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TA~lWAlERRA'f~ GCUR.VEA AlYSES

SLI Document No. 505573·3001-4HER-0023-00

Nalcor Reference No. MFA-SN-CD-2000-CV-RP-0005-01 Rev. B1

S. Thomas Lavender Sr. Hydraulics Engineer

Date: 07-Jun-2012

JM/ier Patarroyo Jr. Hydraulics Engineer

+)) TAIL WATER RATING CURVE ANALYSES Revision

Nalcor Doc. No. MFA-SN-CD-2000-CV-RP-0005-01 81 Date Page SNC • LA VALIN SLI Doc. No. 505573-3001-4HER-0023 00 07-Jun-2012 i

REVISION LIST

Revision Remarks No By Chec Appr. Appr. Date

00 sw DO GS NB 07-Jun-2012 Issued for cl ient acceptance.

PB JP DO MT GS 18-May-2012 Issued for client review and comments.

PA JP DO MT GS 02-May-2012 Issued for internal review and comments.

SNC-Lavalin Inc.

TAIL WATER RATING CURVE ANALYSES Revision Nalcor Doc. No. MFA-SN-CD-2000-CV-RP-0005-01 B1 Date Page

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TABLE OF CONTENTS

PAGE

1 INTRODUCTION ................................................................................................................ 1 1.1 General ...................................................................................................................... 1 1.2 Objectives of the Technical Report ............................................................................ 4

2 EXISTING REFERENCES ADDRESSING TAIL WATER AT MUSKRAT FALLS .............. 5

3 HYDROMETEOROLOGICAL DATA .................................................................................. 7 3.1 Hydrometric Station Records ..................................................................................... 7 3.2 Meteorological Station Records ................................................................................13

4 RIVER MORPHOLOGY CHANGES AT MUSKRAT FALLS ..............................................14

5 OPEN WATER RATING CURVES ....................................................................................16

6 FREEZE-UP RATING CURVES ........................................................................................20

7 WINTER RATING CURVES ..............................................................................................30

8 CONCLUSIONS ................................................................................................................35

9 RECOMMENDATIONS ......................................................................................................36


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List of Figures

Figure 1-1: WSC Station 03OE007 Rating Curve Ranges (At the Foot of Lower Muskrat Falls) 2Figure 1-2: WSC Station 03OE014 Rating Curve Ranges (6.15 km Downstream of Muskrat

Falls) ..................................................................................................................... 3Figure 1-3: At the Foot of Lower Muskrat Falls - Rating Curve Ranges ..................................... 3Figure 3-1: Locations of Stations 03OE001, 03OE007 and 03OE014 ....................................... 8Figure 3-2: Water Levels Station 03OE007 at the Foot of Lower Muskrat Falls ......................... 9Figure 3-3: Water Levels Station 03OE014 - 6.15 km Downstream of Muskrat Falls ................10Figure 3-4: Correlation between Water Level, Discharge and Temperature at Station 03OE014

.............................................................................................................................11Figure 3-5: Total Flows at Muskrat Falls Station 03OE001 1978-2009 .....................................12Figure 3-6: Mean Daily Air Temperature at Station 8501900 Goose Bay 1978-2009 ................13Figure 4-1: Water Level Evolution at Stations 03OE007 at the Foot of Lower Muskrat Falls ....14Figure 5-1: WSC Station 03OE007 Open Water Rating Curve .................................................17Figure 5-2: WSC Station 03OE014 Open Water Rating Curve .................................................18Figure 5-3: At the Foot of Lower Muskrat Falls Open Water Rating Curve ...............................19Figure 6-1: Mud Lake Crossing Looking U/S – Left: 1 Day before Freeze-up –Right: 1 Day after

Freeze-up .............................................................................................................21Figure 6-2: Process of Juxtaposition – 1a ................................................................................21Figure 6-3: Process of Juxtaposition – 1b ................................................................................22Figure 6-4: Process of Juxtaposition – 1c .................................................................................23Figure 6-5: Process of Juxtaposition – 1d ................................................................................23Figure 6-6: Lower Muskrat Falls Flooded (March 14th, 2012) ...................................................25Figure 6-7: The Freeze-up Process ..........................................................................................26Figure 6-8: WSC Station 03OE007 - Freeze-up Rating Curve ..................................................28Figure 6-9: WSC Station 03OE014 - Freeze-up Rating Curve ..................................................28Figure 6-10: At the Foot of Lower Muskrat Falls - Freeze-up Rating Curve ..............................29Figure 7-1: WSC Station 03OE007 – Early Winter Rating Curve ..............................................32Figure 7-2: WSC Station 03OE014 – Early Winter Rating Curve ..............................................33Figure 7-3: WSC Station 03OE014 – Whole Winter Season Rating Curve ...............................33Figure 7-4: At the Foot of Lower Muskrat Falls – Whole Winter Season Rating Curve .............34Figure 9-1: Rating Curves Downstream of Muskrat Falls .........................................................36


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List of Tables

Table 3-1: Muskrat Falls Hydrometric Stations .......................................................................... 7Table 3-2: Goose Bay Meteorological Stations .........................................................................13


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References

No. Description

(1) SNC, Churchill River Complex, Energy Studies, January 1991

(2) SNC–AGRA, Muskrat Falls Hydroelectric Development, Final Feasibility Study Report, January 1999

(3) HATCH, Ice Dynamics of the Lower Churchill River, October 2007

(4) ACRES, Proposed Blackrock Bridge: Estimate of Backwater effects, April 2002

(5) HATCH, MF-1330. Hydraulic Modeling of the River, October 2010

(6) A.I.G.S Robertson; Logarithmic Plotting of Stage-Discharge Observations; Technical Note 3; Water Resources Board; Reading Bridge House, U.K; May 1962.

(7) HATCH, MF-1330. Muskrat Falls Ice Study, March 2011

(8) Kivisild, H.R. (1959), "Hanging Ice Dams" IAHR 8th Congress, Seminar No. 1. Montreal, Quebec

(9) Michel, B. (1971) "Winter Regime of Rivers and Lakes" Corp of Engineers, U.S. Army, Hanover NH, No. AD.724-121


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1 INTRODUCTION

1.1 GENERAL

SNC-Lavalin Inc. has signed an agreement with Nalcor Energy (the Client) to deliver

engineering, procurement and construction management services for the Lower Churchill

Project (LCP) in Newfoundland and Labrador, Canada.

As part of the LCP, the Muskrat Falls Hydroelectric Development is located on the Churchill

River, about 291 km downstream of the Churchill Falls Hydroelectric Development which

was developed in the early 1970’s. The installed capacity of the project will be 824 MW (4

units of 206 MW each).

It is necessary for the purposes of project design, estimating power and energy yield and

operation planning to have knowledge of the water level in the tail race of a hydroelectric

power development as determined by water flow rates. The purpose of the analyses

described herein is to establish this relationship for the Muskrat Falls Development.

Because of the process by which an ice cover develops on the Lower Churchill River in the

early winter months and the cover’s prevalence thereafter to the end of winter, three

different discharge-level relationships are required; namely open water, freeze-up and ice

covered.

Each of the foregoing three states of flow has a degree of uncertainty as follows:

• Open Water: the active alluvial bed of the river results in seasonal and year to year

variations in channel geometry as a consequence of variations in flood flows and winter

freeze-up conditions;

• Freeze-up: in addition to the alluvial bed uncertainty, variation in the properties of ice at

the time of cover development result in variations in freeze-up levels; and

• Ice Covered: in addition to the two foregoing uncertainties, the hydraulic roughness of

the under surface of the established winter ice cover can vary with variations in the

thermal regime of the river in response to climate and flow variations.

As a consequence of the foregoing uncertainties, each state of flow has a range of possible

levels for a specific discharge. This is illustrated by the overview in Figure 1-1 and Figure


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1-2 showing the results obtained for each of the two hydrometric stations subject to study

herein. Figure 1-3 presents the three states for the foot of Lower Muskrat Falls using

03OE014 as surrogate station and applying one-dimensional backwater analysis.

Figure 1-1: WSC Station 03OE007 Rating Curve Ranges (At the Foot of Lower Muskrat Falls)

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000

Gauge Height (m

)

Flow Rate (m3/s)

Open Water

Freeze‐up


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Figure 1-2: WSC Station 03OE014 Rating Curve Ranges (6.15 km Downstream of Muskrat Falls)

Figure 1-3: At the Foot of Lower Muskrat Falls - Rating Curve Ranges

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000

Gauge Height (m

)

Flow Rate (m3/s)

Open Water

Freeze‐up

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000

Gau

ge Height (m

)

Flow Rate (m3/s)

Open Water

Freeze‐up


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1.2 OBJECTIVES OF THE TECHNICAL REPORT

The main objectives of the present report are:

• Establish a rating curve at the foot of Lower Muskrat Falls in open water conditions;

• Obtain a rating curve range during the freeze-up period for design purposes; and

• Establish a rating curve during winter conditions for long-term operations.


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2 EXISTING REFERENCES ADDRESSING TAIL WATER AT MUSKRAT FALLS

Various studies have addressed directly or implicitly the increase in water level due to ice

presence in winter conditions after commissioning of Muskrat Falls. Hereafter are listed four

sources where this condition is mentioned.

− SNC, Churchill River Complex, Energy Studies, January 1991

In this report, it is stated in Appendix C that “modifications of the Churchill river bed due to

the huge ice jams which form every winter since commissioning of Churchill Falls (these

jams deepen the river immediately downstream and create sediment deposits further away)”

and “In winter, after commissioning of Muskrat Falls power plant, huge ice jams will not form

anymore, but friction on the ice cover on the 48 kilometres reach will increase tail water

levels by one to two meters.”

− SNC–AGRA, Muskrat Falls Hydroelectric Development, Final Feasibility Study Report, January 1999

Although this study does not refer directly to the increase in water level due to the ice

formation downstream of Muskrat Falls, the rating curve during winter time is illustrated with

a dotted line, showing an increase in water level due to an ice cover.

− HATCH, Ice Dynamics of the Lower Churchill River, October 2007

This study report mentions that the ice progression from Goose Bay to Muskrat Falls will

continue after the project construction with some delay. “The dam at Muskrat Falls will cut

off the supply of ice to the downstream reach and hence it will take longer for the cover to

progress from Goose Bay towards Muskrat Falls. Results indicate that the progression from

Goose Bay to Blackrock Bridge could take between one and four weeks longer in the post-

project case, and the progression from Goose Bay to the base of Muskrat Falls could take

between one and five months longer in the post-project case, depending on the climate and

flow conditions of the winter. Also due to the lack of frazil ice supplied to the reach once the

dam is in place, there will be no hanging dam at the base of the falls. It is expected that

there will be little difference in the thickness of ice in the reach downstream of the falls.”


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− SNC-LAVALIN, JANUARY 2012

With a letter sent on February 10th 2012, SNC-Lavalin informed Nalcor about the increase in

water level in winter conditions due to processes associated with the ice formation

downstream of Muskrat Falls.

As a result of the letter, Nalcor requested SNC-Lavalin to provide further clarification to

better understand the ice conditions after the implementation of the Muskrat Falls Project,

and define the water level that would be expected during winter conditions.


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3 HYDROMETEOROLOGICAL DATA

3.1 HYDROMETRIC STATION RECORDS

Water level data are available from two Water Survey of Canada (WSC) hydrometric

stations near the dam site. Flow data is available from one WSC hydrometric station

immediately upstream of Upper Muskrat Falls. Details of the hydrometric stations are

presented in Table 3-1 and their location is shown on Figure 3-1. The two hydrometric

stations reporting water level are located downstream of Muskrat Falls (Station 03OE007

and 03OE014).

It is noted that while the levels recorded at Station 03OE014 are referenced to the Geodetic

Datum, those at Station 03OE007 are to a local gauge datum with unknown geodetic

reference.

Table 3-1: Muskrat Falls Hydrometric Stations

Station Name Latitude Longitude Operation Type

03OE001 Churchill River above

Upper Muskrat Falls 53°14’52’’ N 60°47’21’’ W 1953-present Flow

03OE007 Churchill River at foot

of Lower MF 53°14’57’’ N 60°46’08’’ W 1980-1995 Level

03OE014 Churchill River 6.15 km

downstream of MF 53°14’15’’ N 60°40’30’’ W 2008-present Level


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Figure 3-1: Locations of Stations 03OE001, 03OE007 and 03OE014

Figure 3-2 presents the water level records at station 03OE007 from 1980 to 1995. Three

periods with distinct water conditions are identified. The first period is from May to October

where there is no presence of ice on the Churchill River and the river is considered flowing

in open water conditions. The second period is found between November and December,

where a rapid increase in water level of about 2.5 m is observed and corresponds to the

freeze-up period of the river. The third period from January to April is characterized with a

super elevation in water levels due to the formation of a hanging ice dam downstream of

Muskrat Falls. Station 03OE007 was discontinued after 1995.


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Figure 3-2: Water Levels Station 03OE007 at the Foot of Lower Muskrat Falls

In 2008, a hydrometric station 03OE014 was installed 6.15 km downstream of Muskrat Falls.

While not as close to the foot of the falls, it is nevertheless situated strategically at the outlet

of the Muskrat falls tail water pool stretching about four kilometres downstream of Muskrat

Falls. Figure 3-3 shows the water levels reported from Station 03OE014 from 2008 to 2011.

Three periods can be observed; the first period corresponds to open water conditions, from

May to October. The second period observed is the freeze-up in late November and early

December and the third period comprises the December to April winter season.

0

2

4

6

8

10

12

14

16

18

Jan-01 Feb-01 Mar-01 Apr-01 May-01 Jun-01 Jul-01 Aug-01 Sep-01 Oct-01 Nov-01 Dec-01 Jan-01

Leve

l (m

)

1980 1981

1982 1983

1984 1985

1986 1987

1988 1989

1990 1991

1992 1993

1994 1995

Freeze-up

Open Water

Ice Jam

Local Datum


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Figure 3-3: Water Levels Station 03OE014 - 6.15 km Downstream of Muskrat Falls

Figure 3-4 presents the correlation between the water level, discharge and temperature

observed at Station 03OE014. It is clear from the upper chart that there is a correlation

between the water level and the discharge in open water conditions and during the winter

season the water level increases. It can be also seen that there is correlation between

water level and discharge in winter, with the exception of some periods that can be

attributed to local ice jams or clogging.

0

1

2

3

4

5

6

7

8

01-Jan 01-Feb 01-Mar 01-Apr 01-May 01-Jun 01-Jul 01-Aug 01-Sep 01-Oct 01-Nov 01-Dec

Leve

l (m

)

2008

2009

2010

2011

Geodetic Datum

Open Water

Freeze-up

Ice Covered

Local Ice Jams


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Figure 3-4: Correlation between Water Level, Discharge and Temperature at Station 03OE014

-1100

-100

900

1900

2900

3900

4900

5900

0

1

2

3

4

5

6

7

01-S

ep-0

8

31-O

ct-0

8

30-D

ec-0

8

28-F

eb-0

9

29-A

pr-0

9

28-J

un-0

9

27-A

ug-0

9

26-O

ct-0

9

25-D

ec-0

9

23-F

eb-1

0

24-A

pr-1

0

23-J

un-1

0

22-A

ug-1

0

21-O

ct-1

0

20-D

ec-1

0

18-F

eb-1

1

19-A

pr-1

1

18-J

un-1

1

17-A

ug-1

1

16-O

ct-1

1

15-D

ec-1

1

13-F

eb-1

2

Dis

char

ge (m

³/s)

Wat

er L

evel

(m)

Gauge Height (m)

Flow Rate (m³/s)

-60

-40

-20

0

20

40

60

80

0

1

2

3

4

5

6

7

01-S

ep-0

8

31-O

ct-0

8

30-D

ec-0

8

28-F

eb-0

9

29-A

pr-0

9

28-J

un-0

9

27-A

ug-0

9

26-O

ct-0

9

25-D

ec-0

9

23-F

eb-1

0

24-A

pr-1

0

23-J

un-1

0

22-A

ug-1

0

21-O

ct-1

0

20-D

ec-1

0

18-F

eb-1

1

19-A

pr-1

1

18-J

un-1

1

17-A

ug-1

1

16-O

ct-1

1

15-D

ec-1

1

13-F

eb-1

2

Tem

pera

ture

(°C)

Wat

er L

evel

(m)

Gauge Height (m)

Temperature (°C)


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In the absence of concurrent data which would permit a direct correlation of the gauge

heights at the stations 03OE007 and 03OE014, one-dimensional backwater analysis with

HEC-RAS was applied to develop such a relationship at the foot of Lower Muskrat Falls.

This relationship permits the use of WSC Station 03OE014 as a surrogate gauge for the

project tail water levels. It is deemed of critical importance to undertake the field surveys

necessary to validate this relationship.

The historical inflows are presented in Figure 3-5. It can be seen that the river is highly

regulated by the presence of the upstream Churchill Falls hydropower facility with consistent

flows throughout the winter period. The increase in flows during the spring period

corresponds to the spring freshet of the unregulated watershed downstream of Churchill

Falls.

Figure 3-5: Total Flows at Muskrat Falls Station 03OE001 1978-2009

0.0

1000.0

2000.0

3000.0

4000.0

5000.0

6000.0

7000.0

8000.0

01-J

an

01-F

eb

01-M

ar

01-A

pr

01-M

ay

01-J

un

01-J

ul

01-A

ug

01-S

ep

01-O

ct

01-N

ov

01-D

ec

0

1 000

2 000

3 000

4 000

5 000

6 000

7 000

8 000

Dis

char

ge (m

³/s)

Max

Min

5%10%20%50%80%

Probability of exceedance

90%95%


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3.2 METEOROLOGICAL STATION RECORDS

Temperature measurements are available from the Environment Canada meteorological

Station 8501900 located at Goose Bay airport. Table 3-2 shows the coordinates of the

station and the years of record.

Table 3-2: Goose Bay Meteorological Stations

Station Name Latitude Longitude Operation

8501900 Goose Bay Airport 53°19’00’’ N 60°25’00’’ W 1953-present

Figure 3-6 shows the daily temperature at Goose from 1978 to 2009. Temperatures below

0° Celsius can be expected from early November until the middle of April. Between

December and mid March, temperatures below -15° Celsius tend to prevail.

Figure 3-6: Mean Daily Air Temperature at Station 8501900 Goose Bay 1978-2009

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

10.0

20.0

30.0

40.0

50.0

01-J

an

01-F

eb

01-M

ar

01-A

pr

01-M

ay

01-J

un

01-J

ul

01-A

ug

01-S

ep

01-O

ct

01-N

ov

01-D

ec

- 50

- 40

- 30

- 20

- 10

0

10

20

30

40

50

Air t

empe

ratu

re (º

C)

Max

Min

5%10%20%50%80%

Probability of exceedance

90%95%


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4 RIVER MORPHOLOGY CHANGES AT MUSKRAT FALLS

Figure 4-1 presents open water levels reported from station 03OE007 vs. the discharge

reported from Station 03OE001, between July to October 1980 to 1995. It is noted that

there is a trend of the water level constantly increasing over the years of records. This is an

indication of morphological changes in the river bed of the river. There are three factors that

can be the cause of these continuous changes in water level.

Figure 4-1: Water Level Evolution at Stations 03OE007 at the Foot of Lower Muskrat Falls

The first factor, considers that after the commissioning of Churchill Falls hydropower facility

between 1971 and 1974, a disruption in the natural conditions of the Churchill River system

was introduced. It is known that when the balance of sediment load, hydrologic load (in this

case), and/or channel geometry and slope is changed, there is often a response or

adjustment of the fluvial system as it attempts to re-establish the equilibrium condition. In

other words when a stream is in adjustment, it is evolving toward equilibrium or working to

re-establish balance with its watershed inputs. The time required for a stream to adjust to a

given disturbance is difficult to predict owing to the fact that they are influenced by boundary

conditions, climate, and history or persistence of disturbance but can take decades or

centuries. Unfortunately, station 03OE007 stopped recording data in 1995 and it was not

3.0

3.5

4.0

4.5

5.0

600 800 1000 1200 1400 1600 1800 2000 2200 2400

Wat

er Le

vel (

m)

Discharge (m³/s)

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1980

1995


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possible to know whether the observed upward trend continued or decreased at a certain

point.

Another factor of change is the presence of the hanging ice dam that forms every winter

downstream of the falls. This ice dam is produced by the frazil ice coming from the fast

flowing river upstream of Muskrat Falls. The ice deposits over the course of the winter,

reducing the river conveyance and increasing the flow velocity. Whenever the equilibrium of

the deposition velocity of ice exceeds the threshold erosion velocity of the alluvial material,

further erosion of the river channel is occurring, contributing to the dynamic changes of the

river morphology.

The third factor is the construction in 2006 of the Blackrock Bridge 18 km downstream of

Muskrat Falls. This condition has changed the channel geometry and conveyance capacity.

One response of the river seeking equilibrium subsequent to this kind of disruption is

aggradation. Channel aggradation may occur when there is an introduction of a

downstream hydraulic constriction, such as bridges and culverts. In addition, the report

made by Acres in 2002 (Ref 4), states that the Blackrock Bridge will have a backwater effect

at the foot of Lower Muskrat Falls by about 0.23 m for a discharge of 2,500 m³/s. However,

this increase in water level is not possible to be confirmed since the station 03OE007 was

decommissioned in 1995.

In 2008 a hydrometric station 03OE014 was installed 6.15 km downstream of Muskrat Falls.

This station in georeferenced and was used to calibrate the HEC-RAS model prepared by

HATCH in 2007 (Ref 5) with water levels recorded in 2008 to 2011. According to this

calibration, the water levels in the rating curve presented in the SNC-AGRA report (Ref 2)

have raised by about 0.40 m for the period between 1998 and 2011.


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5 OPEN WATER RATING CURVES

The open water rating curve analyses applied the methodology developed by A.I.G.S.

Robertson (Ref 6). This methodology logarithmically transforms the flow-level data set for a

gauging station, identifies the possibility of multiple hydraulic controls, separates the data

into inter-control segments and then linearizes the logarithmic relationship for each segment

by adjusting the gauge datum constant for each segment.

The resulting equation for each segment takes the traditional form:

Q a GH b

Where Q = flow rate;

GH = Gauge Height;

A = constant representing the cross-sectional area and hydraulic roughness

of the channel;

b = datum constant; and

c = a constant that represents the shape of the controlling channel cross-

section.

Inverting the equation yields:

GHQ

b,

which shows correctly the dependency of water level (GH) on flow rate (Q).

In the current work, only a single (channel friction) control was identified at each subject

station so that only a single datum constant (b) was required for the entire range of flow in

each case. The accepted adjustments were those that were found to maximize the

correlation coefficients for the logarithmic flow-water level relationship.


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The slope of the relationship (1/c) thus derived was found to be characteristic of a near

parabolic cross-section, which is consistent with the known channel bathymetry, thereby

lending confidence to the result. In order to be able to compare results, the values of Station

03OE007 were adjusted with the georeferenced datum of Station 03OE014 translated to the

tail water of Muskrat Falls through the backwater computations of the calibrated HEC-RAS

model mentioned previously. The results of the analyses for 03OE007 and 03OE014 are

provided in Figure 5-1 and Figure 5-2, respectively, including envelope curves to define the

uncertainty previously noted.

Figure 5-1: WSC Station 03OE007 Open Water Rating Curve

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

500 1000 1500 2000 2500 3000 3500

Gau

ge H

eigt

h (m

)

Flow Rate (m³/s)

1980-1995 Data

GH=0.082*Q^0.513-0.805

GH=0.066*Q^0.537 -0.805 {+/-0.14}

GH=0.095*Q^0.498-0.805

Datum adjusted by translation of 03OE014 to the location of 03OE007 using HEC-RAS simulations

Note:


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Figure 5-2: WSC Station 03OE014 Open Water Rating Curve

Knowing that Station 03OE007 was decommissioned in 1995, Station 03OE014 was

retained as more representative of the most recent riverbed conditions. Therefore, the

rating curve at the tail water of the falls was obtained with the HEC-RAS model calibrated

with Station 03OE014. Figure 5-3 presents the computed rating curve for open water

conditions immediately downstream of Muskrat Falls.

As mentioned before, it is of utmost importance to validate this curve through a hydrometric

survey and to confirm the geodetic datum at Station 03OE014.

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

500 1000 1500 2000 2500 3000 3500

Gau

ge H

eigt

h (m

)

Flow Rate (m³/s)

2008-2011 Data

GH=0.206*Q^0.410-1.30

GH=0.172*Q^0.430 -1.30 {+/-0.13}

GH=0.144*Q^0.450-1.30

Note: Geodetic Datum


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Figure 5-3: At the Foot of Lower Muskrat Falls Open Water Rating Curve

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

500 1000 1500 2000 2500 3000 3500

Gau

ge H

eigt

h (m

)

Flow Rate (m³/s)

GH=0.189*Q^0.424-1.3

GH=0.168*Q^0.436 -1.3 {+/-0.13}

GH=0.148*Q^0.449-1.3



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6 FREEZE-UP RATING CURVES

To understand the derivation of rating curves for the freeze-up period in which transition

from open water to an ice covered state is achieved, it is necessary to understand the

mechanics of ice cover development on the river. A brief description of this process follows.

The Lower Churchill River downstream of Muskrat Falls, while a gently sloping channel, has

a velocity of flow too great for a thermal ice cover to develop. A cover develops instead by

the following processes:

• Shore-fast border ice grows throughout the length of the river, narrowing the open water

top width of open water flow. Figure 6-1 shows the Mud Lake crossing during the

freeze-up process. In the photo to the left, ice pans are seen to be floating through the

section at Mud Lake crossing of the Lower Churchill River (landing area in center

background). The spaces between pans are also seen to be growing in the downstream

direction from the landing section, this being the consequence of the ice pans

accelerating away from the ‘closure’ section. In the photo to the right, the previously

moving ice pans are seen to be arrested and frozen in place. From its downstream

(trailing) edge, to a point upstream of the Mud Lake crossing section, the ice pans are

clearly identifiable. Upstream of this, the ice texture is rougher for a short reach of the

river, with thickening by shoving having occurred to attain equilibrium thickness of the

cover through this reach. Upstream of this shoved reach, the form of the ice pans is

again evident. The leading edge Froude number appears to have been low enough to

permit the progression of the cover from the initial closure on upstream to beyond the

limits of the photo. Also note the striations in the border ice on the near bank in the

photo, these being a consequence of the buttering process.


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Figure 6-1: Mud Lake Crossing Looking U/S – Left: 1 Day before Freeze-up –Right: 1 Day after Freeze-up

• At the river mouth, a full ice cover develops across the full width of the channel by

thermal growth in the relatively quiescent flow at the entrance of the river into Goose

Bay.

• Pans and cakes of ice generated on the upstream open water reaches up to and beyond

Muskrat Falls arrive at the downstream closure to juxtapose against the downstream

(leading edge) closure. With continuing juxtaposition of the incoming ice, the leading

edge of the established downstream cover steadily advances upstream, effecting full

cover of the channel across its width as it goes (Figure 6-2).

Figure 6-2: Process of Juxtaposition – 1a

• At the leading edge, a certain minimum thickness of cover is required to maintain

mechanical equilibrium between the hydraulic forces acting on the juxtaposing ice and

the resistance provided by the already established cover.


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• Once established the cover loses heat to the atmosphere, gaining strength and, if the

initial formation thickness is less than the thermal equilibrium thickness for the

accumulating degree-days of freezing, continues to thicken with thermal growth, as

shown in Figure 6-3.

Figure 6-3: Process of Juxtaposition – 1b

• In its upstream advance, the juxtaposing cover will arrive at sections of the channel

where velocities are too high to permit mechanical equilibrium for the ice arriving at the

leading edge. In this instance, incoming ice is submerged by the hydraulic forces at the

leading edge and is carried under the leading edge to be deposited at the first location

downstream where the velocity is low enough to permit it to do so.

• As the deposition advances downstream from the leading edge, the hydraulic resistance

to flow under the downstream cover increases, and thereby the depth of flow at the

leading edge is increased, with a corresponding reduction in the velocity of flow there.

• When enough deposition has occurred to increase the leading edge water depth

sufficiently, mechanical equilibrium of the inflowing ice at the leading edge is achieved

and the upstream progress of the ice cover by juxtaposition can resume until the next

channel section with excessive velocity is reached. Thereafter, the process repeats.

This stage of the process can be seen in Figure 6-4.


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Figure 6-4: Process of Juxtaposition – 1c

In some instances, the mechanical strength of the established ice cover on the water

surface slope steepened by deposition under it will be inadequate to carry the hydraulic

forces and its own body weight and the cover will “telescope” to a greater thickness to

achieve internal mechanical equilibrium. Such thickening contributes to the achievement

of greater leading edge depths of flow, as is presented in Figure 6-5.

Figure 6-5: Process of Juxtaposition – 1d

The water levels in a reach of river between controlling sections is determined largely by

the requirement for mechanical equilibrium of the leading edge at its downstream

controlling section and to a lesser degree by the hydraulic resistance of the reach.

Field observation and theoretical analyses have shown that a Froude number can define

the state of equilibrium at a critical section. If the Froude number at the leading edge is

less than a critical value a state of equilibrium will exist: i.e. if / , then

equilibrium will prevail, where:


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F = Froude number,

v = velocity at the leading edge,

g = gravitational constant;

y = depth of flow at the leading edge; and

Fc = critical Froude number value.

• Field observation and theoretical analyses have shown that the value of Fc lies between

0.080 and 0.140 and that the prevailing value at any specific site and time depends upon

the properties of the inflowing ice.

• The first critical section downstream of the Muskrat Falls tail water pool is in the river

reach in which the WSC gauging station 03OE014 is situated. Thus, during the initial

formation of an ice cover on the pool, the water level in the pool is primarily determined

by the leading edge stability requirement in the downstream channel in which the

03OE014 gauging site is located.

• Under current conditions, the ice leading edge stalls at the foot of Lower Muskrat Falls

and inflowing ice generated in the falls and on open water upstream reaches of the river

accumulates under the established cover in the pool at the foot of the falls as described

previously. In this case, the water level rise required to achieve leading edge stability is

so great that only on rare occasions is the winter cold enough to generate the volume of

ice required to raise the pool level enough to drown out even the upper part of Muskrat

Falls. Figure 6-6 shows the lower falls flooded on March 14th, 2012.


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Figure 6-6: Lower Muskrat Falls Flooded (March 14th, 2012)

Completion of the second stage diversion river closure will raise the water level immediately

upstream of Muskrat Falls (km 43) to El 25 m, ceasing flow over the falls and permitting a

full ice cover over the upstream channel to develop almost to Sandy Lake (km 80).

Generation of ice in these areas will cease. Analyses by Hatch (Ref 7) indicate clearly that

there would be sufficient capacity in the reservoir to store the total supply of ice generated in

open water reaches upstream of the diversion head pond even in the severest winter of

record (1972-73). Thus the development of an ice cover on the Muskrat tail water pool will

be complete with its initial freeze-up as described before and the formation of a hanging

dam of any significance will be eliminated.

• Subsequent to its initial formation, the ice cover in any given reach is subject to two

possible changes; namely,

a. a smoothing of the underside of the cover, thereby reducing the hydraulic resistance

of the ice covered channel and resulting in a corresponding reduction in depth of flow

for a given flow rate, and

b. thermal erosion of the cover to yield open water reaches or patches, if the initial

cover leading edge equilibrium thickness is greater than the thermal equilibrium

thickness for the prevailing air temperatures over and flow velocity under the cover.

Such smoothing and erosion, result in a drop in the water level from the formation level.

That is, the Froude leading edge stability requirement no longer prevails and water level


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control reverts to the hydraulics of flow in an open channel, albeit with an increased wetted

perimeter due to the presence of the ice cover.

• It is clear, then, that there are three flow regimes for the Muskrat Falls tail water pool;

namely,

a. open water state;

b. freeze-up state; and

c. ice covered state.

These three states are illustrated in the following Figure 6-7. In this case, the transition from

open water to freeze-up required about 8-days, with the freeze-up enduring for about 4-

days. Subsequent smoothing of the cover to arrive at the ice covered state required

between 3 and 4 days.

Figure 6-7: The Freeze-up Process

It is clear from the chart that the highest levels realized for any given freeze-up flow rate will

be determined by the need for leading edge stability. Thus a rating curve for this condition is

useful.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

1 49 97 145 193 241 289 337 385 433 481 529 577 625 673 721 769 817

Wat

er L

evel

m

Number of Hours from Start Time

Hourly Water Levels

Average for Indicated Period

Open Water State

Rise with approaching ice front

Freeze-Up State

Fall with smoothing anderosion of ice cover

Ice Covered State

Station 03OE0142011-11-15 12:00 AM -2011-12-20 12:00 AM


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Rearranging the foregoing Froude equation and substituting v Q/By, where B = channel

top width and y = hydraulic mean depth yields;

yQ

B F/ c ,

in which the terms are as before and c’ is a datum constant relating the water level

measured at a gauging station to the elevation of the leading edge control section.

Evidently, the water level as determined by leading edge stability is proportional to the

ratio Q

B/ . A plot of water level data available from a gauge site for this state of flow

charted against the corresponding value of Q

B/ would thus be expected, with an

appropriate datum adjustment, to lie in a ‘cloud’ bounded by two straight lines the slopes of

which are determined by the limiting values for Fc of 0.080 (upper bound, Ref 8) and 0.140

(lower bound, Ref 9).

The results of application of this methodology to the data sets in terms of flow rate vs. gauge

height from the subject gauging Stations 03OE007 and 03OE014 are shown in Figure 6-8

and Figure 6-9, respectively. Figure 6-10 shows the freeze-up rating curve at the foot of

Lower Muskrat Falls using 03OE014 as surrogate station. Taking into account that the

upper bound limit and the lower bound limit have to remain the same, the datum adjustment

was found using the one-dimensional model, where the upper and lower freeze-up rating

curves found for 03OE014 were imposed as control sections respectively.


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Figure 6-8: WSC Station 03OE007 - Freeze-up Rating Curve

Figure 6-9: WSC Station 03OE014 - Freeze-up Rating Curve

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

500 1000 1500 2000 2500 3000

Gauge Height (m)

Flow Rate m3/s

1983 ‐ 1994 Freeze‐up Data

Froude # = 0.140: GH = [(Q/960)^(2/3)]*1.730 + 2.30

Froude # = 0.080: GH = [(Q/960)^(2/3)]*2.518 + 2.30

Winter Data 1985‐1995

Datum adjusted by translation of 03OE014 to the location of 03OE007 usingHEC‐RAS simulations

Note:

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

500 1000 1500 2000 2500 3000

Gauge Height GH (m)

Flow Rate m3/s

2008 ‐ 2011 Freeze‐up Data

Froude # = 0.080: GH = [(Q/960)^(2/3)]*2.518 + 1.50

Froude # = 0.140: GH = [(Q/960)^(2/3)]*1.730 + 1.50

Winter Data 2008‐2011



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Figure 6-10: At the Foot of Lower Muskrat Falls - Freeze-up Rating Curve

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

500 1000 1500 2000 2500 3000

Gau

ge H

eigh

t GH

m

Flow Rate m3/s

Froude # = 0.080: GH = [(Q/960)^(2/3)]*2.518 + 1.68

Froude # = 0.140: GH = [(Q/960)^(2/3)]*1.730 + 1.68



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7 WINTER RATING CURVES

Immediately following the freeze-up state, the established cover undergoes another

transition as previously noted, with “smoothing” of the underside of the cover and in some

cases where the velocities are higher (e.g. at the Blackrock Bridge crossing), the

development of open water reaches or longitudinal leads along the thalweg as a state of

thermal equilibrium develops for the recently established cover. The consequence of these

adjustments is a reduction in the hydraulic resistance to flow with a consequent reduction in

water depth required to carry the prevailing flow.

Subsequent to this adjustment, a steady state condition prevails and the hydraulics of the

flow reverts to an “open water” regime, but now with the additional hydraulic resistance

rendered by the presence of the ice cover. The ice cover increases the wetted perimeter of

the flow, consequently reduces the hydraulic radius for the channel and increases the depth

of flow required to carry the prevailing flow. In addition, the overall hydraulic roughness of

the channel is altered by the addition of the ice cover roughness. The consequences of

these alterations can be demonstrated algebraically as follows.

Rearranging the Manning open channel flow equation to separate the independent variables

(LHS) from the independent variables (RHS) yields:

AR / nQ/S / ,

where A = area, R = hydraulic radius, n = Manning’s roughness coefficient, Q = flow rate

and S = channel slope.

Substituting the appropriate approximations for a wide rectangular channel yields:

byyx

by

xnQ/S / ,

where b = channel top width, y = hydraulic mean depth, x = 1 for open water flow and x = 2

for ice covered flow.

Solving for the hydraulic mean depth then yields:

y ~ xnQ

bS /

/


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Taking the ratio of values for the two states x1 = 1 and x2 = 2 with Q, b and S held constant

yields:

yy

~ 2nn

~ 1.32nn

Thus, adding an ice cover to a wide-open channel is seen to require about 1/3rd more depth

of flow to compensate for the change in hydraulic radius with the introduction of an ice

cover. For example, a 6 m open water flow depth would increase for the same discharge to

about 8 m with an ice cover in place.

The effect of a change in average roughness coefficient for the channel section with an ice

cover in place is also evident. This roughness adjustment may be positive or negative,

depending upon the roughness of the channel bed relative to that of the ice cover.

Referring again to the Manning open channel flow equation, Q a GH b , the

proportionality constant ‘a’ would be expected to change with the addition of an ice cover

because this constant represents the cross-sectional area and the roughness coefficient and

as noted, the hydraulic mean depth and roughness would be altered by the addition of an

ice cover.

The datum constant ‘b’ and the index ‘c’ would be expected to remain the same as for the

open water condition; the former because it represents the physical difference between the

gauge zero and the true elevation of the hydraulic control for the river reach; the latter

because it represents the channel cross-section shape and as this is a function of the

alluvial bed material, which has not changed, would not be expected to be different from the

open water state.

On the basis of this reasoning, the ice covered rating curves have been derived for the

subject gauging stations as shown in Figure 7-1 and Figure 7-2.

In Figure 7-1, it is noted that the level/data sets available for this analysis were limited to one

observation per year, taken as a short term average immediately after completion of the

smoothing transition for the developing ice cover. Levels beyond a short time after

conclusion of this transition were rendered unusable because of the onset of the process of

deposition at the foot of Lower Muskrat Falls, as previously noted, influences the water

levels in the pool. With the termination of this process, this influence is no longer relevant.


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Also as previously noted, it is expected that once the diversion closure of the Stage II of

construction is effected, the development of any significant hanging dam in the Muskrat Falls

tail water is expected to cease.

Figure 7-1: WSC Station 03OE007 – Early Winter Rating Curve

Figure 7-2 shows the early rating curves immediately after completion of the smoothing

transition for the developing ice cover for station 03OE014. Figure 7-3 presents the rating

curve for the winter season at station 03OE014. Using backwater computations with the

one-dimensional hydraulic model HEC-RAS, the long-term average winter curve was

calculated at the foot of Lower Muskrat Falls (Figure 7-4).

1.8

2.2

2.6

3.0

3.4

3.8

4.2

4.6

5.0

5.4

5.8

6.2

6.6

7.0

7.4

7.8

500 1000 1500 2000 2500 3000

Gau

ge H

aigt

h (m

)

Flow Rate (m³/s)

g

1983-1992 Finish Level Points

GH=0.161*Q^0.513-0.805

GH=0.133*Q^0.537-0.805

GH=0.101*Q^0.498-0.805

Winter Data after Freeze-up 1983-1992 Begining of Winter

Datum adjusted by translation of 03OE014 to the location of 03OE007 using HEC-RAS simulations

Note:


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Figure 7-2: WSC Station 03OE014 – Early Winter Rating Curve

Figure 7-3: WSC Station 03OE014 – Whole Winter Season Rating Curve

1.8

2.2

2.6

3.0

3.4

3.8

4.2

4.6

5.0

5.4

5.8

6.2

6.6

7.0

7.4

7.8

500 1000 1500 2000 2500 3000

Gau

ge H

eigh

t (m

)

Flow Rate (m³/s)

2008- 2011 Finish Level Points

GH=0.297*Q^0.410-1.30

GH=0.244*Q^0.430-1.30

GH=0.201*Q^0.450-1.30

Winter Data after Freeze-up 2008-2011


1.8

2.2

2.6

3.0

3.4

3.8

4.2

4.6

5.0

5.4

5.8

6.2

6.6

7.0

7.4

7.8

500 1000 1500 2000 2500 3000

Gau

ge H

eigh

t (m

)

Flow Rate (m³/s)

2008- 2011 Finish Avg Level Points

GH=0.297*Q^0.410-1.30

GH=0.240*Q^0.430-1.30

GH=0.193*Q^0.450-1.30

Data after Freeze-up 2008-2011 Winter Season



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Figure 7-4: At the Foot of Lower Muskrat Falls – Whole Winter Season Rating Curve

1.8

2.2

2.6

3.0

3.4

3.8

4.2

4.6

5.0

5.4

5.8

6.2

6.6

7.0

7.4

7.8

500 1000 1500 2000 2500 3000

Gau

ge H

eigh

t (m

)

Flow Rate (m³/s)

GH=0.275*Q^0.424-1.30

GH=0.235*Q^0.436-1.30

GH=0.199*Q^0.449-1.30



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8 CONCLUSIONS

General conclusions regarding the overall study are provided below:

• There are three different discharge-level relationships on the Lower Churchill River

downstream of Muskrat Falls; namely open water, freeze-up and ice covered;

• On the basis of the open water rating curve found in the current analysis, the water

levels in the rating curve presented in the SNC-AGRA report (Ref 2) have increased by

about 0.40 m for the period between 1998 and 2011;

• It is expected that once the diversion closure of the Stage II of construction is effected,

the development of any significant hanging dam in the Muskrat Falls tail water is

expected to cease; and

• Adding an ice cover to a wide-open channel is seen to require about 1/3rd more depth of

flow to compensate for the change in hydraulic radius with the introduction of an ice

cover.


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9 RECOMMENDATIONS

• The rating curves presented in this study are to be used as follows:

• Setting infrastructure design criteria:

o Freeze-up extreme values have to be used.

• Values to be used for estimation of power and energy yield:

o average values to obtain long term average energy;

o extreme values to define upper and lower values for dependable capacity.

• Figure 9-1 shows the established three different discharge-level relationships

downstream of Muskrat Falls.

Figure 9-1: Rating Curves Downstream of Muskrat Falls

• It is deemed of critical importance to undertake water level measurements at the

downstream pool of Muskrat Falls in order to validate the open water rating curve found

in the present study and to confirm the geodetic datum at the hydrometric stations.

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Gau

ge H

eigh

t (m

)

Flow Rate (m³/s)

Freeze-up Rating Curve GH=[(Q/960)^(2/3)]*2.518+1.68

Winter Long-Term Average Rating Curve GH=0.235*Q^0.436-1.30

Open Water Long-Term Average Rating Curve GH=0.168*Q^0.436-1.30

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