Evolution of bed load grain size distribution with increasing flow strength and the effect of flow duration on the caliber of bed load sediment yield in ephemeral gravel bed rivers

The grain size distributions of bed load collected during flows that range from the threshold of motion to near bankfull in Nahal Eshtemoa, a coarse‐grained ephemeral stream of southern Israel, give an unequivocal quantification of the change from unequal to near‐equal mobility of grains of all available sizes. This second threshold occurs at ∼4.5 times the shear stress associated with initial motion (4.5тc). The level determined in Eshtemoa is much higher than previously defined by laboratory flume studies. The difference probably reflects the tighter packing and the greater interlock of natural streambeds and carries implications for a number of issues, including the modeling of sediment transport, especially in the context of dryland reservoir sedimentation. The proportion of time that flow exceeds 4.5тc determines the size distribution of cumulative bed load. Using a flow duration/sediment transport approach, in which fractional transport rates by grain size class are predicted with Parker's [1979] bed load function, it can be shown that the size distribution of bed load coarsens as the flow duration curve of individual flash floods incorporates progressively higher flows of variable duration. The method has utility because simple flood parameters such as peak discharge are imperfect predictors of sediment flux, particularly in desert streams where the shape of the flood hydrograph varies considerably from event to event. It is also shown that over a longer period (annual or decadal) the caliber of cumulative bed load depends upon the spectrum of flows in incident floods. The 4‐year hydrograph record in Eshtemoa provides a model‐derived bed load size distribution just finer than the unarmored bed material. The Eshtemoa data set can also be used to show clearly that water discharge in this type of ephemeral stream is “effective” or “dominant” over a wide range of flow stage ranging from 0.4 to 1.1 times bankfull and that bankfull discharge is no more significant than a wide range of other states of flow in transporting bed load.


Introduction
It is generally recognized that greater strength of flow is required to entrain the coarser fractions of the material that make up a riverbed Komar and Shih, 1992] and that complete mobilization of each size fraction occurs over a range of flow strength [Wilcock andMcArdell, 1993, 1997]. At comparatively modest levels of flow, coarser fractions are transported at rates that are typically several orders of magnitude less than those of finer fractions. Consequently, the size distribution of the bed load is often reported as being finer than that of the surface bed material [e.g., the bed load grain size distribution should converge with thatof the surface bed material [Wilcock, 1992].
The changing nature of the transport processes associated with the evolution of bed load grain size distributions has been most extensively and most successfully investigated in laboratory flumes. Here, it is possible to conduct experimental programmes that cover a range of conditions from incipient motion to full mobilization. For example, the flume experiments of Wilcock and McArdell [1993] involved a permutation consisting of 28 variously coupled observations of flow, sediment transport, and bed surface grain size distribution that were subjected to a seventeenfold range of bed shear stress and yielded a fivefold variation in transport rate. In the field the determination of bed load transport rates by grain size over a similar range of transport conditions is probably impossible. In part, this is because bed load transport in many gravel bed rivers is marginal or fairly small even at comparatively high levels of flow [Parker, 1979;Andrews, 1984]. This, together with the dangers and difficulties of undertaking fieldwork in highenergy environments, has limited most field data sets to shortterm observations that cover a narrow range of comparatively low shear stresses and commensurably low bed load discharges. Although such studies have resulted in important and invaluable insights into a number of bed load transport processes [e.g., Ashworth and Ferguson, 1989;Gomez, 1995], they provide only limited snapshots of the transport dynamics of the rivers under study. An extrapolation of the trends that are perceived in such data sets to higher flow intensities may be inviting , but the often erratic nature of river sediment transport urges caution if stepping beyond the bounds of the empirical data [Reid and Frostick, 1986]. Any attempt to extend the range of flow conditions incorporated in an analysis by compiling transport measurements from different sites or from different epochs at the same location is usually complicated by differences in the nature of the sediments of each river, such as clast shape or sorting, or by differences in the field and analytical methods that have been deployed in collecting data [Richards, 1990].
In attempting to assess the evolution of bed load grain size the data collected at Oak Creek [Milhous, 1973], Goodwin Creek [Kuhnle, 1992], and the Alt Dubhaig [Wathen et al., 1995] using permanently installed sediment samplers have been particularly valuable. Although such measurement programmes are difficult to establish and expensive to maintain, they allow sediment transport data to be collected over a wider range of hydraulic conditions than is usually possible by the manual deployment of portable samplers. However, even here, only the data set for Goodwin Creek documents the transition from marginal to unrestricted sediment transport as flow intensity increases.
The evolution of grain size distributions with flow strength inevitably has implications for the nature of the bed load sediment yield of a water catchment. The significance of this might be seen, for example, in the accumulation of the deltas in water supply reservoirs, where unforeseen reductions in impoundment capacity may have serious consequences, especially in the world's drylands [Reid et al., 1998a]. An understanding of the caliber of sediment entering a reservoir might provide a basis for allowing a suitable volume for sedimentation in design and preproject cost-benefit analyses. It might also reduce the need for the postproject maintenance, such as dredging and sluicing, that bedevils reservoir construction in drylands [e.g., Tolouie et al., 1993]. There are other areas of fluvial geomorphology where an understanding of bed load grain size evolution would be invaluable. For example, in situations where regulated low flows require periodic maintenance of riverbed character for ecological reasons, an assessment of the entrainment thresholds of progressively larger size fractions can be invaluable in determining levels of flow that will provide sufficient activation of the bed material [Kondolf and Wilcock, 1996]. Where riverbed aggradation or degradation would bring adverse consequences, e.g., in the vicinity of bridge piers and other structures, the stability of the bed sediment might be assessed if the relation between flow and the armor layer grain size distribution were understood [Habersack, 1998]. Indeed, understanding this relation might assist in classifying channels as capable of transporting bed load at either "capacity" or "subcapacity" rates, thus helping to predict river behavior in situations where transport data are unavailable .
In this paper, we analyze the bed load grain size distributions of Nahal Eshtemoa in an attempt to unravel further the com-plexities of grain-size-dependent bed load sediment transport. This is part of a wider investigation of sediment transport processes in dryland ephemeral streams [Laronne and Reid, 1993;Laronne et al., 1994;Reid and Laronne, 1995;Reid et al., 1996Reid et al., , 1998b. The data have been collected using a permanently installed sediment transport monitoring station. They characterize the change from low to high rates of bed load transport that occurs with increasing flow intensity. The sensitivity of bed load grain size to changing flow strength is described first. The findings are then used to consider the implications of this for the size distribution of lumped bed load that is transported out of the catchment during individual storms of varying magnitude and over longer time intervals that incorporate a spectrum of flood magnitudes.
The fact that the data were derived under a wide range of hydraulic conditions using the same technique throughout and that they were collected at a single site gives a homogeneous set of information with which to demonstrate that increasing flow strength brings a shift from unequal to near-equal mobility of bed material grains of different sizes. The fact that the data are field-based removes those complications that are inherent in flume studies and which arise from an unknown degree of artificiality, such as the under looseness that inevitably accompanies the construction of an alluvial bed of coarse-grained material and the need to feed sediment.

Nahal Eshtemoa Study Site
Nahal Eshtemoa is a fifth-order stream that drains the southwestern flanks of the Hebron Hills •100 km south of Jerusalem. With a mean annual rainfall of only 220-350 mm the channels of this region do not maintain perennial flow but are subject instead to discrete flash floods . Flood hydrographs are typically multipeaked, with rates of rise as high as 0.24 m/min. However, the channel bed is usually dry within 12 to 96 hours. An analysis of flow duration for the period 1991-1995 indicates that the channel of the Eshtemoa is hydrologically active for only -2% of the time, or -7 d/yr [Reid et al., 1998b]. The study reach is straight, and the channel is 6 m wide with near-vertical banks of 1.2 m height. The mean bed slope is 0.0075. The bed immediately upstream of the samplers is planar and consists of poorly sorted pebbles and granules with an interstitial mix of fines. Approximately 20% of the bed material is <1 mm. Size distributions truncated at 1 mm yield median surface (D•,) and subsurface particle sizes of 17 and 18 mm, respectively, indicating that the channel is not armored ( Figure  1). The lack of a streambed armor is thought to reflect the sparsely vegetated gullied hillslopes of the upper catchment, which ensures that sediment is freely supplied to the river channel ]. This characteristic is shared with other channels where sediment is readily moved into the stream network from adjacent hillslopes [e.g., Lisle and Madej, 1992].

Field Instrumentation and Data
Comprehensive details of the instrumentation are given by Laronne et al. [1992] and Powell et al. [1999]. Briefly, bed load transport rates are obtained with five automatic Birkbeck-type recording bed slot samplers [Reid et al., 1980] installed across the width of the stream. Each sampler operates independently and continuously weighs the bed load that falls through a slot The du Boy's equation expresses the balance between the downslope component of the weight of water and the total force of bed resistance and is strictly limited to flows that are uniform and steady. Although most naturally occurring flows are nonuniform and unsteady, the equation can be reasonably applied if (1) the measurements of water surface slopes are made over a streamwise distance that is greater than that over which an open channel flow responds to a change in boundary conditions and (2) the time variation of the flow is sufficiently slow that it does not play an important role in the force balance [Paola and Mohrig, 1996]. Although our slope measurements approximate Paola and Mohrig's critical length scale for flow uniformity, the time variation of flow is sufficiently strong that we cannot rule out some error in our estimates of shear stress arising from the unsteadiness of the river's discharge regime.
Analysis of the bed load record and observations of the movement of painted pebble tracers suggests a threshold shear stress for incipient motion (rc) of -7 N m -2 [Reid et al., 1998b]. This is equivalent to a critical dimensionless shear stress of 0.03 for the D•,. a value increasingly used to describe incipient motion in gravel bed streams [Parker, 1979;Andrews, 1994]. Above this threshold, channel-average transport rates approximate the transporting capacity of the flow [Reid et al., 1998b;Powell et al., 1999]. Because transport capacity is high, the samplers fill rapidly and sampling is generally confined to the first few tens of minutes of each flood event. However, in judging the length of each record it should be remembered that a flash flood hydrograph can rise and fall within the hour and that the time of rise is typically <20 min so that a wide range of hydraulic conditions is being monitored on each occasion.
An analysis of the spatial pattern of bed load transport rate [Powell et al., 1999] indicates that transport rates at the channel center are about twice those recorded at the channel margins. This pattern reflects the variation in velocity and shear stress that would be generated by sidewall drag in a symmetrical trapezoidal cross section and is consistent with laboratory evidence of variations in shear stress [e.g., Knight et al., 1994].
After each event, bed load grain size distributions were obtained by sampling in 0.1 m layers the material that had accumulated in each sampler, ignoring the layer immediately below the slot. Because a Birkbeck sampler continuously records the accumulation of bed load, each of the bed load layers can be assigned to an interval for which transport rates and contemporary hydraulic conditions can be defined ( Figure  2). This procedure depends upon the assumption that bed load accumulates evenly within the sampler. In fact, this is an approximation. Inspection of the shape of those deposits formed during the few events that did not fill the samplers indicates that bed load accumulates as a ridge, its apex lying directly beneath, and parallel to, the longitudinal slot in the sampler cover. The gradients on the sides of the ridge are variable but indicate dispersal of sediment as it settles within the sampler. This allows us to have confidence that within reason, each layer is representative of the material in transport during a defined interval for which we can specify hydraulic conditions. However, in addition to deriving information for each layer, the size distributions have been combined to provide a single curve for each sampler and each flood event, effectively yielding data for the bulk sample of material collected at each location and on each occasion.
Although material moving in suspension may have been carried into the samplers through the slot in each cover, we do not expect the amounts to be significant. Consequently, we can

Size Distributions
The above analysis demonstrates that the bed load grain size coarsens as shear stress rises over the range 1 < Z/Zc < 4.5 but remains constant between 4.5 < Z/Zc < 8.5. However,  , 1988]. Different curves must be plotted for different values of z since the overall transport rate will vary with the applied stress. The degree to which the curves deviate from horizontal indicates by how much the particle size distribution of the bed load departs from that of the bed material.

the full significance of these trends cannot be understood without reference to the size distribution of what may be considered as the sediment that is available for transport, i.e., that of the channel bed in the immediate approach reach of the samplers. A comparison of bed load and bed material grain size distributions can be undertaken if the transport rate of an individual fraction (qsi) is scaled by the proportion of the surface bed material in that size fraction (f i) and plotted against the geometric mean of the size fraction (Di). Since qsi/fi is equivalent to qs (pi/fi), where pi is the proportion of the bed load in fraction i, a plot of q,i/fi versus D i gives the transport grain size distribution in the form p•/fi scaled by the total transport rate q, [Wilcock and Southard
In Figure 5 we plot the arithmetic mean fractional transport rates for each of 11 ranges of shear stress corresponding to progressively higher classes of transport stage (Z/Zc), the up-per bounds of which are shown in the key. To ensure that any bed material which has been moved in suspension does not enter the comparison of bed load and bed material particle size distributions, both have been truncated to eliminate material finer than 2 mm. This lower size limit is based on a suspension criterion, ro• = u* = (z/p) ø'5 for the range of hydraulic conditions for which we have bed load transport data; in this formula, to, is the particle settling velocity estimated from the work of Dietrich [1982] with a Corey particle shape factor set at 0.7, u* is the shear velocity, and p is the density of the flow. Figure 5 shows clearly that fine fractions are overrepresented and coarse fractions are underrepresented in the bed load at low to moderate shear stresses but that these discrepancies become less pronounced as shear stress increases. For example, the mobility of fine and coarse fractions differs by 2 orders of magnitude during flows that exert up to twice the threshold shear stress but differs by only a single order of magnitude during flows that exert 3 times the threshold. At shear stresses >-4.5 times the threshold the trends are essentially horizontal, with fractional transport rates varying by <10% and with all values ofpi/fi insignificantly different from POWELL ET AL.: EVOLUTION OF BED LOAD CALIBER WITH FLOW STRENGTH unity at the 95% level of probability. At these comparatively high intensities of flow, there is close similarity between the grain size distributions of the bed load and the bed material that is in the immediate approach reach of the samplers. The shift in the bed load size distribution confirms the now widely held view that bed load transport is strongly size selective when shear stress only just exceeds the threshold of the size fractions concerned and that a condition of equal mobility is approached as levels of excess shear stress become high Wilcock and Southard, 1988;Kuhnle, 1992;Wilcock and McArdell, 1993;Laronne et al., 1994].
However, it should be noted that the Nahal Eshtemoa data set indicates that a near-equivalence between bed load and bed material grain size distributions is only reached when shear stress exceeds 4.5 times the threshold value. This is more than twice that suggested by flume studies [Wilcock, 1992], a value which is increasingly quoted as significant for gravel bed stream behavior [e.g., Thorne, 1992].

Modeling Procedure
Analysis of the Eshtemoa bed load size distributions indicates that bed load is fine grained at low flow but coarsens as flow rises during a flood event, converging with the grain size distribution of the bed at */*c • 4.5. As a function of this variable degree of clast size selection, the size distribution of the total bed load transported during an indMdual event should vary systematically with the magnitude of the event and the duration of the flow at various transport stages. In the same way, the size distribution of the sediment load evacuated from the catchment over a flood season or over a period of years should reflect the aggregate effect of the spectrum of competent flows.
In order to provide some insight into these matters the size distribution of the bed load transported during three contrasting flow events and during the 4-year study period was modeled using the flow duration/sediment transport method of Andrews and Nankervis [1995]. The procedure uses a relation between dimensionless shear stress and water stage in concert with a bed load transport function to calculate the quantity of bed material in each particle size fraction which is transported during increments of flow depth over a period of record. Given the similarity between observed and predicted fractional transport rates, it is not surprising that the bed load function also models the caliber of the sediment load reasonably well. Figure  6b compares the median grain size of the observed and predicted sediment loads at different shear stresses. Although the predicted sediment load is slightly finer than that which is observed at all but the highest shear stresses, it is apparent that the predicted values are broadly comparable with observed values. The similarity of the observed and predicted fractional transport rates ( Figure  6a) and of the respective grain size distributions (Figure 6b) suggests that application of the flow duration/sediment transport method utilizing the bed load function of Parker [1979] may produce reasonable estimates of both the bed load yield and its size distribution in Nahal Eshtemoa.

Floods
The floods of January 4, 1994, January 11, 1993, and November 23, 1994, are used to illustrate the sensitivity of the bed load grain size distributions to increasing flood magnitude (Figure 7). These three floods were chosen as representatives of very low-, low-, and medium-magnitude events, respectively.
The event of January 4, 1994, was one of the lowest flow events to generate bed load during the study period. Peak transport stage did not exceed the threshold value (Z/Zc • 4.5) required to mobilize quasi-equally all the grain sizes in the approach reach, and size-selective transport processes prevailed for the duration of competent flow. As a result, the coarsest size fraction entrained by the event was finer than the coarsest fraction of the bed material and, with a Dso of only 3 mm, the predicted size distribution of the bed load was considerably finer than that of the bed material. In marked con-

Size Distribution of Longer-Term Bed Load Yield
The significance of this last point is well illustrated with reference to longer-term estimates of the size distribution of bed load transported out of a water catchment. Using the flow duration/sediment transport method described in section 5.1 and a flow duration curve derived from the 4-year study period, Figure 8 shows the accumulative quantity of bed material in each size fraction that is transported at 0.05 m increments of flow depth during the course of a year. The area between adjacent curves is the mean annual quantity of sediment transport for each size fraction. For example, the shaded area represents the mean annual sediment yield of pebbles whose size is 4-13 mm. The mean annual quantity of sediment transported in all size fractions is therefore the total area below the top curve. Integration gives a bed load sediment yield of 38.9 t km -2 yr -•. Were we to vary the hiding function used to parameterize the bed load equation by _+10%, the change in outcome would be negligible with a range in yield between 38.6 and 39.1 t km -2 yr-•. It is of interest that these yields computed using the flow duration/sediment transport method are corroborated by a previously published estimate of 39 t km -2 yr -•, which was derived from a sediment rating-curve method based on the empirical total bed load flux data . However, as expected, varying the hiding function by _+ 10% has an effect upon the predicted cumulative annual bed load size distribution, though this varies across the size spectrum. So, for example, D • 6 shifts from 2.7 to 3.2 mm; D so shifts from 10.7 to 13 mm; and D84 shifts from 35 to 42 mm. should be borne in mind that the flow record used here covers only four flood seasons. As the record extends, the pattern might be expected to become less spiky as the number of floods, each with its peculiar hydrograph, smoothes the flow duration curve. However, it is interesting to speculate that the pattern for ephemeral streams would remain more complex than that of perennial systems, regardless of the length of the flow record, because of differences in the nature of rainfallrunoff between drylands and regions that have greater rainfall.
Of more interest to this paper is the grain size distribution of the sediment load. Figure 1 shows that the mean size distribution of the Nahal Eshtemoa bed load, estimated using the flow duration/sediment transport method, is only slightly finer than that of the bed material. So in this stream the size distribution of bed load generated over four flood seasons is almost the same as that of the bed material, even though flows under which bed load and bed material grain size similarity is achieved are only experienced for 27% of the time the channel is transporting bed load (equivalent to 11% of the time the channel is hydrologically active). Even though size-selective entrainment processes produce bed load size distributions that are finer than the size distribution of the bed material for the majority of the time that flow exceeds %, the rate of transport at flows ->4.5% almost serves to compensate, rendering the lumped bed load only slightly finer than the bed material.

Conclusion
The data set obtained from Nahal Eshtemoa provides an almost unique opportunity to assess the evolution of bed load transport processes in the field. Because the samplers are fully automatic, they facilitate sampling as transport stage increases to levels as high as 8.5%, covering flow conditions that range from incipient motion to the mobilization of all grain sizes that are represented in the bed surface immediately upstream of the monitoring station. The outcome is an identification of a second major threshold at •4.5%, below which entrainment is size selective and above which a condition approaching equal mobility prevails. The level of this threshold is about twice that previously suggested by flume studies which use sediment mixtures with comparable sorting coefficients [Wilcock, 1992;Wilcock and McArdell, 1993]. This difference is not inconsiderable. It might reflect the fact that a natural water-lain sediment with its interstitial fines will almost certainly exhibit a degree of interlock and adhesion that is impossible to replicate under laboratory conditions. It is of interest here that when Kuhnle's [1992, Figure 7.9] plot of qsi/f• versus Di for Goodwin Creek is interpreted in terms of */*c, it can be suggested that equal mobility (i.e., horizontality of the curves) is reached somewhere between 3.9 and 5•c, given that fractional transport rates at 3.9•c vary by half an order of magnitude whereas this discrepancy is virtually absent in the next curve in Kuhnle's [1992] Figure 7.9, i.e., at 5•c.
The difference is significant for predicting the flux and caliber of bed load because flow duration decreases rapidly with increasing water stage in most low-order streams and rivers. A threshold of 2•c would give a much longer interval for nearequal mobility of all grain sizes than would a threshold of 4.5•c. For the 4-year study period in Nahal Eshtemoa, for example, adoption of the higher threshold would decrease the period of flow that lies within the near-equal mobility transport domain by 50%.
The use of a flow duration/sediment transport method to assess both the total and size-fractional bed load yields of individual floods and the extension of this method to provide estimates of the seasonal efflux of bed load is encouraged by the simple relation between bed load and hydraulics in this ephemeral channel [Reid et al., 1998b]. It is possible to fit a bed load function such as that of Parker [1979] with some confidence and to use this in conjunction with a flow duration curve to arrive at credible estimates of yield. However, the high degree of scatter in the bed load/shear stress relation that is typical of many perennial streams of similar size [Reid and Laronne, 1995] makes a similar analysis for these somewhat less prospective. The application of the flow duration/sediment transport method provides a further indication of the difficulties of attempting to link sediment transport and channel crosssectional form in concepts such as "effective" and "dominant" discharge [Graf, 1988;Knighton, 1998]. Taking the peaks of mean annual bed load transport shown in Figure 8, it can be seen that Nahal Eshtemoa is "efficient" in transporting sediment over a wide range of water stage ranging from ---0.4 to ---1.1 times bankfull. No single water stage is dominant. Indeed, it might be argued that bankfull stage (1.2 m) is not particularly significant, and the Eshtemoa data confirm Pickup and Warner's [1976] rather speculative but nonetheless perceptive assertion that subbankfull water stages are more important and channel formative. It may be that the wide range of flow depths over which the Eshtemoa is efficient demonstrates a particular characteristic of ephemeral channels, given the poor armor layer development that typifies these systems . However, it reinforces the suggestion that caution is required in trying to define either short-or long-term river behavior with simple parameters of flow. It certainly illustrates that inbank flows are just as significant as bankfull flow in moving bed material and thereby maintaining channel geometry, at least in ephemeral streams. POWELL ET AL.: EVOLUTION OF BED LOAD CALIBER WITH FLOW STRENGTH