A Multi-Channel Suspended Sediment Transport Model for the Mackenzie Delta, Northwest Territories

Journal of Hydrology 197 (1997) 128–145

A multi-channel suspended sediment transport model for the Mackenzie Delta, Northwest Territories

Steven R. Fassnacht*

Department of Civil Engineering University of Waterloo Waterloo, Ont. N2L 3G1, Canada Received 6 February 1996; revised 30 August 1996; accepted 5 September 1996

Abstract

To model the suspended sediment transport through the Mackenzie River Delta, Northwest Territories, Canada, a one-dimensional multi-channel suspended sediment model (FOSH-MC) has been developed. The model links an established network flow model that has been successfully applied to the Mackenzie Delta with an existing suspended sediment model. Sediment travel times along channels, that are useful to establish suspended sediment sampling schedules, are estimated as a model output product. The sediment output also includes total loads at each network node and reaches suspended sediment concentrations. The model can route both cohesive and non-cohesive suspended sediment. This research is a first attempt to dynamically model sediment transport through the Mackenzie Delta. All previous efforts have examined long-term fluxes. The FOSH-MC model has the potential to trace the pathways of contaminants through the Mackenzie Delta. The model also has the potential to be applied to other multi-channel networks that primarily carry suspended sediment. ᭧ 1997 Elsevier Science B.V.

1. Introduction

The Mackenzie River drains almost two million km2 of northwestern Canada into the Mackenzie Delta before emptying into the Beaufort Sea. It is the second largest arctic delta in the world, covering an area of approximately 13 000 km2 (Fig. 1). The Mackenzie Delta is a unique ecologically sensitive environment that has fascinated researchers for numerous years (eg. Mackay, 1963). Since the late 1960s, with the discovery of vast quantities of hydrocarbon reserves located in the Beaufort Sea near the Mackenzie Delta, the oil and gas industry has become particularly interested in the area. During the 1970s, various

* Tel: +1 519 888 4567 ext. 3828; fax: +1 519 888 6197; e-mail: [email protected]

Fig. 1. Location map of the Mackenzie Delta. consultants, acting on behalf of the oil and gas companies, performed initial hydrometric studies at various locations throughout the delta. At the same time, the Federal Govern- ment Departments of Environment, and Fisheries and Oceans performed related studies. From 1991 to 1994, various Canadian government agencies participated in the Northern Oil and Gas Action Program (NOGAP). Environment Canada’s involvement was to 130 S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 provide information on the hydrologic and sediment regime of the Mackenzie Delta area, required for the assessment of environmental impacts and adequacy of engineering design of future oil and gas infrastructure (Jasper, 1991). The hydrologic and hydraulic components of NOGAP were accomplished by the com- pletion of a delta hydraulic model (ONE-D) that routes delta inflows through major distributary channels to the lower delta channels near the Beaufort Sea (Jasper and Kerr, 1994). The Mackenzie Delta flow regime is modelled using 85 reaches, and is supported by data from 10 hydrometric stations (see Fig. 2). The NOGAP sediment component consisted of the development of a delta sediment flux model based on the flow model and the evaluation of the pathways of contaminants bound to delta sediments. Various regression relationships were calculated by Carson (1994) in order to establish the sediment flux model. A multi-channel suspended sediment model (FOSH-MC) was developed to analyze the movement of sediment and estimate suspended sediment concentrations throughout the Mackenzie River Delta.

2. Background

Numerous suspended sediment models have been developed to simulate suspended sediment transport along river reaches, as well as in lakes and estuaries. Many of these models have been discussed and compared by various researchers, such as, the CSCE Task Group on River Models (1987), the ASCE Task Committee on Fine Sediment Transport Processes (1989), van Rijn (1989), Gailini et al. (1991), and Ziegler and Nisbet (1994). Eight suspended sediment models that have had a variety of application are summarized in Table 1. Each of these models have been applied to various settings and each model has its advantages and limitations, as discussed in the aforementioned references. The RIVFLOC model incorporates the following considerations: applicability to a riverine environment; erosion/deposition/resuspension capabilities; ﬂocculation of cohesive particles; particle chemical reactiveness capability (for potential contaminant modelling); and the model’s development from an advection–dispersion model. These characteristics make the model suitable for application to reaches within the Mackenzie Delta. Although the various suspended sediment models have had numerous applications, no suspended sediment model has been encountered in the literature that is applicable to multi-channel networks. Therefore, the network ﬂow model (ONE-D), already applied to the Delta, has been linked with the single-reach cohesive suspended sediment (RIVFLOC) to create a multi-channel suspended sediment model for the Mackenzie Delta.

3. Model characteristics

The FOSH-MC multi-channel suspended sediment model developed in this research consists of four components: one-dimensional multi-channel hydrodynamic ﬂow modelling (ONE-D); data extraction to select the necessary hydraulic data; hydraulic data assembly to compile the hydraulic data and sediment characteristics; and the sediment transport component, based on the RIVFLOC model and a nodal scheme. S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 131

Fig. 2. Mackenzie Delta model schematic (conﬁguration 2A).

The model topology is illustrated in Fig. 3. Details of the ONE-D model are described in Water Modelling Section (1988) and details of RIVFLOC are described in Krishnappan (1991).

3.1. Discharge

The discharge component is built around Environment Canada’s ONE-D that has been 132 S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145

Table 1 Summary of suspended sediment transport models

Model Agency Developers Spatial Flow Features represented dimensions

STUDH University of Ariathuri and 2-D Finite element California, Davis Krone, 1976 cohesive sediment HEC-6 US Army Corps US Army Corps 1-D 1990 version of Engineers of Engineers, incorporates 1977 cohesive sediment GSTARS US Bureau of Molinas and Semi-2-D Reclamation Yang, 1984 CSTM-H University of Hayter and 2-D Estuaries Finite element Florida, Metha, 1986 cohesive sediment Gainesville SUSTRA-3D Delft Hydraulics van Rijn et al., Quasi-3-D 2-D velocity Uses 3-D 1990 WAQUAbased convective- on Reynolds dispersion equations FLUVIAL-12 San Diego State Chang, 1988 Quasi-2-D Alluvial channels University SEDZL University of Ziegler and 2-D Steady state Resuspension, California, Lick, 1986 deposition and Santa Barbara transport of cohesive sediment in shallow water HydroQual Ziegler and non-cohesive Nisbet, 1994 component added RIVMIX Canada Centre Lau and Quasi-2-D Steady state Advection- for Inland Krishnappan, dispersion Waters 1981 RIVFLOC Krishnappan, Flocculation, 1991 chemical reactions, deposition, erosion, resuspension

applied to numerous river regimes throughout Canada by Sydor et al. (1989). The model is capable of simulating flows in the unsteady state for river networks with rigid beds. It is a finite difference scheme formulated from the St. Venant equations. The scheme was obtained by applying a weighted residual method of optimization to a linearized version of the governing equations and the discrete approximations (CSCE Task Group on River Models, 1987). The ONE-D model uses water levels or flows as the upstream boundary conditions and water levels at the downstream boundary. The input parameters are the river topology network and the channel hydraulic properties (Environment Canada, 1988). The ONE-D model output file provides water levels or hydrographs at the locations within the network specified in the input file. S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 133

Fig. 3. Multi-channel cohesive suspended sediment topology model.

3.2. Data extraction

The suspended sediment model scheme used in this research uses a quasi-two- dimensional steady-state transport component, as well as an optional ﬂocculation component. Hence, one value of discharge is required for each reach to simulate one suspended sediment pulse. The data extraction portion of the FOSH-MC model interpolates the reach discharge from the ﬂow model output hydrographs based on suspended-sediment travel time estimates from the upstream boundaries to the top node of each reach. The travel 134 S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 times are initially estimated and subsequently calculated in the hydraulic data assembly component of the model (Fassnacht, 1996).

3.3. Hydraulic data assembly

The data assembly component of FOSH-MC prepares the hydraulic data and sediment related data for each reach in the channel network and estimates the sediment travel times. Owing to a lack of data, the suspended sediment is assumed to travel at approximately the water velocity. In the review of suspended sediment theory, Alonso (1981) states that particles carried in suspension move at a rate quite close to the stream velocity, however, at times this may not hold true owing to deposition and/or resuspension, especially at confluences and bifurcations (B.G. Krishnappan, 1994, personal communication). The mean cross-sectional velocity at the upstream and downstream nodes of each reach are used to determine the mean water travel time between the nodes of a reach. An initial estimate of the travel times between the upstream boundary to each node is required as model input. The multiple reaches that meet at a confluence have different average channel velocities. Since the travel time of water in each reach is different, a flow- weighted time scheme is used to estimate the mean ‘‘slug’’ travel time (Fassnacht, 1996). The succession of data extraction and hydraulic assembly programs are iterated until the slug travel time solution converges to less than the user-defined convergence- criterion. The Mackenzie Delta model used 0.01 days, or 15 min which is at least an order of magnitude more accurate than the measured hydraulic data.

3.4. Sediment movement

Since the discharge rates cannot be directly correlated to sediment concentrations and an inverse relationship is difficult to define for any large watershed with multiple different inflow basins, neither a coupled flow-transport nor an implicit finite approach was used to model the suspended-sediment transport. Instead sediment was routed along each reach and nodal activity was considered individually. The suspended-sediment concentrations are routed along each reach using advection– dispersion transverse mixing. The model considers flocculation of cohesive particles as well as considering particulate chemical reactions, deposition, erosion, and resuspension (Krishnappan, 1991). The physical processes that are ongoing at each reach are a function of the nodal geometry and bed characteristics, as well as the incoming and outgoing flows and sediment loads. To add and split the sediment load coming into and going out of a nodal region, a source/sink rate coefficient (l3), which is similar to the reach source/sink term, is applied to the upstream and downstream areas of any particular reach within the nodal influence zone. This coefficient is defined: =− ( − ) l3 WS 1 SCb (1) where WS is the settling velocity, S is the scouring parameter, and Cb is the near-bed suspended sediment concentration. The location-specific scouring parameter is a function S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 135 of the slope and velocity at the channel mouth. The value of S must be spatially and temporally defined since the nodal area is a very active.

4. Model operation and ﬁeld measurements

The one-dimensional multi-channel suspended-sediment transport model requires the following input parameters: network topology; upstream boundary ﬂows or water levels; downstream boundary water levels; reach characteristics, that is, hydraulic parameters; initial travel time estimates; bed–water interface and related sediment characteristics; and upstream boundary sediment concentrations. The outputs of the model are the suspended- sediment concentrations at the downstream end of each reach, the daily suspended- sediment load at each node, and the calculated water and sediment travel times.

4.1. Flow component

The flow modelling input requires the estimation of channel hydraulic properties, specifically representative cross-sections at the upstream and downstream nodes for each reach and estimation of channel roughness. Prior to 1992, channel cross-sections had been profiled for 57 of the 85 Mackenzie Delta reaches, as part of the regular Water Survey of Canada hydrometric program or for special studies. To complement this work, the 1992 NOGAP field program profiled cross-sections of 24 other reaches (Fassnacht, 1993). Topographic maps were used to impose representative cross-sections on reaches that had not been profiled. Manning’s roughness coefficients between 0.020 and 0.040 were estimated for each reach based on channel characteristics and bed material (fine sand, silt and clay). These coefficients were used as a calibration tool, dependent upon the boundary conditions.

4.2. Reach sediment modelling

The rate of source or sink (l2) in a channel is a measure of the erosion–sedimentation– resuspension potential within reaches, per particle size class (Krishnappan, 1991). There are three factors that affect the estimation of the in-channel source/sink coefficient: the scouring parameter (S) based on the reach physical characteristics; the particle settling velocities (WS) based on the representative particle sizes; and the near bed concentrations (Cb) based on the flow conditions. Owing to the size of the Mackenzie Delta and the fluctuations in suspended load, it is logistically impossible for the suspended-sediment mass balance to be measured on for each reach. The scouring parameter was thus estimated from topographic maps, channel erosion studies (for example Lapointe, 1986), and traditional knowledge (for example Kilmister et al., 1995). The particle settling velocity was based on the settling velocity of the representative particle size for each particle class. The representative particle diameter was the square root of the average of the squares of the maximum and minimum diameters bounding each size class (see Table 2). Sand and silt particles were assumed to be approximately spherical 136 S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145

Table 2 Characteristic settling velocity and representative particle diameter for each size class

Particle type Particle size class Characteristic settling Representative particle (microns) velocity (m s −1) diameter (microns)

Silt 4 Ͻ d Ͻ 8 7.87 × 10 −6 6.32 8 Ͻ d Ͻ 16 3.15 × 10 −5 12.6 16 Ͻ d Ͻ 31 1.20 × 10 −4 24.7 31 Ͻ d Ͻ 62 4.73 × 10 −4 49.0 Sand 62 Ͻ d Ͻ 125 1.92 × 10 −3 98.7 125 Ͻ d Ͻ 250 7.69 × 10 −3 197 and follow Stokes’ Law. Stokes’ Law is not directly applicable to cohesive particles, since clays can be plate-like in shape, and the net density of flocculated particles is different from the density of individual sediment grains. An equivalent spherical diameter (equal to the diameter of a spherical particle that would settle at the same velocity as the cohesive, non-spherical particle) and an effective density (that considers the additional drag forces on non-spherical particles and flocs) could have been assumed so that the Stokes’ settling velocity could be determined. However, the cohesive particle settling velocities approximated by Ziegler and Nisbet (1994) were used for this research. Changes in the flow regime throughout a channel network alter the concentrations of sediment transported near the solid–water interface. Methods to approximate the near-bed concentrations of suspended sediment have been summarized by Zyserman and Fredsoe (1994), however these methods could not be used for the Mackenzie Delta owing to a lack of data. Thus, as an approximation, the near-bed concentrations were taken to be greater than the suspended sediment concentrations, as has been illustrated by numerous estuary studies. Depending on the inflowing concentrations and location, the Mackenzie Delta carries 20–60% fine cohesive suspended sediment. However flocculation was not used since a majority of the sediment flocs were assumed to be stable, that is, a majority of the flocculation and breakage was assumed to be likely to occur upstream of the delta. Although the last major inflow into the Mackenzie system was more than 200 km upstream of the delta, the influx of Peel River sediments as well as other considerations (for example, storage release) may result in less stable floc particles.

4.3. Nodal sediment modelling

The nodal source–sink coefficient (l3) uses the same parameters as the in-channel source–sink coefficient. It is more difficult to measure the parameters related to l3 than to l2, as the physics of nodal activity is more poorly understood than is that for single reaches, especially the scouring parameter. All nodes were examined individually, with the net activity in each channel about the node described as erosion, deposition or neither. To approximate the nodal activity that occurs about confluences and bifurcations, changes in flow, flow distributions and nodal geometry were considered, based on the angle of bifurcation/confluence, the channel cross-section size with respect to the other channels S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 137 and other cross-sectional information available for the reach. The bottom elevation of each of the merging or splitting channels was a minor consideration, nevertheless, an elevated sill was indicative of a dynamic sediment flux at the mouth of a channel. The mean channel velocities were not used, but could have also been considered with the cross-section size as another indicator of a dynamic flux.

5. Calibration

Continuous flows are recorded throughout the year at the Mackenzie Delta inflow stations (gauges 10LC014 on the Mackenzie River at Arctic Red and 10MC002 on the Peel River above Fort McPherson). From break-up in the late spring to freeze-up in the early fall, water levels are recorded at four lower delta stations (gauges 10LC012, 10LC013, 10MC010, and 10MC011). Also, water levels are recorded at three (occasion- ally five) hydrometric stations in the mid-Mackenzie Delta. To complement the regularly recorded hydrometric data, an intense field program was undertaken in mid-July 1993 to collect various flow and suspended sediment data. These July 1993 data were used to calibrate the FOSH-MC model for application to the Mackenzie Delta.

5.1. Flow modelling

The Mackenzie Delta ONE-D flow model was calibrated and verified for the period between 1982 and 1988 by Environment Canada in Yellowknife (Kerr, 1993). For the 1993 data, additional calibration was performed (Fassnacht, 1994). Results of the flow modelling calibration are best illustrated by comparisons of the observed and simulated water levels at mid-delta stations, as shown in Fig. 4(a) and Fig. 4(b) for the East Channel at Inuvik and for the Middle Channel below Raymond Channel gauges, respectively.

5.2. Sediment travel time

Initial estimates of the travel times through the Mackenzie delta were produced based on generally accepted time lags used in field measurements by WSC at Inuvik and Environment Canada at Yellowknife. Carson (1994) used travel time ranges between hydrometric stations for his sediment flux module. The hydraulic assembly component of FOSH-MC was run for suspended-sediment sampling on 19 July 1993 at Mackenzie River–Arctic Red River using the initial travel time estimates. After three iterations of the hydraulic assembly and data extraction components, the travel time solutions converged to within less than 15 min. There is a con- siderable difference between the initial estimates and the calculated travel times. For the mid-July 1993 flow conditions, the time lag between 10LC014 and the lower delta stations is between three and four days (see Table 3). The travel time to Inuvik is three-and-a-half days, whereas the initial estimate was two days. The travel time between the Peel River above Fort McPherson station and the Peel Channel above Aklavik station is six days for the mid-July 1993 conditions. Initial estimates were two to three days. The travel times should be used for sampling when similar flow and sediment load conditions exist. 138 S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145

Fig. 4. (a)ﬂow calibration plots for station 10LC002 for mid-July 1993; (b) ﬂow calibration plots for station 10MC008 for mid-July 1993.

Actual calibration of the suspended-sediment travel times was not possible since the times were not measured in the ﬁeld.

5.3. Sediment concentrations

The FOSH-MC model was calibrated using the measurements. The suspended sediment calibration results for mid-July 1993 are presented in Fig. 5, as a comparison of simulated and measured suspended sediment concentrations. As can be expected, the simulated concentrations were almost the same as the measured concentrations. Although the mid-July 1993 data were the most complete set of concentrations, the concentrations were low and the S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 139

Table 3 Approximate sediment travel times in days from station 10LC014 to Mackenzie Delta hydrometric stations for various ﬂow events

Station July July July July Aug. Aug. July Aug. Aug. 6th 24th 25th 29th 17th 26th 19th 17th 31st 1988 1988 1991 1991 1991 1991 1993 1993 1993

10MC002 −1.9 −1.4 −1.9 −1.9 −0.4 −0.7 −1.75 −2.1 −2.6 10LC002 1.5 1.8 2.1 2.0 3.1 3.4 3.5 3.0 3.6 10LC006 1.9 2.2 2.5 2.3 3.3 3.6 3.2 3.2 3.7 10MC008 1.0 1.1 1.2 1.2 1.5 1.6 1.5 1.5 1.7 10MC005 1.8 2.0 2.7 2.3 3.3 3.8 3.1 3.2 1.8 10MC003a 2.4 + 2.8 + 3.5 + 3.3 + 4.1 + 5.0 + 4.5 + 4.9 + 2.5 + 1.9 = 1.4 = 1.9 = 1.9 = 0.4 = 0.7 = 1.75 = 2.1 = 2.6 = 4.3 4.2 5.4 5.2 4.5 5.7 6.25 7.0 5.1 10MC009 1.8 2.1 2.2 2.1 3.0 3.2 3.0 2.9 3.3 10MC012 1.9 2.2 2.4 2.3 3.2 3.4 3.6 3.0 3.5 10MC013 2.0 2.4 2.6 2.5 3.8 3.8 3.4 3.5 4.0 10LC016 2.5 2.9 3.2 3.0 4.2 4.5 4.1 4.1 4.8

a Figures taken from 10MC002. measured travel times were signiﬁcantly different from those calculated. For example, the travel time differences from 10LC014 to 10MC002 and 10MC008 were 194% and 147%, respectively. The Peel River was sampled more than three-and-a-quarter days earlier than the calculated time of sampling. Although the Peel River concentrations were low, the actual waters that mixed with the 19 July 1993 Mackenzie waters could have been more- or-less sediment laden. This inﬂuences the sediment regime throughout the western delta.

6. Veriﬁcation

6.1. Sediment travel time

The mid-July 1993 computed travel times were used as initial estimates for the July 1988 storm events. (Approximate travel times from the Mackenzie River at Arctic Red River to the hydrometric stations are summarized in Table 3.) Owing to the high flows during this period, the travel times through the delta are almost one half the mid-July 1993 travel times. As the early July 1988 discharges were the highest on record, the travel times should be considered during storm event sampling and possibly spring break-up. The mid-August 1991 flow conditions were simulated. The suspended sediment con- − centrations were high (1211 mg L 1) on 18 August 1991 in the Peel River above Fort McPherson, while the Mackenzie concentrations were lower than average (101 mg L−1). The travel times are very similar to the mid July 1993 travel times, except that there is a one day lag in the Peel River, owing to the travel time difference between mid-July 1993 and mid-August 1991. In mid-July 1993 the travel time along the Peel River was 1.71 days whereas the travel time was only 0.68 days during mid-August 1991. Six other flow conditions were also simulated to approximate the travel times during 140 S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145

Fig. 5. Calibration of the suspended sediment component (measured versus simulated). various different ﬂows, including a small storm event during late July 1988, a storm event at the end of July 1991, late August 1991, and mid and late August 1993 (Table 3).

6.2. Sediment concentrations

There are limited complete discharge and sediment load data-sets available for the Mackenzie Delta. The Mackenzie River suspended-sediment samples collected in late July 1991 showed that the river was carrying high concentrations, however, there were no corresponding Peel River suspended-sediment samples collected. The concentrations used to model the sediment flux were, thus, calculated from discharge. The early July 1988 sediment data were collected only at the delta inflow stations. Since these data-sets are incomplete, the August 1991 and August 1993 concentrations were used to verify the July 1993 calibration. The results show reasonable agreement between measured and simulated concentrations for the four flow events (see Fig. 6), with the exception of two concentrations being significantly overestimated.

6.3. Sediment ﬂux module

The simulated outputs for the high and medium concentration events that occurred in 1988 were compared with the concentrations estimated using the regression model developed by Carson (1994). The ﬂux module predicted higher concentrations than the FOSH-MC model (see Fig. 7). These differences exist partially owing to the lack of travel time consideration in the sampling, and data regression by Carson.

7. Discussion

The suspended sediment concentrations were high during mid and late August 1991 in S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 141

Fig. 6. Verification of the suspended sediment component (measured versus simulated). the Peel River (1200 mg L−1 and 800 mg L−1, respectively). However, the Mackenzie concentrations were low (approximately 100 mg L−1). These conditions are different from the calibration conditions. The variation in simulated and observed concentrations is also due, in part, to travel time differences. As a suspended-sediment load moved downstream, sampling was not of the same water at the different hydrometric stations, that is, different points on the sediment hydrograph were sampled owing to difficulties in field logistics. Calibration problems may also occur as result of seasonal flow regime variations. To overcome this problem, it is recommended that sampling over the entire channel network should be performed at high-, medium- and low-concentration regimes. The effects of bifurcations, confluences and mixing are significant, however, they cannot be accurately calculated. An example is node 23 where mixing at a confluence of 182 mg L−1 and 118 mg L−1 sediment concentrations yield a resultant concentration of

Fig. 7. Model output comparison to Carson’s flux module. 142 S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 150 mg L−1. It should be noted that the concentrations in channels below the calibration reaches are extrapolations. The nodal area is an important consideration, because hydrometric sampling usually occurs outside of areas that could potentially be affected by bifurcation or confluence processes. Where possible, sampling locations are established at a cross-section that is assumed to be representative of the entire reach. In these locations sediment distributions across the channel are relatively uniform and channel geometry is regular. Since there have been few sediment studies performed in the western-central delta (the Shallow Bay area), the depositional rates and tidal activity in this area are not well defined. Hence, the suspended sediment concentrations in these reaches are difficult to estimate and the results of the suspended sediment model should be used with discretion. In any channel network, particularly deltas, connecting channels exist that link larger channel systems, whose upstream activities may be independent of each other. The flow in the connecting channel is a function of the flow and water level of the larger upstream channels. In some instances, the direction of flow may reverse as different flow regimes develop in each of the larger channels. Two examples of reversing channels are Putu Channel in the Colville River Delta, Alaska and Aklak Channel in the Mackenzie River Delta, Northwest Territories. A dominant flow direction is assumed for modelling purposes. When conditions of flow reversal occur, the resultant predicted flow will be negative. To avoid the errors that this may cause in the RIVFLOC model, the nodal topology can be reversed and the flow can be taken to be a positive value in the opposite direction. This can be performed by switching the nodes in the topology and by removing the negative sign in the reach flow file. The RIVFLOC model considers the flocculation of cohesive suspended particulates. Although the Mackenzie and Peel Rivers carry cohesive sediment, the flocculation component was not considered, as discussed previously. If flocculation is considered, a majority of the finer particles flocculate, creating primarily larger flocs. The particle size distribution may be relatively constant or the particles carried in suspension may be finer in the downstream portions. There are two explanations for this observation: the particle size analyses for the suspended sediment are incorrect and/or the particles are at a flocculation equilibrium as they enter the system. The second consideration should be used with caution and the particle size distribution should be compared throughout the channel network. Cohesive sediment samples analyzed by laboratory procedures are not neces- sarily representative of the in-situ size distributions. Sampling of suspended sediment and sample processing break sediment floc that exist instream. The particle size distribution of the primary sediment constituents can be determined in a laboratory while neglecting the actual in-situ conditions. A field instrument capable of measuring in-situ suspended- sediment size distributions should be used where possible. If particles are at a flocculation equilibrium in-channel, then it is possible that sediment-floc breakage and formation activity increases as the flow approaches a bifurcation or confluence of large channels. Nodal flocculation is a localized effect. The potential particle distribution alteration is not known. The quantity of flocculation that occurs in mixing reaches, or in a reversing channel (especially during flow reversal), is likely more than in the other channels. The flocculation potential is a more important consideration in these mixing channels and should be addressed in sampling protocols. S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 143 There are three products of FOSH-MC: sediment travel times, sediment concentrations and sediment loads. The slug travel time can assist sampling logistics. Given certain flow conditions, the sampling lag time between upstream, downstream and other stations can be approximated such that the same water and suspended sediment is sampled throughout the channel network. Radioactive tracers could potentially be used to determine the difference between water and suspended-sediment velocities, and hence, travel times. The concentrations can be linked to contaminant transport and used to estimate contaminant movement, as well as assisting in cleanup strategies. The daily loads are useful estimates to examine sediment movement, that is, influxes into and effluxes out of networks, and erosion, deposition and potential resuspension rates. These FOSH-MC products, however preliminary, can be used in the planning of any future NOGAP hydrometric activities. The Mackenzie Delta travel times will assist in the sampling logistics and the development of cleanup strategies for hydrophobic contaminant spills, such as barge mishaps and pipeline ruptures. The main problems associated with the simulation of suspended sediment transport through channel networks are the data requirements. As with any complex model, proper calibration requires a large quantity of data, specifically data estimates for each reach within the network. This is especially true for the Mackenzie Delta, owing to its size and complexity. For most riverine systems several complete data-sets are usually required for different calibrations depending on the flow regime. At any particular time, the water flowing in the Mackenzie River at the delta is derived from numerous different sources in various geographic settings. Hence, for a given flow, and possibly a particular suspended- sediment concentration, the constitution of the water can vary. The problems associated with a lack of data can be partially overcome by grouping similar channels together. For example, an initial estimate of the scouring parameter can be made for a channel grouping based on general channel characteristics and on topographic maps.

8. Conclusions and recommendations

The FOSH-MC multi-channel suspended-sediment model is a linkage between the ONE-D network flow model and the cohesive sediment transport model RIVFLOC. The computer model routes suspended sediment from an upstream boundary through a multi- channel network to a downstream boundary. Simulation of a channel network will yield estimates of sediment travel times that are useful for evaluating multi-channel sampling strategies. With the estimation of necessary parameters and appropriate data-sets, suspended-sediment concentrations and loads can be calculated. The multi-channel suspended-sediment model has been applied to the Mackenzie Delta with success. The primary limitation of the sediment model is the quantity of required data. This data incompleteness must be overcome before the mechanics of the FOSH-MC model can be thoroughly tested. It should be noted, however, that it is important to define the output-data requirements prior to rigorous modelling of any channel network. For the purposes of the NOGAP project, the application of the FOSH-MC model to the Mackenzie Delta is appropriate. 144 S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 It is obvious that more data are required. It is recommended that sampling programs concentrate on collecting special data-sets, such as for high-concentration conditions, as well as emphasizing the progressive sampling as water travels downstream. This is especially true for suspended sediment transported into and through the Shallow Bay area. Also the use of in-situ samplers is recommended. For further model testing, it is recommended that the model should be applied to a smaller network, such as the Slave River Delta, such that less data are required. This will enable the modelling of chemical processes instead of only physical processes, as performed for the Mackenzie Delta. The FOSH-MC model should be applied to multi-channel suspended sediment regimes using flow and water level data prior to intense suspended-sediment sampling, such that appropriate suspended-sediment sampling strategies can be established.

Acknowledgements

The author would like to thank two anonymous reviewers for their helpful comments in the reformulation of this paper, as well as various individuals at the University of Waterloo for their support.

References

Alonso, C.V., 1981. Stochastic models of suspended-sediment dispersion. ASCE J. Hydrol. Div., 107(6): 733– 757. Ariathuri, R. and Krone, R.B., 1976. Finite element model for cohesive sediment transport. ASCE J. Hydrol. Div., 102(3): 323–338. ASCE Task Committee on Fine Sediment Transport Processes (Chair, A.J. Metha), 1989. Cohesive sediment transport. II., application. ASCE J. Hydrol. Eng., 115(8): 1094–1112. Carson, M.A., 1994. Sediment Flux Model for the Mackenzie Delta. Environment Services Directorate, Yellow- knife, N.T. Chang, H.H., 1988. Fluvial Processes in River Engineering. Krieger Publishing Co., Melbourne, FL. CSCE Task Group on River Models (chair, B.G. Krishnappan), 1987. River models. Proceedings of the 8th Canadian Hydrotechnical Conference, pp. 603–626. Environment Canada, 1988. One-Dimensional Hydrodynamic Model: Computer Manual. Water Modelling Section, Water Planning and Management Branch, Environment Canada, Ottawa, Ont. Fassnacht, S.R., 1993. 1992 Channel Cross-sections for Mackenzie Delta Hydraulic Model. Environment Services Directorate, Yellowknife, N.T. Fassnacht, S.R., 1994. A Multi-Channel Suspended Sediment Transport Model for the Mackenzie Delta. M.Sc. thesis, University of Waterloo, Waterloo, Canada, 186 pp. Fassnacht, S.R., 1996. Suspended sediment transport time estimates for the Mackenzie Delta. In: S. Cohen (Editor), Climate Change and Tourism in the Mackenzie Basin. Mackenzie Basin Impact Study Final Report, 8 pp. Gailini, J., Ziegler, C.K. and Lick, W., 1991. Transport of suspended solids in the Lower Fox River. J. Great Lakes Res., 17(4): 479–494. Hayter, E. and Metha, A.J., 1986. Modelling cohesive sediment transport in estuarial waters. Appl. Math. Modelling, 10(August): 294–303. Jasper, J.N., 1991. Environment Canada’s Northern Oil and Gas Action Program Objectives. Summary sheet prepared by the Water Sciences Group, Environment Canada, Yellowknife, N.T. S.R. Fassnacht/Journal of Hydrology 197 (1997) 128–145 145

Jasper, J.N., and Kerr, J.A., 1994. Routing: Mackenzie River and Delta. Presented at the Sixth Beinniel AES/ DIAND Meeting on Northern Climate. Mackenzie Basin Impact Study Worshop, Yellowknife, N.W.T., April 10–14, 1994. Kerr, J.A., 1993. Mack Delta—ONE-D model—1982–88 calibration and resulting hydrographs. Mack Delta Worknote 50. Environment Canada, Yellowknife, N.T., November 30, 1993. Kilmister, I., Burston, M., Campbell, P. and Dee, M., 1995. Sacriﬁce. CMC International, London, UK, 11 pp. Krishnappan, B.G., 1991. Modelling of Cohesive Sediment Transport. Rivers Research Branch, National Water Research Institute, Environment Canada, Burlington, Ont., 18 pp. Lapointe, M.F., 1986. Mackenzie Delta Channel Dynamics: Miscellaneous Data. NHRI Cold Regions Section, Environment Canada, Ottawa, Canada. Lau, Y.L. and Krishnappan, B.G., 1981. Modelling Transverse Mixing in Natural Streams. ASCE J. Hydrol. Div., 107(2): 209–226. Mackay, J.R., 1963. The Mackenzie Delta Area. Memoir No. 8, Geographical Branch, Mines and Technical Surveys; Energy, Mines and Resources, Ottawa, Ontario, Canada. Molinas, A. and Yang, C.T., 1984. Computer Program User’s Manual for GSTARS (Generalized Stream Tube For Alluvial Simulation). US Bureau of Reclamation. Sydor, M., Brown, G., Cheng, H., Boutot W. and Morasse, B., 1989. Getting the Best of Both Worlds, Application to Computer Modelling in Systems Analysis: From Micro to Supercomputer. Presented at the 4th Canadian Symposium on Systems Theory for the Civil Engineer, University of Manitoba, Winnipeg, Canada. US Army Corps of Engineers, 1977. HEC-6: Scour and Deposition in Rivers and Reservoirs. User’s Manual. The Hydrologic Engineering Centre, Davis, CA. van Rijn, L.C., 1989. The State of the Art in Sediment Transport Modelling. In: S.S.Y. Wang (Editor), Sediment Transport Modelling. Proceedings of the International Symposium, ASCE Hydrol. Div., New Orleans, LA, pp. 693–699. van Rijn, L.C., van Rossum, H. and Termes, P., 1990. Field veriﬁcation of 2-D and 3-D suspended-sediment models. ASCE J. Hydrol. Eng., 116(10): 1270–1288. Water Modelling Section, Environment Canada, 1988. One-Dimensional Hydrodynamic Model: Computer Manual. Water Planning and Management Branch, Environment Canada, Ottawa, Ont. Ziegler, C.K. and Lick, W., 1986. A Numerical Model of the Resuspension, Deposition and Transport of Fine Grained Sediments in Shallow Water. Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA. Ziegler, C.K. and Nisbet, B., 1994. Fine-grained sediment transport in Pawtuxet River, Rhode Island. ASCE J. Hydrol. Eng., 120(5): 561–576. Zyserman, J.A. and Fredsoe, J., 1994. Data analysis of bed concentration of suspended sediment. ASCE J. Hydrol. Eng., 120(9): 1021–1042.