A combined field sampling-modeling approach for computing sediment transport during flash floods in a gravel-bed stream
CERAFRI—Center of Research and Advanced Education for Hydrogeological Risk Prevention, Retignano di Stazzema (LU), Italy
Corresponding author: S. Francalanci, CERAFRI—Center of Research and Advanced Education for Hydrogeological Risk Prevention, via XI Febbraio 2, IT-55040 Retignano di Stazzema (LU), Italy. (email@example.com)
 Field sampling in unwadeable and flashy flood events encounters the problem that lateral variability of flow hydraulics and sediment transport cannot be captured adequately, and there is also an accuracy problem because parameters change while being measured. Moreover, event based gravel-sand mixed transport data in rapidly changing conditions are largely missing, in particular for gravel-bed rivers in small catchments. In this study, field measurements of bed load, suspended load, flow velocities, water depths, and cross-section geometry were collected during flood events at a monitoring station near the mouth of the Versilia River, Italy. Since the observed hydrographs are characterized by short durations, to the order of a few hours, an analysis of the lateral and temporal flow variability was carried out to enable the design of a sampling strategy and to minimize the errors created by the time variations of discharge associated with unsteady flow conditions. The measurements were interpreted using a 1-D hydro-morphodynamic numerical model simulating the dynamics of flow and sediment discharges during a flood event for a given return period. The flow and sediment rating curves were then developed through an integrated approach combining different methodologies: field measurements, laboratory analyses, and mathematical modeling. The developed approach allows one to capture the main physical mechanisms associated to the transport of sand-gravel mixtures, such as selective transport, and the hysteretic behavior of sediment transport produced by rapid and intense flood events.
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 Knowledge of the sediment load carried by a river is a fundamental, yet difficult, task. The determination of sediment load is required for stream restoration, river engineering, and hydrogeological risk evaluation. Fluvial and coastal morphodynamics modeling, water quality management and the analysis of deposition in reservoirs, estuarine, and coastal areas require reliable sediment transport equations which can be adequately calibrated and verified only by using field data [Ferguson, 1986; van Os et al., 2004; Barkdoll and Duan, 2008]. However, when carried out under field conditions, sediment transport measurements may encounter difficulties mainly due to lateral and temporal flow variability, the irregularities of bed topography and the interaction of the samplers with the local flow [Garcia et al., 2000; Bunte et al., 2004, 2008]. For gravel-bed rivers, the difficulties increase for the high variability of flow regime, the wide range of sediment size and the rapidly varied flow during flood events. Even in the simplest and most hypothetical case of a steady flow, bed load exhibits an inherent intermittency due to various factors such as flow turbulence, sediment patchiness, and granular structures and bed forms [Hassan and Church, 2000; Papanicolaou and Schuyler, 2003; Singh et al., 2009]. Moreover, the heterogeneity of grains adds further complexity giving rise to additional phenomena such as the hiding effect, bed armoring, and selective transport (see Parker , for a review of sorting processes). In addition to this, continuous monitoring of sediment load requires significant financial support, the execution of engineering works, and can only be applied to a limited extent. As a matter of fact, the development of the sedimentograph (i.e., sediment transport rate as a function of flow discharge) in gravel-bed rivers is still one of the most difficult tasks, and in particular in relatively small river catchments characterized by flashy flood events and high temporal and spatial variability of the sediment transport rate. Sediment transport relations reported in the literature are typically developed from laboratory data or from sampling campaigns in rivers. The former are notoriously inaccurate; the latter require a significant commitment of resources and may still not achieve an acceptable accuracy [Wilcock, 2001]. When field measurements are available, sediment rating curves are typically derived in the form of a power function using different fitting procedures based on statistical elaborations [e.g., Jansson, 1996; Asselman, 2000]. The fitting procedure for field measured bed-load discharges [Barry et al., 2004] and suspended load concentrations [Wang et al., 2011] is a common approach; however, it has several shortcomings since it does not allow the evaluation of the effects of various physical factors, such as the presence of river bed forms, bed material supply limitation [Bathurst, 2007], and unsteady processes, on the sediment transport relation. Interestingly, bed-load monitoring is far less common than suspended-sediment monitoring [Gray et al., 2000]. Note that rating curves need to be continuously updated to take into account the variability that can occur in streams and in the whole basin related to changes in a number of different factors, such as bed level aggradation/degradation, vegetation, and sediment supply. Very few examples of installations have successfully been applied to the continuous monitoring of bed-load flux in a Mediterranean gravel-bed river, and with a limited amount of data collected [Garcia et al., 2000; Tacconi and Billi, 1987].
 The objective of this contribution is to provide event-based sediment transport measurements at gauging stations in rather wide gravel-bed rivers where flashy floods occur. The measurements allowed the development of a methodology to elaborate reliable sedimentographs, which is here applied in a monitoring station located in the Versilia River (North Tuscany, Central Italy). Field measurements during various flood events were carried out in such a way as to capture the lateral variability in the cross section of the flow velocity and sediment transport while reducing the errors due to the unsteadiness of a rapidly varying hydrograph. To overcome the limitations imposed by the small number of available monitored events, field measurements were carried out in combination with a 1-D hydromorphodynamic numerical model for the propagation of the flood wave in the river reach under investigation. In this way, physically based reliable flow and sediment transport relations were obtained extrapolating field measurements to a wider range of conditions. Results show that the field data are captured well by the numerical model only when the main physical ingredients of the problem (i.e., flow unsteadiness, bed mobility, fractional sediment transport) are included. A simple interpolation of the field data would lead to unrealistic results. Moreover, the field measurements can be useful for understanding the influence of gravel and sand mixture on bed-load intermittency and the hysteretic behavior of sediment transport due to rapidly changing hydrograph.
 The outline of the paper is as follows: first, the problem is presented; then a methodology is proposed, based on field measurements of flow and sediment transport, combined with the results obtained through a numerical model and coupled with a procedure for estimating the errors due to the temporal and lateral variability of the measured quantities during the flood events. The new methodology is then applied to and tested on the monitored events on the Versilia River (North Tuscany, Central Italy).
1.1. The Problem of Monitoring Sediment Transport in Flush Flow Regimes
 Gravel-bed rivers are characterized by a wide variety of bottom topography, hydrological regimes, flow, and sediment discharges. There are many gravel-bed streams which are characterized by giving ample time during a high flow season to carry out all the field measurements to describe flow and sediment variability along the cross section and in each vertical [Emmett, 1980], but there are also gravel-bed streams in small river catchments which are characterized by a very short-term duration of flood events. These conditions are typical of many gravel-bed rivers in Italy. For example, the Versilia River is rather wide (35 m at the monitoring station), has a very flashy runoff regime, during which it rises and falls by several meters. The bed is composed of a gravel-sand mix which is easily entrained and transported on several occasions throughout the year. The short duration events and the extreme unsteadiness of the flow not only limit the amount of field samples that can be taken to cover the lateral variability of the flow and sediment transport rates but also introduces the problem that flow and sediment conditions change while a measurement is taken. The limited number of verticals which were collectable introduced possible errors due to the fact that sediment transport may have significant time variability even under steady-flow conditions, while its lateral variation is strongly affected by cross-section geometry and local bed morphology [Habersacketal., 2008].
 To overcome all these difficulties arising from the limited amount of available measured data, we combined field measurements of flow hydraulics and sediment transport with a morphodynamic numerical modeling. Additionally, the method is combined with an analysis of how to minimize errors in a computed discharge (through selection of a suitable number of sampling verticals) arising from the inability to sample a large number of verticals and from the unsteadiness of the flow in which discharge and sediment transport change while being measured. In this way, the effect of lateral and temporal variability on field measurements is estimated.
 The presented topic appears of interest and importance to many field applications where sediment transport needs to be computed in flashy flow regimes; importantly, there are many other streams in the world with similarly flashy regimes, e.g., ephemeral streams [Billi, 2011], Alpine rivers [Habersack et al., 2008].
1.2. Study Site Description
 The Versilia River basin (Figure 1) extends over an area of about 100 km2 from the Apuane Alps to the Tyrrhenian sea in the northern part of Tuscany (Italy).
 The climate in the Versilia basin is sub-Mediterranean with an average annual rainfall of 1600 mm. The average monthly temperatures reach maximum values in summer time (16–28°C) and minimum values in January (4–12°C). Mean monthly flow at the stream gauging station of Ponte Tavole (located in the lowland portion of the basin) shows a summer dry period with minimum flows of 0.25 m3/s in August and a winter high flow period with flows of up to 5 m3/s. The analysis of the recorded daily discharge during the period 1996–2010 showed the frequency of occurrence of flow discharges (Figure 2a): for example, the mean daily discharge which occurs for at least 10 days in a year is 8.9 m3/s, which was found to be close to the incipient motion conditions; from these data we can expect, on average, to have floods capable of mobilizing sediments for only a few days in a year. The hydrographs with given return period were obtained using the hydrological model “AlTo” developed by the Region of Tuscany [Preti et al., 1996] based on a regional extreme rainfall frequency analysis coupled with a runoff model (Figure 2b): it appears that the peak flow discharge ranges from 63 m3/s for a flood return period of 0.5 yr to 511 m3/s when the return period is 200 yr.
 The Versilia basin was struck by an extraordinarily violent event on 19 June 1996, causing the loss of human lives and the destruction of wide-urbanized areas. The event was characterized by a remarkable intensity: discharge had an estimated return period 200–300 years and peaked at about 600 m3/s in the downstream reaches; 2,300,000 m3 of solid and floating material coming from the upper mountainous area of about 30 km2 produced remarkable channel changes throughout the drainage network. Due to this event, the Versilia basin has been subject to wide restoration work and, at present, the sediment production in the mountain portion of the watershed appears to be limited by several factors, such as, hillslope stabilization works and various slit-check dams built within the river [Catella et al., 2005a, 2008].
 The study monitoring station is located in the lowland portion of the basin close to the river mouth (Figure 1), about 5.5 km from the coast. Approximately 500 m downstream from the monitoring station is the location of the gauging station “Ponte Tavole” managed by the Regional Hydrological Agency (“Centro Funzionale”); at this station, water levels are automatically monitored at a time interval of 15 min, and the data are accessible online. Note that no flow rating curve is currently available at this gauging station.
 In this reach, the Versilia River has an average bed slope of 0.2%, a constant width of about 32 m and flows between vertical concrete walls. The monitoring station is positioned on a 34.4 m wide bridge with no piers; on the right bank there is a sediment bar (Figure 3).
2. Methods and Accuracy
 The methods here employed to derive flow-sediment rating curves include (i) field measurements, (ii) laboratory analyses, and (iii) numerical modeling, as described below. A procedure to estimate the effects of lateral and temporal variability on the field measurements is here proposed.
2.1. Field Methods
 The field measurements consist of hydrometric data (free-surface water and bed levels, flow velocities) and samples of bed load and suspended load collected during various flood events.
 Moreover, during dry periods, the sediment of the riverbed was collected and analyzed.
 Flow velocity was measured by means of an USGS type AA current meter; sampling of suspended load and bed load were collected using, respectively, the depth-integrating reel type US D-74 and classical Helley-Smith bed-load sampler with a 7.6 cm2 intake opening and a sample bag with a 0.25 mm mesh of polyester. According to Emmett , a reliable calibration of the sampling efficiency of the Helley-Smith sampler is limited to particle sizes smaller than about 16 mm. In the present work, the Helley-Smith sampler was used with a slightly coarser bed material, assuming that the contribution of the largest particles to the total sediment transport rate can be considered to be negligible and the trap efficiency still acceptable [Emmett, 1981].
 The current meter, together with a sounding weight, were supported by a sounding reel mounted on a crane. Depth and position, in each of the vertical measurements, were obtained by use of a sounding weight suspended from a cable. The Helley-Smith was mounted on a different crane.
 Measurements were carried out during flood events along five verticals (see V1 … V5 in Figure 4); these verticals are not evenly distributed because, due to the presence of a gravel bar along the inner bank, the cross section is lightly asymmetric with the highest flow velocity line shifted toward the left wall. The depth-integrating sampler was used to sample the water column in each vertical by lowering the apparatus as close to the bed as possible at a uniform transit rate, and then immediately raising the sampler back until the nozzle cleared the water surface at the same rate, according to Edwards and Glysson .
 The typical field procedure was subdivided into two phases: the preparatory phase and the measurements phase. The former was carried out during the dry season with the aim of surveying the river reach, defining the operative strategy and characterizing the river bed material. To this purpose, grain-size distributions were obtained using two different techniques. Particles in the surface layer were sampled with the pebble count technique [Wolman, 1954] through systematic sampling along various transects (i.e., a measuring tape) placed along the emergent bar. The sampled bar had a longitudinal extension of several channel widths and a lateral extension of more than half of the channel width. The sampled surface appears therefore rather large and representative, also by visual inspection, of the channel reach. Sample size was set on the basis of the criterion by Petrie and Diplas ; in particular, in order to limit the errors around the D50 percentile within ±10% and considering 20 size classes, it was necessary to collect at least 200 particles, which were sampled along transects equally distributed from the front to the end of the bar deposit, such that they were representative of the whole bar. Particles in the subarmor layer were collected through volumetric sampling, assuming that an armor layer depth was equal to the embedded depth of the largest particle in the sample area, after removing the armor layer with a shovel at the bottom side beneath the largest particle [Church, 1987]; sample size was set on the basis of the criterion by Church et al.  based on the size of the largest particle found in the sampling reach. The coarser fraction (diameter ≥ 4 mm) of the sediments collected was directly sieved on the field, while about 25% of the remaining finer portion in weight was taken to the laboratory and sieved.
 The measurement phase was as follows: after unloading the instruments from a van, the Helley-Smith was mounted on the first crane and initially positioned on the vertical V5; in the meantime, the current meter was placed on the second crane on the vertical V1, flow velocities were typically taken in three points at different water depths (typically at 0.2, 0.4, and 0.8 times the local flow depth from the bed); subsequently, the depth integrating suspended sediment sampler was mounted on the second crane and the suspended load sample was collected in the vertical V1. When these operations were completed, the cranes were moved to the remaining verticals.
 The sampling periods were typically 40 s for each measure with the current meter and about 30–40 s per vertical for the depth integrating sampler, depending on local flow velocities. Preliminary measurements have indicated a sampling time of 10–15 min per vertical for the Helley-Smith sampler, such that the sampling bag was not overfilled and sampling efficiency was guaranteed. Note that we carefully checked that the sampling bag was not full; if this were the case, we reduced the sampling time so that the bag was only partially full. Sampling times of the same magnitude were also adopted by Batalla et al. , and Habersack et al. .
 The time required to carry out all the measurements (typically around 10–15 measurements of flow velocity, 5 water levels, 5 bed levels, 5 samples of bed load, and 5 samples of suspended load) in the five gauging verticals was between 1 and 2 h, and this was considered representative for the collection of one cross-sectional sample of flow velocity, suspended sediment and bed load.
 Since the field team and the van with the instruments and equipment were located about 120 km away from the monitoring station, and due to the rapid and sudden characteristics of flood events in the Versilia catchment, some alert procedure had to be set. This was based on information from the long-term weather forecast and on data regarding the rain intensity and water levels registered by the various sensors managed by the Regional Hydrological Agency and distributed in the river basin. In particular, a cumulative rain threshold reference (to the order of 45–60 mm in a few hours) to give rise to “relevant” flow and solid discharges was established.
 Once the field data were acquired, flow and sediment discharges were estimated. The flow discharge Q was estimated from the measured local values of flow velocities according to the classical “competence area method”: each value of the flow velocity acquired along the gauging vertical was related to the corresponding partial liquid cross section.
 The suspended sediment transport Qs was estimated as the product between the average suspended sediment concentration in each gauging vertical, and the related partial flow discharge; the latter is associated with a rectangular area extending laterally half the distance from the preceding gauging vertical location to half the distance from the next, and, vertically, from the water surface to the sounded depth. Qs is further subdivided into the suspended load associated with the transport of sand available in the bed Qss, and with the wash load due to the transport of silt and clay sediment, Qswl. These fractions were estimated from the laboratory analyses.
 The bed-load transport discharge Qsb was estimated from the weights of the sediment collected by the Helley-Smith sampler in the given sampling period, and assuming that the bed-load transport per unit width is constant along the portion of the river bed of competence of each gauging vertical.
2.2. Laboratory Analyses
 The laboratory analyses were aimed at obtaining concentrations and grain-size distributions of the sediments sampled.
2.2.1. Suspended Load Samples
 Due to the small weight of the sediment samples, generally to the order of a fraction of a gram, the partitioning between suspended-bed material load and wash load required particular attention. In the present study, a double filtration method was applied to the samples. First, total sample weight was recorded, then sodium polyphosphate was added as a deflocculating agent to all of the samples in order to break up the clay or silt blocks, giving it 30 min to react. Then, each sample was poured into a two filter stack, composed of a 0.062 mm grid sieve and a paper filter underneath. The sand remained trapped in the top filter, whereas the finer particles were held back by the paper filter. Sometimes, some distilled water was added into the grid filter to aid the filtration process. When filtration was complete, the paper and grid filters were placed into a low-temperature oven. After the oven-drying process, the filters were weighed with a high-precision balance (resolution of 0.1 mg) and the sediment weight was estimated from the difference between the filter weights. The sediment fraction finer than 0.062 mm has been assumed as the wash load component.
2.2.2. Bed-Load Samples
 Standard laboratory procedures were adopted. For median sediment diameter D in the range 32 mm ≥ D ≥ 1.41 mm, the grain-size distribution was obtained by the well-known dry-sieving technique. When D ≤ 1.41 mm, first the wet-sieving methodology was employed in order to break up the clay and silt lumps; then sediment ≥0.062 mm was analyzed by means of the dry-sieving technique.
2.3. Hydromorphodynamic Numerical Modeling
 The flood wave and sediment transport dynamics in the reach under investigation were studied using a one-dimensional hydromorphodynamic model based on the equations of motion and continuity for water and sediments. The numerical code “SNUMB,” developed at the University of Florence solves the governing equations written in conservative form by employing a finite volume method where the variables are: wetted cross-sectional area, liquid discharge, and average bed elevation within each cell. SNUMB has been proved to be robust when dealing with irregular geometries and the occurrence of abrupt changes both in flow and bed topography [Catella et al., 2005a, 2005b, 2008]. The numerical scheme was implemented adopting a variable spatial grid, where each cell represents the portion of the river between two topographic cross sections, and using the total sediment load equation formulated by Ackers and White  and modified by Day  in order to take into account the mobility of graded sediment. The Ackers and White equation was selected in the model because it turned out to be the best predictor when fitting sediment load data during monitored events with several sediment transport formulas.
 The numerical model was implemented to estimate the flow and sediment rating curves at the monitoring station of the Versilia River. The river reach under investigation stretches 6.1 km from the shoreline and is specified through 82 cross sections with a variable distance of up to 320 m. The Manning coefficient was estimated using the Strickler type formula based on the D90 of the surface material: the adopted value is 0.028. Due to the limited length of the reach under investigation, the Manning coefficient is maintained constant through all the cross sections.
 Regarding the boundary conditions, at the upstream end, the flood hydrograph is assigned with the condition of fixed bed elevation, while at the downstream end, a mean sea water level elevation is imposed.
 With regard to the sediment transport, the subarmor grain-size distribution was divided into five classes: three for the sediment in the gravel range and two for sand. After calibration, the model was used to simulate flood events at various return periods (Figure 2b).
2.4. Effects of Lateral and Temporal Variability on Field Measurements
 Due to the high variability of flow observed during the flood events, a specific analysis was carried out to evaluate the reliability and accuracy of the measurement procedures.
 In general, flow and sediment transport characteristics show both a lateral and temporal variability which need to be related to the time and space resolution adopted in the measurement procedures. The hydraulic quantities, such as cross-sectional mean velocity, U, mean water depth, Y, flow discharge, Q, generally show a time and space variability which is much more regular than that associated with the sediment parameters. Since it appears quite difficult to define the lateral and temporal variability of sediment transport at the study site, an evaluation of the accuracy of the measurement procedures is presented here referring only to the variability of flow discharge. Under unsteady conditions, two main sources of errors need to be considered: one associated with the lateral flow variability, the other associated with the temporal flow variability. The magnitude of both types of errors is a function of the number of verticals along which the measurements are carried out across the fluvial section. In the following, these two sources of error are analyzed and discussed.
 Let us introduce the relative error due to lateral flow variability, El, as the relative difference between the actual flow discharge Q and the measured flow discharge Qm:
 As defined, the error El is expected to decrease as the number of verticals increases. On the other hand, an increase in the number of verticals leads to greater El when flow characteristics change rapidly with time. To describe this behavior, let us consider the unsteady water discharge at the monitored station, i.e., Q(t). Along the cross section, both local water depth, y, and depth-averaged flow velocity, u, are also functions of the transversal coordinate, l, i.e., y(l, t), u(l, t). According to the continuity equation:
where L is the channel width. If a rectangular cross section is considered, at any given time, equation (2) gives:
where the integral depends on the lateral distribution of velocity across the fluvial section. If u is obtained through measurements carried out at n verticals along the cross section, estimation of Q is provided by the following sum:
where ui is the depth-averaged velocity along the ith vertical and Δli is the distance between two consecutive verticals, here assumed equally spaced.
 Hence, the relative error due to flow lateral variability, El, can be expressed as:
 As already mentioned, El is expected to decrease as the number of verticals is increased, while it approaches zero when the number of verticals n tends to infinite.
 Equation (5) can be solved once the true velocity distribution u(l) across the fluvial section is known. This distribution can be estimated by interpolating the real measured depth-averaged velocity values u obtained during all the measurements carried out. The relative error El can be calculated considering various scenarios with a different number of verticals of measurement.
 In order to estimate the errors associated with the flow unsteadiness, named Eu, both the number of verticals and the time period Tm required to carry out the measurements along each vertical, need to be considered.
 The depth-discharge rating curve at the monitoring station can be expressed as follows:
the validity of this expression will be shown later.
 According to equation (6), any time variation of water depth induces the following variation in the discharge:
 Denoting by Tm = tf–ti, the average time required to carry out measurements along one vertical, the total variation of the discharge over the time interval Tm is therefore:
 In equation (8), the quantity can be estimated from the available recorded hydrographs. Denoting by and , the time-averaged quantities over Tm; equation (8) is expressed as follows:
 If n > 1 verticals of measurement are considered, the variation of the discharge with respect to an initial value Q0 during the measurements taken along the n verticals is:
where denotes the depth variation over the time interval Tmi at the ith vertical. After substitution, it is found that:
 The quantity can be considered as the error of measurements induced by flow unsteadiness. Hence:
and the relative error:
 Assuming for Q0 the value given by the rating curve when y = y0, that is, the discharge corresponding to the water depth at the beginning of measurements, i.e., i = 1, it appears that:
 The quantities y0, yi, and can be derived from the recorded data at the monitoring station. The coefficient b has been derived from the results of the hydro-morphodynamic model, as will be shown later.
 The equations (5) and (14) can be used to calculate El and Eu for the monitoring site under consideration: as expected, these two variables show an opposite pattern with respect to n. If the total error E = El + Eu is considered, it will show a minimum value for a certain value of n.
 Notwithstanding the approximations, this analysis demonstrates that flow unsteadiness and the time required to carry out the measurements must be taken into account in planning correctly the number of verticals across the river section during rapidly changing flood events.
 The above results cannot be directly transferred to sediment transport discharge. As far as temporal variability is concerned, stochastic behavior of sediment supply, bed-form dynamics and migrating sheet layers of bed-load transport superimpose on the unsteady-flow conditions making the quantification of the measurements' accuracy very difficult. According to Habersack et al. , a periodicity between 15 and 25 min can be detected in bed-load discharge at which a peak or a low value occurs; these periodicities have been also pointed out by Gomez et al. [1989, 1990], while variations of average bed-load discharge up to 4.0 times have been observed by Emmett , and up to 25 times by Bunte and MacDonald . To reduce the effects of temporal variability, the sampling time needs to be comparable to the periodicity of bed-load transport.
 The estimation of lateral variability presents even more difficulties, since it depends on many factors such as plan and cross-section geometry, local bed morphology, and their trend to change at each flood event. In the case of bed-load transport, these variabilities are related to the trajectories of sediment particles in a curved reach which can be estimated once the local topography and the details of the flow field are known [Seminara et al., 1997; Julien and Anthony, 2002; Bunte et al., 2006], considering also gravitational effects that enhance nonlinearities in bed-load transport [Francalanci et al., 2009, 2012].
3. Monitored Events in the Versilia River
3.1. Field Measurements
 In the preparatory phase, the river bed material was surveyed in November 2006 and later repeated in September 2009; sample sizes were 326 and 420 particles for the surface sediment and 697 and 640 kg for the subarmor layer, respectively. The sampling accuracy was ±8% around the D50 [Petrie and Diplas, 2000] in case of the surface samples, and a precision of ±9% around the D50 in the case of subarmor layer samples [Church et al., 1987; Ferguson and Paola, 1997].
 It appears that the grain-size distribution of bed material has not changed significantly over 3 years, although the subarmor layer seems to have slightly coarsened (Figure 5). The subarmor layer sediment was bimodal, with one mode in coarse sand and one in very coarse gravel. The median diameter of the bed surface and subarmor layer are, respectively, 22 mm and 8 mm; the percentage of sand in the subarmor layer appears to be 32%. On the bed surface, no sand is present; this can be either due to the occurrence of minor floods capable of mobilizing only the smaller diameters in the sand range, or to limited sand supply conditions. Note also that the fraction of silt-clay (sediment finer than 0.062 mm) particles in the bed appears to be negligible.
 The measurements phase lasted from January 2007 to November 2010, during which 11 flood events were monitored at the gauging station of Ponte Tavole. A summary of the characteristic data for each event is reported in Table 1: the date of each measurement, the time and lateral averaged free surface elevation z (above sea level), flow depth Hw, sampling time Tsampling, the return period T of the monitored hydrograph, and the limb of the hydrograph (R-Rising, P-Peak, F-Falling). The flow depths of the events M3–M6 are in the same range, but the different phase of the hydrograph while the measurements were taken can explain the different condition of flow discharge and sediment transport.
Table 1. Field Measurements in the Versilia Monitoring Stationa
z (m a.s.l.)
The date is the day of the field measurements; z is the time and lateral average free surface water elevation above sea level; Hw is the time and lateral average water depth in the cross section, Tsampling is the duration of sampling; T is the return period of the monitored hydrograph; and Limb indicate when the measurements were taken during the stage hydrograph (R = Rising, P = Peak, and F = Falling).
 In the first two measurements (M1 and M2) no bed-load transport was found; these events were monitored in order to estimate the incipient motion condition in the field. M3 and M4 were acquired in two distinct but similar flood events which occurred in January 2008, after a relatively long period without relevant flood events; in particular, M3 was measured during the peak-flow conditions of the flood hydrograph, while M4 during the rising limb of another flood event. The measurements M5 and M6 were collected during the falling limb of the flood event registered on the 18 April 2008; the measurements M7 and M8 refer to the biggest flood event observed during this monitoring activity, on 31 October 2008, which had an estimated recurrence interval of almost 2 years for flow discharge. In particular, M7 was measured during peak-flow condition and, due to the woody debris transported by the flow, it was not possible to lower into the flow either the Helley-Smith or the current meter (however, suspended samples were regularly collected and the flow depth was measured). For this reason, only the average velocity on the free surface was estimated by means of the floating material method; the flow discharge was then calculated considering the relationship between the ratio of the surface velocity to the average velocity with the flow discharge observed in other measurements. M8 was collected a few hours after M7, during the falling phase of the flood event.
 The measurements M9 and M10 were taken during a multipeak flood event which occurred on 25 October 2010; while the last measurement M11 was collected on the 1 November 2010. The other events then M7 and M8 had an estimated recurrence interval of about 0.5 year or even less. As an example, Figure 6 shows the flood hydrograph which occurred on 31 October 2008 (the river stage refers to the local gauge datum) registered at the nearby gauge station “Ponte Tavole”; the time period taken to carry out the measurements M7 and M8 was about 1 h and half and 1 h, respectively (see the gray area).
3.2. Laboratory Results
 The five samples of bed load and five samples for suspended load collected in each vertical of measurements were analyzed and the average results are reported in Table 2. Note that the fraction of sediment transported in suspension in the range of a silt and clay dimension was ascribed to wash load since it was not present in the subarmor layer; sand in the bed could be either transported as suspended and/or as bed load.
Cm = averaged concentration of suspended sediment in the cross section; Pss = percentage of suspended sediment from bed material; Pwl = percentage of suspended sediment from wash load; Ps = percentage of sand in the bed load samples; Pg = percentage of gravel in the bed load samples; D16, D50, and D84 diameters (in mm) for which 16, 50, and 84% of the particles are finer; and σ = average standard deviation. Each data is obtained by averaging the samples collected over five lateral verticals of measurement.
 The following observations can be drawn: the cross-sectional averaged concentration of sediment transported in suspension (both silt-clay and sand) ranges from 0.12 g/l for measurement M1 to 5.44 g/l in the case of M7; the wash load was the dominant component, the sand percentage always being smaller than 25% (maximum value for M3); for measurements M1 and M2 no bed load was observed, while for measurement M7 it was not possible to collect bed load due to the high-flow intensity. The bed load is mostly composed of gravel in all measurements, except M3 and M4 where sand is the dominant fraction; the D50 of the bed load samples falls in the range of gravel in all but the M3 measurement.
 The grain-size distributions of the samples collected by the Helley-Smith during the various measurements are reported in Figure 7. These distributions are laterally averaged over the weight of different samples taken on the measurement verticals; the size distributions of the surface and subarmor layers are added to highlight similarities between the mobilized fractions and the sediment composing the bed. The finest bed-load distributions (M3 and M4) occurred during the smallest discharges (see, however, comment above). The predominant sand transport suggests that the flow did not fully mobilize the surface gravel. The grain-size distributions for events M5–M10 are coarser and very similar in their percentage of sand and gravel. Those distributions approach the subarmor layer distribution, suggesting that the flow was able to mobilize nearly the entire range of particles in the bed. Importantly, the fact that the M5–M10 are very similar being carried out in a time period spanning over 2.5 years, seems to provide an indication of the repeatability of these measurements.
 M11 shows a somewhat different behavior with a very coarse distribution and a small percentage of sand. This distribution appears to be remarkably similar to the surface layer. The reason for this behavior could be ascribed to a combination of factors: (i) hydraulic conditions which mobilize just the surface particles and (ii) a limited sand supply from the upstream reach due to the repeated and frequent flood events which occurred previously in that period of time.
3.3. Flow and Sediment Discharges
 The results of the field data analysis are summarized in Table 3. M1 and M2 reflect conditions below the incipient sediment motion with the absence of bed-load transport and a small amount of suspended sediment. M3 and M4 refer to higher values of flow and solid discharges compared to the first two. M5 and M6 show values of water depth, flow, and solid discharges consistent with the field evidence (falling limb of the hydrograph). Comparing two similar values of flow discharges, such as M3 and M6, it appears that the values of bed load and suspended load can be very different; this suggests that the instantaneous components of sediment transport are related not only to the local flow discharge but also to additional factors such as the time of the measurements in the different phases (rising, peak, falling) of the flood event, or the sequence of flow discharges before the flood event, which may wash out the river basin from finer particles. For example, M3 was measured after a relatively long dry season which led to the presence of larger quantities of fine particles, while M6 was measured in the falling limb of a hydrograph corresponding to higher return period events, which were probably able to mobilize the whole bed material. In addition, it is well known that the bed-load phenomenon is inherently characterized by fluctuations [Singh et al., 2009] which are difficult to quantify.
Table 3. Summary of Field Discharges (Average Over Sampling Time)a
Q = water discharge; Qsb = bed load discharge; Qss = suspended sediment discharge from bed material; Qst (Qsb + Qss) = total sediment discharge; and Qswl = wash load. The asterisk * means the data were estimated.
 Overall, it appears that the dominant component of sediment transport associated with bed material is the suspended load in all but the measurement M6. The field data confirm that the suspended sediment transport due to wash load is not directly related to the flow discharge conditions, but it is also a function of a number of different factors taking place at the scale of the river catchment [Einstein and Chien, 1953]. On the other hand, total sediment transport discharge (Qst) of sand and gravel given by the sum of bed-load transport (Qsb) and suspended load (Qss) appears to correlate well with the flow discharge.
3.4. The Accuracy of the Measurement Procedures
 The error analysis proposed in the previous section is here applied to the test case of the Versilia River. Equation (5) is used to calculate the error due to the lateral variability El: this equation can be solved once the true velocity distribution u(l) across the fluvial section is known. This distribution is obtained here by interpolating the real measured depth-averaged velocity values u collected during all the measurements carried out.
 The equation derived is the following:
where the normalized velocity u/umax is expressed as a function of the nondimensional spanwise coordinate l/L.
 This result allows one to calculate El considering various scenarios with different verticals of measurement. Using equations (5) and (14), errors El and Eu can be evaluated for the monitoring station Ponte Tavole in terms of the number of verticals n (Figure 8), assuming Tm = 18 min. As expected, they show an opposite pattern with respect to n. In particular, the error due to the flow unsteadiness, Eu, appears to grow rapidly when n increases; conversely, the error due to lateral flow variability El drops rapidly under 5% for a number of verticals n => 3.
 The total error, E = El + Eu shows a minimum value of about 12% for n = 3, while it is smaller than 15% for 2 ≤ n ≤ 5. Notwithstanding the approximations, this analysis may be useful in providing reliable support for planning correctly the number of verticals when measurements during rapid flood events must be made.
 In the case of the Ponte Tavole monitoring station, the number of verticals of measurement was set as varying between 4 and 5, depending on the characteristics of the event to be monitored.
4. Flow and Sediment Rating Curves
 The flow and sediment rating curves were derived employing the hydro-morphodynamic numerical model and pursuing calibration of the model and comparison with field measured data.
 Based on the highest flow discharge monitored in the field (measurement M7), the comparison is carried out by considering a flood hydrograph with a return period of 10 years (Figure 2b). No attempt to reproduce the details of each single hydrograph observed during the measurements is carried out, as the main goal of this study is to provide an estimate of the sediment rating curve.
 With regard to the flow rating curve, it appears (see Figure 9) that the numerical model is able to capture the field observations. In the case of a 10 year return period, the effects related to the flow unsteadiness begin to be appreciable, as the falling limb exhibits a higher water level for a given discharge.
 The sediment rating curve relative to the total sediment transport was derived comparing the sediment discharge predicted by the hydro-morphodynamic numerical model with the field measurements. Before making such a comparison, the bed-load discharge which occurred during the measurement M7 was estimated by extrapolation from the other bed load data. The total discharge given by the sum of bed load and suspended load in the case of measurement M7 resulted as approximately 233 kg/s.
 The sediment rating curve relative to the total sediment transport, here calculated as the sum of the fractional discharges, with the flow discharge is shown in Figure 10. The numerical model satisfactorily captures the sediment discharges monitored. Discrepancies between predicted and observed values may be due to the fact that the flood events were modeled by synthetic hydrographs, thus simplifying real behavior (such as multipeaking) and therefore affecting some aspects of the river dynamics and the relationship between flow and sediment discharge. Overall, the numerical model seems to provide a good interpretation of the field data, both for the flow and sediment discharges.
 Finally, an attempt to define rating curves for the considered size ranges of bed material has been made: the five size ranges are grouped to form two classes, one of sand and the other of gravel; both sand and gravel transport rates appear to be a power law of flow discharge. In Figure 11, each fraction transport rate is normalized using the D50 of the gravel and sand distribution and is plotted in function of the excess Shields parameter τ*- τ*ref. It can be seen that the two sediment fractions are transported according to relationships which are in close agreement with the classical sediment transport formulae. In fact, the gravel fraction, which reflects conditions of dominant bed-load transport, is a function of the excess Shield parameter with an exponent of 1.35, close to 1.50 of the classical Meyer Peter and Muller formula. On the other hand, the sand fraction shows an exponent of 3.0 which is not far from the 2.5 of the Engelund and Hansen formula for total load. It is worth noting that τ* has been evaluated in terms of effective bed shear stress for the gravel fraction and in terms of total shear stress for sand; in this latter case, τ*ref is negligible with respect to τ*.
 Furthermore, Figure 11 shows whether the stage was rising, falling or at the peak (see also Table 1); it appears that, due to logistic constraint, most of the measurements were taken during the falling limbs of the hydrographs except for M4 (rising limb) and M3, M4, M9 (peaks of the hydrographs).
 The discussion is focused here on the various approaches taken to validate modeled results: (i) the grain-size of the bed load and suspended samples, (ii) the modeling approach required for the development of the sediment rating curves, and finally we discuss about (iii) the hysteretic behavior of sediment transport.
 The bed-load field samples are mostly in the range of gravel. The validity of this finding can be shown using the van Rijn  threshold criterion for the initiation of transport in suspension, and with the Parker  criterion for the initiation of transport as bed load.
 In Figure 12, the van Rijn  threshold value of (u*/w)cr, with u* and w being the bed shear velocity and the particle fall velocity [Dietrich, 1982], respectively, is compared to the observed values for each field measurement as a function of the bed sediment diameters. It can be observed that in the case of the higher flow discharges (M5–M11), the sediment sizes in the range of sand are more likely to be transported in suspension, therefore the bed load is mostly composed of gravel. In the remaining measurements (M3–M4), with smaller flow discharges, sand also appears to be partly transported as bed load; this suggests that in (M3–M4) the percentage of sand transported as bed load should be higher than that of the other measurements. These findings are in agreement with the field samples (see Ps and Pg in Table 2).
 In Figure 13, we compared the critical condition, expressed in terms of the reference Shields number, τ*, for the initiation of bed-load transport referred to the bed-surface sediment and calculated with the Parker  criterion, which includes the hiding effect, with the Shields parameter τ*(Di), which characterized each single event and it was, thus, calculated as a function of the size particle. It would appear that the larger bed particles are on average never set in motion during the various measurements. This remains true also in the case of the highest monitored event M7, where particles having a diameter larger than about 60 mm were expected to be immobile. These results are in general agreement with the size of the transported bed-load fraction reported in Figure 7.
 The predicted total sediment rating curve was derived with a fractional sediment transport equation and considering the aggradations and degradations of river bed during the propagation of the flood event. This type of modeling appears to be crucial in obtaining a reasonable interpretation of the data. This is apparent when the data are compared with the sediment rating curves obtained in the case of more schematic modeling approaches. To this purpose, the numerical model was run alternatively in the following simplified cases: (i) neglecting bed mobility, thus considering a flood wave over a fixed bed and (ii) neglecting sediment heterogeneity by referring sediment transport to unique representative diameter, D50.
 Results in Figure 10 show the following: (i) the sediment rating curve derived considering “fixed-uniform” bed and assuming uniform sediment does not enable the interpretation of the higher sediment discharge; (ii) the rating curve “mobile-uniform” derived in the case of a movable bed but with uniform sediment is still not sufficient to interpret the measured data, revealing that the fractional sediment transport is a central ingredient for deriving a reasonable sediment rating curve; (iii) in the case of fixed bed and fractional sediment approach (“fixed-mixture”), the rating curve is closer to the data, however, the lack of the bed dynamics prevents the model from a more convincing interpretation of the field data. Finally, it is interesting to stress that a much simpler approach, solely based on field data interpolation, gives a rating curve, in the form of a power-law function, which bends sharply upward, giving sediment discharges much higher than predicted by the modeled curve, and greatly unrealistic if extrapolated at higher discharges. This result confirms that sediment transport follows a more complex behavior than the one underlined by a simple power law relationship. For instance, the recent studies by Ferguson  show that the critical Shields stress in a gravel-bed stream not only increases with channel slope but also has a secondary dependence on bed sorting, giving rise to the presence of different thresholds for the transportation of the different sediment sizes.
 The hysteretic behavior of sediment transport in gravel-bed rivers is well known in the literature [see for instance Kuhnle, 1992] and may be associated to some forms of bed surface organization such as bed armoring [Guney et al., 2013] or the presence of sediment clusters [Hassan and Church, 2000; Strom et al., 2004]. Results in Figure 11 show sediment transport at peak conditions is above the interpolating line, thus suggesting that for given τ* bed-load transport during rising and falling stages is different (compare for instance M9 with M5 and M8).
 Regarding bed armoring, Figure 7 shows that this phenomenon might have played some role only in the measurements M3 and M4 at low flow discharges, whereas, at higher discharges, the grain-size distributions of the bed-load samples approached the subarmor layer distribution (with the exception of M11).
 Sediment clusters, i.e., microforms due to grouping of particles in the surface layer of a gravel-bed stream, can also deeply affect mean bed-load intensity and variance; in particular, Strom et al.  observed that, during cluster formation, occurring for values of τ* ranging (1.25–2.0) τ*ref, mean bed-load transport is reduced as clusters act as a sink for the incoming sediment; on the other hand, disintegration of individual clusters, for τ* ∼ 2.25τ*ref, gives rise to an increase of mean bed load as, in this case, clusters become a source of sediment. We can then speculate that in our measurements, for given τ*, bed load sampled at peak conditions (see for instance M9) is higher than bed load sampled during the falling limb (M5 and M8) due to the disintegration of sediment clusters. A more detailed, physically based, understanding of the relationship between hydrodynamics and sediment transport, can be obtained through an improvement in the resolution of particle location in time and space; this can be achieved through the employment of particle tracking technology [see for instance Sear et al., 2000; Habersack, 2001].
 Here an approach to developing reliable flow-sediment rating curves in a gravel-bed river where rapidly varying floods occur is proposed. The approach includes several activities: field measurements during flood events, laboratory analyses of the collected samples, hydro-morphodynamic numerical modeling for simulating the propagation of a flood in the river reach under investigation. In order to optimize the number of field measurements in a way to minimize the errors due to the rapidly varying flow discharge, this approach needs to be coupled with an analysis of the temporal and lateral flow variability. The proposed approach is an attempt to overcome the limitations related to either purely field investigations, which require a large number of measurements, or theoretical studies, which need calibration and validation.
 The overall activities have allowed the development of reliable flow and sediment transport rating curves at the monitoring station which are physically based and are able to capture the field measurements. Note that a simple interpolation of the field data would provide unrealistic results when applied outside of the data range.
 The proposed approach is particularly suitable for gravel-bed rivers where bed-load transport rates are relatively large and cause bed-elevation changes during the flood event, and where flow hydrographs have typically short durations and high peaks. This approach will be useful for river management and restoration practices and for morphodynamic models devoted to predicting the evolution of the river-coastal system.
 This work has been funded by Regione Toscana within the project “Realizzazione del primo stralcio della rete di monitoraggio su tre corsi d'acqua della Regione Toscana”; the authors are grateful to Enzo Di Carlo for his help and useful suggestions. Giulio Bechi, Francesco Canovaro, Andrea Corridori, Beatrice Mengoni, and Filippo Ginanni are acknowledged for their precious help at various stages of this study. CERAFRI-LAV is also acknowledged for sustaining the publication of this work. The Associate Editor, Kristin Bunte, Enrica Viparelli, and an anonymous referee are acknowledged for their precious review and help in improving the presentation of our work.