NOAA Technical Memorandum ERL GLERL-24

UPPER ST. LAWRENCE RIVER HYDRAULIC TRANSIENT MODEL

Alan J. Potok

Great Lakes Environmental Research LaboratoryAnn Arbor, MichiganOctober 1978

UNITED STATES NATIONAL OCEANIC ANDDEPARTMENT OF COMMERCE ATMOSFWERC ADMINISIRATION

Juanita M. Krsps. Secretm-v Rchard A. Frank. Admuxtratat

Enwanmental Research

Lztaratorm

Wht N Hess. Ihector

NOTICE

The NOAA Environmental Research Laboratories do notapprove, recommend, or endorse any proprietary product orproprietary material mentioned in this publication. Noreference shall be made to the NOAA Environmental ResearchLaboratories, or to this publication furnished by the NOAAEnvironmental Research Laboratories, in any advertising orsales promotion which would indicate or imply that the NOAAEnvironmental Research Laboratories approve, recommend, orendorse any proprietary product or proprietary materialmentioned herein, or which has as its purpose an intent tocause directly or indirectly the advertised product to beused or purchased because of this NOAA Environmental ResearchLaboratories publication.

ii

CONTENTS

Abstract

1. INTRODUCTION

2. COMPUTER REQUIREMENTS

3. MODEL DESCRIPTION

4. MATHEMATICAL THEORY

5. MODEL CALIBRATION

6. HYDRAULIC EFFECT OF ICE COVER

7. THE HANGING DAM

8. MODEL STRUCTURE

9. MODEL INITIALIZATION

10. REFERENCES

Appendix A. MODEL INPUT SUMMARY

Appendix B. EXAMPLE PROBLEW

Appendix C. PROGRAM LISTING

iii

Pagt?

1

1

2

2

4

12

14

2 2

2 8

3 0

37

80

FIGURES

1. St. Lawrence River conceptualized transient model.

2. Definition sketch.

3. Time-space grid for implicit solution.

4. Comparison of stage vs. (Q/V%)' forprototype and model.

5. Determination of composite roughness inice-covered channel.

6. Sensitivity of river profile. to icethickness and ice roughness.

7. Sensitivity of fall to ice-cover roughnesswith 12-inch ice cover.

8. The hanging dam.

9. Flow-Chart.

Page

3

6

6

15

20

21

23

24

28

APPENDIX FIGURES

Page

B.l. River profiles for example problems a, b, and C. 65

B.2. Simulation of river profile for the period 7-10 August 1977. 79

iv

TABLES

1. Manning's roughness values.

2. Calibrated Manning's roughness coefficients.

3. Water level simulation error during ice-cover conditions.

”

Page

13

19

25

UPPER ST. LAWRENCE RIVER HYDRAULIC TRANSIENT MODEL

Alan J. Potok

The Great Lakes Environmental Research Laboratory (GLERL)has developed hydrologic response models for simulation studieson precipitation augmentation, ice retardation, system diver-sions, and connecting channel changes. For example, hydraulictransient models developed for use on the Detroit and St. ClairRivers have been used to compute channel flow.

The most recent addition to this series of models, ahydraulic transient model of the upper St. Lawrence River, isdesigned to simulate river profiles and flows on the St. Law-rence River from Lake Ontario to the Moses-Saunders powerhousenear Massena, N.Y. It is capable of simulation on varyingtime increments and includes flow under ice-covered, as wellas open-water conditions. This paper describes the mathemat-ical model, its development, calibration, verification, andtypical applications.

1. INTRODUCTION

As the outlet from Lake Ontario, the St. Lawrence River conveyswater from the Great Lakes Basin to the Atlantic Ocean. It varies from0.25 to 2 miles in width, averages near 30 feet in depth, and normallydischarges between 180 and 320 thousand cubic feet of water per second.Approximately 90 miles downstream of Lake Ontario the river flow isregulated by the Moses-Saunders Power Dam, which was built during thedevelopment of the St. Lawrence Seaway in 1959.

Operation of the power dam is governed by the water level in LakeOntario in accordance with Regulation Plan 1958-D. Regulation of theriver is of vital concern to many interests of national and internationalpower, navigation, recreation, industrial, and domestic users. Althoughregulation of the river occurs on a weekly basis, the river flows andwater levels are monitored and adjusted on an hourly and daily basis tomeet power demands or navigational requirements. During winter iceforms on the river, resulting in a suspension of navigation and reducedpower generation for approximately 15 weeks of the year.

GLERL Contribution No. 181.

The international reach of the river between Lake Ontario and theMoses-Saunders Power Dam has been simulated by a hydraulic transientmodel. Development of the model, designed to simulate river profilesand flows during open-water and partially or totally ice-covered con-ditions, was undertaken at the request of the U.S. Army Corps of Engi-neers, Detroit District. The purpose was to provide a useful tool inxter resources management. The Corps of Engineers needs such a modelto evaluate water surface changes due to channel dredging, changing icecovers, and the effect of extending the navigation season on the St.Lawrence River.

2. COMPUTER REQUIREMENTS

The St. Lawrence River hydraulic transient model is a digital modelrelying on the simultaneous solution of the mass continuity and momentumequations to determine discharge and stage at various points along theriver from Lake Ontario to the Moses-Saunders Power Dam. The programwas developed on a CDC 6600 computer with a FORTRAN IV language com-piler. An implicit solution procedure used in the program requires abanded matrix solution subroutine. Subroutine LEQTlB (l), developed byInternational Mathematical and Statistical Libraries, Inc., was usedduring development of the model. However, any subroutine capable ofsolving the linear equation

may be used in its place.

The model requires a core storage of 58 k (octal) on a CDC 6600machine. Central processing time is a function of the number of timeincrements used in the model run. Estimated computer costs are $3 forinitialization of the model and $.20 for each time step of solutionrequired. Manpower requirements are limited to defining the set ofcircumstances to be examined by the model.

3. MODEL DESCRIPTION

The area of the St. Lawrence River simulated by the model extendsfrom Lake Ontario to the Moses-Saunders Power Dam near Massena, N.Y.The configuration in the model consists of 30 reaches interrelated by 21intersection or "nodal" points as shown in Figure 1. Each reach isassumed prismatic with its own physical characteristics of length,width, wetted area, wetted perimeter, and bed roughness. The nodalpoints describe the river configuration by specifying the sequence ofreaches and the logic of the flow pattern. For example, at a node

2

Figure 1. St. Lawrence River conce,+k2tized transient model.

number 9, the flow leaving reach 13 is an incoming flow to the node.Likewise, the water flowing into reach 14 is an outgoing flow. The flowand stage at the downstream end of reach 13 can then be equated to theflow and stage at the upstream end of reach 14 from the equations ofcontinuity and energy. Information describing the nodal points ismaintained in a separate array. The technique of maintaining an arrayto describe the flow pattern was employed because of the need for ageneralized model during development to allow a changing definition ofthe channels and a changing emphasis on points of information.

The model is capable of simulating a river profile under partial ortotal ice cover, as well as open water conditions. When ice is includedon a reach of the river, the model decreases the hydraulic radius forthat reach and the area is constricted by an amount 0.9 times the icethickness (the specific gravity of ice is assumed to be 0.9). In ad-dition, the Manning's roughness coefficient is adjusted by the compositeroughness formula developed by Belokon-Sabaneev (Sabaneev, 1948). Anyice configuration may be input into the model by specifying the icethickness and roughness coefficient of the ice cover. Each reach isconsidered either open or completely ice covered depending on whether ornot the ice thickness is zero.

The history of the river has shown ice jams to form in the Galopand Ogden Island reaches of the river. These ice jams, called hangingdams, severely restrict river flows and power generation downstream.The model provides for simulation of hanging dams (up to a maximum ofthree), if desired, in addition to the ice cover on the river.

Input to the model consists of the initial stage and flow condi-tions along the river, the respective channel roughness coefficients,ice-cover roughness coefficients, and ice thickness for all the reaches.Generally, a complete set of initial stage and EJ~ow conditions is notavailable. In this case, initial conditions are set at zero dischargeand a level pool at the elevation of Lake Ontario. An initial dischargeis then simulated and a steady state profile is achieved correspondingto the desired discharge to be simulated. All input and output data arein the English system of units.

A net total supply (NTS) hydrograph or water level hydrograph isallowable input as upstream boundary conditions. Downstream boundaryconditions include a discharge or water level hydrograph at the powerhouse. Sample computer runs and a program listing are given in Appen-dices B and C.

3

4. MATHEMATICAL THEORY

The unsteady one-dimensional equations of continuity and mcmentumhave been adapted by numerous authors (e.g., Wylie and Streeter, 1978).In the St. Lawrence model, the equations take the form

Q, + At = 0 (1)

- - 2'Q Q, - Q A + gxH, +A

z2 x

T T0

P(2)

where

Q = mean discharge in a reach,

x = mean area in a reach,

E = mean hydraulic radius, and

A, = the partial derivativex,

of the area A with respect to distance

Hx= the partial derivative

respect to distance x,of the water surface elevation H with

Q, = the partial derivativex9

of the flow Q with respect to distance

At = the partial derivative of A with respect to t (time),

Q, = the partial derivative of Q with respect to t (time).

n = the Manning's roughness coefficient,

g = force of gravity,

T = wind stressx

= Cdp,Vw') '

T = channel top width,

P = density of water (assumed at lOoF),

'd = drag coefficient (Cd - 0.0013),

pa = density of air, and

vw= wind speed along the channel.

Equations (1) and (2) are evaluated over the time-space domain tofind the variation in unknown conditions of stage and flow at the upstreamand downstream end points of each reach as shown in Figures 2 and 3.

Because each end of each reach is uniquely defined, equations (1) and(2) are expressed in terms of four unknown quantities of flow Q andstage H. That is, 30 reaches implies 60 points, each of which has anunknown H and Q. Using finite difference methods, one can evaluateequations (1) and (2) at point m as follows:

O(Qdp - 9,') + (1 - O)(Q, - 9,)

AX

- Hd) + (H ' - HJu 1 =o

2at (3)

- 9,') + (1 - 0) (Qd - Q,) _ 3

AX 1 A2+ C[0 Td(HdP - 2,) - TU(H ' -u Zu)

3

+ (1 - 0) - 2,) - TU(HU - Zu)I +%d - %u

I

O(Hd' - HUP) + (1 - O)(Hd - HU)

AX 1+ g2n2Y$Y&i ’ + 9,' - (Q, + 9,)

2.208 Ti2i;"13+ Qd

2At

T T-x= 0 (4)

P

where 0 = At /At, H is the water surface elevation, and Ab is the areabelow a refe?ence low water datum zb. The subscripts u and d refer tothe upstream and downstream ends of the reach, respectively. The super-script p refers to conditions at time t f At. The magnitude of Ab is

5

t+,At,Atd HEd HE

AtAt Temem

AGYlAGYl

tt Q”, t-4Q”, t-4

Figure 2. Definition sketch.

UTu p s t r e a mu p s t r e a m

AX

QdP, 6

Qd, Hd

downsltreamFigure 3. Time-space grid for implicit solution.

6

normally large with respect to the incremental area T(H - Z). There-fore, substitution of a mean top width T = T = T can be made withoutaffecting the A term in the momentum equatik. $quation (4) can thenbe simplified tg

Is O(Qdp - 9,') + (1 - 0) (9, - 9,)A AX 1 +ti

Ti2AX

x[[0 'Hdp - Z,) - (H '

u- Zd) + (1 - 0)

I(Ha - Zd)

- (H,, - Zu)3 + %d - %u] + f$ [o(Hdp - H;)

+ (1 - O,)(Hd - HU) 3 + g2”2<j~1A

2.208 ;i2i+'3

+ QdP + 9,' - (Q, + 9,) TxT--=

2At0

P(5)

where

3 = 0.5EO(Qdp + 9,') + (1 - O)(Qd + Q,) 1 ,

0 = Atm/At, and

4 = 0.5 + Aup' + (1 - 0) (9, + Q,)] .

Several values of 0 in the range of 0.5 < 0 < 1.0 were examined. It wasdetermined that 0 = 0.75 provided a rapid convergence to a stablesolution. At each of the 21 junction points shown in Figure 1, theequations of steady continuity are applied, giving

19 ’u - CQdp = 0 (6)

7

and,Hup - Hdp = 0 (7)

where Q ', H ' and Q ', H ' correspond to the flow and stage at theenterin!$ (upstream) &d ldeaving (downstream) reaches of each junction.Lake Ontario and the power dam reservoir pool are included in the modelby the use of the reservoir storage routing equation.

as = (I - 0)At (8)

where

AS- = the time rate of change in storage,AtT = the mean inflow over the time period, and

0 = the mean outflow over the time period.

For a reservoir with a large surface area (A ), such as Lake Ontario orthe reservoir pool, the change in storage tag be approximated by:

-=A A!!ASAt sAt .

Substituting into equation (8) and rearranging yields

FNTSl + NTS2 A,,(H' - H)

=u 2

-QP+Q- At z.2

Fd = 'fbP + 'fb Afb(Hp - H)- - 'php + 'ph

2 2 - At = 0,

where

(9)

(10)

(11)

NTS = the net total supply of water to Lake Ontario (includingprecipitation, runoff, evaporation, and Niagara River andWelland Canal inflows;

Q = the flow from Lake Ontario;A0 = the surface area of Lake Ontario, km2;

8

H = the respective water surface elevation at Lake Ontario or thereservoir pool;

;fb= the river flow entering the reservoir pool;= the discharge through the powerhouse; and

Aph =fb

the surface area of the powerhouse reservoir pool, km2.

The superscript p indicates the solution at time increment t + AtEquations (10) and (11) complete the equation set for the model. Equa-tions (3), (5), (6), and (7) are applied to each of the 30 reaches and21 nodal points in the model. These equations, along with equations(10) and (ll), form a matrix of 120 equations and 122 unknowns. Eitherthe net total supply (NTS) or the water level at Kingston, and eitherthe discharge through the powerhouse (Q ) or the water level at thepowerhouse are specified as functions oPhtime, leaving 120 equations and120 unknowns.

The non-linear nature of the equation matrix requires applicationof an iterative solution technique. A Newton-Raphson algorithm withprojected approximations is used in the model. The Newton-Raphsonprocedure can be defined by equations of the form

i" aFiu

aF.Fi +c

i- AHj +aH

c1 AQj = 0 ,

j=id j j=id aQj

(12)

where iu and id represent the upstream and downstream points, respec-tivelx, of each reach i (i = 1 to 30). The partial derivativesaF./aH. and aF./aQ. are evaluated with finite dtfiference techniques andth& pastial d&va$ives of continuity for the i reach (i = 1 to 30)are expressed as

aF aFs = -!? = T/2At

aHiu aHid

aFc1 = -O/L

aQiu

aFci-= O/LaQid

(13)

(14)

(15)

The partial derivatives of the momentum equation are approximated as

OT (7/3)Q- O+gHxl-2,2 $13

@-gA AX x10/3 2

(16)

(17)

aF - 2~!!+w‘2ii;~~~~+6Q”P

4130

aQiu+ 1/2At (18)

AA AX ;i2 x x7/3

aFml

aQid

aF7ni + 4ij 0aQiu n AX (19)

For each nodal point j (j = 1 to 21) the partial derivatives of equations(6) and (7) are

where

2k is the downstream point of the incoming reach k.

aFA = -1

aH2k-l

10

(20)

(21)

where

2k-1 is the upstream point of the outgoing reach k.

IN

caFcj=,

n=laQ2k

where

IN = the number of reaches flowing into the node.

where

IOUT = the numberPartial derivatives of(lo), become

IOUT aF ,*

c cJ= -1

n=laQ2k-l

(22)

(23)

of reaches flowing out of the node.the boundary condition at Lake Ontario, equation

aFu aFd Ao-=-=-aHl aH2 At

aF-2 -1aq, = 1

(24)

(25)

(26)

Finally, the partial derivatives of the downstream boundary at thepowerhouse are

11

aFd 1

aQfb 2

aFd A0aHfb At

(27)

(28)

The partial derivatives equations (13) through (28) form theJacobian matrix C in the model. Equations (3), (4), (5), (7), (8), (lo),and (11) form the functional vector D in the model.

Although there are 120 equations to be solved simulta;eous$y. e$chequation will be a function of no more than 4 unknowns (H , Q , H ,QdP). Assigning the proper row number to each of the equztiong invilvedresults in a banded matrix with all the array elements outside the bandequal to zero. Assignment of row numbers to the equations is accomplishedby the nodal descriptive array B in the model. The number of incomingreaches to each node will determine the number of continuity and energyequations [(6) and (7)] to be evaluated before the reach equationsof continuity and momentum [(4) and (S)] can be evaluated. The advantageto this technique is the savings in core storage (about 60 percent) andCPU time (about 80 percent) obtained by using a banded matrix solutionroutine as opposed to a standard Guassian elimination routine on asquare matrix.

5. MODEL CALIBRATION

Model calibration consisted of determining the bed roughnesscoefficient in each reach. An estimate of the roughness coefficientsbetween two water level gages can be obtained from the adaptation of theequation (2) to steady, uniform flow. Setting Q, = Qt = 0 yields

2-2 -2-9, ~0

2 20; x2$/3 + gAHx A2 x

Solving for n yields

(29)

(30)

12

Initial estimates of bed roughness coefficients were made by applyingequation (30) to recorded stage and discharge data as described by Quinnand Hagman (1977).

Recorded stage data at Cape Vincent, N.Y.; Clayton, N.Y.; Kingston,Ont.; Alexandria Bay, N.Y.; Ogdensburg, N.Y.; Canada, Iroquois Dam,Morrisburg, Ont.; and Long Sault Dam were used to calibrate the segmentsof river between each gage. Each segment contained mre then one reachas conceptualized by the model. The A and R terms of equation (16) wereestimated by weighted averaging of several representative cross sectionsfor each reach within each segment. Cross sections were computed by theU.S. Army Corps of Engineers, Detroit District, from navigation chartsat 1:30,000 and weighted according to the length of each equivalentreach. The time periods examined were selected such that a quasi-steadystate existed along the river, allowing Q to be assumed equal to therecorded discharge at the powerhouse. Flows used ranged from 248 TCFSto 330 TCFS. Typical values of roughness coefficients obtained for eachsegment of the river are shown in Table 1. To complete calibration ofthe model, individual reach roughness coefficients were adjusted toreflect proper flow distribution around islands as determined by theU.S. Army Corps of Engineers (1976, 1977).

Table 1. Manning’s Roughness Vak?s

Segment of River n

Kingston to Clayton 0.022

Clayton to Alexandria Bay 0.042

Alexandria Bay to Ogdensburg 0.033

Ogdensburg to Cardinal 0.035

Cardinal to Iroquois Dam 0.027

Iroquois Dam to Morrisburg 0.034

Morrisburg to Long Sault 0.039

13

Model calibration was verified by using the model to simulaterecorded river profiles for flows ranging from 260 TCFS to 350 TCFS.Errors in river stage were less than 0.2 ft for the cases tested.

Stage-fall relationships were then computed from recorded data forthe following sections of river: Kingston-Ogdensburg, Ogdensburg-Cardinal, Ont., Cardinal-Morrisburg, and Morrisburg-Long Salt Dam.Mean monthly values of fall (F), fl ow (Q), and the stage at the upstream~;y==,""'" to plot the relationship of stage versus the quantity

for each of the four sections. Regression lines and cor-relation coefficients for recorded data were also determined. Simulatedmodel output was then plotted for a series of conditions of flow andstage. As shown by Figure 4, the model compared well with the regres-sion line in all segments of the river, with the Kingston-Ogdensburgsegment showing the largest variation. This is due to the low fall overthis region. 0.01 ft in fall will result in a substan-tial shift in the (Q/r)

A differencelgg axis. This sensitivity is also reflected

in the low correlation and the scatter about the regression line.

Final bed roughness coefficients used in the model are tabulated inTable 2.

6. HYDRAULIC EFFECT OF ICE COVER

The St. Lawrence River is at least partially ice covered 3 monthsof the year. Simulation of the river operation during these wintermonths requires compensation for the drag effect of ice cover on thewetted perimeter and roughness of the channel. A review by Nezhikhovskiy(1964) compared the assumptions and limitations of several formulae forcomputing a composite channel roughness. Three of the methods presented;Pavlovskiy's (1931), B 1 ke o on-Sabaneev's (Sabaneev, 1948), and a meanweighted formulae; were considered for use in the St. Lawrence model.

Equation (30) is applicable to ice covered channels provided thewetted perimeter is adjusted for ice cover and the restriction in flowarea due to ice thickness is known. Since 1963, the St. Lawrence SeawayAuthority has taken periodic ice thickness measurements in the reachbetween the Cardinal and Iroquois Dam water level gages. The channelroughness was computed using equation (30) assuming a 0.90 specificgravity for ice and using recorded river stage at the Cardinal andIroquois Dam water level gages. Channel roughness was computed for 49periods of ice measurement between 1963 and 1975.

Using the Manning roughness coefficient of n = 0.026 calibrated foropen water conditions, the ice-cover roughness was computed according toeach of the three formulae. The ratio of composite roughness to Manning'sroughness coefficient (n/n,) was plotted against the ratio of the iceroughness to the Manning's roughness coefficient (*I/n ) from each ofthe three formulae (Fig. 5) in turn. A distribution o B all the computed

14

/+ +

‘A +A’+

+a+*++ +/+&:i;.l;:

* I* .+ ++/ + *

+ * +*+

+

*+ +’

+ ++

0.0

Figure 4a. CO~~~Y~SOTI of stage VS. i~/fi;i' for prototype (+! and model (A.!(Kingston, Ont., to ogdensburg, N.Y.!.

15

A +

2 125.0135.0 415.0 l55.0 465.0

,4750 485 0 495,c

SORTfO/vmTIF,,

Figure 4b. Comparison of stage vs. (Q/G)' for prototype (+I and modet (A!(Ogdensbmg, N.Y., to CardimZ, 0nt.l.

16

1:2;E<’0 :

“i c 455,3 465 c &o 485.0 195.0 505.0S”RTIO/SORTIFjI

Figure 412. Comparison of stage VS. (Q/F)% for prototype (+) and model (a)(Cardinal to Morrisburg, Ont. ).

17

:

g;

8”

gc‘2

2WC22LG”

N

N

N

5mc 560.0 570.0 580 0 590 0 630~0smT~n/SoRTIFI~

Figure 4d. Comparison of stage vs. (Q/G)' for prototype I+) and model (~5)(Morrisburg to Long Sault, ht./.

18

Table 2. Calibrated Manning’s Roughness Coefficients

Reach n Reach n

1 0.028 16 0.033

2 0.023 17 0.033

3 0.028 18 0.038

4 0.037 19 0.026

5 0.025 20 0.031

6 0.032 21 0.026

7 0.040 22 0.033

8 0.038 23 0.033

9 0.033 .24 0.040

10 0.035 25 0.040

11 0.035 26 0.040

12 0.036 27 0.040

13 0.030 28 0.040

14 0.029 29 0.040

15 0.026 30 0.046

19

Number of Computed Valuesnln,

0-

Total Number of Samples = 49mm- Belokon-Sabaneev

PavlovskiyWeighted Mean

Mean n/nB = 0.86Standard Deviation = f .I2

Error = + .02

x?? 0.6226 0.7

-1

2n3 0.6Em5 0.5

/ Ice Thickness Measurements-St Lawrence Seaway Authority

Flow and River Stage-Ontario Hydra.

n,/nB (Ice Roughness/Bed Roughness)

Figure 5. Determination of composite roughness in ice-covered channel.

values of n/n was also plotted. The mean computed ratio n/n forthese 49 periids was 0.86 and all but four of the values are !bove 0.7.Entering Figure 6 with the mean values of n/n

3of 0.86 indicates that

any of the three formulae being examined woul result in virtually thesame ice roughness coefficient. Of the three formulae, only that ofBelokon-Sabaneev, equation (31), considers a non-linear velocity dis-tribution in the ice-covered channel. For this reason, it was incor-porated into the model in the form

213

n=0.63nB (l+ ( :)le5)

where

(31)

n = composite channel roughness,

*B= Manning's roughness coefficient, and

*I = roughness of underside of ice cover.

20

244r Ice

232 L

M i l e o f R i v e r

Figure 6a. ,%nsitivity of river profile to ice thick-ness. (Flow = 245 thousand cubic feet per second.)

242 - 3.005.OlO

z .015@= 238- .020

234 -.040

2 3 2 -A

;'E A

6 2tj g .z

s 3

$ t?D, 25

wI

0g $

:-IO

I I 7190 170 150 130 110 90 70

M i l e o f R i v e r

Figure 6b. Sensitivity of river profile to ice rough-ness. (Flow = 245 thousand cubic feet per second.!

21

Varying nA

in the range 0.005 < nprofiles recur ed on the St. Lawrence 6.

< 0.03 resulted in duplicating river=ver.

Required input to the model for computation of river profiles underice cover conditions includes the ice roughness coefficient and icethickness. Although adequate data on the characteristics of the St.Lawrence River ice cover is not readily available, the limited datacombined with aerial photographs allowed the following assumptions:

a. The roughness of the underside of the ice cwer has a normalrange of 0.005 < n < 0.03, with a mean valuedetermined through'the use of equations (13)

of n = 0.014 asand (14).

b. Sheet ice at least 12-inches thick is experienced along theentire river, except for the area immediately downstream ofthe Prescott ice boom and Iroquois Dam, which remain ice free.

The river profile is sensitix to both input parameters as exhibited inFigure 6. While ice thickness may be the easier parameter to estimate,it is the least sensitive of the two. Success in simulating riverprofiles was achieved by assuming a uniform 12-inch layer of ice on theriver and adjusting the roughness coefficients to attain the requiredprofile.

Figure 7 represents the sensitivity of river stage to ice rough-ness. The discharges selected are typical of those experienced duringwinter. Entering the curves in Figure 7 with recorded conditions ofstage and flow, a related ice roughness coefficient was obtained. Usingthis coefficient, the river profile over a" entire winter could besimulated, until the ice cover changed during spring thawing. Table 3lists the mean errors and error distribution obtained with a single iceroughness coefficient. A strong point of interest was that the iceroughness remains fairly stable over the winter (although it varies fromseason to season) and the changing fall is due primarily to fluctuatingriver flows.

7. THE HANGING DAM

Conditions of intermittent freezing and thawing of the ice coverand strong winds on the river have been know" to cause portions of theice cover to break free and flow downstream, where they are stopped by asolid sheet of ice cover. Unconsolidated ice forced under the solidcover causes a" ice jam referred to as a hanging dam. Hanging damsoccur most frequently around the areas of Ogden Island and Galop Island.Conditions under the dam include a severely restricted flow area androugher Manning's coefficient. Simulation of a hanging dam (Fig. 8) isaccomplished by considering the energy equation across the dam. If

9, = Q, = Q3 = 9,

22

20i

0 I I I005 ~010 015 ,020Roughness of Ice Cover (N,)

Figure 7a. Sensitimity of fall to ice-coverroughness with 12-imh ice comr (Lake Ontarioto Ogdensburg, N.Y. 1.

4.0 ~

=8=3.0-zY

I015

Roughness of Ice Cover (NJ

I,020

Figure 7b. Sw2sit~ivit.q of fall to ice-roverroughness with lZ-inch ice cover (Ogdensburg, N.Y.,to Cardinal, Ont. 1.

23

=8=3.0=2

2.0 I

I I I,005 010 ~015Roughness of Ice Cover (N,)

Figure 7~. Sensitivity of fall to ice-coverroughness with I%-inch ice cover (Cardinalto Morrisburg, 0nt.l.

4 Hz IQ, Q2 HFLOW I I

I I

.;*.,‘i.?*.‘~;:. . ~ I.o;;,- ‘D, i: *;<.o::~~ STREAM BED”‘~~~P.~~d~~:dd~::~~:i~*.o.. ..O.“O~” ..“._ .

E'igure 8. The hanging dam.

24

TabZe 3. Water LeveZ Simulation Error Durinig Ice-cover C'oonditions

Meall MaximumDifference Difference

Number (Computed- (Computed- Number of Events Whose Difference Was in the Rangeof Recorded), Recorded),

Year Events Feet Feet o-o.1 ft 0.1-0.2 ft 0.2-0.3 ft 0.3-0.4 ft >0.4 ft

1961 8 -0.00 -0.18 7 1 0 0 01962 10 -0.03 -0.16 8 2 0 0 01963 a - 0 . 0 0 -0.14 7 1 0 0 01964 14 -0.00 +0.27 10 2 2 0 01965 14 -0.01 -0.5 9 4 0 0 11968 1 -0.07 -0.0; 1 0 0 0 01969 2 0.00 -0.04 2 0 0 0 0

E 1970 8 +0.03 +0.15 7 1 0 0 01971 7 +0.03 +0.29 4 0 3 0 01972 4 +0.02 +0.32 2 0 1 1 01974 1 +0.03 +0.03 1 0 0 0 01976 5 +d.07 +0.29 3 1 1 0 0

c”^,. .._. .._;_ _,““~ ,.-. _“,._~ .,‘_.,. -.~..^-,_“.“.~~.i ;.~~^__,..^“.~.~ .,.., l_.~;,..l.., ~~--( ,,,.. ~I ,,,...., ~.-..“.l ,.,,.,... _~I..~ . .._.. ‘..., _. _.~ _-.,.~~,~~ ,.~~ _...., ..,_. ;_~“.._._., -,_.~ ,,-..,.. ,,...,.. __ ~. ,~.-____ _; “,I. .;,_,,,. “,_ _.~-‘ ~_~,_-, ..,, ;,~,_ 1..~._“~,_.^ ,,,,,. “.* ,‘.. ^ .,,.,_- “~i,,^.,~,l.;-_,l-_ ~.~ _ ,_,__.__^.._^; ;_,,.~...-.~;.~_..I. ~,-~.~~_-___;~~

andV2 3'

= v

then the energy equation between points (1) and (4) can be written as

hl + vl;;l’ = h4 + !d!$ + fL + he + hd , (32)

where

hl = the hydraulic gradient at

h4 = the hydraulic gradient at

fL = the friction loss through

section 1,

section 4,

he = the entrance loss equal to 1.0 , and

hd = the exit loss equal to 0.5

The friction loss term can be related to the Manning's roughness coef-ficient by

fI> =Q2112L

2 413 .2.208 A2 R2

Rewriting equation (32) yields

hl + vl;;' = h4 + "4;;' + Q2*;L 4,3 + l.o@22 igv12)2.208 A2 R2

+ o 5@3: - V42>

252(33)

Since V2 = V3 and a = V, the equation reduces to

hl+iL+d~h4~L+!d- Q’Ql*;L4,3=0. (34)%A1 GA2 2.208 A2 R2

26

The model assumes that the hanging dam occurs at the upstream endof the reach selected for study. Equation (7) at the particular nodalpoint involving the reach is then modified tcz include the energy lossescreated by the hanging dam represented by equation (34). Input requiredto simulate the effects of a hanging dam include the length of the dam,the ice thickness, and the anticipated roughness of the channel underthe dam. Because the dam may be of substantial length, the length ofthe dam is subtracted from the reach length when solving equations (3),(4), and (5). It is assumed that the hanging dam will not occupy anentire reach length.

8. MODEL STRUCTURE

The physical characteristics of the St. Lawrence River are describedby two arrays in the model. Array R (30, 23) describes each of the 30reaches in terms of length, top width, perimeter, bed roughness, and lowwater datum at each end of the reach. Elements R (N, 16-23) contain thecomputed discharge and stage at each end of each reach N (N = 1 to 30).Channel configuration is defined by array B (21, 9). This array pro-vides the model with information required to define the sequence of flowfrcm reach to reach. Array B is used to develop equations (6) and (7)in the model.

The use of arrays R and B provide a generalized model formulation.As a result, the user is not limited to examining the river in itsexisting state, but by appropriate substitution of the elements in R,can evaluate what will happen if changes are made. Modification ofarray B would allow the user to look at only a portion of the river or adifferent river configuration. While the model is generalized to allowthe user to examine only a portion of the river, it requires a l-imitednumber of programming changes to accomplish this purpose. Figure 9 isthe flow chart representing step by step logic in the model.

The model can be operated on hourly, daily, weekly, or monthly(assuming 1 month = 720 hr) time increments. Required input data in-clude the initial stage and flow conditions in each reach, the initialstage at Lake Ontario, the NTS hydrograph into Lake Ontario, or thestage hydrograph at Kingston, and either the powerhouse dischargehydrograph or Long Sault Dam water level hydrograph. If conditions withice are to be considered, the time variation of ice roughness and thick-ness must also be included. Sample input deck listings and correspondingoutput are given in Appendices A and B.

27

+- &I

\ w /

Figure 9. Flow chart.

9. MODEL INITIALIZATION

The complex configuration of the river, combined with the limitednumber of stage recorders, makes it difficult to estimate an initiallyaccurate river profile with the model. Although this can be estimatedif desired, the inaccuracies caused by the lack of recorded data causethe model to start with an inaccurate condition and thus to spend con-siderable time stabilizing to an accurate solution.

To overcome this drawback, the model can be initiated by assuming alevel pool at the level of Lake Ontario along with entire length of theriver and zero discharge at the powerhouse. A desired discharge thensimulated with a monthly (720 hrs) time increment. The simulationcontinues until the simulated profile is steady. Ten iterations ofmonthly time increments are used in the model to reach the steadyprofile. After the steady profile has been achieved, the time incrementis changed internally to that desired in operation of the model toexamine its response to changing conditions at the boundaries.

28

RECOMMENDATIONS

It has been shown that the hydraulic transient model for the UpperSt. Lawrence River provides an accurate simulation of water levels andflows. Because the model uses the full equations of mass continuity andmomentum, the author believes the model to be a vast improvement overthe stage-fall-discharge methods presently used.

There are many potential uses for the model relating to water re-source studies, including analysis of both physical and operationalchanges in the river. The generalized nature of the model leaves roomfor future operational capabilities. Any improvements made to the modelwill be published in future reports.

29

10. REFERENCES

Belokon, P. N. (1938): Engineering hydraulics of the flow under an icecover. MeteoroZ. and Hydrol., No. n-12.

Carey, K. L. (1967): Observed configuration and computed roughness ofthe underside of river ice, St. Croix River, Wisconsin, GeologicalSurvey Prof. Paper 550-B, National Technical Information Service,Springfield, Va.

Chow, V. T. (1959): Gpen Channel Hydraulics, McGraw-Hill, pp. 136-138.

Coleman, G., and D. G. Decoursey. Sensitivity and model variance analysisapplied to some evaporation and evapotranspiration models. Water&sour. Res., 12(5):873-879.

Larsen, P. (1973): Hydraulic roughness of ice covers. J. Hydraul.niv., ASCE, 99(HYl):lll-119.

McCuen, R. H. (1974): A sensitivity analysis of procedures used forestimating evaporation. Water Resour. Bull., 10(3):486-497.

Muir, L. R. (1975): Unsteady flow in networks of open channels, Manu-script Report Series No. 1. Canadian Center for Inland Waters,Burlington, Ontario.

Nezhikhovskiy, R. A. (1964): Coefficients of roughness of bottom surfaceof slush ice cover. In Soviet HydroZogy, Selected Paper No. 2, theAmerican Geophysical Union.

Pavlovskiy, P. A. (1963): Computations and forecasts of the flows ofslush and ice during the period of freezing of rivers. Trans.State Hydrologic Institute (Trudy G G I) 16s. p. 103.

Quinn, F. H., and E. B. Wylie (1972): Transient analysis of the DetroitRiver by the implicit method. Water Resow. Res., g(6): 1461-1469.

Quinn, F. H., and J. C. Hagman (1977): Detroit and St. Clair Rivertransient models. NOAA Tech. Memo. ERL GLERL-14, National TechnicalInformation Service, Springfield, Va.

Regulation of Great Lakes Water Levels Report to the International JointCommission (1973): Regulation Plan 1958-D, International GreatLakes Levels Board.

Sabaneev, A. A. (1948): On the computation of a uniform flow in achannel with non-uniform walls. Transactions, Leningrad Poly-technic Institute No. 5, Leningrad Polytechnic Institute, Lenin-grad, U.S.S.R.

30

U.S. Army Corps of Engineers, Detroit District (1976): St. LawrenceRiver Velocity and Flow Measurements, Galop Island, New York, OgdenIsland, New York, Copeland Cut, New York.

Wylie, E. B., and V. L. Streeter (1978): Fluid transients. McGraw-Hill, p. 286-297.

31

-

Appendix A. MODEL INPUT SUMMARY

32

*t*t*tt*tttt**t*t***********************.*****.***********.********~***********l * S T L A U R E N C E R I V E R ~HYDRAULIC TRANSIFNT M O D E L I N P U T S U M M A R Y *******tt***t*t*********~**********~**********************~***.**~*.****~~******

P R O G R A M I N P U T IS CIJV1DF.C I N T O T H R E E G R O U P S :R I V E R COYFIGUR1TIONI N I T I A L CO”DITI3NSTI”E DEPENjENT DATA

G R O U P 1 M O D E L C O N F I G U R A T I O N

C A R D 2

C A R D 3 ( A N D 4)

IDATER - D A T E O F R U NIDATE - S T A R T I N G D A T E

(2) - ENDIYG D A T EIPURP - P U R P O S E

FOR”AT( 215)qR - N U M B E R GF R E A C H E S ( U S U A L L Y 30)NB - N U M B E R O F N O D A L P O I N T S ( U S U A L L Y 21)

.* N O T E : A P O R T I O N O F T H E R I V E R M A Y BE E X A M I N E D B YA F P R O P R I A T L Y R E D U C I N G N R A N D N B . L A K E DNTARIOI S A L W A Y S A S S U M E D T O B E T H E U P S T R E A M @OUNDRY.

FOREATC16F5.4)R(CN113) - M A N N I N G S R O U G H N E S S C O E F I C I E N T S F O R

O P E N U A T E R F O R E A C H R E A C H C A L I B R A T E DR E S P E C T I V E L Y T O :.O2A,.023r.028~.0~37r.525r.0321.040.33B~.033,.035r.835r.O35~.03C~.G29.526r.033,.033r.03Br.O2S~.031~.026.G33*.033*.t40*.C43r.040*.04~*.040. c4 t,, .04L

*Z N O T E : S E C O N D C A R D IS N O T N E S S E C A R Y F O R N R L E S STHA!: 1 7 . ( T R U E F O R A L L S I M I L A R C A S E S )

C A R D 5 (AND 6) FORMATC~XI~~FS.OIRCNrl’o - ICE T H I C K N E S S I N E A C H R E A C H

C A R D 7 ( A N D 8, FORMAT(16F5.4);IIcE(rJ) - M A N N I N G S I C E R O U G H N E S S IN E A C H RCACH

C A R D ‘f FORMAT(3F5.U~I5r2F6.2~FlO.0~315)D T T - TInE I N C R E M E N TTMAX- ENDING T I M EP S I - 3.75KIT.- NUMBER OF NEUTCN RAPHSON ITERATIONS ALLOYED.

I IS A S A F E M A X I M U M S I N C E T H E H O D E L U S U A L L YSUCCEEDS IN 4

HL - I N I T I A L S T A G E A T L A K E O N T A R I OHLPN- IxITI4L S T A G E A T DOUSTREAM R E S E R V O I RPi R - A R E 4 O F L A K E DNTARIO IV S Q U A R E M I L E S (7340.1ITIYINT - UNITS OF DTT l-Her 2-OAY, 3-WEEK*

4-NOruTHI P R T Y F = G-PRINT A L L C O M P U T A T I O N S IllCLUDING

I~YITIALI~!ATISNl-DO N O T P R I N T C O M P U T A T I O N S DURTNG

INITIALIZATIONZ-PRINT O N L Y F I N A L D A T A

ISICE’- -2 ICE IS NOT INCLUDED IN THIS RUN~1 ICE IS INCLUDED

C A R D 1 3

CA!?D 11

FORMAT(F19.0*15)ARES - A R E A O F D O W N S T R E A M FORERAY IN S Q U A R E M I L E S

( U S U A L L Y lE.1N E X I T -REACi E N T E R I N G FORERAYCUSUALLY 32)

F09MATC215)N U M !I F - N U M B E R C F R E A C H E S F L O W I N G F R O M U P S T R E A M

R E S E R V O I R ( U S U A L L Y 2r O N E O N E A C H S I D E O FW O L F E I S L A N D )

NHD - :UUMRER 3F H A N G I N G D A M S , A M A X I M U M O F T H R E EIS ALLCWED

C A R D 1 2 FOR’tAT(hFl5.4)HALdG!NG CA!: DESCRIPTICN

f?OUiJrJ(I)- SDUNARY DR NOGE A T W H I C H THE D A M O C C U R R SRN1 (I)- R E A C H NUKBER C(INTAINING T H E D A MTHICK(I)- I C E T H I C K N E S S I N F E E TRL (I)- L E N G T H O F D A M IY F E E TF?N(I) - HANNINGS RDUGHNESS U N D E R D A M .

l * N O T E : GNE C A R D FOR E A C H D A M . CM11 IF YHD=O

IG R O U P L I N I T I A L cONDITIDNS

CA%D 1 FDRMAT(5X,FlS.b)DTSD-INITIAL D I S C H A R G E A T PDVERHOUSI ( U S U A L L Y 0)

C A R D 2 FOR”AT(SX,F13.D)YTSO-IN1 T I A L N E T T O T A L S U P P L Y ( U S U A L L Y ?)

C A R D 3 (GluEI 4) FCR’tAT(SX.liF5.2)R,(N,~G)-TNITIAL U P S T R E A M S T A G E F O R E A C H R E A C H

( U S U A L L Y q H L )

CAR0 5 (4VD 6) FDP”AT(5X,l~F5.2)R(Y,17)-INITIAL DDWNSTREC M S T A G E A T E A C H R E A C H

( U S U A L L Y = H L )

C A R D : ( T H R U 1 1 ) FOR’~AT(5X,7El@.jr5X)R(N,:~)-INITIAL FLOWS IN EPCH R E A C H ( U S U A L L Y 0 )

G R O U P 3 T I M E D E P E N D E N T D A T A

C A R D A ( A N D 2) FORPAT(SX,lSF5.0)R!CTHK(N)- I C E T H I C K N E S S F O R E A C H R E A C H

l * N O T E : O N L Y R E Q U I R E D I F ISICE=

C A R D 3 (AND 4) FOR#AT(16F5.4)R I C E ( N ) - I C E R O U G H N E S S I N E A C H R E A C H

l * N O T E : O N L Y R E Q U I R E D IF ISI’CE=l

C A R D 5 FOPMAT(lOX,iFlG.J,3F5r2r15)31s - DISC-IARGE A T P O W E R H O U S EN T S - NFT T O T A L S U P P L Y A T L A K ESTAGE- C O N T R O L L I N G S T A G E A T D O W N S T R E A M R E S E R V O I R .

IF S T A G E D O E S N O T E Q U A L 0 . D I S IS C O M P U T E DSATHER ThA% I N P U T . F I R S T V A L U E M U S T ~0.

H K I N G - CSSTRCLLIVG S T A G E 47 r(INGSfOlV. IF HKINGT:“ES N O T E Q U A L 9 , T H E R E IS NO N E E D , T OI N C L U D E N T S .

LiIEID- tiI!:D~ S P E E D I N M P H . UIND IS + IND I R E C T I O N O F FLOW A N D - I F O P P O S I T EO F DISECTICN O F FLGU

NHDC- CHPNGE T O BE M A D E I N H A N G I N G D A M .I F N H D C . G T . 01 C A R D 1 2 S H O U L D FER E P E A T E D U S I N G N E U I N F O R M A T I O N .

l * RFPEPT GRijUP : S E Q U E N C E FCR E A C H T I M E INTERV4L. l *********

t*t*****t*tt*r***tt*****t*t*****************~~~~~*~~~~~*~~*.~~~~~~*.~~~~~********

Appendix B. EXAMPLE PROBLEMS

37

a. The Simple Drawdown

The most basic use of the model is to solve for a steady stateprofile given a level of Lake Ontario and a powerhouse discharge. Themodel initially starts as a level pool at the elevation specified (244.00for this case). Using the initial discharge (280 TCFS) as a forcingfunction, the model iterates through 11 steps until a steady profile isachieved. In conditions of very high flow, a small fluctuation of 0.01or 0.02 may be exhibited near Lake St. Lawrence. However, eleven timesteps were found to provide ample time for convergence.

38

Input

A U G U S T 1 9 7 8 S I M P L E C R A U D O U N9

028C 6.370 0250 0323 0400 0 3 8 0 0 3 3 0 0 3 5 0 0 3 5 0 0 3 6 0 03C@ C29q 0 2 6 0 0330il25P 3313 6260 11331. C33C J4CO 04OP 9400 0400 9409 i?4CC C40F

30 210280 023r,8330 038G

0 n0 c0 02 01 115.

2 0OISO

0 c C 0 0 0 t 0 0 0 6 0 0 0

0 0 I, 0 0 0 G a 0 0 0 1

2 0 c 0 0 P 0 0 0 0 0 II 0 00 0 0 0 c 0 3 '0 0 0 0 c

0 . 7 5 8 2 4 5 5 3 2 4 5 0 0 7 3 4 3 . 1 0 c,30

i> 0 0 " 0 D 0c 1 a r: a 0 3F " n 0 0 0

'1 0 c 0 0 0;;

i81 280 0 0

Output

........................................................................................................................................

.......................................................................................................................................

............. ..........

............. .......... ST LlYRENCE RlVER ““DRAULIC TIIWSIE”, “OOEL

............. PRINT OP,,DN 0 ..........

............. .......... DEVELOPED 8”

............. ILL INTERMEDIATE .......... GREAT LIKES C*Y~RO**EW,AL IEOEAICH L*BOI1TOR*

............. Cd~C”~,,~DNS IRE .......... ANN ARBOR*~,CH,CAN

............. PRINTED O” 7. .......... J”L” 1918

............. ..........

. . . . . . ..I.... . . . ..f................. .......... PERIOD: NOLIFPURPOSE: SI.PLET~RAYOOYWPIonE............. ..........

............. ..........

...........................................................................................

...........................................................................................

*. . . . . . . . .**.*..*.... . . . . . . . . .. . . . . . . . . .. . . . * . . . . .. . ...**....f......... . . . . . *.....*....**.*....o.*.**.*...*...r....,....

,..... *.**...*,...... *.**..a

GEOORlPRlCLL XE” 10 REAC” ““WJERS_______----___-_-----------------

I.....IINGSTONP.....CIPE YINCENT3.....NORTH OF YDLFE lSLlN0. . . . ..NORTH OF “0°C IDLIND5.....SO”lr OF HOW IPLLND&.....Fl.OY BEINEN “CAFE IS. A”0 SR,WDOTDNE IS.,.....SO”T* OF GI,NDITONE *SUN0.9.....NORI” OF 6RINDSTO”E ,SLlNOY.....FLOY BETYEEN SRINDSTONC IS. A”0 YELLSLE. IS.

,D.....SO”T~ OF YELLSLE” ,SLIWOII.....NOR*w OF YLLLSLE” fJLA”DIl.....SO”T~ OF YELLSLE” ISL&NDI,.....IO”T” OF 6RE”ADIER ISLANDI4.....“lLLClEIT PO*“,I5.....elOC*YILLE16.....OSOENSB”IS~I.....“ORW OF DILDP ISLINO18.....SO”I” OF SALOP lSLlWOI’).....C,IDI”ILID.....IIOPuoIS21.....“0”,” OF osoc* I,BLAWO**.....“100I*STO**,.....sO”*H OF omtz* ,SLA”D2*.....“Oll**B”R525.....*ol*” OF CROIL ISLllOPL.....SO”T” OF CROlL ,SLllD?I.....FLOY 8CTYEEY CIOIL I*. AND LO”L IAUCT IS..?8.....“O”l” OF LO”S SAUL, ISLA”D29.....fO”T” OF’Lo** SAlAT *SLAY0ll*....LOW Sl”Ll 0.11

.............

.............

.......... e.

......... ..e.

.............,*CL”oEs: .............

........ ..e..WE” “ATEll ONI .............

.............

.............

.............

.............................................

. ................................

................................................................ LAYREWCE *OOEL...............................~...........r........”.

....................................................... JUL” 19111 .......................................................

NWBER OF RELWES ............................ JON”“BER OF MODAL POINTS .......................PSf .......................................... 3:,REA OF LAKE OWTARIO ......................... .Z05E.12SP.FT.MEA OF DOYNSTREL” FOREBA” ................... .,l8E.OSSP.FT.DUllBE R OF RElC”ES FLOY1116 FROM “PSTREA” ...... 2RElC” E”TERIW6 FOREBI” ....................... JO

lWfTI.L O1SC”ll.E ............. O.CFIINITIAL NET TOTAL SUPPL” ...... O.CFS

NODAL POlNT INFOI!4ATION

ND.

:

z5

F

;

if

::

::

:;

::POPI

RE,C”ES lN”OLYEO

:,”

;

:::::;

::

::

::

::2’)

*

!6

::

1:

:P

:t

2:0

::

:i30

(I

:80,”F

p”0

i0

i

:

:0

:0

,”:

:0

::

:

::0

TIM IWCIEIIE., .... 1.11 ““sEWDI*B ,f”E ....... 1.0 “Rr

w*I)m OF “EYTOW‘RW”SO” ,TE”.T,OYS ...... IOUTPUT OPTI.” ............................ 0

:::0:i,”::::

REAC” NO.U.S. PT.D.S. PT.U.S. TOPD.S. TOPU.S. I’EA0.;. .RElU.S. DATUMD.S. DATUMU.S. PER0.S. PERLENGTHpm;’ Rl!ANNINGC R2 tlU.S. B0.9. (iU.S. HP0.S. HP!J.S. BPB.S. BPc

N

REACH NO.U.S. PT.n.s. PI.U.S. TOP0.5. TOPU.S. ARCA0.5. PREPU.S. OAT”*D.S. DATUMU.S. PER0.S. PERLENGT”“PINNINGS RICE THIlllNNlNGS RU.S. nD.S. ”U.S. 00.S. 0U.S. HPD.S. HPU.S. OPn.s. PP

0.13010.000J

245.00012+5.0000

0.P0000.000,

O.O?>O0.0:00

2*5.0:302Y5.P1,0

1.11,>5[1O.CI”P

0.00323.OOC’

215.OCC1245.*32.

0.00”:c.P”o:

PRTNTDUT OF

0.0000D.OOOD

245.0000145.0000

0.00000.000”

CHLNNEL CH*R*CTEI*STICS APRA” FOR REICHES 11 TO 20

0.0000 0.00000.0000 O.OD00

2.5.0000 2.5.00002*5.0000 Z,S.DDOO

0.0000 0.00000.0000 0.0000

.05502.5.0000245.0000

0.00000.0000

245.00002,5.00*0

0.0000D.DDOO

.DJbOO.OJ00.03hl

245.0300215.00110

O.ODOO0.0300

245.030,2u5.OJ”O

E.“DDDO.ODCO

.031”0.“0Q1

.030?2’1.0000245.0000

0.00~03.0003

2.5.0003245.000”

i:E

.0290O.COOD.n,so

2.5.:000245.0000

0.0000O.ilODO

245.00002.5.00110

0.?0000.2tloo

.02&O0.0000

.0260245.00002~5.0000

D.OOOD0.0000

2.5.00002**.00*0

0.00000.0000

.03300.0000.airn

2~5.00002.5.D000

0.00000.0000

2.5.DO(IO2,5.00liD

0.00000.00”0

,,, ,,,,,

------------------- TlllE IN HRS = 9.00 LIKE ONTIiRlO = 2.5.0” LAKE ST LAYRENCL = 2+5.DO--------------------RFACYST,GE 2.5!;0 2,&o *A ,*5:;, ,,A, *,s”;* ,.,I;, 2.30 ,I& 22%FLOW ‘I. ” . I. 0. I. 0. c . 0. 0. 0.REACH 11. . .S,Aix 1.5.00~~2+:100 *&o 2&o *,:I;9 ,.::;o *,::;, ,,::;oFLOY 0.

22000~24::;sil. c. 0. 0. 0. 0. 0.

REACH21.

STAGE .?a.00 a::;, 20 2~0 d’;o 2,:2, ,.:I;, *,::;o ,,::;, 230FLOY I. 0. 0. 0. 3. 0. 0. 0. 0. 0..

---------------_-_- ,,“E IW “RS iI1E.C” 0.00 LIKE WTLRIO = 2.4.98 LIRE $1 uYRE*CE I *,).,2-------------------STALE ,,,!;a ,**f;, *A *.d;1 ,,.I;, d;, ,,,I;, 244% m’;, ,.:“;*FLOY 12150.. 151112. 111246. 5050. 111241. -2OS8D. 118292. 101125. ,,lb(l. &en.REACH I,.STADE 1.a.92 AI;, d”;, *I::;1 2.2, 2x;, *,:I;. *A”;, *,::;* **::;.FLOY 14t19.3. lJlZZ3* 280016. 180013. 280012. 280001. 21%60. 6.1.5. 280012. n9991.IEAC” 21.STASE 2,l.U a::;, 2,::;. *.ci. ,.:“;I ,.:‘;I 23% ,,:“;I *,:‘;, &,FLOY 153061. 126929. 116’)21. 219986. 10105il. ll;ioz. 10~312. 20;m. ,;a,s. z,;sn,.OlfC”lR6E A, P.“.= 280000. ll,s= **0000.

CO”P”lED “1ClPE “*nCEMl 24*.9,KIPl6SlON 2W.98OSDEMSB”R6 2M.06CLlOlnlL 1.2.22,“lO”OlS )I.“. 241.6@lRlP”OII 1.“. PI, .*4YLOO,NGT0W 2.X.06“OMISBURS 210.6,LONBSAULT 01” 234.85--_--_______-__---- ,,“E ,N “RS I 0.00 LWE ONlARlO = 2.4.98 LAKE ST LAYREWCE : 21).~5------.-------------REAC” 1.y:’ .?.a.98 2.428 d;, 2..‘;1 &l ,w”;,. ,,.I;6 246 *,.‘;, d”;,

1ZZ150. 151962. 11,133. *la*. UllJ1. -20.69. 118.2.. 101CID. ,l,IP. l,,J10.M&C” II.STAGE 2.4.91 d’.;, 24:‘;. dk ,,:I;, a::;, 24:1;2 a::;, ,.::;, 2,:0;9fLOY 1.2119. 13,310. 28OOBC. 28EW5. Pe.0086. 280095. 21617.. 63926. 280111. 280121.REACH 2,. .STAGE .?,0.66 ,,:I:6 *,~“;9 2*::;, *,:1,, &l ,,:I;,FLOY 153220. 126921. 126927. 280166. 101222. 119062. 100203DISC”IROE Al P.H.Z 280000. N,SI 280000.

CO”P”,EO “ICAPE “IWE”, P,..98***s*,oI P14.90OSOEYSB”R6 1.3.98CAIcmiAL Lll.95I”*P”Olt H.Y. 2.1.25lRlP”DIS 1.“. 241.09YIoo*ws,D* 2.0.66Ro”“ISI1”“S 240.19LO*S*AilLl 01” 259.29

28. 19. .139.X 239.u A,. 201,,6. ,881,. ao15,.

------_--_______--_ ,,*t m “RS I 0.00 LME ORIlRlO i 214.96 LAKE s, UYIEYCE = Z,l.,z.--------------------MAE” 1.;$a 2W.96 I.&L 24.26 ,,A ,,,I;5 2,*“;5 94.k d;, ,,A *.::;,

11116,. 1,5679. $1661.. 51*1. llb627. -201.8. 176,Jll. 1010~1. IOL01. 135(1*1.

REICH II.s7*6c 2w.92 **:I& dti7 2iE& *AI;9 2*2;9 2*iItb mifi.7 2*?;* 2ff;aFLOY 1.11.5. 1358.4. 211501. 211573. 277581. 21768Z. 113393. 6.319. 271111. 2,183,.

REAC” 11. .STAOE 2.2.25 a::;, *,::;, 24:1;0 ,.:I& &I 2,Ll *.z ,.z, ,,:I;,PLOY 151683. 126111. 126239. 21,995. 10OJII. 1,806,. 1005w. 200959. 1,581. 2711652.OISC”IRbE A, P.“.=

CAPE “INCEW*IW6SlON06DENSB”RbClROlNlLIRfwo*S “.Y.lRIP”DIS 7.“.“100111610*MORIISB”R6LOWGSL”l.7 DA”

2.9000(1. “1s;

CO”P”lE0 “12...96211.96*....?92.3.04212.63

242.50242.251.2.00241.50

-------_-___-_----- 11°C ,N “RS =

RELC”0.00 LAKE ONllRlO = 2M.98 LAM ST LAYREYCE z L,J.6,----.---------------

S11.x 2.A ,.A, &l 2,,1;, 2+,1;, ,,,:;, ,,,I;, ,,,“;, 2,,s;* 2,:“;.FLDY 122229. 15,615. ,1r,,e. 5019. 3⌧7179. -20557. 178232. m671. l i056. n&76.RELCH II.s7A6E 24*.91 a:fL Ati 2*:1;6 **:9L **it& 24iI;* A”.;* nd’ie 2*:“;9FLOY 1.2121. L37116. 219901. 219909. 219910. 219920. 215831. 6.092. 21;931. 21;9,1.Rciw 21.STA6E 1.1.01 2.:fh **:5, ,.c;, ,,:1;, A”;, *,:I;, a::;, &, ,,:“;,FLOY 151050. 126900. 126901. 119965. 101001. 1189W. lOD,IS. 201.22. &a,. 2&l.OISC”A”SE Al P-n.= 2.90000. w1s= 200000.

CAPE YIWCEHT %K:” “’*I*OSlOW He.98OeDE*SwIS *.*.05CAlDIWlL .?.*.I*lRlPtJolJ H.Y. 2*1.,5l”lPvo*s 1.“. 241.39YAOD,YS,OII 2.1.00“O”“IJII”IS a0.mL0161A”Lr DAM 259.77

.-------____.__.--- ,,“E I* “RS = 0.00 LME OWllRlD i I,..98 LIIIE ST LAYRE”CE = *3,.1.------------------“EAC” .SIAM m!;, ,.*‘;1 ,..I;, *,,~;, &6 ,w:;, 14.k d;, ,.A ,.:I,.PLOY 12*261. 15111% 111212. 5055. lll2,2. -20511. 118250. 1016P6. *I*,% 1,11,1.RElC” . . . .STASE d!;, ,A% A5 ,,%l *,::;, ,*::;, ,,:‘;, ,& *do21 *,:“,,FLOY 1.2155. 131191. 2199.6. P199.6. 2799.6. 2199.6. 21iwn. 6.12.. 21bL. r&r.

rJISCRA”OE Ll P.“.Z

CWE “I”CE”I1(1116670*WrJLNSBURSCAIDI”ALIRlPUOIS “.Y.fR,P”OIS 1.“.YIDDI”BIOW*ORRISR”R6LDWbSl”Ll DA”

280000. *Is=

CO”P”IEO nr211.972W.982U.06212.21241.59

**I.*3241.05240.63239.83

REACH: ..--~.!.~~~.._~~_~~I~~..~..~_-.-~..-....~~~~~’-.-.~..~..--1...-~,..-..-~.--.-...---~I-~---*---~~-~---~~.----~.~.-~..,,-.“RI A. d.9, A. Al A. 2L a P0. 5. ,,:.97 IL. 2.L A. A6 A. A6 102. 2.L a.I. *,:.,, A. *CLREICH: -.-.-“.----.---_.ff-----.---..!~-.-....-..-!~-----.---.-!~-----.-----!~-----*-----!~---...--..-!~--.-..--..-!~----...--.-~~..--.“RS P P0. A. A,, I’,,. A,, A. 2.L *ia. Al *to. a:.,, 2%. d.06 A. A6 6.. A.6 A. A, 28). PA3REACH: -~...f!.--....~~~.I’~~~~~.~_~_~21_-......--.~~.---..-...-’~....~...--.~“-~---,I.--‘I..---.~.~--tL....----l’.---~~.~--~.~~-.---*“RS0. A. a:.,, A. ,,:.m I,‘,. d.63 Al. d.6, A. d.99 A. Pd.99 IL. 29.93 4,. 2L :9. ,A, A. *A,,

. .i

:1: 0.z “6Z+

~~~~~~~~~,:::~‘,~~:0.2PLI-O=*::g:““:zz

47

;;;;;----‘....-. ,*“E Iy “RS = 0.00 LAKE o*l*RrO = 2*..ea UKE s.1 LlYllEWCE i

ITASE ,..k i&l a&1 dl ,**I;, ,*A *,*I;, ,,,:;,- 2.4’;. ,,:“;,*,,*88----.----------..

$0” 122.26. 1511*5* 11,355. 5013. 111355. -2oc2*. 11*311. 101~01. &s. 13;m.

IEK” 11.ITME 2,*.92 *A:& d”;, 22, d”;, ,I::;, ,,:I;, ,2&l ,,::;, ,,f’;,FLOY 1.2*91. 111.?89. .?(1m79. 280112. 100110. 28OIS3. 215902. LIP.6. au,,. 2&‘.

“EN” 2,.s7mc ~a.17 mEi **Z 2*:1;6 2*%5 2+Ei5 *So 2*:“;6 24’io 2~~“~~FLOY 155102. 126997. 126991. 280073. 1otos9. 178913. b30383. zoiwo. 7Lsts. r&v.

DISC”ARSE AT Pd.= 280001. “IS‘ *~00~0.

CO”P”,EO “7CAPE “I*CE*l .?,,.9,K*Icsrow 2...98OSDEIJBURO 214.09cA”oI*LL 242.25IRIP”OII “.Y. P41.69lRIP”DIS 1.“. *,I .5*“ID0I”010” 2.1.17“DIIISBUW I.O.16l.O*GSA”Ll DAM 2.040

..----...________-- ,I”E *N “RS = 0.00 LIKE ONT,R10 i ***.90 LAKE 51 LAYI1ENCE 3 P,9.69------------------.-RElC”STABE w!;s 2..% &7 a+:;1 2.426 24& 46 *..:;, ,.,:;, A”;,FL-a” 122300. 151127. 111**5. 5056. 1112+5. -2oSlb. 11*303. 1m124. 4,Dll. &a,.8E.C” II.Jl.SE 214.91 2::;2 2.::;5 a::;, *4:1;3 2.::;. ,*:I;, a::;, a::;, d”;,FLOY 1.2196. 137232. 280028. 280029. 280029. 280031. 215893. 6.139. 1000s.. 280136.MAC” 21.ST&GE 211.04 2.::;. **f’L XL ,d”;, *,::;, 23:7;2 ,,::;, s;, ,,:“;,FLOY 153092.~ 126946, 1269.1. 28U0.1. 1P1091. 118963. 1003.9. 201.*,. 18616. Aw.D,fC”lR6E I, P.“.Z

CAPE YI*CEHl“IY6SlOIDSOflSI)“I~Cl”DlWlLl”lP”o*s “.Y.IIIPUOlS I.“.YLDOWLlDN“0”“1fB”R*Lo**SA”Ll 01”

28C000. *,s=

CO”P”lED HT***.s,211.90244.162.2.21211.58

*.I 422.1.m240.62*?,,.a

280000.

b. The Simple Drawdown Under Ice Conditions

The next basic problem to be solved with the mods1 is similar toproblem 1 with the addition of an ice cover. In the example problem, a12-inch uniform ice cover with a Manning's roughness coefficient of N =0.02 is used. The difference in input can be noted on cards 5, 6, 7,and 8 of the input deck listing. Intermediate results are not shown.

49

Input

A U G U S T30 21

0280 0230$330 03r)r,

12 1212 1 2

c2!?0 0200C2l?C 02:1c

1 115.

2 3CISO

19789

S I M P L E DRAUDOtiN I C E

028C 0370 0250 032C C4*:0 038@ 03311 F35C 0350 0360 C3OC 0291026'Y 0310 0260 rJ3fl 0530 F4!?0 D4CC 040P 04rO 04OC C4CC 04~0

026C 0330

12 12 12 i2 12 12 12 12 12 12 12 12 12 00

0200 ? "2CC C2^" 0C2'"C 02cc C2clC c2oc 0200 0200

0.7502@0 02CC

8 245"' 215GC 734?. 1 0 130

NTSO cU . S . 2453n24~:J024s00245r,.245-~~24~~0245s~245Ci?2450O24500245002450r:245@~24500245@OU.S. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~9.s. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~C.S. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

r 1 nE

n 0 !,c

0. . : !!? 0 0?

0 9 01

Pc 0 ;) n F 0

12 12 12 12 1s 12 12 12 12 12 1212 1212 12 12L 203 12

12 00? 2 12 12 1 2 1 2 L2i2GD 1202?i 12C2?0 1207 12

c2E9 021-i 02”s '~2ac C2Qr: 0260:I 2 c p 0 2 .’ u 02ro 0 2 0 00 2 :: c 020g 020~ 0 2 0 0 n

2 82 :22c c2::1 r,2;.!<? 113CC~ 02'li' C2'?$ 02:p g>"- C2CC C2C"

2R< n c

. . . . ..f...... *.........

.*..t.**...t*

. . . ..a....**.*.**..*.**...

. . . . . . . . . . PER100: NONE NONEf . . . . . . . f . PURPOSE: *I*PLET:IAYocJYNI . ..f **..,......................................................................................................................................................................................

bE06RAP”lC&L KE” TO REACH W”“BERS_--------_-_-__-____----~~-------

I.....KINc.STON1.....CLPE VlNCENT,.....NORTH OF “OWE lSLlND*.....NORT” OF “OYE ISLAND5.....SO”TH OF “OYE ISLANDb.....FLOY RETYEEN YDLFE IS. ANDI.....SO”TH OF BRINDSTDNE ISLANDB.....NORTW OF GRlNDSTclNE lSLlNOY.....FLOY BETYEEN GRlNDSTcJNE 18

10.....SO”TH OF YELLSLE” lSL.NDll.....NORT” OF YELLSLE” ISLIIID12.....SO”TH OF YELLSLE” ISLANO13.....SO”TH OF 6RENADIER ,SLANDI,.....“lLLCREST POINTI5.....RROC~“ILLE,6.....OGDENSB”R6,I.....NORTH OF GALOP II&.&NDl*.....SO”T” OF GALOP IX&ND19.....CAROINAL20.....IROP”OIS

GRINDSTONE

. AND YELLS,

.......... ............

.......... .............

.......... .............

.......... .............

.......... .............

.......... INCLUDES: .............

.......... .............

.......... ICE co*o*,*oYs .............

.......... .... .........

.......... .............

.......... .............

.......... ........ ..“.............................................................................................

IS.

.E” 1

PI.....NORTH OF 06DLN ISL&ND22.....YADDIN6TON23.....SO”,H OF ODDEN ISLAND2,,....HORRlfB”R625...r.NORTH OF CROIL ISLIHDPL.....SO”T” OF CROlL ISLlNDPI.....FLOY BETYEEN CRDlL 1s. AND LO”6 SAUL, IS..?8.....“ORTH OF LOW SAULT lSLlND29.....SO”T” OF LO”6 SAUL, ISLAND,O.....LOWG SWLT 01”

IS.

....................................................................................................................................

............................................................... ......................................................

........ R..C.ES ............................:i

TIM IWCRE”EW ..... 1.00 ............................................. Em116 7l.E ....... 1.0 ...PSI .......................................... .75LREA OF LAKE O”TARfO ......................... .205E.12SP.Fr.ARE& OF DOY”S,Rfl” FOREBb” ................... .418E.D9SP.FT. “““BER OF NEYTOW-RLP”SO* nERATIOIS ...... 8NUMBER OF REAWES FLOYlNB FRO” UPSTREAM ...... 2 O”,P”, OPTlOW ............................ IREAC” EW7ERIWG FOREBI” ....................... 30

ICE IS lNCL”DED_____-___-_----

HA”6,Wb OAH IS INCLUDED____________________---

NUMBER OF HANGING o.*s..... IBO”NDR” OR NODE............ 12.RELCH...................... n.THICKNESS.................. 8.50LENGIH..................... 3”D.“ANNINGS RO”G”NESS......... .I00

INlTIlL DISC”lRSE .............,N,,,,L NET TOTAL SUPPLI ......

-R -RI*, -II-R 1;-R ‘R

O.CFJO.CFS

NODAL POlNT ,NFOR~LTION__________________-------

REeCnES ,“YOL”EDNO. NO. OF NO. OF1NCOMINc. OUTGOlNGRElC”ES REACHES

: : * 1: ::

::

,’ : : 11: : ::: : ::: : ::: : 2:: : ::: : :II 2 :

:

:78

:;13

::16

::20

::I.

::28

: 4

E;

; 1: II

:: 1::: 0

:: :

:: ::

:: 2:0

:: :::: ::29 30

i:::::::Fl:P

::ii::::0:0:0

:0:0

:

:

,”:

::

:D

I’

RElC” “0.U.S. PT.D.S. PI.U.S. TOP04. TOPU.S. lRE&D.S. ARE&U.S. OAIUHD.S. OAT”)1U.S. PERD.S. PLRLENST”“ANNINBS RICE THKflINNI”SS RU.S. ”D.S. wU.S. PD.S. PU.S. HPD.S. HPU.S. PP0.S. OP

REACH NO.U.S. PT.D.S. PT.U.S. TOP0.S. TOPU.S.. AREA0.S. AREAU.S. 01,“”D.S. DATUMU.S.. PERD-S. PEPLENGTHiiLNN,NGS RICE THK“INNINGS RU.S. HD.S. nU.S. 00.S. PU.S. HP0.S. “PU.S. PP0.5. QP

REICH ND.U.S. PT.D.S. PT.U.S. TOP0.S. TOPU.S. AREAO.S. LRE&U.S. D&7”*D.S. DA,“RU.S. PERD.S. PERLENG,”MLNNIWS RICE IHX“ANNIWSS RU.S. ”D.S. nU.S. PD.S. PU.S. “PD.S. “PU.S. PPD.S. PP

21.0000L,.0000.2.0000

1988.00001988.0000

65000.000050000.0000

239.4100239.1200

.0.1.392.

.026.3018fl3OO.DODD

.026012.0000

.0260215.00DO2.5.0000

0.0000

22.0090‘J.OODO4l.OODD

1540.PO001540.0000

.3800.1)000

.JB00.POOD1239.,100239.2600

3136.88313136.88319T50.0000

.033012.0000

.03302*5.00002+5.0000

0.000D

LDNGSl”LT DL” 231.01

.0100 .O,DD2*,.0000 2*5*0000215.0000 2,5.000*

O.DOOD D.00000.0000 O.ODc.0

115.0000 2,5.01)002*5.1)000 2,5.0000

0.000D 0.00000.00DO 0.0000 0.0000 0.0000 1.0000

------_---_______-- TIME ,N “RS = O.DO LII(E ONTLR,O = 2.5.01 LAKE ST LAYRENCE : 2,5.55-------------------.RELCW I. 2.;:n;c 215.01 2.5.01 2.A 2,,:;9 ,,,I;, d;, ,4.7;7 2**% ,w’;, ,,Y,,1130.8. 157185. 116615. 6312. 316675. -22555. 176838. I&.. 3896.. l&74.REACH 11.ST&GE 214.90 **:t;* d’,, 2.k AI;, ,,::;5 ,,:I;* 2x;, *x;, ,,::;,FLDY 139458. 14PBT.. 280333. 28”,31. .?8033.. 280336. 21,641. 65689. 200,,LI. 280310.REICH 21.STLOE 257.3. *df;, d’;, 241; ,,:1;* A:;, *,:1;5 &, 2, A%FLDY 15,122. 129220. 129220. ZBO3.5. 101837. 178526. 97308. 1991.9. a12*1. 280375.OISEHAROE A7 P.“.I 2000001 “7s; 280000.

CDWUTED “7CIPE “*wEfIT 215.01*1*5570* 215.01OSDEISBURG as.15CIRD,PiAL 239.85lRlP”OIS “.Y. 238.08IRIPUOIS 7.“. 237.mWODIWBTON 257.34“ORRlSB”RG 215.96LOYSSA”L, Lb** 233.92

REACH: 1 2 1 4------------*------------.------------.------------.------------*------------*------------.------------.---- 5 6 7 8 9 10“RS P0. Al A. *,:.,I A. a:.,, 0 ” 0 H P ” 100.2&7 P123. A.--------.--------__-.

6. a:.,, 5. A. A. d.94.?a..99 117. *4..9* -23. 1*..97

2 RflC”: 1, 12 13 1. 15 16 I7 19 21“RSP -‘----------.------------.------------*------------.------------*------------.------------.-----!~---H 0 n 0 ”0. (1 H 2:o. n ,:a. ,,:.,, 2;s. ,,:.,,--.------------.--_----_-__.

1x9. D211.90 A*2.*.921.1. 2:.280. *A521*.(10 A.280. A,244.26 H3.82 66.REICH: 2, 22 23 2. P5------------*------------.------------*------------*------------,---- 26 27 28 29HRS P H 30”0.151. 137.34 A.

A. A. 23L ,:o. ,,:.,, A. *AL -2 ‘-‘-R-‘-.--;-“--n---.------------*------------.-----------.237.3* d.0,179. il. d.15 2:,. &,,234.28 97. P3..15

c. The Hanging Dam

The situation from problem 2 is modified by including an ice damwith a length of 320 ft and a depth of 8.5 ft in the reach on the northside of Galop Island (reach 17). The difference in data sets is notedin cards 11 and 12 of the input deck.

Figure B.l is a pictorial representation of the river profilesobtained from example problems a, b, and c.

56

Input

A U G U S T 1 9 7 8 S I M P L E DREUDOUN H . D .311 21

32811 023n3333 03fi!:

12 1212 12

0200 02LJJ29C 02:rn

1 1.15.2 1

90283 3370 J25L :?3?rl 0400 0380 0336 035C Q35t, 0361T 03OC 0291 t260.03300262 J31C 726q ;133Q 033TI 0400 'j4D!l 04Oi", C453 U4iiC C4C? 04Cr

12 12 12 i2 12 12 12 12 12 12 12 12 12 OC'12 30 12 12 12 12 12 12 12 12 12 12

OZCO 7200 0200 02-r; 0200 t200 @20? 3200 0290 rJ2!3' 02OP 02CC 0230 00200 9 1122s 'i2;,r, G2GG C2CD 0201; 0200 0200 0200 0230 02OC0.75 8 245Dri 24500 734s. I 0 1

33

C.S. 245~32459t-!2450C245QD245 ~~245GC2450324SC0245ff3245G02450?245032450245OC245CC245C~245COc 3 9 I, 3

.: 5 ? 0 0 c0 3 n c

3 n G 3 q _) 0c ,

'12 12 12 12 12 !.2 12 12 12 12 12 12 12 l-3 12 00!2 12 12 00 12 12 12 12 12 12 12 12 12 12

'200 cl2rll 02'10 0200 32fir 02-::1 C2'0 2260 02OL J2C,? C2':Q 020: 020n 0207 C2CC a2200 02:'C 02co 0 rr2oc 02'Z3 oznn f2 GO ozflo 02011 02'0 02on '2Ob Q2rjC

2%' 28C c 0

Output

........................................................................................................................................

.............................................................................................................................................................._.~~~~~

.......... .......................... ..........~~~0s .......... ............................. .,,_,.-____ .............

.......... .......................... .......... s, I *YmFUPr mr”Fn Y”“PI.III ,s- ,I(.YS,FYT “0

............. PRIW, OPTlOW 0 .*********“FYC, “OF” R” .......... .......................... .......... I_._ __...

............. LLL INTERHEDIATF ..............~~~-,, LIKES ENYIRONMNTIL RESELRCH LABORITORl ********** *...,*..*..*.

CILC”LA,,ONS IRE _______**. ANN IRBOR,“ICHIblN . . ..a..... f. . . . . . . * . . . .............. INCLUDES:.......J”L” 1978 r......... f.... ** . . . . f.............. PRlNTED 0” ......... . . .

.......... .......... ICE COND,,IO”S .*..........*.............(l......... “INS*NG Oh” . . . . . . . ..f.f.............. ..........

________ . . .......................

GEOGRAPHlCAL XL” TO RELC” N”*BERS_________________________________

,.....IINGSTONZ.....CLPE VlNCENT3.....NOR,” OF “c&FE lSLlND. . . . ..NORTH OF “OYE lSLA”D5.....SO”,H OF HOYE IX&NDb.....FLOY BETKEN “OWE IS. AND GRlNDITONE fS.,.....SO”TH OF tR*NDSTONE lSLlNDB*....NOP.,H OF GRlNOSTONE fSLl”OL).....FLOY BETYEEN 6RIWDSTONE IS. &NO YELLILE” IS.

,D.....SO”T* OF YELLSLE” lSLIND,,.....NOI7” OF YELLSLE” lSLlNO,P.....SO”TH OF YELLSLE” lSLA”D1J.....SO”T” OF GRENADIER lSL.NDl,.....HILLCREST POINTlr,.....RRotK”ILLE16.....0c.clENSWRG1,.....IOR,H OF G&LOP ISLlNO,1.....SO”IH OF GlLOP ,SLILiD19.....CIROINAL*0.....IRO~“O1S21.....NORTH OF 060EN lSLl”O22.....YLDOINGTDNZJ..~..SO”TH OF DtDEW ISLIND1,.....K3RRISB”RG25.....NORTH OF CRO,L ISLlNDZL.....SO”,H OF CROIL ISLlHD2,.....FLOY BETYEEN CROlL IS. &NO LOM SAUL7 If.28.....HOR,H OF LONG SAUL7 lSLlW029.....SO”TH OF LO”G SAUL, ISL**O30.....LOWG SAUL7 011

...............................................................LAYIE”CE ...........................................................

....................................................... J”L” 1978 ....................................................“.

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ICE IS IWCLUDED----______--e-e

IWITIIL OISE”lR6E . . . . . . . . . . . . . O.CFSIWI’IIL YET TOTAL SUPPL”...... O.CFS

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245.0100 2.5.01,245.0700 2*5.01,

0.0000 0.001?.(1000 O.DEl

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22.0000*s.s*ssu.sss,

1SlD.00001s*s.ssss

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s.sso0 0.000,s.sso0 S.OSSS

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o.ssnn s.ssssS.OSOJ S.CPSS

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.s.sss, ,~.I,,,SP.SSSS 52.0100

1570.0100 *s*s.ssssls7s.sPss *s.o.asso

ss.*s.sssPISsss,.s,P,sL,Ds.,,s,1sssss.ssss

23S.L7SS 2ss.17ss*37.‘)900 ZS7.SSSS

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*Gsss.ssss 11900.,,00.s+ss .s.s,

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*.s.ssss 2.5.0000*.s.ssss *.s.s,0,

0.s*ss s.sssss.ssss 0.00110

*,.ssss *s.sssss3.ssss

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:::‘::::. *JI:I*SS,160.3922 SL2..l,2,31ss.5s22 LS2I.SI,S5910.,,00.11110.,101

.s*ss .mss12.SSSP 1P.SSSS

.,ISS .s.ss1.5.000, *.s.ssss*.s.ssss **s;ssss

s.ssss P.SSS0*.ssss s.ss*s

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s.ssss s.ssssS.SSSP *.sss0

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1s1s.ssss s7,,.,,,,1,1,.,,,, s7’),.,0,,

s7sss.ssss*3*sss.ssssSS‘SS.,SSS*S2S...SSSS

2S,.,SS, *37.,*s,*s,.72ss 217.1.1,

**34.0s,, IY.s.+sslll.,.,.SS 1ss*s..s3*

197ss.ssss 1ssss.ssss.s.s* .s**s

1*.,,,, l2.S,,,.s*ss .,,,I

**s.sss* PI,.SSSS**,.sss* **s.ssss

s.ssss s.sssss.ssss 0.1000

**,.*sss 2.s.0000**,.ssss **,.s,,,

S.SSPS s.sssss.ssss s.ssss

,R,D”OlS H.Y. ZJS.14IR,O”DlS 7.“. *s+ .89YAOD,NS7ON 23..16MIRRISSURS 2Sl.S.LD”SSA”L7 SAM 228.54

RE,C”: 3 2 1 4 5 6 I s 9 20____________.____________*_______-___.____________._-___-___---.______------*------------._____-__----.--______-___.-_________-.n*s* H 0 n 0 n P P I!s. 12,. **,.m 15,. **s.ss 11,. **s.s* s. *.:.s* If,. 2ASl A. *A*, A. *+:.s, 1:s. *+L* 2s. a.,.,7 A. A7

REACW II 12 IS 1. 1s 16 I, IS 1, .*s---~_-------*------------.------------~*~---~~~~~---*~-~-~--~---~---------~--.-------~----.---~~---~~~-*--------~-~-.--~~~-~~-,““S0. A. *,L A. *,:.,, *is. *,:.,, *LT. *,:.*s 2:s. *,:.ss 2:s. d.19 A. **:.** is. *,L* A. *A* A. *,:.ssREACW 21 22 2s 2. 2s 2s 2, IS *, 2,------------.------------.------------*------------.------------*------------.-----------.------------.------------.---------*“RS P DI. I,,. *,:.1s 12,. *,:.,s I,‘,. *,:.ss 2:s. *;:.s* I’,,. **:.ss A. **:.ss b. **L IL. **i.,. is. **Ls 2:s. *L

................................................................. LlYlENCE “ODEL ......................................................

........................................................... 19711 .......................................................

N”P!SER OF REICHES ............................::

TIM IYCRE”EW7 .... 1.00 wssNURSER Of NODAL POIWTS ....................... TIM E*D,*S ....... 97.0 “SOPSI .......................................... .7slRE, OF LAKE ON,IR,O ......................... .2PSE.12 SP.FT.ARE& OF DcwNS,RE*” FORESA” ................... “““SER OF WEY7O*-R*PHSo* *,EsA7IO*s ...... 0N”“SER OF RElC”ES FLOYINS FRO* “PSTREA* ......

.*,y SO.FT.O”TP”, OPTION ............................ 2

REACH ENIERINS FORESA” ....................... so

INITIAL DlSC”lROE.. ........... S.CFSIN,,,lL NET 707.u SUPPL” ...... S.CFS

NDDlL POINT INFOR~.aIION

NO.

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RELCHES lN”OLYED

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REAC” HO.“.Sr PT.D.S. PT.U.S. 7OPD.S. TOPU.S. lRCl0.S. AREAU.S. S1,“R0.S. OllUMU.S. PERB.S. PERLENST”“ANNINSS RICE 7°K*ANW*NsS RU.S. H0.2. nU.S. D0.S. PU.S. UPB.S. “PU.S. QPD.S. PP

RELCH NO.u;s. PT.D.S. PT.

“ANNINSS RU.S. H0.S. nU.S. Pcl.,. aU.S. HPS.S. HPU.S. PP0.5. PP

l7.S00”33.sssss..s*ss

1S4S.SS00,S*S.S0SS

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*.*.sss02*0.8,0*

,~40.,.s96,171.,286

27800.0000.03,0

12.ssss.ssm

24s.ss002,S.SSSS

s.sssss.ssss

*1s.ssss245.0000

s.sssss.ssss

1s.ssss :ym& 2s.sss0ss.ssss . ss.0sss,6.0,,, ss.0sss .s.ssss

I0,,.,,,, 2620.000P 2s50.00001sss.ssss *6*s.sssP 2650.0001

,*,,0.,,,, 92900.0000 87700.0000**;w;.m~~ “2~~~‘~~~~‘““~~~‘~~~~

.*4,:,,,, 2,9.sss* *39.*sss

.?,2,.,,,1 S,1S.916S 271b.1SS721,,.6,,5 5303.12911 27J2.1~32

‘““““:~m~~ 23100.0000 IbSDS.SOOS.,*ss .SSlS

12.ssss 12.ssss s.ssss.,,a, .s*ss .SJIS

2.5.000, **s.ss*s 24s.0sss*,,.,,,, 24s.ssss 21s.ssss

,.ssss s.ssss ym:,.ssss s.0000 .

~,,.0S,, 2.s.0sss y:.;“,;;**s.ssss **s.ss,s .

s.ssss yo” y:S.SPSS . .

REAC” NO.U.S. PT.D.S. P,.“.l. TOP0.S. TOPU.S. &SEAD.S. &SEAU.S. OAT”*D.S. DA,“*U.S. PER0.5. PERLEWE,”lllNNIW65 RICE 7°K“ANWlWS I)U.S. n0.S. RU.S. PD.S. PU.S. “PD.8. “PU.S. PPS.S. PP

21.SSSS41.s0ss**.0000

1s.ss.ssssISSS.PSPD

LSSSS.SSS,50000.0000

239.4,“S239.1200

2053.192,2SJS.JBlS

*7~00.0S*S.OP60

s.000,.DlbS

2.s.070,**S.O7110

s.sssss.ss00

2~5.070s*+s.s7ss

0.OSSSS.SPOS

PRIW7O”T OF CnlWnEL CRAIIC7ERIS7ICS ARR.7 FOR REICHEf 21 70 s,

22.000043.0000**.ssss

1SW.000,1S*0.0SSS

*3800.0”,,.1S?S.SSSS1

239.**0,239.2610

1596.88311596.88319750.0000

.033sS.SPOO

.033021s.070021s.070,

s.ss>sO.SDOS

2.,.(1,SS*.s.s7,,

0.000,s.ss0,

23.ssss 24.,,,,~S.SSSS ,7.,,,,*L.ssOs .*.ssss

Is*s.sPPO I7SS.SSSS1SW.SOSS 47,,.,,,,

.~s0*.000011*700.000,198700.sssP2,000,.,,,,

239.2600 239.,2,0239.12s1 238.17,s

IS%.81131 ,s.s.*1171681.16S.s 4(lbJ.6,2,‘“s”:o”m”, 52500.0000

.s*ssS.SSE?I S.OSS0

.ss3s .wss245.07so 21,.O,,,21S.P7Sd 2.S.C700

s.ssss s.nsosO.SSSS a.osoo

2+5.0700 **s.D7ss2*5.*7,0 **s.*,0s

s.sss0 0.000,S.SPS, s.s,ss

*s.ssss 2L~SSSS.9.00ss s1.,,00S..SPSS s**,s*s

1570.0000 **.s.ssss1s70.ssss *s*,.,*,,

sL.00.000015,,,,.*,~,~,*1~SS.SSS,1SSSSS.SSS,

23s.17,0 23&~7,,237.99ss 237.99s*

168S.0637 2945.633,1679.9363 29,,.6,3,

*060s.0s00 119ss.ssss.SISS .,*,s

S.SSSO 0.,,,,.s*ss .,I,,

g;;.;;;,” 2~5.S7SS2.s.0700

s:ssss s.sssss.ssss 0.sws

**s.s700 24s.s70,2.S.O7SS *4s.s7,*

s.ssss s.sssss.ssss S.DOSO

27.ssss 2~.0,,SI.,SSS C.S.SSSSs*.sss0 SL.SSSO

1s3s.ssss J26,.,,,,*s~s.Psss ,26,.,,,,

7SSSP.SSSS1b98SS.SSSS76SS0.SSSS1689SS.PSSS

237.s9ss 237.9900ZJ7.SSSS 237.72,s

16JS.JS22 336*.171slL3S.1922 3363.61965932.ssss “‘““:~m~

.msss.ssss 0.000,.s.ss .s,ss

**s.s7*, **s.s7,,245.0700 *.s.s7ss

s.ssss 0.0000s.ssso s.sss,

2.5.07PS *.s.s,so*.s.s70, *.s.*7,0

s.SSSP s.sssss.ssss s.ssss

*,.ss.s ss.00,I7.02SS ,,.*I,,58.SSSS 61.111,

1s1s.ss0, 679,.,,,,1s1s.ssss 67SS.SS.,

s7Lss.ssss21*sss.sss,‘3600.P,,,212,.,,.,,,,

237.99,s 2,7.7*,,

1:::‘:::: 6:::%:1135:s*sL 6,&,,,,

19700.,P,, *,9,*.,,,,.01ss .O,SP

s.,,,s s.ssss.I.00 .PISS

ZI5.S70, 2.5.070,2~S.S7SS 215.070,

*.ssss O.PSOSs.ssss s.ssss

2.s.0700 *.s.s7,,245.s7ss *+s.s7ss

*.ssss s.s*sss.ssss s.ssss

245 Flow=280Initial Elevation = 245

3 240 -

i

5 235-

=

El 230 -3u)

225-

No Ice':. \

: -., -.'....

'.. --c_ _‘.., - - With Ice

‘..,'... (12” n=.020)

'X,".. . . . . . ..__..._..

With Hanging Damin Reach 19

A E * ;FJs 2 2 P 5

tj 2 .g 2 rzF hP $Epg _

I 88I

190'I I I I

170 150 130 110 90 70

Mile of River

Figure B. 1. River profiles for example problems a, b, and c.

65

d. The Unsteady Condition

The advantage to using a flood routing model or transient modelover a backwater model is its capability to examine a time varyingcondition on the river. The period 7 through 10 August 1977 is examinedusing recorded hourly values of the stage at Kingston and the powerhousedischarge.

The primary difference between problem d. and problem a. is theaddition of a flow hydrograph and water level hydrograph for each of 96hourly periods.

Two cases are examined. The first uses the flow hydrograpb at thepower dam as a downstream control to determine river profiles. The seconduses the stage at the Moses-Saunders Power Dam as a downstream controlto derive a flow hydrograph (Fig. B.2).

66

Input

J U L Y 1 9 7 8 A U G U S T 791977 A U G U S T 1011977 9 6 HOUR 9UN3t 21 9

6280 C23i; 028C 0379 0250 032:j il4i1C 0380 0 3 3 3 3350 0350 0 3 6 0 0 3 0 0 029C 0 2 6 0 0 3 5 0C353 0403 n26fi 0 3 1 3 3260 ri33:i 033C 04OC C4OC 3403 04ilc 0430 3430 c4uo

r 1 0 . 7 5 8 24530 24593 7 3 4 c .1 5 . 3Q

1 2 0

2I S 0 iT S O4500245C~245";24500~450~2453C245~~~45~~~245~~245~G2450~245~~245@~245~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~450;2453i2459?245O;245ilr245?:f-45':245c~245(‘r245 3~245j~~24~13245UP24501245jo245OC45002455~245:b245i024503245" ~,2453C245"t24500245~~245~~245~~245~~245G~245~~245~0

P 0 D 0 cl 03 0 n 0 !I 0

0 c 0 0 c 00 3 c 0 3 0P 0

254214227330225120223RRO22199G?239302237902236602287102466702614iiC26741"27417~2775102765532759CO?75130?7683327491027522')2775992782212ht?27P2541412393802257SJ2 2 2 4 !i u22338C,22378$223C8?2232892 2 4 ': !, !j229556248123?6'iR6J26639112749102772:'327X202558~027837027834027832C27836027965627935026956??56?10

245S724598245('824511245ii3245'7245.'3245(;:

245Q4245?6245:'7245~124581245,424526245-4245:2245;l245115245$124514245C.n245::s2 4 E ci 2245072451,h245?8245"5745-42451224514245782 4 5 Y.? 6245'~7245L6245 i,r_245-4245q224513245112451524512245162451324512245142451:2 4 E: :: 9

IIII1IIIIIIIIIIIIIIII

238355224930223?6322341'l222925223313223920?24340229300245?60263450268239277800276240274270273850276961,275r)3027739027583027735C2771702686702559502393502232702243GO223533T7.2911:22475022425022436022789324998076236326651027542r)2749302737CO27541027622C276H302746902742202773"O27772027C25Q15797'!

245071451G245ti824555245142453724500244992449424499245"l245 ;'324536245?4245242452724""H24;;82453724527245fG245iic245~31244S92449t2449024479244952443824493244962449924FPe245182452624521245192451124595245"16245t6245 '14245C624553245?4245192451324510

68

Output

............. .......... DEVELOPED 8” .......... .............

............. NO IN,ER”EDIA,E .......... GREAT LllES E”“IROW”F”TIL REXARC” L*Bo*A,oI ” * . . ..f.. *. . . . . . . . . . *..*

...................................... INN IRBOR.MIC”I6AW .......... ,WCL”DES: .............

............. PRlNTED OUT. .......... JU” 1978 .......... .............

............. .......... .......... “DC” Y.,CO ““I” .............~~~~~ -.-.. _” ._.. -..-. ----.

. . . . . . . ...**. t.***t.t*. *..o..*... .*.*..*......

..f.......... f......... PERIOD: AUGUST 7.1977 TO .“D”ST Il.IP77 . . . . ..f... .f...........

............. .......... PURPOSE: 96 HOUR RUN .......... .............

............. .......... .......... .............

........................................................................................................................................

........................................................................................................................................

Ib.....06DENSB”R6II.....NORT” OF GALOP ISLlNOI8.....SO”TH OF 6ALOP ISLAND19.....CIROIWAL20 . . . ..I ROPUOlS21.....NORTH OF OGDEN ISLLiNO22.....“10DI~6TONZS.....SO”T” OF OGOEN ,SLANO2,.....“ORR,SI”RO25.....NORTW OF CROlL ISLlND2L.....SO”TH OF CROlL ISL*NO27.....FLOY BETYEEN CROlL IS. &ND28.....NORT” OF LONG SA”LT ISL,*O29.....SO”TH OF LDNS SAUL, lSLlN0JO.....LOWS fl”LT DA”

GRIM

. AND

I

,STONE

YELLS,

SNLT

IS.

.E” IS.

IS.

“RS =

HRS =

HRS =

HRS =

“RS =

HRS i

IiRS =

HRS i

HRS =

“RI =

HRS 1

HRS =

HRS E

HRS i

HRS i

“RS =

HRS i

HRS i

HRS =

“R5 =

HRS i

HRS c

“RS i

“RS i

HRS =

HRS :

“RF, :

HRS :

HRS :

.20 ..f (I....

0.00 LAKE ONTARIO 1245.07 I.&ICE ST LAYRENCE = 2.1.17--------------------

0.00 LAKE ONIARIO = 245.07 LAKE ST LAYRLWE = PIO.,8--------------------

1.00 LIKE ON**RIO z 2ca.08 LAKE ST LAYRENCE i 2.0.81--------------------

2.00 LAKE ONTARIO i 245.08 LAKE IT LAYREWCE = .?ll.00.-------------------

,.00 LIKE ONTlRIO = 2,5.11 LAKE ST LAYRE”CE i 2,1.10--------------------

q.00 LAKE O”TlRlO = 245.03 LllE IT LlYREWCE i 2.1.20--------------------

5.00 LIKE ONTARIO = 215.07 LAKE ST LAYRENCE = 2.1.30-------------------

6.00 LME ONTARIO i 2.5.00 LAKE ST LIYREWCE = 211.38--------------------

I.00 LAKE CLNTARIO = 2q5.00 LAKE ST LlYREllCE i 2,1.,5--------------------

8.00 LAKE O”TLR,O = 245.0. LIKE ST LAYRENCE = 211.5*--------------------

9.00 LAKE ONTARIO i 245.06 LAKE ST LAYRENCE = 211.,9--------------------

10.00 LllE ONTARIO = 2.5.07 LAKE ST LLYRENCE i 2,1.+1--------------------

11.00 LAKE DNTlRlO I245.01 LAKE ST LAYREWCE i 2.1.,1--------------------

12.00 LME DN,,RfO = 2.5.0, LAKE ST LAYRENCE = 1.,.21--------------------

13.00 LME ONTARIO I1.5.D. LAKE ST LAYRE”CE = 24*.1,-----------‘-----~--

11.00 LAKE DNTIRlO i 2.5.06 LAKE ST LAYRENCC = 2.~.00--------------------

15.00 LAKE ONTIRIC = *,5.01 LAKE ST LIYr(ENCE = 240.91--------------------

16.00 LME ONTLRIO = .?,5.02 LAKE I, LAYRE”CE = 2.0.BJ--------------------

11.00 LAKE ONT1RIO i 2.5.01 L&ICE ST LAYRENCE = ~.0.,b--------------------

18.00 UKE ONTARlD = 245.05 LIKE ST LAYRENCE = 240.69--------------------

19.00 LAKE ONTlRlO = 2,5.01 LIKE ST LAYREWCE = 2*0.64--------------------

20.00 LAKE ONTARIO = 2.5.1, LAKE ST LAYRENCE i 240.51--------------------

21.00 LAKE ONTAR, = 215.00 LAKE ST LAYRENCE = 2*0.51--------------------

22.00 LIKE OWT&RIO = 215.05 LAKE ST LlYRENCE = 2,0.,9--------------------

23.00 LAKE rJN,,RlO i 2e5.02 LAKE ST LAYRENCE = 2,0.53--------------------

2.40 LAKE ONTAP, i 215.07 LAKE ST LAURENCE i 240.6*--------------------

25.00 LAKE ONTARIO = 215.06 LlKE SI UYRENCE i 210.7*--------------------

26.00 LME ONTAR, I 2.5.08 LllE ST LLYRENCE f 1,0.87--------------------

27.00 LLKE ONTARIO i 295.05 LAKE ST LAYRENCE = 21D.99--------------------

“RS T 28.00 LAKE D”,IR,O = 215.0. LIKE ST LAYRENCE I 241.09--------------------

HRS 1

HRS =

HRS =

HRS =

“RS =

“RS =

HRS i

“RS =

“RS i

“RS i

“R-3 =

“RS i

“RS =

“RS =

HRS i

“RS =

“RS =

nas =

HRS i

HRS i

IiRS =

HRS =

“RS I

“RS T

HRS =

HRS I

HRS =

HRS i

HRS =

HRS =

HRS i

HRS I

29.00 LIKE ONTARIO = 215.12 LAKE I, LIYREYCE = 2,1.20----------.-.-------

JO:00 LAKE ONTARIO = 145.01 LAKE ST LAYREWCL i 2,1.29--------.---..------

51.00 LAKE ONTARIO = 2~5.08 LAKE ST LAWEWE i 2,1.51-------.------------

32.00 LAKE ONTARIO = 2a.u LAKE ST LAYRENCE = P,l.,3----------.-.-.-.-----

33.00 LAKE ONTARIO = 215.0, LAKE ST LlYREIlCE = ~,,.,I--------...---------

34.00 LIXE DNTIRIO = 245.08 LAKE ST LAYRENCE = 2.,.,L--------------------

35.00 LAKE ONTlRIO = Z(5.06 LlXE ST LAYRf”CE z 2,1-L,-----.------.-------

36.00 LAKE ONTARIO = 2.5.01 LAXE ST LAYRE”CE =2,1.18-----.--------.------

37.00 LllE ONTARIO = P15.02 LAKE ST LAYRENCE = 2,*~0,-----...--------..---

38.00 LAKE DNTARIO = 2.5.13 LIKE ST LlYREltCE = 210.98-----------..-------

39.00 LAKE ONTARIO = 245.11 LAKE ST LAYRENCE = .?.0.95--------------------

ao.00 LAKE DNTIRID = 2.5.15 LAKE ST LAYREWCE i 2.8.89--------------------

41.00 LAKE ONTARIO = 245.12 LAXE ST LAYRENCE = 210.19‘-------------------

12.00 LIKE ONTAR, = 245.16 LME ST LIYRENCE I 2*0.7,--------------------

43.00 LAKE ONTlRID = 145.13 LAKE ST UYRENCE = 2.0.bB-------‘------------

w.00 LAKE ONTARIO = 2.5.11 L&XE f, LAYRENCE i 140.61----.-------------.-

(5.00 UKE ONTlRlD = 2.5.11 LAKE ST LAYRENCE i 2,0.57--------------------

e6.00 LAKE DNTlRlO = 245.10 LllE ST UYRENCE = PII.55--------------.------

.I.00 L&KC ONTlRlD = 2.5.09 LAKE ST LlYRENCE i *,0.58--------------------

48.00 LME ONTIRlO = 2.5.01 LAKE ST LLYRENCE i 2.0.6~--------------------

$9.00 LAKE DNTLRfO = 245.10 LAKE ST LAYRENCE i 140.BO--------------------

50.00 LME oNI,R*O = 245.08 LAKE ST LAYRENCE i 2,0.93--------------------

51.00 LAKE ONTlRlO i 2.5.05 LAKE ST UYRCNCE i Z,l.0,--------------------

52.00 LAKE ONTARIO = 245.0, LAKE ST LAYRENCE =2.*.,5--------------------

53.00 L&XC ONTlRlO = .?+5.07 LAKE ST LAYRENCE I 2,1.25--------------------

5..00 LIKE DNTlRlO = 215.00 LAKE ST UYRENCE i 2,,.,3-----------------.---

55.00 LII(E ONTlRID = 2.9.99 LAKE ST LAYRENCE = 2,1.,1--------------.--.----

56.00 LIKE ONTARIO = 2...9* LAKE ST LAYRENCE = 2**.,5--------------------

51.00 LAKE ONTlRIlJ = 2w.99 LIKE ST LlYRENCE i 2,,.,,--------------------

SB.DD LAKE OLlTlRlO = 2e5.01 L,lE ST LAYRENCE = *,,.,e-----------------..-

59.0* LAKE ONTARIO = 245.0, L,KE ST LIYRENCE = 241.2b--------------------

60.00 LAKE ONTARIO = 2W.06 LA”E ST LAYRENCE = 2,~.~,--------------------

-_____------------- T,*E IN

-____-____-____---- T,ME IN

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HRS i

“RS =

HRS i

HRS I

“RS =

HRS =

HRS =

HRB =

HRS =

“RS =

“a?, =

“I73 =

HRS =

HRS =

“RS =

HRS i

“RS =

HRS =

HRS =

“RS =

“RS =

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HRS =

“RS =

HRS =

“RS =

“RS =

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62.00 LME ONTARIO = 2.5.04 LAKE ST LI\YRENCE = 210.95--------------------

b,.OD LAKE ON,IR,O = 2a5.07 LllL ST LAYRE”CE = 2,0.87------------------‘-

61.00 LAKE ONTARIO i 245.08 LIKE ST LLYREWCE = 2.0.10--------------------

65.00 LPKE o*T*R,O = 2,5.08 LAKE ST LAYREWCE i 2.0.13--------------------

66.00 LAKE DNTlRID i 2*5.01 LAKE ST LAYRENCE 5 2,0.L,--------------------

61.00 LAKE ONIARIO i 2.5.07 LllL ST LAYREMCC i 2,0.bl--------------------

68.00 LAKE ONTIRIO = 215.00 LAKE ST LAYREWCE = *,0.5+-------------------

69.00 LIKE DNTlRlO = 215.00 LAKE ST LAYREWCE = 2.0.51--------------------

70.00 LLIE DNTbRlO i 215.01 LAKE ST LAYRENCE = 2.0.,9--------------------

71.00 LAKE ONTARlO i >a..99 LAKE ST LAYRENCE = 2.0.51--------------------

72.00 LIKE ONTARIO i .?,,.50 L&ICE ST LAURENCE i 2,0.59--------------------

I3.00 LIKE DNTlRlO i 244.98 LIKE IT LlYRENCE = 2*0.,2--------------------

7,.00 LIKE ONTlRlO = 2.4.99 LAKE ST LAYRE.RCE = 2.0.8.--------------------

15.OD LllE ONIlRlD = P.4.95 LAKE ST LLYREHCE = *.0.94--------------------

76.CO LAKE ONTlRlD = 2.9.98 LIKL ST LAYRENCE = Z.l.DI--------------------

17.00 LAKE ONTLRID i 24*.93 LAKE ST LLYREWCE i 211.13--------------------

,8.OD LME ONTAR, = 11..96 LIKE BT LAYRENCE = 2,1.21--------------------

19.06 LIKE O”,ARlO i Zll.99 LAKE ST LIYRENCE = 241.29--------------------

80.00 LIKE DNTIRIO = 2.5.08 LAKE ST LAYRENCE = 1.1.34~-------------------

RI.00 LIKE ONTARfO i 1.5.18 LIKE IT UYRENCE = 2.1.,3--------------------

R2.00 LAKE ONTART I245.26 LAKE ST LAYREHCE i 2.1.25~-------------------

a,.00 LAKE O”TAR,O = 2*5.*1 LIKE ST LAYRE”CE = 241.19~-------------------

8,.00 LLIE ONTARIO = 245.19 LAKE ST LLYRENCE i 2.1.12--------------------

85.00 LIKE DNIlRlO = 245.11 LAKE ST LAYRENCE = 2,1.05-----~--------------

86.00 LIKE ONIARlO i 2.5.05 LAW ST LAYREKE = 2,1.00--------------------

87.00 LAKE OPITARID I H5.06 LAKE ST L).YRENCE = 2.0.9.--------------------

88.00 LAKE ONTARIO E 215.06 LAKE IT LAYREWCE = *,0.81--------------------

89.00 LllE ONTLRlO = 215.0, LAXE ST LIYRENCE = 2,0.,9--------------------

90.00 LAKE ONTARIO = 245.06 LME ST LAYKWCE = .?40.12--------------------

91.00 LAKE ONTARlO =2*5.00 LAKE ST LAYREWCE = 241.66--------------------

92.00 LAKE ON,lRIO = a5.01 LIKE *I LAYREWCE = 240.60-------------------

93.00 LAKE ON,lR,O i 245.10 LAKE ST LIYRENCE = *40.5.--------------------

9e.00 LAKE DWrlRIO = 215.13 LAKE 0, LlYREWCE i .?+0.51--------------------

i______-----_-----_ T,#E IN “RS = 95.00 LANE OWTARIO = 2.5.10 LAKE ST LAYREWCE i 2,0.53‘-‘.---.---------~-~----___------_----- ,I”[ INREIC”: 1 * “R-3 ? 96.00 LAKE ONTIRID i 215.23 LAKE ST LAYRE*CE z 2.0.bO-----..--..-.-.----

3 * 5 6 1 II 9 10HRS ------------.------------*------------.------------*------------.------------.------------*------------*------------.------------- 0 Y D Y 0 ”p0. li6. Z.S.O?1. 148. 2.5.C8 5. **:.a6 A. d.06 -L. *+:.o, A. 2,: i,. *A!.,,062.

5. z&s245.57 110. 245.07147. 215.08-19. 2W.06 166.5. 95. 2.S.OL2.5.07

3.110. 215.01154. **5.11

-19. 2.5.07 166. 2.5.0,5. 95. 2.5.07215.10 113.*.

2.5.09 -19.130. 2.5.03215.09 168. 2M.09 96.

5.3. 245.012.5.05 x0*. 215.06 -20.1.1. 245.07

Z15.06 160. 245.06 91.1. 2r5.05

245.06102.

6. 125. 2.5.0. -20.215.00

2.5.01 156. 245.013. 88. 2.5.047.

245.01 98. a5.02 -19.129. 245.(10215.01 153.

3. 2.a.99*IS.** 86. 2ws.12

95. 2.4.991.3. 2.5.04-19. 2W.98 1.1. 2*,.9(15. 24e.9983.245.021.7. 10.. 2.5.01

.?*5.06-II. 2.5.00 155. 2.5.00

I. *,5.05 81. 245.00129. 2.5.05I... 245.01-16. 245.0, 162. 245.04 92. 2.5.05

123. 2.5.01 :. 107. **5.07 -1s. 245.06 160. 2,5.06 92. 215.01125. 2,5.?1

3: g::.;; 96. 2.5.03 -19. 215.03 150. 245.03 86. 2.5.01*Loo 92.139. *,5.(10 -19. 24e.99245.01

I... 2.e.995. *.=A.**

81. 2.5.02101.1.6. 245.01 -II.245.06

2.5.01 152.5. 86. 2,5.002.5.0,2e.05 108. 245.041.0. 2e5.31

-16. 245.01 160. 2.5.01 92.. . 245.04 215.04105. 2.5.04155. -1s. 2*5.0*2.5 .“2

160. 2.5.0,. . 215.02 93. 215.0,101. 2.5.02136. 2.5.m

-19. 2.5.01 151. 2.5.0,4. 2.5.0290.2,5.60 102. **5.00 -19.151. 2.5.C5

2.1.99 156. *...99 89.6.

2.5.002.5.03 110. 215.02 -17.1.1. 2.5.01

2.5.01 163. 2,5.01 9..5.

245.0,245.52 1”B.17,. 2.5.02 -18.

295.1.215.01 164. 2*5.01

132. 2.5.00I. 1::: z-22.5.10 121. 215.07 -17. 2.5.01 115. 2+5.014. 2*5:07*+5.04 108. lss:**5.06**5.0s -19.1.5. 215.55

2.5.06 98.4. 215.02 103.1.1. 245.02 -21.

2q5.12215.01 160. 245.01 91.5. 215.02 215.02107. 245.01158. 2.5.CI

-19. 215.DI 16,. 2.5.016. 215.0193.*+5.05 11.. 2.5.0115.. -18. 215.*3

2.5.06169. 2.5.0,

245.06 115. 215.66155. 6. 1::: ::::“,:-19. 2.5.052.5.iB

173. 2.5.055. *+5.*7 II,. 2,*.07I... **5.35

-19. 2.5.06 172. 2.5.06 99.*.

2,5.0,215.0 109. 245.06 -20.1.0. 2.6.05

245.0416.9.

101. 2.5.OJ*,5.05 96. 2,5.06

4. 235.03 101.160. 2.5422.5.01 -20. 215.03 161.

116. 26.092a5.0, 91.

6. 2e5.09215.D.

111. 245.0715s. -18. 2.5.0,2.5.0.

168. 245.07 95.4. 2.5.0,245.06 106.

110. 2.5.082*5.081.1. -19. 215.07

2.5.08163. 2.5.0, 93.4. *a.06 245.08

105. 245.06102. 245.06 -20.136. Z15.86

215.05 156. 2.5.05 88.4. 2’5.06 2*5.06103.108. 215.0,

2*5.06 -1s.138. 2.5.01 4. 2.5.062.5.06, 151. **5.0688. 2.5.06102.

109. 2.5.08215.06 -18.1.0. 2*5.08

2.5.05 155. 2.5.05. . 2.5.27 88. 2.5.06

102. 2.5.06101.133. 245.01

245.36-1s. 2.5.0, 156. 245.07 84. 245.07

*. 245.06 100.98. 245.0.

2.5.06 -18. 245.06128. 245.04154. 2.5.06 88.

3. *,5.0.2.5.06

97. 245.01 -19.121. 2.5.032+5.0*

150. 215.0,3. 2.5.0..85.215.01 96. 215.0116,. -18.

245.13215.Pl I*&7. 2.5.21215.01 84.

215.09 113. 2*5.01153. 245.11-16. 2.5.06 163..2.5.06 91. 295.06

6. 2.5.12 117. 2.5.12 -16.156. 2.5.152.5.11 171. 215.116. *45.*+ 2.5.12100.11.. 245.1.1.3. -19. 215.13

2,5.1*170. 215.1,5. 245.1.245.13 99.1D9. 2.5.13 -19.152. 2.5.16

2,5.13 161. 215.1, 96.5.

245.13245.14 110. 245.13 -19.1,x. *,5.,x

2.5.13 166.5. *a.,,245.1, 91.2.5.13 109. **5.131.0. 2,*.**

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2a5.10 165. 215.104. 2.5.10245.0895.105. 245.08 -20.1.1. 245.07

2.5.01 163. 245.01 93.. . 2.5.06

245.08106. 2.5.06 -29.154. 2e.102.5.06 163. 215.06 93.

5.2,5.06

2.5.08 112. 2.5.011.9. 245.08-19. 215.01 168.5. 96. 2.5.012.5.08

2.5.01112.

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:o. *Am60. 213.8259. 2.3.8259. 2.3.8558. 2.3.9058. 2.3.9357. 2.3.9.56. 213.9,55. 2.3.9355. 243.9,55. 243.9556. 2.3.9656. 2.3.9,57. 2,3.8957. 243.8358. 213.8158. 213.8059. 2.3.7859. 213.7659. 213.13bC. **3.7*61. 243.7361. 243.7561. 2,3.,261. 2.,.7060. **x.7*60. 2.X.1660. 243.8259. 243.8658. 243.8957. 213.9157. 2,3.9.51. **3.9156. 2.3.9856. 293.9756. 293.9651. 243.9357. 2.3.8951. 213.8558. 213.8359. **3.m60. 2,X.8760. 2,X.8,60. 243.8561. 213.8361. 2.3.8061. 295.7861. 233.1161. 2.3.1660. 243.1160. 2.3.8059. 213.8158. 2,s.m58. 213.9057. 2.3.9156. 2b3.9256. 2.3.9255. 2.3.9155. 243.89

243.912.3.322q3.92

213.9,243.89

*A,,***.I6212.22242.30***.s242.152.2.50242.552.2.58212.59242.58242.5.2.2.18242iw2.2.52242.25*,*.*o242.X2.2.11212.06242.02242.002.1.97211.46241.98242.03242.122,2.22***.,I2.2.38212.11242.50212.55212.58212.56242.522.*..5242.392I2.31242.262+2.*.242.22212.18212.1,2.2.102.2.06212.03242.01242.03242.092IP.17212.26212.3.*,*..I2.2.w

242.51212.552.2.56242.53

REICH: 11 12 13 1, 15 16 17 18 19 PO-----_-____-.----_-------.------------._-__--------*---------___.------------.------------*------------.----________.___________.

“IS Y Y Y

A.129.12.9.126.121.131.13,.135.1.32.129.126.129.133.130.129.136.136.131.12,.124.126.133.1.1.1.6.139.126.Ilk.112.116.125.131.133.13,.130.136.x*3.1.2.133.

2.i.98***.*I245.0$**5.*O2.5.00245.022.5.03245.032.5.822W.982.4.9.211.932.*.9.2.4.902,4.*12.4.92*a..93244.92*+*.912M.90214.92244.992.5.092.5.192.5.23215.l.32.5.102.5.022W.98244.9824a.992.4.992.4.982W.97245.002.5462W.08215.03

2.i.992.5.01245.02215.002.5.012.5.032.5.012.5.0S245.02*4*.992.4.95

22.123.122.121.122.126.127.121.126.II..122.124.128.125.121.130.130.126.123.120.122.127.134.138.133.122.114.110.112.120.125.121.126.125.130.136.135.128.

,I&.250.250.2.8.249.255.260.260.259.256.251.25..261.258.255.

*:I.2.6.

P**:.5*244.5.244.5524b.5.

H P Y P w 0 Y

262.265.

211.94*...952.1.902,. .BB24*.932...9.24*.93211.92214.91*.*.932.5 .m2.5.10245.20*.5.232.5.18215.ll2451.02244.9824,.992+5.00215.002.e.99244.97

258.251.2.5.2.6.255.267.216.211.26.3.23,.228.2.31.245.256.260.2%.256.263.21..216.265.

2.5.01245.012.5.082,5.03

n244.932W.952...962.1.952W.952W.9624a.9,PW.9124. .962.1.712W.902W.882...882.) 45***.g*241.852.4.882.. .88249.872W.8621. .*724..92245.02215.132G.182.5.16245.08244.99241.92244.912W.93*4..9*2W.9,244.9224. .4*21, .99215.0221, .99

*,‘*.246.2.9.250.251.25..258.260.261.260.258.258.260.262.*,9.*5*.259.257.252.2.7.245.2.6.252.25.9.262.258.250.21,.2.2.216.253.258.259.259.260.266.211.269.

244.702re.n241.742W.732*4*122*..112**.,22.L.132,,.7*244.702,..672...632.4.6224..612.1.59*a*.5921..6321..6524..66211.65244.652W.68***.I62W.862W.9424L.96214.892U.802.4.11244.6,2.1.612W.692.1.692,1.68244.6,*+,.7X2**.152.4.15

2.9.250.251.25..258.260.261.260.259.258.260.262.255.258.,259.251.252.29,.2.5.2.6.251.251.260.258.251.2.5.2.3.*a,.253.258.259.259.260.265.210.269.

244.53211.51***.522**.*22.1.522...502,4.,?2+*..,**...I24..4”2**.39214.39**...*Z....b**,.I12*..*1214.97214.5024..562...662.e.n2L4.7624,.722W.6,2.4.5*2.4.482**.*72.1.W2.4.19211.w2...*72W.W2**.55214.5.

2.0.24,.2.8.251.253.255.251.260.261.262.262.262.262.262.

260.251.255.253.251.297.2.).2.3.215.2.9.25..PSI.256.253.25,.251.253.251.259.260.261.264.267.26s.

2...31Z...,,*.*.3*2**.33211.31244.292,+.2924e.29241.29*.*.21211.242.1.20***.I8z,..,,2W.17***.I12*..*02.,.25***.*12.,.28*.*.*a**,.30241.35*WA520.52211.552*,.522,4..J2...JJx,”*w:**2M.26*a*.*5211.2,211.24*,..*a2.,.,X

Y243..¶82.J.W243.882,3.862.3.83243.802.J.192.3.182e3.7,2.3.15213.72213.68243.65243.65

A.188.191.1%.195.196.198.200.201.202.202.202.202.202.200.198.196.194.193.190.

::7181:190.19..191.198.1%.1%.194.195.19,.199.200.201.203.205.206.

2.3.66243.682e3.12213.172,3412.3.822.5.832.3.86213.91243.98244.0.244.07*,*.*I243.962.J.86213.19213.16213.16243.15243.7.2,3.12:;:.;i**3:17

:::::::::59.2,“::::2::2:.59..2.:;:::::;:2:2:2:2:ii:E:.2.

2.3.88243.88213.882.3.M2.3.832.3.LID2e3.19243.782.3.17243.75213.12213.68243.65243.652.5.66213.682.3.122.3.71243.812,X.82243.8,2.3.862.3.912.3.982.4.012.4.0124..04243.96243.862.5.19243.lfr2.3.16243.152*3.1*243.122.3.122.3.1.2.3.1,

**0.241.219.252.25..256.258.260.262.263.263.263.26,.262.260.256.253.251.2.9.2.1.24..2.2.***.2.6.252.256.2%.251.255.253.25..251.259.261.262.26,.26‘.261.

242.01***.w2.2.93*a*.1192.2.8.***.a*2.2.11**2.752.2.12**P&9212.66212.622*2.592.2.592.2.63212.682e2.11212.8,2.2.872.2.91*,*.w

242.982.3.02213.06243.09243.092.3.05242.912.2.892.2.82212.11242.1.2.2.12212.692.2.66242.6.2,2.65242.68

2.1. 24P.W2.5. ***..I24,. 2.2.2.5253. 212.2925%. *,*.*I257. 242*19258.. *+*.I+26,. 242.10262. 242.0126,. 212.03264. 241.99264. 241.95263. 2.1.93261. 241.94259. 2.2.00255. 2.2.0,252. 242.15250. 2.2.232,s. 212.302.6. 242.242.3. 212.412.1. 2.2.452.2. 242.492w. 2.2.51251. 242.50256. 212.48259. 2.P.M*511. 212.27256. 242.29255. 2.2.22255. 292.16251. 2.2.11260. *.*.cd261. 242.05*a. *.*.o*26.. 241.98265. 241.9126L. 212.01

A. *,:.,I162. 2.1.06151. 211.11155. 241.29154. Zll.38153. 2.1..8152. 2,1.5615,. 2.1.63150. 291.68152. 2.X.68156. **I.62160. 2.1.53163. *+I..*165. 2.1.3.166. 2.1.2.166. *,1.,5167. 241.07168. 2,1.00169. 2.0.9.169. 240.88110. 210.82111. 2.0.17171. 2.0.1,169. 2.0.75165. 2.0.82160. 2.0.93157. 211.05156. 211.18155. 241.28155. 2,1.X8153. 241.17152. 2.1.55152. 2.,.6,154. 291.63159. 2,1.57162. 2.1.4916,. Zll..,165. 211.31166. 2.1.2,165. 2.1.16165. 241.12169. 2.1.05111. 2.0.98112. 2.0.93112. 240.81113. 240.82112. 210.79169. 240.80165. 2.0.87160. 2)0.98151. 2.1.11156. 241.21155. 211.3515.. 291.43152. 241.51151. 241.58151. 241.63152. **I.61156. 2.1.58

,“::6b::63.2:2:2,“:70.2::::::--:‘,::::i:.83.8..as;.E:it:.2.Z:2:96.

152.1%.131.139.140.1.0.1.1.143.I...1.4.1.5.II..1**.1.3.1.1.139.131.136.135.13..133.132.132.13..13,.1.0.1.2.1.1.1.0.139.140.141.X.2.1,s.I...I...1.5.1.5.

2.2.21242.132.2.06241.99241.93**I.88241.832,1.78211.14241.712.,*662,1.632.1.61241.65241.692.1.782.1.812.1.952*2.03212.092.2.15212.192.2.232q2.23212.21212.18212.13212.062.1.99241.92241.86211.802.1.16241.132.X.68212.652,,.6.2.1.68

110.112.11,.115.116.117.118.ll8.119.120.120.120.119.118.117.115.11..113.112.111.110.109.109.111.11..111.118.1,8.117.116.116.Ill.ile..119.119.120.120.120.

2.2.2,2.2.13212.06241.99241.9,241.88211.83**I.78*,I.,.24 I .112.1.66241.63*I* .6124, .b,2,,.692.1.782.1.872.1.952L2.03242.09292.152.2.192.2.23242.2,2.2.21242.18**2 43212.06241.99241.922.1.862.1.8024, .76211.73*,I 68*,I .65**I 4.211.68

110.112.II..116.116.117.11s.119.119.120.120.120.119.118.117.115.113.112.112.111.110.109.109.111.11..117.118.118.117.116.A16.117.118.119.120.120.120.120.

2,1.952.1.85*,I.16241.68211.622.1.562.1.502q1.45*,1..02.1 .J62.1.322.1.282.1.262.1.29**I.312*1.*12,1.57211.662ll.I.*+I.812.1.812.1.93241.96241.95*,I .91**I.812.1.81*+1.15211.682.1.61241.5.**I..8*+a .,3211.39211.3.241.30241.29Zll .SJ

2.3.2.1.252.255.257.258.260.262.26..265.265.265.26.3.2b?.256.252.2.9.2.7.2*6.**..2.2.2.0.2,1.216.252.258.260.260.258.257.257.259.261.263.261.265.265.26..

211.93241.81241.752,l.U291.612q1.55241.50**I.*.**I.**2.1.36241.31**I.28241.26211.29241.37*.I.*1241.572.1.66241.71**I.81241.87241.932,1.96291.9,241.902.1.86**I.81**1.1*291.612.1.60241.532*1..7241.43241.38241.3.2.1.30241.29*.I.,,

9D. *.I.*892. 2.1.3793. 241.2691. 241.1894. 2.1.1195. 241.0195. 2.0.9796. 2.0.9196. 2.0.8697. 2LO.8197. 210.7796. 2*0.7395. 2.0.7493. 2LO.7990. .?*0.91188. *+1.0288. 241.1387. 2.1.22

160.163.165.161.161.168.169.170.Ill.111.172.171.168.16,.159.156.155.15..153.153.152.151.15,.159.16,.16,.169.169.168.161.168.168.169.110.17,.171.169.166.

*.I..82.1.37241.262.1.18**I.11291.0.2,0.9,*+0.41210.86210.81210.71210.7,240.1,2LO.192.0.90241.022.1.132.1.22*,I.,,Z(1.392,1.162.1.52**1.5,**I.*8241..22L1.56*,1.29*+I.**241.112.1.10241.03240.96240.90240.852.0.19240.152.0.76210.82

;::4..22:2:;::;::2:i’,:,“,“:2:i::2:22:2:95.2:.2.2

*.I.,32.1.32211.212.1.1,241.062,O.W2.0.922.0.862.0.812.0.762.0.71240.682.0.69240.752.0.8621U.98211.092.1.182*1.21241.35*.I.*3241.182.1..92*1.*52.1.37241.312.1.2.2,1.192.1.1,211.05210.982.0.91290.85240.80210.1,2.0.702.0.1,240.71

182.185.188.189.189.190.191.192.193.19..19..19,.189.183.171.II..17,.172.112.171.110.169.173.181.186.189.192.192.190.190.190.190.191.192.194.193.190.186.

2.1.40211.29**,*I*241.10*,I.032.0.96240.89240.832.0.782.0.132,0.68240.65210.66240.72240.8.230.962.1.06**I.162*1.25211.332.1..0241..62.1.16241.+02.1.5.2.1.28241.212.1.16211.102,1.02240.942.0.812r0.82240.762,0.11210.6,2,0.682.0*7*

2:

:::

:::

:::75.::::::72.

2.2::2::267.:::::::::::::::::::::12.

2.1.W241.322~1.21241.13241.06240.99210.922.0.862*0.*1240.76240.7,**P.~68210.69210.75290.86210.982a1.09241.18211.27241.35**1.+32ll.W*.I.*92**.,32.1.31241.51*41.*+21X.192*1.132.1.05240.9182.0.91240.852.0.80240.71240.102LP.1,2,0.77

:' r_ ;qb z-t

,i 1~

1'1,~~~~ ~,~~Zji

i j

>,~ ,,,,

;~!4 L. I-

D ;1 i-4

2 ,,,,,,,,,,.,,,,,,,,,,,,,,,,,,,,_~T,~,I ,I, ,,,,,, ,,,,,,,,,,,,,,,,,, m

0 12 0 12 0 12 ,- II 12 0TIME (~0bRs)

Figure B.2. Simulation of river profile for the period 7-10 August 1977.

Appendix C. PROGRAM LISTING

80

A R EA FUMC TION INCLIJDIN[; ICL C O V E R ( .F75'R(%t14) I S SUDTRACTED)

REAU(5,2?2) IDATER,IDATE,IPURF

a2

L O A D ‘ B O U N D A R Y N O D E S I N T O A R R A Y B

D O 9 T=lrNBD O 9 J=1,9M=(I-l)*S+J

9 B(IIJ)=E(M)

D O U N S T R E A M BDUNDARY A N D R E A C H N U M B E R

READ15r9117) ARESqNEXITARES=‘ARES+2.78784E7

R E A D N U M B E R O F R E A C H E S A T U P S T R E A M B O U N D A R YA M A X I M U M O F T U O IS ALLDUED

A N D NUM$ER OF H A N G I N G D A M S

1c=1READ(Sr902) NUMUPtNHD

R~EAD I N HANG~ING D A M . I N F O R M A T I O N , BOUNDARYIREA,CHITHICKNESS O F ICE,

1 1 3

1 1 4

112

LENGTH AND ICE ROUGHNESS

IF(NHD-0) 112r112r1'13D O 114’ I=hNHDREAD(5r9IO) BOUND(I)~RN1(I)~THICKLI)rRLorRN(I)NS=RNl(I)RCN3 r12)=R(N3rlZ)-RLCI)G O T’l(l1’2r432) rI,CC O N T I N U EIC=2REAC(5r9051 DISOREADC5r905) N T S O .

R E A D I N . I N I T I A L S T A G E S F O R U P S T R E A M A N D DOJNSTREAM,ENDS O F E A C HREA.CH.READtSr9ii4) (R(N+lfi)rN=lrNR)READ(Sr904) tRIN117trN=lrNR)

R E A D IN I N I T I A L D I S C H A R G E ’ IN E A C H R E A C H ( U S U A L L Y 0)

READt5.905) tRtN118)rN=l~NR)

R E A D IN F I R S T TIME D E P E N D E N T D A T A

IF(ISICETEQ.U) GO T O 145,READ(5q936.) (RICTHK(I)rT=l,NR?READ(5rSOE) (RICE(I)qI=lrNR)

1 4 8 READ(599391 DISINTSISTAGE~HKTNGIUIND

a3

DO 15 N=lrNftR(N~~~)=R(N~I~)R(Nv21)=R(Nv17)R(N*19)-=it(Nv18)R(N+22)=R(Nt19)R(Nr23)=R(~,19)

15 CONTINUE

YRITE OUT INPUT DATA

URITE(6q7601) IDATERYRITE(6r76521 NR~DTT~TU~RD~ITIMINT)~NB~TMAX~T!,IORD~ITIMINT~~~PSI~ARIARESIKITINUMUP~IPRTYP~NEXITIF(ISICE.EO.0) GO TO 6340URITE(br7663)IF(NHD.EQ.6) GO TO 634C1'biRITE(6r76t4) NHDtPOUND~RNlrTHICK,RLIRN

6340 WRITE(b,7665) DISOYNTSOWRITE(6r76Cb)DO 11 I=lrNR

11 URITE(6r76CT) (F(I,J)tJ=l,S)WRITE(6k7603)DO 779 'il=lr~ltl3h!2=N1*9WRITE(6.761) YlrN2DO 777 I=1923

777 WRITE(5r776)ICHAR(I)r (R1N,I)rN=Nl,N2)779,CONTINUE

TOLH =.JuGO&+32.2+NR

INITIAL Q#S,PLL SET

NOU SET TOLERANCES

TOLQ=lO;1J.K=lT=Q

URITE TITLE PAGE

WRITE(6r76Ou)~URITE(6.762:)WRITE(6r7621)IYGX-IPRTYP'lWRITE(6r7622) IPRTYPIIPHIT(IYGX)~IDATERIF(IS1CE.EQ.G) GO TO 6291YRITE(br7610) (IkCCON(I),I=l,2)IF(NHD.EO.0) GO TO fiZ91WRITE(6r761S) (INCCON(IIII=~~~)GO TO 6231

6290 wRITE(6r761i) (INCCCIN(I),I=Srb)6291 WRITE(697623) ICATE,IPURF

84

--

:READ I N NUMB~ER O F REAtHES A N D ROUNDRIES

REAG(5r902) NRINR

R E A D I N PERYANEN.T C H A N N E L CHARACTERISl.ICS. RA,S5~eSP.IflETERS-( R(I.10) A N D ‘R(T,ll) j MAY- B E LEfT R L A N K A S T H E Y ARE CQ,MPUTED

‘RY P R O G R A M . .D O 5 N=lr13D O 5 J=lr23M=(N-1)+23+J

5 R(NIJ)=U(M)D O 7 N=l4*20D O 7 J=lr23

M=(N-14)+23+J7 R(N,J)=UZ(M)

D O 6 N=21r30D O 6 J=lr23M=(b-21)*23*J

6 R(NvJ)=V(M)READ(Sw908) (‘RtN113)rN=lrNR)READ(SrSG6) (R(k!114)qN=l,NR)READ(5r9;S) (RICE(J)vJ=l~NR)

‘ R E A D P R O G R A M D A T A ( T I M E INTERVALqMAX TIYEIPSIIITERATIONSUPSTRAM R E S E R V O I R E L E V A N D D O U N S T R E A M E L E V

A R E A O F UPSTEAM R E S E R V O I R , T I M E I N T E R V A L tl=HR, 2=DAYt~3&~~~K+FlDN-T:H)] -_.PR~i..NT.. FORM’AT AND ISICE)

REAbtSr??S) DTTITMAX~PS~~KITIHLIHLDN~AR~ITIMINT,IPRTYP,ISICEFACTOR=3600.NCOND=TMAX/DTT+.Y9999DT=723*FACTORTCAL=25920050.AR=AR*2.78784E7PSI!.=l-~PSI

C O M P U T E C H A N N E L PERIMCTER, TOP UIDTHqAND LENGTH

DO 10 I=lvNRR(Ir15)=R(Ir13)ZETA=O.IFtRt1114).GT.0.) ZETA=l.R(It6)=R(I,6)*10UO.R(Is7)=R(I,7)*1~00.R(I112)=R(1112)flG.R(I~B)=R(I~8)+2OO.R1Iq9)=R(Ir91*2CO.R~I~10~=2*R~I~6~/R~I~4~~*R~I~4~~~l~*ZETA~R~I~l1~=2~R(I~7~/R~I.~~+R~IIS~*~l.*ZETA~CPERU(I)=R(II~O)CPERD(I)=R(II~~)

10 CONTINUE

85

URITE(67762,l)URITE(6*76251URITE(br76261URITE(6r76001DIS2= I S 0

%NTS2=N O.-.03*NTSDELH=(HLDN-STAGE!/ll.DO 4 .J=ltNR.I~~R~J~14~.GT.O.~R1J113~=R!J115~~O.~3~~l.+~~ICE~

c+1,5 “‘IJl/R(J115)1

ll,i**667"4 ~,Rl(Ji=R(J,l31

I F , (IPRTYP.E~O.21,G.O T O 3>URITEf6r912) (R(JI~~)~J=I,NR)IF(ISICE.EQ.0) GO T O 3 0yRITE(6*914) (RICE(J)gJ=lwNR)

3 0 TH:T/FACTORIF(IFRTYPoNE.O.AND.T.~~.T~~~l Go T O 40,

URITE'INT~R‘HE'DIATE CALCULATIONS

N2=EIF(TH.GT.TMAx) TH=U.URITE(6~9181 TWORD(ITIMINTlqTH~HL'vHLDNIF(IPRTYP.EQ.21 G o T O 4 5

D O 3 1 I=lr3Nl=N2+1

N2=N,l+9NRITE(6*')191 ~R~N~l)rN=NliN2)~~,R~N,l6~,N=Nl,N2~,~R~NIl~),N~N~',~

.N,? )3 1 C O N T I N U E

URITE(6q5611 DIS2rNTS2. ,, YRITE(br560) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$20+6)r ~R(2jr16)~R,(24!16)rR(30*16)

3 3 C O N T I N U E ',35 CONT,INUEBEGIN S E TT I N G C~EFF FIATRICES FOR ,SOLUTIDN,

.40 C O N T I N U EIF(T.GT*TCALl G O T O 4 1T=T*'DTTCl=O.SDISl=DIS2NTSlzNTS2NTS2=NTSIF(~STAGE.NE.0.) G O T O 39DIS2=DISG O T O 4 3

3 9 HLDN=HLDN-DELHG O T O 4 3

4 1 C O N T I N U ENR2=2+NROUTtl)=THD O 4 1 7 IOA=2rNR2+2

8 6

I'OB=IOA/ZOUTtIOA~=RfIOB~lB~/lUG~.OUT(IOA+1l=R~IOB~16)

4 1 7 C O N T I N U ENR2=NR2+3OUT(NR2-ll=DIS /lGOG*OUT(NR2l=HLDN

WRITE O U T P U T T O F I L E T A P E 7

URITE(79418) COUT(I~lrI=lrNR21DI~St=DIS2FACTOR=TMUCT(ITIMINT1DT=DTT*FACTORT=T-TCAL*l.l*DTTCAL=O.K=K*l

R E A D I N T I M E D E P E N D E N T D A T A

484

486487

,481, 4 8 2

IF(ISICE.EQ.01 G O T O 4 8 7D O 484 IRIC=~*NRRICTHKl(IRIC)=RICTHK(IRIClREAD(5,906)(RICTHKfI)rI=lrNRlIF(EOF(511 1201486READ(~9Ua)(RICE(I1rI=lrNRlREAD(5.9391 DISINTSISTAGEIHKING~UINDINHOCIFCEOF(51,) 12Gr4BlI F C N H D C . G T . 01 G O T O 1 1 3IF(ISICE.EQ.01 G O TO,49-D O 48 J=lrNR

lI**w667R(J~13)=PSI'CR2+PSI1+CR1oCRl'CJl=CR2ZETA=O.IF~R(J,14l.GT.O..AND.RICTHK1o.LE.O.I G O T O 5 2IF(H(J~141.LE.O..AND.RICTHKlCJl.GT~O.l G O T O 5 3G O T O 5 4

.52 ZETA=l.I F ( I P R T Y P . E Q . 2 ) G O T O 5 4WRITE(6r561 JG O T O 5 4

5 3 Z E T A = - 1 . 0IF(IPRTYP.EQ.21 G O T O 5 4URITE(6r57) J

5 4 CPERU(Jl=R(JtlO)CPERD(Jl=R(JilllR~J,10~=R~J~l~~+ZETAcR~JI41R~J~11~=R~J~11~*ZETA*RfJ~5~I F ( I P R T Y P . E Q . 2 ) G O T O . 4b

87

IFtZETA.NE.3.) b1RITEt6~58) Rt~~lC)~RtJ~lll*4R C O N T I N U E

-1FtIPRTYP.EQ.2) G O T O 4 9YRITEt6r9121 tRtJ113lrJ=lrNRIURITEt6r913) tRtJ114)qJ=lrNR)URITEt619141 tRICEtJ)rJ=lrNRlURITEt6,915) tPERtJ),J=?,tiR)

.49 CONTIN.UENTSl=NTSZNTS2=NTSIFtSTAGE.NE.,fiI G O T O 4 2DIS2=DISG6 T O 43

4 2 HLDNFSTAGE4 3 C O N T I N U E

TAUX=6.77 E-6+UIND+ABStYINDlD O 1 0 0 K6=lqKITD O 4 5 I=19122D O 4 5 J=lr31

45 CtIrJ)=O.OD O 4 6 I - 1 1 1 2 2

4 6 DtI)=O.

. U P S T R E A M B O U N D A R Y C D N D A T K I N G S T O N A N D . PSEljDO REACY ABOVE C A F EVINCENT. RiACH ‘1:KINGSTONI R E A C H F . 2 I S pSEUD0 R E A C H

QDUT=O.GQPOUT=O.OD O 4 4 N=lrNUMUPQOUT=QOUT+RtN*lS)QPOUT=QPOUT+RtNy22)

4 7 AP=tRtN,2Cl-RtN,Bl)+RtN~4I*RtN~61-0.075 +RtN*14l*RtNv41AAPtNl=AP

4 4 C O N T I N U ENl=lN - lN2H=2*RtNr21-1NZH=N2H+16-NlN2Q=N2H+lAP=RtN,22)+RtN,22)+RtN*4)/t32.2*AAPtl)*AAPtl)*AAP(l))c1=1.I F t R t l r 2 2 I . L T . G . l Cl=O.THETA=AR/DTIFtHKING.NE;Dl G O TO 2 5 2Ctl,N2H)=tl-AP*ClMTHETA

5 0 CtlrN2Q)=THtTA*RtN~22)/t32.2*AAPtl~~AAPtl~~+G.5D(l)=TH~TA~t~tN,2J~+RtN,22)*~t~;22)1(64.4~AA~tl~~~APtll~

*Cl-HL): lttNTSi+NTS2j+TClftQPOUT+QOUT) in.5 1G O T O 2 4 9

2 5 2 CtlrN2HJ=l.CtlvN2Q)=O.Dtll=RtN120l-HK1NG

249. C O N T I N U E

2 5 3

5 1

NP=CIFt;:U+lUP.iQ.,l,, G O T O 5 1c2=1*Nl=Nl*lIF,tRt2r22),.LT.O.) C2=0.L=Rtl,2)H=Rt2r2)L=2*L-lL=L+16-?JlM=2'M-1M?=M+16-N1

l c 1,

C(2r~)=~-~.~+R(2r22)*R(~,22)*Rt2,4)/(32.2*AAPC2)~AAP(2)*AAPt2))‘*c2

UP’STREAM B O U N D A R Y C O M P L E T E

a 486

P=5N4=NB+lD O 6 5 N=lrN4IF(N.EQ.N4) GO T O a 4N7=ECN,21G O T O 86~N7=1C O N T I N U EDO 6 0 N8=lrN7P=P+lPEdR=PERtP).AREARFAREAtP)DAP=PSI+tRtPe5) +~R(P,~~)-R(P,~))-R(P;~)~(R~PI~~)-R(PIB))*

tR(P,7)-lRtPv6)) -d.075+R(P114)*(R(P,~~-~(P.4)))DA=PSI~+(R(PI~)~*(R(pr17)‘-R~tP,9))-R(Pr4)*(RfP,16)-RtPrB))’+

(RtF.7)-iR(Pe6)) -0.075*R(P.l4)*CR(P.,5)-R(F14)~)DQb=PSI+tRtP,23)-RtP.22))DQ=PSIl+(R(P,lS)-RtP.18))DHP=PSI+tRtP,21)-RtP.20))DH=PSIl*tR(P,17)-RtP116))

C O N T I N U I T Y E Q U A T I O N

Nl=Nl*lN2H=RtP,2)*2-1

N2H=N2H+l6-NlN3H=RtPq31*2-1N3H=N3H+16-NlN2Q=N2H+lN3Q=N3H+lC(Nlrkl?H)=R'(P,4)/(2*DT)CtNlrN3H~l=RCP15l/t2*DTlCtNlrN2Ql=-PSI/RtP,l21CtNlrN3Q1=PSI/RtP,121D(N~)=(DQP+DQ)/R~PI~~)*~R(P~S)*(R~P,~~)-R(P,~~))~R(P,~)~(R(~,

2O')-lR(pt16)))/(2rDT)' M O M E N T U M E Q U A T IO N

Nl=Nl+lN2H=N2H-1N3H=N3H-1N2Q=N2Q-1N3Q=N3Q-1TUOQA=2*QDIStP)/AREARSF2'32.2*RtP,13I+RtP113)/(2.208*( AREAR**2.333)1+

PERR**l.333SF=QDIStPI+ABStQDIStP1l*SF2DQX=~DQP+DQ)/R~PI~~)DAX=tDAP+DA)/RtP,f2)CtNlrN2H)=-.TUOQA/tAREAR)*DQX*PSI*RtP~4)*.5

l+TUOQA*+2/(2* AREAR)*DAX*PSIrRtP*4)/22+TWOQA*TWOQA/Y+PSI+R(P14)/H(P112)3 - 3 2 . 2 l AREAR+PSI/RtP~12)+32.2*tDHP+DHl/RfP~l2l4*PSI*RtPq4)/2-2.333*SF/t AREARl*PSI*RtPv4)/25*1.333+SF/tPERR)*PSI

DN=PSI*RtP*51/2CtNlrN3H) =-TUOQA/tAREARl*DQX*DN+TUOQA**2/(2+ AREAR)*DAX

1+DN-TWOQA*TWOQA*DN/t~2*RtP~l2~l*32~2* AREAR*PSI/RtPq12)

+32.2*td~P+2DHl/RtPr12l*D~-2.333*SF*DN/tA~REARl+le333*SF*PSI!tPERR)~f~NlrN3Q)=DQX*PSI~tAREAR)*TWOQA~PSIIR(P,l2~-TUOQA*DA~~PSIlr.5/tAREARl+SF2*ABStQDIStP))*PSI l ll(DT+2)CtNI,N2Q)=CtNlrN3Q)-2*TWOPA*"SI/RoD(Nll=TWOQA*DQX-TWOQA*TUOOA*DAX/4*32.2*AR~A~P~~tDHP

~DH)/R(prl2)+1SF+tRtPr23~*R~Pr22~-tR~Pr19~+RtPrl&~~~/12*DT~l-TAUX*RtPq4)/1.94

6 0 C O N T I N U E

R E A C H E Q U A T I O N S oF,MOMENTUM A N D CO N T I N U I TY CO MP L E T E D . N O U NEEDNopAL CO N D I T I O N S O F S T E A D Y S T A T E C O N T I N U I T Y A N D E N E R G Y."

IF CN.EQ.N41 GO TO 65IFtNHD.EQ.01 GO, T O 1 1 6IFLAG=GD o 1 1 5 J=lrNHDNBOuN=BOUNDtJ)

.115 IFtN.EQ.NBOUN'l IFLAG='J, 1 1 6 C O N T I N U E

90

Nl=Nl+lIN=tlfN12)IOUT=B(Ng3)

CONTINUITY'

61

62

FLOWOUT=O.OFLOWIN=O.ODO 61.I=lrINIPt=B(Nv3*1)'FLOWIN=FLOUIN+R(IPTI~~)IPT=R(IPTIJ)IQIN=2+IPTIQIN=IQIN+16-NlCtNlrIQIN)=l.ODO 62 I=lrIOUTIP=B(N,3+IN+I)FLOWOUT=FLOWOUT+R(IP122)IP=RcIP*2)IQOUT=2*IPIQOUT=IQOUT*16-NlC(Nl,IQOU~T)='l.OD(Nl)=F.LOUI4-FLOUOUT

ENERGY EQUATION

64

IPT=B(N*4)IFIN=R(IPTe3)*2-1ITOT=IN+IDUT-1DO 63 IJC=l*ITOTNl=Nl+lIHIN=IFIN+16-NlLN=4+IJCIP=B(N,LN)IF(IJC.GE.IN) GO TO 64IHOUT=R(IP,3>+2-1IHOUT?IHOUT+16-NlC(Nl.IHIN)=l.C(NlrIHOUT)=-1.D~Nl~=R~IPT~2l~-R~IP,21)GO TO 63CONTINUEIHOUT=R(IPIZ)+Z-1IHOUT=IHOUT*16~NlCCNl,IHIN)=l.C(NlrIHOUT)=-1.D(Nl)=R(IPT~21)-R~IP120)J=IFLAGIF(J.EQ.0) GO TO. 117N3=RNl(J)IF(IP.NE.N31 GO TO 117DIA=R~IpTt21~+R~IP~6~/R~~P,4~-~R~IPle)+TH~CK~J~~A=DIA+R(IPvQ)

91

Al=(R(IPT~21~-R~IPT~9~~*R~IPT15)+R~IPT~7~COEF=.023+RN'(J)*RN(J)*RLCJ)/(O.ki76*DIA**1.333)DH=COEF*RCIP~22~~ABS~R~IP12L~~/~A*A~-R~I~T~23~*ABS~R~IPT~23~~/

1(42.93*Al*Al)I F (IPRTYP.'lE.@l GO T O 63~1WRITEt6r400.2)WRITE(6r4003) DIAqArCOEF*DH

6 3 0 1 C(N~.IHIN)=~.+~.~~~'((COEF-~.O~~)/~IA)+R~IPT~Z~*lABS~R~IP~22~~/~A*A~+2.*CO~F~RfIP~22~*ABS~R~IP~22~~/~A~A~DIA~2-R(~IPT,23)*ABSfH(IPT~23))+R(IPfr5)/('21.47*Al**3)

IHOUT=IHOUT+1C(Nl,IHOUT)=-2.*COEF*ABS(R(IP122))/0IHIN=IHIN+lC~NlrIHIN~=C~N1~IHIN~-ABS~R~lPT~23~~/(21.47*A~*Al~I H I N = I H I N - 1 'D(Nl)=D(Nl)-DH

1 1 7 C O N T I N U EIF(N.NE.14) G O T O 63FALL=.Ol‘+*(R(20.20) -E39.)-(R420r22)-280030)+

1;000001-.19IF(FA,LL.GE.O.) G O T O 6 3C(NlrIHOUT)=C(NliIHOUT~+.Ol4D(Nl)=D(Nl)?FALL

6 3 C O N T I N U E6 5 C O N T I N U E

CGNDITIUNS A T N O D E S C O M P L E T E D . N O U DO DOUNSTREAH B O U N D A R Y

6 7

Nl=Nl*lLN=R(NEXIT,3)N3H=2*LN-1N3H=N3H+16-N1N3Q=N3H+lLN=NEXITIF(STAGE.EG.0.) G O T O 61C(NlrN3H)=l.C(NlrN30)=0.D(N~)=R(LNI~~I-HLDNNl=Nl+lc(NlrN38)=.5N3Q=N30-1.C O N T I N U ETHETA=ARCS/DTC(NlrN3H)=THETAC(NlrN30)=-3.5D(Nl)=THETA*(R(LN,21)-R(LNI17))+ (~DIS1+DIS2)+TC1-CR(LN~23l~

lR(LN,19))*0.5)

R E V E R S E S I G N O F E Q U A T I O N M A T R I X

D O 6 6 N=lvNl6 6 D(N)=-D(N)

9 2

E Q U A T I O N S A L L D O N E

S O L V E .llATRIX

IER=OC A L L LEQT1B~C~N1;15r151122rDtl~l22~~~~B~IER~IF(IER.EQ.0) GO T O 7ilWRITE(br909) IERqK6

7 0 SD&aSDQ=;N3=4.+NRCNR=l.OI F ( K 6 . L T . 3 ) CNR=J.5

U P D A T E V A L U E S OF-HP AN D Q P E A S E D O N D E L T A SQLUTION V E C T O R

D O 7 2 I=lrNRL=2+R(I12)-1M=2*R(I*3)-1R(Ir21)=R(I*21)+D(~)+CNuRCI,20)-R(I,20)+D(L)*CNRSDH=SDH+A@S( D(L))L=L*li+l=f4*1,R(I,22)=R(I,22)+D(L)+tNsR(I,23)=R(Iq23)*D(R)*CNRIF(STAGE.NE.J.1 M=M+lIF(STAGE.NE.9.) DIS2=DIS2+D(Y)

7 2 SDP=SDQ+ABS(D(L))

A L L DOUNSTREAM QP AYU H P R E P L A C E ”

IF(K6.EQ.KIT)- WRITE(6qSIl) K~~SDHISDQIF(SDH.LE.TOLH.AND.SDQ.LE.TDLQ) G O T O lC'5

100 C O N T I N U E1 0 5 C O N T I N U E

DO 110 N=lrNRHBUP-R(N.16)HBDN=R(N*17)R(Ntl6)=R(N*20)RtNq17)=R(N+21)R(N,21)=2+R(N,17)-HE~NR(N,20)=2+R(~~r16)-HfUPQBUP=R(NvlB)QBD~N=R(N,lS)R(Nq18)=R(N,22)R(Nq19)=R(Nr23)R(N,22)=2+R(N,lR)-0nUP

110 R(N,23)=2+R(N,19)-04~~JHL=R~l~16~+R~lr18~+5~l,lh~/~64.4*~R~lr41*~R~l~l6~-R~l~~~~

l R~l~6~-10.075*R~l~14~~R~lr4~~*+~~.~HLDN=H(NLxITI~~)

9 3

'GO TO 3:,120 CONTINUE

FINAL OUTPUT

D'O 3363 IOPUT=lr3REUIND 7IRE2=IOPUT*l!lIREl=IREZ-9IF (NCOND.LT.141 GO TO 3290h'RITE(6,341G). (J,J=IRElrIRE2),GO TQ 3291

3290 URITE(br34201 (JqJ=TRElrIRE2).329lURITE(6r34191

URITE(693417) TUORD(ITI'!INT)3293 :IF(XOPUT-21 325lr3252r3i533251 READ(7r1314) (OUT(I)~I=1121)

GO TO 33:t3252 READ(7rlOlSl (OUT(I)rI=lP21)

GO TO 33i0325,3 READ(7r1316) (OUT(IlrI=i~2113300 IF (EDF(7)) 3363r33013301 URITE(6r1017) (OUT(I)rI=19211

GO To 32933363,CONTINUE121 CONTINUE56 FORMAT(# ICE FORMED OY REACH #+X5)57 FORMAT(t ICE MELTED ON REACH #*I5158 FORMAT(# PERIMETER CHANGES IN CHANNEL U.S.9 D.S. = l #,2FlO.O)

202 FORMAT(XA10)418 FORMAT(F5.0,31(F5.0~F6.21)560 ~FORMAT(~HOI~CX~# COMPUTED H'T z1

/t , CAPE VINCENT1 (4XvF6.2)/;# K'IN:!TON tr (4XqF6.2)/r

Z*# OGDLNSRURG 2(4X,F6.2)/,#

:r (4X+F6,2)/r# CARDI'JALIR'IQUOIS:

'3H.W. tr (4xqF6.2),/3 # IRIQUOIS T.U. fcl-(7XqF6.21/*# YADDINGTON fr (7XgF6.2)/r# MORRISRURG~3 t, (IX,F6.2)/c.# LSYGShULT DAM fr (7X*F6.21////)

561 FORMAT(# DISCHARGE AT P.H.= ZIF~~.CI# NTS= #rFlO.O?776 FOR"AT(2X~dlGr2X110Fll.4178YZFOR~AT(1HC,35X~#PRINTOUT~OF CHANNEL CHARACTERISTICS ARRAY FOR

REAC lH,ES‘frI2r# TO #,12,/l902 FORMAT(2151903 FORMAT(3F5.O~I5r2F6.2,Fi~.~~315~904 FORMAT(SXI~~FS.~~9C5 FORMAT(5X*7FlO.C*5X)

9 0 690-I9 0 89 0 99 1 09 1 19 1 29 1.3914915918

FORMAT(5X,15F5.01FORMAl(F10.01151FORM4T(lSF5.4)FORMAT(# TROUBLE I N M A T R I X A T IEk=f,I5rtKIT=#rI5)FORMATtFORMAT{FORHAT(FORMATCFORMAT(FORMAT{FORMATt

bF10.4)# N U M B E R O F ITERATIONS=#,I5~#SDH~SDQ=#~2~lX~F8~f+ROUGHNEss FOR E A C H REACH:f/2(lkrlSF6.4/))#+ICE THI.CKNESS FO'R E A C H REA'tH:#/2(1X115F6.0/))'#*ICE R O U G H N E S S F O R E A C H REACH:f/2~1x~f5F6.4/))#+PERIMETER F O R E A C H REACH:#/2(1X~15F6.0/,1)~:/20(#-#),# T I M E 1N #rASr# = tqF6.2rt L A K E ONTAR

lrF6,2,# L A K E S T L A U R E N C E = #rF6,2r20(?-t))9 1 9 FORMAT{+ R E A C H tr10(F5.3r3X)/r# S T A G E f~lO(F6.2rZX1!~

#‘rLOY tr 110(~8.01/1

211

10 = #

9 3 9 FORMAT(~~X;~F~O.OI~F~.~.I~)1 0 1 4 FORMAT(F5.0~10(F5.O~F,6.2~~20~llX1~1 0 1 5 FORNAT(F~.0~10~ltX~rlOCF~.O~F6.Z~~lO~llX'~~1 0 1 6 FORMAT(F5.o~20(11X)rl0~FS.O~F6.2~)1 0 1 7 FORMAT(FS.OI~XI~O(F~.O~F~~~~# f))3 4 1 7 FOR~AT(~XIA~~LX*~O(~X~~O~~~X~~H~~~X))3 4 1 8 FORMAT(ClREACH:#r10(17~6X1)3 4 1 9 FORMAT(7X,lO(#------------+2))3 4 2 0 FORMAT(.#CREACH:#rlO(I7rbX))4 0 0 2 FORMATff H A N G I N G D A M R O U T I N E IS ENTERED+)4 0 0 3 FORMAT('tFl2.4)7 6 0 0 FORMATWlt)7 6 0 1 FORMAT(Zl#r55(f*#),#DATA F O R S T L A U R E N C E NODEL#t55IZ*f)/# f,

1 55(#*f)r3X.~2A10~3X~55(f+f)///)7 6 0 2 FORYATt4XqtNUMBER O F REACHES~tTA(f.#)tI5r3'3X~,

l#TIME ~INCR'EMENT....trF6.2,A5/4X,#NUMBER O F N O D A L POINTS#r223CL.#)rI5r33Xv#TIME E N D I N G . . . . . ..CIF~.~~A~/~X~#PSI*~~~C#.#)3rF5.2/4X$ZAREA O F L A K E ONTARIO#.25(#.#),E9.3q# SQ.FT.f/4Xv4tAREA O F D O U N S T R E A M FOREBAY#,l9(f.f)rF9.3v# SQ.FT.Z*19XqS#NUMSER O F N E W T O N - R A P H S O N ,ITERATIONS......#q13/4X*6ZNUMBER O F R E A C H E S FLOLIING F R O M UPSTREAM......frI5rSOX17ZOUTPUT OPTIONfr28(#.#)rI3/4XICREICH E N T E R I N G FORERAY**8 23(f.#)r15///)

7 6 0 3 FORYAT(5x,#ICE IS INCLUDEOtlfiX~lS(#-f)///)7 6 3 4 FORMAT(6X,#HANGING D A M I S INCLUDED#/~X~~~(#-#)/~XI

1fNUMEER O F H A N G I N G @AMS.....tq15/4X12ZBOUNDRY O R NODE.......~...;#r3F5.U/4X~#9EACHfr22~#.#)r

3F5.0/4X, 2#T~JCKNESS#~18~#.#~r3F~~~,/4X,tLENGTH~~21~~~#~#~~3F5;0/4X,,4>HANNiNGS ROUGHNESS.....;...Z,3F5.3///)

7 6 0 5 FORMATC4X,#INITIAL U~SCHARGE~~~~(~.~),F~~.~,~C~S#/~X,-l#INITIAL N E T T O T A L S U P P L Y ..,.*.#rFlO.~l,#CFS#///~

7 6 0 6 FORMAT(ZlX,#NODAL P O I N T IYF@RMATION#/21X~25(#-#~/8X~ltNO.fr6XvtNO. O F NO. OFt,9XvtREACHES INVOLVED#IlGXv2#INCOMING#~2x~#OUTGOING#/l3X~2~3X~#REACHES#~~1

7607 FORMAT(41101515) *

95

-7610 ~ORMAT~1X~13~#*#~r21X,~~~~#*~~~~JX~l~~#*#~,2Ai~~l3~#~#~~762C FORMAT<////./)7621 FOR~~4T~1Xil3h~#*#~iIx,l~6~#*#~~7622 FDRMAT~1X,l3~~~#~~20Xr1'~#*1~~5?x~10~#*f~r2OXrl3~f~f~/lX~

1 13(f*f)r2'OX*lO(Z*#)r21 S T L A U R E N C E R I V E R HYDRPULIC TRANSIEVT M O D E L #*lJ(#+t)*320X,13(#+#)/lX.l3(L~#~~:X,#PRINT 9PTION#rI2r3X~lO(#*#)r50X1410~#*f~,2tiX~13~#*#~/lX,l.3~#*#~,2~x.lO~~~#~~l~~~#@EVELOPED BYfr519X~10~#~#~,2~X~13~f*f)/lXI13~~~#~~A6,# I N T E P M E D I A T E #rlOt#*#)6rf G R E A T L A K E S ENVIROh'!ENT4L R E S E A R C H L A P O R A T O R Y #r713(#+#),20X,13(#*f)/~X*~3(j*#)*# CALCULATIONS ARE Irlo(t*f)R,l6x,#AN~ ARBORrtlICHIGA~~#rlSXrlL'~f*f~‘~ # INCLUDES:tr7Xi.313~#+C~/lX~13~f~#~~4X,#PRI~~~TED CUT.#~4X~lO~#*#~r15X,2A~O~~15X*lC~#+#~~20X~13~#~#~~

7623 FORMAT~1X~13~#*#~r2UX~l~~#*#~~5~~X~lO~#~#~~2~X~l3~#~#~/lX~113~#+#~r20X~10~#*#~~# P;RIOD:#r2A1C~#TO#~2Al~~lG~#*#~~2~X2,l3~#tf~/l~,l3~#*#)r20X11O~#*#~~l~X~#PURPDSE: #*2410*10X*310~#+#~r20X,13~t*C~/lX~~3~#~#~~ ?~~X*iO~#*#~r53X~1u~#*#~*2ox*413(#*#11

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