Water Resources Research

Mobility of river tracer pebbles over different timescales

Authors


Abstract

[1] Tracer pebbles are widely used to learn about gravel transport along rivers. Movement over short times and distances is dominated by factors controlling entrainment: relative particle size and shear stress. Movement at longer scales also involves depositional factors: burial and reexposure and exchange between channels, bars, and other depositional environments. We mapped mixed-size tracers in six reaches of a small Scottish river after 2 and 8 years to investigate differences in relative and absolute mobility and infer the importance of burial and exchange. Patterns of relative mobility according to size and shear stress, both within and between reaches, did not change significantly. Some local bunching of tracers was apparent in both surveys, with redistribution from pools into riffles and bars. The main change was that virtual velocities were ∼50% lower, and estimated gravel fluxes were also lower, in the longer term. This slowdown is attributed to vertical mixing giving decreased mobility as surface-seeded tracers become buried, long-term storage in bars and other less active parts of the system, and in this channel, advection of tracers downstream onto a finer bed giving higher relative size.

1. Introduction

[2] Gravel movement along rivers is highly variable in time and space because flow conditions seldom exceed the threshold for entrainment and then not by much. Usually, it is further complicated by the presence of a wide range of grain sizes. The critical shear stress τc for significant movement of a uniform bed is linearly proportional to the grain diameter D, but in mixed beds, differences in mobility between sizes are greatly reduced by the hiding of finer-than-average grains and protrusion of coarser ones, often accentuated by the development of a coarse surface layer and bed structures. Eulerian studies of size fraction fluxes past a point show size selectivity in marginal conditions when the applied shear stress τ only just exceeds the critical stress τcb for some representative average bed surface diameter Db, but once τ/τcb exceeds ∼1.5, all sizes are equally mobile [e.g., Wilcock, 1992]. Lagrangian studies of the dispersion of individual tracer pebbles from a common starting point also show size selectivity [e.g., Hassan et al., 1992], and Wilcock [1997] has gone some way toward integrating the two approaches by considering the grain-related components of bed load flux.

[3] Most of our understanding of pebble mobility is based on controlled flume experiments or very short-term and local field measurements, with almost steady and uniform flow. In such conditions, movement will be dominated by factors controlling entrainment: relative grain size D/Db, applied shear stress τ, and starting position relative to bed structures. In the longer term, though, additional factors come into play. Even in steady uniform conditions, vertical mixing of tracers seeded on the surface must lead to some reduction in mobility. And river flow is far from uniform or steady over many kilometers and years: the presence of pool-bar-riffle units leads to spatial variation in τ and Db, and this is compounded by temporal variation in τ as floods rise and fall. Both types of variability generate partial transport conditions and local sorting of bed material into patches [e.g., Lisle and Madej, 1992], which in turn can affect mobility [Paola and Seal, 1995]. Divergence in bed load flux causes scour and fill to much greater depths than the active layer observed in equilibrium transport in a flume, giving opportunities for deep burial of transported particles which may thereby be stored for relatively long periods [Church and Jones, 1982]. This could be particularly important for inferences about travel velocities of tracer pebbles [Ferguson and Wathen, 1998] or long-term-average gravel fluxes [Haschenburger and Church, 1998].

[4] This paper exploits an opportunity to investigate whether such effects are important. In a previous study, reported by Ferguson et al. [1996] and Ferguson and Wathen [1998], we analyzed the dispersion over 2 years (1991–1993) and >30 competent floods of tracer pebbles at six sites along a small gravel bed river in Scotland, UK. The tracers were replaced where they were found in or on the bed. In 1999 we remapped them after another 6 years and a total of >100 floods. The aim was to see whether patterns and rates of mobility to 1999 were qualitatively and quantitatively similar to those for 1991–1993. Any differences will tell us about processes important in the longer term. Emphasis is placed on whether tracers became concentrated in particular sedimentary environments, to what extent virtual velocities decline over time, and whether mobility still depends mainly on relative grain size and dimensionless shear stress. A second paper [Ferguson and Hoey, 2002] proposes transferable models for vertical mixing and other longer-term processes and compares simulated with observed changes in tracer velocity from the 2-year to the 8-year timescale.

2. Field Site and Methods

[5] Allt Dubhaig is a small stream (∼10 m wide) which emerges from moraine-covered bedrock onto the alluvial floor of a glacial trench in the Scottish Highlands. Its gradient declines rapidly over 3.5 km to the local base level set by a late glacial fan. It has no significant tributaries or lateral inputs of sediment, flow is unregulated, and the metamorphic and plutonic bed material does not suffer significant abrasion over this distance. The dominant control of river behavior is therefore the downstream reduction in slope, which forces strong downstream fining of the gravel bed material followed by an abrupt gravel-sand transition at ∼3 km [Ferguson et al., 1996]. The changes in slope and grain size are accompanied by changes in channel pattern from near-braided proximally, through wide-bar meandering, to equiwidth with occasional bends and submerged alternate bars [Ferguson and Ashworth, 1991].

[6] A total of 1220 tracer pebbles containing magnets and 240 without were seeded in 1991 at six positions (referred to hereafter as T1–T6) at distances ∼0.2, 0.5, 0.8, 1.3, 1.8, and 2.4 km downstream from the head of the alluvial channel. Each tracer set experienced different values of τ and Db but essentially the same flood discharges. Sets comprised 40 (occasionally 60) pebbles in each of five to seven half phi size classes. The tracers without magnets were the coarsest ones in T1–T4 and T6. Dispersion was mapped periodically to 1993 with tracers replaced each time where they were found in or on the bed. This experimental setup allowed Ferguson and Wathen [1998] to identify differences in mobility both within reaches (through size selectivity) and between reaches (according to bank-full shear stress and average bed surface grain size) and to collapse them onto relationships predicting the mobility of any size in any reach.

[7] To investigate longer-term behavior we remapped the tracers in August–September 1999. The search covered the entire channel length from T1 to the end of the gravel-sand transition, beyond which no tracers were visible, and took ∼100 person days. Searching was done systematically in marked strips in the channel and on exposed bars, using more sensitive detectors than in 1993. Those of us involved in both searches think we recovered some tracers in 1999 that would have been missed in 1993. Buried tracers were recovered by digging; the maximum depth of recovery was 0.55 m, compared to 0.45 m in 1993. Streamflow was low throughout, and only a few short narrow stretches of pool, comprising <0.3% of the total search area, were too deep for the detection equipment and so could only be searched visually. Recovered tracers were mapped into the 1991 coordinate system using an electronic theodolite and distance measurer. Positioning errors are thought to be <1 m. Burial depth from the mean top surface of the bed to the top of the tracer was recorded along with a note of the type of depositional environment. Some 23% of recovered tracers did not have fully legible identification numbers and had to be identified from measured a/b/c axes, half phi size class, and mass. A time-consuming iterative comparison with the list of tracers of the correct half phi size class that had not yet been recovered and had not been seeded farther downstream in 1991 or found farther downstream in 1993 eventually enabled all but three tracers to be identified confidently and used in analysis.

[8] Travel distances were calculated as the sum of straight line distances between the talwegs of successive cross sections surveyed in 1991, ending at a point perpendicular to the tracer recovery position. To check for possible channel changes since 1991, we resurveyed 27 of the 123 sections at a fairly regular spacing of ∼100 m. In a few cases the talweg position had migrated or switched laterally across a bar, but such changes seldom exceeded 1 m, and there was no overall change in sinuosity, so the use of 1991 surveys does not bias the calculated travel distances. The resurveyed sections were processed to obtain updated values of bank-full width, cross-section area, wetted perimeter, and maximum depth. From these were derived mean depth, hydraulic radius, and the average of mean and maximum depth (used as by Ferguson and Wathen [1998] to estimate shear stress). Changes since 1991 in these variables were not significantly different from zero (paired sample t test, α = 0.05) and showed no systematic correlation with distance downstream. The shear stresses calculated from the 1991 surveys were therefore considered valid for use in analyzing 1991–1999 tracer movement. Pebble counts were also done at these 27 sections to allow comparison of 1991 and 1999 values of D50 and D84. Neither showed any significant difference. The 1991 values were therefore considered valid for the whole period.

3. Results

3.1. Recovery Rates

[9] The 1999 search recovered and identified 829 tracer pebbles, 57% of the total seeded in 1991. Only a small proportion (12%) of the seeded tracers were found on the surface, as would be expected after a prolonged period of vertical mixing. Recovery rates were therefore very low for the nonmagnetic tracers in T1–T4 (15% overall), though much higher in T6 (62%), where scour and fill is much more limited. The recovery rate for magnetic tracers was much higher with an overall mean of 64%. We presume most of those not recovered were deeply buried, but any tracers just below the bed surface in the few pools too deep to search using magnetometers would also be missed and the vegetated margins of the channel were not searched thoroughly. The T1–T4 nonmagnetic tracers are excluded from subsequent analysis because of the low recovery rate. This leaves a population of 1260 tracers of which 64% were recovered, with a range of 53–80% for individual reaches and 45–100% for size classes within reaches. As in 1993, recovery rates tended to increase with D/Db and were higher in T5 and T6 where scour/fill depths are lower. The overall recovery rate for the population of 1260 is only 3% lower than in 1993. This might suggest that tracers had approached vertical equilibrium by 1993, with deep burial almost balanced by reexposure through scour, but other evidence discussed in section 4.2 casts doubt on this; the high 1999 recovery rate must then be attributed to more efficient searching. In any case it is regarded as sufficient to draw valid inferences about the long-term behavior of the population.

3.2. Tracer Dispersion and Depositional Environments

[10] Tracers were substantially more dispersed by 1999 than 1993 (Figure 1), with a maximum travel distance of 1.89 km for one T2 tracer. The frontrunners from T1–T6 had reached close to the T4 start line, close to T6, well beyond T5, close to T6, well beyond T6, and close to the last gravel bar in the stream, respectively. However, many tracers had not moved far since 1993, and some had not moved at all. The distributions of travel distance are all positively skewed, but there is a change in character from upstream to downstream that is associated with the general reduction in mean travel distance. Few T1 or T2 tracers were recovered close to the seeding positions; peak concentrations are instead at ∼0.2 km downstream, and gamma distribution fits (not shown in Figure 1) have nonzero modes. From T3 onward, though, the main concentration is close to the seeding point, and gamma fits are monotonically declining. This is particularly clear in T4 and T5, although a second mode is apparent in T4.

Figure 1.

Dispersal of tracer pebbles along Allt Dubhaig from 1991 to 1993 (symbols) and 1999 (curves). Curves show cumulative percentage of tracers recovered at different distances downstream, separately for each of six seeding positions labeled T1–T6.

[11] Short-term tracer experiments have often showed preferential storage of pebbles in riffles or bars [e.g., Kondolf and Matthews, 1986; Schmidt and Gintz, 1995]. The ability of travel distance data to reveal preferential storage via steps in cumulative curves is limited by the inevitably low density of tracers (∼1 per 30 m2 of streambed in this study), some apparent bunching is inevitable in any quasi-random process, and a longitudinal plot may not capture preferential storage associated with lateral differences in sedimentological environment (e.g., bunching in a side bar offset by a deficit in the pool running parallel to it). Nevertheless, Figure 1 does show some concentration of recovered tracers into particular locations, and most of it appears to be systematic since it occurs in the same locations in both years and in some cases involves tracers from more than one starting point. The most obvious bunching is near the T4 and T5 seeding positions, where many tracers were buried in side bars before moving far. This does not necessarily indicate anything special about those bars; had the seeding points been elsewhere, the concentrations would have been in different bars. The second mode in T4, at ∼1.6 km, is more significant and marks bars and a backwater area at the junction of the one small tributary to the mainstream. Steepenings in the T3 and T4 curves at ∼1.4 km and the T3 curve at ∼1.1 km relate to bars at sharp bends. The kink in the T3 and T2 curves at ∼0.85 km relates to bars and an abandoned channel in the unstable reach just below T3. The main concentration of T1 tracers at ∼0.4 km occurs in aggrading bars at a gentle bend, and the main concentration of T2 tracers at ∼0.65 km is near a sharp bend with an incipient chute channel. Minor steps in the T5 and T6 curves mainly correspond to riffles.

[12] We also investigated bunching in the positions of tracers which did not move between 1993 and 1999. Allowing a tolerance of 1 m for survey error, 151 pebbles did not move. Two thirds of them were in locations already mentioned: the first two point bars below the T5 seeding point, the first two side bars below T4, the bends below T1 and T2, and the abandoned channel below T3. This again emphasizes continuity in the locations of storage, though presumably in the even longer term, channel shifting might reactivate bars which are currently aggrading and side channels which are currently inactive.

[13] The depositional environment of each recovered tracer was noted as it was mapped, using eight categories which were subsequently reduced to five: low-flow pools, low-flow riffles, exposed but unvegetated bars, inactive channels, and vegetated bars or floodplain. The relative frequency of recovery from different environments alters downstream (Figure 2). Only 1% of tracers were found on the floodplain, mainly where floods avulse from the shallow proximal channel over gravel ramps at the outsides of the T1 and T2 bends already mentioned. Inactive channels do not occur beyond 1.7 km, and only 4% of tracers were found in them, mainly in the T3 site already mentioned. Half of the recovered tracers were found in or on exposed bars, with the rest shared nearly equally between pools and riffles. The proportion recovered from pools tends to increase downstream, with a corresponding reduction in recovery from bars. This broadly reflects changes in channel morphology, with more exposed bars in the laterally active proximal channel than in the stable and narrower distal channel. However, there is also evidence of preferential storage of tracers in particular depositional environments. Figure 2 plots not only the proportion of tracers recovered from each environment but also the proportion of total reach area represented by that environment in five subreaches covering ∼50% of the total distance over which tracers dispersed. The areal extents in T3 and parts of T1, T4, T5 were estimated from near-vertical photographs taken from a model plane in 1996, midway through the study period, at a similar low discharge to that during the 1999 remapping. Areal extents in the narrower and simpler T6 reach were estimated visually from the bank. It can be seen from Figure 2 that the proportion of tracers recovered from pools in all five subreaches is substantially less than pool extent would suggest. This shortfall is made up by preferential recovery from riffles in T4, T5, and T6; bars in T1, T3, T4, and T6; and inactive channels in T3 and T4. As previously noted, very few pools were too deep for thorough searching and recovery, so the shortfall between areal extent of pools and tracer recovery from them appears to indicate a genuine systematic process of redistribution of sediment into topographically higher areas. The areal concentration of recovered tracers in riffles exceeded that in pools by a factor of ∼2 in the T6 reach and at least 4 in the other five reaches. The concentration in bars exceeded that in pools by a factor of ∼2 in T5 and T6 and at least 5 elsewhere.

Figure 2.

Percentage of tracers recovered from pools and riffles (solid curves in top plot) and bars and inactive channels (solid curves in bottom plot) in 11 subreaches along Allt Dubhaig. Areal extent is shown for five subreaches (dashed curves). Values are plotted midway along each subreach. Mean number of tracers per subreach is 74. Recovery percentages have standard errors of up to 10% in T1b, T4b, and T5c but are generally <5% elsewhere.

3.3. Travel Distances

[14] The mean 1991–1999 travel distances for each half phi size class and seeding point are shown in Figure 3a, with 1991–1993 results in Figure 3b for comparison. The standard errors of the means are rather higher for 1999 than 1993 because of greater dispersion and slightly lower recovery rate but still average only 13% compared to a twentyfold range in means. In general, mobility declines with grain size within each reach, as expected. It also declines downstream, with grand average 1991–1999 travel distances of ∼300 m for T1 and T2 but only ∼100 m for T5 and T6. To put these distances in perspective, typical riffle spacing along Allt Dubhaig is ∼50 m. The T3 tracers are anomalous in showing lower mobility than T4 and the weakest size selectivity. The same was true in 1991–1993; Ferguson and Wathen [1998] attributed it to burial of most of the T3 tracers near the seeding site early in the study period. This legacy evidently persisted for many years, though higher travel distances in 1999 show that some pebbles were still mobile.

Figure 3.

Mean travel distances of tracers in each half phi size class from each starting position over periods (a) 1991–1999, (b) 1991–1993, and (c) 1993–1999. Error bars are omitted for clarity but are discussed in text. Subsamples of n ≤ 10 tracers are omitted; plotted points have n = 18–42 in Figure 3a, 12–42 in Figure 3b, and 11–39 in Figure 3c.

[15] The size selectivity shown by size-class averages in Figure 3a is also present when travel distances of individual pebbles are regressed on their mass or b axis diameter. Either predictor has a significant negative effect, strongest in T4 and T6 and weakest in T3. On top of this size effect, there is a small but significant positive relationship with the sphericity index (c2/ab)1/3 in some reaches.

[16] Much of the 1991–1999 movement shown in Figure 3a took place in 1991–1993, and 74% of the tracers found in 1993 were also found in 1999, so some similarity with the results of Ferguson and Wathen [1998] is inevitable. Movement from 1993 to 1999 is completely independent and could be seen as a surer guide to any long-term change in behavior; it is therefore plotted in Figure 3c. However, the standard errors of the mean travel distances in this plot are higher than for Figure 3a or 3b because not all tracers were recovered in both years. Even after omitting subsamples of ≤10, standard errors range from 13 to 55% with a median of 29%. Despite the substantial uncertainty of the means the general downstream decline in mobility is similar to that in 1991–1993, including the higher travel distances in T4 than T3. To the extent that the results are reliable, it appears that the general patterns of relative mobility apparent in 1991–1993 are preserved.

3.4. Virtual Velocities

[17] The simplest way to compare 1991–1993 and 1991–1999 travel distances would be using distance traveled per calendar year, but this would not allow for any difference in the occurrence and duration of floods before and after 1993. A fairer comparison uses virtual velocities, i.e., distances divided by the duration of competent flow [Hassan et al., 1992]. Strictly speaking, duration decreases with Di to the extent that entrainment is size selective, but we follow Hassan et al. [1992] and Ferguson and Wathen [1998] in using a single threshold discharge. This will lead to a slight exaggeration of the dependence of velocity on grain size in subsequent analysis.

[18] Ferguson and Wathen [1998] estimated the duration of competent flow over the 1991–1993 tracer experiment by identifying a threshold flow corresponding to the transport of gravel as well as sand into a bed load trap in the T6 reach. For the present analysis the threshold was redefined to exclude a few small events which transported only gravel <16 mm, smaller than any of the tracers. The flow record was maintained less thoroughly after the end of the original study, with an increasing frequency of gaps and no updating of the rating curve, and ceased entirely in late 1996. To estimate the duration of competent flow for the post-1993 period, we therefore used data for the nearest unregulated river with a permanent gauging station: the River Dee at Mar Lodge, 45 km away. The Dee catchment is much larger (290 km2 compared to 16 km2) but has very similar topography, vegetation, and hydrology, and during the period of overlap, there is a good correspondence in the incidence and relative magnitude of floods. The Dee record was used to identify two events during gaps in the 1991–1993 Allt Dubhaig record, for which durations were estimated, and to exclude one apparently spurious event. The revised threshold was exceeded in the adjusted flow record for 1.21–1.25% of the tracer experiment period. The range is because final searches were done at different times in different reaches, and the values are lower than in the work of Ferguson and Wathen [1998] because of the higher threshold used in the present analysis. The exceedance frequency in the three calendar years 1991–1993 is 1.15%, with a probable error of ±0.02% for gap filling. We then used flow duration data for individual calendar years in the Dee first to identify the discharge that was exceeded for 1.15% of the time in 1991–1993 and then to calculate its exceedance frequency in the full 1991–1999 period. The resultant value of 1.12% was then used to calculate virtual velocities for the 1991–1999 tracer experiment.

[19] The 1991–1993 and 1991–1999 virtual velocities for each starting point and size class, denoted by V93 and V99, respectively, are compared in Figure 4. The relationship is roughly linear with slope close to 1, showing that patterns of relative mobility within and between reaches remained similar over the longer period. There is no obvious pattern in relation to grain size or reach. What is striking about the plot, though, is that V99 is always lower than V93. The ratio V99/V93 ranges from 0.33 to 0.99 with mean of 0.50 (0.41–0.55 in individual reaches) and median of 0.49. An almost identical result is obtained if one fits V99 = k V93 to the data by minimizing the sum of squares of perpendicular deviations from the relationship log V99 = log V93 + log k; this is appropriate since there is error in both variables, and the scatter is heteroscedastic in an unlogged plot. This procedure gives k = 0.49, or 0.51 if the velocities are weighted according to the number of tracers each represents. This result is insensitive to any error introduced by our indirect estimation of the post-1993 duration of competent flow; an error of ±10% in this duration alters k by only ±0.05. Thus, whichever way one quantifies it, virtual velocities over the 8 years 1991–1999 were ∼50% lower than over the 2 years 1991–1999. By implication, velocities in 1993–1999 were <30% of those during the first 2 years of the experiment. This indicates a drastic slowing down of the tracer population as a whole. Individual pebbles could obviously deviate from the population average, but the maximum velocities in each reach likewise show a slowdown of 23–56%.

Figure 4.

Comparison of virtual velocities of each size class in each reach as estimated from movement to 1999 (vertical axis) and 1993 (horizontal axis). Reference lines are shown for equal short- and long-term velocities and for 50% slowdown.

3.5. Nondimensional Generalization of Results

[20] Ferguson and Wathen [1998] found that the 1991–1993 virtual velocities for individual size classes and reaches could be collapsed onto a single nondimensional relationship for the velocity V* = Vi/(gDi)0.5, using as predictors the relative grain size D* = Di/Db, and reach Shields stress τ* = τ/(ρs − ρ)gDb. Here Vi is the virtual velocity for size Di, Db is represented by the active layer bulk D50 in the reach as estimated from pebble count D50 using the conversion given by Hoey and Ferguson [1994], and τ is the mean bank-full shear stress in the reach. Ferguson and Wathen [1998] proposed a regression of log V* on D* and τ*, but in retrospect, an exponential increase in velocity with shear stress seems a risky extrapolation from a narrow range of data, and we now prefer a different functional form:

equation image

which has R2 = 0.87 and standard error of estimate s = 0.36. When antilogged with bias correction [Ferguson, 1986], this corresponds to

equation image

The intercept of equation (2) probably depends on the typical frequency of competent flows and might have to be changed for another river, but the exponents may represent a general parameterization of overall mobility and the extent to which it is size selective.

[21] Before repeating this analysis on the 1991–1999 data the predictor values Db and τ for each reach were recalculated as means of section-by-section values from the seeding points up to the new mean travel distance. The values used are listed in Table 1. The least squares fit is

equation image

with R2 = 0.84 and s = 0.38. The coefficients of D* and τ* are both somewhat smaller in equation (3) than equation (1), indicating a slight reduction in the estimated strength of size selectivity and shear stress dependence, but in neither case is the difference statistically significant at the 5% level. Patterns of relative mobility within and between reaches are not therefore statistically distinguishable over 2 and 8 years. However, the intercept of equation (3) is significantly lower than that of equation (1), indicating a reduction in absolute mobility. Taking D* = 1 and τ* = 0.06 as typical, equations (1) and (3) imply that 1991–1999 velocities are 52% lower than those in 1991–1993. This is very similar to the slowdown estimates from the raw data in section 3.4.

Table 1. Reach Characteristics Used for Nondimensional Regression Analysisa
ReachTracer Diameter, mmBed D50, mmShear Stress, N m−2Reach Shields Stress τ*
  • a

    Range of tracer diameters excludes nonmagnetic tracers in T1–T4. Grain size and shear stress values are averaged over cross sections from seeding point to mean travel distance in each reach. D50 is median diameter of active layer, estimated from pebble counts using the count–to–bulk conversion equation given by Hoey and Ferguson [1994]. Shear stress is based on depth-slope product, using midpoint of mean and maximum depth at each section.

T132–1281001060.065
T216–12890770.053
T316–9061730.074
T416–9032510.100
T516–9038190.031
T616–9023280.075

[22] The weaker dependence on τ* in the 1991–1999 results implies a very weak dependence after 1993, and this is confirmed when the same analysis is performed on 1993–1999 virtual velocities. The best fit relationship is

equation image

with R2 down to 0.62 and s up to 0.62. The coefficient for τ* is not significantly different from 0, and the predicted velocity for D* = 1 and τ* = 0.06 is 76% lower than in 1991–1993. The lack of systematic shear stress effect, slightly lower degree of size selectivity (coefficient of D*), and greatly reduced absolute mobility all agree with what can be seen in Figure 3c.

4. Discussion

[23] Pebble tracing has its problems, notably as regards recovery rate, but it provides an integrated view of sediment transport that is not otherwise available. Results are evidently more reliable the larger the sample size and the higher the recovery rate. Our study is based on 160–280 seeded tracers per reach. Samples of this size are accepted as adequate for estimating mean travel distances (Hassan and Church [1992], reply to discussion), and our overall recovery rate of 64% is regarded as good for a long-term study (M. Church, personal communication, 2001; M. Hassan, personal communication, 2001), but it has been suggested that 1000 plus tracers are needed to get detailed insight into patterns of vertical as well as spatial dispersion within a reach [Hassan and Church, 1992; M. Hassan, personal communication, 2001]. We see no obvious reason why our results should be systematically biased, but a study using even more tracers would evidently have given more precise results and differences in detail. We compare the 2 year and 8 year results under two headings: relative mobility, by which we mean the pattern of variation in velocity between reaches and by size within reaches, and absolute mobility, by which we mean the virtual velocity (in km yr−1) for a given size and reach.

4.1. Relative Mobility

[24] The size class mean travel distances in Figure 3, regression analysis of individual distances, and nondimensional analysis of class velocities all show that long-term gravel transport remains size selective, with smaller pebbles traveling more rapidly. This is not because of preferential availability on the surface; our results show some tendency for preferential burial of small tracers, as expected in a stream with a coarse surface layer. Nor is it likely to reflect greater hop lengths for smaller pebbles once entrained; the evidence of detailed studies, reviewed by Wilcock [1997], points the other way. The observed size selectivity therefore requires quite strongly preferential entrainment of those finer grains that are available in the surface layer. The implication is that transport conditions are marginal for much of the time and that any episodes of equal mobility during flood peaks do not dominate gravel dispersion despite the high fluxes at such times. This is consistent with our previously published results from a bed load trap near T6 [Wathen et al., 1995].

[25] Mobility also varies between reaches, with a general downstream decline. This is partly a real effect and partly an artifact of the experimental design. Allt Dubhaig has a strongly concave long profile along which slope, shear stress, and average bed diameter Db all decline by ∼75% from T1 to T6. The reach Shields stress τ* is therefore much the same in T6 as T1 (though it increases farther downstream as the bed becomes sandy). If the tracer pebbles covered the same range of relative grain size D* = Di/Db in each reach, we might therefore expect similar behavior in each reach, but as can be inferred from Table 1, D* tended to increase from T1 to T6. This was for practical reasons: there was an upper limit of D* ∼ 1 to the size of magnetic tracers in the two proximal reaches because bigger ones could not be manhandled to the road for drilling and emplacement of magnets, and there was a lower limit of D* ∼ 1 in the distal reach because smaller pebbles would have split during drilling. This biases the comparison, tending to increase the mobility of the T1–T3 tracers and reduce that of the T4–T6 tracers. Also, there are differences in the local rate of decline of τ compared to that of Db, so that reach Shields stress τ* fluctuates around its overall average value. The 1991–1993 nondimensional analysis demonstrated that for the same D*, there are differences in mobility between reaches (for example, the higher mobility in T4 than T3) that relate to differences in τ*. The analysis of 1991–1999 results confirms this finding and shows no statistically significant difference in the patterns of within-reach and between-reach variation in mobility over 2 years and 8 years.

[26] This is encouraging in terms of the generality of the analysis, though there is still a need to test it on data from other sites and see what allowance has to be made for differences in flood frequency. It also shows that the 2 year study was a fairly reliable guide to the longer-term pattern of relative mobility in this stream. This generally optimistic conclusion requires qualification, though, in the light of the 1993–1999 analysis. This indicated a slight reduction in the dependence of velocity on D* and a sharp reduction in dependence on τ*, which became nonsignificant. A possible explanation for this can be found in the progressive burial of surface-seeded tracer pebbles. The wider implications of this are discussed in section 4.2 and 4.3. What is immediately relevant is that burial occurs not just by mixing within a shallow active layer during equilibrium bed load transport but also to greater depths where bed load flux divergence causes accretion to bars or as bed forms migrate within the channel. Deep scour and fill are more likely to occur where reach shear stress is high, so that the channel is actively changing. This will inhibit overall mobility, offsetting the tendency for greater mobility of active layer gravel where τ* is higher.

4.2. Absolute Mobility

[27] Although the relative mobility of different-sized pebbles stayed roughly the same after 1993 as before, their absolute mobility was extremely different. As seen in Figure 4 and inferred from equations (1), (2), (3), and (4), the virtual velocity of a given sized tracer in a given part of the stream was ∼50% lower over the 8 year period than in the first 2 years and ∼70% lower in 1993–1999 than in 1991–1993. Put the other way around, the 2 year study overestimated longer-term mobility by a factor of 2 and was not a reliable guide to absolute rates of movement.

[28] This finding has implications for the use of tracer velocity to estimate gravel flux. We have calculated 1991–1993 and 1991–1999 gravel fluxes in each reach from the product of virtual velocity, an active width estimated from cross-section data and a threshold Shields stress, and an active depth estimated from tracer burial depths. Three different depth statistics were tried: mean, upper quartile, and maximum. The T6 estimates for 1991–1993 bracket the observed 1991–1993 bed load trap total in T6, and both methods show a plausible downstream pattern with a reduction in flux from T1 to T6 of 93–99% and especially big drops from T1 to T2 and from T4 to T5. However, the 1991–1993 and 1991–1999 estimates were drastically different in all six reaches. In T1–T5 the flux estimates are 25–80% lower over 8 years than 2 years because velocity decreased much more from 1991–1993 to 1993–1999 than burial depth increased. In T6, though, burial depth increased more than velocity decreased, leading to a 150–300% increase in the flux estimate. It would appear that great caution is needed in using short-term tracer results to predict absolute mobility in the longer term, whether for flux estimation or for other purposes such as predicting the dispersal of contaminated sediment.

[29] The slowdown is an overall tendency not restricted to particular grain size classes or reaches, so it must relate to general factors affecting tracer dispersion over extended time and space scales. Three such factors can be proposed. The first is fairly site-specific: the strong downstream fining along Allt Dubhaig as its slope declines toward the local base level. As tracers of given size Di move downstream, the local bed average diameter Db declines, and the relative grain size D* increases. Once it exceeds 1, mobility falls rapidly. A 64–90 mm tracer is highly mobile in the proximal reaches of the river where Db ∼ 100 mm but far less mobile once it has traveled 1 km downstream to where Db is only 30–40 mm. This is reflected in the order-of-magnitude difference in mean travel distance apparent in Figure 2 for this size fraction in reach T4 compared to T1 and T2. This example exaggerates the effect since Figure 1 shows that few of the tracers traveled anything like 1 km during our study. For this reason, we doubt that this is the main explanation for the observed slowdown after 1993. Nevertheless, a downstream change in sedimentary or hydraulic environment remains a factor to bear in mind when considering the upscaling of short-term results to the longer term. The effect could be insignificant in a river without pronounced concavity, but that situation is most common in large sand bed rivers in alluvial plains. Detailed studies of downstream fining along gravel bed rivers mostly show polycyclic situations in which low overall downstream fining conceals stronger local fining along concave sedimentary links between discrete lateral sources of coarse material [Rice, 1999]. Particle mobility is likely to diminish appreciably along such links even though the low overall fining suggests otherwise.

[30] A second, universal, factor which could explain why short-term tracer studies overestimate long-term gravel mobility is vertical mixing. Tracers are generally seeded in or on the bed surface, so all of them are exposed to the next flood and most will move. Over time, more and more will become buried to various depths until an equilibrium is reached in which deeper burial through fill is balanced by reexposure through scour [Hassan and Church, 1994]. The average mobility of an ensemble of tracer pebbles that has been fully mixed vertically must be lower than that of a freshly seeded ensemble on the surface, as found for sand by Crickmore and Lean [1962] in a flume experiment with radioactively tagged sediment. In short-term studies, vertical equilibrium will either not have been attained at all or only late in the study, so that mobility is exaggerated by the bias toward surface conditions. The long-term equilibrium velocity will be more and more accurately estimated in studies over longer and longer periods, at least if advection effects are not significant. The Allt Dubhaig results suggest full vertical and lateral mixing had not been achieved by 1993 despite the occurrence of >30 floods competent to transport at least the smaller tracer pebbles. Burial depth statistics for the two surveys (Table 2) give some support for this inference. Mean burial depths were much higher in 1999 than 1993 in T6 and T1, substantially higher in T4, and slightly higher in T2 and T3. The increase in T1 may partly reflect the availability of more sensitive detectors in 1999, but burial in T6 was too shallow for nondetection to be a factor, and all six tracer sets show a reduction in surface recovery in 1999. This was particularly large in T6, and three sets (T1, T4, and T6) also show an increase in deep burial and nonrecovery. We suspect progressive burial is the main cause of the observed slowdown in tracer movement. There may be a linkage with size selectivity: if coarser pebbles tend to stay nearer the surface, size-related differences in mobility may diminish over time as the intrinsically more mobile smaller tracers become preferentially buried. This could explain the progressive decline in the strength of dependence of V* on D* in 1991–1993, 1991–1999, and 1993–1999 (equations (1), (2), (3), and (4)).

Table 2. Vertical Mixing of Magnetic Tracers Seeded on the Surface in Each Reach in 1991a
ReachMean Burial Depth, mPercent Recovered From SurfacePercent Buried <0.2 mPercent Buried ≥0.2 mPercent Not Recovered
  • a

    First value in each case is for 1999, and the second (in parentheses) is for 1993.

T10.14 (0.07)14 (23)26 (28)18 (6)43 (43)
T20.11 (0.09)13 (17)31 (27)10 (11)46 (46)
T30.14 (0.12)9 (16)33 (23)19 (17)40 (44)
T40.16 (0.10)8 (13)25 (38)20 (18)47 (31)
T50.12 (0.12)11 (21)48 (30)20 (30)22 (20)
T60.05 (0.01)30 (63)51 (22)3 (0)16 (15)

[31] The third possible reason why gravel mobility falls in the long term is similar to but conceptually distinct from the burial effect. Vertical mixing reduces mobility because tracers buried deep in the bed are effectively stored there until deep scour occurs, which may be a very long time in aggrading rivers, but prolonged storage can in principle occur without deep burial if tracers become concentrated in less mobile parts of the channel or stranded in locations which only rarely if ever experience competent flows. Our analysis of the depositional environments in which tracers were found showed a strong tendency for dispersal from pools to riffles and bars and sequestration of a few tracers in abandoned channels or on the floodplain. Locations high on point or side bars experience less frequent competent flow, and while riffles are permanently submerged, they may have a coarser and more imbricated bed than pools so that entrainment requires a higher discharge than elsewhere. The latter hypothesis is supported by Ashworth's [1987] painted pebble experiments in Allt Dubhaig, which showed that tracers seeded in riffles had lower entrainment probability and lower mean travel distance than those seeded in pools. Lateral storage is probably also important, but while it and deep burial are conceptually distinct, our experience is that they often go together making it hard to separate the two effects. For example, the pronounced clusters immediately below the T3, T4, and T5 seeding positions are all in side or point bars which experience competent flows only occasionally, but nearly all the tracers are also buried by >0.2 m, suggesting it may be burial that matters rather than elevation as such.

4.3. Toward a Quantification of Tracer Slowdown

[32] Our overall conclusion is that the 1991–1993 study gave a reliable indication of differences in relative gravel mobility within reaches and a fairly reliable guide to differences between reaches but overestimated absolute rates of long-term movement because of the combined effect of the factors just discussed and particularly of deep burial. The near invariance of the relative differences suggests a two-part strategy to assess the overestimation of absolute mobility. First, the effect of advection of tracers to different environments can be quantified using the relative mobility results together with observed short-term travel distances which show how far downstream a typical tracer moves in a given period. Second, if a quantitative model can be devised for the vertical and lateral dispersion of tracers into temporary storage, constrained by our knowledge of burial depths at different times, it should be possible to assess the rate of approach to an equilibrium distribution in each reach. Together with assumptions about the magnitude of the ensuing reduction in velocity relative to that of a tracer on the bed surface of the channel, this would allow assessment of how the ensemble average tracer velocity declines over time. Pursuing this strategy involves detailed work in developing, calibrating, and validating a generic vertical/lateral mixing model and investigating the implications of both mixing and advection for tracer slowdown. A first attempt at this is made by Ferguson and Hoey [2002], which compares the simulated slowdown for reaches of Allt Dubhaig with the data discussed above and goes on to consider wider implications for the design and interpretation of tracer experiments and the upscaling of short-term studies of gravel mobility.

Acknowledgments

[33] The 1999 resurvey was funded by the UK Natural Environment Research Council (grant GR9/4329 to R. I. Ferguson). We thank Roger Adams and the Kennedy family for access to their land and Adam Comerford, Judith Cudden, Aileen Gemmell, Dan Parsons, Phil Roper, Louise Sime, Tracey Talbot, and Rhona Thomson for their meticulous searching, spirited digging, and good company. Two anonymous reviewers made helpful suggestions on presentation and interpretation.

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