river basins
148 draining to the Mediterranean Sea not in Atlantic conditions. The
149 present work is focused on rivers draining to the Bay of Biscay where
150 climate conditions are Atlantic and humid and where quantitative
151 data on sediment transport processes are lacking. Similar works in com-
152 parable coarse bed-streams are those fromGintz et al. (1996) or
153 Haschenburger and Church (1998), for example.
154 In this sense, the main goal of the present research is on determining
155 bedload transport rates for the studied gravel- and cobble-bed streams.
156 Also, an attempt to analyze the threshold conditions of incipient motion
157 was made. Furthermore, the last step of the tracer data analysis looked
158 for a functional relation between estimated bedload transport rates and
159 the magnitude of theflow. This work portends to be a first step in order
160 to get a proper understanding of the geomorphological function of these
161 rivers. As stated above, this is important for scientific and applied
162 reasons.
163 2. Regional setting
164 The study site is in NW Spain, on the northern side of the Cantabrian
165 Mountain Range (Fig. 1A). Rivers from this area are characterized by a
166 short path from its headwater areas at roughly 2000 m height to its
167 base level in the Bay of Biscay. So they drop by 2000 m in as much 70-
168 km horizontal. This fact gives rise to high gradient river channels rela-
169 tively close to the headwater areas, hence with an important contribu-
170 tion of coarse bedload transport in their sediment transfer dynamics.
171 In thisfluvial context, five coarse-bed streams were selected for the
172 tracer experience. All of these streams belong to the drainage network
173 of the River Narcea basin.
174 The River Narcea basin has a catchment surface of ~1800 km2, which
175 grossly represents 9% of the total catchment area of the rivers draining
176 to the Bay of Biscay. In that region, climate is Atlantic and the mean an-
177 nual rainfall is about 1100 mm. Lithology of the basin comprises a diver-
178 sity of Paleozoic sedimentary rocks (mainly, siliciclastic). The vegetation
179 cover consists of an alternation of bush areas (mainly heather), beech
180 and oak forests, and also pastures. Headwater channels are streams
181 with highly coarse-bed sediment and irregular (but not ephemeral)
182 hydrologic regimes (Santos Alonso, 2011). By its side, higher order
183 channels are alluvial reaches that are characterized by a pluvionival
184 hydrological regime that typically develop coarse beds (cobble and
185 gravel). Some gauge stations are located along the River Narcea basin;
186 their locations are shown inFig. 1B.
187 Two major dams are installed in the River Narcea basin: Pilotuerto
188 dam built in 1952, with a storage capacity of 0.8 hm3; and La Barca
189 dam, built in 1966, with a storage capacity of 33.2 hm3. Both dams
190 were built with hydroelectric purposes and they only affect the main
191 River Narcea channel; none of thefive channels studied here are down-
192 stream of these dams. Impoundment index (Batalla et al., 2004) of these
193 dams is around 3.8% (Vázquez-Tarrio et al., 2011), suggesting a low ca-
194 pacity to store water inputs; this is in agreement withMarcuello and
195 Incio (2009)andJiménez Álvarez et al. (2012), who suggested a low ca-
196 pacity offlood lamination.Vázquez-Tarrio et al. (2011)andFernández
197 et al. (2012)did not found that these dams had an influence in flood
198 recurrence.
199 The average mean annual discharge in the main River Narcea chan-
200 nel (data coming from Requejo's gauge station) is 47.4 m3/s and the
201 maximum and minimum annual discharge are, respectively, 79.9 m3/s
202 and 27.9 m3/s. Higher values are recorded between December and
203 March, corresponding to the more persistent rains of the year. The
204 bankfull discharge value is 250 m3/s; this discharge corresponds to a flow with a recurrence interval of 2 years. The maximum registered 205
206 discharge in almost 40 years of gauging records was 593 m3/s.
207 The selectedfive coarse-bed streams are distributed along the tribu-
208 tary network of the drainage basin in order to have a complete treat-
209 ment of the whole catchment (Fig. 1B). The selected reaches were
UNCORRECTED PR
OOF
210 chosen for several reasons. Firstly, they were chosen in channels with 211 geomorphological features representative of the coarse-bed rivers 212 from the Northern Cantabrian watershed. Also, they constitute accessi- 213 ble points and are easy to work in. Finally, around the selected reaches 214 human intervention is minimum when compared with other channels 215 in the same basin.
216 Tracers were not placed in the main River Narcea channel because 217 the width and depth features of this channel make thefield work diffi- 218 cult and unsafe. In all cases, tracers were seeded along the surface of a 219 lateral gravel (and cobble) bar (Fig. 2), with the exception of River 220 Cibea, where tracers were deposited over a longitudinal central bar 221 very close to the pillar of a small bridge. InTable 1, the main features 222 of the studied channel reaches are summarized.
223 FollowingMontgomery and Buffington (1997), channels could be 224 classified as riffle and pool in River Pigüeña, River Coto, and River 225 Nonaya sections of the study area. By its side, in River Muniellos and 226 River Cibea, channel characteristics resemble those of a plane-bed
227 channel. With the only exception of River Cibea, all studied channels
228 are associated with smallfloodplain deposits.
229 There is a gauge station placed in the River Pigüeña, 1 km down-
230 stream from the studied point (Fig. 1B). The mean annual discharge in
231 this gauge records a value of 4.4 m3/s and the average maximum and
232 minimum discharge are respectively, 1.1 and 9.5 m3/s. The maximum
233 discharge registered in almost 40 years of gauge records has been 155
234 m3/s. In River Pigüeña, the bankfull discharge takes a value of 70 m3/s,
235 which corresponds to a recurrence interval of roughly 1.5 years. Close
236 to River Coto, but still in the River Narcea channel, exists another gaug-
237 ing station (Corias gauge station;Fig. 1B). Mean annual discharge takes
238 a value of 15 m3/s in this station, and the maximum discharge registered
239 in this gauge station has been 250 m3/s. Bankfull discharge in River Coto
240 takes a value of 17 m3/s, which corresponds to aflow with a recurrence
241 interval of roughly 1.5 years.
242 In the remaining three reaches (River Cibea, River Nonaya, and River
243 Muniellos), there are no gauge data close enough, so it is not possible to
A
B
Fig. 1. (A) Location of River Narcea drainage basin in the northern Cantabrian Range watershed.(B) Location of the studied reaches and gauge stations along the River Narcea basin.
UNCORRECTED PR
OOF
244 properly define detailed hydrological features and bankfull discharge.
245 This fact explains why, despite placing tracers in thesefive reaches, 246 quantitative analysis of bedload transport rates were only made in the 247 River Pigüeña and River Coto; those are the only ones of the study 248 reaches that are close enough to a gauge station to make reasonable 249 and reliable estimations of the time duration and magnitude of the 250 flow for the studied flood episodes. Despite this, data provided by the 251 tracer technique in the remaining three channels were essential in 252 order tofind a functional relation between displacement and grain 253 size. This is why the tracer experiment was carried out also in these 254 three channels. We tried to get enough data about tracer displacement 255 and have it well distributed along the whole basin in order to apply 256 Church and Hassan's (1992)model; the idea was tofind a good fit be- 257 tween the distance of travel of the sediment and the grain size, which 258 is indispensable to apply the method used here (explained below).
259 3. Materialsand methods 260 3.1. Field and laboratory stage 261 3.1.1. Grain size analysis
262 The grain size distribution analysis was done for the bed surface sed- 263 iment following the pebble count method ofWolman (1954). A grid of 264 roughly 15×10 m was defined over each study site. Around 100–150 265 clasts were measured in each study site. In order to randomly sample 266 the surface of the bed, the sampling was started in one corner of the 267 grid, and one clast was measured after every step; without looking to 268 the ground when stepping, the clast that touched the tip of the boat 269 was taken to be measured (Kondolf et al., 2003). Axis-b was measured 270 for each clast using a steel template similar to that used byHey and 271 Thorne (1983).
272 Also, a bulk sediment grain size analysis was done in the River 273 Pigueña and River Coto section, where the quantitative estimations 274 will be concentrated. Using a sprayer, bed surface was painted. A square 275 with a side of 3 times the diameter of the biggest clast observed in the 276 bed was covered with the paint. Then, all the colored clasts were ex- 277 tracted and not used in the sampling, in order to avoid the sediment 278 from the armored layer (Bunte and Abt, 2001). After that and using a 279 shovel, it was extracted all the sediment until reaching a depth of
280 roughly 500 mm, followingDiplas and Fripp (1992). A mass of 120 kg
281 of subsurface sediment was taken in the River Pigueña and a mass of
282 90 kg was taken in the River Coto. The sediment extracted was sieved
283 and weighted. The coarsest size classes were sieved and weighted in
284 thefield; the rest were carried to and weighted in the laboratory. At
285 the end, the heaviest measured clast has not represented more than
286 the 5% of sample mass, neither in River Pigüeña or River Coto.
287 3.1.2. Tracer preparation and seeding
288 Four experiences of collecting, tagging, and seeding of tracers were
289 carried out (Table 2). Clasts of thefirst experience were painted in
290 situ; then it is reasonable to assume that they had the same grain size
291 distribution as the surface sediment. Clasts used to make the tracers of
292 the remaining experiences were picked up from the surface of the bed
293 belonging to three different size classes, followingEaton et al. (2008):
294 the semi-ϕ size class corresponding to the surface D50and the semi-ϕ
295 classes immediately upper and lower.
296 The surface of each painted tracer received two hands of paint. Blue
297 and yellow colors were used and the paint employed was the same that
298 is typically used in swimming pools in order to minimize the environ-
299 mental impact. To insert the magnets, each clast was drilled, opening
300 a hole with a diameter of 10 mm and with an average depth of roughly
301 2.5 cm (when the size of the clast let it). After drilling, a couple of ceram-
302 ic disc magnets of 10 mm diameter were inserted into each hole; then,
303 the hole wasfilled slowly with epoxy resin. Once the resin dried, each
304 tracer was painted in blue color.
305 When preparing the tracers in the lab, grain size of each clast was
306 measured (through the measurements of a-, b- and c-axes); also, each
307 clast was weighted. Afterwards each clast was labeled with a number.
308 Tagged stones were then seeded over the surface of the bed of each
309 study reach. They were seeded following a line transverse to the main flow direction. FollowingEaton et al. (2008), once placed over the sur- 310
311 face, clasts were crushed with the heel of the boat. This was done in
312 order to recreate in some way the natural arrangements of gravel clasts
313 on the bed of a river.
314 3.1.3. Field measurements
315 After preparing the clasts and seeding them on thefield, tracer dis-
316 placements were measured after eachflood with the capacity to move
t1:1 Table 1
t1:2 Main characteristics of the channel in each reach selected for the work described in the current paper.
Study reach Low water channel width (m) Bed slopea D50surface (mm) Bar maximum width (m) Bar maximum length (m) t1:3
Pigüeña 25 0.007 56 20 90
t1:4
Coto 15 0.01 88 15 60
t1:5
Cibea 10 – 65 5 10
t1:6
Muniellos 11 0.014 60 7 15
t1:7
Nonaya 10 – 81 7 12
t1:8
t1:9 aTopographic profile done with Total Station (Leica TCR 703).
Fig. 2. (A) Lateral gravel bar in River Pigüeña (location 1 inFig. 1A) and (B) Lateral bar in River Coto (location 2 inFig. 1A).
UNCORRECTED PR
OOF
317 them. Painted clasts were searched visually.“Magnet tracers” were 318 searched visually and also using a magnetic detector Schondstedt GA- 319 52 CX. Axis-b of the recovered tracers was measured when the label 320 was lost and/or unidentifiable, making it difficult to track a particular 321 tracer. Tracer displacements were measured with a tape measure 322 following the main longitudinal axis of the channel.
323 3.2. Data analysis stage
324 3.2.1. Bedload transport estimates
325 By means of a dimensional analysis, bedload transport rates (ib) 326 could be expressed by the following product (Hassan et al., 1991;
327 Haschenburger and Church, 1998):
ib¼d.
t w h 1−pð Þ ρ ð1Þ
329
329 where d is the average travel distance of bed sediment, t is the time du- ration of the transport episode, w and h are the active channel width and 330 depth, respectively, p is the sediment porosity andfinally, ρ is the den- 331 sity of mineral grains, which is conventionally assume to be 2.650 g/m3. 332 This equation represents the ratio between the mass of sediment 333 transferred (expressed as a density-volume product) during a transport 334 episode and the time duration of the transport episode. In this work, 335 bedload transport estimates were made for the sixfloods registered in 336 the River Pigüeña and River Coto channels. Estimating bedload trans- 337 port rates implied determining the values for each of the constraining 338 parameters involved in Eq.(1).
339 For the active channel width (w), the channel bed perimeter was 340 measured over the channel section profiles drawn with total station 341 data. A value of 40 m was measured in River Pigüeña and 20 m in 342 River Coto.
343 Estimating active depth (h) was a bit more complicated because 344 “magnet tracers” did not give the expected information: only some 345 buried tracers werefinally recovered. So an indirect approach had to 346 be followed using the scour-and-fill depth model developed by 347 Haschenburger (1999)for similar gravel-bed streams from Canada 348 and England.
349 Time duration of transport events (t) was extracted from the gaug- 350 ing records. During thefirst hydrological year spanned by this research 351 (2009–2010), visits to thefield were made regularly. The idea was to 352 define a reasonable value of discharge for which it could be expected 353 to see disturbance in tracer positions. Then, the maximum time duration 354 of each transport episode could be established as the time interval be- 355 tween thefirst and last moment when those values were reached dur- 356 ing the hydrograph. Some of the studied episodes were multipeaked;
357 followingHassan et al. (1991)andHaschenburger (1996), only the 358 time interval of thefirst, more intense peak was used as time duration 359 for those transport events.
360 A value of porosity (p) equal to 0.28–0.29 is obtained by using 361 Komura's formula (1961), whileCarling and Reader's (1982)relation 362 gives a value of 0.17–0.19. The authors decided to use 0.2, an intermedi- 363 ate value similar to that used byHaschenburger and Church (1998)and 364 in the same range of porosity used byMartin and Church (1995)and 365 Ham and Church (2000)in comparable streams.
366 For the travel distance term (d), distance data coming from 367 displaced tracers were used. A question arises suddenly: tracers only
368 reflect the displacement of some size classes, not the total grain size dis-
369 tribution. So it is necessary to infer in some way the distance travelled
370 by the rest of the size classes. To accomplish this we used the heuristic
371 model proposed byChurch and Hassan (1992). These authors took the
372 best published data about tracer experiments coming from gravel-bed
373 rivers in a variety of environments and hydrological regimes. They
374 searched for a functional relation between travel distance and grain
375 size diameters and they found how the following expressionfits very
376 well the analyzed data:
L.
L50¼ a 1− logD.
D50
b
ð2Þ 378 378 where L is the mean travel distance for clasts of size D, L50is the mean travel distance for the median size clasts in the surface grain size distri-
379 bution, and D50is the median of the subsurface grain size distribution.
380 Here, grain size data were scaled by D50surface, not subsurface; for
381 this reason, scaled grain size was multiplied by a factor of 2.2 in the
382 Eq.(2), followingWilcock (1997). This was done to preserve the origi-
383 nal form of the relation found byChurch and Hassan (1992). We used
384 data coming from thefive studied channels in order to have enough
385 data tofind a better fit.
386 So in the present work, data of travel distances coming from the trac-
387 er experiments were plotted against grain size diameter. By means of a
388 wild-bootstrapping goodness-of-fit and regression method (Stute et al.,
389 1998), the best intercept and exponent in Eq.(2)— with a thrust confi-
390 dence level of 95%— was searched for the field data obtained here.
391 Wild-bootstrapping goodness-of-fit test worked with the following
392 null hypothesis: regression equation belongs to the parametric family
393 of functions represented by Eq.(2). Using this Eq.(2)and thefitted
394 values, it was possible to determine mean travel distance for each
395 semi-ϕ size class.
396 Then, using Eq.(1)(with all the values assumed for the constraining
397 parameters), a fractional transport rate ibiwas estimated for each size
398 class. Hence, mean bedload rate for the total event could be calculated
399 as the sum of all fractional transport rates, weighted by the proportion
400 of each size class in the grain size distribution; that is:
ib¼X
ib j fj ð3Þ
402 402 where ibis the average transport rate of the event, and fjis the propor- tion of the j-size in the grain size distribution. FollowingWilcock and
403 McArdell (1993)we decided to use surface distribution proportions to
404 do the weighted sum (Eq.(3)). At a scale event, clasts are put in motion
405 directly from the surface, so it seems more reasonable to use the surface
406 distribution.
407 3.2.2. Threshold stresses
408 Threshold stresses for incipient motion of a clast are quantified by
409 the following expression (Komar, 1987; Church, 2006):
τ ¼ θ ρð s−ρÞ g D ð4Þ
411 411 whereρsis the density of sediment,ρ is the density of water (1000 g/m3), g is the gravity acceleration (9.81 m2/s), andθ is the critical Shields
412 parameter for entrainment of the clasts of size D. Some authors argued
413 that the critical Shields parameter could vary inside a sediment mixture
t2:1 Table 2
t2:2 Brief description of the different experiences with tracers: date of seeding, tagging method, sample size and grain diameter of tracers.
Seeding date River Number of tracers Tracer sizes (mm) Tagging method
t2:3
Experience 1 July–August 2009 Pigüeña/Coto/Cibea Roughly 225 in each river All grain sizes of bed In situblue paint t2:4
Experience 2 May 2010 Pigüeña/Coto/Cibea 186/204/152 16–128/32–128/32–256 Laboratoryyellow paint
t2:5
Experience 3 September/November 2010 Pigüeña/Coto 177/125 32–128/32–256 Inserted magnets/blue paint
t2:6
Experience 4 October 2010/February 2011 Nonaya/Muniellos 220/218 45–128/32–128 Laboratoryblue paint
t2:7
UNCORRECTED PR
OOF
414 following an exponential function (hiding function) (Parker and 415 Klingeman, 1982; Parker et al., 1982; Andrews, 1983):
θ ¼ a D D50
−b
ð5Þ 417
417 where the intercept a represents the critical Shields parameter for the median size (D50) and the intercept b varies between 0 and 1. A 418 0-value corresponds to“totally selective transport” and a 1-value 419Q4 corresponds to “equal mobility” conditions (Batalla and Martín 420 Vide, 2001; Parker, 2008), while intermediate values are somehow 421 a combination of the two styles of entrainment: relative size effects, 422 related to hiding and protrusion, are important, but still absolute 423 effects of size have influence on incipient motion. Equal mobility 424 has been found by some authors (Parker et al., 1982; Andrews, 425 1983; Parker, 1990), whileothers have found some degree of size- 426 selective entrainment (Komar, 1987; Ashworth and Ferguson, 1989;
427 Church and Hassan, 2002).
428 In principle, tracer data could allow us to determine the threshold 429 stresses for the studied streams. To do this, four different methods of 430 analyzing tracer data were used here: (i) combiningfield observa- 431 tion of tracer positions in regular visits to thefield and interpretation of 432 the discharge values recorded in gauging stations; (ii) assumption of a 433 constant value of 0.045 for the critical Shields parameter (Miller et al., 434 1977; Church, 1978; Yalin and Karahan, 1979; Haschenburger and 435 Church, 1998; Bigelow, 2005; Church, 2006); (iii) the“largest clast” 436Q5 method (Wilcock, 1988;Batalla and Martín Vide, 2001; Church and 437 Hassan, 2002); and (iv) the“reference stress” method (Parker et al., 438Q6 1982; Wilcock, 1992;Hassan and Church, 2002;Wilcock et al., 2009).
439 3.2.3. Relation“Bedload transport rates-Shear stress”
440 Stress values for each transport episode were estimated as the 441 hydraulic radius—slope product:
τ ¼ ρ g S R ð6Þ
443
443 where S is the channel bed slope, and R is the hydraulic radius; this equation implies assuming normalflow conditions (Parker, 2008).
444 Some authors suggested dividing shear stress in one component linked 445 to form resistance and another one linked to grain resistance (Jarret, 446 1985; García et al., 1999; Wilcock et al., 2009); these authors suggested 447 using only the component of shear stress linked to grain resistance.
448 However,Parker and Peterson (1980)argued that form resistance 449 could be neglected in gravel-bed rivers during transport conditions;
450 otherwise,Hey (1988)andMillar (1999)still suggested that in certain 451 situations form resistance could be significant. Finally, in this work we 452 decided to followParker (2008), who claimed that a good and reliable 453 method is still not available to properly decompose shear stress in 454 coarse-bed rivers, making Eq.(6)a good choice.
455 Minimum values of water depth for each transport episode were 456 determined in thefield looking for evidence (floating deposits, log 457 deposits, water marks, etc.) of the water level reached by theflow 458 (Fernández Iglesias, 2012). Then, knowing the water stage, the hydrau- 459 lic radius could be directly measured over the drawn channel section 460 profile.
461 Several authors have stated that sediment transport rates covari- 462 ate with shear stress according to an exponential function of the“ex- 463 cess shear stress”(Meyer-Peter and Müller, 1948; Wilcock et al., 464 2009): this is the difference between the actual basal shear stress 465 acting on the grains and the critical shear stress needed for entrain- 466 ment. Here, an exponential regression of this kind was searched over 467 the data.
468 To correlate transport rates with shear stress, dimensionless bedload 469 transport rates (ib⁎) and dimensionless shear stress were used in order 470 to avoid scale differences between River Pigüeña and River Coto.
471 Dimensionless shear stresses are calculated by the Shields number; by
472 its side, dimensionless bedload transport rates (ib⁎) are computed by
473 the dimensionless Einstein number:
ib¼ ib ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s−1 ð Þ g D3
q ð7Þ
475 475 where q is the bedload transport rate per unit width (in volume units), s is the specific weight of sediment (s = 1.65), and D is the grain size.
476 4. Results
477 4.1. Field observations
478 InFig. 3the grain size distribution curves are shown. In River
479 Pigüeña and River Coto, surface grain size distribution seems to be
480 coarser than the subsurface, suggesting some degree of armoured
481 texture.
482 As stated above, regular visits to thefield sites during the first stages
483 of the research let authors determine a minimum discharge for which it
484 was reasonable to expect tracer displacements. Thus, a minimum value
485 of 10 m3/s was determined in the River Pigüeña study section and a
486 value of 21 m3/s in the River Coto study section; in the remaining
487 study sections, no gauging data were available.
488 During the hydrological years 2009–2010 and 2010–2011, 10flood
489 episodes with the ability to disturb tracer positions were analyzed
490 (Table 3). The displacements measured after each studiedflood are
491 shown inTable 4. In River Pigüena and River Coto, displacements do
492 not seem to be simply correlated with peak discharge: in River Pigüeña,
493 the higher displacements were measured for the“June (2010)flood”,
494 the one with the lowest peak; also, in River Coto, the larger displace-
495 ments were measured for the“January (2010)flood.” Related to active
496 width, all the transport episodes produced disturbance of tracers
497 along the whole length of the transverse line where tracers were
498 seeded.
499 In the case of River Pigüeña, the maximum peak discharge for the
500 registeredflood events represented discharges between 1.4 and 1.6
501 times the bankfull. In the case of River Coto, the maximum peak dis-
502 charge for the registeredflood events represented discharges around
503 1.5–1.8 times bankfull. In the remaining studied sites, the lack of
504 gauge data makes defining the ratio between registered flow and
505 bankfull discharge impossible. Nevertheless, the observed water and flood marks suggest flows only a bit higher than, and close to, bankfull 506
507 discharge.
508 4.2. Tracer recovery
509 A total number of 1960 tracers were used in this work. After the 10
510 studiedfloods, 942 clasts were recovered (around 47%).Table 4is a
511 summary of tracer recovery of the different events. Mean tracer recov-
512 ery in the River Pigüeña was roughly 43%; in River Coto tracer recovery
513 was around 22%. In River Nonaya, tracer recovery was also very good
514 (56%). In River Cibea, theflood episode of June was very severe and no
515 tracers were recovered. Finally, in River Muniellos, all tracers were re-
516 covered, but only one event could be studied and it was a low intensity
517 one.
518 Recovered buried clasts were scarce, and the maximum depth found
519 for buried clasts was around 15 cm (around 0.8 times D90) in River
520 Pigüeña and 10 cm (around 0.5 times D90) in River Coto.
521 4.3. Bedload transport rates and travel distances
522 Wild-bootstrapping goodness-of-fit test gives a p-value of 0.78
523 (p-valueN 0.05). Null hypothesis is not rejected: with an error
524 level of 5%, sampling data do not allow rejection of the parametric
525 model represented by Eq.(2)as a regression model for the data;
UNCORRECTED PR
OOF
526 that means, Eq.(2)is statistically significant as a regression model.
527 Then, the regression analysis was done. Results appear onTable 5 528 and Fig. 4. There are some differences with the original fit of 529 Church and Hassan (1992), but in general thefit obtained here de- 530 scribed the same behavior: travel distances are weakly dependent 531 on grain size for clastsfiner than 2.2 times the subsurface D50diam- 532 eter; otherwise, clasts coarser show travel distances strongly depen- 533 dent on grain diameter.
534 Total transport rates and unit transport rates are higher in River 535 Pigüeña than in River Coto (Tables 6 and 7).Fig. 5shows the fractional 536 transport rates for the different size classes. It is possible to see how 537 transport rates slightly decrease with grain size in both reaches.
538 4.4. Threshold stresses
539 As stated above, the highest discharge determined in River Pigüeña
540 without tracer movement was 10 m3/s. In River Coto a value of 21 m3/
541 s has been estimated. Field evidence of water stage made it possible to
542 estimate the basal shear stresses associated with this discharge: 31 Pa
543 in River Pigüeña and 112 Pa in River Coto. Those values represent a min-
544 imum shear stress for incipient motion.
545 Table 8summarizes the threshold shear stresses determined by the
546 different methods employed here. Results obtained assuming a constant
547 value of 0.045 for the critical Shields parameter suppose a shear stress of
548 41 Pa for D50incipient motion and 131 Pa for D90incipient motion in 100
Subsurface-Pigüeña
70 80 90
Passing fraction (%)
Subsurface-Pigüeña Surface-Pigüeña Tracers-Coto Subsurface
50 60
Subsurface-Coto Surface-Coto Tracers-Coto
30 40
0 10 20
1000 100
10 1
0,1 0,01
Grain size (mm)
Fig. 3. Grain size distribution in River Pigüeña and River Coto sections of study. The grain size distribution of the samples of tracers is also plotted. Surface and subsurface D50in River Pigüeña measure 56 and 28 mm, respectively. In River Coto they measure 88 and 70 mm, respectively.
t3:1 Table 3
t3:2 Brief description of the studied transport episodes (in the table there is no information about transport episodes that occurred in Cibea, Nonaya or Muniellos: that is because the absence of t3:3 gauging data).
Date Main peak time duration (h) Maximum mean
discharge (m3/s)
Maximum peak discharge (m3/s)
Water level derived from marks (m)
Basal shear stress (Pa) t3:4
15–18 January 2010 (Pigüeña river) 72 32.04 103.53 2.2 114.8
t3:5
10–24 June 2010 (Pigüeña river) 102.25 80.35 100.00 2.1 112.1
t3:6
31 October–20 November 2010 (Pigüeña river) 43 78.71 107.54 2.2 117.6
t3:7
13–16 January 2010 (Coto river) 96 26.93 28.4 1.75 131.0
t3:8
11–17 June 2010 (Coto river) 46.75 27.60 30.1 1.80 135.4
t3:9
6–8 January 2011 (Coto river) 44.25 25.40 25.6 1.6 130.7
t3:10
t4:1 Table 4
t4:2 Summary offield results with the tracer experiences: Lmean—mean displacement of tracers; Lmax—maximum displacement measured for tracers; L50—displacement measured for the D50 t4:3 size class.
Studyreach Transport event Tagging method Initial number of tracers Number of recovery tracers Recovery ratio (%) Lmean(m) Lmax(m) L50(m) t4:4
Pigüeña January 2010 Painted aprox. 225 97 Aprox. 43 50 208 54
t4:5
June 2010 Painted 186 21 11 66 243 66
t4:6
November 2010 Magnets 177 136 77 6 27 9
t4:7
Coto January 2010 Painted aprox. 225 45 Aprox. 20 19 37 21
t4:8
June 2010 Painted 204 35 17 11 34 11
t4:9
January 2011 Magnets 125 38 30 15 53 14
t4:10
Cibea January 2010 Painted aprox. 225 225 Aprox. 100 2 2.2 1
t4:11
June 2010 Painted 152 0 0 – – –
t4:12
Nonaya February 2011 Painted 220 124 56 7 27 7
t4:13
Muniellos March2011 Painted 219 219 100 3 12 4
t4:14
Total 1958 940 48
t4:15
UNCORRECTED PR
OOF
549 River Pigueña. In River Coto, obtained values of shear stresses were 550 64 Pa for D50and 145 Pa for D90.
551 In both streams, shear stresses for D50are higher than those deter- 552 mined byfield observation of tracer positions but lower than the 553 shear stresses estimated for the transport events. In relation to shear 554 stresses for D90entrainment, values obtained assuming a constant critical 555 Shields parameter are higher than the shear stresses estimated for the 556 transport episodes.
557 Largest measured clast sizes in River Pigüeña were 170 mm (January 558 2010), 130 mm (June 2010), and 110 mm (November 2010). In River 559 Coto, largest measured clasts sizes were 160 mm (January 2010), 140 560 mm (June 2010), and 160 mm (January 2011). InFig. 6, largest moved 561 clast sizes are plotted against the shear stresses. In thisfigure, the 562 outer envelope curve of the plotted data follows the next coupled 563 expressions:
τ ¼ 0:0498 Dj.
D50sub
0:215
ð8Þ 565
565 566
τ ¼ 0:275 Dj.
D50sub
−1
ð9Þ
568 568 where Eq.(8) is applied when clasts of j-size have a diameter Djb 4.08 · D50suband Eq.(9)when diameter of clast DjN 4.08 · D50sub.
569 D50subis the diameter of the median size in the subsurface grain size
570 distribution.
571 In River Pigüeña, a value of 52 Pa was obtained with this set of ex-
572 pressions for D50entrainment, and a shear stress of 125 Pa was obtained
573 for D90entrainment. By its side, values of 75 Pa for D50entrainment and
574 202 Pa for D90entrainment were obtained in River Coto. Again, shear
575 stresses for D50entrainment calculated by this method are higher than
576 minimum values determined by observation and lower than the basal
577 shear stresses of the transport episodes; shear stresses for D90incipient
578 motion are much higher than those shear stresses determined for the
579 transport episodes.
580 InFig. 7, dimensionless fractional transport rates (W⁎) are plotted
581 against shear stress. Using visuallyfits, it is possible to determine ref-
582 erence shear stresses for each size class (Fig. 8). A shear stress of
583 roughly 133 Pa is found for the entrainment of all size classes in
584 River Pigüeña. In River Coto, a value around 126 Pa was found for
585 almost all size classes (Table 8). These shear stresses are much
586 higher than the minimum values for the entrainment determined
587 byfield observation of tracer positions; in the case of River Pigüeña,
588 those values are even higher than the basal shear stresses calculated
589 for the transport events.
590 4.5.“Transport rates-shear stress”regression model
591 Using a value of 0.045 for the critical Shields parameter, a goodfit
592 was found between dimensionless transport rates and excess of dimen-
593 sionless shear stresses (p-valueb 0.05). Results of thefit are shown in
594 Table 9andFig. 9. Regression equation follows the next expression:
ib¼ 12:16 τ −0:0454:14 ð10Þ
596 596 where ib⁎ is the dimensionless transport rate and τ⁎ the dimensionless shear stress. Dimensionless shear stresses and dimensionless transport
597 rates were scaled according to surface D50.
598 5. Discussion
599 5.1. Bedload transport estimation
600 Bedload transport rates have been estimated following Eq.(1), used
601 by other authors in previous works; for example,Hassan et al. (1991)or
602 Haschenburger and Church (1998). Reliability in the results depends in
603 some way on the criteria followed when defining the constraining pa-
604 rameters of that equation.
605 As explained above, channel bed perimeter was used as active chan-
606 nel width. Tracers were recovered across the whole surface of the stud-
607 ied reaches, without appreciable differences toward one margin or the
t5:1 Table 5
t5:2 Fit test of applying Eq.(2)to the tracer data;fitted values are compared with the original values inChurch and Hassan (1992)and also with values found byHaschenburger (1996).
Bestfit Thrust interval (c.l. 95%)
Q3t5:3 Church y Hassan (1991) Haschenburger (1996)
Intercept a 1.33 0.87–1.88 1.77 1.16
t5:4
Exponent b 0.65 0.09–1.14 1.35 1.15
t5:5
Hassan and Church (1992) Best fit
0,01 0,1 1 10
10 1
0,1
Pigueña river Coto river Cibea river Muniellos river Nonaya river
D/D50 L/L50
Fig. 4. Normalized travel distance plotted against scaled grain size. Three things are shown in the plot: (i) distances travelled by the tracers used in this research; (ii) the bestfit found for these data followingChurch and Hassan (1992), and (iii) the originalfit found by Church and Hassan (1992)using the best published data (see the main text).
t6:1 Table 6
t6:2 Mean travel distances of bed sediment estimated for each studied transport episode using
t6:3 Eq.(2)and the exponent and intercept obtained in the regression test (Table 5).
Pigüeña Travel distance Coto Travel distance t6:4
January 2010 56 m January 2010 23 m t6:5
June 2010 55 m June 2010 11 m t6:6
November 2010 8 m January 2011 15 m t6:7
UNCORRECTED PR
OOF
608 other. Furthermore, tracers were seeded following transversal lines that 609 were disorganized in practically its whole length. So it seems reasonable 610 to assume that the whole bed was active during at least one moment 611 through the course of the studied transport episodes.
612 On the other hand, more uncertainty exists with the quantification 613 of active channel depth. Using the scour-and-fill depth model devel- 614 oped byHaschenburger (1999), we found active depth values of rough- 615 ly 20–25 cm in River Pigüeña and around 7–7.5 cm in River Coto. Those 616 represent values around D90in River Pigüeña and around D50in River 617 Coto.“Magnet tracers” did not give the expected information about ac- 618 tive depth, as only a few buried clasts werefinally recovered. The max- 619 imum depths found for the buried clasts do not seem incompatible with 620 those estimated here byHaschenburger's (1999)model. But while the 621 totality of tracers from the original samples were not recovered, it is 622 not possible to assure if the remaining were buried below the limit of 623 sensitivity of the magnetic detector or were carried long distances.
624 Bigelow (2005)has pointed out some limitations of theHaschenburger 625 (1999)model. Handling in mind the main points ofBigelow (2005), we 626 still considered thatHaschenburger's (1999)model could be assumed 627 as a good approximation in coarse-bed rivers similar to the two streams 628 studied here, at least for the average active depth.
629 Talking about the time duration of transport events, we should em- 630 phasize how values handled here represent maximum mean values.
631 Existent information does not let us to be more precise. Furthermore,
632 three of the studied events were multipeaked (June 2010 in River
633 Pigüeña and River Coto, and November 2010 in River Pigüeña). We de-
634 cided to use the time duration of thefirst peak for those events, assum-
635 ing that clasts interact with each other during a transport episode and
636 rapidly adopt stable arrangements and steady positions. Field observa-
637 tions made during the November 2010flood agree with this behavior.
638 Furthermore, observing data inTable 4, it seems as if time duration of
639 the transport event is more important than peak discharge when talking
640 about the mean distance of bed sediment displacement; in fact, higher
641 displacements are observed for the longest studied events.
642 Lastly, distance parameter in Eq.(1)relies on thefield measures of
643 recovered tracers. The tracer recovery for the painted tracers is in the
644 range of other similar works. Recovery ratios of 60% were found by
645Q7 Schick and Sharon (1974), 40% of tracers were recovered byHassan
646 et al. (1984), and around 10% were recovered byLaronne and Carson
647 (1976). Recovery values of magnet tracers were 77% in River Pigüeña
648 and 30% in River Coto.Hassan (1990)recovered 50% of tracers, while
649 Lekach (1992)andHaschenburger (1996)recovered more than 80%.
650 Values of River Pigüeña are good compared with the values obtained
651 by other authors; values for River Coto are low, but comparable to the
652 30% given byHassan et al. (1999). In general, recovery values are
653 lower for River Coto than River Pigüeña; this is probably related to the
654 more difficult working conditions in its channel: a deep pool existing
655 roughly 100 m downstream made searching for the tracers extremely
656 difficult.
657 5.2. Bedload transport rates
658 Bedload transport rates found here seem to be consistent with trans-
659 port rates obtained by other authors on mountain coarse-bed rivers
660 (Table 10). Mountain and upland coarse-bed rivers have been named
661 by other authors as low “transport intensity” rivers (Church and
t7:1 Table 7
t7:2 Bedload transport rates; unit transport rate is the transport rate per unit of width.
River Event Transport rate (kg/s) Unit transport rate (kg/m∙s) t7:3
Pigüeña January 2010 4.06 0.10
t7:4
June 2010 2.54 0.06
t7:5
November 2010 1.1 0.03
t7:6
Coto January 2010 0.20 0.01
t7:7
June 2010 0.21 0.01
t7:8
January 2011 0.28 0.01
t7:9
Pigüeña river (January 2010) Pigüeña river (June 2010) Pigüeña river (November 2010) Coto river (January 2010) Coto river (June 2010) Coto river (January 2011) D(mm)
10-6 10-4 10-3 10-2
500 50
5
Fractionaltransport rates (g/ms)
Fig. 5. Fractional transport rates: transport rates for each size class and each studiedflood event.
t8:1 Table 8
t8:2 Summary of the analysis of threshold of motion (in the table appears the threshold shear stresses for several sizes of the surface grain size distribution and obtained with the different t8:3 methods employed in the data analysis).
Reach Method Grain diameter
t8:4
D20 D40 D50 D70 D84 D90 D99
t8:5
Pigüeña Shields 23.3 Pa 33.5 Pa 40.8 Pa 65.6 Pa 94.7 Pa 131.1 Pa 364.2 Pa
t8:6
“Largest clast” 26.5 Pa 41.2 Pa 52.4 Pa 93.2 Pa 124.6 Pa 124.6 Pa 124.6 Pa
t8:7
“Reference stress” 131.9 Pa 132.7 Pa 133.1 Pa 134.2 Pa 135.0 Pa 135.7 Pa 138.0 Pa
t8:8
Coto Shields 35.0 Pa 52.4 Pa 64.1 Pa 87.4 Pa 123.8 Pa 145.7 Pa 218.5 Pa
t8:9
“Largest clast” 35.7 Pa 58.4 Pa 74.5 Pa 108.6 Pa 165.8 Pa 202.0 Pa 311.0 Pa
t8:10
“Reference stress” 126.1 Pa 126.5 Pa 126.8 Pa 127.1 Pa 127.5 Pa 127.7 Pa 128.2 Pa
t8:11
UNCORRECTED PR
OOF
662 Hassan, 2005a, b). Indeed, because of its coarse and rough bed, sediment 663 transport in those rivers mainly occurs close to the threshold conditions 664 of entrainment (Church, 2006). Thus, size selective and partial transport 665 (Wilcock and McArdell, 1993, 1997) tends to occur— although all grain 666 sizes are taking part in the movement, the proportion of inactive clasts 667 is higher for the coarser sizes; as it was shown inFig. 5, fractional 668 transport rates slightly decrease with grain size, suggesting a kind 669 of size-dependent transport in the studied channels. These transport 670 mechanisms partially determine a sediment transport regime of low 671 intensity in this kind of mountain coarse-bed streams (Church and 672 Hassan, 2005a,b).
673 The bedload transport rates estimated here are compatible with this 674 scheme. The studied transport episodes represented frequentfloods of 675 moderate intensity. Possibly during higherflow episodes, transport 676 rates could be higher than those found here.
677 5.3. Threshold stresses
678 Fig. 10andTable 8compare the results of the threshold analysis ob- 679 tained following each method in River Pigüeña and River Coto. No 680 method gives satisfactory results. Field observation of tracer positions 681 gives a good approximation to the incipient motion of the bed as a 682 whole, but it says nothing about differences in mobility between differ- 683 ent size classes. Furthermore, observed values are only minimum values
684 of stress because there is a small gap between maximum observed
685 discharges without movement and minimum discharges with tracer
686 disturbance.
687 Assuming a constant value for the critical Shields parameter maybe
688 could constitute a good approximation to the incipient transport of
689 the bed as a whole, but it does not seem valid as an approach to the
690 entrainment values of the different size classes. This assumption sup-
691 poses neglecting contribution of hiding and protrusion effects on en-
692 trainment and also neglecting all the roughness effects at a clast scale,
693 which all of them are claimed to be important in gravel-bed rivers by
694 all authors. Even some authors have talked of equal mobility (Parker
695 and Klingeman, 1982) in gravel-bed rivers: that means, sediment trans-
696 port in these rivers seems to occur suddenly for all clasts independently
697 of their sizes, at least with unimodal sediments (Wilcock, 1993). All of
698 these facts escape from consideration when assuming a constant critical
699 Shields value.
“Largest clast” method results imply size-selective transport for the 700 finer sizes and equal mobility for the coarser ones. This method gives re- 701
702 sults that do not seem conflicting with field observations. But its meth-
703 odological biases (largest tracer displaced could not be synonymous
704 with largest clast displaced), and the limited number of observations
705 forces us to be very cautious.
“Reference shear stress” method produces results that mean equal 706 707 mobility. The problem with this method is purely quantitative: it gives
708 very high values for the beginning of transport— in River Pigüeña,
709 these values are even higher than the discharge value of theflood epi-
710 sodes analyzed. Also, fractional transport rates are in some degree size
711 dependent and slightly decrease with grain size. But these two facts
712 are not necessarily inconsistent: certainly, entrainment could be equal
713 for all sizes (equal mobility); while at the same time, displacement
714 could be size dependent (Church and Hassan, 1992; Hassan and Church,
715 1992), and the proportion of inactive clasts could increase with size class
716 (Wilcock and McArdell, 1993, 1997), giving rise to both effects of decreas-
717 ing fractional transport rates with grain diameter (partial transport
718 conditions).
719 In summary, the threshold question is not well solved with the
720 obtained data, and results of the different methods are in some ways
721 inconsistent. Differences between several methods have also been
722 found by other authors (Wilcock, 1988;Batalla and Martín Vide, 2001; Q8 723 Church and Hassan, 2002).Buffington and Montgomery (1997)attrib-
724 uted these differences to methodological reasons and suggested putting
725 more emphasis“on choosing defendable values for particular applica-
726 tions, given the methodological biases” than in searching a definitive
727 value of threshold stresses.Kirchner et al. (1990)have demonstrated Dmax /D50sub
0,01 0,1
10 Dimensionless shear stress
1
Pigüeña river Coto river
Fig. 6. Dimensionless shear stress plotted against the largest tracer mobilized during each studiedflood event. The outer envelope curve of the data could be used as an approxima- tion to the critical dimensionless shear stresses (see the main text). D50represents the me- dian size of the subsurface grain size distribution.
Fig. 7. Dimensionlessfractional transport rates (W*) against basal shear stress. Reference shear stress ofParker et al. (1982)was superimposed over the data (Wr = 0.002). In dashed lines are represented the visuallyfit used to determine reference dimensionless shear stress.
