ML24109A104
| ML24109A104 | |
| Person / Time | |
|---|---|
| Site: | Monticello  |
| Issue date: | 04/17/2024 |
| From: | Xcel Energy, Northern States Power Company, Minnesota |
| To: | Office of Nuclear Reactor Regulation |
| Shared Package | |
| ML24109A128 | List:
|
| References | |
| L-MT-24-002 | |
| Download: ML24109A104 (1) | |
Text
MONTICELLO
APPENDIX G
PROBABLE MAXIMUM FLOOD
MISSISSIPPI AT MONTICELLO MINNESOTA
MAY 26, 1969
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APPENDIX G
PROBABLE MAXIMUM FLOOD MISSISSIPPI RIVER AT MONTICELLO, MINNESOTA
TABLE OF CONTENTS
CHAPTER PAGE
I INTRODUCTION G.1-1
Scope G.. 1-l Definition G~l-1 Authorization G.. 1-2 Data G. l""'.'2 Investigations G.l-2 Acknowledgements G.1-3
II CLIMATE AND HYDROLOGY OF THE STUDY AREA
General G.2-1 Reference Data G.2-1 The Study Area G.. 2-1 Climate G.:2-2 Precipitation -G:.2-3 Snow G.,2-3 Temperature G.2-3 Wind G-..2:-5 Hydrology G.-2-5 Annual Runoff G.. 2-5 Floods G.2-5
III PROBABLE MAXIMUM FLOOD DETERMINATION G.3,...1
Probable Maximum Storm G.3--1 Snow Cover G.3-3 Temperature Sequence G.. 3-4 Snowmelt G.3-5 Infiltration and Retention G.3-5 Runoff Sequence G. 3--6 Unit Hydrographs G.3-7 Flood Routing G. 3-8
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TABLE OF CONTENTS (Continued)
CH.APTER, PAGE
IV STAGE DISCHARGE RELATIONSHIP G.. 4-1
Procedure G.4-1 Computer Program G.4-2 Cross Sections G.4-2 Starting Elevations G.4-3 Manning's Roughness Coefficients G.4-4 Verification of Procedure.. ~.4-5 G.4-4 Stage Discharge'Curve
V CONCLUSIONS G.5-1
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LIST OF FIGURES
Exhibit l General Location Map
Exhibit 2 Isohyetal Map Spring Storm Orientation No. 2
Exhibit 3 Isohyetal Map Summer Storm Orientation No. 2
Exhibit 4 Depth-Duration Curve for 15, ooo* Square Mil;spring Storm OR 1-15
Exhibit 5 Depth-Duration Curve for 15,000 Square Mile Summer Storm UMV 1-22
Exhibit 6 Basin Snow Cover (Water Equivalent in Inches) lio Probability, March 16-31
Exhibit 7 24 - Hour Unit Hydrographs Basins 3, 4, 6 and Ba
Exhibit 8 Discharge Rating Curve Mississippi River at Monticello, Minnesota
Exhibit 9 Probable Maximum Flood Hydrograph Mississippi River at Monticello, Minnesota
G-iv REV 4 12/85 Northern States Power Company Monticello Generat:ing Plant Probable Maximum Flood Study
Ch.apter!
INTRODUCTION
Scope
This report describes the determination of the probable maximum flood level on the Mississippi River at the Monticello Nuclear Generating Plant. The plant site is on the :right bank of the Mississippi River, about 3. 5 miles upstream of Monticello and about 70 river miles north west of Millnea.polis-St. Paul.
The study area for the probable ma:d.mum. flood includes the Mississippi River dram.age above the. plant site; about 13,900 square miles.
Hydrologic and meteo:-ologic data developed by Harza for the Prairie Island nuclear generating plant site have been used extensively to develop the probable maxim.um flood for the Monticello site whose drainage area lies entirely within the boundaries of the northern portion of the Prairie Island drainage area.
Definition
The term 11 probable maximum. £load, n as used herein, is the hypo thetical flood that would :result if all the factors that contribute to the generation of the flood were to reach their.tnost critical values that could occur concurrently. The probable maxiinum £loo;! is derived from
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hydrometeorological and hydrological studies and is independent of his torical flood frequencies.
- It is the estiinate of the boundary between possible floods and iinpossible floods. Therefore, it would have a re
turn period approaching infinity and a probability of occurrence, m any particular year, approaching zero.
Authorization
Authorization to conduct this study was given by the Northern States Power Company, Minneapolis, Minnesota, by Purchase Order M-79613 dated May 1, 1969.
Data
Data used in the study included U. S. Geological Survey maps, Northern States Power Co~ detailed topographic maps for the area near the site and publications on water supply and.floods in the study area, U. S. Army Corps of Engineers reports on river hydraulics and storm data, U.. S. Weather Bureau :reports and technical pape;"S on meteorologi
c~ data and Technical Bulletins of the University of Minnes eta Agricul tural Experiment Station on the clim.ate of Minnesota. In addition, soil m.aps of the basin were obtained from the U. S. Department of Agricul
ture.
Investigations
Determination of the probable maximwn flood in"" 1 uded studies of the probable max:unum precipitation for both spring and swnme't' storms,
infiltration rates for various soil conditions, snowfall and snow cover, and historical temperature sequences and snowmelt rates. Unit hydrographs
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were developed and studies of flood runoff were made for each of the.
sub-basins comprising the drainage area. above tt.:: r~ ject site.
Ac know led gements
The assistance of the administra.to::-s and engmeers of the Northern
... c.*......
States Power Company is gratefully acknowledged. Th.eir cooperation and provision of materials used in the study were very helpful.
The assistance of the U. S. Army Corps 0£ Engineers, the U. S.
Weather Bu:rea".l and the U. S. Geological Survey, who provided valuable hydrological and meteorological information, is greatly appreciated.
Principal pal"ticipants of th.e consulting engineering staH were:
Project Spans or K. E. Sorensen Project Manager L. L. Wang Chief Hydrologist R. W. Revell
Overall Report Responsibility J. C. Ringenoldus Civil Eng:ineer A. A. Muel~e:r
The report was reviewed by Dr. R. A. Clark, Professor in the Department of Meteorology, College of Geo-Sciences, Texas A&:M University, as a consultant to Harza Engineering Company.
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Chapte'I' II
CL'-ATE AND HYDROLCGY OF THE STUDY AREA
General
Data were taken from -reports and technical papers to descri~
the general climatic and hydrologic conditions of the basin. The de
gree of variance f:rom normal conditions of climatic events was studied to dete'I'mine the.range of expected values under reasonable but very
- rare conditions.
Reference Data
U. S. Geological Survey maps of the basin at a scale of 1 to 24.,000
with a 10-foot contour interval were u.sed in the study. In addition, de tailed topographic maps near the project site were obtained from the Client. Special purpose maps were *also a"railable in.many 0£ the re
ports on the climate and hydrology of the bas in.
Technical bulletins on the "Climate of Minnesota," published by the University of Minnesota, Agricultural Expe*runent Station, were used extensively in describing the climate of the basin.
The Studv Area
- The Mississippi River basin above the plant site has a drainage
area of appro:rir.nately 13,900 square miles and lies entirely in the state o£ Minne s ota.
The topography of the basin is characterized by level to rolling
prairie land interspersed with areas of glacial moraines whoe-e hills rise from 50 to 300 feet above the surrounding land.
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Elevations in the basin range f:rom 900 to 2100-feet, msl. The
elevation at the project site is about 930 feet above mean sea level, and the average elevation 0£ the basin is about 1200 feet.
Most of the basin is covered with glacial deposits and the land sur~
face consists. of features derived from' the several different ice sheets that ad'V'a.nced and then retreated from the area. The principal feature,
from the hydrological standpoint, is the nu.m.erous lakes that were formed m the surface depressions created by the movement of ice. As the ice ret:reated, depressions were le:ft, which filled with water to form lakes.
The stream.flow c...l:1.aracte:ristics of the !vfississippi and of all its c...'iiie.£ tributaries are largely determined by the natural storage provided by these lakes and the many swamps.
Clim.ate
The study area lies within a zone of marked continental clim.ate
characterized by wide and rapid variations in tempe:-ature, ~ ager winter precipitation and usually am.ple summ.e r :ram.fall. lt has a tendency to
extremes m all climatic features, although this is moderated somewhat by the large numbe:- of bodies of water in the area.
Atmospheric moisture mamly.flows :into the region along tv.ro water
vapor st=ear.n.s: a strong southerly D:ow fro::i the Gulf of Mexico and a comparatively diifuse westerly movement from the Pacific Ocean. 0£ the two, Gu.Ji moisture is the more important, ace ounting for most of the precipitation in the study a:rea. During the months when the southerly winds :reach Minnesota, May through September, about 65 percent oi the annual ra.iniall is recorded. Because these air masses must travel 1200 to 1500 miles before reaching Minnesota, minor wind changes 'can account
) for large variations from normal precipitation..
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Precipitation
Annual normal precipitation over the study area ranges from about 28 inches in the east to about 24 inches in the west, Extremes of annual precipitation recorded at Minneapolis - St. Paul range from 49.7 inches to 10.2 inches. Monthly normal precipitation also ranges widely across the study area but reaches a high of about 5.5 inches in June in the south ern portion of the area. Minimum normal monthly precip.itation li-about one-half inch in.January and December in the western part of the area.
The maximum 24-hour precipitation recorded was 8.07 inches at Marshall, which is near the study area, in Julx 1909.
Snow
Most winter precipitation occurs as snow, which largely is stored on the ground until the spring thaw. Normal annual snowfall in the study area averages about 50 inches. A maximum annual fall of 107 inches was recorded about one hundred miles to the northeast of the study area, in Cook County, Minnesota. Accumulations of three to four feet of snow within the study area are not unusual. Runoff is most affected by snow conditions. Gradual melting of snow. on unfrozen ground may result in much moisture entering the soil and sub soil, but sudden thaws in the spring may cause rapid runoff of the entire winter accumulation of snow, especially with deep frost penetration.
Temperature
The study area, lying within the heart of the North American land mass, displays a typically continental climate. It has great extremes in temperature, not only from season to season and month to month, but
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on a diurnal basis as well. The only nearby water body of sufficient size to rnodify clilnate on more than an extremely localized basis is L *
- Superior. However, its m.fluence on the study area is restricted essen tially to coniines of the shoreline due essentially to prevailing westerly winds and also to the abrupt rise oLthe land from the lakeshore.
Normal average daily te;nperatu:res at St. Cloud, which i~ app:rox im.ately 25 miles upst:ream of the plant site, :range from about 10°F in
late January to about 72°F in late July. Normal maximum a::id mini.mum daily temperatures for the same station are about 20°F and 0°F in Janu ary and about 83°F and 5 9°F in July.
Norm.al temperatures over the basin for each season of the year are as follows:
Season Temoerature.
Winter (December., January and 7°F February)
Spring (March, April and May) 37°F
Sum.mer (June, July, and August)
Fall (September 1 October, and 42°F November)
The great extremes of temperature in the area are apparent from
the absolute range of 173°F.that has been :recorded. The extreme maxi mum temperature recorded during the total record period was l 14°F in July while the extreme minimum recorded was -59°F in January. Ex treme maximum and minimum temperil.tures £or each month of the year
from St. Cloud are shown below. Temperatures given are in degrees Fahrenheit.
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J F M A M J.r A s 0 N D
Extreme Maximum 55 58 81 91 105 102 107 105 106 90 71 63
Extreme Minimum -42 -35 -32 2 18 33 41 34 18 6*-23 -32
Wind
~r -i;.--a Prevailing winds are from the north.west during the winter and
early spring., and from the southeast during the sum.me::- and latter part o:f spr:ing. Montbly*mean wind speeds vary slightly over the basin. An nual averages are from about 10 to 13 miles per hour with mean monthly variation from about 9 to 15 miles per hour. The highest monthly mean
wmds are attained in April.
Hydrology
Annual Runofi
The annual runoff from the rivers and streams throughout the basin
is directly affected by the a.mount of lake or swamp are*a as evaporation losses reduce the yield. Then long-term mean annual runoff for the basin is approximately 5. 0 :inches '\\Nl. th a range in mean annual :runoff from 1. 22
to 8. 93 inches.
Floods
Two types of flooding occur :in the basin -- open-water flooding and
backwater.flooding. Flooding W11ile open-water conditions prevail is caused by runoff producing rains, or by melting snow, or by a combination o{ the two. Flooding because of backwater is usually caused by ice jams. The most serious flooding throughout the basin has been associated with exces sive snowmelt and rainfall. The tune of occurrence of floods shows the
greatest frequency in April during the spring thaw. A second peak occurs
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in June due to thunderstorms. A smaller peak occurs in the fall. Local flash floods occur in the s~aller streams in the spring thaw and also in the warmer season from locally-intensive rainfall.
The maxim.um flood of record on the Mississippi River at the plant site was ~l_,Q_OO cubic feet per second (elevation 916. 2 feet) in April~
1965.. Records for the station at St. Paul indicate that this was probably the maxim.um flood since 1851. This flood which established record high stages at many stations in the Upper Mississippi Basin resulted from a severe winter and a combination of' clL"na.tic events that led to a deep snow cover on top of an ice layer. Moderate to heavy rainfall and a return to normal temperatures during April produced rapid melting and extremely high runoff.
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Chapter III
PROBABLE MAXIMUM FLOOD DETERMINATION
The probable _maxi.mum flood at the plant site was determined by t:ranspos:ing an actual, c:ritical-spring storm to the drainage basin and maximizing the precipitation for potential moisture: *- Potentfalsnow cover and a critical temperature sequence were developed for deter-..
mining snowmelt cont:ribution to flood runoff. Flood runoff at the plant site was determined by developing u~it hydrog:raphs for four sub-basin~,
applying :rainfall and snowmelt excesses to the unit hydrographs and :rout ing the resultant hyd:rog:raph_s fo~ the sub-basins to the project site.
A probable ma..**dm:wn sum.mer storm over the project area was also studied in. detail and the resulting flood at the project site deter mined. Although the summer storm was much larger than the spring storm, the much lower :retention rates under ordinary spring conditions, and the sncrwmelt contribution to runoff, :resulted in the spring storm pro ducing the more critical flood. Exhibit 1 shows the gerie:ral location of the study area.
Pr ob able Maximum. Storm
A probable maxim.um spring storm and a probable maximu..T-su.!'.!'1.
mer storm were determined by transposing and ma..ximizing*actual re-
c o:rded storms.
The storms selected were the March 23-27., 1913 storm centered at Bellefontaine., Ohio, (OR 1-15, U.S. Army Corps of Engineers.,
"Storm Rainfall :in the United States") and the August 28-31, 1941 storm centered at Hayw-a:rd, Wisconsin (UMV 1-22). These storms represent
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near maxim.um conditions of meteorological events for spring and sum mer conditions.
Maximization of these storms involved multiplying the observed
- rainfall values. by the ratios of the ma..*,dmu.m. precipitable water in an air colu.m.n over the study area to the observed precipitable water in an air colwn.n for the actual storm. Under the assumption **of a sattira.ted
pseudo-adiabatic atmosphere, the amount of moisture is a unique func tion of the ground elevation and surface dewpoint. Precipitable water was thus determined from the inflm-'7 barriers to the storm centers and observed and maximum persisting 12-hou.:r dewpoints. Persisting 12-hour dewpoints for the actual storm were obtained f:rom U. S. Weather Bureau data. In accordance with frontal theory, the storm dewpoi:nts were measured in the warm air rather than at the point of rainiall.
Maxim.um persisting 12-hour dewpo:.nts for the study area were taken from the National Atlas _E! the United States, 11Maxirnu.m Persisting 12-Hou:r 1000-MB Dewpoints (°F), Monthly and of Record. " For the trans posed storms, the maxi.mum persisting 12-hour dewpoi't;its were taken
from the atlas at a point equally distant from the center of the study area as the point at which the observed dewpoints.were from the recorded storm centers. The distances were measured in a direction into the
general path of air fiow from the Gulf of Mexico.
The original observed storm patterns were superimposed over the study area and the weighted average precipitation over each sub-basin
determined by planimetering the areas.~between isohyetal lines. The precipitati_on was then adjusted for ma.."'Cimu.m. moisture charge in accord ance wit.1/2. the above criteria.
- Superposition of the observed s'torm pat terns over the study area is justified because the areas are meteorologically
homogeneous, and no major orographic differences exist betw'een the study
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area and the observed storm areas. Rotation of the transposed storm patterns was limited to 20 degrees from the observed storm.
The depth-duration relationships for 15,000 square miles from the recorded storms were used to determine rainiall increments for each
sub-basin. The rainfall increments were then arranged into a sequence considered to be the most critical *that could reasoriably occur*.<_ The re
sulting depth-duration curves for the spring and sum.m.er storms are shown on Exhibits 4 and 5. Exhibits 2 and 3 show the transposed is ohyetal patterns and the maxiniized precipitation !or each storm.
Following the determination of the flood resultL'rlg from the spring
sto:rm,the is ohyetal pattern was re:-oriented over the study area to find the most critical rainfall pattern. Although an inf:inite number of ori entations is possible, the effect on the resulting flood was found to be come negligible with additional orientations.
Snow Cover
Snow cover over the basin was taken from the U. S. Weather Bw:-eau, Technical Paper No. 50, "Frequency of Maximum. Water Equi
valent of March Snow Cover in North Central Uni:ed States. 11 For the purpose of the probable maximum flood study, maximum water equiva
lent (:inches) for March 16-31 having one percent probability was used.
L:ines of equal snow cover, taken from the report, were superinlposed
over the basin ~nd th~ weighted average snow cover £or each sub-basin determined by planinletering. Exhibit 6 show~ the assumed basin snow
cover.
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Temnerature Seauence
For purposes of snowmelt computations, it was necessary to de
termine a critical temperature sequence *that could reasonably be ex pected to occur while the snow cover was at a maxim.urn.. Weather :re
cords £or the Minneapolis station offered the longest record of observed temperatures near the basin (54 years) and this record was used to de termine a critica.l temperature sequence. As a large percentage of the total snow cover could be melted in about five days the maximwn histori cal five-day mean daily temperatul'e sequence occurring from April l to
15 was selected. This was the period April 2-6, 1921. It was assumed th.at this temperature sequence could occur a.t any time bet-ween April 1 and April 15 and that it could occur following a period of extremely cold weather such th.at the snow cover would be a.ta maximum.
Since temperatures vary considerably ove:r the basin, several sta
tions located throughout.the basin were selected and the observed April 2-6, 1921, temperature sequence recorded. These temperatures were assumed to be representative of the sub-basin which they*were nearest and we:re used in the snowmelt computations.
- Table III-1 shows the re
cord five-day temperature sequence used for each sub-basin. Te.rnpera tu.res subsequent to the maxi.mum five-day sequence were assunied to be the same as those :recorded in 1921.
TABLE ill-1
Mean Daily Tem-oeratu:re Seauence Sub-Basin Station l 2 3 4 5
3 Bra:inard 46.0 54.5 57.0 57.5 57.0 4-8a St. Cloud 48.5 54.0 69. O 62.. o 57.5 6 Pokagama 40.5 53.5 54.0 54.0 53.5
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Snowmelt
Sncwmelt for the probable maxim.um flood study was computed using methods developed by the U. S. Army Corps of Engineers and de scribed in their Manual EM 1110-2-1406, 5 January 1960, 11 Runoff from Snowmelt." These methods utilize basic data on temperature., precipi tation, wind velocities, ins elation, snow albedo, ha.sin expos~-;e and canopy cover, and a convection-condensation-melt factor which repre sents the mean exposure 0£ the basin to wind. Average monthly values of insolation anc; wind velocity were determ~ed from Minnesota weather records for use in the c amputations. Ins elation of 45 0 Langleys was used throughout, and average wind velocities were determined to be 12 miles per hour for the snowmelt period preceding precipitation and 20 miles per.hour during precipitation. Snow surface albedo wa.s as su.m.ed to be 45 percent.at the start of the melting period. Basin exposure was asswned to be high due to the lack of large topographic variations and basin canaopy cover was determined £or each sub-basin by estimating the percentage of forested area from map:-:; showing for~st cover. A mean relative hUII1idity of 70 percent was used for converting air tem peratures to dewpoint temperatures during the days of high ins elation melt.
Infiltration and Retention
Infiltration and initial retention losses were assumed to be extremely low at the start of the runoff period. Documented flood events in the Upper Mi~sissippi Basin indicate that it is not unusual to have very high runoff in the early spring due to surface conditions at this time o: year.
Commonly., early warm spells will cause melting of a light snow cover with the free water percolating through the soil to fill surface voids and
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depressions. This is often followed by the return of freezing tempera
,__;-es that cause ice to form over the ground surface, and a heavy snow pack accumulation. II these conditions are followed by an extremely warm period and rainfall there is almost no loss of free water and run off is maxiinized. Since records of frost depth indicate that three to five.feet of frozen ground at the end of March are not unusua.1 1 retention rates are not likely to :increase significantly for some tiine after melting starts. Initial retention was assumed to be zero in this study 1 and other losses were assumed to be O. 02 inches per hour during the snowmelt period and 0. 03 inches per hour during the period following the beginning of r ainiall.
Runoff Seouence
The most critical sequence of.events leading to a major :flood.wo~d be to have an unusually heavy spring snowfall and low temperatures after a period of intermittent warm spells and sub-freezing temperatures has formed an inipervious ground surface and then a period -of extremely high temperatures followed by a major storm. This sequence of events is not unusual in the study area and the maximization of rainfall, snow-cover, and temperature would produce a probable maximum. flood.
For the purposes of this study., antecedent conditions were assumed to be such that extremely high runoff rates would result from sno-..v melt and precipitation. Snow water equivalent having a one percent probability, was asswned to cover the study area on March 31. On April 1, the ma.."C imwn historical temperature sequence was started *. By the fifth day the high temperatures were below the dewpoint temperatures of the storm and the probable maximum spring precipitation was assumed to beg:in April 5.
Temperatures Jar the period following the maximum five-day sequence
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were assumed to be the same as those recorded for the April 7-16, 1921, period.
Unit Hydrograohs
The study area w.as divided into four major sub-basins and syn---........
thetic unit hydrographs were developed for each using Snyder 1 s method, which.. is derived from the various physical basin characteristics. The equations which Snyder developed are:
l} t = C (LL,°*3 tune to peak p t *
- ca
- 2) q_ "= C x 640 peak rate of discharge
-P P T p
- 3) T = 3 + (t + 8) p duration of unit hydrograph
Where: t = Lag tim.e from center of rainfall period to peak oi P unit hydrograph in hours
L = Length of river to the most remote portion of the bas in, in miles
L ca = Distance along the water course to the geographical center of gravity oi the drain.age bas in
= Peak rate of discharge, in cubic feet per second per square mile
T = Duration of unit hydrograph in days
Ct and C p are constants
The constants C and C are critical values in determining the t p basin lag and the peak discharge. Data exists at several gaging stations in Minnesota on the Missis.sippi and Minnesota rivers, so unit hydrographs
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could* be constructed based on actual* data. After these unit hydrog:raphs were developed, known values were applied to Snyder's equations and a range of values for Ct and Cp were determined. The ave:ra*ge value oi Ct was 8. 0 and the average value of Cp was 0. 75. These two values were then used in Snyder's equations to develop synthetic unit hydrog:raphs
- £or the sub-basins used in the study.
Vnit hydrog:raph peaks were increased by 25 percent and basin lag decreased by one-sixth in accordance with standard Corps of Engineers practice. E*ibit 7 shows the unit hydrographs for each sub-basin.
Flood Rquting
Snowmelt and rainfall excesses were a*pplied to the unit hydrographs and the resulting hydrographs we re determined for each sub-basin. Sub bas in hydrog:raphs were then routed to th~ pl"oject site by computer pro gram using the modified Wilson method -- the equation used in the method is:
t where K = 2 T + t
01' 02 = Instantaneous discharge or outflow from a basin
Il, Iz = Instantaneous discharge or inflow to a basin
t = Routing bte rval - 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> for this study
'I'* = Travel ti.me - hours
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Travel time T for flood routing were taken from Corps of Engineers recorded travel times for large floods. Base flow was determined from long-term. USGS records for the stream gage at Elk River, Minnesota with a drainage area. of 14., 500 square miles. Examination of the records indicated that for the months of March - April,. a base flow of 5000 cfs was.............
reasonable. The base fl.ow of 5000 cfs was then added to the total of the routed flood hyd:rographs. The resultant probable maximum flood hydro graph is shown on Exhibit 9.
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Chapter IV
STAGE DISCHARGE RELA.TIONSHIP
The stage-discharge curve at the nuclear plant site was extended
above the rai. 6 e of historical experience by means of hydraulic computa tions based on the river channel downstream. This was done* by a series a£ backwater computations based on a range of discharges. The back
water computation procedure takes into account channel conditions over a reach_ of river and tends to converge on the true stage at the **upstream end of.the reach even though the starting elevation at the downstream end
of the :reach cannot be established. *selection of an adequately long :reach of river for analysis will provide the correct upstream stage :regardless of errors in starting elevation.
Procedure
River profiles were d~rived by the "Standard Step Method II of back water calculations, using an electronic computer. The term 1'backw'ater., 11 as applied in the discussion of natural channel (mild slope) hydraulics,
generally refers to a depth 0£ flow, or water surface elevation, which is greater than normal.depth because of a downstream control such as a dam or channel Condition.
Since the depth of flow is greater than normal under these conditions, the cross-sectional area is greater than normal, and the velocity is less
than normal. Normal velocity corresponds to a rate of head loss equal to channel gradient, so the :rate of head loss must be less than the channel gradient. Thus, the water surface slope is less than the bed slope.
This slope-reduction caused by a downstreani depth greater than normal extends with d:im.inishing effect upstream from the control until the "backwater profile" becomes coincident with the normal depth profile..
The standard step method utilizes the Manning formula in a com putational procedure designed to take into account the effects of gradually
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varied flow. As utilized in computations for a natural channel, this pro c-edure includes effects of downstream channel conditions and constric-tions in the determination of the water surface elevation at upstream points. The Bernoulli equation of conservation of energy is successively appl:i:ed for channel reach segments using the Manning formula for deter mination of head losses.
- Comnuter Pr-ogra..."l'l
Backwater computations were made on an IBM 1130 computer sys tem, using a program prepared by the Hydrologic Engineering Center, Corps of Engineers, Sacramento, California. The effective cross-sections were completely described to the computer and Manning's nn 11 values for left overbank, right overbank and channel for each section were read in.
Discharge and starting water _surface elevations were read into the com puter at the first section and the computer carried out computations of water surface elevation for each section-in upstream order. Elevations at each succeeding upstream section were determined by the computer by assuming a water surface elevation equal to that of the last section raised by the product 0£ the slope and the distance between sections. Computa tions were made of average slope., velocity., discharge in left and right over bank as well as the channel, velocity head, eddy loss due to expansion or contraction, ene:-gy gradient, and water surface elevation.
Output data include discharge, velocity and area £or each over bank and channel section, slope., head loss and water surface elevation.
Cross Sections
Channel and overbank cross-sections were determined from large scale two-foot topographic maps near the plant site furnished by North ern States Power Company and from smaller scale 10-foot contour inter val maps prepared by the USGS. Points in the cross-section were
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described at each major break in the side slope so that sub-areas com puted by assumed trapezoidal sections would not differ from the true area by a significant amount.
Cross-sections were determined at average intervals of about one fourth mile near the power station and about one and one-half miles in
the downstream reaches of the river near Monticello...,....
Starting Elevations
The first cross-section on the Mississippi River in the study a=-ea is about five and three-quarter miles below the generating plant site and about one mile below Monticello, Minnesota. A stage-discharge relation ship was determined for this cross-section using Manning 1 s formula.
Q = L 48:6 A R Z/3, S l/Z n
where Q = Discharge, cfs,
n = Manning 1 s coefficient of roughness
A = Area of the cross-section
R = Hydraulic radius which is equal the Area divided by the wetted perimeter
S = Average channel slope
The rating curve was develo.ped by assuming various values for
water surface elevation. The area 1 hydraulic radius and dis charge 0 were then determined for each value. The average channel slope, S, was obtained from topographic maps.*
G.4-J REV 4 12/85 MONTICELLO
Manning's Roughness Coefficients
Values cf Manning's "n" coefficient used in the study were deter mined from e:xaniination of detailed topographic maps of the plant site and of USGS IO-foot contour maps with.a scale of l :24, 000. Average values of "n 11 determined were
- 032 for -the main channel,
- 050 for the left overbank and
- 045 for the right overbank. A ~ omewha~- !_l_!gher value of. 065 was used for the right overbank in Monticello and a value of *. 060 was used for the island imm.ediately upstream of the plant site. These "n" values were determined by assUIIJ.ing a basic "n" value and then making adjustments for irregularity, changes in shape, obstructions, vegetation, and meander.
Verification of Procedure
The maximum flood of record at the site occurred in April, 1965, with a discharge of approx::i.mately 51.. 000 cubic feet per second. For this flood, records of water surface elevation exist at several points along the river near the plant site. A trial backwater.computation was made starting from a point of known water surface elevation slightly more than a mile downstream from the plant site. The trial computation yielded a water surface elevation at the plant site which agreed within O. 2 feet of the meas*.ired water surface elevation for the flood of record.
For the determination of the water surface elevation corresponding,
to the probable maximum flood, two different starting elevations we re selected from the rating curve downstream of Mo:iticello. Elevations were selected for stages somewhat higher, as well as somewhat lower, than that anticipated for the probable-maxunwn flood. Analysis was then made to determine backwater prof:i.;le s for the river reach extending to the plant. The profiles converged to within 0. 4 feet at the plant site,
G.4-4 REV 13 4/95 MONTICELLO
indicating that the river stage at Monticello plant would not be greatly
effected by ad"justment of the stan.1..ub elevation. An average of their values was used for the probable maxum.un flood stage.
As a further verification 1 it was decided to determine what maxi mum. stage would occur at the plant site if the values for Manning's roughness coefficient 11 n 11 were lowered for the overbank sections of the
channel reach. Lmvering "n" for both the left and right overbank by
- 0. 005 yielded a probable max:imum flood stage elevation of 938. 9 or about O. 3 feet lower than the elevations obtained by *using the higher "n"
values. It is believed that any further decrease in the roughness coef ficient would be unrealistic in view of the channel and overbank char acteristics.
Stage Dis cha:r~e Curve
Several sets of backwater computations we:re made using water
- surface elevations and their corresponding discharges as determined from the :rating curve downstream from Monticello. Using the dis charges and the water surface elevations determined, a stage dis charge curve was then constructed for the plant site (Exhibit 8).
REV 4 12/85 MONTICELLO
Chapter V
CONCLUSIONS
The probable maximum. flood at the project site was determined to be 364, 900 cubic feet per second and to have a corresponding peak stage of 939. 2 feet MS~. The probable maximum f.l.ood hyd-rograph is shown on Exhibit 9. The occu:r:rence of the sequence of events de scribed in Chapter m would cause the flood to reach its maxim.um. level about l 2 days after the beginning of high temperatures and would remain above elevation 930. 0 for about 11 days.
G.5-1 REV 4 12/85 MONTICELLO
EXHIBIT
0 II 0 IO ~ rt')
en O> a>
... 'fill,........
47°
46°
Scale 0 10 20 30 Miles GENERAL LOCATION MAP
HARZA ENIINEER1N; COMPANY DWG NO, -41:!IF I MAY, 1989
REV 4 12/85 MONTICELLO
EXHIBIT 2
t N
ISOHYETAL MAP Seclo O 10 20 30Milu h?Jl!ttU1 J f SPRING STORM ORIENTATION N0.2
KARZA UUIIH~~fllNII (;OWP.AHY owe NO. 41 J f' Z MJ.Y, ll!UUI REV 4 12/-85 MONTICELLO
EXHIBIT 3
- I
\\O
Scali O IO 20 30 Miles ISOHYETAL MAP 1 re,.t l t.
SUMMER STORM ORIENTATION N0.2
HM1.zA ENGtNEERhio cowPANY r:>wit ffo. 4, 3, 3 101, 1s69
REV 4 12/85 MONTICELLO
EXHIBIT 4
- 90 ~
80 /1
C
- / V. --,.._ ~~
70
c 60 I
~ a a:: I
C
0 I I 1-! 50 0
-C:
CD I u 40 Cl Q..
NOTE: I l For flood stud(c purposes a~sume 30 I 1009/a of rain oil occur_red -in 4 doys.
20 I
to l r
0- 0 2 3 4 5
T1me in OQys
DEPTH - DURATION CURVE FOR 15,000 SQ. Ml..
REV 4 12/85 MONTICELLO
EXHIBIT 5 100 ~-------,-------r------::z-,--------,-------.
I
901-------+------H------'I--------+----~
80 1-------+--...,.-~-+--:+---------......... ----j.....;_.....;_____,;, __ -+-------1
70_.__ ____ -+----#---------;..---...;.;..._-------1--.....;....--__,j...------.....;_---1
so -----....J.......J.....;_ ____,..._ ____ -+- _____ _._ __.;.___;_--------'
0
--c c:,
a:. 501-------1-.1-------;-...-----1-------I--------I
Q_
0
-* 401-----'--+--......--........_ ___ ---:..--------i------.;.._------------1 C
~
u Q. -
301----1----+-------+-------+------+-------1
201----+-----+-------+---'----------+--..:....;.;.---------'--------1
JO 1--1------4-------+----------+-----,---+-----------t
0 _____ ___._.....;_ _______......._ __.....;_ _ __,_ _____ -'--_____ _
a 2 3 4 Time in Days
DEPTH - DURATION. CURVE FOR 15,000 SQ. ML SUMMER STORM UMV 1-22
HARZA EHGIHE'!RING COl,IPANY l)Wll HO. 41~ F' 5. llAY, rau REV 4 12/85 MONTICELLO
EXHlBIT 6
12
Scola O fO 2. 0 30 Mile$ BASIN SNOW COVER
t ' {WATER EQUIVALENT IN INCHES) 1% PROBABILITY, MARCH 16-31
HARZA EHOINEERIHGI COMPANY owe NO. I.II F' 6 MAY 1 1968
REV 4 12/85 MONTICELLO
EXHIBIT 7
24-HOUR UNIT HYDROGRAPHS BASINS 3, 4, 6 AND Sa
25 --------------------.---------
3 6 /..
, \\
20 \\
)
-.--:.:.,..,..-- '° '
-0 \\
0 0 15 0
C: \\ \\
(I) c:r, C 10
..c:
(.,)
in '\\ \\
0
\\
5 ~/'/ "
j/f I \\80 '. ' '
'/ ' "
0.... 0 5 to 15 20 25
Time in days LEGE ND:
BASIN 3
--- BASIN 4
--- BASIN 6
BASIN Sa
'ffARZ.l EN81NEERIN0 COMPANY D'ff8, NO. 413 F 7 MAY, 1969 REV 4 MONTICELLO
EXHIBIT 8
1000 990 980 970 -.
960
950
.... 'C:......
V
/ /
940 939.2--.J;..--~-v,
/I I
I I
L V 36.49 920 JV
'; 919.. /' I
~ 918 JV ' I
.:, 917 V I
_g 916,,, /
... /'
~ 915
UJ 9(4 I I I
913 -
912 I i
I
9 J '2 I f.
3 4 5 6 7 8 9 10 20 30 40 50 60 708090)00 Discharge in 10,000 cfs
DISCHARGE RATING.CURVE MISSISSIPPI RlVER AT MONTICELLO, MlNN.
IU."RZ~ EHGINE£R1NO COMP-A.NY OWG HO. 413 r a IU,1', /9-0l:I REV 4 12/85 MONTICELLO
EXHIBIT 9
4O0r-----,-----r-----r------
..
- 250 0
','i J 0 0 L.-_,:_... 0 200
.5
USO CD t,I
_g -
u 0
- 100
10 20 30 40 50 Tlme In days PROBABLE MAXIMUM FLOOD HYDROGRAPH MISSISSIPPI RIVER AT MONTICELLO, MINN.
REV 4 12/85