nafziger et al 2009

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17thInternational Northern Research Basins Symposium and Workshop

Iqaluit-Pangnirtung-Kuujjuaq, Canada, August 12 to 18, 2009

Nafziger et al. 1

Hydraulic Model of River Flow and Storage Effects in theMackenzie Delta, Canada

Jennifer Nafziger1, Faye Hicks1*, Robyn Andrishak1, Philip Marsh2and Lance Lesack3

1Dept. Civil and Environmental Engineering, University of Alberta, Edmonton, AB, T6G 2W2, CANADA

2National Hydrology Research Centre, Environment Canada, Saskatoon, SK, S7N 3H5, CANADA

3Depts.Geography and Biological Sciences, Simon Fraser University, Burnaby, BC, V5A 1S6, CANADA

*Corresponding author, e-mail: [email protected]

ABSTRACT

This paper reports on the development and application of a hydrodynamic model of river flows

and off-channel storage effects in the Mackenzie Delta, Canada, being developed in support ofthe Canadian International Polar Year (IPY) project entitled Polar Terrestrial Freshwater: State

and Flow to the Ocean. This modelling effort is aimed at addressing questions related to

transport of fresh water and nutrients to the Arctic Ocean under open water and ice affectedconditions, and to estimate how water levels through the delta may change in response to

changing river flows, reduced or increased ice jamming, increasing sea-level, and enhanced storm

surges from the Beaufort coast.

The Mackenzie Delta Hydrodynamic Model (MDHM) is being built upon the University ofAlberta'sRiver1Dhydrodynamic and ice process model, capable of handling the highly dynamic

flows associated with events such as storm surges and ice jam formation and release. With an

area of more than 13,000 sq. km., and containing more than 45,000 lakes, the Mackenzie Delta isa large and complex hydrodynamic system that presents unique modelling challenges. This paper

will present the details of the model application, and in particular, will focus on the unique

challenges involved in establishing a hydrodynamic model of such a large and complex northerndelta, in the face of limited topographic data on channel and lake geometry and flow connections,sparse flow and water level monitoring, and complex river and ocean ice effects.

KEYWORDSMackenzie River, Mackenzie Delta, hydraulic model, storage, nutrients, climate change

1. INTRODUCTION

The Mackenzie Delta, comprised of a vast network of interconnected lakes and channels, lieswhere the Mackenzie River flows into the Beaufort Sea in Canada's western arctic. It is Canada's

largest delta, and the second largest delta draining into the Arctic Ocean (after the Lena Delta inRussia). Beginning at Point Separation, approximately 26 km downstream of the community ofTsiigehtchic at the confluence of the Arctic Red River (Figure 1), the Mackenzie Delta is

dominated by anastamosting stream channels, small thermokarst lakes and wetland areas within a

permafrost-influenced sand-silt plain (Mackay 1963, Emmerton et al. 2007). The major channelsof the Mackenzie Delta include the: Middle, East, West, Peel, Reindeer and Napoiak Channels.


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2 Hydraulic Model of River Flow and Storage Effects in the Mackenzie Delta, Canada

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Hydrometric Stations

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Model Channels

Primary Implementation

Secondary Implementation

Tertiary Implementation

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Figure 1: Location Map of the Mackenzie Delta including Water Survey of Canadahydrometric monitoring stations (see Table 1 for station names), MDHM channels,

and photo of spring conditions in the Mackenzie Delta.


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Nafziger et al. 3

The Mackenzie Delta is biologically productive (Squires et al. in press) and recognized as an

environmentally and ecologically sensitive area, as it supports a diversity of plant, fish, and other

wildlife and represents important habitat for waterfowl species (Mackenzie River BasinCommittee 1981). The annual hydrograph of the Mackenzie River is dominated by a high spring

runoff peak, followed by a declining trend in discharge throughout the open water season, and

low winter flows (Figure 2). The delta channels and lakes are ice covered or ice affected for upto 8 months of the year. Since 1974 initiation of spring breakup of the East Channel ice coverhas occurred most often between May 30 and June 14 (Goulding 2008), with a trend of peak

water levels occurring earlier in the spring (Marsh et al. 2002). Spring breakup is characterized

by peak water levels and the flooding of many of the delta lakes (Marsh & Hey 1989).

Because inflows to the Arctic Ocean are considerably higher per basin volume than in any otherocean, river influxes can have important effects on phenomena such as costal sea ice formation

and nutrient supply to marine food webs (Aagaard & Carmack 1989, Carmack et al. 2005).

Further, it has been shown that that off-channel storage has an appreciable effect on themagnitude and quality of river sediments and nutrients entering the Beaufort Sea (Emmerton et

al. 2008). Emmerton et al. (2007) estimate that there is a total surface area of 3,331 km2of lakes

(> 45,000) and 8,060 km2of wetlands within the 13,135 km2 of the delta. Off-channel storage(lakes, wetlands, and floodplains) comprise as much as 87% of the total delta area, though the

actual flooded area depends upon the event peak magnitude. The water stored in these off-

channel areas is subsequently released back to the river channel as water levels fall through thesummer. The photo in Figure 2 illustrates an example of a channel at high stage flowing into off-

channel lakes during spring breakup 2008. Marsh & Hey (1991) investigated the spatial

distribution of different lake elevations and concluded that the proportion of lakes that do not

flood on a yearly basis decreases in a down-delta direction.

0

5000

10000

15000

20000

25000

30000

J F M A M J J A S O N D

MeanDailyDischarge(m3/s)

2008

WSC Gauge 10LC014

Figure 2: 2008 Annual hydrograph for WSC gauge 10LC014 (Mackenzie River at Arctic Red

River) and photo illustrating channel-lake storage interactions during spring runoff.

Because it is logistically difficult to measure hydraulic and water quality parameters over such a

vast area, especially during the spring breakup season, a hydrodynamic model presents animportant potential tool for characterizing how water and nutrients flow through the delta.

Previous models of the Mackenzie Deltas hydraulic processes include a one dimensional finite-

difference hydraulic model (ONE-D) prepared by Environment Canada (Kerr 1993) that was


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capable of routing unsteady flows through an 85 reach representation of the major distributary

channels (Jasper & Kerr 1994). Fassnacht (1997) also used this model as a basis for suspended

sediment modeling in the delta. However, to characterize the deltas hydraulics fully, a model is

required that can handle: the dynamic flows associated with ice jam events; possible reversing

flows that occur due to tidal, storm surge, and ice jam events; and that can incorporate the off-channel storage effects of the delta lakes. This paper describes our efforts to date in the

development of such a model, focusing primarily on the development of the input geometry.

2. MODELING APPROACH

The Mackenzie Delta Hydrodynamic Model (MDHM) is being built upon the University of

Albertas River 1D hydrodynamic and ice process model. This model is capable of handlingdynamic events such as storm surges and ice jam effects (e.g. She et al. 2009) as well as the

effects of off-channel storage. This version of the River1D model extends the finite element

hydrodynamic computational abilities of previous versions to include channel networks. River1D

employs the characteristic-dissipative Galerkin finite element scheme (Hicks & Steffler 1992) tosolve the conservation form of the one-dimensional, unsteady, open channel flow equations

assuming rectangular channel geometry of varying width:

( )oA A Qq

t x

+ + =

[1]

022

)/( 2=+

++ fo gASgAS

dx

dB

B

gAhgAh

xx

AQ

t

Q

[2]

Where:

A = cross sectional area perpendicular to the flow;

Ao = the inactive, or storage flow, cross sectional area;

B = the channel width;

g = acceleration due to gravity;

h = depth of flow;

Q = discharge;

q = lateral tributary (inflow) or distributary (outflow);

Sf = longitudinal boundary friction slope;

So = longitudinal channel bed slope;

t = temporal coordinate; andx = longitudinal coordinate.

Channels are connected at network junctions through dynamic boundary conditions, computed

internally by the model during a simulation. Specifically, the water surface elevation at theboundary of interconnected reaches is assumed constant and used as a boundary condition on the

lateral (or minor) channel. The discharge to the lateral channel is accounted for in the main


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Nafziger et al. 5

channel as a point source flow change to conserve mass within the entire system. In mathematical

form,

( ) ( )tHtH jl = [3]

and

( ) ( )tQtQ lj = [4]

where:

H = stage or water surface elevation;

Q = discharge;

l = subscript denotes the lateral channel at the junction;

j = subscript denotes the main channel at the junction;

This arrangement permits flow reversals and surges to pass through the channel network withfewer computational difficulties than conventional (diffusive wave) network models.

Geometrically, the computational nodes on the main and lateral channels at the junction are eitheroverlapping or very close together so that Eq. [3] can be considered valid. Momentum or energy

losses due to the junction are assumed negligible in the present form of the model.

3. AVAILABLE DATA AND MODEL GEOMETRY ADOPTED

Developing a comprehensive and deterministic model of such a large and complex network of

channels and lakes requires detailed cross section geometry for all channels, water surface slopes

along all channels under varying flow conditions for the definition of flow gradients, as well asdetailed topography and lake level data to define lake-floodplain-channel interactions and off-

channel storage relationships. Discharge data that is both accurate and well distributed in time

and space is important in model testing, calibration and validation. Unfortunately, only minuteamounts of any such data are actually available for the Mackenzie Delta, because of its vast size,

remote nature, and small number of stable geodetic benchmarks. As a result, data limitationshave been the primary challenge in developing this model, and have necessitated the adoption of

a more conceptual approach. Here, we describe the available data, and the resulting geometric

model employed.

Air Photo and Map Data: Several data sets available from the Northwest Territories Centre forGeomatics (NWTCG) (http://www.gnwtgeomatics.nt.ca) were used in the initial planning and set

up of the geometry input to the MDHM. Georeferenced digital colour air photos, created as part

of the Mackenzie Valley Air Photo Project, were imported into a geographic information system(GIS) and channel centerline locations and channel widths were then measured off of these air

photos. The clarity and resolution of these photos were helpful in the interpretation of the

channels interconnections and their relative hydraulic importance. Digital elevation model

(DEM) data, also collected as part of the Mackenzie Valley Air Photo Project, were also obtainedfrom the NWTCG. This raster data with a 30 m pixel size was used to help determine the slope

of the delta topography. Also, a mosaic of 3-band Landsat 7 satellite images was obtained from

the GNWT. This georeferenced raster image with a 15 m pixel size was helpful in determining


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the location of channels and their interconnectivity, owing to the large colour contrast between

channels (blue), vegetated land (green), and bare land or exposed sandbars (pink). Canadian

Hydrographic Service (2008) charts, based on 1:50,000 National Topographic Service charts

include water depth information for many of the delta channels navigable by small and large

watercraft. These charts were scanned and linearly georeferenced in a GIS, then used to verifythe hydraulic importance of channels based on their depth. They were also used to determine the

most hydraulically significant path around islands and through island groups. All spatial datawas incorporated into a single GIS database to facilitate comparisons.

Cross Section Data: Cross sections, dating back to the 1970s, are available at various sites in the

Mackenzie Delta (e.g. Hollingshead & Rundquist 1977, Lapointe 1985, Carson 1994, Fassnacht

1993). Of those, only the cross sections from Fassnachts (1993) study were referenced to ageodetic datum. As part of this IPY project, new cross sections were surveyed on the Middle,

East, and Peel Channels by during the summers of 2007 and 2008 (Beltaos, unpublished data),

and these were all referenced to a consistent geodetic datum. All of the available geodeticreferenced cross sections were used to estimate the slope of the delta.

Discharge data: Fourteen WSC hydrometric stations provide data relevant to the development of

the MDHM, including 12 stations located within the delta itself and two stations located

upstream on the Mackenzie and Peel Rivers (Figure 1 and Table 1). Continuously-monitoreddischarge data is available at only three of the Mackenzie Delta stations, as stage-discharge rating

curves are not well developed for the other sites due to tidal and storm surge backwater

conditions that result in poor stage-discharge relationships. The water levels at 7 of these stationsare referenced to a geodetic datum. Water Survey of Canada staff made direct measurements of

channel discharge at all delta stations in 2007, and at 3 central delta stations throughout 2008.

Figure 3 shows some examples of the variable availability of flow data for 2007 and 2008.

Flow data for the 3 central delta stations is quite complete, with several direct measurements in

all seasons and more measurements taken during 2008 than 2007. These data are useful indetermining the proportion of flow split between the Middle, East and West Channels. However,they do not assist with proportioning the flow between the many channels of the lower delta.

Water level data for the outer delta stations is generally quite sparse, with only a single direct

measurement, often from June 2007.

Flow Split Data: Anderson & Anderson (1974) measured flow splits for select channels of thedelta under ice covered conditions. That study concluded that under winter conditions the

Mackenzie River contributes 97% to >98% of Mackenzie Delta flows, and that at a point in the

Middle Channel approximately 1 km upstream of the Napoiak Channel still often carried in

excess of 80% of the Delta inflow. At a point in the Middle Channel directly west of ReindeerStation, flows varied between 50 to 91% of total inflow over 3 winter surveys. Finally, the

authors estimated that of the total outflow of the delta 33 to 62% entered the Arctic Ocean from

Shallow Bay area west of Ellice Island including Reindeer Channel, and 25-35% entered from thenortherly section east from Ellice Island to Richards Island.


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Nafziger et al. 7

a)

0

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J F M A M J J A S O N D J F M A M J J A S O N D

MeanDailyDi

scharge(m3/s)

2007 2008

WSC Gauge 10LC002

Direct Measurement

0

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MeanDailyDis

charge(m3/s)

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WSC

Gauge

10MC003

Direct

Measurement

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MeanDailyDischarge

(m3/s)

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WSC

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10MC008

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Measurement

b)

8

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GaugeHeightAboveStation

Datum(

m)

2007 2008

WSC Gauge 10LC021

Direct Measur ement Including Discharge

8

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GaugeHeightAboveStation

Datum(

m)

2007 2008

WSC Gauge 10MC010

Direct Measurement In cluding Discharge

Figure 3: Examples of varying availability of discharge data 2007-2008 a) data available for the

central Mackenzie delta b) examples of data availability for outer (northern) portionof the Mackenzie Delta.

Flow split data interpreted from Water Survey of Canada direct measurements in June 2007 are

summarized in Table 1. The proportion of total inflow is also shown, defined here as the average

inflow from the Mackenzie River (station 10LC014) and Peel River (station 10MC002) fromJune 1 to June 15, 2007.


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Table 1: Flow splits based on directly measured flows in June 2007.

StationNumber

Station DescriptionDate of

MeasurementDischarge

(m3/s)

% of

TotalInflow

10LC002 East Channel at Inuvik June 21 409 1.8

10LC012 East Channel at Tununuk Point June 18 89.4 0.4

10LC015 Mackenzie River at East Channel June 15 1110 4.8

10LC019 Kumak Channel Below Middle Channel June 19 2830 12.3

10LC021 Kuluarpak Channel at Taglu Island June 19 268 1.2

10MC003 Peel Channel Above Aklavik June 14 1190 5.2

10MC008 Middle Channel Below Raymond Channel June 14 16900 73.6

10MC010Outflow Middle Channel Below Langley

IslandJune 19 2680 11.7

10MC011 Reindeer Channel at Ellice Island June 20 4630 20.2

10MC022 Peel River at Frog Creek June 15 725 3.2

10MC023 Napoiak Channel Above Shallow Bay June 20 1010 4.4

Figure 4 shows the proportioning of flow between the Middle, East, and West/Peel Channels; thetotal monthly flow volume measured at each continuously-monitored station is shown as a

percentage of the total monthly inflow from the Mackenzie and Peel Rivers.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

March 2007 March 2008 June 2007 June 2008 August 2007 August 2008

ProportionofTotalM

onthly

(Mackenzie+Peel)Inflow

Dif ference f rom Total(Mackenzie + Peel) Inflo w

10LC002 - East Channel at

Inuvik

10MC003 - Peel ChannelAbov e Aklavik

10MC008 - Midd le ChannelBelow Raymond Channel

Figure 4: Proportioning of total Mackenzie Delta inflow between Middle, East, and West/PeelChannels in the central delta on a monthly total basis 2007-2008.

Differences between the total flow in the central delta and the total inflow are likely due to stream

routing and off-channel storage effects, measurement error, (particularly in the ice-affectedseason) and the short circuiting effect of inter-channel connections. The winter season has the

smallest difference between the inflow and central delta flow, suggesting that, as expected, delta

storage effects are less pronounced in winter when water levels are lower and channel-lake

connections are less significant.


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Nafziger et al. 9

The proposed final layout of the MDHM is illustrated on Figure 1. Based on the available data,

the proposed network consists of approximately 65 channel reaches and 110 junctions.

Computational nodes are spaced along the centerline of the modeled channels approximately 3 to4 channel widths apart. Each node has an associated northing, easting, channel station, width,

invert elevation, and off-channel storage value. The proposed model layout includes many of the

same channels included in the ONE-D model (Kerr, 1993), with some added complexity wherenew data suggested additional important channels. The model will be implemented in sections,increasing in complexity as stable initial conditions are determined. Off-channel storage will be

incorporated with varying magnitudes along and across the delta, taking into consideration the

trends described by Marsh & Hey (1991).

4. SUMMARY AND FUTURE WORK

The paper reports on the progress to date in developing the MDHM. TheRiver1Dmodel has

now been adapted to incorporate network channel interactions and (empirical) off-channelstorage effects. A geometric model of the delta, consisting of 65 channel reaches and 110

junctions, has been developed based on the available data geometric data. Hydraulic modeling

has commenced, beginning with subcomponents to determine stable initial conditions. Work alsocontinues to integrate the dynamic ice jam components into the network model. Ultimately, the

MDHM will be used to simulate changes in delta flow patterns as a result of climate change.

Lesack & Marsh (2007) postulated that two climate-influenced mechanisms affecting delta lake-channel interaction are sea level rise and changes in peak water levels due to changes in ice

jamming activity.

ACKNOWLEDGEMENTSFunding for this study is provided through an NSERC scholarship to the first author and Canada

IPY funding to the second, fourth and fifth authors. This support is gratefully acknowledged.

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Social Committee, Northern Pipelines Task Force on Northern Oil Development, ReportNo. 74-12. Ottawa, ON, Canada.

Carmack, E.C., Macdonald, R.W. & Jasper, S. 2004 Phytoplankton productivity on the Canadian

Shelf of the Beaufort Sea.Marine Ecology Progress Series 277,37-50.Carson, M.A. 1994. Sediment station analysis: Mackenzie Delta, 1993 Update. M.A. Carson and

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