science 

USGS

for a changing world

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Flood Hydrology for Dry Creek, Lake County, Northwestern Montana

-Charles Parrett and Robert D. Jarrett

GO

Abstract

Dry Creek is a small stream that drains 

about 8.74 square miles of rugged 

mountainous terrain upstream from 

Tabor Dam in the Mission Range near 

St. Ignatius, Montana. Because of uncertainty in plausible peak discharges 

and concerns regarding the ability of 

the Tabor Dam spillway to safely convey these discharges, the flood hydrology for Dry Creek was evaluated on 

the basis of three hydrologic and geologic methods. The first method involved determining an envelope line 

relating flood discharge to drainage 

area on the basis of regional historical 

data and calculating a 500-year flood 

for Dry Creek using a regression equation. The second method involved paleoflood methods to estimate the 

maximum plausible discharge for 35 

sites in the study area. The third method involved rainfall-runoff modeling 

for the Dry Creek basin in conjunction 

with regional precipitation information to determine plausible peak discharges. All of these methods resulted 

in, estimates of plausible peak discharges that are substantially less than 

those predicted by the more generally 

applied probable maximum flood 

technique.

INTRODUCTION

Dry Creek is a small stream that drains 

about 4.5 square miles of rugged 

mountainous terrain before entering 

St. Mary Lake in the Mission Range 

near St. Ignatius, Montana (fig. 1). St. 

Mary Lake was a natural lake impounded by glacial debris prior to the 

construction of Tabor Dam in 1930.

Initial construction included an embankment across the outlet of Dry 

Creek, a second embankment across 

the low saddle of the existing glacial 

moraine at the downstream end of the 

lake, and a spillway. Subsequent construction in 1940 and 1952 raised both 

embankments about 20 feet and widened the spillway (Lockhart, 1993). 

The total drainage area upstream from 

the dam is about 8.74 square miles.

Because of concerns about the safety 

of Tabor Dam in the event of a large 

earthquake or flood, the Bureau of 

Reclamation evaluated the geologic 

stability of the embankments and 

foundation and the ability of Tabor 

Dam to safely pass the Probable Maximum Flood (PMF)--the flood that can 

be expected from the most severe 

combination of critical meteorologic 

and hydrologic conditions that are reasonably possible in a region (National 

Research Council, 1988). Although 

the geological investigation determined that the foundation was generally stable and that the embankments 

had relatively low potential for liquefaction, the calculated PMF would 

overtop the embankments and exceed 

the spillway capacity. The estimated 

costs to upgrade the spillway to PMF 

standards are about $2.5 million 

(Mike Brown, Safety of Dams Coordinator, Confederated Salish and 

Kootenai Tribes, oral commun., 

1998).

Purpose and Scope

To help determine whether the PMF 

estimates for Dry Creek are reasonable in light of historical and geological evidence, the U.S. Geological 

Survey (USGS), in cooperation with 

the Confederated Salish and Kootenai 

Tribes, undertook a flood hydrology 

investigation of Dry Creek and other 

nearby basins on the west side of the 

Mission Range in Lake County, Montana. This report describes the results 

of that investigation. The investigation used three essentially independent methods to estimate extreme 

floods for Dry Creek. First, recorded 

flood-discharge data from 9 sites in 

the Mission Range study area (fig. 1) 

and 81 sites in western Montana were 

used to develop a regional envelope 

line relating flood discharge to drainage area, and a regional regression 

equation was used to calculate a 500- 

year flood magnitude for Dry Creek. 

Second, plausible maximum discharge was estimated for 35 sites in 

the Mission Range study area using 

paleoflood techniques. Third, rainfall-runoff modeling was used to estimate an extreme flood discharge for 

Dry Creek using a synthetic storm 

based on regional extreme precipitation in Montana. Results from the 

three independent methods were compared to two PMF estimates, one 

based on a thunderstorm and one 

based on a general storm.

Acknowledgments

Many individuals and landowners assisted with the study. Particular 

thanks are given to Mike R. Brown, 

Safety of Dams Coordinator for the 

Confederated Salish and Kootenai 

Tribes, who provided background

U.S Department of the Interior 

U.S. Geological Survey 1

WRIR 00-4069 

June 2000
R.21W. 114°15' R.17W. 113°45'

CSKT 356200. E*PLANATION 

12378000A STREAMFLOWGAGING STATION 

AND NUMBER

34 « PALEOFLOOO 47 °'=' 

ESTIMATION SITE 

AND NUMBER

Figure 1 . Location of streamflow-gaging stations and paleoflood estimation sites on streams draining the west side of the Mission 

Range, Montana.

reports, hand tools and equipment, letters of authorization for access to 

streams in the study area, and general 

support for the project. Thanks also 

are given to Dave R. Johnson and 

Stephen R. Holnbeck (USGS), who 

assisted with field work and helped 

the authors interpret and review the 

data, and to J.E. O'Connor (USGS), 

whose thorough review of the report 

resulted in many improvements.

FLOOD HYDROLOGY

Information about past floods in the 

study area, both from streamflow-gaging station records and geologic evidence, together with information 

about rare storms and the rainfall-runoff process, can increase understanding of the magnitude of extreme 

floods in the study area. The following sections describe (1) flood history 

of the study area and use of an envelope line and a regional regression

equation to estimate large floods for 

Dry Creek, (2) paleoflood methods for 

determination of plausible floods and 

application to the study area, (3) rainfall-runoff modeling of an extreme, 

synthetic storm on the Dry Creek basin above St. Mary Lake, and (4) comparisons of these results with PMF 

estimates for Dry Creek.

Flood History

Dry Creek drains the western side of
the southern part of the rugged Mission Range in northwestern Montana. 

The core of the Mission Range was 

deeply gouged by Pleistocene glaciers, and headwater streams, such as 

Dry Creek upstream from St. Mary 

Lake, are very steep with alternating 

sections of bedrock cataracts and alluvial, bouldery V-shaped channels. 

Away from the core of the Mission 

Range, stream slopes decrease, and 

the gravelly channels are flanked by 

levees of debris-flow deposits and isolated terrace remnants.

Mean annual precipitation in the study 

area ranges from about 15 inches in 

the valley floor to about 60 inches at 

the Mission Range crest (Parrett, 

1997). Most precipitation falls as 

snow, and most runoff peaks result 

from snowmelt in conjunction with 

spring rainstorms.

Large storms in the Mission Range 

typically originate in the Pacific 

Ocean and arrive from the west. 

Large storms that arise in the Gulf of 

Mexico and produce large floods in 

some mountainous areas of Montana 

do not significantly affect the west

side of the Mission Range. For example, the large 1964 storm that came 

from the Gulf and caused extreme 

flooding along both sides of the Continental Divide in Montana caused relatively minor flooding on Mission 

Range streams (Boner and Stermitz, 

1967).

Nine streamflow-gaging stations that 

have at least 10 years of peak-discharge data are located on streams that 

drain the west side of the Mission 

Range. The stations, drainage areas, 

number of years of record, and maximum annual-peak discharges are 

shown in table 1. Although the peakdischarge records are relatively short 

(10 to 26 years) and mostly recent, 

two peaks shown on table 1 are for the 

flood of 1908, one of the largest regional floods in western Montana in 

the last 100 years (Merritt, 1990).

The log-Pearson probability distribution was fit to the peak-discharge 

record at each station in table 1 as described by the Interagency Advisory 

Committee on Water Data (1982). 

The fitted log-Pearson probability distribution can be used to calculate peak

discharge for any specified exceedance probability. The reciprocal of 

exceedance probability, commonly referred to as recurrence interval, represents the average time, in years, 

between exceedances of a given flood 

magnitude and may be used to characterize extreme floods on a probabilistic basis. For example, a flood 

magnitude having an exceedance 

probability of 0.002 is an extreme 

flood that is exceeded, on average, 

once in 500 years. The peak discharge 

having a 500-year recurrence interval, 

commonly referred to as the 500-year 

flood, was calculated for each of the 

nine stations in the Mission Range 

study area (table 1). Because the logPearson probability distribution may 

yield unreliable estimates of flood 

magnitude when the record length is 

significantly shorter than the recurrence interval, the calculated 500-year 

floods for the Mission Range study 

area were compared with those for a 

larger regional data set.

The Mission Range study area lies in 

the West Region, a portion of western 

Montana having common floodTable 1. Streamflow-gaging stations and flood data for streams draining the west side of the Mission Range, Montana

Station 

number

12371100

CSKT 356200

CSKT351200

12375900

12376000

12377150

12378000

12381400

12383500

-

,

Station name

Hell Roaring Creek near Poison

Mud Creek above Pablo Feeder Canal

North Crow Creek at campground

South Crow Creek near Ronan

Crow Creek near Ronan

Mission Creek above reservoir, near St. Ignatius

Mission Creek near St. Ignatius

South Fork Jocko River near Arlee

Big Knife Creek near Arlee

Drainage

area 

(square *

miles)

6.22

2.34

10.6

7.57

46.1

12.4

74.8

56.0

6.88

Years of 

record

26

13

16

16

10

16

11

16

17

Period of 

record

1917-32,1948,

1959-67,1980,

1982-97

1982-97

1983-98

1983-98

1907-17

1983-98

1907-17

1983-98

1982-98

Maximum

peak

discharge

(cubic feet

per second)

160

90

685

312

'1,400

706

'1,700

1,220

100

Peak 

discharge

having

500-year 

recurrence

interval

(cubic feet

per second)

280

120

1,200

600

1,200

880

1,100

1,700

130

Maximum peak discharge occurred in 1908 and is believed to be the largest in past 100 years.
frequency characteristics defined by 

Omang (1992). Omang (1992) 

applied the log-Pearson probability 

distribution to 81 stations in the West 

Region having a total of 1,710 stationyears of record and calculated peak 

discharges having recurrence intervals 

up to 500 years. To indicate the range 

of maximum flood experience in the 

West Region compared to that in the 

Mission Range study area, the maximum known flood at each of the 9 stations in the study area and at each of 

the 81 stations used by Omang (1992) 

was plotted on a log-log basis relating 

discharge to drainage area, and an envelope line encompassing the plotted 

data was hand-drawn (fig. 2). Maximum recorded floods in the Mission 

Range study area plotted well within 

the range of maximum floods in the 

West Region and well below the envelope line.

The calculated 500-year flood discharges for stations in the Mission 

Range study area (table 1) and those 

calculated by Omang (1992) also were 

plotted on a log-log basis relating discharge to drainage area (fig. 3). The 

calculated 500-year floods in the Mission Range study area were well within the range of calculated 500-year 

floods for the West Region. The envelope line encompassing maximum recorded floods in the West Region (fig. 

2) is also shown on figure 3 for comparison of maximum recorded floods 

with calculated 500-year floods. The 

relatively good agreement between recorded maximum and calculated 500- 

year floods in the Mission Range 

study area with those in the West Region indicate that extreme flood experience is similar in the two areas and 

that methods for estimation of large 

floods in the West Region are applicable in the Mission Range study area. 

Accordingly, a regression equation 

using drainage area and mean annual 

precipitation as explanatory variables 

developed by Omang (1992) was used 

to calculate a 500-year flood magnitude of 490 cubic feet per second for

Dry Creek at Tabor Dam (drainage 

area = 8.74 square miles). The standard error of prediction for the regression equation, 55 percent (Omang, 

1992), was used to calculate an upper 

bound for the estimated 500-year 

flood for Dry Creek as 490 cubic feet 

per second plus 55 percent of 490 cubic feet per second, or 760 cubic feet 

per second. Both values of calculated 

500-year flood are plotted on figure 3.

Although figures 2 and 3 provide reasonable information about the magnitude of large floods on Dry Creek 

based on regional flood experience, 

the information is not sufficient to estimate the magnitude of large floods 

necessary for assessing dam safety. 

Two independent methods for estimating flood magnitudes for dam 

safety are based on paleoflood estimation methods and rainfall-runoff modeling using regionalized extremestorm depths.

Paleoflood Methods

Paleoflood hydrology is the study of 

floods that occurred prior to the collection of systematic flood records or 

direct measurements (Costa, 1986). 

Such prehistoric floods are evidenced 

by geologic and botanical features in 

and adjacent to the stream channels. 

In mountainous areas of the western 

United States where glaciation has extensively reworked channel deposits, 

paleoflood evidence pertinent to modern climatic regimes generally is limited to about the last 10,000 years. 

Paleoflood evidence in mountainous 

areas generally consists of bouldery 

bar deposits, gravel deposits on flanking terraces, and, on a shorter time 

scale, scars on trees in the flood plain. 

This kind of evidence serves to identify the maximum height or stage of 

floodwater from large-magnitude 

floods at a site. Although some paleoflood studies have identified a series 

of past flood stages, commonly the 

only identifiable stage is that for the 

largest flood. An identifiable deposit

or mark associated with a paleoflood 

is termed a paleostage indicator (Jarrett, 1991).

The absence of flood evidence can 

also provide useful information on 

past large-magnitude flood stages. 

The altitude of a streamside land surface that shows no evidence of paleoflood deposition or erosion can be 

considered a maximum limit for the 

stage of past floods (Levish and 

others, 1994, and Ostenaa and others, 

1996, 1997).

Once a paleostage indicator or maximum limit for flood stage has been 

identified, discharge can be calculated 

by application of various hydraulic engineering methods, such as slope-area 

calculations, critical-depth calculations, normal-depth calculations, or 

step-backwater analyses (Barnes and 

Davidian, 1978). Slope-area calculations and step-backwater analyses are 

based on the principle of the conservation of kinetic and potential energy 

through a stream reach and require 

measurement of cross-sectional flow 

areas at several locations in the reach. 

Critical-depth and normal-depth calculations provide at-site estimates of 

discharge and require measurement of 

cross-sectional flow area at a single 

location. Thus, an implicit assumption for application of all hydraulic 

methods is that channel geometry has 

not significantly changed since the paleoflood. This assumption limits strict 

application of paleoflood methods to 

stream channels, such as those in 

mountainous settings, whose dimensions are largely controlled by bedrock outcrops.

Although the slope-area and stepbackwater methods require more 

channel-geometry data than the critical-depth and normal-depth methods, 

their use may be unwarranted for 

many paleoflood applications where 

stages, cross-sectional areas, and 

knowledge about channel friction 

losses during paleoflood conditions
100,000

o 

o

LU 

CO

DC 

LU 

Q_

LLJ 

C3

tr 

<

o

CO

Q

10,000

LU 

LL

O 1,000 

CQ

O

100

10

0.1 1 10 100 1,000 10,000 

DRAINAGE AREA, IN SQUARE MILES

EXPLANATION

Maximum recorded flood in 

West Region

Maximum recorded flood in 

Mission Range study area

Envelope line for maximum 

recorded floods in West 

Region

Figure 2. Maximum recorded floods in the study area and in the West Region, Montana.

100,000

o 

o

LLJ 

CO 

DC 

HI 

0_

LU

o

EC

< I 

o

CO

Q

10,000

L1J

LL

9 1,000

CO

o

100

10

n

n

0.1 1 10 100 1,000 

DRAINAGE AREA, IN SQUARE MILES

10,000

EXPLANATION

Envelope line for maximum 

recorded floods in West 

Region (from fig. 2)

Calculated 500-year flood discharge 

in West Region

Calculated 500-year flood discharge 

in Mission Range study area

Calculated 500-year flood discharge 

for Dry Creek at Tabor Dam

Calculated 500-year flood discharge 

for Dry Creek at Tabor Dam plus one 

standard error

Figure 3. Estimated 500-year floods in the study area and the West Region, Montana.

are very imprecise, at best. The 

critical-depth method, which is based 

on the assumption that critical flow 

occurs at the cross section, is the only 

method that does not require an estimate of channel friction loss (Manning's roughness coefficient). 

Because super-critical flow conditions 

are very unlikely for extended reaches

in natural streams (Jarrett, 1984), critical flow generally represents the 

maximum discharge for a given stage. 

In addition, because flow conditions 

that approach critical flow are likely 

only for very steep natural channels, 

the critical-depth method is particularly well suited for paleoflood estimation on steep mountain streams.

Under these conditions, estimates 

from the critical-depth method are 

most likely to overpredict peak discharge. Thus, all paleoflood discharge 

estimates for this study were based on 

the critical-depth method. The equation for calculation of critical discharge (discharge at critical depth) in 

an irregular channel (Henderson,
1969, p. 51) is the following:

Q = (gA3 /T)°- 5 (1)

where Q is the discharge, in cubic 

feet per second,

g is the acceleration of 

gravity (32.2 feet per second squared),

A is the cross-sectional area 

of flow, in square feet, 

and

T is the top width of flow, 

in feet.

In the study area, no evidence of 

paleoflood erosion or deposition was 

found at most sites. Large, ancient 

mid-channel flood bars were found at 

three sites (table 2), Mission Creek 

above Mission Reservoir (sites 14 and 

15) and Dry Creek above St. Mary 

Lake (site 18). Because of uncertainty 

about channel geometry at the time the 

ancient bars were formed, the discharge at the time of bar formation 

could not be estimated. Nevertheless, 

the altitude of these bars represent 

maximum limits for flood stage since 

bar formation, and maximum flood 

discharge was estimated at these sites 

by calculating the discharge that 

would significantly overtop the bars. 

Because flood depth on a bar greater

than about 1 foot was considered likely to severely erode soil surfaces and 

deposit additional sand or gravel bars, 

significant overtopping was considered to be a depth of 1 foot. Although 

no bars were age dated, the period 

since formation was assumed to be at 

least several hundred years, on the basis of the large fir and cedar trees 

growing on the well-developed soil 

profile on the bar surfaces.

At other estimation sites, the maximum limits for flood stage were the 

tops of adjacent stream banks where 

no evidence of previous flood erosion 

or deposition was found. Flood stages 

greater than about 1 foot above the 

banks were considered likely to leave 

evidence of erosion and deposition. 

Consequently, the limit of paleoflood 

discharge was estimated at these sites 

by making critical-depth calculations 

for stages corresponding to the tops of 

banks, plus 1 foot.

The paleoflood discharge estimation 

sites are shown on figure 1, and the resulting limits on paleoflood discharge 

are tabulated in table 2. Table 2 indicates the values of the variables used 

in the critical-depth calculations and, 

for some sites, the estimated age of the

bank surfaces used as the maximum 

limits of flood stage. At some sites, 

the ages of the bank surfaces were estimated on the basis of estimated ages 

of large trees or surface soils. These 

estimated ages, although highly approximate at best, provide some gross 

indication of the frequency of large 

overtopping floods. At one site on 

Dry Creek (site 17), the age of the 

bank surface could be determined fairly reliably because of the presence of 

undisturbed ash deposits. Based on 

previous age dating of ash deposits in 

northwestern Montana (Carrara, 

1989), the ash deposit on the Dry 

Creek site was identified as the late 

Quaternary Mazama ash from about 

6,800-6,900 years before present. 

Thus, the frequency of overtopping at 

this Dry Creek site is less than once 

every 6,800-6,900 years, indicating 

that floods larger than the overtopping 

flood are extremely rare. One other 

site, Post Creek above McDonald 

Lake (site 13), had undisturbed, finegrained soil on the bank surface that 

also might be Mazama ash.

Because Dry Creek was the particular 

stream of interest for this study,

Late Quaternary Mazama ash about 4 inches below the surface found on the right bank of Dry Creek
Table 2. Paleoflood estimation sites for streams draining west side of Mission Range, Montana

Site 

number 

(fig. 1)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17 

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Stream

Mud Creek above Pablo Feeder Canal

Mud Creek above Pablo Feeder Canal

Mud Creek above Pablo Feeder Canal

Mud Creek above Pablo Feeder Canal

North Crow Creek above Pablo Feeder Canal

North Crow Creek above Pablo Feeder Canal

North Crow Creek above Pablo Feeder Canal

North Crow Creek above Pablo Feeder Canal

Lost Creek above Pablo Feeder Canal

South Crow Creek above Pablo Feeder Canal

South Crow Creek above Pablo Feeder Canal

South Crow Creek above Pablo Feeder Canal

Post Creek above McDonald Lake

Mission Creek above Mission Reservoir

Mission Creek above Mission Reservoir

Mission Creek above Mission Reservoir

Dry Creek above St. Mary Lake 

Dry Creek above St. Mary Lake

Dry Creek above St. Mary Lake

Dry Creek above St. Mary Lake

Dry Creek above St. Mary Lake

Dry Creek above St. Mary Lake

Dry Creek above St. Mary Lake

Dry Creek above St. Mary Lake

Dry Creek above St. Mary Lake

Dry Creek above St. Mary Lake

Dry Creek below St. Mary Lake

Dry Creek below St. Mary Lake

Power Creek near mouth

Power Creek near mouth

Unnamed Dry Creek tributary above unnamed reservoir

Unnamed Dry Creek tributary below unnamed reservoir

Cold Creek near mouth

Sabine Creek near St. Ignatius

Middle Fork Jocko River near Arlee

Drainage area 

(square miles)

2.34

2.34

2.34

2.34

10.6

10.6

10.6

10.6

2.77

7.53

7.53

7.53

16.4

12.3

12.3

12.3

3.95

4.54

4.54

4.54

4.54

4.54

4.54

4.54

4.54

4.54

8.74

8.74

1.31

1.31

2.16

2.85

4.07

1.73

25.7

Flow area 

(A) 

(square 

feet)

124

72

142

176

315

430

290

685

176

105

280

268

324

194

237

490

174 

314

173

190

204

173

164

330

150

380

180

204

47

41

40

21

21

100

380

Flow width 

(T) 

(feet)

35

23

31

35

85

127

83

215

35

30

50

72

144

53

61

83

88 

41

41

50

36

74

31

66

25

81

45

60

24

28

65

21

14

100

90

Limit of 

palcoflood 

discharge

(Q)

(cubic feet per 

second)

1,300

720

1,700

2,200

3,400

4,500

3,100

6,900

2,200

1,100

3,800

2,900

2,700

2,100

22,800

6,800

1,400 

3 4,900

2,000

2,100

2,800

1,500

2,100

4,200

2,100

4,700

2,000

2,100

370

280

180

120

150

570

4,400

Estimated age 

of bank 

surface 

(years)

--

200

>500

--

--

>500

--

--

--

<100

--

'6,800-6,900

200

--

'6,800-6,900

-

-

-

100

100

-

-

--

-

"

-

--

--

~

100

-

--

Age estimated from possible late Quaternary Mazama ash sample. 

Includes overbank flow estimated at 130 cubic feet per second. 

Large discharge estimate may reflect channel degradation.
several estimates of the limits of 

paleoflood discharge were made 

above St. Mary Lake, and two esti- ,. . 

mates were made below St. Mary 

Lake. The estimates below St. Mary 

Lake were just downstream from Tabor Dam, where the drainage area for 

Dry Creek was the same as for Dry 

Creek at Tabor Dam. Multiple estimates were made at several other 

streams as well. The multiple estimates sometimes varied widely, 

largely due to the variable channel geometry at sites where maximum limits 

of flood stage could be identified. For 

example, the estimated overtopping 

flood discharge might be relatively 

small for banks that were only a foot 

or two above the present water surface. Conversely, the estimated overtopping flood discharge might be 

relatively large where the bank surface 

was a terrace several feet above the 

present water surface. The estimated 

ages of the bank surfaces also varied 

widely; but surfaces that were higher, 

relative to the present water surface,

tended to have larger trees and thicker, 

well-formed, undisturbed soils than 

bank surfaces that were lower.

The stream cross section for the Dry 

Creek site (site 17) having undisturbed 

Mazama ash on the bank surface is 

shown in figure 4. The limit of paleoflood discharge for site 17 1,400 cubic feet per second is considered to 

be the best single estimate for the 

study area because the maximum limit 

of flood stage was readily identifiable 

and reliably age dated, and the bedrock-controlled channel geometry was 

considered to be stable over time.

Rainfall-Runoff Modeling

Rainfall-runoff modeling based on 

precipitation events with large recurrence intervals offers an independent 

means for estimating low-frequency 

flood magnitude. A recent report by 

Parrett (1997) described methods for 

estimating rainfall depths for 2-, 6-, or 

24-hour duration rainstorms having 

recurrence intervals up to 5,000 years.

The method is based on application of 

the Generalized Extreme Value 

(GEV) probability distribution to 

pooled dimensionless rainfall-depth 

data for three regions in Montana. 

Within each region, the estimated 

equivalent record length of the pooled 

data ranged from 660 to 4,900 years. 

Equivalent record length is significantly shorter than total station years 

of pooled data because of the effects 

of interstation correlation. At-site 

storm rainfall depths for various nonexceedance probabilities (quantiles) 

are calculated from the dimensionless 

data as follows:

Q,{F) = n (2)

where

Qi(F) is the quantile of nonexceedance probability F at site /,

jl, is the mean storm rainfall depth at site i, and

q(F) is the dimensionless 

regional quantile of 

non-exceedance probability F.

10

ti

UJ

D 

CC

CD 

CC 

< 

LJJ

O 6

CD

CL 

LU

Estimated maximum limit of paleoflood. Top width ( T ) = 88 feet

Significant overtopping depth = 1 foot

Maximum limit for flood stage

Flow area ( A ) = 174 square feet

Location of 

undisturbed 

late Quaternary 

Mazama ash

10 20 30 40 50 60 70 80

DISTANCE FROM LEFT EDGE OF CHANNEL SECTION, IN FEET

90 100

Figure 4. Channel geometry of Dry Creek above St. Mary Lake at paleoflood estimation site 17, Montana.

8
The dimensionless regional quantiles 

are calculated from the GEV distribution as follows:

, (3)

where

ly a, and K are GEV distribution parameters that 

vary by region and by 

storm duration.

Equation 3 was used to calculate dimensionless storm rainfall depths for 

two 2-hour duration storms in the region that includes the Mission Range 

study area. One depth was calculated 

for a recurrence interval of 500 years 

(non-exceedance probability = 0.998) 

so that the rainfall-runoff model could 

be calibrated to match the upper 

bound of 500-year flood discharge for 

Dry Creek at Tabor Dam determined 

from the regional regression equation 

(760 cubic feet per second) developed 

by Omang (1992). The second depth 

was calculated for a recurrence interval of 5,000 years (non-exceedance 

probability = 0.9998), the largest recurrence interval for which the 

method for storm-rainfall-depth estimation is considered to provide reliable results (Parrett, 1997). The 2- 

hour duration storm, rather than the 6- 

or 24-hour duration storm, was used

for rainfall-runoff modeling because 

the 2-hour duration was considered to 

be more applicable to a small drainage 

basin (Parrett, 1997) such as Dry 

Creek at Tabor Dam than the longer 

duration storms. The resultant 2-hour 

duration dimensionless rainfall depths 

for a 500-year and a 5,000-year recurrence interval storm were 3.54 and 

5.47, respectively.

Storm rainfall depth expressed in 

inches is calculated from equation 2 

by multiplying dimensionless storm 

rainfall depth by the mean value of annual maximum 2-hour storm rainfall 

depth for the selected site. Mean annual maximum storm rainfall depth, in 

turn, is calculated from regression 

equations using latitude, longitude, 

and mean annual precipitation (Parrett, 1997). Values of mean annual 

maximum 2-hour storm rainfall depth 

were calculated for five locations 

evenly distributed within the Dry 

Creek basin above Tabor Dam and averaged to produce a basin-mean estimate of 0.584 inches.

Finally, the basin-mean storm rainfall 

depths for Dry Creek at Tabor Dam 

for a 500-year and a 5,000-year recurrence interval were calculated from 

equation 2 as:

Qi(0.998) = fii? (0.998),

2/0.998) = 0.54(3.54),

fi,<0.998) = 2.07 inches,

and

£{0.9998) = 0^(0.9998), 

£(0.9998) = 0.584(5.47) 

£ (0.9998) = 3.19 inches

A design hyetograph for each 2-hour 

rainstorm was developed using methods that are based on a probabilistic 

assessment of storm data in Montana 

(Parrett, 1998). Each design hyetograph was developed for a total period 

of storm activity of 4 hours to account 

for rainfall that typically occurs before 

and after a period of intense precipitation (Parrett, 1998, p.7, 29). The hyetographs were based on median or 

typical temporal distribution patterns 

for large storms described by Parrett 

(1998), and the calculated at-site rainfall depths for 5-minute time increments were adjusted to provide basinmean values for the 8.74 square mile 

basin above Tabor Dam. Figure 5 

shows the resultant design hyetographs for the 500-year and 5,000- 

year recurrence intervals for the Dry 

Creek basin above Tabor Dam. Total 

rainfall depths for the 4-hour periods

CZI

0.5 1.0 1.5 2.0 2.5 3.0 

TIME FROM BEGINNING OF STORM, IN HOURS

3.5 4.0

EXPLANATION

5,000-year recurrence interval 

(total depth for 4 hours = 3.31 inches)

500-year recurrence interval 

(total depth for 4 hours = 2.14 inches)

Figure 5. Storm hyetographs for the area of Dry Creek basin above Tabor Dam, Montana.
of storm activity for the 500-year and 

5,000-year recurrence intervals were 

2.14 and 3.31 inches, respectively.

To determine the flood peaks resulting 

from the storm hyetographs in figure 

5, the HEC-1 rainfall/runoff model 

(U.S. Army Corps of Engineers, 1990) 

was used. This model uses one of several unit-hydrograph and infiltrationloss methods to develop a discharge 

hydrograph resulting from a basinaveraged rainfall input. For this analysis, the Clark unit hydrograph and the 

runoff Curve Number method (U.S. 

Army Corps of Engineers, 1990) for 

estimating infiltration losses were 

used to determine the discharge 

hydrographs for the Dry Creek basin 

above Tabor Dam.

Application of the Clark unit hydrograph requires estimates of basin 

time of concentration, tc, and storage 

coefficient, R. These values were estimated from regression equations developed for large storms in Montana 

(Holnbeck and Parrett, 1996) and 

found to be 1.2 hours and 5.7 hours, 

respectively. The runoff Curve Number was used as the calibration variable and was varied until the peak 

discharge from the model for the 500- 

year storm hyetograph matched the 

upper bound of 500-year peak discharge determined from the regional 

regression equation (760 cubic feet 

per second). The resultant runoff 

Curve Number of 85 is representative 

of a mountainous, partly forested basin having relatively low infiltration in 

western Montana.

The HEC-1 model with the selected 

values for tc, R, and runoff Curve 

Number was considered to be calibrated for use in modeling large-storm 

runoff from Dry Creek and was then 

used to calculate the discharge peak 

from the 5,000-year storm hyetograph. The resultant peak discharge 

from the 5,000-year storm hyetograph 

was 1,340 cubic feet per second. The

HEC-1 model calculates runoff from 

the storm only and does not include 

stream baseflow preceding the storm. 

As discussed by Parrett (1998), the 

most likely time for a large storm to 

occur in the Mission Range study area 

is in May or June, when streamflow is 

already high from snowmelt runoff. 

For this analysis, the baseflow was 

presumed to be about bankfull discharge, or about 120 cubic feet per 

second, at the time of the 5,000-year 

storm. Thus, the total estimated 

5,000-year peak discharge for Dry 

Creek basin above Tabor Dam is 

1,460 cubic feet per second.

Comparison of Extreme Flood 

Estimates

The results from the three methods for 

evaluating extreme floods on Dry 

Creek are summarized on figure 6. 

The envelope line for maximum recorded floods in the West Region, two 

estimates of 500-year flood discharge 

for Dry Creek at Tabor Dam based on 

a regional regression equation, the estimated 5,000-year flood discharge 

determined for Dry Creek at Tabor 

Dam by rainfall-runoff modeling, and 

the 35 estimates of maximum limit of 

paleoflood discharge in the Mission 

Range study area are plotted on figure 

6. The estimated limit of paleoflood 

discharge for Dry Creek at the site 

having the undisturbed late Quaternary Mazama ash is highlighted on figure 6, because it was considered to be 

the best estimate based on paleoflood 

methods. The best estimate for extreme flood discharge based on paleoflood methods (1,400 cubic feet per 

second) is remarkably close to the estimated 5,000-year flood discharge 

from rainfall-runoff modeling (1,460 

cubic feet per second), but the drainage area for the paleoflood estimate 

(3.95 square miles) is less than half 

that for the rainfall-runoff estimate 

(8.74 square miles). Expressed in 

terms of unit discharge (discharge 

divided by drainage area), the best

paleoflood estimate for Dry Creek 

(354 cubic feet per second per square 

mile) is larger than the 5,000-year unit 

discharge from rainfall-runoff modeling (167 cubic feet per second per 

square mile). Given that the paleoflood estimate represents a limit on 

extreme flooding since the time of 

Mazama ash deposition (about 6,800- 

6,900 years before present), the larger 

paleoflood unit discharge is not unexpected.

Figure 6 also includes two estimates 

of PMF for Dry Creek basin above Tabor Dam provided by the Bureau of 

Reclamation (Kamstra, 1998). One 

estimate (27,900 cubic feet per second) is based on the assumption that a 

thunderstorm provides the Probable 

Maximum Precipitation (PMP) over 

the basin, and the other estimate 

(10,000 cubic feet per second) is based 

on the assumption that the PMP results from an areally larger, but less 

intense, general storm. The depth for 

the thunderstorm PMP was 10.6 inches over a 6-hour duration, and the 

depth for the general storm PMP was 

28.0 inches over a 72-hour duration. 

As shown on figure 6, both PMF estimates plot well above the extreme 

flood magnitudes estimated for Dry 

Creek using the three independent 

methods for this study.

SUMMARY

Three methods of hydrological and 

geological analysis to evaluate the 

magnitude of extreme floods in the 

Dry Creek basin of northwestern 

Montana provided mutually consistent estimates of plausible peak discharges. The first method used 

limited recorded flood data from within the Mission Range study area together with more extensive flood data 

from a larger region in western Montana. Maximum recorded discharges 

in the study area were within the range 

of maximum recorded discharges in 

the West Region and well below an 

envelope curve encompassing all

10
100,000

o 

o 111

w 10,000

DC

LU

Q.

LLJ 

LLJ 

LL

O 

m

Z>

o

LU 

O

rr 

<

o

CO 

D

1,000

100

10

0.1 1.0 10 100 

DRAINAGE AREA, IN SQUARE MILES

1,000

EXPLANATION

Envelope line for maximum d Calculated 500-year flood discharge

recorded floods in West Region 

(from fig. 2)

Maximum limit of paleoflood 

discharge in Mission Range 

study area

Maximum limit of paleoflood 

discharge for Dry Creek above 

St. Mary Lake (site 17)

Calculated 500-year flood discharge 

for Dry Creek at Tabor Dam 

(from fig. 3)

for Dry Creek at Tabor Dam plus one 

standard error (from fig. 3)

O Estimated 5,000-year flood discharge 

for Dry Creek based on rainfall-runoff 

modeling

^ Estimates for probable maximum 

flood (PMF) for Dry Creek 

( Kamstra, 1998)

Figure 6. Summary of maximum recorded and estimated flood discharges in the study area and the West Region, Montana.

maximum recorded discharges in the 

West Region. Calculated 500-year 

flood discharges for stations in the 

study area also were comparable to 

those for stations in the West Region. 

A regression equation developed for 

use in the West Region was used to 

calculate the 500-year flood (490 cubic feet per second) and an upper 

bound value for the 500-year flood 

(760 cubic feet per second) for Dry 

Creek above Tabor Dam.

The second method used paleoflood 

techniques to estimate maximum limits of paleoflood stage at 35 sites in the 

Mission Range study area. The critical-depth method was used to estimate

discharge for the maximum limits for 

paleoflood stage. The single best estimate for the limit of paleoflood discharge (1,400 cubic feet per second) 

was for a site on Dry Creek above St. 

Mary Lake where the maximum limit 

of flood stage was readily identifiable 

and reliably age-dated, based on the 

presence of undisturbed Mazama ash, 

at about 6,800-6,900 years before 

present.

The third method used regional extreme precipitation data for Montana 

to develop a synthetic storm for the 

Dry Creek basin having a 5,000-year 

recurrence interval. The synthetic 

storm was used in a rainfall-runoff

model to estimate a 5,000-year flood 

discharge for Dry Creek at Tabor Dam 

(1,460 cubic feet per second). Results 

from all three methods were significantly smaller than two previously estimated values of PMF (10,000 and 

27,900 cubic feet per second).

REFERENCES

Barnes, H.H., Jr., and Davidian, Jacob, 

1978, Indirect methods, in Hershey, 

R.W., ed., Hydrometry-Principles 

and practices: New York, Wiley, p. 

149-204.

Boner, F.C., and Stermitz, Frank, 1967, 

Floods of June 1964 in northwestern 

Montana: U.S. Geological Survey 

Water-Supply Paper 1840-B, 242 p.

11
Carrara, P.E., 1989, Late Quaternary

glacial and vegetative history of the 

Glacier National Park region, 

Montana: U.S. Geological Survey 

Bulletin 1902, 64 p.

Costa, J.E., 1986, A history of paleoflood 

hydrology in the United States: EOS, 

Transactions of the American 

Geophysical Union, v. 67, no. 17, p. 

428-430.

Henderson, F.H., 1969, Open channel 

flow: New York, MacMillan 

Company, 108 p.

Holnbeck, S.R., and Parrett, Charles,

1996, Procedures for estimating unit 

hydrographs for large floods at 

ungaged sites in Montana: U.S. 

Geological Survey Water-Supply 

Paper 2420, 60 p.

Interagency Advisory Committee on 

Water Data, 1982, Guidelines for 

determining flood flow frequencyBulletin 17B of the Hydrology 

Subcommittee: U.S. Geological 

Survey, Office of Water Data 

Coordination, 183 p.

Jarrett, R.D., 1984, Hydraulics of highgradient streams: Journal of 

Hydraulic Engineering, v. 110, no. 

11, Nov. 1984, p. 1519-1539.

Jarrett, R.D., 1991, Paleohydrology and 

its value in analyzing floods and 

droughts: U.S. Geological WaterSupply Paper 2375, p. 105-116.

Kamstra, L.A., 1998, Tabor Dam

Montana, probable maximum flood 

study: Bureau of Reclamation, 

various paging.

Levish, D.R., Ostenaa, D.A., and

O'Connell, D.R.H., 1994, A noninundation approach to paleoflood 

hydrology for the event-based 

assessment of extreme flood hazards, 

in Association of State Dam Safety 

Officials, 11 th Annual Conference 

Proceedings, Lexington, Kentucky, 

p. 69-82.

Lockhart, A.C., 1993, Geologic report for 

deficiency verification analysis, 

Tabor Dam, Flathead Agency 

irrigation division, Montana: Bureau 

of Reclamation, various paging.

Merritt, L.A., 1990, Montana floods and 

droughts, in National Water 

Summary 1988-89: U.S. Geological 

Survey Water-Supply Paper 2375, p. 

369-376.

National Research Council, 1988,

Estimating probabilities of extreme 

floods, methods and recommended 

research: Committee on Techniques 

for Estimating Probabilities of 

Extreme Floods, Water Science and 

Technology Board, National 

Research Council, National 

Academy Press, 141 p.

Omang, R.J., 1992, Analysis of the

magnitude and frequency of floods 

and the peak-flow gaging network in 

Montana: U.S. Geological Survey 

Water-Resources Investigations 

Report 92-4048, 70 p.

Ostenaa, D.A., Levish, D.R., and

O'Connell, D.R.H., 1996, Paleoflood 

study for Bradbury Dam, Cachuma 

Project, California: Seismotectonic 

Report 96-3, Bureau of Reclamation, 

various paging.

Ostenaa, D.A., Levish, D.R., O'Connell, 

D.R.H., and Cohen, E.A., 1997, 

Paleoflood study for Causey and 

Pineview Dams, Weber Basin and 

Ogden River Projects, Utah: 

Seismotectonic Report 96-6, Bureau 

of Reclamation, various paging.

Parrett, Charles, 1997, Regional analysis 

of annual precipitation maxima in 

Montana: U.S. Geological Survey 

Water-Resources Investigations 

Report 97-4004, 51 p.

Parrett, Charles, 1998, Characteristics of 

extreme storms in Montana and 

methods for constructing synthetic 

storm hyetographs: U.S. Geological 

Survey Water-Resources 

Investigations Report 98-4100, 55 p.

U.S. Army Corps of Engineers, 1990, 

HEC-1 flood hydrograph package, 

user's manual: Davis, California, 

Hydrologic Engineering Center, 

283 p.

Looking west at St. Mary Lake and Tabor Dam from Dry 

Creek above St. Mary Lake.

For more information, contact:

Charles Parrett 

U.S. Geological Survey 

3162 Bozeman Avenue 

Helena, MT 59601 

(406) 457-5928 

cparrett@usgs.gov

For information about all USGS products 

and services, call:

1-888-ASK-USGS 

http://www.usgs.gov I

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