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15

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


2. Channel linings - If more than 50 percent of
the length of the main drainage channel and principal
tributaries in each basin third has been lined with an
impervious material, such as concrete, then a code of 1
is assigned to this aspect. If less than 50 percent of
these channels are lined, then a code of zero is
assigned. The presence of channel linings would obvi-
ously indicate the presence of channel modifications as
well. Therefore, this is an added factor that indicates a
more highly developed drainage system.

3. Storm drains (storm sewers) - Storm drains are
defined as enclosed drainage structures (usually pipes),
frequently used on the secondary tributaries (those that
drain directly into the principal tributaries) where the
drainage is received directly from streets or parking
lots. Many of these drains empty into open channels;
however, in some basins they empty into channels
enclosed as box or pipe culverts. When more than 50
percent of the secondary tributaries within a subarea
(third) consist of storm drains, then a code of 1 is
assigned to this aspect; if less than SO percent of the
secondary tributaries consist of storm drains, then a
code of zero is assigned. It should be noted that if 50
percent or more of the main drainage channels and
principal tributaries are enclosed, then the aspects of
channel modifications and channel linings would also
be assigned a code of 1.

4. Curb-and-gutter streets - If more than 50 per-
cent of a subarea (third) is urbanized (covered by resi-
dential, commercial, and (or) industrial development)
and if more than SO percent of the streets and highways
in the subarea are constructed with curbs and gutters,
then a code of | is assigned to this aspect. Otherwise, it
receives a code of zero. Drainage from curb-and-gutter
streets frequently empties into storm drains.

The above guidelines for determining the vari-
ous drainage-system codes are not intended to be pre-
cise measurements. A certain amount of subjectivity
will necessarily be involved. Field checking should be
performed to obtain the best estimate. BDF is the sum
of the assigned codes; four drainage aspects to which
codes are assigned in each of the 3 basin thirds. The
maximum value for a fully developed drainage system
would be 12. In contrast, if the drainage system were
totally undeveloped, then a BDF of zero would result.
Such a condition does not necessarily mean that the
basin is unaffected by urbanization. In fact, a basin
could be partially urbanized, have some impervious
area, and have some modification of secondary tribu-
taries and still have an assigned BDF of zero.

The BDF is a fairly easy index to estimate for an
existing urban basin. The 50-percent guideline will
usually not be difficult to evaluate because many urban

areas tend to use the same design criteria and therefore
have similar drainage aspects throughout. Also, the
BDF is convenient for projecting the effects of future
development. Obviously, full development and maxi-
mum urban effects on peaks would occur when BDF
equals 12.

Limitations and accuracy of the technique

The computed urban peak flow (UQ,) should be
compared to the equivalent rural peak flow (RQ,) to
make sure that the urban peak-flow estimate is reason-
able. This is especially true if the drainage-basin wet-
lands variable (ST) from the urban equations (which is
calculated using USGS topographic maps) differs by
more than 50 percent from the basin wetlands variable
(W) from the rural equations (page 23, calculated using
USS. Fish and Wildlife National Wetland Inventory
Maps).

The urbanization of a drainage basin generally
causes peak flows to increase for those basins that do
not have significant in-channel or detention storage.
The increase in peak flows is usually most dramatic for
lower recurrence interval flows (which occur fre-
quently) and less pronounced for higher recurrence
interval flows (Sauer and others, 1983).

The location of urbanization in a drainage basin
may have an effect on peak flows that is not accounted
for in the urban regression equations. For example, if
the lower part of a basin is urbanized and the upper part
is not, rapid removal of floodwaters from the lower part
may occur before the upper part can contribute signifi-
cant runoff. This pattern of urbanization could poten-
tially decrease peak flows from a drainage basin (Sauer
and others, 1983).

At gaging stations that were used to compute the
urban regression equations, at least 15 percent of their
drainage area was covered with some type of commer-
cial, industrial, or residential development. For this
reason, the urban equations may not be applicable to
basins containing less than 15 percent developed land.

The ranges of the explanatory variables used in
the urban regression equations are listed in table 10,
and the standard errors for the equations are given in
table 9. If values outside the ranges of the explanatory
variables are used, then the standard errors may be con-
siderably higher than the listed standard errors.

As discussed by Sauer and others, the drainage
basin wetlands variable (ST) does not include in-chan-
nel storage of a temporary nature (resulting from deten-
tion ponds, roadway embankments, or other
structures). This type of storage tends to reduce peak

36 —_ Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


Limitations of the technique

Equations 6 through 11 are applicable to
ungaged sites on gaged, unregulated streams in rural
drainage basins that are between 50 and 200 percent of
the drainage area of the gaging station(s), except for
sites that are plus or minus 3 percent of the drainage
area. For ungaged sites within 3 percent of the gaging-
station drainage area, the weighted-average peak-flow
estimates (table 1, page 8) should be used. If the differ-
ence in drainage areas is less than 3 percent and the
weighted-average peak-flow estimate is not available
for a station, the gaging-station peak-flow estimate
from table 1 should be used.

This method is not applicable to urbanized drain-
age basins or to regulated streams (see “Choosing the
appropriate section of this report to obtain estimated
peak flows” in Part 1 of this report for definitions of
these terms); neither is it applicable if the area between
the ungaged site and the gaging station(s) is urbanized
or contains regulation (using the same definitions of
urbanized and regulated just referred to, but using
drainage-area difference instead of drainage area in
these definitions).

There may be other situations where the tech-
niques in this section are not applicable. One known
example is the Saco River between Conway, New
Hampshire, and Cornish, Maine. As shown in table 1,
the estimated peak flows are larger at Conway than at
Commish even though the drainage area at Cornish is
more than 3 times the drainage area at Conway. The
calculation of Qy in equation 9 would obviously give
unreasonable results in this situation. It is unknown
how close (in terms of drainage area) a site would have
to be to the gaging stations at Conway or at Cornish for
the calculation of Q,, to be reasonable. The large
amount of natural storage in the Saco River valley
between Conway and Cornish may be the cause of this
unusual situation.

Section 5: Estimating peak flows for
ungaged, unregulated streams in
urbanized drainage basins

Sauer and others (1983) computed regression
equations that consider the effects of urbanization on a
drainage basin. Data from 269 gaging stations in 31
states (56 cities) were considered for use in computing
these equations. Although no stations from Maine were
used, tests by Sauer and others indicated that the equa-
tions are not geographically biased.

Sauer and others presented seven-variable and
three-variable regression equations in their report.

Although the three-variable equations are easier to
apply, a later study using new data (Sauer, 1985)
showed the three-variable equations to be biased in
some areas of the country (mainly in some southeastern
states). For this reason, the seven-variable regression
equations are presented here. Data from 199 gaging
stations across the United States were used to compute
the seven-variable equations.

Application of the technique

The seven-variable regression equations are pre-
sented in table 9. Explanations of the variables used in
table 9 are presented below. These regression equations
are referred to as the “urban” regression equations. The
average standard error of estimate and the average
standard error of prediction are discussed in “Limita-
tions and accuracy of the technique” at the end of this
section.

These regression equations are statistical models
and are not based directly on rainfall-runoff processes.
For this reason, when applying these equations, the
explanatory variables should be computed by the same
methods that were used in the development of the equa-
tions. Using “more accurate” methods of computing
the explanatory variables (for example, using maps
other than the 1961 National Weather Service (NWS)
maps to compute the 2-hour, 2-year rainfall) will result
in peak-flow estimates of unknown accuracy. It is nec-
essary to use inch-pound units for these equations.

Definitions of equation variables in table 9:

UQ,, - The peak flow, in cubic feet per second,
for the urban drainage basin for recurrence interval n;
that is, UQ) = 2-year urban peak flow, UQs = 5-year
urban peak flow, and so forth.

A- The contributing drainage area, in square
miles (not square kilometers). In urban areas, drainage
systems sometimes cross topographic divides. Such
drainage-area changes should be accounted for when.
computing A. This may require field inspections.

SL - The main channel slope, in feet per mile,
measured from points that are 10 percent and 85 per-
cent of the main-channel length upstream from the
study site. The main channel, where two channels join,
is the one that drains the largest area. The main-channel
length is measured as the distance from the study site to
the basin divide. For sites where SL is greater than
70 ft/mi, 70 ft/mi is used in the equations.

Ro - The rainfall, in inches, for the 2-hour 2-year
occurrence. Determined from NWS maps (1961). The
Maine section of the appropriate NWS map is repro-
duced as figure 4.

32 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


Appendix—Detailed descriptions of gaging-station locations—Continued

[at, latitude; long, longitude; km, kilometers; m, meters; right and left
bank are referenced facing downstream]

USGS
gaging-station Gaging station name Station location
number
01028000 West Branch Penobscot River near Lat 45°36'25”, long 68°32’25”, Penobscot County, on left bank
Medway, Maine just above Nichatou Rapids at Nichatou Island, 0.8 km upstream
from confluence of East and West Branches, and 0.8 km west of
Medway.
01029500 East Branch Penobscot River at Lat 45°43’49”, long 68°35’22”, Penobscot County, on left bank
Grindstone, Maine 150 m downstream from Bangor and Aroostook Railroad
bridge, 0.8 km south of Grindstone, and 15.3 km upstream from
confluence with West Branch Penobscot River.

01030000 Penobscot River near Lat 45°34’00”, long 68°24’ 10”, Penobscot County, on left bank

Mattawamkeag, Maine 550 m downstream from Mattaseunk Dam and powerhouse,
2.0 km upstream from Mattaseunk Brook, and 7.2 km upstream
from Mattawamkeag.

01030300 Trout Brook near Danforth, Maine Lat 45°41°43”, long 67°54’07”, Washington County, at culvert in
road between Bancroft and Danforth, 2.1 km upstream from
mouth and 5.0 km northeast of Danforth.

01030400 Gulliver Brook near Monarda, Lat 45°44’23”, long 68°18’30”, Aroostook County, at culvert in

Maine U.S. Highway 2, 0.8 km upstream from mouth and 6.6 km south
of Monarda.

01030500 Mattawamkeag River near Lat 45°30°03”, long 68°18’22”, Penobscot County, on left bank

Mattawamkeag, Maine 1.0 km downstream of Gordon Falls, 1.0 km upstream from
Mattakeunk Stream, 5.8 km upstream from Mattawamkeag, and
6.4 km upstream from mouth.
01031500 Piscataquis River near Lat 45°10°31”, long 69°18’55”, Piscataquis County, on left bank
Dover-Foxcroft, Maine 9 m downstream from Lows Bridge, 1.6 km upstream from
Black Stream, and 7.6 km upstream from Dover-Foxcroft.
01031600 Morrison Brook near Sebec Lat 45°14’17”, long 69°03’06”, Piscataquis County, on left bank
Corners, Maine 18 m upstream from culvert in State Highway 16, 3.9 km east of
Sebec Corners, and 6.1 km upstream from mouth.

01033000 Sebec River at Sebec, Maine Lat 45°16’ 12”, long 69°06'44”, Piscataquis County, on right bank,
305 m downstream from highway bridge and dam at outlet of
Sebec Lake at Sebec.

01033500 Pleasant River near Milo, Maine Lat 45°16’58”, long 69°00’ 13”, Piscataquis County, on left bank
4.0 km northeast of Milo on Pleasant River Road, and 12.7 km
upstream from mouth.

01034000 Piscataquis River at Medford, Maine Lat 45°15’40”, long 68°52’07”, Piscataquis County, on left bank
3.2 km southwest of Medford and 5.3 km downstream from
Pleasant River.

01034500 Penobscot River at West Enfield, Lat 45°14’ 12”, long 68°38’56”, Penobscot County, on left bank

Maine 9 m downstream from highway bridge, 305 m downstream from
Piscataquis River, and at West Enfield.

01034900 Coffin Brook near Lee, Maine Lat 45°20’ 18”, long 68°21°42”, Penobscot County, 4 m upstream
from culvert on Lee Back Road, and 6.0 km southwest of Lee.

01035000 Passadumkeag River at Lowell, Lat 45°11°04”, long 68°28’29”, Penobscot County, on right bank

Maine at Lowell, 0.8 km downstream from dam and highway bridge on

Fogg Brook Road, and 18.0 km upstream from mouth.

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervais—USGS WRIR 99-4008

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Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence intervals—USGS WRIR 99-4008


tory variable in this study, basin wetlands, was deter-
mined from U.S. Fish and Wildlife Service National
Wetland Inventory Maps (scale 1:24,000). The Cana-
dian Wildlife Service has produced Wetland Inventory
Maps at a different scale (1:50,000). Because it is not
known if these two sets of maps are comparable, the
five stations with Canadian drainage area were not used
in the regression analysis: St. John River at Ninemile
Bridge, Maine (01010000); Big Black River near
Depot Mountain, Maine (01010070); St. John River at
Dickey, Maine (01010500); St. Francis River near
Connors, New Brunswick (01011500); and St. John
River below Fish River at Ft. Kent, Maine (01014000).
Seventy unregulated, gaged basins were used in the
final Maine regression analyses.

Development of the technique

Ordinary least squares (OLS) regression tech-
niques (Helsel and Hirsch, 1992) were used to select
the explanatory variables that would appear in the final
regression equations. Linear relations between the
explanatory and response variables are necessary in
OLS regression. For this reason, variables must often
be transformed. For example, the relation between
drainage areas and peak flows is typically not linear,
however, the relation between the logarithms of drain-
age areas and the logarithms of peak flows often is lin-
ear. Homoscedasicity (a constant variance in the
response variable over the range of the explanatory
variables) and normality also are important in OLS
regression. Linearity, homoscedasicity, and normality
in the relation between explanatory variables and
response variables were examined with component-
plus-residual plots (Cook and Weisburg, 1994).

OLS regression of all possible subsets was used
to determine the best combination of explanatory vari-
ables to use in the final regression equations. Initially,
the 14 explanatory variables or transformations of
these variables were used with the response variables
(the base-10 logarithms of the n-year peak flows; n= 2,
5, 10, 25, 50, 100, 500) from 53 gaged drainage basins.
These 53 stations were used because most of the
explanatory variables at these stations were computed
in a previous study (Morrill, 1975). The best combina-
tion of the variables was chosen on the basis of Mal-
low’s Cp statistic, the PRESS statistic, the amount of
variability in the response variables explained by the
explanatory variables, the statistical significance of the
explanatory variables, and the difficulty of calculating
the explanatory variables. Basin wetlands and the base-
10 logarithms of drainage area were chosen as the final

variables from all possible combinations of the 14
explanatory variables. Both of these variables were
highly significant (the p-values from the T-statistics for
both variables were less than 0.00005).

OLS regression of all possible subsets was then
used for the full 70 gaging stations for the following
explanatory variables: drainage area, basin wetlands,
upper third wetlands, middle third wetlands, lower
third wetlands, and slope. On the basis of the results
from the 53-station regressions, it was not considered
useful to compute additional values for the rest of the
explanatory variables. Basin wetlands and the base-10
logarithms of drainage area were again the best choice
as final explanatory variables. Both variables were still
highly significant (p-values were still less than
0.00005). The values of drainage area and percentage
of basin wetlands for the 70 stations are listed in
table 2.

Regression diagnostic tools were used to test the
adequacy of the OLS regressions at the 70 gaging sta-
tions (response variables were the base-10 logarithms
of the 2-, 5-, 10-, 25-, 50-, 100-, and 500-year peak
flows; explanatory variables were percentage of basin
wetlands and the base-10 logarithms of drainage area).
Multicollinearity of the explanatory variables was
measured by the variance inflation factor (VIF). The
influence of individual stations on the regressions was
measured by Cook’s D statistic. There were no prob-
lems with multicollinearity or high influence points.

Different types of residual plots were analyzed.
The regression residuals were plotted against predicted
values to look for linearity, homoscedasicity, normal-
ity, and the presence of outliers. Normal probability
plots of the residuals also were analyzed. Residuals
were plotted against the explanatory variables to look
for biases in the explanatory variables over their range.
All regression diagnostics indicated that the use of per-
centage of basin wetlands and the base-10 logarithms
of drainage area as explanatory variables resulted in a
very good regression model.

The regression residuals (for the 2-year and 100-
year peak flows) were plotted at the centroid of their
respective drainage basins to look for geographical
biases and to determine whether Maine should be
divided into more than one hydrologic region. Separate
regression equations would have been computed for
each region if more than one hydrologic region was
called for. No distinct pattern, however, was seen in the
mapped residuals.

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008 19


Table 10. Ranges of explanatory variables used in the urban regression equations

{From Sauer and others, 1983]

Variable Minimum Maximum Units
A 0.2 100 Square miles
SL 3.0 70" Feet per mile
Ro 02 28 Inches
ST 0 ll Percent
BDF 0 12 None
1A 3 50 Percent

Maximum value of slope for use in urban equations is 70 feet per mile, although numerous
drainage basins used in this study had SL values as high as 500 feet per mile.

flows. Reservoir- and channel-routing techniques are
recommended to determine the effect that temporary
in-channel storage has on peak flows in an urbanized
basin.

The average standard error of estimate is, by def-
inition, one standard deviation on each side of the
regression equation and contains about 68 percent of
the data within this range. The average standard error
of estimate is a measure of how well the regression
equations estimated the response variable (UQ,) at the
stations used to develop the equations. The average
standard error of prediction is a measure of how well
the regression equations will estimate peak flows when
they are applied to ungaged drainage basins. The aver-
age standard errors of prediction (ASEP’s) in table 9
were computed by Sauer and others using a validation
method (split sampling) unlike the ASEP’s computed
earlier in this report. The ASEP’s in table 9 are compa-
rable to (PRESS/n)'” in tables 3 and 8.

There is a 68 percent probability that the true
value of a peak flow at a site (a site where a peak flow
is being estimated) will be within the average standard
error of prediction range. The standard errors in table 9
are based on 199 gaging stations nationwide, none of
which are in Maine. Standard errors for Maine are
assumed to be similar to those in table 9 but could be
larger or smaller.

Section 6: Estimating peak flows for
ungaged sites on regulated streams

Techniques for estimating peak flows for regu-
lated streams are beyond the scope of this report
because peak flows on regulated streams are dependent
on variable human actions. A potential procedure for
estimating peak flows for ungaged sites on regulated
streams would be to route peak inflows through the reg-
ulated reservoir(s), taking into account regulation prac-
tices. The applicable method of this report could be
used to estimate the magnitude of the peak inflows.

Equation 6 in section 4, “Estimating peak flows
for ungaged sites on gaged, unregulated streams in
rural drainage basins” is not applicable to regulated
streams because there are no regulated regression equa-
tions to use in the weighting scheme of this method.
Also, equations 9 and 10 in section 4, are not, in gen-
eral, considered reliable for regulated streams. Several
reaches of streams in Maine show these equations to be
unreliable for regulated streams: Kennebec River
between The Forks and Waterville; Androscoggin
River between Gorham, New Hampshire, and Rum-
ford, Maine; and Presumpscot River between the outlet
of Sebago Lake and Westbrook.

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence intervais—USGS WRIR 99-4008 37


TABLES

1. Estimated peak flows and maximum recorded flows for selected U.S. Geological Survey
streamflow-gaging stations
2. Drainage areas and percentage of basin wetlands for 70 gaging stations used in regression equations.
3. Full regression equations and their accuracy for estimating peak flows for ungaged, unregulated streams in
rural drainage basins in Maine...
4. Estimated model error variance and average sampling error variance for the full regression equations
5. ct as xy! matrices for the n-year full regression equations..
6. Accuracy comparison of Maine Department of Transportation and USGS techniques to estimate 50-year
peak flows for ungaged, unregulated streams in rural drainage basins using weighted-average flows
as true flows ...
7. Accuracy comparison of Maine Department of Transportation and USGS techniques to estimate 50-year
peak flows for ungaged, unregulated streams in rural drainage basins using gaging-station flows
as true flows ..
8. Simplified regression equations and their accuracy for estimating peak flows for ungaged, unregulated
streams in rural drainage basins in Maine...
9. Urban regression equations and their accuracy for estimating peak flows
10. Ranges of explanatory variables used in the urban regression equations

CONVERSION FACTORS AND UNIT ABBREVIATIONS

Multiply By To obtain
meter (m) 3.281 foot
kilometer (km) 0.6215 mile
square kilometer (km?) 0.3861 square mile
cubic meter (m?) 35.31 cubic foot
cubic meter per second (m/s) 35.31 cubic foot per second
cubic meter per square cubic foot per square
kilometer (m/km”) 91.45 mile (ft*/mi?)
inch (in) 25.4 millimeter
foot (ft) 0.3048 meter
mile (mi) 1.609 kilometer
square mile (mi?) 2.590 square kilometer
cubic foot per second (ft/s) 0.02832 cubic meter per second

Vv Contents


Limitations and accuracy of the simplified
technique

The regression equations for the simplified tech-
nique are significantly less accurate than those devel-
oped in section 2, “Estimating peak flows for ungaged,
unregulated streams in rural drainage basins” (see the
measures of accuracy in table 3 and table 8). The latter
regression equations are referred to as the “full regres-
sion equations.”

The regression equations in this section of the
report are not applicable to regulated or urbanized
drainage basins. “Choosing the appropriate section of
this report to obtain estimated peak flows” in Part 1 of
this report defines “regulated” and “urbanized” and
indicates the appropriate techniques for such basins.

The accuracy of the equations will be reduced if
the explanatory variable (drainage area) used in the
simplified regression equations is outside the range of
the values used to develop the equations (2.41 km? to
4,280 km). The magnitude of this reduction in accu-
racy is unknown and potentially large. The potential for
large reductions in the accuracy of the regression equa-
tions increases as the distance outside the range
increases.

The regression equations in the simplified tech-
nique may seriously underestimate the peak flows for
sites that have very steep slopes (slopes, as defined in
“Data used for the technique” of section 2, of greater
than 50 m/km). As explained in section 2, preliminary
regression equations significantly underpredicted the
peak flows for three very steep-sloped basins in New
Hampshire.

The average standard error of prediction (ASEP)
is a measure of how well the regression equations will
estimate peak flows when they are applied to ungaged
drainage basins. The ASEP is the square root of the
average variance of prediction at a group of sites that
have the same basin characteristics as the gaged sta-
tions used in development of the regression equations.
The standard error of prediction varies from site to site,
depending on the value of the explanatory variable
(drainage area) for each site. The standard error of pre-
diction will be smaller for sites that have a drainage
area near the mean of its range; however, the error asso-
ciated with the different values of the explanatory vari-
able is a small part of the total standard error of
prediction. For this reason, the ASEP can be used as an
approximate standard error of prediction for individual
sites. The probability that the true value of a peak flow
at a site is between the positive-percent ASEP and the

negative-percent ASEP is approximately 68 percent.
For example, there is a 68 percent probability that the
true 50-year peak flow at an ungaged site is between
+77.8 percent and -43.8 percent (table 8) of the com-
puted peak flow. In comparison, there is a 68 percent
probability that the true 50-year peak flow from the full
regression equations will be between +46.9 percent and
-31.9 percent (table 3, page 23) of the computed peak
flow.

Another overall measure of how well regression
equations will estimate flood peaks when applied to
ungaged basins is the PRESS statistic. The PRESS sta-
tistic is a validation-type statistic. To compute the
PRESS statistic, one gaging station is removed from
the stations used to develop the regression equation,
then the value of the one left out is predicted. The dif-
ference between the predicted value from the regres-
sion equation and the observed peak flow at that station
is computed. The gaging station left out is then
changed and the above process repeated until every sta-
tion has been left out once. The prediction errors are
then squared and summed. PRESS/n is analogous to
the average variance of prediction, and the square root
of PRESS/n is analogous to the average standard error
of prediction. Values of the square root of PRESS/n
close to the values of the average standard error of pre-
diction provide some measure of validation of the
Tegression equations.

The average equivalent years of record is a third
measure of the overall accuracy of the regression equa-
tions. This measure represents the average number of
years of gaging-station data needed to achieve results
with accuracy equal to the regression equations. The
average equivalent years of record is a function of the
accuracy of the regression equations, the recurrence
interval, and the average variance and skew of the
annual peak flows at gaging stations (Hardison, 1971).

Section 4: Estimating peak flows for
ungaged sites on gaged, unregulated
streams in rural drainage basins

If an ungaged site is relatively near (see “Limita-
tions of the technique” later in this section for details)
a USGS streamflow-gaging station and on the same
stream, a weighted peak flow is calculated. The
weights are determined by how far (in terms of drain-
age area) the ungaged site is from the gaging station.

30 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


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Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

16


Table 2. Drainage areas and percentage of basin wetlands for 70 gaging stations used in regression equations—Continued

USGS gaging-
‘station number

Gaging-station name

Areal percentage
of wetlands in
drainage basin

Drainage area
(square kilometers)

01060000 Royal River at Yarmouth, Maine 365 96
01062700 atte Brook near Bethel, Maine 14.6 58
01064200 —Mill Brook near Old Orchard Beach, Maine 5.57 3.8
01064380 East Branch Saco River near Lower Bartlett, New Hampshire 82.8 07
01064500 Saco River near Conway, New Hampshire 997 21
01065000 —_Ossipee River at Effingham Falls, New Hampshire 855 103
01065500 Ossipee River at Cornish, Maine 1,170 98
01066000 Saco River at Cornish, Maine 3,350 8.6
01066100 Pease Brook near Cornish, Maine 12.4 5.4
01066500 —_Little Ossipee River near South Limington, Maine 435 12.2
01067000 Saco River at West Buxton, Maine 4,070 94
01069700 Branch Brook near Kennebunk, Maine 26.7 13
01072850 Mohawk Brook near Center Strafford, New Hampshire 23.0 83
01073000 Oyster River near Durham, New Hampshire 313 10.8

Station formerly published as Cold Brook near Northern Maine Junction, Maine

Generalized least squares (GLS) regression tech-
niques (Stedinger and Tasker, 1985; Tasker and Ste-
dinger, 1989) were used to compute the final
coefficients and the measures of accuracy for the
regression equations, using the computer program
GLSNET (G.D. Tasker, K.M. Flynn, A.M. Lumb, and
W.O. Thomas Jr., U.S. Geological Survey, written com-
mun., 1995). Stedinger and Tasker found that GLS
regression equations are more accurate (and provide a
better estimate of the accuracy of the equations) than
OLS regression equations when streamflow records at
gaging stations are of different and widely varying
lengths and when concurrent flows at different stations
are correlated. GLS regression techniques give less
weight to streamflow-gaging stations that have shorter
periods of record than other stations. Less weight is also
given to those stations whose concurrent peak flows are
correlated with other stations.

Application of the technique

Peak-flow regression equations for recurrence
intervals of 2, 5, 10, 25, 50, 100, and 500 years are pre-
sented in table 3. The variables used in the equations
are described in the text that follows the table. These
regression equations are referred to as the “full” regres-
sion equations. The average standard error of predic-
tion, the PRESS statistic, and the average equivalent
years of record are discussed in “Limitations and accu-
racy of the technique” at the end of this section.

All of the regression equations in this report are
statistical models. They are not based directly on rain-
fall-runoff processes. For this reason, when applying
these equations, the explanatory variables should be
computed by the same methods that were used in the
development of the equations. Using “more accurate”
methods of computing the explanatory variables (for
example, determining the basin wetland variable by
making field delineations) will result in peak-flow esti-
mates of unknown accuracy.

22 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


Section 2: Estimating peak flows for
ungaged, unregulated streams in rural
drainage basins

Peak flows for ungaged drainage basins for
selected recurrence intervals are generally estimated by
rainfall-runoff procedures or by regression-based pro-
cedures. Newton and Herrin (1982) analyzed several
procedures of both types. The rainfall-runoff models
that they analyzed, including the Natural Resources
Conservation Service TR-20 and TR-55 models, the
U.S. Army Corps of Engineers HEC-1 model, and the
rational method, were not calibrated to at-site flow
data. Newton and Herrin concluded that certain regres-
sion-based methods (specifically, the USGS state
regression equations and index flood methods) are the
most accurate and reproducible procedures for estimat-
ing peak flows for given recurrence intervals.

Regression equations are used in this section of
the report to compute peak-flow estimates for ungaged,
unregulated streams in rural drainage basins in Maine.
The response (dependent) variables used in developing
the regression equations were the peak flows computed
at USGS gaging stations and the explanatory (indepen-
dent) variables were drainage basin characteristics
such as drainage area and stream slope.

Data used for the technique

Regression equations are used to estimate a
response variable (in this case, a peak flow for a given
recurrence interval) for an ungaged drainage basin by
measuring explanatory variables (such as drainage
area). Explanatory variables should make hydrologic
sense, explain a significant amount of the variability of
the response variable, and be reasonably easy to mea-
sure. A set of explanatory variables that were qualita-
tively judged to best meet these criteria was selected
for testing.

The values of 14 explanatory variables were
determined for gaged, unregulated streams in rural
drainage basins in Maine and New Hampshire. These
14 explanatory variables were: drainage area, the area
of a drainage basin; main-channel length, the length of
the main channel from the gaging station to the basin
divide; main-channel slope, the slope of the main chan-
nel between points that are 85 percent and 10 percent
of the main-channel length from the gaging station;
elevation, the mean basin elevation; forest cover, the
percentage of a basin covered by forests; snow, the
average water content of the snow in a basin on March

1; lake area, the areal percentage of lakes, ponds, and
reservoirs in a basin; basin wetlands, the areal percent-
age of all types of wetlands (which includes lakes,
ponds, reservoirs, and rivers) in a basin; upper third
wetlands, the areal percentage of all types of wetlands
in the upper third of a basin; middle third wetlands, the
areal percentage of all types of wetlands in the middle
third of a basin; lower third wetlands, the areal percent-
age of all types of wetlands in the lower third of a basin;
mean annual precipitation, the mean annual precipita-
tion in a basin; 24-hour, 2-year rain, the maximum 24-
hour rainfall having a recurrence interval of 2 years;
and 24-hour, 100-year rain, the maximum 24-hour
rainfall having a recurrence interval of 100 years.

The peak flows for 72 unregulated streamflow-
gaging stations in Maine, New Hampshire, and New
Brunswick were reported in table 1 (page 8). The peak
flows from all of these stations were considered for use
as response variables in the regression equations. Peak
flows for six additional stations in New Hampshire are
not reported in table 1 (individually they are not useful
for estimating peak flows in Maine) but were consid-
ered for use in the equations: Ellis River near Jackson,
N.H. (station number 01064300); East Branch Saco
River near Lower Bartlett, N.H. (01064380); Lucy
Brook near North Conway, N.H. (01064400); Cold
Brook at South Tamworth, N.H. (01064800); Mohawk
Brook near Center Strafford, N.H. (01072850); and
Oyster River near Durham, N.H. (01073000).

Some of the 78 unregulated streamflow-gaging
stations were not used in the final regression analysis.
When examining the results of preliminary regressions,
three of the six New Hampshire stations listed in the
previous paragraph (Ellis River, Lucy Brook, and Cold
Brook) were noted as having extremely steep stream
slopes (75.2 m/km to 102 m/km). In addition, the
regression residual values were large (the regression
equations significantly underpredicted peak flows at all
three stations). The steepest gaged stream in Maine is
Mountain Brook near Lake Parlin with a slope of
49.1 m/km. It is unknown whether Maine sites with
slopes similar to the three New Hampshire stations
would have similar residual values. Because of this,
and because including these stations would change the
regression equations, the three New Hampshire sta-
tions were dropped from the Maine regression equation
analyses.

Five gaging stations in northern Maine were not
used in the regression analyses because part of their
drainage basins are in Canada. An important explana-

18 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence intervals—USGS WRIR 99-4008


Application of the technique

Equation 6 provides the means for calculating a
final weighted peak flow at an ungaged site on a gaged
stream by weighting the peak flow from the gaging sta-
tion with the peak flow from the regression equation. A
different approach is given (equation 10) for sites (1)
whose explanatory variables (drainage area and per-
centage of basin wetlands) are outside the two-dimen-
sional range of the variables used in the development of
the regression equations (fig. 3, page 25); or (2) sites
that drain Canadian land. Yet another approach (equa-
tion 11) is provided for ungaged sites located between
two gaging stations.

Quit = Qy(W,) + Qu(1 - Wy), (6)
where

Qu is the final weighted peak flow for a given
recurrence interval (for example, the 50-year
peak flow) for an ungaged site on a gaged
stream, and

Q, is the regression estimate of the peak flow, at
the ungaged site, for a given recurrence interval
(for example, the 50-year peak flow) from table
3 in section 2, “Estimating peak flows for
ungaged, unregulated streams in rural drainage

basins”,
W, is a weighting factor:
For Ay > Ag, W, = (Ay/ Ag) - 1, and (7)
For Ay < Ag, W, = (Ag/ Ay) - 1, (8)
where

A, is the drainage-basin area of the ungaged
site, and

Agis the drainage-basin area of the gaging
station.

Q, is the peak flow from the gaging station with a
drainage area adjustment:

Qu = Qy (Au/ Ag)? (9)
where

Qy is the weighted-average peak flow for a
given recurrence interval (such as the 50-
year peak flow) for the gaging station
from table | in section 1, “Estimates of
peak flows and maximum recorded flows
at USGS streamflow-gaging stations” (or
from future reports), and

b is the coefficient of the simplified (drain-
age area only) regression equation for
the appropriate recurrence interval:

b = 0.825 for a recurrence interval of 2 years,

b = 0.797 for a recurrence interval of 5 years,

b = 0.783 for a recurrence interval of 10 years,

b = 0.767 for a recurrence interval of 25 years,

b = 0.757 for a recurrence interval of 50 years,

b = 0.748 for a recurrence interval of 100 years, and

b = 0.729 for a recurrence interval of 500 years.

If the explanatory variables (drainage area and percent-
age of basin wetlands) are (1) outside the 2-dimen-
sional range of the variables used for the regression
equations (fig. 3, page 25); or (2) if the ungaged site has
Canadian drainage, then

Qu = Qw (Au/ Ag)®, (10)
where

Qu is the final weighted peak flow for a given
recurrence interval (for example, the 50-year
peak flow) for an ungaged site on a gaged
stream, and

Qy is the weighted-average peak flow for a given
recurrence interval (such as the 50-year peak
flow) for the gaging station from table 1 in sec-
tion 1, “Estimates of peak flows and maximum
recorded flows at USGS streamflow-gaging
stations” (or from future reports). If the
weighted-average peak flow is not available,
the gaging-station peak flow should be used.

Au Ag and b were defined in equations 7, 8, and 9.

If the ungaged site is located between two gaging sta-
tions, then

Quit = (Qur(Aga - Au) + Quta(Au - Agi) / (Age - Agi), (1D)
where

Quit is the final weighted flow for an ungaged
site between gaging stations 1 and 2,

Qut1 is computed in equation 6 or 10 (as appro-
priate) for the upstream gaging station,

Aga is the drainage-basin area of the downstream
gaging station,

A, is the drainage-basin area of the ungaged site,

Que is computed in equation 6 or 10 (as appro-
priate) for the downstream gaging station, and

Ag1 is the drainage-basin area of the upstream
gaging station.

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008 31


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Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


requires that the data have no correlation over time
(serial correlation). Annual peak-flow data can exhibit
some serial correlation. This correlation can cause the
Mann-Kendall trend test to indicate a significant trend
when there is none, especially at gaging stations with
less than 30 years of peak-flow data (G.D. Tasker, U.S.
Geological Survey, written commun., 1997). For this
reason, some judgement is necessary to determine
whether the results of the Mann-Kendall trend test are
significant. The Mann-Kendall test was not performed
at stations with 10 to 15 years of peak-flow data
because trends cannot be distinguished from serial cor-
relation at stations with this length of data. No gaging
stations in this study were determined to have a signif-
icant trend in their annual peak-flow data. The annual
peak flows at all stations were also plotted to look for
large changes in the distribution of peak flows over
time, especially at gaging stations whose basins are
regulated.

In the Bulletin 17B analyses, the sample of
annual peak flows from a gaging station is assumed to
be representative of future peak flows. Therefore, use
of all peak flows from a gaging station is not always
appropriate. There are several regulated gaging stations
in Maine where significant regulation was added
(sometimes in addition to significant regulation already
in place) during the period for which annual peak flows
are available. The older, less regulated annual peak
flows were not used in the Bulletin 17B analyses if the
drainage basin regulation, at the time of the older
peaks, differed by more than 49,200 m? of usable stor-
age per square kilometer (Benson, 1962) from the reg-
ulation at the time of newer peaks. In addition, older
peaks were not used if the annual peak-flow data at a
station indicated that the regulation of peak flows had
changed significantly over time.

Bulletin 17B guidelines were followed for the
treatment of high and low outliers, for the conditional
probability adjustment, for the adjustment for historical
information, and for weighting the station skew coeffi-
cient with a generalized skew coefficient. In some
cases, multiple low outliers that were near, but not
below, the Bulletin 17B low outlier threshold were cen-
sored (dropped from the data set) if doing so improved
the fit between the logs of the observed annual peaks
and the Pearson Type III distribution. Most of the his-
torical information used in this study came from Thom-
son and others (1964). The station skew was not
weighted with the generalized skew if the annual peak
flows at a gaging station were significantly affected by

regulation. A station was considered significantly reg-
ulated if its drainage basin had more than 49,200 m of
usable storage per square kilometer (Benson, 1962).
The annual peak flows from the gaging stations in this
study did not show obvious evidence of being caused
by multiple generating mechanisms. The procedures
used to handle this situation were therefore not used.
Expected probability adjustments were not made.
These adjustments are explained in Bulletin 17B.

A generalized skew coefficient was developed
for Maine. This new skew coefficient is 0.029, with a
mean square error of prediction of 0.088 (or a standard
error of prediction of 0.297). To compute this skew
coefficient, the station skews from 44 gaging stations
(37 in Maine, 6 in New Hampshire, and 1 in New Brun-
swick) were computed using the procedures in Bulletin
17B. None of these stations are significantly affected
by regulation, diversions, or urbanization. At least 25
years of annual peak-flow data were available for all
stations, except for five stations that were included to
increase the representation of small-drainage-area sta-
tions. The 44 stations had an average of 53 years of
annual peak-flow data. The five small-drainage-area
stations had an average of 18 years of annual peak-flow
data. The computed station skews were adjusted for
bias (Tasker and Stedinger, 1986).

Four methods were tested to find the most accu-
rate generalized skew for Maine. The first method was
to compute an arithmetic mean of the 44 station skews.
The second method was to calculate a weighted mean
for the 44 station skews. The weight was the number of
annual peak flows at a station divided by the average
number of annual peak flows for the 44 stations. In the
third method, a state skew isoline map was created by
plotting the station skews on a map at the centroid of
their drainage basins. In the fourth method, an attempt
was made to develop a multiple regression equation
with station skew as the response variable and drainage
basin characteristics (such as drainage area and stream
slope) as the explanatory variables. No significant mul-
tiple regression models were found. For the first three
methods, the mean square error of prediction was com-
puted using the predicted and observed values of sta-
tion skew for the 44 stations in this analysis. The
weighted mean skew had the smallest mean square
error and was therefore considered the most accurate
generalized skew.

The accuracy of the new Maine generalized
skew (the weighted mean skew) was compared to the
accuracy of the Bulletin 17B generalized skew (the

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008 5


used for the methods. For this reason, the number of
stations used to calculate the overall accuracy of Ben-
son’s method was 44, and the number for Potter’s series
was 33. The RMSE is converted to percentage errors
using formulas from Riggs (1968). Approximately 68
percent of the estimated flows for each method are
within the given percentages of the true flows. The
RMSE values in table 6 were computed using the
weighted-average peak flow at each station (table 1) as
the true peak flow.

Because the weighted-average peak flows are
weighted with peak flows estimated from the full 50-
year regression equation (table 3), the computed

RMSE is a biased measure of error for the full regres-
sion equation. For this reason, the overall accuracy of
the estimation methods also was computed using the
gaging-station peak flows as the true flows, even
though the weighted-average peak flows are consid-
ered the best estimate of the true flows. The RMSE val-
ues in table 7 were computed using the gaging-station
peak flows (table 1) as estimates of the true flows to
calculate each RMSE.

Based on the RMSE values in tables 6 and 7, the
full regression equation from this report is the most
accurate method of computing the 50-year peak flow in
Maine.

Table 6. Accuracy comparison of Maine Department of Transportation and USGS techniques to estimate 50-year
peak flows for ungaged, unregulated streams in rural drainage basins using weighted-average flows as true flows

[RMSE, root mean square error; USGS, U.S. Geological Survey; FHWA, Federal Highway Administration}

Method (lojunits) (persentage)
Potter’s series 0.355 126.6 to -55.9
Benson’s method 0.257 80.9 to -44.7
USGS method 0.166 46.6 to -31.8
FHWA method 0.170 47.9 to -32.4
Full regression equation (table 3) 0.133 35.7 to -26.3
Simplified regression equation (table 8) 0.247 76.5 to -43.3,

Table 7. Accuracy comparison of Maine Department of Transportation and USGS techniques to estimate 50-year
peak flows for ungaged, unregulated streams in rural drainage basins using gaging-station flows as true flows

(RMSE, root mean square error; USGS, U.S. Geological Survey; FHWA, Federal Highway Administration]

Method dagunts) (pertentage)
Potter’s series 0.375 137.2 to -57.8
Benson’s method 0.282 91.6 to -47.8
USGS method 0.191 55.2 to -35.6
FHWA method 0.190 55.0 to -35.5
Full regression equation (table 3) 0.167 47.0 to -32.0
Simplified regression equation (table 8) 0.261 82.3 to -45.2

28 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008,


BASIN WETLANDS (PERCENTAGE)

500 1,000 2,000 5,000 10,000

DRAINAGE AREA (SQUARE KILOMETERS)

Figure 3. Two-dimensional range of explanatory variables for the full regression equations.

ference between the predicted value from the regres-
sion equation and the observed peak flow at that station
is computed. The gaging station left out is then
changed and the above process repeated until every sta-
tion has been left out once. The prediction errors are
then squared and summed. PRESS/n is analogous to
the average variance of prediction, and the square root
of PRESS/n is analogous to the average standard error
of prediction. Values of the square root of PRESS/n
close to the values of the average standard error of pre-
diction provide some measure of validation of the
regression equations.

The average equivalent years of record is a third
measure of the overall accuracy of the regression equa-
tions. This measure represents the average number of
years of gaging-station data needed to achieve results
with accuracy equal to the regression equations. The
average equivalent years of record is a function of the
accuracy of the regression equations, the recurrence
interval, and the average variance and skew of the
annual peak flows at gaging stations (Hardison, 1971).

Advanced accuracy analysis

The standard error of prediction at individual
sites (a more accurate standard error of prediction than
the average standard error of prediction (ASEP) dis-
cussed in the previous section) can be calculated using
the following methods. The fortran computer program
included in this report computes the standard error of

prediction for any study site as well as the 50-, 67-, 90-
and 95-percent prediction intervals. As an example, we
are 90 percent confident that the true peak flow at a
study site lies within the 90-percent prediction interval.
In generalized least squares regression, the aver-
age variance of prediction is divided into two parts: the
model error variance and the sampling error variance.
The average standard error of prediction is the square
root of the average variance of prediction. The esti-
mated model error variance and average sampling error
variance from the regression equations in this section
of the report are given in table 4. The model error vari-
ance is a measure of the error resulting from an incom-
plete model if the true values of the estimated peak
flows at gaging stations were known at all streams in
Maine (rather than the sample values that were used).
In other words, the explanatory variables of drainage
area and basin wetlands in the regression model would
not explain all of the variation in the peak flows from
the complete population. The true model error variance
cannot be reduced by additional data collection,
although the estimated model error variance may
change if additional data are obtained. The average
sampling error variance for the regression equations is
a measure of the error due to sampling only a subset of
the total population of streams in Maine (space-sam-
pling error) and sampling only a subset of the total
years of data at gaging stations (time-sampling error).

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008 25


This report gives estimates of, and presents tech-
niques for estimating, the magnitude of peak flows for
streams in Maine for recurrence intervals of 2, 5, 10,
25, 50, 100, and 500 years. Peak flows and the maxi-
mum recorded flows are listed for USGS streamflow-
gaging stations with 10 years or more of recorded
flows. Two techniques are presented for estimating the
peak flows for ungaged, unregulated streams in rural
drainage basins. Techniques also are described for esti-
mating peak flows at ungaged sites on gaged streams
(for unregulated sites in rural drainage basins) and for
estimating peak flows on ungaged, unregulated streams
in urbanized drainage basins. A technique for estimat-
ing peak flows for ungaged sites on regulated streams
is beyond the scope of this report, although a possible
approach is mentioned and cautions about inappropri-
ate approaches are given.

Many peak-flow studies have been published for
Maine and New England since the 1940’s, including
Morrill (1975) and Benson (1962). The estimates and
estimating techniques in this report should provide
more accurate estimates of peak flows for Maine than
previous reports because of the use of additional data
and more rigorous statistical procedures.

The following USGS employees provided sig-
nificant help analyzing the data, reviewing the data,
and (or) preparing the final report: William P. Bartlett
Jr., Robert W. Dudley, Laura E. Flight, Gloria L. Mor-
rill, and Joseph P. Nielsen. Gary D. Tasker wrote the
computer program that is included in this report and
provided very helpful guidance on many complex tech-
nical issues.

This report would not be possible without nearly
100 years of peak-flow data collection, often under
hazardous conditions, by USGS hydrologic technicians
and hydrologists. This historical data collection was
funded primarily by the USGS and the State of Maine.

CHOOSING THE APPROPRIATE SEC-
TION OF THIS REPORT TO OBTAIN ESTI-
MATED PEAK FLOWS

Peak flows in this report refer to peak flows of a
specified recurrence interval. The recurrence interval is
the average period of time between peak flows that are
equal to or greater than a specified peak flow. For
example, the 50-year peak flow is the flow that would
be equaled or exceeded, on long-term average, once in
50 years. This does not imply, however, that flooding
will happen at regular intervals. Two 50-year peak
flows could occur in the same year. In contrast, a 50-
year peak flow might not occur in 100 years.

The reciprocal of the recurrence interval is called
the annual exceedance probability; that is, the probabil-
ity that a given peak flow will be equaled or exceeded
in any given year. For example, the annual exceedance
probability of the 50-year peak flow would be 0.02. In
other words, there is a 2 percent chance that the 50-year
peak flow will be equaled or exceeded in any given
year.

To obtain estimated peak flows for streams in
Maine, information on the site (site refers to a location
on a stream) of interest is needed, including whether
the site is at or near (and on the same stream as) a U.S.
Geological Survey (USGS) streamflow-gaging station
and whether the site drains an urbanized or regulated
drainage basin. The different peak-flow estimates and
estimating techniques in this report are appropriate to
various combinations of these site characteristics.

The flowchart in figure 1 should be used to
choose the appropriate method of obtaining estimated
peak flows. The boxes in the right column of the flow-
chart show the appropriate section of the report for
obtaining the peak flows. The “Limitations and accu-
racy” statements in each section should be read before
applying that section. Although the discussions on lim-
itations are intended to be comprehensive, it is possible
that other specific limitations will arise in the applica-
tion of these sections. Figure 1 does not show an option
for ungaged sites on gaged, unregulated streams in
urbanized drainage basins because no current (1998) or
historical urbanized streamflow gages exist in Maine.

The following definitions apply to figure 1:

Site at a gaging station—the drainage area of the
study site is within 3 percent of the drainage area of a
USGS streamflow-gaging station and on the same
stream (see figure 2 for a map of the gaging stations and
the appendix for detailed descriptions of the gaging sta-
tion locations);

Regulated—the drainage basin above the site
contains more than 49,200 cubic meters of usable res-
ervoir storage per square kilometer (Benson, 1962)
(usable reservoir storage is the volume of water nor-
mally available for release from a reservoir, between
the minimum and maximum controllable elevations);

Urbanized—more than 15 percent of the drain-
age-basin area above the site is covered by some type
of commercial, industrial, or residential development;

Site near a gaging station—the drainage area of
the site is between 50 and 200 percent of the drainage
area of a USGS gaging station (excluding the plus or
minus 3 percent considered “at a gaging station”) and
on the same stream.

2 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


Estimating the Magnitude of Peak Flows for Streams in
Maine for Selected Recurrence Intervals

by Glenn Hodgkins

ABSTRACT

This report gives estimates of, and presents
techniques for estimating, the magnitude of peak
flows for streams in Maine for recurrence intervals
of 2, 5, 10, 25, 50, 100, and 500 years. A flowchart
in this report guides the user to the appropriate
estimates and (or) estimating techniques for a site
on a specific stream.

Section 1, “Estimates of peak flows and
maximum recorded flows at USGS streamflow-
gaging stations,” contains peak-flow estimates and
the maximum recorded flows at 98 U.S. Geologi-
cal Survey (USGS) streamflow-gaging stations. In
the development of the peak-flow estimates at gag-
ing stations, a new generalized skew coefficient
was calculated for Maine. This single statewide
value of 0.029 (with a standard error of prediction
of 0.297) is more accurate for Maine than the
national skew isoline map in Bulletin 17B of the
Interagency Advisory Committee on Water Data.

Two techniques are presented to estimate
the peak flows for ungaged, unregulated streams in
rural drainage basins. These two techniques were
developed using generalized least squares regres-
sion procedures at 70 USGS gaging stations in
Maine and eastern New Hampshire. Section 2,
“Estimating peak flows for ungaged, unregulated
streams in rural drainage basins,” uses the final
explanatory variables of drainage area and basin
wetlands. The average standard error of prediction
for the 100-year peak flow regression equation in
section 2 was 48.6 percent to -32.7 percent. Drain-
age area was the only explanatory variable used in
section 3, “Estimating peak flows for ungaged,

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

unregulated streams in rural drainage basins—
Simplified technique.” The average standard error
of prediction for the 100-year peak flow regression
equation in section 3 was 80.3 percent to

-44.5 percent.

Section 4 of the report describes techniques
for estimating peak flows for ungaged sites on
gaged, unregulated streams in rural drainage
basins. Section 5, “Estimating peak flows for
ungaged, unregulated streams in urbanized drain-
age basins,” describes regression equations for use
when a drainage basin is urbanized. These urban
regression equations come from a previous USGS
nationwide study. As stated in section 6, because
peak flows on regulated streams are dependent on
variable human actions, estimating peak flows at
ungaged sites on regulated streams is beyond the
scope of this report.

PART 1: PURPOSE AND USE OF THIS
REPORT

INTRODUCTION

Estimates of the magnitude of peak streamflows
(such as the 50-year-recurrence-interval peak flow) are
necessary to safely and economically design bridges,
culverts, and other structures that are in or near
streams. These estimates are also needed by Federal,
State, regional, and local officials for effective flood-
plain management. This report, prepared by the U.S.
Geological Survey (USGS) in cooperation with the
Maine Department of Transportation (MDOT), will
help MDOT and many others better estimate the mag-
nitude of peak flows for streams in Maine.


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Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

14


PART 2: ESTIMATING THE MAGNITUDE
OF PEAK FLOWS

Section 1: Estimates of peak flows and
maximum recorded flows at USGS
streamflow-gaging stations

The 2-, 5-, 10-, 25-, 50-, 100-, and 500-year peak
flows for streamflow-gaging stations discussed in this
section were calculated using the guidelines (Bulletin
17B) of the Interagency Advisory Committee on Water
Data (1982). The calculations involved fitting the Pear-
son Type III probability distribution to the logarithms
(base 10) of the observed annual peak flows at a gaging
station. This required computation of the mean, stan-
dard deviation, and skew of the logarithms of the
annual peak-flow data. The peak flow for any selected
recurrence interval was determined from the fitted
curve.

Data used for the estimates

The USGS has been collecting and publishing
streamflow data for gaging stations in Maine since
1901. The data currently are published by the USGS in
the annual report series titled “Water Resources
Data—Maine.” The data from 99 Maine stations, 6
New Hampshire stations, and 1 New Brunswick station
(106 total stations) that have at least 10 years of
recorded annual peak flows were considered for use in
this section of the report. Annual peak flows available
at streamflow-gaging stations through September 30,
1996 were used, except for six stations: Presumpscot
River at Westbrook, Maine (USGS gaging station num-
ber 01064118); Diamond River near Wentworth Loca-
tion, New Hampshire (01052500); Wild River at
Gilead, Maine (01054200); Big Black River near
Depot Mountain, Maine (01010070); Dennys River at
Dennysville, Maine (01021200); and Oyster River near
Durham, New Hampshire (01073000). More recent
data were used at these stations because of large peak
flows that occurred after September 30, 1996. The peak
flows from the Oyster River are not reported in this sec-
tion because they are not relevant by themselves for
estimating peak flows in Maine.

The peak flows from several gaging stations are
not reported for various reasons. The data at two sta-
tions were combined into one station if the drainage
area for a station was less than 10 percent different
from the drainage area of another station and if doing

so appeared reasonable on the basis of the data. A
drainage-area correction (Morrill, 1975) was applied
when combining the stations if the drainage areas
differed by 3 to 10 percent. Drainage area corrections
were not applied to stations for which the drainage
areas differed by less than 3 percent. The following
stations were combined: Mattawamkeag River at
Mattawamkeag (01031000) combined into
Mattawamkeag River near Mattawamkeag
(01030500); Kenduskeag Stream near Bangor
(01037000) combined into Kenduskeag Stream near
Kenduskeag (01036500); Kennebec River at North
Sidney (01049265) combined into Kennebec River
near Waterville (01049205); and Saco River at Salmon
Falls (01067500) combined into Saco River at West
Buxton (01067000).

The peak flows for St. John River above Fish
River at Fort Kent (01012500) and St. John River at
Van Buren (01015000) are not reported because the
annual peak flows at these stations appear to have been
collected during an unrepresentative short period when
compared to other St. John River stations. Similarly,
peak flows for Penobscot River at Eddington
(01036390) are not reported because the annual peak
flows at this station appear to come from an unrepre-
sentative short period when compared to those at
Penobscot River at West Enfield (01034500). The peak
flows for St. Croix River near Baileyville (01020000)
are not reported because the peak flows at St. Croix
River at Baring (01021000) appeared more reasonable.
The logarithms of the annual peak flows at Baring
appeared to fit a Pearson type III distribution better
than those at Baileyville.

Development of the estimates

The guidelines (Bulletin 17B) of the Interagency
Advisory Committee on Water Data (1982) require that
the peak-flow data used for statistical analysis at a gag-
ing station be a reliable and representative sample of
random, homogeneous events. The annual peak flows
at gaging stations in this report are assumed to be ran-
dom, reliable, and independent of each other.

The peak flows in a drainage basin will not be
homogeneous if the hydrologic conditions in the basin
change significantly over time because of urbanization
or other human activities. A two-sided Mann-Kendall
trend test (Helsel and Hirsch, 1992) was performed on
the annual peak flows at most gaging stations to test for
changes in drainage basins over time. To produce accu-
rate results for the significance of a trend, this test

4 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervails—USGS WRIR 99-4008


20

Tabie 2. Drainage areas and percentage of basin wetlands for 70 gaging stations used in regression equations

Areal percentage

ues ot aging station mane ges) arenas
01011000 Allagash River near Allagash, Maine 3,180 9.4
01013500 Fish River near Fort Kent, Maine 2,260 15.5
01014700 Factory Brook near Madawaska, Maine 15.2 2.8
01015700 Houlton Brook near Oxbow, Maine 14.1 21.2
01015800 Aroostook River near Masardis, Maine 2,310 14.0
01016500 Machias River near Ashland, Maine 852 8.8
01017000 Aroostook River at Washburn, Maine 4,280 12.0
01017300 Nichols Brook near Caribou, Maine 10.3 9.1
01017900 Marley Brook near Ludlow, Maine 3.81 09
01018000 Meduxnekeag River near Houlton, Maine 453 17.6
01021300 Wiggins Brook near West Lubec, Maine 13.0 13.1
01021500 Machias River at Whitneyville, Maine 1,190 15.5
01021600 Middle River near Machias, Maine 21.4 14.0
01022000 East Machias River near East Machias, Maine 648 23.5
01022260 Pleasant River near Epping, Maine 157 26.7
01022500 Narraguagus River at Cherryfield, Maine 588 15.0
01022700 Forbes Pond Brook near Prospect Harbor, Maine 23.7 19.0
01023000 West Branch Union River at Amherst, Maine 386 18.9
01024200 Garland Brook near Mariaville, Maine 25.4 719
01026800 Frost Pond Brook near Sedgwick, Maine 12.5 15.3
01030300 Trout Brook near Danforth, Maine 10.8 15.4
01030400 Gulliver Brook near Monarda, Maine 28.5 20.0
01030500 Mattawamkeag River near Mattawamkeag, Maine 3,670 19.0
01031500 Piscataquis River near Dover-Foxcroft, Maine 7712 10.2
01031600 Morrison Brook near Sebec Corners, Maine 13 1.1
01033500 Pleasant River near Milo, Maine 837 97
01034000 Piscataquis River at Medford, Maine 3,010 12.7

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008




Appendix—Detailed descriptions of gaging-station locations—Continued

[lat, latitude; long, longitude; km, kilometers; m, meters; right and left
bank are referenced facing downstream]

usGs
gaging-station
number

Gaging station name

Station location

01048500

01049000

01049100

01049130

01049205

01049300

01049373

01049500

01049550

01049700

01050900

01052500

01053500

01054000

Kennebec River at Waterville,
Maine

Sebasticook River near
Pittsfield, Maine

Hall Brook at Thorndike, Maine

Johnson Brook at South Albion,
Maine

Kennebec River near
Waterville, Maine

North Branch Tanning Brook near
Manchester, Maine

Mill Stream at Winthrop, Maine

Cobbosseecontee Stream at
Gardiner, Maine

Togus Stream at Togus, Maine

Gardiner Pond Brook at Dresden
Mills, Maine

Four Ponds Brook near
Houghton, Maine

Diamond River near Wentworth
Location, New Hampshire

Androscoggin River at Errol, New
Hampshire

Androscoggin River near Gorham,
New Hampshire

Lat 44°33’45”, long 69°37’ 10”, Kennebec County, at dam and mill
of Hollingworth and Whitney Co. at Winslow, 3.2 km above
Sebasticook River, and 5.6 km above Messalonskee Stream.

Lat 44°43°00”, long 69°24’56”, Somerset County, on right bank
2.7 km upstream from Twentyfive Mile Stream, and 8.0 km
south of Pittsfield.

Lat 44°34’52”, long 69°16’50”, Waldo County, at culvert in State
Highway 139, 0.3 km northwest of Thorndike, and 0.5 km
upstream from mouth.

Lat 44°29°53”, long 69°29” 12”, Kennebec County, on right bank
approximately 1.3 km downstream from Dutton Pond, and
approximately 0.8 km southwest of Albion.

Lat 44°31'38”, long 69°39°09”, Kennebec County, on right bank
at Waterville Sewage Treatment Plant, 2.1 km downstream from
Sebasticook River, and 0.6 km upstream from Messalonskee
Stream.

Lat 44°21700”, long 69°51'07", Kennebec County, on right bank
8.5 m upstream from culvert under Prescott Road, 0.3 km north
of the intersection with Puddle Dock Road, 550 m upstream
from mouth, and 2.9 km north of Manchester.

Lat 44°18'24”, long 69°58’ 18”, Kennebec County, on right bank
150 m downstream from bridge on Main Street, at Winthrop.

Lat 44°13’42”, long 69°46’42”, Kennebec County, on left bank
90 m upstream from Winter Street bridge in Gardiner, 0.6 km
upstream from mouth, and 1.3 km downstream from Gardiner
Water District Dam.

Lat 44°15°57”, long 69°41’55”, Kennebec County, on right bank
30 m downstream from mouth of Chase Meadow Stream and
185 m downstream from State Route 226 bridge, and 2.4 km
northeast of Chelsea.

Lat 44°06’29”, long 69°43’21”, Lincoln County, 5 m upstream
from culvert in town road from Dresden Mills to Head Tide,
185 m upstream from mouth, and in northeast section of village
of Dresden Mills.

Lat 44°49’55”, long 70°42’08”, Franklin County, 8 m upstream
from culvert in State Highway 17, 1.5 km upstream from mouth,
and 10.9 km north of Houghton.

Lat 44°52’40”, long 71°03’25”, Coos County, on left bank, 1.6 km
upstream from mouth, and 2.6 km north of Wentworth Location.

Lat 44°46’57”, long 71°07’46”, Coos County, on right bank
0.6 km downstream from Errol Dam, 0.6 km northeast of Errol,
and 1.0 km upstream from Clear Stream.

Lat 44°26’ 10”, long 71°11’27”, on right bank at Pulsifer Rips,
3.5 km downstream from Dead River, and 6.4 km upstream
from Gorham.

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

43


oe,
/ bor Ore GBP
2

& “mal, cc NY

ee ee :
47° v L
7
t
froipt0070
Ae 010173004
70°, 4010170001
401010000

“Ac o1ore500

|
|
|

crores |
proreoook 1

(01054009,

EXPLANATION
& Station location
01010000 Station number

SCALE
0 40 MILES

bt
to) 50 KILOMETERS

Figure 2. U.S. Geological Survey streamflow-gaging stations used to estimate
the magnitude of peak flows for streams in Maine.

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008 7


national skew isoline map). The national skew isoline
map was used to predict the station skews for the 44
stations used in the previous skew analyses. The mean
square error of prediction was then computed. The Bul-
letin 17B generalized skew had a much larger mean
square error of prediction (0.188) than the new Maine
generalized skew (0.088).

Recorded peak flows at individual gaging sta-
tions, especially those with short periods of records,
may not be representative of peak flows from longer
periods of record. Because of this, peak flows for given
recurrence intervals at each gaging station were com-
bined with the regression-equation peak flows at that
station to compute the best estimate of peak flows for
that station. If two independent estimates are weighted
inversely proportional to their variances, the variance
of the weighted average is less than the variance of
either estimate (Interagency Advisory Committee on
Water Data, 1982). In other words, the weighted aver-
age will produce the most accurate estimates (number
of years of record is inversely proportional to variance
and thus the weighting in equation 1 becomes direct
with years of record). The weighted-average peak flow
(Qy) was calculated using the following equation:

Qw = ((Qg)(n) + (Q,)(e)) / (n +e), (ly
where

Qg is the gaging-station peak flow for a given
recurrence interval, calculated by the methods
described in this section,

n is the number of annual peak flows at a gaging
station,

Q, is the regression-equation peak flow calculated
by the methods in section 2, “Estimating peak
flows for ungaged, unregulated streams in rural
drainage basins”, and

é is the average equivalent years of record for the
appropriate regression equations. Equivalent
years of record are listed and defined in
section 2.

Presentation of the estimates

The peak flows for recurrence intervals of 2, 5,
10, 25, 50, 100, and 500 years at USGS streamflow-
gaging stations with 10 years or more of record (with
the exceptions noted in “Data used for the estimates”)
are listed in table 1. Three different peak flows are
given (where appropriate) for unregulated stations: the
gaging-station estimate (G), the regression-equation

estimate (R), and a weighted average (W) of these two
estimates. As discussed in “Development of the esti-
mates”, the weighted average is the most accurate
peak-flow estimate for each gaging station. For regu-
lated stations, the regression-equation estimate cannot
be weighted with the gaging-station estimate because
the regression equations do not apply to regulated sta-
tions. Regression estimates were not computed for sta-
tions that include Canadian drainage. Also included in
table 1 are the USGS gaging-station number and name,
the magnitude and date of the highest peak flow known
at the gaging station, the period of known peak flows
(the period includes recorded peak flows at the gaging
station and relevant historical information at or near the
gaging station), the regulated or unregulated status of
the station, and the drainage-basin area for the gaging
station. Detailed location descriptions for the gaging
stations are in the Appendix. Station locations are
shown in figure 2.

Limitations and accuracy of the estimates

The recorded annual peak flows used to compute
the peak flows for given recurrence intervals at gaging
stations in this section are assumed to be representative
of recorded and unrecorded peaks. Generally, more
years of data at a station lead to more accurate esti-
mates of peak flows. The estimated peak flows at gag-
ing stations will not be reliable if the drainage basin of
a station becomes significantly more regulated or
urbanized than it was during the period used to calcu-
late the peak flows. In addition, if the flow management
at a regulated station (a station with more than
49,200 m? of usable storage per square kilometer)
changes, the estimated peak flows presented in this sec-
tion may not apply, depending on the magnitude of the
changes. The actual peak flows at stations were ana-
lyzed to identify significant changes in flow manage-
ment. Subtle or recent changes in flow management
may have gone undetected.

If an extreme flood did not occur at a regulated
station during the period of streamflow-data collection
for that station, the estimated peak flows may seriously
underestimate the true peak flows. This underestima-
tion could occur because a very large inflow to a reser-
voir may cause outflows to be regulated differently
than at any time in the past.

The estimated peak flows in this section do not
consider the possibility of dam failures on peak flows.
The peak flows on streams with dams that store large
quantities of water could be significantly greater than
the given peak flows if a dam failure occurs.

6 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


Appendix—Detailed descriptions of gaging-station locations

{lat, latitude; long, longitude; km, kilometers; m, meters; right and left
bank are referenced facing downstream]

USGS
gaging-station Gaging station name Station location
number
01010000 St. John River at Ninemile Bridge, Lat 46°42’00”, long 69°42’59”, Aroostook County, on right bank
Maine in T12 R1S, 0.2 km downstream from Ninemile Brook, and
0.6 km downstream from Ninemile Bridge, and 17.7 km north-
west of Clayton Lake Post Office.
01010070 Big Black River near Depot Moun- _Lat 46°53’38”, long 69°45’08”, Aroostook County, on left bank at
tain, Maine the Six Mile Landing Road Bridge, 6.4 km northeast of Depot
Mountain, 43.1 km upstream from mouth.

01010500 St. John River at Dickey, Maine Lat 47°06’44”, long 69°05’25”, Aroostook County, on right bank
150 m downstream of highway bridge at Dickey, 0.6 km down-
stream from Little Black River, and 4.5 km upstream from Alla-
gash River.

01011000 Allagash River near Allagash, Lat 47°04’ 14”, long 69°04’51”, Aroostook County, on left bank

Maine 4.8 km upstream from mouth and village of Allagash.

01011500 St. Francis River at outlet of Glasier — Lat 47°12’25”, long 68°57’25”, Madawaska County, on left bank

Lake, near Connors, New Brun- at outlet of Glasier Lake, 6.4 km upstream from mouth, and
swick, Canada 10.5 km west of Connors.

01013500 Fish River near Fort Kent, Maine Lat 47°14’ 14”, long 68°34’56”, Aroostook County, on right bank
90 m upstream from highway bridge at Fort Kent Mills, 3.0 km
upstream from mouth, and 3.0 km south of Fort Kent.

01014000 St. John River below Fish River, at Lat 47°15°27”, long 68°35’35”, Aroostook County, on right bank

Fort Kent, Maine at Fort Kent and 0.3 km downstream from Fish River.

01014700 Factory Brook near Lat 47°21'09”, long 68°17’55”, Aroostook County, 4 m upstream

Madawaska, Maine from culvert in U.S. Highway 1, 0.8 km upstream from mouth
and 1.8 km east of Madawaska.

01015700 Houlton Brook near Oxbow, Maine _Lat 46°26’ 18”, long 68°24’21”, Aroostook County, at culvert in
road west from State Highway 11 to Oxbow, 3.1 km upstream
from mouth, and 6.9 km northeast of Oxbow.

01015800 Aroostook River near Masardis, Lat 46°31721”, long 68°22’23”, Aroostook County, on left bank,

Maine 55 m upstream from highway bridge, and 2.9 km downstream
from St. Croix Stream and Masardis.

01016500 Machias River near Ashland, Maine _Lat 46°37’42”, long 68°26’07”, Aroostook County, on right bank
30 m upstream from highway bridge, 1.3 km upstream from
mouth, and 2.4 km west of Ashland.

01017000 Aroostook River at Washburn, Lat 46°46’36”, long 68°09’29”, Aroostook County, on right bank,

Maine 15 m upstream from Bangor and Aroostook Railroad bridge,
0.2 km downstream from Salmon Brook, and 1.6 km south of
railroad station at Washbum.

01017300 Nichols Brook near Caribou, Maine _Lat 46°51’31”, long 67°56’ 18”, Aroostook County, at culvert in
road north from Grimes Mills to State Highway 223, 90 m
upstream from mouth and 5.6 km east of Caribou.

01017900 Marley Brook near Ludlow, Maine Lat 46°08’ 42”, long 68°03’42”, Aroostook County, on left bank at
upstream entrance of culvert under U.S. Route 2, 0.7 km
upstream from mouth, and 1.8 km west of Ludlow.

01018000 Meduxnekeag River near Lat 46°06’ 17”, long 67°52’00”, Aroostook County, on right bank

Houlton, Maine

0.5 km downstream from South Branch, and 3.2 km upstream
from Houlton.

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

39


Table 5. (xT A’! X)! matrices for the n-year
(n =2, 5, 10, 25, 50, 100, 500) full regression
equations

[Numbers are in scientific notation]

(XT At xy? matrix

2-year recurrence interval
0.58123E-02 -0.15009E-02 -0.10490E-03
-0.15009E-02 0.60524E-03 -0.44046E-05
-0.10490E-03 -0.44046E-05 0.94475E-05

5-year recurrence interval
0.65716E-02 -0.16938E-02 -0.11312E-03
-0.16938E-02 0.66864E-03 -0.43865E-05
-0.11312E-03 -0.43865E-05 0.10050E-04

10-year recurrence interval
0.7488 1E-02 -0.19256E-02 -0.12376E-03
-0.19256E-02 0.74673E-03 -0.45182E-05
-0.12376E-03 -0.45182E-05 0.10878E-04

25-year recurrence interval
0.88850E-02 -0.22793E-02 -0.14074E-03
-0.22793E-02 0.86835E-03 -0.48668E-05
-0.14074E-03 -0.48668E-05 0.12244E-04

50-year recurrence interval
0.10014E-01 -0.25652E-02 -0.15473E-03
-0.25652E-02 0.96761E-03 -0.52042E-05
-0.15473E-03 -0.52042E-05 0.13387E-04

100-year recurrence interval
0.11175E-01 -0.28591E-02 -0.16918E-03
-0.28591E-02 0.10700E-02 -0.55727E-05
-0.16918E-03 -0.55727E-05 0.14574E-04

500-year recurrence interval
0.14051E-01 -0.35887E-02 -0.20624E-03
-0.35887E-02 0.13277E-02 -0.66561E-05
-0.20624E-03 -0.66561E-05 0.17670E-04

Comparison of estimated peak flows for ungaged,
unregulated streams in rural drainage basins
computed using Maine Department of
Transportation and USGS techniques

The 50-year peak flows estimated from six dif-
ferent methods were compared to the weighted-aver-
age 50-year peak flows and the gaging-station 50-year
peak flows (table 1) for 53 gaging stations in Maine.
Four of these estimating methods are described in “A
guide for the hydrologic and hydraulic analysis of
bridge drainage structures” (Maine Department of
Transportation (MDOT), Design Division, Bridge Sec-
tion, written commun., 1995). The four methods in the

MDOT guide are “Potter’s series,” “Benson’s
method,” “USGS method,” and “FHWA method.” The
fifth method is the full 50-year regression equation
(table 3) from this report and the sixth method is the
simplified 50-year regression equation (table 8) from
this report. The “USGS method” uses Morrill’s (1975)
regression equations. The “FHWA method” is the aver-
age of FHWA methods A and B.

After the 50-year peak flows were computed by
these six methods, the logarithms (base 10) of the flows
were calculated. The logs of the weighted-average 50-
year peak flows (considered the best estimate of true
flows) and the gaging-station 50-year peak flows
(another estimate of true flows) were subtracted from
the logs of the flows from the method estimates. These
differences were the basis for the rest of the compari-
son discussed here. By computing the difference of the
logs of the peak flows, the ratio of the estimated flows
to the true flows are calculated rather than the arith-
metic difference. If this had not been done, the differ-
ence between the estimated and true flows for small
watersheds would have looked insignificant when
compared to the difference calculated for large water-
sheds. For example, if the true 50-year peak flow was
10,000 m?/s and the estimated 50-year flow was
11,000 m?/s, the absolute difference between the two
would be 1,000 m?/s. For a true flow of 100 m/s and
an estimated flow of 200 m/s, the absolute difference
would be 100 m?/s. This difference appears much
smaller than the 1,000 m/s difference; however,

200 m/s is twice as large as 100 m/s, whereas
11,000 m?/s is only 1.1 times as large as 10,000 ms.
Also, by using the logarithms of the flows, an estimated
flow that is half of the true flow will show the same dif-
ference as one that is twice the true flow. For example,
with a true flow of 100 m?/s and an estimated flow of
200 m?/s, the logarithm of the estimated flow minus the
logarithm of the true flow is 0.3. For a true flow of
100 m?/s and an estimated flow of 50 m/s, the differ-
ence of the logarithms is -0.3.

The root mean square error (RMSE) was used as
an overall measure of accuracy for the six estimating
methods. A lower RMSE indicates a better overall
accuracy. The RMSE is computed as the square root of
the mean of the squared differences between the logs of
the true and estimated flows. For Benson’s method and
Potter’s series, it was not possible to calculate the esti-
mated 50-year peak flows for several of the 53 stations
used in this comparison. The input data for these two
methods were outside the range of data that could be

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008 27


Appendix—Detailed descriptions of gaging-station locations—Continued

(lat, latitude; fong, longitude; km, kilometers; m, meters; right and left
bank are referenced facing downstream]

USGS

gaging-station Gaging station name Station location

number

01054200 Wild River at Gilead, Maine Lat 44°23°27”, long 70°58’47”, Oxford County, on right bank
61 m upstream from highway bridge on U.S. Route 2, 600 m
upstream from mouth, and 0.6 km west of Gilead.

01054300 Ellis River at South Andover, Maine Lat 44°35’37”, long 70°44’01”, Oxford County, on left bank 30 m
upstream from covered bridge at South Andover.

01054500 Androscoggin River at Rumford, Lat 44°33'04”, long 70°32’38”, Oxford County, on right bank

Maine below lower power plant of Rumford Falls Power Co. in Rum-
ford, and 300 m upstream from Swift River.

01055000 Swift River near Roxbury, Maine Lat 44938732”, long 70°35’ 17”, Oxford County, on left bank
0.3 km downstream from Philbrick Brook 3.4 km downstream
from Roxbury, and 11.6 km upstream from mouth.

01055300 Bog Brook near Buckfield, Maine Lat 44°15’57”, long 70°18°58”, Oxford County, 5 m upstream
from culvert in State Highway 117, 275 m upstream from
mouth, and 5.0 km southeast of Buckfield.

01055500 Nezinscot River at Turner Lat 44°16’ 10”, long 70°13’49”, Androscoggin County, on left

Center, Maine bank 150 m upstream from State Highway 117 bridge at Turner
Center, and 5.8 km upstream from mouth.
01057000 Little Androscoggin River near Lat 44°18" 12”, long 70°32’22”, Oxford County, on island 15 m
South Paris, Maine upstream from Snow Falls, and 9.6 km upstream from South
Paris.
01058500 Little Androscoggin River near Lat 44°03’49”, long 70°16’28”, Androscoggin County, on right
Auburn, Maine bank 30 m upstream from highway bridge at Littlefields, 5.0 km
southwest of Auburn, and 7.4 km upstream from mouth.

01059000 Androscoggin River near Auburn, _Lat 44°04°20”, long 70°12’31”, Androscoggin County, on right

Maine bank 2.4 km downstream from Little Androscoggin River, and
3.4 km downstream from North Bridge between Auburn and
Lewiston.

01059800 Collyer Brook near Gray, Maine Lat 43°55’03”, long 70°19’02”, Cumberland County, 15 m down-
stream from U.S. Highway 202, 3.9 km northeast of Gray, and
5.5 km upstream from mouth.

01060000 Royal River at Yarmouth, Maine Lat 43°47°57”, long 70°10°45”, Cumberland County, on right
bank 45 m upstream from East Main Street bridge in Yarmouth.

01062700 Patte Brook near Bethel, Maine Lat 44°20'41”, long 70°47°32”, Oxford County, 5 m upstream
from culvert in town road between State Highway 5 and West
Bethel, 550 m upstream from mouth, and 7.2 km south of
Bethel.

01064000 Presumpscot River at Outlet of Lat 43°49°03”, long 70°27°01”, Cumberland County, at dam of

Sebago Lake, Maine hydroelectric plant at Eel Weir Falls 1.6 km downstream from
lake outlet.

01064118 Presumpscot River at Lat 43°41"13”, long 70°20°49”, Cumberland County, on right

Westbrook, Maine bank 0.6 km downstream from Cumberland Street Bridge in
Westbrook, at S.D. Warren Co. owned bridge.
01064200 Mill Brook near Old Orchard Beach, _ Lat 43°32’40”, long 70°23’31”, York County, on abutment of dis-

44 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

Maine

mantled bridge, 23 m upstream from culvert in Portland Ave-
nue, 2.8 km upstream from mouth, and 3.0 km northwest of Old
Orchard Beach.


Table 4. Estimated model error variance and average sampling error variance for the full regression equations

Q, - Peak fiow for recurrence interval n

Estimated model error Average sampling

(n= 2, 5, 10, 25, 50, 100, 500 years) (eacei0 less) error variance
Q2 0.0206 0.0017
Qs 0.0211 0.0019
Qio 0.0220 0.0021
Qos, 0.0236 0.0025
Qs50 0.0250 0.0028
Qio0 0.0265 0.0031
Qs00 0.0308 0.0039

The sampling error can by reduced by collecting more

data at existing gaging stations, collecting data at new
gaging stations, or some combination of both.

The standard error of prediction at an individual
study site can be calculated using matrix algebra. The
general regression model can be represented in matrix
form (ignoring errors) by

Y=XB,
where

Y is the 70-by-1 column vector of the logarithms
(base-10) of gaging-station peak flows at the
70 stations used in the development of each
regression equation in this section of the
report;

X is the 70-by-3 vector containing a column of
ones, a column of the logarithms of the drain-
age areas for each of the 70 stations, and a col-
umn of the percentage of basin wetlands for
each station; and

B is the 3-by-1 column vector of regression coef-
ficients.

(2)

The sampling error variance at a site (SEs) is defined
by
SEg? = xp (KT AT XY! xl, @)

where

Xo is the row vector for the study site, containing
a one, the logarithm of the drainage area for
the study site, and the percentage of basin wet-
lands for the site;

26

T is the matrix algebra symbol for “transpose”;

and
the «xt “! xy! matrix for the n-year (n = 2, 5,
10, 25, 50, 100, 500) regression equations in
this section (table 5) was computed by
GLSNET, a computer program for generalized
least squares regression.
The standard error of prediction (SE,) for a study site
is then calculated as

SEp = ( SExy’ + SEg? )!?,

where

(4)

SExy? is the estimated model error variance
(table 4) and
SEg? is calculated in equation 3.

The prediction interval for a study site can than be com-
puted as

(17 V)Qn < On < (V)Qn>
where

log (base-10) V = (t(qy2, 67) SEp) for the regression
equations in this section (the value of 67 is the
degrees of freedom for the t-distribution for
these regression equations, and o is the proba-
bility of a Type 1 error),

Q, is the computed peak flow (from the appropri-
ate regression equation) for recurrence interval
n(n=2, 5, 10, 25, 50, 100, 500 years) at the
ungaged study site, and

, is the true peak flow for recurrence interval n.
We are 100(1-c) percent confident that the true
value lies in the prediction interval.

(5)

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


Figure 1. Flowchart for choosing the appropriate means of obtaining estimated peak flows in Maine

Site at a
gaging station ?

Yes

Appropriate section of the report

No

Site
regulated ?

Yes

No

Section 1: Estimates of peak flows and
maximum recorded flows at USGS
streamflow-gaging stations (p. 4)

Section 6: Estimating peak flows
for ungaged sites on regulated
streams (p. 37)

Drainage basin
urbanized ?

Yes

Section 5: Estimating peak flows for
ungaged, unregulated streams in
urbanized drainage basins (p. 32)

No

Site near a
gaging station on
the same stream ?

Yes

Section 4: Estimating peak flows for
ungaged sites on gaged, unregulated
streams in rural drainage basins (p. 30)

No

Lower accuracy
and easier

application desired ?

Yes

Section 3: Estimating peak flows for un-
gaged, unregulated streams in rural drain-
age basins—Simplified technique (p. 29)

No

Section 2: Estimating peak flows for
ungaged, unregulated streams in rural
drainage basins (p. 18)

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

3


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17

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


is |
isan
a5 nes

putin oe

RG

EZ

Base from U.S. Department of
Commerce, National Weather Service

SCALE EXPLANATION

0) 200 MILES — 1.2— line of equal precipitation
. in inches
0 250 KILOMETERS

Figure 4. National Weather Service 2-hour, 2-year rainfall for Maine.

34 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


Middle
Third

Middle \
Third

Outlet

B Fan-shaped basir
A Long, narrow basin an-snaped basin

Y ° in age pivide

oe mmm le oem et mes, |

. Middle
Third \ Upper

\

\

\
jee

C Short, wide basin
Outlet

Figure 5. Typical drainage-basin shapes and subdivision into basin thirds (from Sauer and others, 1983).

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008 35


Table 3. Full regression equations and their accuracy for estimating peak flows for ungaged, unregulated streams in rural

drainage basins in Maine

{Qs peak flow, in cubic meters per second; A is drainage area, in square kilometers; W is percentage of basin wetlands]

recurencelncrsifecurenceimevae tom? rerpracisn —(PRESSM)"* Average equaent
to 500 years) (percent) (percent) years of record
Qy = 1.075 (A)°-848 4 9°0.0268(W) 40.6 to -28.9 42.2 to -29.7 1.82
Qs = 1.952 (A)°820 4 9°0.0288(W) 41.9 to -29.5 43.5 to -30.3 2.47
Quo = 2.674 (A)°-808 4 9-0.0300(W) 42.9 to -30.0 45.2 to -31.1 3.20
Qyg = 3.740 (A)®-790 4 9°0.0312(W) 45.2 to -31.1 48.3 to -32.5 4.14
Qsq = 4.637 (A)°-780 4970.0820(W) 46.9 to -31.9 51.0 to -33.8 4.78
Qroo = 5.629 (A)°771 49°0.0326(W) 48.6 to -32.7 53.5 to -34.8 5.37
Qso9 = 8.283 (A)%754 10°0-0340(W) 53.5 to -34.8 60.0 to -37.5 641

Definitions of equation variables in table 3:

Qy - Peak flow - The calculated peak flow, in
cubic meters per second, for recurrence interval n (n
equals 2, 5, 10, 25, 50, 100, or 500 years).

A - Drainage area - The contributing area, in
square kilometers, of a drainage basin. The term “con-
tributing” means that flow from an area could contrib-
ute flow to a study site on a stream. This definition is
intended to exclude only closed subbasins (subbasins
with no outlet) of a drainage basin. Noncontributing
drainage area in Maine of any significant size is rare.
Contributing drainage area, as defined for this report,
does include parts of drainage-basin area that may not
contribute significant flow to a peak flow because of the
timing of peak flows from different parts of a basin.

All units of drainage area, except square kilome-
ters, will result in incorrect estimates of peak flows. If
inch-pound units are desired for the estimated peak
flows, the conversion should be made to the peak flows
after applying the equation(s).

The drainage area can be computed from a num-
ber of sources. A series of drainage area reports that list
drainage areas at selected points on most streams in
Maine have been published by the USGS (Cowing and
Caracappa, 1978; Cowing and McNelly, 1978; Fon-
taine, 1979a, 1979b, 1980, 1981, 1982a, 1982b; Fon-
taine, Herrick, and Norman, 1982). Drainage areas can
also be computed by digitizing the area of a drainage
basin, after delineating the drainage-basin boundaries
on topographic maps. Drainage areas can be computed
from geographic information system (GIS) coverages.
However, these coverages currently (1998) are not

available in an easily usable form. The drainage areas
for the 70 streamflow-gaging stations used in the devel-
opment of the Maine regression equations (table 2)
were calculated using the first two methods in this para-
graph. The values of drainage area measured by all
three methods are expected to be very similar.

W - Basin Wetlands - The areal percentage of
all types of wetlands in a basin (which includes lakes,
ponds, reservoirs, and rivers). The areal percentage
should be computed with National Wetland Inventory
Maps because these maps were used in the develop-
ment of the regression equations. The National Wet-
land Inventory Maps are produced by the U.S. Fish and
Wildlife Service at a scale of 1:24,000. The types of
wetlands on the maps (palustrine, lacustrine, and so
forth) are not relevant to this study. If a drainage area
of interest contains Canadian land, Wetland Inventory
Maps are available from the Canadian Wildlife Service
at a scale of 1:50,000. It is not known if the Canadian
wetland maps are comparable to United States wetland
maps, however, these maps are the Canadian product
that is most likely to be similar to the United States
wetland maps. One known difference between the
Canadian and American maps is that the Canadian
maps do not include all lake, pond, reservoir, and river
areas in their wetland categories. The calculation of the
basin wetlands variable for sites that have Canadian
drainage area should include the area of these bodies of
water plus the Canadian wetland area. The accuracy of
the regression equations (table 3) may not be applica-
ble to sites with Canadian drainage area.

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008 23


CONTENTS

Abstract...
PART 1: PURPOSE AND USE OF THIS REPORT.
Introduction .....
Choosing the appropriate section of this report to obtain estimated peak flows
PART 2: ESTIMATING THE MAGNITUDE OF PEAK FLOWS .....
Section 1: Estimates of peak flows and maximum recorded fiows at USGS streamflow-gaging station:

Data used for the estimates...
Development of the estimates
Presentation of the estimates

Limitations and accuracy of the estimates

Section 2: Estimating peak flows for ungaged, unregulated streams in rural drainage basins

Data used for the technique ..
Development of the technique
Application of the technique.

Limitations and accuracy of the technique

Advanced accuracy analysis......
Comparison of estimated peak flows for ungaged, unregulated streams in rural drainage basins

computed using Maine Department of Transportation and USGS techniques...

Section 3: Estimating peak flows for ungaged, unregulated streams in rural drainage basins—
Simplified technique...
Application of the simplified technique.
Limitations and accuracy of the simplified technique

Section 4: Estimating peak flows for ungaged sites on gaged, unregulated streams in rural drainage basins
Application of the technique.
Limitations of the technique ..

Section 5: Estimating peak flows for ungaged, unregulated streams in urbanized drainage basins.
Application of the technique.
Limitations and accuracy of the technique

Section 6: Estimating peak flows for ungaged sites on regulated streams
PART 3: SUPPLEMENTAL INFORMATION .......
References cited.
Appendix—Detailed descriptions of gaging-station locations

FIGURES

1. Flowchart for choosing the appropriate means of obtaining estimated peak flows in Maine ...
2. Map of U.S. Geological Survey streamflow-gaging stations used to estimate the magnitude of peak flows

for streams in Maine...
3. Graph of two-dimensional range of explanatory variables for the full regression equations.
4. Map of National Weather Service 2-hour, 2-year rainfall for Maine ...
5. Schematic of typical drainage-basin shapes and subdivision into basin third:

Contents ill


Appendix—Detailed descriptions of gaging-station locations—Continued

Ulat, latitude; long, longitude; km, kilometers; m, meters; right and left
bank are referenced facing downstream]

USGS
gaging-station
number

Gaging station name

Station location

01036500

01037200

01037430

01038000

01041000

01041900

01042500

01043500

01045000

01046000

01046500

01046800

01047000

01048000

01048100

42 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

Kenduskeag Stream near
Kenduskeag, Maine

Shaw Brook’ near Northern Maine
Junction, Maine

Goose River at Rockport, Maine

Sheepscot River at North
Whitefield, Maine

Kennebec River at Moosehead,
Maine

Mountain Brook near Lake
Parlin, Maine

Kennebec River at The Forks,
Maine

Dead River near Dead River, Maine

Dead River at The Forks, Maine

Austin Stream at Bingham, Maine

Kennebec River at Bingham, Maine

South Branch Carrabassett River at
Bigelow, Maine

Carrabassett River near North
Anson, Maine

Sandy River near Mercer, Maine

Pelton Brook near Anson, Maine

Lat 4495348”, long 68°53’04”, Penobscot County, on right bank
90 m upstream from highway bridge on State Route 15, 2.9 km
downstream from Black Stream, and 4.7 km south of
Kenduskeag.

Lat 44°46°39”, long 68°50’59”, Penobscot County, 8 m upstream
from culvert in U.S. Highway 95, 1.8 km upstream from mouth,
and 1.9 km southwest of Northern Maine Junction.

Lat 44°11'21”, long 69°04’49”, Knox County, 2 m upstream from
culvert in U.S. Highway 1, 0.6 km upstream from mouth, and
0.6 km northeast of Rockport.

Lat 44°13'23”, long 69°35’38”, Lincoln County, on left bank 15m
upstream from highway bridge on State Route 126 at North
Whitefield, at mouth of Finn Brook, and 0.5 km east of North
Whitefield village.

Lat 45°35°08”, long 69°43’05”, Somerset County, on right bank
215 m downstream from dam at East Outlet of Moosehead
Lake, and 0.3 km northwest of Moosehead.

Lat 45°28’ 12”, long 70°03’54”, Somerset County, at culvert in
U.S. Highway 201, 2.9 km upstream from mouth and 6.1 km
southeast of Lake Parlin.

Lat 45°20"45”, long 69°57°48”, Somerset County, on right bank at
The Forks, 0.6 km upstream from highway bridge, and 1.1 km
upstream from Dead River.

Lat 45°13’48”, long 70°11’58”, Somerset County, on right bank at
foot of Long Falls, in T3 R4, 0.5 km upstream from Black
Brook, and 0.8 km downstream from Flagstaff Lake Dam.

Lat 45°20°59”, long 69°59’26”, Somerset County, on left bank
2.4 km northwest of The Forks, and 2.9 km upstream from
mouth.

Lat 45°03’55”, long 69°52’55”, Somerset County, at Bingham,
and 1.2 km upstream from mouth.

Lat 45°03’06”, long 69°53’ 12”, Somerset County, on right bank at
Bingham, 15 m downstream from highway bridge, 0.6 km
downstream from Austin Stream, and 2.6 km downstream from
Wyman Dam.

Lat 45°04’45”, long 70°19°03”, Franklin County, at bridge in State
Highway 27, and 915 m southeast of Bigelow.

Lat 44°52'09”, long 69°57’20”, Somerset County, on left bank
5.5 km upstream from Mill Stream and North Anson.

Lat 44°42'26”, long 69°56’21”, Somerset County, on right bank
1.4 km upstream from Bog Stream, 3.4 km north of Mercer, and
13.8 km upstream from mouth.

Lat 44°45’58”, long 69°54’32”, Somerset County, on wingwall of
abandoned highway bridge just downstream from State High-
way 43, 1.1 km upstream from mouth, and 3.9 km southwest of
Anson.


Appendix—Detailed descriptions of gaging-station locations—Continued

[at, latitude; long, longitude; km, kilometers; m, meters; right and left
bank are referenced facing downstream]

USGS
gaging-station
number

Gaging station name

Station location

01018500

01019000

01021000

01021200

01021300

01021500

01021600

01022000

01022260

01022500

01022700

01023000

01024200

01026800

40 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

St. Croix River at Vanceboro, Maine

Grand Lake Stream at Grand Lake
Stream, Maine

St. Croix River at Baring, Maine

Dennys River at Dennysville, Maine

Wiggins Brook near West Lubec,
Maine

Machias River at Whitneyville,
Maine

Middle River near Machias, Maine

East Machias River near East Mach-
ias, Maine

Pleasant River near Epping, Maine

Narraguagus River at
Cherryfield, Maine

Forbes Pond Brook near
Prospect Harbor, Maine

West Branch Union River at
Amherst, Maine

Garland Brook near Mariaville,
Maine

Frost Pond Brook near
Sedgwick, Maine

Lat 45°34’08”, long 67°25’47”, Washington County, on right bank
at international highway bridge in Vanceboro, and 120 m down-
stream from outlet of Spednik Lake.

Lat 45°10°23”, long 67°46’06”, Washington County, on left bank
at Big Falls, 0.8 km southeast of village of Grand Lake Stream,
and 1.3 km downstream from outlet dam of Grand Lake.

Lat 45°08’ 12”, long 67°19°05”, Washington County, on right bank
at site of destroyed international highway bridge at Baring.

Lat 44°54’03”, long 67°14’56”, Washington County, on right bank
305 m upstream from railroad bridge, 1.4 km upstream from
Cathance Stream, and 1.6 km west of Dennysville.

Lat 44°45’26”, long 67°05"23”, Washington County, 3 m upstream
from culvert in State Highway 191, 7.1 km southwest of West
Lubec.

Lat 44°43’23”, long 67°31’ 15”, Washington County, on right bank
245 m downstream from highway bridge on U.S. Route 1A at
Whitneyville.

Lat 44°44’ 14”, long 67°29°35", Washington County, 12 m
upstream from highway bridge in connecting road between
State Highway 192 and U.S. Highway 1A, 3.5 km northwest of
Machias and 5.5 km upstream from mouth.

Lat 44°46’05”, long 67°24’30”, Washington County, just down-
stream from outlet of Hadley Lake and 5.0 km upstream from
East Machias.

Lat 44°41°52”, long 67°47’ 16", Washington County, on right bank
at Saco Falls, 30 m upstream from East Base Road bridge in
Columbia, 1.0 km upstream from North Branch Pleasant River,
and 2.6 km northeast of the village of Epping.

Lat 44°36°29”, long 67°56’ 10”, Washington county, on left bank
245 m upstream from railroad bridge at Cherryfield, and 1.1 km
downstream from West Branch of Narraguagus River.

Lat 44°24’33”, long 68°01°37”, Hancock County, on abutment of
highway bridge in State Highway 186, 30 m upstream from
mouth and in the village of Prospect Harbor.

Lat 44°50°25”, long 68°22"22”, Hancock County on right bank
60 m upstream from site of old tannery dam, 1.0 km upstream
from Indian Camp Brook, and 1.1 km northwest of Amherst.

Lat 44°43’17”, long 68°24’40”, Hancock County, on left bank
6.7 m upstream from State Highway 181, 1.9 km upstream from
mouth, and 2.4 km north of Mariaville.

Lat 44°22” 12”, long 68°39°29", Hancock County, at culvert in
State Highway 15 between Grays Corner and Black Corner,
215 m upstream from mouth, and 8 km northeast of Sedgwick.


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Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

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Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence intervals—USGS WRIR 99-4008

12


U.S. DEPARTMENT OF THE INTERIOR
Bruce Babbitt, Secretary

U.S. GEOLOGICAL SURVEY
Charles G. Groat, Director

The use of firm, trade, and brand names in this report is for identification purposes
only and does not constitute endorsement by the U.S. Geological Survey.

For additional information contact:

District Chief

U.S. Geological Survey
26 Ganneston Drive
Augusta, ME 04330

Telephone: (207) 622-8201

Copies of this report can be purchased
from:

U.S. Geological Survey
Branch of Information Services
Box 25286, Federal Center
Denver, CO 80225

Telephone: (303) 202-4200


Table 9. Urban regression equations and their accuracy for estimating peak flows

[Qis peak flow in cubic feet per second, dash indicates not available]

Peakslow regression equation fr sven recurrence interval ‘ror of estimate eer ot prediction
(percent) (percent)

UQg = 2.35 (A)°-41 (SL)°-17 (Rp+3)2-%4 (ST+8) 0-85 (13 - BDF) °*2 (1A)°-15 (RQ2)°47 46 to -31 54 to -35

UQs = 2.70 (A)°-35 (SL)°-18 (Ro+3)188 (ST+8) 959 (13 - BDF)" (1A)°1 (RQs)°54 44 to -31 -

UO yo = 2.99 (A)? (SL)915 (Ro+3)"75 (ST+8) 057 (13 - BDF) (1A)?-9 (RQ40)58 45 to-31 55 to -35

UQgys = 2.78 (A)°31 (SL)°-"5 (Ro43)"-76 (ST+8)°-55 (13 - BDF)°29 (1A)°97 (RQg5)°5° 48 to -32 -

UQsp = 2.67 (A)°29 (SL)°-15 (Rg+3)"-74 (ST+8) 953 (13 - BDF)028 (1A)° (RQ50)° 50 to -34 -

UQ 99 = 2.50 (A)°29 (SL)°-"5 (Ro+3)"78 (ST+8)0-52 (13 - BDF)O28 (1A)2-8 (RO 499) 54 to -35 66 to -40

U9 = 2.27 (A)°29 (SL)TM18 (Ro+3)"88 (ST+8) 4 (13 - BDF)°27 (1A)5 (RO5q9)°°% 61 to -38 -

ST - Drainage basin wetlands, the areal percent-
age of the drainage basin occupied by lakes, reservoirs,
and wetlands. In-channel storage of a temporary nature
caused by detention ponds, roadway embankments, or
other structures is not included in the computation of
ST. This variable should be computed from USGS
topographic maps (not U.S. Fish and Wildlife Service
National Wetland Inventory maps or by other meth-
ods).

\A - The percentage of the drainage basin occu-
pied by impervious surfaces, such as houses, buildings,
streets, and parking lots. This variable should be com-
puted from the best available maps or aerial photo-
graphs. Field inspections to supplement the maps are
useful.

RQ, - The peak flow, in cubic feet per second,
for an equivalent rural drainage basin for recurrence
interval n. For Maine, the equations in table 3 in section
2, “Estimating peak flows for ungaged, unregulated
streams in rural drainage basins” should be used to cal-
culate RQ,,. Note that the peak flow must be converted
from metric to inch-pound units before entering this
variable into the urban regression equations.

BDF - The basin development factor, an index of
the prevalence of the drainage aspects of (a) storm sew-
ers, (b) channel modifications, (c) impervious channel
linings, and (d) curb-and-gutter streets. The range of
BDF is 0 to 12. A value of zero for BDF indicates that
the above drainage aspects are not prevalent, but it does
not necessarily mean the basin is nonurbanized. A
value of 12 indicates full development of the drainage
aspects throughout the basin.

BDF can be easily determined from drainage
maps and field inspections of the drainage basin. After

the basin has been delineated on a topographic map, the
basin is divided into upper, middle, and lower thirds on
the same map. Each third contains approximately one-
third of the drainage area and drains the upper, middle,
or lower reaches of the basin. Because travel time is
considered when drawing the lines separating the basin
into thirds, distances along main streams and tributar-
ies can be marked to help locate the boundaries of the
basin thirds. This drawing of the boundaries means that
not all thirds of the basin have equal travel distances
but that within each third, the travel distances of two or
more streams are about equal. Because precise defini-
tion of the lines dividing the basin into thirds is not con-
sidered necessary, the lines can generally be drawn on
the drainage map by eye, without precise measure-
ments. Figure 5 shows schematics of three typical basin
shapes and their division into thirds. Complex basin
shapes and drainage patterns are sometimes encoun-
tered; they require more judgment in subdividing.

Within each drainage-basin third, four aspects of
the drainage system are evaluated, and each is assigned
a code as follows:

1. Channel modifications - If channel modifica-
tions such as straightening, enlarging, deepening, and
clearing are prevalent for the main drainage channels
and principal tributaries (those that drain directly into
the main channel) in a basin third, then a code of 1 is
assigned. Any or all of these modifications would qual-
ify for a code of 1. To be considered prevalent, at least
50 percent of the main drainage channels and principal
tributaries must be modified to some degree over natu-
ral conditions. If channel modifications are not preva-
lent, then a code of zero is assigned.

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008 33


Table 2. Drainage areas and percentage of basin wetlands for 70 gaging stations used in regression equations—Continued

USGS gaging-
‘station number

Gaging-station name

Drainage area
(square kilometers)

Areal percentage
of wetiands in
drainage basin

01034900
01035000
01036500
01037200
01037430
01038000
01041900
01046000
01046800
01047000
01048000
01048100
01049000
01049100
01049130
01049300
01049373
01049550
01049700
01050900
01052500
01054200
01054300
01055000
01055300
01055500
01057000
01058500

01059800

Coffin Brook near Lee, Maine

Passadumkeag River at Lowell, Maine

Kenduskeag Stream near Kenduskeag, Maine

Shaw Brook* near Northern Maine Junction, Maine
Goose River at Rockport, Maine

Sheepscot River at North Whitefield, Maine
Mountain Brook near Lake Parlin, Maine

Austin Stream at Bingham, Maine

South Branch Carrabassett River at Bigelow, Maine
Carrabassett River near North Anson, Maine

Sandy River near Mercer, Maine

Pelton Brook near Anson, Maine

Sebasticook River near Pittsfield, Maine

Hall Brook at Thorndike, Maine

Johnson Brook at South Albion, Maine

North Branch Tanning Brook near Manchester, Maine
Mill Stream near Winthrop, Maine

Togus Stream at Togus, Maine

Gardiner Pond Brook at Dresden Mills, Maine
Four Ponds Brook near Houghton, Maine

Diamond River near Wentworth Location, New Hampshire
Wild River at Gilead, Maine

Ellis River at South Andover, Maine

Swift River near Roxbury, Maine

Bog Brook near Buckfield, Maine

Nezinscot River at Turner Center, Maine

Little Androscoggin River near South Paris, Maine
Little Androscoggin River near Auburn, Maine

Collyer Brook near Gray, Maine

5.49
769

479

233
36.5
914
1,340
38.6
1,480
13.3
7.56
2.41
84.7
614
20.7
10.7
394
180

337

438

190

850
35.7

15.1
22.8
13.2
5.2
65
14.8
3.2
8.6
2.0
16
Vd
46

3.9
13.1
6.0
16.6
213

18.8

3.4
0.7
73
3.0
13.8
11
75

113

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008

21


Estimating the Magnitude of Peak Flows for
Streams in Maine for Selected Recurrence

Intervals

by Glenn Hodgkins

U.S. DEPARTMENT OF THE INTERIOR
U.S. GEOLOGICAL SURVEY
Water-Resources Investigations Report 99-4008

Prepared in cooperation with the
MAINE DEPARTMENT OF TRANSPORTATION

Augusta, Maine
1999


Appendix—Detailed descriptions of gaging-station locations—Continued

{lat, latitude; long, longitude; km, kilometers; m, meters; right and left
bank are referenced facing downstream]

USGS
gaging-station Gaging station name Station location
number
01064500 Saco River near Conway, New Lat 43°59°27”, long 71°05’29”, Carroll County, on left bank at
Hampshire Odell Falls, 2.9 km downstream from Swift River and Conway.
01065000 Ossipee River at Effingham Falls, Lat 43°47°44”, long 71°03’36”, Carroll County, on left bank
New Hampshire 0.5 km upstream from bridge on State Highway 153 at Effing-
ham Falls, 0.5 km downstream from outlet of Ossipee Lake, and
6.4 km northwest of Effingham.

01065500 Ossipee River at Cornish, Maine Lat 43°48’26”, long 70°47°55”, Oxford County, on left bank 30 m
downstream from highway bridge in Cornish, and 2.1 km
upstream from mouth.

01066000 Saco River at Cornish, Maine Lat 43°4829”, long 70°46'53”, Cumberland County, on left bank
90 m upstream from State Highway 117 bridge at Cornish, and
0.6 km downstream from Ossipee River.

01066100 Pease Brook near Cornish, Maine Lat 43°47°19”, long 70°45’58”, York County, 2 m upstream from
culvert in State Highway 25, 365 m upstream from mouth, and
3.0 km southeast of Cornish.

01066500 Little Ossipee River near South Lat 43°41'22”, long 70°40’ 15”, York County, on right bank, 8 m

Limington, Maine upstream from highway bridge, 3.0 km southeast of South Lim-
ington, and 9.3 km upstream from mouth.

01067000 Saco River at West Buxton, Maine Lat 43°40’00”, long 70°36'05”, York County, at hydroelectric
plant of Central Maine Power Co. at West Buxton, and 9.6 km.
downstream from Little Ossipee River.

01069500 Mousam River near West Lat 43°25'04”, long 70°39°32”, York County, on right bank 30 m

Kennebunk, Maine upstream from highway bridge, 2.3 km downstream from Mid-
dle Branch, and 6.4 km west of West Kennebunk.

01069700 Branch Brook near Kennebunk, Lat 43°22'44”, long 70°34’56”, York County, on wingwall of cul-

Maine vert in State Highway 9A, 3.4 km west of Kennebunk, and
5.3 km upstream from mouth.
01072100 Salmon Falls River at Milton, New Lat 43°24’50”, long 70°59’ 15”, Stratford County, on right bank
Hampshire just downstream from Milton Pond, at Milton.
01072500 Salmon Falls River near South Leb- Lat 43°19°40”, long 70°55’40”, York County, on left bank at Stair

anon, Maine

Falls, 2.4 km southeast of South Lebanon, and 4.0 km upstream
from Little River.

Station formerly published as Cold Brook near Northen Maine Junction, Maine

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


Section 3: Estimating peak flows for
ungaged, unregulated streams in rural
drainage basins—Simplified technique

The regression equations for the simplified tech-
nique were developed using drainage area as the only
explanatory variable. Use of this single explanatory
variable results in regression equations that are much
less accurate than the full regression equations in sec-
tion 2, “Estimating peak flows for ungaged, unregu-
lated streams in rural drainage basins”, but the
technique takes less time to apply.

Application of the simplified technique

The simplified peak-flow regression equations
for recurrence intervals of 2, 5, 10,25, 50, 100, and 500
years are presented in table 8. The average standard
error of prediction, the PRESS statistic, and the aver-
age equivalent years of record are discussed in “Limi-
tations and accuracy of the technique” at the end of this
section.

Definitions of equation variables in table 8:

Q,, - Peak flow - The calculated peak flow, in
cubic meters per second, for recurrence interval n (n
equals 2, 5, 10, 25, 50, 100, and 500 years).

A - Drainage area - The contributing area, in
square kilometers, of a drainage basin. The term “‘con-
tributing” means that flow from an area could contrib-
ute flow to a study site on a stream. This definition is
intended to exclude only closed subbasins (subbasins

with no outlet) of a drainage basin. Noncontributing
drainage area in Maine of any significant size is rare.
Contributing drainage area, as defined for this report,
does include parts of drainage-basin area that may not
contribute significant flow to a peak flow because of the
timing of peak flows from different parts of a basin.

All units of drainage area, except square kilome-
ters, will result in incorrect estimates of peak flows. If
inch-pound units are desired for the estimated peak
flows, the conversion should be made to the peak flows
after applying the equation(s).

The drainage area can be computed from a num-
ber of sources. A series of drainage area reports that list
drainage areas at selected points on most streams in
Maine have been published by the USGS (Cowing and
Caracappa, 1978; Cowing and McNelly, 1978; Fon-
taine, 1979a, 1979b, 1980, 1981, 1982a, 1982b; Fon-
taine, Herrick, and Norman, 1982). Drainage areas can
also be computed by digitizing the area of a drainage
basin, after delineating the drainage-basin boundaries
on topographic maps. Drainage areas can be computed
from geographic information system (GIS) coverages.
However, these coverages currently (1998) are not
available in an easily usable form. The drainage areas
for the 70 streamflow-gaging stations used in the devel-
opment of the Maine regression equations are located
in table 2. These drainage areas were calculated using
the first two methods in this paragraph. The values of
drainage area measured by all three methods are
expected to be very similar.

Table 8. Simplified regression equations and their accuracy for estimating peak flows for ungaged,
unregulated streams in rural drainage basins in Maine

[Qs peak flow, in cubic meters per second; A is drainage area, in square kilometers]

k-Fle

Peal given recurrence iierval. ‘er Average standard (PRESSin)"? equivatent

(recurrence intervals from 2 to 500 error of pred 10" (percent) years of

years) (percent) record

Qp = 0.601 (A)°-825 65.2 to -39.5 65.6 to -39.6 0.85

Qs = 1.028 (A)°797 69.0 to -40.8 70.6 to -41.4 1.08

Qyo = 1.363 (A)°783 71.8 to -41.8 73.8 to -42.5 1.39

Qos = 1.844 (A)°767 75.4 to -43.0 78.6 to -44.0 1.81

Qso = 2.244 (A)°-757 77.8 to -43.8 82.0 to -45.0 2.13

Qyo0 = 2.680 (A)°748 80.3 to -44.5 85.4 to -46.0 2.42

Qso0 = 3.836 (A)°722 86.2 to -46.3 93.6 to -48.4 3.04

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008 29


PART 3: SUPPLEMENTAL INFORMATION

REFERENCES CITED

Benson, M.A., 1962, Factors influencing the occurrence of
floods in a humid region of diverse terrain: U.S. Geo-
logical Survey Water-Supply Paper 1580—B, 64 p.

Cook, R.D., and Weisburg, S., 1994, An introduction to
regression graphics: New York, John Wiley and Sons,
253 p.

Cowing, D.J., and Caracappa, D., 1978, Drainage areas of
surface water bodies of the Saco River basin in south-
western Maine: U.S. Geological Survey Open-File
Report, 25 p.

Cowing, D.J., and McNelly, J.L., 1978, Drainage areas of
surface water bodies of the Royal and Presumpscot
River basins in southwestern Maine: U.S. Geological
Survey Open-File Report, 23 p.

Fontaine, R.A., 1979a, Drainage areas of surface water bod-
ies of the Androscoggin River basin in southwestern
Maine: U.S. Geological Survey Open-File Report, 42 p.

1979b, Drainage areas of surface water bodies of

southern Maine coastal river basins: U.S. Geological

Survey Open-File Report, 23 p.

1980, Drainage areas of surface water bodies of the

Kennebec River basin in southwestern Maine: U.S.

Geological Survey Open-File Report, 83 p.

1981, Drainage areas of surface water bodies of the

Penobscot River basin in central Maine: U.S. Geologi-

cal Survey Open-File Report, 92 p.

1982a, Drainage areas of surface-water bodies of

eastern Maine coastal river basins: U.S. Geological

Survey Open-File Report, 54 p.

1982b, Drainage areas of surface water bodies of
central Maine coastal river basins: U.S. Geological Sur-
vey Open File Report, 27 p.

Fontaine, R.A., Herrick, E., and Norman, N., 1982, Drainage
areas of surface-water bodies of the St. John River basin
in northern Maine: U.S. Geological Survey Open-File
Report, 70 p.

Hardison, C.H., 1971, Prediction error of regression esti-
mates of streamflow characteristics at ungaged sites:
U.S. Geological Survey Professional Paper 750—C,
p. 228-236.

Helsel, D.R., and Hirsch, R.M., 1992, Statistical methods in
water resources: New York, Elsevier, 522 p.

Interagency Advisory Committee on Water Data, 1982,
Guidelines for determining flood flow frequency—Bul-
letin 17B of the Hydrology Subcommittee: U.S. Geo-
logical Survey, Office of Water-Data Coordination,
183 p.

Morrill, R.A., 1975, A technique for estimating the magni-
tude and frequency of floods in Maine: U.S. Geological
Survey Open-File Report 75-292, 44 p.

National Weather Service, 1961, Rainfall frequency atlas of
the United States: U.S. Department of Commerce Tech-
nical Paper 40, 61 p.

Newton, D.W. and Herrin, J.C., 1982, Assessment of com-
monly used methods of estimating flood frequency:
Transportation Research Record 896, p. 10-30.

Riggs, H.C., 1968, Some statistical tools in hydrology: U.S.
Geological Survey Techniques of Water-Resources
Investigations, book 4, chapter A1, 39 p.

Sauer, V.B., Thomas, W.O. Jr., Stricker, V.A., and Wilson,
K.V., 1983, Flood characteristics of urban watersheds
in the United States: U.S. Geological Survey Water-
Supply Paper 2207, 63 p.

Sauer, V.B., 1985, New studies of urban flood frequency in
the southeastern United States: Proceedings 1985 Inter-
national Symposium on Urban Hydrology, Hydraulic
Infrastructures, and Water-Quality Control, University
of Kentucky, July 23-25, 1985, Lexington, Ky.,

p. 195-201.

Stedinger, J.R. and Tasker, G.D., 1985, Regional hydrologic
analysis 1. Ordinary, weighted, and generalized least
squares compared: Water Resources Research, v. 21,
no. 9, p. 1421-1432.

Tasker, G.D. and Stedinger, J.R., 1986, Regional skew with
weighted LS regression: Journal of Water Resources
Planning and Management, v. 112, no. 2, p. 225-237.

1989, An operational GLS model for hydrologic
regression: Journal of Hydrology, v. 111, p. 361-375.

Thomson, M.T., Gannon, W.B., Thomas, M.P., Hayes, G.S.,
and others, 1964, Historical floods in New England:
U.S. Geological Survey Water-Supply Paper 1779-M,
105 p.

38 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


To compute the basin wetlands variable, the
drainage-basin boundaries must be delineated. After
this, the percentage of all wetlands in the basin (total
surface area of wetlands divided by the drainage area,
multiplied by 100) is computed. The area of wetlands
can be computed from GIS coverages. Currently
(1998), coverages do not exist for all drainage basins in
Maine. The total area of wetlands in a basin also can be
digitized. This is tedious, however, for basins with a
large percentage of wetlands. In either method, the total
surface area of wetlands is divided by the drainage area
(and multiplied by 100) to compute the areal percent-
age of wetlands in a basin. Grid sampling can also be
used to compute the percentage of wetlands in a basin.
In this method, after delineating the drainage-basin
boundaries, a grid of evenly spaced points is placed
over the National Wetland Inventory maps. The total
number of points that fall within the drainage-basin
boundaries are counted. The total number of points that
fall in a wetland (within the drainage-basin boundaries)
are then counted. The number of wetland points
divided by the number of points in the drainage basin
(multiplied by 100) is the percentage of wetlands in the
basin. Based on experience, for the grid-sampling
method to be accurate, at least 400 points in the basin
must be sampled. In addition, the percentage of wet-
lands in the basin must be at least 4 percent. The per-
centage of basin wetlands for the 70 streamflow-gaging
stations used in the development of the Maine regres-
sion equations are listed in table 2. These basin wetland
values were computed by all of the methods described
except for GIS coverages. The GIS coverages of the
National Wetland Inventory Maps are expected to be
very similar to the paper copies.

A fortran computer program is included on a
disk in the back of this report that calculates peak flows
using the regression equations in table 3. The program
runs on all 80386, 80486, and Pentium based PC’s
compatible with MS DOS and Microsoft Windows. To
run the program from DOS, type ME in the directory
with the program. To run the program from Windows,
double click the left mouse button with the cursor on
the file ME.EXE. The program will prompt the user for
the drainage area and basin wetlands of each site.

Limitations and accuracy of the technique

These regression equations are not applicable to
regulated or urbanized drainage basins. “Regulated”
and “urbanized” are defined and the appropriate meth-
odologies for these conditions are described in “Choos-
ing the appropriate section of this report to obtain
estimated peak flows” in Part | of this report.

If the explanatory variables (drainage area and
basin wetlands) used in the regression equations in this
section are outside the two-dimensional range of the
values used to develop the equations (the gray area in
figure 3), the accuracy of predictions of peak flows
from the equations will be reduced. The magnitude of
this reduction in accuracy is unknown and potentially
large. The potential for large reductions in the accuracy
of the regression equations increases as the distance
from the gray area in figure 3 increases.

The regression equations in this section may
seriously underestimate the peak flows for sites that
have very steep slopes (slopes, as defined in “Data used
for the technique”, of greater than 50 m/km). As
explained in “Data used for the technique”, preliminary
regression equations significantly underpredicted the
peak flows for three very steep-sloped New Hampshire
basins.

The average standard error of prediction (ASEP)
is a measure of how well the regression equations will
estimate peak flows when they are applied to ungaged
drainage basins. The ASEP is the square root of the
average variance of prediction at a group of sites that
have the same basin characteristics as the gaging sta-
tions used in development of the regression equations.
The standard error of prediction varies from site to site,
depending on the values of the explanatory variables
(drainage area and basin wetlands) for each site. The
standard error of prediction will be smaller for sites that
have explanatory variables near the mean of their
range; however, the error associated with the different
values of the explanatory variables is a small part of the
total standard error of prediction. For this reason, the
ASEP can be used as an approximate standard error of
prediction for individual sites. If a standard error of
prediction for an individual site is desired, it can be cal-
culated as explained in “Advanced accuracy analysis”,
which immediately follows this discussion. The proba-
bility that the true value of a peak flow at a study site is
between the positive-percent ASEP and the negative-
percent ASEP is approximately 68 percent. For exam-
ple, there is a 68 percent probability that the true
50-year peak flow at an ungaged site is between +46.9
percent and -31.9 percent (table 3) of the computed
peak flow.

Another overall measure of how well regression
equations will estimate flood peaks when applied to
ungaged basins is the PRESS statistic. The PRESS sta-
tistic is a validation-type statistic. To compute the
PRESS statistic, one gaging station is removed from
the stations used to develop the regression equation,
then the value of the one left out is predicted. The dif-

24 Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008


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11

Estimating the Magnitude of Peak Flows for Streams in Maine for Selected Recurrence Intervals—USGS WRIR 99-4008