New strategies for upscaling high-resolution flow and overbank sedimentation models to quantify floodplain sediment storage at the catchment scale

Journal of Hydrology (2006) 329, 577– 594

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New strategies for upscaling high-resolution flow and overbank sedimentation models to quantify floodplain sediment storage at the catchment scale A.P. Nicholas *, D.E. Walling, R.J. Sweet, X. Fang Department of Geography, University of Exeter, School of Geography, Archaeology and Earth Resources, Rennes Drive, Amory Building, Exeter, Devon EX4 4RJ, UK Received 13 September 2005; received in revised form 9 March 2006; accepted 12 March 2006

KEYWORDS

Summary Quantitative models of catchment scale floodplain sediment storage must balance competing demands. For example, such approaches must incorporate a physically-based representation of controls on overbank sedimentation rates at the reach scale, but should also be computationally efficient so that catchment scale analysis remains a realistic goal. This paper reports the development of a novel nested modelling strategy that combines a high-resolution hydraulic model based on the shallow water form of the Navier–Stokes equations, with a reduced complexity overbank sedimentation model and coarse-resolution catchment sediment budget model. The approach is implemented within a Monte-Carlo framework to allow an assessment of uncertainty in the parameterisation of overbank sedimentation processes, and to derive uncertainty-bounded estimates of floodplain sedimentation rates over a range of spatial scales. This strategy is applied to a 26 km reach of the River Culm, Devon, UK. The relative performance of a wide range of model structures is evaluated by comparing model predictions with estimates of actual mean annual sedimentation rates derived by analysis of the caesium137 content of floodplain sediment cores at 20 locations within each of eight study sites distributed throughout the catchment. The results of the current model application demonstrate the potential of the nested modelling strategy as a means of upscaling physically-based flow and sediment transport codes. Furthermore, the novel reduced-complexity overbank sedimentation model presented here is shown to provide a means of simulating complex patterns of suspended sediment transport and deposition, while reducing computing costs by 2–3 orders of magnitude compared with conventional high-resolution advection–diffusion codes. Uncertainty-bounded estimates of floodplain sediment storage for the River Culm confirm that floodplain sedimentation represents a primary component of the fine sediment budget of lowland catchments.

Floodplain; Numerical model; Suspended sediment; Overbank sedimentation; Catchment

* Corresponding author. E-mail address: [email protected] (A.P. Nicholas).



0022-1694/$ - see front matter c 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2006.03.010

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A.P. Nicholas et al. Consequently, the modelling strategies developed here may also be of considerable value in attempts to quantify the fate of sediment-associated nutrients and contaminants at the basin scale. c 2006 Elsevier B.V. All rights reserved.



Introduction Recent years have seen a growing awareness of the environmental importance of overbank sedimentation on river floodplains. For example, research conducted in a global distribution of river basins has highlighted the potential for a significant proportion of fine sediment eroded from the land surface to go into storage on floodplains before reaching the basin outlet (Goodbred and Kuehl, 1998; Walling et al., 1999; Fryirs and Brierley, 2001). Consequently, overbank sedimentation represents an important control on downstream sediment loads and on the transport and fate of sedimentassociated nutrients and contaminants (Middelkoop, 2000; Walling and Owens, 2003). Furthermore, accumulation of fine sediment on floodplains over historic time-scales may lead to modification of channel conveyance capacity and associated changes in flood frequency (Trimble, 1981; Moody and Troutman, 2000). Understanding and managing these issues requires the adoption of a catchment scale perspective, which seeks to evaluate the role of fine sediment storage on floodplains in the context of the catchment sediment budget as a whole. However, despite this requirement, the majority of research into contemporary floodplain sedimentation has been carried out at the reach scale (i.e., within sites with downstream dimensions less than a few km). Comparatively little research has been conducted to quantify floodplain sediment storage within whole drainage basins, largely as a result of the methodological and logistical problems that are inherent in working at this scale. Calculation of suspended sediment conveyance losses between upstream and downstream river gauges provides an effective means of estimating both annual and event-based floodplain sediment storage (e.g., Gretener and Stromquist, 1987; Lambert and Walling, 1987). However, this approach is subject to uncertainties associated with discharge and sediment load estimates, is dependent upon the availability of continuous records of discharge and sediment concentration, and provides little insight into spatial variability in sediment storage. Several recent studies have demonstrated the potential for using fallout radionuclides to quantify mediumterm (ca. 40–100 years) floodplain sediment storage at the catchment scale (Walling et al., 1996; Owens and Walling, 2002). This approach has the advantage that it is not dependent on the availability of long-term sediment load data. However, it is limited by practical constraints on the number of sediment cores that can be obtained for analysis and the difficulty of assessing the extent to which the chosen sampling locations provide representative estimates of average rates of sedimentation. These limitations may be overcome by combining such empirical data sources with modelling approaches capable of quantifying floodplain sediment storage at the catchment scale (Sweet et al., 2003). Critically, such approaches must incorporate a physically-based representa-

tion of controls on overbank sedimentation rates at the reach scale, but should also be computationally efficient so that catchment scale analysis remains a realistic goal. At the reach scale, overbank sedimentation rates are characterised by a high degree of local spatial variability, which is a product of the relationships between floodplain topography, overbank hydraulics and suspended sediment transport and deposition processes (Walling et al., 1996; Nicholas and Walling, 1998). Consequently, patterns of sedimentation rarely conform to trends predicted by simple, computationally efficient functions parameterised by distance from the main channel and relative floodplain elevation (e.g., Pizzuto, 1987; Howard, 1992). Increasingly, two- and three-dimensional numerical models have been implemented in floodplain environments to simulate overbank hydraulics (Bates et al., 1996; Nicholas and Mitchell, 2003; Nicholas and McLelland, 2004) and suspended sediment transport and deposition (Nicholas and Walling, 1997; Middelkoop and Van der Perk, 1998; Stewart et al., 1999; Nicholas, 2003). This work has highlighted the critical role of meso-scale topographic features (e.g., abandoned channels, levees, drainage ditches, etc.) that control flow and sedimentation processes. However, while high-resolution spatially-distributed models may provide the necessary level of process representation to account for these effects, the computational demands of such approaches preclude their application over large time and space scales. In addition, despite their strong physical basis, many processes remain heavily parameterised, particularly in the case of the representation of fine sediment deposition within two-dimensional depth-averaged models. The latter typically represent sedimentation processes using semi-empirical formulae that have been developed in the laboratory (cf. van Rijn, 1993), hence considerable uncertainty surrounds the suitability of such functions and the definition of appropriate parameter values in applications involving vegetated floodplains. Recent advances in environmental modelling have highlighted the difficulty of identifying optimum model structures and have presented methods that allow the quantification of uncertainty in model outcomes due to the existence of a range of acceptable model parameterisations (Beven and Binley, 1992; Beven and Freer, 2001). However, implementation of such approaches necessitates conducting multiple model runs, in order to examine a wide range of model structures. Evidently, this represents a significant problem in the case of the computationally-expensive flow and sedimentation models that have been used in floodplain applications to date. This paper reports the development and application of a procedure that aims to overcome this problem and obtain uncertainty-bounded estimates of floodplain sediment storage at the catchment scale. This is accomplished by utilising a nested modelling strategy that incorporates a highresolution hydraulic model, a reduced complexity spatially-

New strategies for upscaling high-resolution flow and overbank sedimentation models

hydraulic and sediment transport models have been applied, and interpolation of these predictions in intervening reaches. The sediment budget model is applied separately for each parameter combination used in the spatially-distributed sediment transport simulations. The relative performance of the model for each parameter combination (i.e., the likelihood that a particular parameter combination provides an acceptable representation of sedimentation processes in the real world) is determined by comparing model predictions with estimates of mediumterm mean annual sedimentation rates derived from measurements of the caesium-137 (137Cs) inventories of floodplain sediment cores obtained at selected locations within each of the study reaches. Model predictions are then combined within an uncertainty framework (cf. Beven and Freer, 2001; Hankin et al., 2001) to derive uncertaintybounded estimates of floodplain sediment storage rates throughout the study catchment. The approach outlined above was implemented along a 26 km reach of the River Culm, Devon, UK (Fig. 1). Spatially-distributed hydraulic and sedimentation models were applied to eight floodplain sites selected along the main valley floor of the River Culm. Land use at all floodplain sites is permanent pasture. Sites were chosen to include a range of floodplain and channel morphologies (site characteristics are summarised in Table 1). Each of the eight sites was surveyed in detail using a Leica System 500 Global Positioning System (GPS) and Geodimeter 600 total station. Survey density was varied according to topographic complexity with between 3000 and 12,000 points sampled at each site. Data were interpolated by kriging, using a spherical data distribution model, in order to construct Digital Elevation Models (DEM) for use in spatially-distributed modelling. DEM resolu-

distributed overbank sedimentation model, and a coarse-resolution catchment sediment budget model.

Methodological framework The methods developed here are implemented by first subdividing the entire main valley floor of a drainage catchment into a series of floodplain reaches each approximately two times the valley floor width in length. The procedure for estimating rates of fine sediment storage within each of these floodplain reaches involves three stages. In the first stage a two-dimensional hydraulic model is used to simulate spatial patterns of overbank flow depth and velocity for a range of discharges within a representative subset of floodplain reaches. In the second stage these hydraulic predictions are used to implement a simple model of suspended sediment transport and deposition in order to generate spatially-distributed estimates of mean annual sedimentation rates within this reach subset. The sediment transport model that is applied here is based upon a modified form of the standard advection–diffusion equation which allows patterns of suspended sediment dispersion to be determined without recourse to conventional numerical techniques for solving two-dimensional partial differential equations. This reduces the computational demands of the model, so that it becomes feasible to calculate sedimentation rates within each floodplain reach using a large number of model parameter combinations. In the final stage of the procedure, a simple sediment budget model is used to calculate rates of sediment storage for all floodplain reaches within the basin and associated changes in suspended sediment load. This involves integration of spatially-distributed sedimentation rate predictions in reaches where the

0

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2 Uffculme 7

3 Woodrow

4 Hayne Barton

4 5 Woodmill

6 Kensham 7 Killerton 8 Rewe Stoke Canon

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Study Area

Study site

Figure 1 The drainage basin of the River Culm and the eight study reaches at which spatially-distributed flow and sediment transport modelling was conducted.

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Table 1 Morphological characteristics of the eight study reaches at which spatially-distributed flow and sediment transport modelling was conducted Reach

Drainage area (km2)

Bankfull discharge (m3 s1)

Number of channels

Mean sinuosity

Floodplain width (m)

Culmstock Uffculme Woodrow Hayne Barton Woodmill Kensham Killerton Rewe

77 111 123 126 222 233 245 274

8.4 23.9 18.7 17.3 42.2 17.2 17.3 14.3

1 1 2 2 1 2 1 1

1.37 1.97 1.21 1.58 1.03 1.45 1.55 1.50

145 320 500 650 280 350 550 720

tion varied from 1 to 2.5 m according to the spatial scale and topographic complexity of individual sites.

Overbank hydraulics Overbank flow patterns within each of the eight study reaches were simulated using a two-dimensional hydraulic model (hydro2de) which solves the depth-averaged shallow water form of the Navier–Stokes equations. The conservation of mass and momentum equations solved by hydro2de are written as: oh oq or þ þ ¼0 ot ox oy oq oðq2 =hÞ oðqr=hÞ g oðh2 Þ oz þ þ þ þ gh ot ox oy 2 ox ox 1 oðhsxy Þ 1 oðhsxx Þ sbx  þ  ¼0 q oy q ox q or oðr2 =hÞ oðqr=hÞ g oðh2 Þ oz þ þ þ þ gh ot oy ox 2 oy oy 1 oðhsyx Þ 1 oðhsyy Þ sby  þ  ¼0 q ox q oy q

ð1Þ

ð2Þ

ð3Þ

where h is flow depth, q and r are unit discharge in the x and y directions, respectively, t is time, z is bed elevation, g is acceleration due to gravity, q is the fluid density, sxx, syy, sxy and syx are turbulent stresses and sbx and sby are bed shear stresses. Turbulent normal stresses are assumed to be negligible, while shear stresses are modelled using the Boussinesq approximation   ou ov sxy ¼ syx ¼ qmt þ ð4Þ oy ox where u = q/h and v = r/h and mt is the eddy viscosity which is estimated as mt ¼ 0:07u h

ð5Þ

where u* is the friction velocity. Bed shear stresses are determined as a quadratic function of velocity: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 sbx 2u u þv ¼ gn ð6Þ 1=3 q h pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sby v u2 þ v 2 ¼ gn2 ð7Þ q h1=3 where n is the Manning roughness coefficient. Hydro2de uses a finite volume method and solves Eqs. (1)–(3) by explicit time integration to calculate the flow

depth and two horizontal unit discharge components throughout a regular grid representing the river bed and floodplain topography. Numerical fluxes are estimated using Roe linearisation (Roe, 1981) and second order accuracy is achieved using a variable extrapolation (MUSCL) approach (van Leer, 1977). Further details of the numerical solution techniques used in the model are given by Connell et al. (1998) and Beffa and Connell (2001). Roughness parameter values were assigned using a simple delineation between channel and floodplain areas within each reach. A value of 0.06 for Manning’s n was assumed for floodplain regions based on a previous application of hydro2de at a site on the River Culm (Nicholas and Mitchell, 2003). Roughness parameter values within the main channel were determined by optimising the fit between modelled and observed bankfull discharge at each site. The approach to roughness parameterisation adopted here is necessarily simplistic and reflects the lack of distributed hydraulic data required to specify parameter values with greater precision. However, evidence from numerous recent model applications demonstrates that even where such data are available it is not generally possible to identify a single optimum model parameter set (Romanowicz et al., 1996; Hankin et al., 2001; Nicholas and Mitchell, 2003; Nicholas, 2003). The relative sensitivity of hydraulic predictions to channel and floodplain roughness parameter values is complex and stage dependent (see Nicholas and Mitchell, 2003). In the context of the central aim of this study (i.e., to derive uncertaintybounded estimates of floodplain sediment storage) application of the hydraulic model using a range of possible roughness parameterisations at each site is not warranted for a number of reasons. The use of a single floodplain roughness coefficient is justified, to a certain extent, by the uniformity of valley floor land use and vegetation within the catchment. While the precise value that this parameter should take is subject to uncertainty, changes in this parameter value do not affect spatial patterns of modelled sediment deposition at a site significantly in relative terms. Rather, modelled patterns of sediment concentration and sedimentation are more sensitive to the parameterisation of deposition processes (see below) than hydraulic roughness. Furthermore, there are good reasons to expect that varying the floodplain roughness coefficient in hydraulic simulations will not lead to systematic changes in either the predicted mean sedimentation rate at a site or the range of these predictions (see the discussion of the sediment budget model results below).

New strategies for upscaling high-resolution flow and overbank sedimentation models

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The hydraulic model has been validated previously at sites on the River Culm using spatially-distributed measurements of overbank flow depth and depth-mean velocity, and dGPS surveys of floodwater inundation extent (Nicholas and Mitchell, 2003). In addition, patterns and mechanisms of inundation simulated by the model were compared with visual observations and ground photography obtained at all eight study reaches. Fig. 2 shows modelled inundation patterns for a range of discharges, on the rising limb of the hydrograph, at two floodplain reaches on the River Culm. Fig. 3a and b show patterns of flow depth and unit discharge for the regions enclosed within boxes in Fig. 2a. It should be noted that the results presented in Fig. 3a and b are for a single discharge and that, in order to assist visualisation of flow patterns, vectors are shown at greatly reduced spatial resolution compared to that of the hydraulic model (see figure captions). These results illustrate the non-uniformity of overbank hydraulics, which is itself a product of the topographic complexity that is a common feature of natural lowland floodplains and which represents a primary control on suspended sediment transport and deposition processes. Initial stages of inundation are characterised by localised

Initial hydraulic model runs were conducted at two sites using flood hydrographs of varying peak discharge. Modelled flow depths and velocities generated for equivalent discharges but different hydrographs were then compared, in order to assess the extent to which overbank flow characteristics vary between flood events of different magnitude. In conjunction with earlier simulations that examined the influence of hydrograph duration (Mitchell, 2002), these model runs suggest that while hydraulic conditions for a given discharge differ substantially between rising and fall limbs, they are relatively insensitive to peak discharge or hydrograph shape (for single peaked events). This observation may not hold in environments characterised by flashier flood regimes. However, for the purpose of the current study of lowland floodplain sedimentation it was deemed reasonable to derive hydraulic information by simulating a single flood hydrograph with a peak discharge equivalent to that of an event with a return period of 40 years (the time period over which 137Cs-based sedimentation rate estimates are averaged). Data with which to specify these peak discharges were provided for each site by the Environment Agency of England and Wales.

Flow

Flow

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Inundation extent at Q (m3 s-1) a

20

25

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Inundation extent at Q (m3 s-1) b

10

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35

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Figure 2 Modelled inundation extents for a range of discharges (up to the peak of a flood with a return period of 40 years) at two sites on the River Culm: (a) Uffculme; (b) Kensham.

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A.P. Nicholas et al. Depth (m) 0.01 0.1 0.25 0.5 0.75 1.0 1.5

a

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50m

Depth (m) 0.01 0.1 0.25 0.5 0.75 1.0 1.5

b

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Figure 3 Modelled patterns of flow depth and unit discharge for areas within the Uffculme study site enclosed in boxes in Fig. 2a, at a discharge of 60 m3 s1. Unit discharge vectors are plotted on an 8-m resolution grid. Model grid resolution is 2 m. Vector length is proportional to the square root of unit discharge (to assist visualisation of flow patterns in areas of low unit discharge). The maximum unit discharge in these images is 4.5 m2 s1.

backwater ponding, breach flow and floodwater routing along drainage ditches. In many areas water is transferred to the back or centre of the floodplain and the inundation front expands from these areas back towards the main channel as discharge rises. Even at discharges >3 times bankfull when the majority of the floodplain is inundated, the magnitude and direction of overbank flow vectors is highly spatially variable and strongly dependent upon relatively subtle topography. Floodplain flow vectors inclined obliquely to

the main channel are common, and are indicative of strong advective mixing of channel and floodplain water. These patterns are consistent with a growing body of field observations and numerical simulations (Middelkoop and Van der Perk, 1998; Nicholas, 2003; Nicholas and McLelland, 2004) that highlight the dominance of water and sediment transfer to the floodplain by advection rather than by diffusive mechanisms as has been assumed traditionally (e.g., Pizzuto, 1987; Marriott, 1992).

New strategies for upscaling high-resolution flow and overbank sedimentation models

Suspended sediment transport and deposition In several previous studies, patterns of overbank sedimentation have been simulated using suspended sediment transport models based upon two- and three-dimensional advection–diffusion equations (Nicholas and Walling, 1998; Stewart et al., 1999; Nicholas, 2003). Despite the benefits of such physically-based approaches, they are computationally expensive, thus restricting the potential for conducting multiple simulations to evaluate a wide range of model parameter sets. A central aim of the current study was to derive estimates of the uncertainty in model predictions of overbank sedimentation rates by conducting multiple simulations within each study reach. However, existing computationally-efficient models of floodplain sedimentation typically determine deposition rates as simple functions of distance from the main channel and relative elevation. Critically, such approaches do not account for the relationship between overbank hydraulics and sediment transport and deposition processes. Furthermore, since they do not incorporate a formal statement of mass conservation, they do not provide a suitable framework for use in sediment budget investigations. In order to address these limitations, a novel suspended sediment transport model was developed that enables efficient calculation of spatially-distributed patterns of suspended sediment concentration and deposition rates as a function of overbank flow characteristics. When compared with conventional approaches based on the solution of two-dimensional depth-averaged advection–diffusion equations, the method outlined below is associated with a typical reduction in computing costs in the order of 2–3 orders of magnitude. Sediment transport calculations are conducted using output from the hydraulic model described above. Hydraulic model results were taken at ca. 200 equally-spaced instants in time over the duration of the simulated 40-year flood event, on both rising and falling limbs of the hydrograph. Patterns of suspended sediment concentration and overbank sedimentation were derived separately for the flow fields at each of these ‘time-slices’. Local floodplain sediment concentrations are defined in terms of a dimensionless sediment concentration (C) equal to the local absolute concentration divided by the main channel concentration. This approach allows sedimentation rates to be determined from the model results for a range of main channel sediment concentrations. The first step in the calculation procedure is to define the dimensionless sediment concentration at all cells within the main channel to equal unity. This involves the implicit assumption that the sediment concentration in the main channel is spatially-uniform. Calculations proceed by comparing all pairs of inundated cells in the model domain where one cell contains sediment and the adjacent cell does not. A potential dimensionless sediment concentration is then determined for the sediment-free cell by evaluating the one-dimensional mass balance relationship describing suspended sediment transport between the two cells and sediment deposition in the intervening region:   oðhCÞ oðqCÞ o oC þ  eh þ DC ¼ 0 ð8Þ ot ox ox ox

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where h is flow depth, t is time, q is the unit discharge in the x-direction, C is the depth-averaged dimensionless suspended sediment concentration, e is the sediment diffusivity (equal to the eddy viscosity divided by the Prandtl– Schmidt number for sediment particles), and D is the net sediment deposition rate (i.e., deposition less resuspension). It is immediately clear from this equation that, in its current form, the model is only applicable where net erosion does not occur in overbank areas. This approach is justified for low gradient, vegetated floodplains such as those considered in the current study, and could easily be modified in other situations by including a term representing erosion in Eq. (8). A number of other simplifying assumptions must be introduced to solve this equation for a single pair of cells in the model domain. Most significantly, we assume that the conditions in the region between the two cells in question are steady and uniform. In this situation the exact solution to Eq. (8) is given by a simple exponential relationship (cf. Pizzuto, 1987), which describes the decline in sediment concentration between the two cells: Ciþ1 ¼ Ci ewDx

ð9Þ

where w is a decay coefficient, the value of which must be determined in order to calculate the concentration at the sediment-free cell (Ci+1) as a function of that at the sediment-laden cell (Ci). In this situation, the time-dependent term in Eq. (8) is equal to zero, and the following expressions are obtained for the remaining terms: oðqCÞ oC ¼q ¼ qCi wewx ox ox   o oC o2 C eh ¼ eh 2 ¼ ehCi w2 ewx ox ox ox DC ¼ DCi ewx

ð10Þ ð11Þ ð12Þ

where x is the distance from the midpoint of cell i in the direction of cell i + 1. Given a suitable expression for the deposition rate per unit sediment concentration (D), Eqs. (10)–(12) can be combined to yield a simple quadratic function in w, the decay coefficient, that can be solved to find the unknown dimensionless sediment concentration in any cell that is adjacent to a cell for which the sediment concentration is known. Traditionally, overbank deposition of suspended sediment has been conceptualised as a process driven by particle settling, and has been modelled as a function of particle fall velocity and local flow conditions relative to a hydraulic threshold (e.g., Nicholas and Walling, 1997; Middelkoop and Van der Perk, 1998; Stewart et al., 1999). However, more recently it has been recognised that sediment deposition occurs even where the depth-mean flow velocity exceeds the threshold for particle settling, and that this may reflect the occurrence of sediment entrapment by floodplain vegetation (Nicholas, 2003). With this in mind, deposition rates are determined here as a function of both particle settling and vegetative trapping:  2 ! V D ¼ kV S 1  þ qpE ð13Þ V cr where k is an empirical constant, VS is the sediment particle fall velocity, V is the local flow velocity magnitude, Vcr is

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the critical velocity for sediment deposition, p is the proportion of the water column occupied by vegetation and E is the vegetation trapping efficiency per unit distance (which has units 1/L). The first term in Eq. (13) represents deposition due to particle settling and is set to zero where V > Vcr. The second term represents the entrapment of sediment by vegetation. In the current application, p is defined by assuming a constant vegetation thickness of 0.1 m (based on field observations). The particle fall velocity (VS) is specified using existing data for the River Culm (Nicholas and Walling, 1996). Precise values of the parameters k, Vcr and E cannot be determined a priori. Instead, multiple simulations are conducted using a range of values of these parameters (see below). The procedure outlined above allows the potential sediment concentration at any cell to be determined as a function of the known sediment concentration in an adjacent cell and the intervening hydraulic conditions. Implementation of this procedure to determine spatially-distributed patterns of sediment concentration must also account for the fact that any given location on the floodplain may receive sediment from the main channel via a number of routes, and that the shortest route need not necessarily be the one that controls the local sediment concentration. For example, Fig. 4 illustrates a situation in which cell A is likely to receive sediment from cell B, rather than nearby cell C. To account for this, calculations are performed in a series of iterations. At the start of each iteration a minimum sediment concentration is specified. This represents the minimum sediment concentration that will be assigned during the current iteration to an inundated cell that contains no sediment at the start of the iteration. During a sin-

C

A

B Figure 4 Simple example of a situation where sediment concentration at cell A is determined largely by sediment supply from cell B, rather than from adjacent cell C. Vectors indicate flow directions, shaded cells are those where sediment concentrations are known, unshaded cells are those where concentrations are unknown.

gle iteration, each pair of adjacent cells is examined, where one cell contains sediment and the other is sediment-free. The potential sediment concentration at the sediment-free cell is calculated using the procedure outlined above. Where this potential concentration exceeds the minimum concentration for the current iteration the sediment concentration in the sediment-free cell is set equal to the potential concentration. Where several potential concentrations exceed the minimum concentration the highest value is used. Where the potential sediment concentration at the cell does not exceed the minimum concentration for the iteration, the concentration in the sediment-free cell is not updated. This approach ensures that sediment spreads out from the main channel in the direction of the maximum sediment flux. The rationale behind this approach is that suspended sediment transport on natural floodplains is dominated by advection rather than diffusion, as illustrated by recent monitoring and modelling studies (Middelkoop and Van der Perk, 1998; Nicholas, 2003). At the end of an iteration the minimum concentration is reduced by a specified amount. Iterations cease when the minimum concentration reaches zero. The smaller the change in the minimum sediment concentration between iterations the greater the number of calculations required. In the current application this change in the minimum concentration was set equal to 1% of the main channel concentration (i.e., DC = 0.01). As noted above, patterns of sediment concentration derived using this approach reflect predominantly the role of sediment transport by advection and, consequently, underestimate the role of sediment redistribution by diffusive processes. In a final stage of the calculation procedure values of local concentrations in each cell are averaged with values in the four adjacent cells to represent the effects of diffusive transport. Fig. 5 shows results obtained using this simple model for a single combination of the parameters k, Vcr and E, for a discharge 60 m3 s1 at the Uffculme study reach. Interpretation of the simulated pattern of sediment concentration is best achieved by comparison with the hydraulic model results shown in Figs. 2 and 3. Patterns of sediment dispersion are clearly a strong function of overbank hydraulics, with a gradual reduction in sediment concentration along major floodplain flow paths (e.g., along line AB), and steeper concentration gradients in areas where overbank flow vectors are aligned parallel to, or directed back towards, the channel (e.g., C and D). Validation of these sediment concentration predictions in the absence of fine resolution field data are not possible. However, comparison can be made with sediment concentration predictions derived by solution of the two-dimensional depth-averaged mass balance equation describing suspended sediment transport by advection and diffusion:     oðhCÞ oðqCÞ o oC oðrCÞ o oC þ  eh þ  eh þ DC ¼ 0 ot ox ox ox oy oy oy ð14Þ where r is unit discharge in the y direction and all other terms have been defined previously. Fig. 6 shows patterns of suspended sediment concentration derived by solving Eq. (14) using a first order upwind scheme for steady-state conditions at a discharge of 60 m3 s1.

New strategies for upscaling high-resolution flow and overbank sedimentation models

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D

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Sediment concentration (%) 0

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Figure 5 Patterns of suspended sediment concentration at the Uffculme study reach derived using the simple sediment transport model for a discharge of 60 m3 s1. Arrows indicate lines of significant overbank flow conveyance. See text for references to labels A–D.

Figure 6 Patterns of suspended sediment concentration at the Uffculme study reach for a discharge of 60 m3 s1, derived by solving the two-dimensional depth-averaged mass balance equation describing sediment transport by advection and diffusion.

Visual comparison of Figs. 5 and 6 demonstrates that patterns of sediment concentration derived using the two models are broadly consistent, with major sediment dispersal pathways located along lines of significant overbank flow conveyance. It should be noted that concentrations derived using the simple model are consistently greater than those obtained using the two-dimensional model. This reflects the fact that the simple model determines the reduction in concentration with distance from the channel along the pathway that maximises the horizontal sediment flux. Concentration differences between the results of the two approaches are generally small (e.g., <10% of the main channel concentration over the majority of the floodplain). Furthermore, it should be stressed that while comparison of results obtained using the two models is informative, and provides some confidence in the spatial patterns predicted using the new approach developed here, this simple model is not intended to reproduce the results of the more sophisticated model exactly. Rather, it provides a processbased, computationally efficient means of simulating spatial patterns of suspended sediment concentration and overbank

deposition. As noted above, a key objective of this work is to conduct multiple simulations that allow sedimentation rate predictions to be derived for a wide range of model parameter sets. It is worth noting in this context that the differences in local sediment concentration (and hence deposition rates) between the new sediment transport model developed here and the conventional two-dimensional advection–diffusion model are small compared to differences in sedimentation rates associated with changes in the parameters of Eq. (13). For example, varying these parameters across a realistic range results in sedimentation rate predictions that vary over 2–3 orders of magnitude at most floodplain locations. This issue is addressed in the following section.

Catchment sediment budget modelling For any single combination of the parameters k, Vcr and E in Eq. (13), the procedure described in the previous section enables the overbank deposition rate per unit main channel sediment concentration to be determined at all locations within a study reach, for each of the flow fields derived

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for the 40-year flood hydrograph. These data can be used to determine spatial patterns of predicted mean annual sedimentation rate using the following relationship: Si ¼

Q max X

ð15Þ

T Q DQi CQi MQ

Q bf

where Si is the mean annual sedimentation rate at location i, TQ is the average time spent at discharge Q during a year, DQi is the deposition rate per unit sediment concentration for this discharge at location i, CQi is the local dimensionless sediment concentration at discharge Q, MQ is the main channel sediment concentration at discharge Q, and the summation is carried out over all discharges in excess of bankfull (Qbf) up to the maximum discharge that occurs at the site (Qmax). Flow duration curves needed to specify values of TQ for each study reach were based on the relationship between catchment area and 40-year peak flow for the River Culm, combined with a dimensionless flow duration curve derived for instrumented sites. These hydrometric data were provided by the Environment Agency of England and Wales. Values of MQ are defined by the sediment rating curve at a site, which can be modelled as: MQ ¼ aQ b

ð16Þ

where a and b are empirical constants. Values of b are typically in the range 1–2 for British Rivers, with a mean of about 1.2 (Walling and Webb, 1987). If the mean annual sediment load (L) at a site is known, the value of the constant (a) can be determined for a given value of the exponent (b) simply by integrating Eq. (16) over the flow duration curve: a ¼ PQ max 0

L

ð17Þ

T Q Q bþ1

Eqs. (15)–(17) allow spatial patterns of local mean annual sedimentation rate to be calculated for each study reach given the mean annual sediment load (L) entering the reach. Integration of these predictions over the reach allows the total mean annual sedimentation rate for the reach as a whole to be determined. Changes in suspended sediment load throughout a catchment are calculated using the following mass balance relationship: LOUT ¼ LIN  S þ B þ LLAT IN

OUT

LAT

ð18Þ

and L are, respectively, the mean annual where L , L sediment load entering the reach from upstream, the sediment load exiting the reach, and the sediment load entering the reach from tributary catchments, S is the total mean annual sedimentation rate within the reach, and B is the mean annual rate of bank erosion. We use this expression to carry out suspended sediment budget calculations by first subdividing the entire main valley floor of the River Culm into a series of floodplain reaches each approximately two times the valley floor width in length. Calculations begin at the outlet from the catchment (at Rewe) where sediment concentrations have been monitored for ca. 30 years so that an estimate of the mean annual sediment load is available. Calculations proceed in an upstream direction by determining each of the components of the sediment budget to enable the sediment load leaving the next floodplain reach to be determined. Mean annual volumetric rates of bank

erosion were determined for each floodplain reach in a GIS by using measured channel depths and estimates of channel migration rates obtained using digital aerial photography flown in 1998 and Ordnance Survey maps from 1967. Sediment supply associated with tributaries was quantified by assuming that the ratio of the sediment load of the tributary to that of the main catchment upstream of the tributary junction is equal to the ratio of the associated discharges (i.e., that sediment concentrations in water originating in the tributary and main channel upstream are the same). This is a reasonable first approximation in the absence of monitored records of sediment load from a network of gauging stations. The only term that remains to be defined in the sediment budget expression (Eq. (18)) is the mean annual floodplain sedimentation rate, which is itself a function of the local sediment load. At reaches where spatially-distributed modelling was conducted the procedures described in the previous two sections were used to calculate the mean annual overbank sedimentation rate per unit sediment load. To determine sedimentation rates in the intervening reaches the potential for using the spatially-distributed model results to derive relationships between mean annual overbank sedimentation rates and reach morphology (e.g., floodplain width, channel numbers and sinuosity, valley gradient) was investigated. However, the only statistically significant relationship that emerged from this analysis was between the total sedimentation rate within a reach and floodplain area. This implies that reach-averaged sedimentation rates do not vary as a simple function of channel and/or floodplain morphology. Consequently, the mean annual sedimentation rate in the floodplain reaches where spatially-distributed modelling was not conducted was estimated as the product of the sediment load (determined by the sediment budgeting procedure), the total floodplain area, and the mean annual sedimentation rate per unit sediment load per unit floodplain area, where the latter is interpolated between the two reaches for which spatially-distributed model predictions are available, either side of the floodplain reach in question. The procedure outlined above can be used to derive predictions of the mean annual sedimentation rate for each floodplain reach within a catchment, and the associated changes in sediment load between the catchment outlet and headwaters, for any single combination of the parameters k, Vcr and E in Eq. (13). It is important to note that these parameters affect sedimentation at individual sites both by controlling local deposition rates (determined by Eq. (13)) and, in so doing, by promoting changes in sediment load between individual sites. In order to account for the uncertainty in the values that these parameters should take, and derive bounded estimates of sedimentation rates that reflect this uncertainty, the catchment sediment budget model was implemented within a Monte-Carlo framework (cf. Romanowicz et al., 1996; Hankin et al., 2001). In order to do this it is first necessary to determine a physically plausible range for each parameter. Suitable ranges for these parameter values were constrained in two ways. First, using evidence from previous applications of Eq. (13) in lowland floodplain environments (Mitchell, 2002). Second, by conducting preliminary simulations for a wide range of parameter values and comparing average predicted overbank

New strategies for upscaling high-resolution flow and overbank sedimentation models sedimentation rates for the River Culm as a whole with existing estimates based on suspended sediment conveyance loss calculations (Lambert and Walling, 1987). Using these methods, plausible values for the three parameters were determined to lie in the ranges; 0.01–1.0 (k), 0.01– 1.0 ms1 (Vcr), and 0.0001–0.01 m1 (E). Following this preliminary stage, the catchment sediment budget model was implemented using 600 combinations of the three parameters drawn at random from the ranges indicated above by assuming a uniform probability distribution for each. In addition, for each parameter combination the model was applied using five values of the parameter b in Eq. (16) (e.g., 1.1–1.5 at increments of 0.1) to give a total of 3000 model runs. Fig. 7 shows predicted patterns of overbank sedimentation at the Uffculme study reach derived for two of these model parameter sets. Fig. 7a shows model predictions for a case where sedimentation is dominated by vegetative trapping of sediment (i.e., low value of k and high value of E). In this situation, spatial patterns of deposition are strongly correlated with overbank flow conveyance pathways, since these are associated with high suspended sediment fluxes through the water column (and hence the vegetation layer). Fig. 7b shows model predictions for a case where sedimentation is dominated by particle settling (i.e., low value of E and high value of k). In this situation, spatial patterns of deposition are characterised by greater local variability, with higher deposition rates in areas that typically experience lower velocities or are prone to floodwater ponding. The relative performance of the model for each of the 3000 parameter combinations was evaluated by comparing model predictions with estimates of actual mean annual sedimentation rates at 20 locations within each of the eight study reaches. Estimates of actual sedimentation rates were derived using the 137Cs whole core approach (Walling et al., 1996; Walling and He, 1997). Full details of this approach

587

are summarised by Walling (1999). In brief, floodplain sediment cores were obtained to a depth of 0.6 m and analysed to determine the total inventory of 137Cs for each whole core. Comparison of the 137Cs inventory for a floodplain core with a reference inventory, determined for a geomorphologically stable site above the level of overbank inundation, allows the excess 137Cs associated with overbank sedimentation to be calculated. The excess 137Cs inventory is then converted to a mean annual sedimentation rate over the period since 137Cs fallout began (post 1950). This is carried out using an estimate of the sedimentation rate per unit excess 137Cs, which is obtained for a sectioned core sampled from a representative location within each reach. These calculations are also adjusted to take account of contrasts in particle size and the known preferential association of 137 Cs with finer sediment fractions. Assessment of the relative performance of the model for each of the 3000 parameter sets was conducted within a Generalized Likelihood Uncertainty Estimation (GLUE) framework (cf. Beven and Binley, 1992; Hankin et al., 2001). The quality of fit between model predictions and 137Cs-derived estimates of overbank sedimentation was calculated for each parameter set and study reach as: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 PN  k n¼1 SP  SE ð19Þ F j;k PN 1 ¼ n¼1 SE =N where F j;k 1 is the measure of fit for reach j using parameter set k, N is the number of locations at which sediment cores were obtained within the reach, SkP is the predicted mean annual sedimentation rate for parameter set k at each core location and SE is the associated 137Cs-derived sedimentation rate estimate. Goodness-of-fit measures for each study reach are combined to yield a measure of the overall goodness-of-fit, for the catchment as a whole, for each parameter set using the expression:

Mean annual sedimentation rate (g cm-2 yr -1 )

Mean annual sedimentation rate (g cm-2 yr -1) 2.0 1.0 0.5 0.1 0.01 0 None

1.0 0.5 0.1 0.05 0.01 0 None

0

a

0

100m

100m

b

Figure 7 Patterns of predicted mean annual sedimentation rate derived using two different combinations of the parameters in Eq. (13): (a) k = 0.057, Vcr = 0.813, and E = 0.002; (b) k = 0.513, Vcr = 0.344, and E = 0.00013.

588 F k2 ¼

A.P. Nicholas et al. 8 Y

j;k

eF 1

ð20Þ

F k2 RPMk ¼ P3000 k¼1

j¼1

0.8 0.6 0.4 0.2 0 10

15

0.6 0.4 0.2 0 5

10

15

0.8 0.6 0.4 0.2 0 0

5

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5

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Core number

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Woodmill

1 0.8 0.6 0.4 0.2 0 0

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Woodrow Farm

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Uffculme

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Hayne Barton

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Killerton

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Kensham

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Sedimentation rate (g cm-2)

0

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Sedimentation rate (g cm-2)

Rewe

1

Relative possibility measures quantify confidence in the model predictions for each parameter set, and can be interpreted as defining the probability that each parameter set

0

Sedimentation rate (g cm-2)

Sedimentation rate (g cm-2)

where F k2 is the total measure of fit for parameter set k, which can be used to calculate an associated relative possibility measure (RPMk):

ð21Þ

F k2

5

Culmstock

1 0.8 0.6 0.4 0.2 0 0

5

Core number

Figure 8 Caesium-137-derived estimates of mean annual overbank sedimentation rates for 20 core locations in each study reach (solid diamonds), associated weighted mean model predictions (open squares) and prediction limits (bars indicate range between 1st and 99th percentiles of cumulative sedimentation rate probability distributions). Cores are ordered based on distance from the channel (cores nearest the channel plot to the left).

New strategies for upscaling high-resolution flow and overbank sedimentation models provides an adequate representation of deposition processes in the natural environment. RPM values can then be used as weighting coefficients to determine weighted mean sedimentation rate predictions ðSP Þ at locations where sediment cores were obtained: 3000 X SP ¼ SkP RPMk ð22Þ k¼1

In addition, ranking of the 3000 model predictions (by sedimentation rate) at each core location enables the relation-

589

ship between predicted sedimentation rate and cumulative RPM to be determined. These cumulative distributions can then be used to derive percentiles of the modelled sedimentation rate distributions that quantify the uncertainty in model predictions. Fig. 8 shows model predictions and 137Cs-derived estimates of mean annual overbank sedimentation rates at 20 floodplain locations within each of the eight study reaches at which spatially-distributed modelling was conducted. Cores are ordered in each plot from left to right according

10-1

10-2

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10-3

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10-6 0

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0.006

0.008

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Vcr

a 10

10

RPM

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10

10

10

-1

-2

-3

-4

-5

-6

0

0.002

0.004

E

b 10-1

10-2

RPM

10-3

10-4

10-5

10-6 0

0.2

0.4

c

Figure 9 Relationships between the parameters Vcr, E and k, and the RPM values determined using Eq. (21). Note that plots are truncated at a RPM value of 106.

590

A.P. Nicholas et al.

to distance from the nearest channel. Caesium-137-derived estimates are shown as single values although there are a number of sources of uncertainty in these estimates. For example, limits on precision inherent in sample analysis, spatial variability in the 137Cs reference inventory, and spatial and temporal variability in the 137Cs content of deposited sediment. These factors contribute to a level of uncertainty in the 137Cs-derived sedimentation rates that is in the order of at least 0.05 g cm2. At approximately 50% of core locations the difference between the weighted mean model prediction and 137Cs-derived sedimentation rate is smaller than this value. In addition, approximately 60% of the 137Cs-derived sedimentation rate estimates lie within the limits of the numerical model predictions. Substantial differences between weighted mean predictions and estimated sedimentation rates are evident in some locations. There are several reasons for expecting such differences to occur irrespective of the existence of errors and/or uncertainty in either the model or 137Cs-derived data. For example, model predictions represent sedimentation rates averaged over areas >1 m2 and are derived for flow conditions associated with the current floodplain topography. In contrast, 137Cs-derived sedimentation rates have been averaged over a smaller area (<40 cm2) and incorporate the effects of changes in floodplain configuration over a period of ca. 40 years (although such changes are small in most cases). Differences between model predictions and 137Cs-derived sedimentation rate estimates are also a product of the fact that RPM values are determined on the basis of the goodness-of-fit at all study reaches, as expressed by Eq. (21). A narrower range of predictions and a better fit between modelled and estimated sedimentation rates would be obtained for each reach by calculating RPM values as a function of the local reach goodness-of-fit measure (F1). However, on the assumption that the parameters in Eq. (13) should have a strong physical basis, it is deemed more appropriate to implement the sediment budget model using a constant value of these parameters at all

1

sites. It might be argued that spatial variations in particle size throughout a catchment should lead to systematic changes in particle settling velocity. However, since insufficient data are available to derive a robust relationship describing changes in VS this parameter must be treated as a constant in the current application. Fig. 9a–c shows the relationships between the parameters Vcr, E and k, and the RPM values determined using Eq. (21). These figures include only those parameter sets with RPM values >106 (550 parameter sets in total). Parameter sets characterised by lower RPM values effectively make no contribution to the weighted model predictions of overbank sedimentation rates. Fig. 10 shows plots of cumulative RPM against each parameter. In combination these diagrams provide an indication of the sensitivity of predicted sedimentation rates to changes in each parameter, and of the uncertainty in the identification of optimum parameter values. Optimum model performance (in the context of the available 137Cs data and definition of goodness-of-fit) is associated with high values of Vcr in the range 0.5–1, and low values of k in the range 0.03–0.06. The relatively flat top to Fig. 9b indicates that values of E across the full range examined here are equally acceptable, although there is some suggestion that higher values of E lead to a better fit with field data. As in previous environmental modelling applications that have implemented uncertainty analysis, there is clear evidence in these plots that a wider range of model structures need to be investigated in order to obtain more conclusive results. For example, the long vertical sections in Fig. 10 and the relatively sparse sections of Fig. 9a for values of Vcr in the range 0.6–0.9 indicate that the 3000 simulations conducted here are not sufficient to explore the model parameter space fully. Fig. 11 shows the total mean annual floodplain sedimentation rate within each of the eight study reaches predicted by the sediment budget model, compared with estimates derived using the 137Cs data. Caesium-137-derived estimates were determined simply as the product of the total flood-

Vcr E

Cumulative RPM

0.8

0.6

0.4

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0 0

0.2

0.4

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0.006

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Vcr 0

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E 0.01

Figure 10

0.1

Plots of cumulative RPM for each of the parameters Vcr, E and k.

New strategies for upscaling high-resolution flow and overbank sedimentation models

591

Mean annual sedimentation rate (t y -1 )

500

400

300

200

100

0 Culmstock

Uffculme

Woodrow Farm

Hayne Barton

Woodmill

Kensham

Killerton

Rewe

Figure 11 Total mean annual floodplain sedimentation rate within each of the eight study reaches. Dark grey bars represent estimates based on floodplain area and the average of the 20 137Cs-derived sedimentation rates. Light grey bars with error bars represent the weighted mean and 1st and 99th percentiles of the modelled sedimentation rates, respectively.

plain area in each reach, the average estimated sedimentation rate for the sampled sediment core locations, and a correction factor introduced to account for bias in core locations. The correction factor was set equal to the mean predicted sedimentation rate for the floodplain reach as a whole divided by the mean predicted sedimentation rate at the 20 core locations. Model results represent the weighted mean sedimentation rate predictions and the 1st and 99th percentiles of the cumulative sedimentation rate distributions. It is important to recognise that the latter reflect the level of precision in model predictions and do not provide an indication of confidence in model accuracy. Similarly, estimated sedimentation rates derived by radionuclide analysis do not provide a test of the model predictions, since they were used in the calculation of RPM values. However, it is encouraging that downstream trends in sedimentation rates (from Culmstock to Rewe) are consistent between model results and field-based estimates. Integration of predicted sedimentation rates across all floodplain reaches within the catchment provides a value for the weighted mean total annual floodplain sediment storage rate (7656 t y1) and associated 1st and 99th percentiles (4147 t y1 and 13,247 t y1, respectively). Based on the available estimate of the mean annual suspended sediment load for the River Culm at Rewe (approximately 7500 t y1), this implies that between 36% and 64% of the fine sediment entering the main channel system goes into storage on the 26 km of floodplain bordering the main channel before reaching the catchment outlet. The best estimate of this figure derived from the weighted mean model predictions is 51% for the catchment as a whole, and 33% for the reach between Woodmill and Rewe. The latter is consistent with a previous estimate of the sediment conveyance loss between Woodmill and Rewe of 28% (Lambert and Walling, 1987).

Discussion The work presented here represents the first attempt to upscale the results of high-resolution flow and overbank sedimentation models to obtain estimates of floodplain sediment storage at the catchment scale. The model has been applied here to calculate rates of floodplain sedimentation for the whole main valley floor along a 26 km length

of the River Culm, Devon, UK. Clearly, it would be easy to extend this approach in future applications to include main channel tributaries in situations where these are characterised by a well-developed floodplain. The relatively high degree of uncertainty that is evident in predicted mean annual sedimentation rates derived using this procedure reflects the fact that multiple model structures provide an acceptable fit to the available 137Cs-derived sedimentation rate data. This situation may, in turn, be a product of the relatively small field dataset available to discriminate between alternative model structures, limits on the accuracy of the 137 Cs-derived sedimentation rates, and uncertainty in the extent to which 137Cs-derived data and model predictions are directly comparable. Uncertainty in model predictions might be reduced by identifying non-behavioural simulations and removing these from further analysis. Previous studies (e.g., Hankin et al., 2001) have identified criteria for doing so that include cases where simulations are: (a) associated with large mass balance errors; (b) involve solutions to the governing equations that fail to converge; or (c) are associated with predictions that are inconsistent with established physical laws. No simulations in the current study satisfy these criteria and, consequently, it was deemed inappropriate to restrict the set of model runs on which the uncertainty analysis was based. The current study has only examined the effects of variations in four model parameters (Vcr, E, k, and b) and each of these has been assumed to be spatially and temporally uniform during a single simulation. In addition, floodplain roughness, particle settling velocity and sediment load at the catchment outlet have all been treated as constants. Logically, one would expect that accounting for variability in these parameters would lead to an increase in model uncertainty and, consequently, wider prediction limits. However, simulations conducted using a range of sediment load estimates at the catchment outlet demonstrate that this need not be the case. In fact, varying the outlet sediment load over a realistic range had no significant systematic effect on either the weighted mean or limits of the predicted sedimentation rate distributions. Instead, model predictions remained approximately unchanged while the optimum region within the parameter space shifted so that, for example, a reduction in sediment load was compensated by an increase in the optimum values of k and E, so that a

592 larger proportion of the available load was deposited. One important implication of this observation is that uncertainty in model parameter values must also result from uncertainty in model boundary conditions, and that propagation of boundary effects through the model domain may lead to systematic spatial variations in parameter uncertainty. The approach adopted in the current study has been to apply spatially-distributed flow and sediment transport models to a subset of floodplain reaches within a drainage catchment, and to upscale the resulting predictions using a simple sediment budget model. A number of alternative strategies exist for deriving catchment scale sedimentation rate estimates. For example, recent advances in the development of computationally efficient flow routing schemes (Bates and De Roo, 2000; Bradbrook et al., 2004), coupled with the development of simplified suspended sediment transport and deposition models such as the one presented here, may provide a means of generating spatially-distributed sedimentation rate predictions throughout whole catchments. However, further development of hydraulic codes may be necessary before this can be accomplished, because the models listed above neglect convective acceleration terms in the conservation of fluid momentum equation, which strongly influence flow directions in areas of low water surface gradient. Alternatively, output from hydraulic models that solve the full shallow water equations may be used to develop statistical models of floodwater flow characteristics (e.g., Nicholas and Mitchell, 2003), which could be used to drive catchment scale sedimentation predictions. Whichever approach is adopted, prediction of future changes in floodplain sediment storage would also necessitate the inclusion of soil erosion and sediment delivery processes within the model framework, as an alternative to the current approach, which is to use estimates of contemporary basin sediment yield to circumvent the need for erosion prediction. In addition, development of a better understanding of overbank deposition processes represents a pre-requisite for reducing uncertainty in predicted sedimentation rates and patterns. The parameterisation of deposition processes implemented here is based on a conceptual model that represents a significant advance over conventional approaches developed for flow over sediment beds (cf. van Rijn, 1993), in that it recognises the importance of both particle settling and sediment trapping by vegetation. The results shown in Figs. 9 and 10 illustrate the range of acceptable parameterisations of overbank deposition in the current study and provide evidence supporting the view that vegetation may play a critical role in controlling sedimentation rates, both by trapping sediment and modifying hydraulic conditions throughout the water column. This is suggested by the fact that high RPM values are weakly associated with high values of E and strongly associated with high values of Vcr. The latter may be particularly significant, and is consistent with previous studies that have noted the need to use higher than expected values of hydraulic parameters to define the threshold for fine sediment deposition in depth-averaged simulations (e.g., Middelkoop and Van der Perk, 1998). Evidence from three-dimensional Computational Fluid Dynamics model applications in natural floodplain environments (Nicholas and McLelland, 2004) demonstrates that this situation reflects the occurrence of strong vertical shear above

A.P. Nicholas et al. the vegetation layer, such that conditions within this layer may be conducive to sedimentation even where depth-mean velocities and turbulence characteristics exceed theoretical thresholds. The development of robust parameterisations of these three-dimensional processes for use in depth-averaged models should go some way towards improving model performance, and hence reducing the uncertainty in predicted sedimentation rates. However, progress in this area may require further detailed monitoring and modelling of three-dimensional flow and sediment transport processes in the laboratory (e.g., Lo ´pez and Garcia, 1998). Ultimately, the capacity to discriminate between the predictive capability of alternative process parameterisations is dependent upon the quantity and quality of available empirical data. Evaluation of model performance using 137Cs data is undoubtedly compromised by the fact that estimated sedimentation rates represent the net effect of multiple flood events over a period of several decades. Further insights into issues of model accuracy and uncertainty are likely to be gained by conducting model validation using event-based sedimentation data derived from new techniques involving the use of short half-life radionuclides such as beryllium-7 (Blake et al., 2002).

Conclusions Quantitative models of catchment scale floodplain sediment storage must balance competing demands for computational efficiency and physically-based process representation at fine spatial resolutions. This paper has outlined a nested modelling strategy designed to achieve this objective by combining a high-resolution hydraulic model, with a reduced complexity overbank sedimentation model and coarse-resolution catchment sediment budget model. The development of such nested approaches should be based upon an assessment of the dominant process controls on the phenomena of interest, on the minimum level of physics required to capture these effects, and on the degree of uncertainty present in each element of the model parameterisation. Such an assessment will, inevitably, be subjective and application-dependent, since these issues are a function of both scale and environment. The approach developed here reflects two key criteria identified on the basis of experience gained in previous field and modelling studies in floodplain environments. First, a hydraulic model based on the shallow water form of the Navier–Stokes equations was required to provide the necessary level of process-representation to capture the relationships between floodplain topography and overbank flow characteristics at the scale that controls within-reach spatial variability in sedimentation rates. Second, since there is considerable uncertainty in the parameterisation of overbank sedimentation processes in high-resolution models, a computationally efficient modelling approach that allowed multiple model structures to be evaluated was desirable. In this context, the reduced-complexity overbank sedimentation model presented here represents a significant advance, since it is capable of simulating complex patterns of suspended sediment transport and deposition, while reducing computing costs by 2–3 orders of magnitude compared with conventional high-resolution advection–diffusion codes.

New strategies for upscaling high-resolution flow and overbank sedimentation models By implementing the strategy outlined here within a Monte-Carlo framework, estimates of the precision of sedimentation rate predictions have been obtained that reflect a range of sources of uncertainty. However, these estimates are, in part, a product of both the overall modelling stratetgy, the quantity and quality of available field data and the GLUE methodology (and associated goodness-of-fit measures used here). Although, the GLUE approach is well established (e.g., Beven and Freer, 2001), and represents a significant advance over the concept of a single optimal parameter set, it necessarily focuses on the accuracy of model predictions. Consequently, definition of what constitutes an acceptable parameter set or model structure is based upon a purely quantitative assessment of model performance, rather than on consideration of the physical realism of model process representation. Addressing this potential weakness in the context of floodplain sedimentation must await a better understanding of the interactions between turbulent flow and fine sediment transport and deposition in the presence of vegetation. Notwithstanding these sources of uncertainty in both model predictions and field data, the results presented here for the River Culm, UK, demonstrate that floodplain sediment storage represents a primary component of the fine sediment budget of lowland catchments, with up to two-thirds of fine sediment that enters the main channel system going into storage on floodplains before reaching the catchment outlet. This confirms that overbank sedimentation in lowland environments has substantial implications for the fate of sediment-associated nutrients and contaminants, and for geochemical cycling.

Acknowledgements This work was funded by the Natural Environment Research Council (Grant GR3/12635 and Studentship GT16/1999/FS/ 0006). We are grateful to the Environment Agency of England and Wales for providing hydrometric data, to local landowners for permitting access to study sites, and to Helen Jones for production of the figures. Thanks to two anonymous referees for their positive comments on the manuscript.

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