The Hydrogeology and Freshwater
Influx of Buttermilk Bay with
Regard to the Circulation of
Coliform and Pollutants
Polly Lu Moog
Boston University
BBP-88-10
The Buzzards Bay Project is sponsored by The
OS Environmental Protection Agency and The Massachusetts
Executive Office of Environmental Affairs
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BOSTON UNIVERSITY
GRADUATE SCHOOL
Master's Thesis
THE HYDROGEOLOGY AND FRESHWATER INFLUX OF
BUTTERMILK BAY, MASSACHUSETTS WITH REGARD TO
THE CIRCULATION OF COLIFORM AND POLLUTANTS: A MODEL STUDY
AND DEVELOPMENT OF METHODS FOR GENERAL APPLICATION
by
POLLY LU MOOG
A.B., University of California, Berkeley, 1983
Submitted in partial fulfillment of the
requirements for the degree of
Master of Arts
1987
-------
THE BUZZARDS BAY PROJECT
US Environmental Protection Agency
WQP-2100
John F. Kennedy Federal Building
Boston, MA 02203
Massachusetts Executive Office of
Environmental Affairs
100 Cambridge Street
Boston, MA 02202
FOREWORD
In 1984, Buzzards Bay was one of four estuaries in the country
chosen to be part of the National Estuary Program. The Buzzards
Bay Project was initiated in 1985 to protect water quality and
the health of living resources in the bay by identifying resource
management problems, investigating the causes of these problems,
and recommending actions that will protect valuable resources
from further environmental degradation. This multi-year project,
jointly managed by United States Environmental Protection Agency
and the Massachusetts Executive Office of Environmental Affairs,
utilizes the efforts of local, state, and federal agencies, the
academic community and local interest groups in developing a
Master Plan that will ensure an acceptable and sustainable level
of environmental quality for Buzzards Bay.
The Buzzards Bay Project is focusing on three priority problems:
closure of shellfish beds, contamination of fish and shellfish by
toxic metals and organic compounds, and high nutrient input and
the potential pollutant effects. By early 1990, the Buzzards Bay
Project will develop a Comprehensive Conservation and Management
Plan to address the Project's overall objectives: to develop
recommendations for regional water quality management that are
based on sound information, to define the regulatory and
management structure necessary to implement the recommendations,
and to educate and involve the public in formulating and
implementing these recommendations.
The Buzzards Bay Project has funded a variety of tasks that are
intended to improve our understanding of the input, fate and
effects of contaminants in coastal waters. The Project will
identify and evaluate historic information as well as generate
new data to fill information gaps. The results of these Project
tasks are published in this Technical Series on Buzzards Bay.
-------
This report represents the technical results of an investigation
funded by the Buzzards Bay Project. The results and conclusions
contained herein are those of the author(s). These conclusions
have been reviewed by competent outside reviewers and found to be
reasonable and legitimate based on the available data. The
Management Committee of the Buzzards Bay Project accepts this
report as technically sound and complete. The conclusions do not
necessarily represent the recommendations of the Buzzards Bay
Project. Final recommendations for resource management actions
will be based upon the results of this and other investigations.
David Fierra, Chairman, Management Committee
Environmental Protection Agency
Thomas Bigford
National Oceanic and Atmospheric Administration
Steve Bliven
Massachusetts Office of Coastal Zone Management
Leigh Bridges
Massachusetts Division of Marine Fisheries
Jack Clarke
Cape Cod Planning and Economic Development Commission
Richard Delaney
Massachusetts Office of Coastal Zone Management
Meriel Hardin
Massachusetts Department of Environmental Quality
Engineering
Dr. Russell Isaac
Massachusetts Division of Water Pollution Control
Dr. Susan Peterson
President, Coalition for Buzzards Bay
Dr. Don Phelps
Environmental Protection Agency
Ted Pratt
Chairman, Buzzards Bay Citizens Advisory Committee
Stephen Smith
Southeast Regional Planning and Economic Development District
Bruce Tripp
Massachusetts Executive Office of Environmental Affairs
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Approved by
First Reader c
Dr. Oabney W. Caldwell
Associate Professor of Geology
Second Reader
Dr. Christopher T. Baldwin
Associate Professor of Geology
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I would like to dedicate this thesis to
the one who suggested Geology to me in the
first place, my grandfather, Ky Lewis.
-------
Acknowledgments
This work, could not have been completed without the
help of: Professors Chris Baldwin and D. Caldwell, who
thoughtfully reviewed the manuscript; Lillian Paralikis,
who provided endless moral support and encouragement; John
Stewart, whose constant cheerfulness and storehouse of
equipment was invaluable; the Environmental Protection
Agency; my parents, Nancy and Lou Marino, and Don and Nancy
Brown, for their continual love, support, and drafting
assistance, when necessary; and my extremely patient and
supportive husband, Douglas B. Moog.
IV
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THE HYDROGEOLOGY AND FRESHWATER INFLUX OF
BUTTERMILK BAY, MASSACHUSETTS WITH REGARD TO
THE CIRCULATION OF COLIFORM AND POLLUTANTS: A MODEL STUDY
AND DEVELOPMENT OF METHODS FOR GENERAL APPLICATION
(Order No. )
POLLY LU MOOG
Boston University, Graduate School, 1987
Major Professor: D.W. Caldwell Professor of: Geology
Abstract
Shellfishing in Buttermilk Bay, at the head of
Buzzards Bay, is threatened by bacterial pollution. The
amount of freshwater influx is needed to determine the
nutrient and bacteria concentrations that will locate
pollution sources. The influx of freshwater was calculated
with four different methods:
1. A regional hydrologic equation for mean annual
discharge, developed from USGS gauging station records, was
applied to the drainage area of Buttermilk Bay. This
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yielded a value of 28,473,354 m /yr for freshwater
discharge to Buttermilk Bay.
2. Discharge measurements and a 2-year stage record of
Red Brook, the largest source of freshwater, enabled the
calculation of surface and ground water discharges. This
resulted in value of 8,360,255 m /yr for 1985 discharge to
3
the Bay and 14,311,866 m /yr for the 1986 discharge.
3. Yearly water budgets were done for three
consecutive water years. The amount of runoff calculated in
inches from the water budget was converted to the amount of
freshwater discharge from the Buttermilk Bay drainage area.
The water budget for and average year produced a value of
28,682,638 m /yr of freshwater discharge to the Bay.
4. A water table map drawn from peizometer data and
hydraulic conductivities found from ground water modeling
and stream discharge were used in a stream tube analysis to
calculate the discharge into Buttermilk Bay. Since the
watershed is composed of permeable material, little
overland flow occurs and this value should closely
approximate the total freshwater influx. This yielded a
freshwater discharge value of 9,793,314 m /yr.
This integrated approach increases the confidence in a
quantity difficult to calculate accurately.
VI
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Table of Contents
Title Page . i
Reader's Approval ii
Dedication iii
Acknowledgments iv
Abstract v
Table of Contents vii
List of Tables x
List of Figures xi
Introduction 1
Notation and Metric SI Units 5
I. Surficial Geology . . . 6
I.A Surficial Deposits 7
I.A.I Diamicton 1 7
I.A.2 Diamicton 2 7
I. A. 3 Outwash 8
I. A.4 Collapsed Outwash 8
I.B Topographic Features 9
I.B.I Druml ins 9
I. B. 2 Kame Moraine Segment 9
I.B. 3 Outwash Plains 10
I.B.4 Collapsed Outwash Plains 10
I.C Regional Late Wisconsinan Chronology 11
I.D Local Late Wisconsinan Chronology 13
II. Surface Water 16
II.A Climate 16
II.B Regional Surface Water Characteristics 19
vii
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II.B.I Streamflow 21
II.B.2 Discharge as a Function of Drainage Area 29
II .B. 3 Flow Duration 36
II.B.4 Flood Analysis 41
II.B.5 Low Flow Analysis 50
II.C Buttermilk Bay Surface Water Characteristics 56
II.C.I Red Brook Streamflow 58
II.C. 2 Red Brook Flow Duration 63
II.C.3 Regulation 64
II.C.4 Red Brook Discharge
from Regional Equations 66
II.C.5 Red Brook Rating Table ' 68
III. Water Balance 72
III.A Description of Methodology 72
III.B Buttermilk Bay Water Budget 77
III.B.I Average Year Water Budget 77
III.B.2 Water Budgets for Water Years 1984-1986 81
III.C Comparison with Measured Streamflow 87
III.C.I Theoretical Considerations 87
III.C.2 Sources of Error 88
III.C.3 Summary 89
IV. Buttermilk Bay Ground Water 91
IV.A Peizometer Data 91
IV. B Water Table Map 98
IV.C Hydraulic Conductivity and
Ground Water Discharge .... 100
IV.C.I Published Hydraulic Conductivity 101
IV.C.2 Hydraulic Conductivity from
Red Brook Discharge Data .. 103
IV.C.3 Ground Water Model ing 105
viii
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V. Freshwater Influx to Buttermilk Bay 117
V.A Regional Equation Method (#1) 118
V.B Red Brook Streamflow Method (f2) 119
V.C Water Budget Method (#3) 120
^V.D Streamtube Analysis (#4) 121
VI. Summary and Conclusions 125
Appendix A Figures 128
Appendix B Annual Flood Series 129
Appendix C Streamtube Calculations 156
Appendix D Conversion Tables 158
References 160
ix
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List of Tables
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table 10
Table 11
Table 12
Table 13
Table 14
Table 15
Table 16
Table 17
Table 18
Table 19
Gauging Stations Included in Study
Long Term Average Streamflow Data
Extreme Yearly Average Streamflow Data ..
Flow Duration Data
Annual Flood Series Data
7-day Mean Low Flow Data
10-year Annual Minimum Discharge Data . . .
Red Brook Flow Duration Data
Red Brook Flood Discharge Predictions ...
Stage-Discharge Relations .for Red Brook .
Average Year Water Budget /
Water Budget for Water Years 1984-1986 ..
Water Budget Totals
Water Table Elevation in USGS Wells
Water Table Elevation in BU Wells .,
Hydraulic Conductivity from Red Brook
Discharge Data
Drawdown Data for 1971 Pump Test
Results of the Jacob Straight-Line Method
Drawdowns for 1971 Pump Test from
Computer Model ...
20
23
33
38
42
51
52
63
69
70
78
82
86
92
93
104
107
110
115
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List of Figures
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Appendix
Appendix
Appendix
Location Map
Surficial Map after Larson/ 1982
Average Temperature and Precipitation . . .
1981 Herring River Hydrograph
1973 Herring River Hydrograph
Drainage versus Discharge Graph
Bar Graph of Persistence
Flow Duration Graphs
Homogeneity Test
7-day Consecutive Discharge
Red Brook 1985 Hydrograph
Red Brook 1986 Hydrograph
Red Brook Rating Curves
Average Year Water Budget
. 1984-1986 Water Budgets
Peizometer Water-level Measurements
Peizometer Water-level Measurements
Peizometer Water-level Measurements
Pump Test Location Map
Jacob Straight-Line Solution
Computer Initial Conditions
. Calibrated Water Table Map
Streamtube Map
Figure A-l Large Location Map
Figure A-2 Surficial Geology Map
Figure A-3 Water Table Map
3
12
18
27
28
31
35
39
49
53
59
61
71
80
84
94
95
96
106
108
112
114
123
128
128
128
xi
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INTRODUCTION
The shellfishing industry in Buttermilk Bay, at the
head of Buzzard's Bay in southern Massachusetts, once
thriving, has been severely limited due to the
contamination of the shellfish beds with bacteria. In
response to the closure of many of the shellfish beds in
Buttermilk Bay and other coastal embayments in
Massachusetts, the Environmental Protection Agency (EPA)
has funded a study to locate the sources and transport of
pollution to and inside this Bay, as well as develop a
general method for studying similar contamination problems.
This is a four part study involving several groups;
Boston University Hydrogeology Research Group, Boston
University Marine Biology Department, and Barnstable County
Health Department. The Hydrogeology Research Group is
responsible for the determining the ground and surface
water hydrogeology of the Buttermilk Bay drainage area and
the circulation of water in the Bay. The Marine Biology
Department has investigated the effects of the pollution on
shellfish and the flux of nutrients in the Bay. Lastly, the
Barnstable County Health Department is responsible for
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determining the sources and magnitudes of bacteria entering
the bay.
Buttermilk Bay is located at the head of Buzzards Bay
in Wareham and Bourne, Massachusetts (Figure 1), just north
of the Cape Cod Canal. The drainage area of the bay
(Appendix Figure A-l) lies between 70'35'W and 70'39'W
longitude and 41°45'N and 41»51'N latitude, and includes
parts of both thc Sagamore and Wareham quadrangles.
Approximately 65% of the drainage area is forested. The
rest is primarily residential except for some commercial
cranberry bogs scattered throughout the drainage area. The
residential areas directly adjacent to the Bay are densely
populated, especially on the western edge where the lot
size is only a quarter acre. All the houses have either
septic tanks or cesspools for sewage treatment. There are
fewer houses on the eastern side of the Bay. However, there
is a large farm near the eastern edge of Little Buttermilk
Bay and a horse farm that drains directly to the Bay. There
are many new houses under construction along the northern
side of the Bay as well as in the northern and central
parts of the drainage area, in the town of Plymouth.
In this portion of the study/ the ground and surface
water hydrogeology of the Buttermilk Bay drainage area
(Appendix Figure A-l) has been investigated in an effort to
determine the amount of freshwater discharge to Buttermilk
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Figure 1. Location map of Buttermilk Bay
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Bay. The freshwater influx is crucial to the determination •
of the concentration and flux of pollutants to the bay,
thus to the location and quantification of the pollution
sources and the design of remedial measures. In addition,
the methodologies adopted here are considered as potential
components of possible 'blueprint1 strategies to be used in
the monitoring of other similarly polluted near-coast
sites.
A comprehensive investigation of the hydrogeology of
the Buttermilk Bay drainage area involves:
1. a summary of its glacial history,
2. a description of both the local and regional
surface water hydrological characteristics,
3. a water balance describing the input and output of
water to the system, and
4. a description of the aquifer underlying the
drainage area.
The glacial history of Buttermilk. Bay is an important part
of the hydrogeology because the aquifer underlying the bay
is composed entirely of material deposited by or in
association with glaciers in the Pleistocene epoch. The
local and regional surface water characteristics will
provide information not only on the amount of surface water
discharged to the bay, but also on the hydrologic
connection between the surface water and the aquifer. This
-------
information will also lead to flood prediction and
freshwater discharge calculation. The water balance allows
the use of precipitation/ input of water to the system, by
plants, soil water recharge and streamflow to be
quantified. Lastly, quantification of aquifer
characteristics is imperative to the calculation freshwater
flux to the bay. The following is an attempt to describe
the hydrogeology of Buttermilk Bay using these four
criteria. The goal and final section is a determination of
the amount of freshwater entering Buttermilk Bay.
Notation and Metric SI Units
In keeping with modern scientific writing the material
presented here is discussed in terms of metric and decimal
units. However, practically all U.S. hydrological data are
presented in imperial units. Where practical and necessary
both imperial and (metric units) are indicated and a
variety of conversion tables are presented in Appendix C.
-------
I. SURFICIAL GEOLOGY
A description of the surficial deposits of the
Buttermilk Bay drainage area is important in developing an
understanding of the hydrogeology of the area. A map of the
surficial geology (Appendix Figure A-2), description of the
deposits, and glacial history are presented here. The map
area coincides with the drainage area of Buttermilk Bay,
described briefly above. No bedrock exposures occur in the
map area, however subsurface information indicates that
undifferentiated schist, gneiss, and porphyritic granite of
Proterozoic age underlie surficial deposits (Zen, 1983) at
depths of 15 m or more (Williams and Tasker, 1974).
Previous work includes regional mapping by Mather, e_t
al (1942), Larson (1982), and Stone and Peper (1982). These
authors discuss the sequence of glacial events, the
formation of recessional moraines and associated outwash
plains. This report presents a detailed surficial map and
chronology of late Wisconsinan events for part of the
Wareham pitted outwash plain.
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I.A SURFICIAL DEPOSITS
Surficial deposits are distinguished by lithology and
by topographic expression.
I.A.I Diamicton 1
Diamicton 1 is sandy and weathers to a dark reddish
brown. It is composed of medium to very coarse sand with
some silt and clay. Granite boulders up to 2.5 m in
diameter are common, along with granules and cobbles. Sand
to boulder sized material is angular to subrounded.
Diamicton 1 is firm and compacted, unstratified, and very
poorly sorted. It occurs in large streamlined hills
(drumlins) and its thickness is unknown but likely be as
deep as 23 m (Williams and Tasker, 1974).
I.A.2 Diamicton 2
Diamicton 2 is sandy with lenses of crudely to well
stratified sand and gravelly sand (Mather, et al, 1942).
The main body of the diamicton weathers to reddish brown
and is composed of fine sand to cobbles, some silt, and
granite boulders up to 4m in diameter, some striated, are
common. The material, sand to boulders, is angular to
subrounded. Diamicton 2 is somewhat firm and compacted,
unstratified to crudely stratified, and poorly sorted. The
occasional sandy lenses contain fine sand to gravel, that
is subangular, crudely to well stratified, and some lenses
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8
exhibit small-scale cross-stratification. The lenses are
moderate to well sorted. Till 2 is exposed in the Tarkiln
Hill region and is locally pitted and hummocky. Its
thickness is likely to exceed 23 m (Williams e_£. al, 1977).
I.A.3 Outwash
The white areas labeled outwash (Appendix Figure A-2)
are composed of interbedded medium sand to granules,
gravel, gravelly sand, and sandy gravel. It is tan to light
brown with beds up to 1m thick. There are some cobble and
gravel lag deposits. The sand to gravel component is
subangular to subrounded and the sandy layers are commonly
cross-stratified and range from well to poorly sorted. The
outwash occurs as gently sloping, even topographic surfaces
that decrease in elevation to the southwest. There is some
minor collapse in some areas producing local hills and
depressions. Its thickness locally, probably exceeds 30.5m
(Williams ejfc. al, 1977) .
I.A.4 Collapsed Outwash
The -stipled areas labeled collapsed outwash are
composed of medium sand to granules, with gravel, some fine
sand and cobbles, as well as scattered boulders. Its color
is tan to light brown. The sand to gravel fraction is
angular to subrounded and the deposits are massive to
crudely stratified and poorly to moderately sorted. The
collapsed outwash occurs as kames and in highly collapsed
-------
areas. Its thickness probably similarly exceeds 30.5m
(Williams g£ al, 1977).
I.B TOPOGRAPHIC FEATURES
I.B.I Drumlins
Two drumlins occur in the southeastern portion of the
map area. Both are composed of diamicton 1 and rise
approximately 12m above the surrounding terrain. The
northern one has a long axis orientation of 118* and the
southern has an orientation of 171°. These orientations are
in agreement with regional late Wisconsinan ice flow
.directions indicated by other drumlins in the area (Larson,
1982) .
I.B.2 Kame Moraine Segment
Tarkiln Hill, located along the southwestern edge of
the drainage area, is composed of diamicton 2 and fits the
description of kame moraine segments near the southwestern
margin of the Wareham pitted plain (Mather et aJL., 1942;
Stone and Peper, 1982). These features trend across local
bedrock (north and west of drainage area) ridges and
valleys and parallel distant coastal moraines (Stone and
Peper, 1982). They are composed of material similar to
diamicton 2 and, like Tarkiln Hill, are covered with
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10
boulders. Kame moraines generally rise 10m to 30m above
surrounding deposits (Stone and Peper, 1982). Tarkiln Hill
stands 10 m higher than adjacent outwash, and exhibits
collapse features including an ice-contact slope adjacent
to a deep kettle on the southeastern side.
I.E.3 Qutwash Plains
Outwash plains (mapped as ^outwash'), occurring mainly
in the northern and central parts of the map area, are
gently sloping even surfaces that slope to the south with a
gradient of 3.2m/km. However, Mather, fii. aL (1942) report a
southwestward slope at a gradient of 2.8m/km to 5.6m/km for
the entire Wareham plain. Minor collapse features, kames
and kettles, occur on some surfaces. Ice-contact slopes
commonly form the border between outwash plains and
collapsed outwash plains.
I.B.4 Collapsed Qutwash Plains
Collapsed outwash plains (mapped as ^collapsed
outwash,), found adjacent to Buttermilk Bay and in the
central portion of the map area, segment the uncollapsed
outwash plains. Abundant kames, kettles, and kettle ponds
distinguish this area from outwash plains. Kames tend to be
oriented northeast-southwest and may have been formed in
crevasses parallel to the ice front (Stone and Peper,
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11
1982). The collapsed outwash plains are generally lower
than the outwash plains and kame elevations reflect the
local outwash gradient.
I_.C REGIONAL LATE WISCONSINAN CHRONOLOGY
Regional late Uisconsinan glacial events were
controlled by nonsynchronous retreat of the Cape Cod Bay
and Buzzards Bay ice lobes (Larson, 1982). Although the
features seen in southeastern Massachusetts are primarily
formed glacial retreat, some glacial advance features are
not obliterated. The drumlins scattered throughout the
region seen in Figure 2 (from Larson, 1982) were deposited
by advancing ice (Sugden and John, 1984). The diamicton
composing the drumlins may underlie the outwash sediments
as lodgement till, although it has not been revealed by
borings (Williams e_fc. a_L, 1977). Approximately 18,000 BP ice
reached the late Uisconsinan maximum at an ice front
position marked by the Nantucket and Martha's Vineyard
terminal moraines (D.W. Caldwell, personal communication,
1985). From this position, the Cape Cod Bay lobe retreated
northward leaving the Sandwich moraine and the Buzzards Bay
lobe retreated westward and deposited the Buzzards Bay
moraine. Both recessional moraines rise above surrounding
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12
Figure 2. Positions of moraines and outwash plains in
the Plymouth-Buzzards Bay area (after Larson, 1982).
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13
areas and consist primarily of stratified sand and gravel
with minor sandy till. Approximately 15,300 BP ice began
retreating from the Sandwich and Buzzards Bay moraines
nonsynchronously (Larson, 1982). Ice retreat progressed
from west to east as the smaller Buzzards Bay lobe
retreated more rapidly than the larger Cape Cod Bay lobe.
Periods of minor readvance or stillstand formed a series of
ice-cored recessional moraines, composed primarily of
stratified sand and gravel and, associated outwash plains
(Figure 2). By 14,250 BP the ice front had retreated to a
position north of Boston (Larson, 1982).
As the Buzzards Bay lobe recessed from the Buzzards
Bay moraine, it paused 16 km to the northwest to form the
Hog Rock moraine. Sometime after ice left the Buzzards Bay
moraine, the Cape Cod lobe retreated northward from the
Sandwich moraine, pausing 8 km away to form the Ellisville
moraine (Mather ft£ ai., 1942). While ice lobes were at the
Hog Rock and Ellisville moraine positions, an interlobate
outwash plain, the Wareham pitted plain, was formed. This
plain extends from the northern part of the Onset and
Marion quandrangles northward to the southern quarter of
the Plymouth and Manomet quadrangles. Surface slope is to
the southwest at a gradient of 2.8m/km to 5.6m/km and
parallels the regional bedrock slope (Mather &£. aL, 1942).
Grain size generally decreases from coarse gravel to fine
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14
sand from the Ellisville moraine southward to Buttermilk
Bay. Different areas of the Wareham plain were constructed
at different times by outwash from both ice lobes, and in
places, outwash buried portions of the moraines (Mather et
al, 1942).
Ice remained at the Ellisville moraine as the Buzzards
Bay lobe retreated northwest from the Hog Rock to the
Snipatuit Pond moraine. Later, the Cape Cod lobe retreated
northward and formed the Monks Hill moraine (Larson, 1982).
At this time, ice no longer directly controlled
sedimentation in the map area. Following deglaciation and
before complete melting of isolated ice blocks in kettles,
eolian reworking of surficial deposits occurred and many
ventifacts formed near the northern margin of the Wareham
plain (Mather et al, 1942). Eolian deposits cover the
entire plain excepting the kettle holes, implying that wind
abrasion was not effective after the melting of the buried
ice (Mather e_£. aL, 1942). Melting of buried ice blocks
within the Wareham plain formed abundant kettles, kames,
and ice contact slopes.
I.D. LOCAL LATE WISCOMSINAM CHRONOLOGY
Late Wisconsinan ice of the Buzzards Bay lobe formed
the two drumlins in the map area as it advanced
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15
southeastward. Diamicton 1, deposited at this time, may
consist in part of reworked older drift and probably occurs
throughout the area as lodgement till that is now buried by
younger drift.
When the ice retreated from the Buzzards Bay moraine/
it paused for a relatively short time to form the Tarkiln
Hill kame moraine, diamicton 2. Retreating ice of both
lobes left behind large blocks of stagnant ice in areas
mapped as collapsed outwash. The ice blocks were buried by
the outwash from the forming Ellisville and Hog Rock
moraines. Lower areas underlain by till 2 adjacent to
Tarkiln Hill were also buried by outwash of the interlobate
sandur.
After ice retreated, first from the Hog Rock moraine
and later from the Ellisville moraine, deposition of
outwash on the Wareham plain ceased. Buried ice blocks
later melted, forming collapsed outwash areas with kames,
kettles, and ice contact slopes adjacent to areas of
uncollapsed outwash. Post-glacial modifications of the
landscape include stream dissection and alluvial deposition
by Red Brook and other smaller streams and formation of
marshes, bogs, and swamp deposits in kettles and other low
lying areas. Many kettle-s have been modified by man for
commercial cranberry farming.
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16
TT. SURFACE HATES
II.A CLIMATE
Climate exerts important control on the amount and
timing of surface water runoff. Consequently, a general
overview of climatic characteristics is an essential part
of a hydrological analysis. Ruffner (1985) compiled data
from the National Oceanic and Atmospheric Administration
(NOAA), in "Climates of the States", to provide general
climatic descriptions of the climates of the United States.
The subsequent climatic information is condensed from
Ruffner's (1985) compilation.
The climate of Massachusetts is especially noted for
the rapid variability in weather conditions. Other major
climatic features are the large daily and annual
temperature ranges, even distribution of precipitation over
time, considerable differences of seasons from year to
year, as well as diversity from place to place. The
"prevailing westerlies" that blow over Massachusetts
contain air masses from both the Arctic and the Tropics.
The cold dry air and warm moist air produce large storm
systems which pass over or near Massachusetts more than
most other sections of the country. Because the winds are
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17
generally offshore, the weather is affected more by these
air masses than the cool, damp North Atlantic breezes.
However, in coastal Massachusetts, the ocean modifies the
weather more than in other parts of the state, especially
in the spring and summer when the cool ocean breeze may
penetrate about 16 km inland. This causes retardation of
spring growth and cool temperatures in the summer (Ruffner,
1985).
The study area is contained in the coastal division of
Massachusetts, a strip 16 to 32 km (10 to 20 mi) wide along
the coast. The average annual temperature in this division
is about 10°C (50*F), but this may vary considerably with
elevation, slope, and state of urbanization. The long term
average temperature for July ranges from 21°C to 23'C (70*F
to 74°F). Days with temperatures over 32*C (90*F) are few
in the coastal division, averaging less than one per year.
The summer diurnal range is from -12*C to -9.4'C (10*F to
15'F), although in the marshes the it can be as high as
4.4»C to 10°C-(40«F to 50»F) (Ruffner, 1985). The average
winter temperature is near -10°C (30°F) on the coast with a
lower diurnal range than in the summer. There are only a
few days per year with subzero temperatures (Ruffner,
1985). The average monthly temperature and precipitation
for the Buttermilk Bay area are shown in Figure 3. These
data were obtained from long term records from the NOAA
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18
Average Precipitation and Temperature
for Buttermilk Bay
80-
70-
60-
Temperalure
*F
40-
30-
20-
6-
5-
4-
Precipitation
in 3
2-
Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
Average Water Year
-25
-20
-15
i i i i i i r i I i i
Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
Average Water Year
-10
-5
-0
--5
-15
Temperature
10
Precipitation
cm
-5
Figure 3. Average temperature and precipitation for
Buttermilk Bay during a water year.
-------
19
meteorological recording station at the Cranberry
Experiment Station in East Wareham.
Like most of the Northeast, precipitation in
Massachusetts is evenly distributed throughout the year.
Most of the precipitation is from storm systems, but
patches of thunderstorms provide rainfall in the summer
when storm activity is low. Total annual precipitation in
the coastal division, which is the driest in the state,
averages about 100 to 125 cm (40 to 50 inches). However,
the coastal storms make this division the wettest part of
the state in the winter, with most of the precipitation in
the form of wet snow or rain. The coastal division receives
an average of 65 to 76 cm (25 to 30 inches) of snow in a
year. There are about 8 to 15 days with snowfall of 2.5 cm
(1 inch) or more. Lasting snow cover in this area is
uncommon. Precipitation usually occurs on 1 day in 3
(Ruffner, 1985).
II.B REGIONAL SURFACE WATER CHARACTERISTICS
In an effort to compute the freshwater influx to
Buttermilk Bay, this section will characterize the
streamflow in southeastern Massachusetts using data from
stream gauging stations operated by the United States
Geological Survey (Table 1). The information from these
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20
gauges is available in the U.S. Geological Survey
Water-Supply Papers 1301, 1721, 1901, and 2101. For years
1971-1984 the data is published by state for the individual
year. The Geological Survey publishes all the hydrologic
data in imperial units. Consequently, the following
analyses were performed using imperial units. Where
practical, the results have been converted into SI units.
Number
Table 1
Gauging Stations Included in Study
Name Abbreviation
01105730
01105870
01105880
01106000
01107000
01108000
01108500
01109000
01109060
01109070
01114000
01117000
Indian Head River at Hanover, MA
Jones River at Kingston, MA
Herring River at North Harwich, MA
Adamsville Brook at Adamsville, RI
Dorchester Brook near Brockton, MA
Taunton River at State Farm
near Bridgewater, MA
. Hading River at West Mansfield, MA
Hading River near Norton, MA
Threemile River at North 'Dighton, MA
Segreganset River near Dighton, MA
Moshassuck River at Providence, RI
Potowomut River near East Greenwich, RI
IND
JON
HER
ADM
DOR
TAU
HHM
HAN
THR
SEG
MOS
POT
-------
21
This quanitification provides long term information
that may be applied to any stream within the region. In
such an area of homogeneous climate and geology, the
discharge equations found for mean streamflow, flood, and
low flow conditions may be used to predict the discharge of
any stream.
Specifically, analysis of the regional streamflow of
southeastern Massachusetts can be extrapolated to Red
Brook. The resulting equations can then predict the
discharge for Red Brook, during flow situations not observed
in this research period, such as floods and extreme low
flows. This discharge information is necessary in the study
of pollutant loading to Buttermilk Bay because it will
allow the concentrations of the various contaminants
discharging from Red Brook under widely varying flow
situations to be predicted.
II.B.I Streamflow
Ground water and surface run-off from precipitation
(rain and snow) constitute streamflow. It is controlled
principally by climate and to a lesser extent by geology.
The major climatic factors affecting streamflow are
precipitation, temperature, and amount of sunlight. The
fraction of precipitation the stream receives is dictated
by the intensity of rainfall and snowmelt, the amount used
by plants, and the amount evaporated into the atmosphere.
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22
The latter two processes are grouped under the term
evapotranspiration, and are affected considerably by
temperature and amount of sunlight. Streamflow is related
to precipitation and evapotranspiration as follows:
Q - P - ET, (1)
where Q is streamflow, or discharge, P is precipitation,
and ET is evapotranspiration.
Table 2 summarizes the streamflow for 12 gauges in the
area. The mean annual discharge (Qma) is the average daily
discharge over the period of record for a gauge and is
expressed in cubic feet per second (cfs) or cubic meters
per second (m /s). The discharge is computed from the gauge
record by multiplying the measured average depth, by the
width and velocity of the stream. In other words, Q = wdv,
3
where Q is the discharge (cfs or m /s), d is the stage (ft
or m), w is the width (ft or m), and v is the velocity
(ft/sec or m/sec). The CFSM value is the amount of water
discharged by one square mile of the drainage area. It is
calculated by dividing the mean annual discharge (Qma in
cfs) by the drainage area (Ad) in square miles. In order to
convert the CFSM value into the number of inches of
precipitation that becomes streamflow in one year (in/yr),
it is multiplied by the conversion factor 13.57. This
conversion factor is the product of the number of seconds
in a year (31,536,000 sec/year) times the number of inches
-------
23
Table 2
Long Term Average Streamflow Data
Mean Drainage
Gauge Annual Area
Discharge Ad
Qma (mi )
(cfs)
CFSM Inches of
Discharge Rainfall
per Becoming
Square Streamflow
Mile (in/yr) & (cm/yr)
Qma/Ad
(cfs/mi )
ADM
DOR
HER
IND
JON
MOS
POT
SEG
TAU
THR
WAN
WWM
Avers
14.
8.
10.
63.
32.
41.
46.
23.
464.
178.
74.
33.
iges (
30
33
20
80
90
90
30
30
00
00
10
50
weic
7
4
9
30
15
23
23
10
260
84
43
19
ihted
.91
.67
.40
.20
.70
.10
.00
.60
.00
.30
.30
.50
)
1
1
1
2
2
1
2
2
1
2
1
1
1
.81
.78
.09
.11
.10
.81
.01
.20
.78
.11
.71
.72
.86
CFSM x
24.
24..
14.
28.
28.
24.
27.
29.
24.
28.
23.
23.
25.
53
21
72
67
44
61
32
83
22
65
22
31
28
13.
62
61
37
72
72
62
69
75
61
72
58
59
64
57
.31
.49
.39
.82
.24
.51
.39
.77
.52
.77
.98
.21
.21
Period
of
Record
(yrs)
38
12
18
18
18
21
44
18
47
18
59
31
in a foot (12 in/ft) divided by the number of square feet
2 2
in a square mile (27,878,400 ft /mi ).
The average annual precipitation in the coastal
division of Massachusetts is between 40 to 50 inches (100
and 125 cm) (Ruffner, 1985). From Table 2, the average
amount of Streamflow from precipitation is 25.28 in/yr
(64.21 cm/yr). Using equation 1, Q = P - ET, the annual
evapotranspiration in this area averages 19.72 inches
(50.09 cm). This means that slightly less than half the
precipitation in a year is consumed by evapotranspiration.
-------
24
The familiar seasonal variations of temperature and
amount of sunlight in New England cause a similar variation
in the rate of evapotranspiration. The growing season lasts
from late April or May through late September or early
October, 160 to 200 days. However, it is shorter in easily
frosted areas such as the many cranberry bogs. As expected,
this season has the fastest rate of evapotranspiration.
This large amount of evapotranspiration results in less
streamflow from precipitation and less baseflow as well,
since there is little moisture left over from
evapotranspiration to recharge the ground water, the source
of baseflow in a stream. Accordingly, as sunlight and
temperature begin to decrease in September or October, so
does evapotranspiration. From December to early March or
slightly later the evapotranspiration actually falls to
zero while plants are in their winter dormant state and the
temperature is too low for evaporation to take place.
During this period and the snowmelting period that follows,
ground water recharge takes place and baseflow increases as
a result. Streamflow also increases with higher baseflow in
this period of ground water recharge. In the Buttermilk Bay
area, the ground water may be an important source of
-------
25
bacterial pollution from septic systems into Red Brook and
the Bay.
These seasonal variations of streamflow are exhibited
in the annual hydrographs of the Herring River (HER) for
1973 and 1981 (Figures 4 & 5). The Herring River is similar
geologically and climatically to Red Brook and Buttermilk
Bay and will exhibit similar streamflow characteristics. In
Cape Cod, 1973 and 1981 were extremely wet and dry years,
respectively. The characteristics seen in these hydrographs
will be similar to those of Red Brook during extreme wet
and dry conditions. The seasonal variations seen in the
streamflow on Cape Cod are more subdued than in the rest of
New England. This is due to the longer growing season,
little lasting snow cover (Ruffner, 1985) (insignificant
snowmelt runoff), and permeable aquifers found in this
region.
The hydrograph is a plot of the discharge of a stream
over the length of a year. The discharge is plotted on a
logarithmic scale and time on an arithmetic scale by day.
The smooth lower line indicates baseflow, whereas the
jagged upper line shows the peaks and subsequent ebbs of
precipitation events. The annual hydrograph starts in
October and ends in September as does the water year. The
reason for the discrepancy between the calender year and
the water year lies in the pattern the baseflow makes on a
-------
26
hydrograph in New England. The baseflow starts to rise in
October, continues to rise until the end of April, where it
falls until the end of September. The bell shape exhibited
by the baseflow from October through September is a clear
symbol on which to base the water year.
The first hydrograph (Figure 4) is for the year 1981,
an especially dry year. Although the amount of baseflow in
the stream is significantly lower than usual, a ground
water recharge period with increasing baseflow is apparent,
as is a striking decline of the baseflow in August. The
summer baseflow decline is magnified here because of the
previous low levels of baseflow and small amounts of
recharge. Figure 5 is a hydrograph from 1973, an
exceptionally wet year. The high amount of baseflow
indicates a high water table, or ground water level. The
distribution of baseflow over the year in this hydrograph
is extremely steady and reflects the permeable quality of
the sandy aquifers of the Cape and southeastern coast. The
percentage of the streamflow contributed by ground water
varies widely between the wet and dry years. In 1973, this
value is 81% and in 1981 the baseflow was 50% of the
streamflow. The high percentage reflects the high water
table and the subsequent greater ground water discharge to
the Herring River in a wet year. An average of the two
percentages, 65%, should reflect the ratio of baseflow to
-------
27
Herring River Hydrograph for Water Year 1981
50
40
30
20
10-
Oischarge
Q
c«s
0.5
0.4
0.3
-0.2
0.1
Discharge
m/s
-0.005
Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
Water Year 198
Figure 4. 1981 hydrograph for the Herring River at
North Harwich, Massachusetts, showing the irregular
baseflow curve typical of a dry year; as in this case.
-------
28
Discharge
Q
cfs
100
50
40
30
20
10
Herring River Hydrograph for Water Year 1973
I/
Oct Nov Dec Jan Feb Mar Apr May
Water Year 1973
Jun
Jul
Aug
Discharge
Q
0.5
04
0.3
0.2
0.1
0.05
Sep
Figure 5. 1973 hydrograph for the Herring River at
North Harwich, Massachusetts showing the steady baseflow
discharge typical of a river in permeable material during a
wet year.
-------
29
streamflow in a normal year on Cape Cod, and for Red Brook.
On the 1973 hydrograph, the baseflow declines from April to
September, a reflection of the long growing season here.
II.B.2 Discharge as a Function of Drainage Area
The following method of analysis as presented in Dunne
and Leopold (1978) is standard in hydrologic research.
The discharge of a stream is related to the size of
the area it drains, as well as the climate and geology of
that area. The relationship between discharge and drainage
area is described by the following equation:
Q = b(Ad)n, (2)
here Q is the discharge of a certain frequency, b is the
discharge of a unit drainage area. Ad is the drainage area,
and n is the rate at which discharge changes with drainage
area. On a logarithmic plot with drainage area and
discharge on the x and y axes, respectively, b is the
y-intercept of the line, and n is the tangent of the acute
angle the line makes with the horizontal.
The mean annual discharge (Qma), as stated previously,
is the average of all the daily flows in the period of
record for a particular stream gauge. A regression analysis
is performed to determine the relation between mean annual
discharge (Qma) and drainage area for the gauges in Table 2
(Figure 6). This relation for this part of southeastern
Massachusetts is:
-------
30
Qma « 1.64
-------
31
Drainage Area versus Discharge
0'amage Area Aa km2
to
10'
10
100.000
50.000
20.000
10.000
s.ooo
2.000
1.000
500
200-
100-
Ducharge
o 50"
clj 20-
10-
5
2
1-
0 5-
0.2
0.1-
0.05-
0.02-
001-
o.oos-
0.002-
1
^ ' *
^r *r y
j^1/ / x t /
4's ' •'
0,0 =6149Ad°'»v >^^ ''•''/ /
0, •«2-06A/«^\sX^' ,'/'//
°J33 26 26A«X^^ \(<^'X ^' / /
." S& / '.' ',' "^^
•?*,?*£' ' ''•$// ^S\
&S / ' ' 7-* / 103
^/y/ ' ' /' 4^ ' ^M* ' ®4A«
&"&?,/ t ' / '° /
/%/' ^)/f/ ^ /
&' /''/ /y
/ °y'X /
/ / ' „•• /
' S / ^ /
x/'' ' »•"'
' ' JV
x /' y O /
' ' / &/
' / ?/
•' / //
/ */
/ Q,0 10-year Flood
/ Q5 5-year Flood
/ Oj jj Mean Annual Flood — — —
f* . U ta f%' *«
/ O»VL *v*"9* Lov» Discharge ^~—
/ O10m-)10-y«ar Low Flow
/
10 102 103 10* to
Drainage Aiea Aa mi2
1.000
•500
-200
-100
50
20
-10
5
Discrinrge
•1 0
0.5 m°'»
•0.2
0 1
005
0.02
0 0 1
0005
0 002
0001
0.0005
00002
0.0001
O.OO005
5
Figure 6. Discharge as a function of drainage area
relations for southeastern Massachusetts showing discharge
2
equations for Q in cfs and Ad in mi .
-------
32
term fluctuations in the average discharge of single years,
and eliminate a computational error that could cause the
under- or overestimation of water and pollutants. For
example, if a mean annual discharge computed from a number
of successive wet years is used to calculate pollutant
loading to Buttermilk Bay, there could be a severe
underestimation of bacterial concentration in the water in
the event of a mild drought. In this part of Massachusetts,
very few of the gauges have significantly long records.
Consequently, this relation between mean annual discharge
(Qma) and drainage area (Ad) may be somewhat inaccurate for
other than average conditions.
In order to help reduce the error associated with
insufficiently long periods of record, the high (Qaah) and
low (Qaal) extremes of yearly average flow, the mean of all
daily flows in a single year, can also be related to
drainage area to determine a range of annual average flows.
Table 3 contains these extreme values for the gauges used
in this.regional study. The relation for extreme high
average annual flows is:
1 04
Qaah = 2.36(Ad)A* , (5)
where Ad is in mi2 and Qaah in cfs. In contrast, the
relation for the extreme low average annual flows is:
-------
33
Table 3
Gauge
ADM
DOR
HER
IND
JON
MOS
POT
SEG
TAU
THR
HAN
UHM
Extreme
Drainage
Area
Ad
(mi2)
7.91
4.67
9.40
30.20
15.70
23.10
23.00
10.60
260.00
84.30
43.30
19.50
Yearly Average
Highest
Yearly
Average
Discharge
Qaah
(cfs)
21.5
11.2
17.8
83.3
51.4
62.5
72.5
30.8
741.0
238.0
115.0
49.6
Streamflow Data
Mean
Annual
Discharge
Qma
(cfs)
14.3
' 8.3
10.2
63.8
32.9
41.9
46.3
23.3
464.0
17.0
74.1
33.5
Lowest
Yearly
Average
Discharge
Qaal
(cfs)
6.32
3.64
3.54
27.60
14.90
20. 20
17.70
7.68
171.00
64.40
28.80
11.10
Correlation Coefficient .99
.99
.98
Qaal = 0.69(Ad)1>01,
(6)
where Ad is in mi and Qaal is in cfs. In SI notation where
2 3
Ad is in km and Qaah and Qaal are in m /s, equations 5 and
6 appear as follows:
1 04
Qaah - 0.. 2048(Ad)x' ,and
Qaal = 0.0075(Ad)
1.01
(7)
(8)
The CFSM values of 2.36 and 0.69 represent the range of
average discharge (cfs) that one square mile of drainage
-------
34
area may contribute. An exponent of 1.04 in the high flow
equation indicates that in wet years, the amount of
increase in discharge with increasing drainage area is
slightly larger than in normal years. Conversely, in dry
years, each square mile of drainage area yields almost the
same amount of discharge, as reflected in the exponent of
1.01. However, because the exponents, 1.04, 1.03, 1.01, are
very close and the rate of increase of discharge with
drainage area is small, the range of CFSM values is more
crucial in determining the discharge of ungauged streams,
such as Red Brook, when sufficiently long records are not
available.
Long term fluctuations in streamflow do occur. This
feature is called persistence, and is not well understood
(Dunne and Leopold, 1978). Figure 7 is a plot of the
average discharge for each year from 1926 to 1983 on the
Hading River near Norton, MA (HAN). This watershed was
chosen for this analysis because of its long period of
record. The fluctuation seen is natural and not a result of
stream regulation for industrial or urban use upstream. A
pattern of wet and dry years is evident, but there is no
way to predict the occurrence of either period.
Consequently, a long gauge record is indispensable to
accurate hydrologic analysis.
-------
35
Yearly Average Discharge on the Hading River
near Norton. Massachusetts
Year
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
194S
1946
1947
1948
1949
I960
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
25
cts
I
50
cfs
I
75
cfs
I
100
cfs
I
Discharge
cfs
69. 1
70. 1
84.4
73.7
39 5
73. 1
46.2
91. 3
72.2
73.2
78.3
77.6
105.0
74
66
46
50
66
36
86
92
52
92
57.9
35.8
66
82
81
90
90
98
54
84
69.4
74.6
85
68
74
68
35
28
74
78
69
87
57.1
83.1
107.0
78 ?
70. 4
92.6
73.4
115.0
103.0
71.1
30.7
88.8
101.0
Figure 7. Bar graph showing persistence, long term
fluctuations in streamflow, on the Hading River near
Norton/ Massachusetts.
-------
36
JI.B.3 Flow Duration
Geology, along with climate, affects streamflow. The
geology of a region dictates the amount of water storage
available in the soil and rock below, as well as the rate
of water infiltration into the soil and bedrock. A
permeable layer will result in a large amount of ground
water recharge and consequently streamflow with a large and
constant amount of baseflow, such as in this study area
which is composed primarily of thick glacial outwash.
Impermeable layers produce a stream with flows of greater
range that are more reflective of precipitation than ground
water.
A plot of the flow duration is a good graphical
representation of this concept (Figure 8 & Table 4). It is
a plot of the percentage of time that the discharge in a
stream equals or exceeds a chosen value. All the discharges
in a year or period of years are placed into intervals for
this analysis. The frequency of flows in the interval is
calculated by dividing the number of days in the interval
by the number of days in the period of analysis. The
frequencies are then summed to find the cumulative
frequency, which is plotted against the discharge interval
for the flow duration curve.
Flow duration can be used to determine the percentage
of time that the flow will be too low to dilute
-------
37
contaminants in the stream to acceptable levels. For
example, if bacteria enters Red Brook primarily from ground
water flow, then the concentrations of bacteria in the
stream will be higher during low flows than large
discharges. The high concentrations of bacteria in the
water being discharged from the stream may be more
dangerous to swimmers near the mouth of Red Brook that may
accidentally swallow water than to the shellfish.
The flow duration for several of the coastal streams
(Table 4 & Figure 8) have been reproduced from USGS
Hater-Resources Investigations Report 84-4288 (Wandle and
Morgan, 1984). The small ranges of discharge, reflected by
the flatness of the flow duration curves, on the Jones and
Herring rivers suggest that the soil and underlying
sediments are permeable, causing much of the precipitation
to infiltrate into the ground instead of becoming
streamflow immediately. In fact, on Cape Cod and
geologically similar areas, such as Buttermilk Bay,
overland flow occurs only on a few occasions in winter when
rainfall and snowmelt occur simultaneously over frozen
ground. This overland flow usually runs off into kettle
holes or kettle ponds to recharge the ground water or
discharge through a chain of cranberry bogs to an outlet
stream, such as Red Brook. Consequently, most of these
streams do not obtain water from overland flow, instead the
-------
38
Table 4
Flow Duration Data from Handle and Morgan, 1984
Station
2
Drainage Area (mi )
(km2)
Data Period
Percent
of
Time
Discharge
was
Equaled
or
Exceeded
Median
Average
99%
95%
90%
75%
70%
50%
25%
10%
Standard-Deviation
Error in
***
SD
IND
30.2
78.2
1968-82
2.2
4.6
7.1
16.7
21.2
41.4
77.4
142.0
41.4
61.2
47.5
34%
JON
15.7
40.7
1968-82
Discharge
4.5
6.7
8.4
13.6
15.4
23.6
39.1
59.9
23.6
30.4
18.85
29%
HEW
56.1
145.3
1970-71
(cfs)
11.3
13.0
15.6
24.9
31.4
56.4
117.0
167.0
56.4
NA
60.1
37%
HER
9.4
24.3
1979
2.25
3.38
4.65
7.70
8.45
10.70
14.60
19.60
10.7
11.5
6. 3
25%
* WEW = 01105895 Weweantic River at South Wareham, MA
USGS Partial Record Station 1970 -71
** Not from Handle and Morgan, 1984 Computed from 1979
gauge record
*** Since these curves do exhibit a perfect shape, the
standard deviation is the average of differences between
the median and 84% and 16%, respectively. The error is the
%error between the real value and the average
standard-deviation.
-------
39
Flow Duration for Regional Rivers
Weweantic River
Indian Head River
Jones River
Herring River
Red Brook 1986
Red Brook 1985
10
10 20 30 40 50 60 70 80 90 100
0.05
0.04
0.03
Percent of Time Daily Flow Equaled or Exceeded Given Discharge
Figure 8. Flow duration curves for several streams in
southeastern Massachusetts including curves for Red Brook
for 1985 and 1986. The more horizontal the curve, the more
permeable the aquifer material underlying the stream.
-------
40
flow originates mainly from ground water recharge
(Strahler, 1972) or increased baseflow and subsurface
stormflow during storms (Dunne and Leopold, 1978).
The median flow, that equaled or exceeded 50% of the
time, and the average flow fall nearer the high end of the
range for the Jones and Herring River. These figures imply
that most of the time the streamflow is composed primarily
of baseflow, and that the flow does not increase
dramatically with precipitation. The standard-deviation,
that amount of discharge greater or less than the median
into which 68% of the flow falls, along with the error in
its calculation, are low for these two rivers. These
reflect the flatness of the flow duration curve (seen in
Figure 8), or the steady character of the baseflow
discharge of these two rivers. These quantities also
confirm that the basins are underlain by highly permeable
material, medium to coarse sand and fine to coarse gravel
(Williams and Tasker, 1974).
In contrast, the flow duration curves of the Ueweantic
and Indian Head rivers show a much greater range of
discharges indicative of the fine to medium sand and
compact silty till in the Ueweantic basin (Williams and
Tasker, 1974) and similarly impermeable material in the
Indian Head basin. The high standard-deviations and
-------
41
accompanying error characterize the more flashy behavior of
streams in less permeable material.
XJ.B.4 Flood Analysis
The flood potential of a stream is critical to
pollution studies and to development near the stream.
During a flood of known magnitude, bacteria and nutrient
levels can be measured so that plans for the timing of Bay
closures and pollutant retention in future flood events can
be made. Secondly, the increase of gro'undwater levels near
a stream during and after a flood snould be an important
consideration in septic system placement for the more rural
sections of the drainage area. To evaluate flood potential,
a flood frequency analysis, the annual flood series, has
been carried out using gauge records for the 12 streams in
Table 1. At each station, the annual momentary maximum
discharges for each year in the period of record were
arranged in order of decreasing value and assigned a
magnitude (Appendix B). The largest discharge was given a
magnitude of one. A recurrence interval was then calculated
for each magnitude. The recurrence interval for a flood of
a particular magnitude is the average period of time in
which a flood of that magnitude is expected to be equaled
or exceeded one time. The recurrence interval is computed
from the following equation:
RI = (n+l)/m, (9)
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Basin
42
Table 5
Annual Flood Series Data
Drainage Mean 5 Year 10 Year 25 Year 50 Year
Area Annual Flood Flood Flood Flood
(mi ) Flood
ADM
DOR
HER
IND
JON
MOS
POT
SEG
TAU
THR
WAN
WWM
7.91
4.67
9.40
30.20
15.70
23. 10
23.00
10.60
260.00
84.30
43.30
19.50
Q2.33
(cfs)
169
124
41
710
248
990
390
430
2500
1290
510
185
Q5
(cfs)
225
215
56
1050
350
1380
520
595
3190
1720
700
279
Q10
(cfs)
282
335
73
1400
460
1810
655
775
3900
2160
910
388
Q25 Q50
(cfs) (cfs)
375
885
4990
1260 1600
587
Corr. Coef.
.83
.81
.80
.99
where RI is the recurrence interval in years, n is the
number of years of record, and m is the magnitude. For each
station, the recurrence intervals of the floods are then
plotted against their discharges on Gumbel Type III graph
paper and a straight line is fitted to the data. Regional
flood relations for this region were then formulated by
plotting the mean annual flood (Q2.33), the 5-year flood
(Q5), the 10-year flood (Q10), and the 25-year flood (Q25),
where the records are long enough to yield reliable
results, for each gauge against its drainage area (Ad)
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43
(Figure 6). The mean annual flood is the average flood that
will occur in a watershed and it has a recurrence interval
of 2.33 years. Equations for the lines, found by performing
regression analyses, enable a prediction of the size of a
flood of particular frequency to be made for a watershed of
any area in a homogeneous region.
Table 5 summarizes the results of the annual flood
series analysis done for the study area. The equations
generated for the particular flood frequencies are:
Q2.33 * 26.26(Ad)'85 (10)
for the mean annual flood,
Q5 = 42.06(Ad)'81 (11)
for the five year flood,
Q10 = 61.49(Ad)*78 (12)
for the ten year flood, and
Q25 = 74.67(Ad)*75 (13)
2
for the twenty-five year flood, where Ad is in mi and Q is
2
in cfs. Using SI notation, where Ad is in km and Q is in
3
m /s, equations 10 through 13 are rewritten as follows:
2.33 = 0.3312(Ad)'85, (14)
for equation 10, the mean annual flood,
Q5 = 0.5511(Ad)'81, (15)
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44
for equation 11, the five year flood,
Q10 = 0.8290(Ad)*78, (16)
for equation 12, the ten year flood, and
Q25 = 1.04(Ad)'75, (17)
for equation 13, the twenty-five year flood. The exponents
for each equation indicate that as the drainage area
increases the flood discharge increases at a slower rate.
There are two possible reasons to account for this
characteristic. The first is that precipitation events are
localized. Consequently, a large storm will have a greater
impact on a small drainage basin than a large one. The
second reason is that as drainage area increases, channel
slope and flow velocity decrease allowing water a longer
time to travel to and in a stream channel, increasing the
chance it has to seep into storage. In other words, channel
storage and seepage into the unsaturated zone increase with
drainage area. The values of the exponents are close to the
typical 'value (.75 for Q2.33) for many regions in the
United States where channel storage and topography are
important factors that reduce the increase of the flood
discharge with drainage area (Dunne and Leopold, 1978).
Mountainous regions have larger exponents because of the
small drainage basins, steeper stream channels and small
floodplains (Dunne and Leopold, 1978).
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45
The geology of an area or river basin can play an
important part in determining the amount of flood
discharge. The infiltration capacity of a soil is the
amount of water a soil can store or absorb in a given
period of time. It is dependent on soil properties,
vegetation cover, land use, and rainfall characteristics.
Coarse soils, such as sandy soils or those held together in
aggregates by organic matter, have large pores and can
easily drain water, giving them higher infiltration
capacities than clay-rich soils. However, long and intense
rainfall packs down loose soil particles, decreasing the
pore size and the ability to drain water, or may saturate
the soil completely. The soil can be protected from this
packing by vegetative cover, which can also increase the
organic binding of the soil. Consequently, land use affects
infiltration capacity and flood potential through quantity
and type of vegetation, as well as, the lack of vegetation
due to urbanization. The infiltration capacity of a soil
decreases dramatically after the onset of a storm, then
levels off at a lower rate in approximately 2 hours until
rainfall ceases (Dunne and Leopold 1978). The sandy soils,
formed on glacial outwash, in the Buttermilk Bay area,
although low in organic content (2% - 4%, generally), have
high permeability rates (between 6.0 and 20 in/hr),
implying high infiltration capacities (Soil Conservation
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46
Service, 1982). As a result of the high infiltration and
storage capacities in the Buzzards Bay area, floods have
not caused major damage, except in the hurricanes of 1938,
1944 and 1954 (Williams and Tasker, 1974).
Urbanization greatly affects runoff processes in an
area and therefore is an an important consideration for
flood potential in Buttermilk Bay. The higher the
proportion of the catchment covered with impervious
surfaces, such as parking lots, roads, and rooftops,
decreases the amount of flood storage in a watershed. The
infiltration capacity of the impervious surfaces, along
with many urban soils that have been packed down to near
impervious, is zero. This increases the volume and rate of
overland flow in a watershed as well as decreasing the
amount of recharge to ground water (Dunne and Leopold,
1978). Sewers, storm drains, and gutters also increase the
rate at which water travels to a stream. Consequently, the
lag time between precipitation and the flood wave is
decreased and the volume of a flood is increased (Dunne and
Leopold, 1978). In Buttermilk Bay, where much of the
surface near the bay is impervious, bacteria picked up in
overland stormflow does not have a chance to seep into and
be filtered by the soil. The sewers convey the runoff and
the bacteria quickly to the Bay before any bacteria die.
Consequently, the bacteria counts in the Bay will be high
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47
during a storm. Stormflow retention basins with high
infiltration rates could allow bacteria to seep into the
unsaturated zone and thus ease the bacteria problem during
flood events. The size of these basins would depend on the
magnitude of flood expected in a particular time period, as
calculated with the annual flood series.
Two other important controls on floods are
interception and antecedent conditions. Interception of
rainfall by tree leaves and needles prevent or slow the
transfer of water to the ground, cutting down flood size.
Needles intercept more water simply because they remain on
the trees all year round. Consequently, the pine trees
which make up approximately half (estimation from
topographic map) of the vegetation of the Buttermilk Bay
watershed, exert an important modifying affect on flood
size. Antecedent conditions are the conditions that exist
in the soil prior to the onset of storm. For example,
frozen or saturated ground can severely reduce the
infiltration capacity of a soil, causing overland flow to
occur in areas where the slower subsurface stormflow and
increased baseflow dominate storm runoff. Snowmelt
associated with large amounts of rainfall is the usually
the cause of large floods in New England (Strahler, 1972).
The correlation coefficients for the annual flood
series relationships are shown in Table 5. Their values are
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48
practically the same for each frequency of flood. This
agreement implies that the basins used for the analysis are
in fact in a homogeneous region. However, because only five
of the gauges had records over 25 years, the higher
correlation coefficient for the 25-year flood may not
indicate more agreement, only fewer data points.
Dalrymple (1960) a method to test flood frequency data
for regional homogeneity. Figure 9 shows the results of the
homogeneity test applied to this study area. According to
Dalrymple, the gauges which plot inside the curve are in a
homogeneous region. Although all these gauges appear to be
in a homogeneous region in the Figure, their short periods
of record significantly enhance their apparent homogeneity.
As a result, the error in these relations may be high and
other sources of flood information for Buttermilk Bay
should be consulted before any pollution retention plans
are undertaken. Again, gauges with long periods of record
are better suited to accurately calculate the annual flood
series as well as mean annual discharge.
River stage, or height, is of special interest in
septic tank placement in the for those living in the flood
plain, such as some of the existing and new houses near Red
Brook. The groundwater levels rise with river stage and may
inundate the leach fields of systems near the Brook. The
height of the mean annual flood is usually presumed to be
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49
Homogeneity Test for Annual Flood Series
Gauge
ADM
DOR
HER
IND
JON
MOS
POT
SEG
TAU
THR
WAN
HUM
Mean
Annual
Flood
Q2.33
(cfs)
169
124
41
710
248
990
390
430
2500
1290
510
185
10 year
Flood
(cfs)
282
335
73
1,400
460
1,810
655
775
3900
2160
910
388
Ratio
Q10
Q2.33
1.67
2.70
1.78
1.97
1.85
1.83
1.68
1.80
1.56
1.67
1.78
2.10
(Q2.33)
X
Ratio
Average
(1.87)
316.0
232.0
76.7
1,328.0
464.0
1851.0
729.0
804.0
4675.0
2412.0
954.0
346.0
Recurrence
Interval
for Q in
Column 5
(yrs)
14.5
5.6
12.6
8.9
10.4
10.5
14.3
11.2
19.9
14.2
11.7
7.8
Period
of
Record
(yrs)
38
12
18
18
18
21
44
18
47
18
59
31
Ratio Average 1.87
Length
of
Record
(yrs)
~1.0 2 S 10 20 SO 100
Recurrence Interval for Discharge in Column 5
(yrs)
Figure 9. Homogeneity test for the annual flood
series from Dalrymple (1960) showing homogeneity of the
gauges used in this analysis.
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50 .
the bankful stage, that which fills the river channel
completely. However, some hydrologists have found that Q1.5
is the bankful discharge (Wolman and Leopold, 1957). The
stage of a stream with a certain discharge can be found by
examining a published rating table or curve for the stream,
which shows the relationship between stream height and
discharge.
II.B.5 Low Flow Analysis
In order to competently examine pollution hazards due
to increased pollutant concentrations in small discharges,
extreme low flow conditions must be analyzed. In New
England, regulation is more often than not the cause of the
annual minimum daily flow. Other factors affecting low flow
may be low precipitation, low water table, or high
evapotranspiration.
In order to evaluate the low flow conditions in
southeastern Massachusetts, Handle and Morgan (1984) have
published the estimated annual minimum 7-day mean low flows
with 2 and 10 year recurrence intervals for a number of
permanent and partial-record stations (Table 6). This
number represents a prediction of the average discharge of
the driest week of a year that will be exceeded once in a
given recurrence interval. The 7-day consecutive low flow
is used instead of the lowest flow of the year because the
lowest flow of the year is usually caused by regulation
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51
(Dunne and Leopold, 1978). However, pollutant
concentrations will be the same in a single low flow day as
in a week of low flows. In addition to the 7-day mean low
flow values in Table 6, Table 7 contains the 10-year annual
minimum for the gauges used in the surface water analyses
above. The 10-year minimum was found from the lowest
discharge in the drought period 1961 to 1970. These low
flow values, plotted against drainage area and subjected to
Table 6
7-day Mean Low Flow Data from
Handle and Morgan (1984)
Gauge
7-day
Drainage Area minimum discharge
Qmin (cfs)
at given recurrence
interval
2-year 10-year
Halls Brook, Kingston
Town Brook, Plymouth
Eel River, Plymouth
Beaver Dam Brook
Herring River, Bournedale*
Red Brook, Buzzards Bay
Agawam River, Ellisville
Agawara River, East Uareham
Uankinko River, Uareham
Ueweantic R., S. Uareham
IND
JON
3.98
9.04
14.70
5.52
7.74
9.84
6.71
17.10
20.50
56.10
30.20
15.70
3.8
11.0
18.0
6.2
3.8
3.8
8.0
25.0
12.0
15.0
4.6
6.8
2.2
9.2
15.0
4.6
2.3
1.8
7.0
20.0
8.C
10.0
1.3
2.2
Correlation Coefficients
.48
.23
* This is not the same Herring River as in Table 1.
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52
Table 7
10-Year Annual Minimum Discharge
Gauge
ADM
DOR
HER
IND
JON
MOS
POT
SEG
TAU
THR
HAN
HUM
Drainage Area
AoL
y
(mi )
7.91
4.67
9.40
30.20
15.70
23.10
23.00
10.60
260.00
84.30
43.30
19.50
10 -year
Annual
Minimum
(cfs)
0.07
0.01
1.00
2.80
1.70
1.70
0.10
0.00
17.00
9.70
0.90
0.36
Year
of
Occurrence
1964,1965
1964,1965,1970
1970
1968,1969
1968
1970
1969
1969
1965,1966
1970
1965
1970
Correlation Coefficient
.82
a regression analysis (Figure 6), can be used to form a
regional relation which can then be used to predict low
flows in ungauged areas.
Although all the gauges in Table 6 are closer,
geographically, to Buttermilk Bay than the gauges in Table
1, the correlation coefficients of the low flow data are
extremely low implying inhomogeneity among the data. The
graphic reresentation of the low correlation can be seen by
the scatter in Figure 10. The reasons for such low
correlation may lie in the pattern of regulation and in the
short periods of record for the stations used by Wandle and
Morgan (1984). The equations developed from the regression
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53
7-day Consecutive Minimum Discharge
with 2-year and 10-year
Recurrence Intervals
Drainage Area
Ad
km2
345 10 20304050 100 200
i i i | i i i i _ •. j i
100
40-
30-
20-
Discharge
10H
Q
cfs
5-
4-
3-
2-
«Q10 2.81Ad°'4210-yr Low Flow
*Q2 2.42Ad°-282-yr Low Flow
i i i
345
-2
-1
-0.5
-0.4
-0.3
•0.2
-0.1
Discharge
Q
m3/s
-0.05
10 20304050 100
Drainage Area
Ad
mi2
Figure 10. Relations for the 7-day minimum low flow
data with recurrence intervals of 2 and 10 years showing
the scatter of points resulting in the low correlation
coefficients. Equation are in imperial units with Q in cfs
2
and Ad in mi .
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54
analysis of the 7-day mean low flow data are of no use as
predictive tools because of the low correlation among the
data points. The equations for the
7-day mean low flow data are:
Q2(7-daymin) = 2-»KA<» -42. (18)
for the 2-year recurrence interval, and
Q10(7-day .in) = 2.42(Ad)'28, <">
2
for the 10-year recurrence interval, where Ad is in mi and
2 3
Q in cfs. In SI units where Ad is in km and Q is in m /s,
equations 18 and 19 can be rewritten as follows:
Q2(7-day .in) = ° ' °534( Ad) ' ' ( 2° )
for equation 18, the 2-year recurrence interval, and
00
Q10(7-day »ln. = °-0525(M> ' <21)
for equation 19, the 10-tear recurrence interval.
The equations are meaningless because they state that
the lowest flow from 1 square mile of drainage area is
2.81 cfs or 2.42 cfs, greater than the mean annual flow
(Qma) from 1 square mile of drainage area (1.64 cfs). This
is impossible. Most likely, such spurious relations result
from the short periods of record used to estimate the data.
Urbanization may also be responsible for low flows in a
stream. Some of the streams located near municipal or
private wells may experience more extreme low flows due to
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55
additional lowering of the water table during dry periods
when there is no natural recharge, but continued pumping in
the vicinity of the stream.
The correlation for the 10-year annual minimum is much
higher. Most likely, the reason for the better correlation
lies in the longer periods of record used in the annual
minimum evaluation. Many of the stations in the Handle and
Morgan (1984) were only in operation for two years and the
low flow is an estimate based on only a 2-year record. The
equation for the 10-year annual minimum data in Table 7 is:
Q10, . , = 0.0044(Ad)lt61, (22)
(mm;
2
where Ad is in mi and Q is in cfs. In SI units, where Ad
2 3
is in km and Q is in m /s, equation 22 rewritten as:
Q10, . , = (2.69 x 10~5)(Ad)1>61. (23)
(mm;
Although the correlation is higher, the equation may not
accurately describe natural low flow conditions, but the
lowest flow due to regulation in a period of drought.
However, from this relation, the pollution hazard in the
form of higher bacteria concentration in low discharges
from Red Brook can be estimated for extremely dry
conditions. This would be helpful in determining when to
regulate swimming near the mouth of Red Brook, if
necessary.
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56
II.C BUTTERMILK BAV SURFACE HATER CHARACTERISTICS
The Buttermilk Bay watershed is composed primarily of
permeable sand and gravel. Because overland flow is rare in
this type of material (Strahler, 1972), there is not a well
developed drainage system in the watershed. Of the three
streams (Appendix Figure A-l) that flow into Buttermilk
Bay, only Red Brook has a steady discharge greater than 1
cfs. Most of the streams, including Red Brook, discharge
from cranberry bogs, presumably developed in pre-existing
kettles. Consequently, the drainage pattern is natural and
not induced from the development of the bogs. The total
2 2
watershed has an area of 17.83 mi (46.18 km ), including
the 9.84 mi2 (25.49 km2) of the Red Brook drainage area.
The watershed extends from just south of Halfway Pond in
the north to route 6 in the south. The east and west sides
are bounded by the Great Herring Pond watershed and the
Agawam river drainage area, respectively. The watershed is
partly urbanized in the area adjacent to the Bay, and is
currently experiencing rapid expansion. Many new houses are
under construction, as well as an extension of Route 25
which passes over Tarkiln Hill and continues toward the
Bourne Bridge to Cape Cod.
Route 25 will pass very near the public water supplies
of Buzzards Bay and Wareham. Consequently, there has been
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57
some recent study by the USGS to determine the effects of
road salt (Church, personal communication, 1986), (Pollock,
1984). Operation of a stage recorder on Red Brook near the
highway and monitoring of wells is part of this currently
active engineering work. Other studies in the area include
salt studies by Caldwell (1971) and a Master's Thesis by
Frank (1972), the latter also dealing with the potential
hazard of road salt to the public water supplies. In
1969 - 1971 the USGS installed a partial recording station
on Red Brook. Williams and Tasker (1974), as well as Handle
and Morgan, (1984) have used the low flow information from
this gauge.
In order to further describe the surface water
hydrogeology of the Buttermilk Bay watershed, another
stage-recorder was installed on Red Brook in December, 1985
(Appendix Figure A-l). The drainage area of this gauge is
2 2
9.13 mi (23.65 km ). In addition to the river stage record
from the gauge, periodic discharge measurements have been
made in order to formulate a rating curve for Red Brook.
Discharge measurements have also been made at several of
the smaller streams entering the Bay. The results of this
section of the study will help to quantify the amount of
freshwater entering Buttermilk Bay.
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58
II.C.I Red Brook Streamflow
Annual hydrographs from Red Brook are available for
water years 1985 and 1986 (Figures 11 & 12). The annual
hydrograph for water year 1985 (Figure 11) has been
prepared with data from the USGS gauge near the junction of
Red Brook and the new Route 25 (Church, personal
communication, 1986). The drainage area for this gauge is
2 2
6.63 mi (17.17 km ) . The characteristic shape of the
hydrograph explained above, is absent in the 1985
hydrograph. Instead of the usual rise in baseflow in the
late winter and early spring, the baseflow declines in
%.•
February and early March, then rises in April and May, the
usual start of decline, due to increased rainfall. The
baseflow begins to decline in June and July, then to rises
again in August, the usual period of high
evapotranspiration and declining baseflow. This rise is a
result of heavy rain throughout August. Because 1985 was a
dry year, the rise and decline of baseflow depends strongly
on rainfall, rather than the pattern of annual
evapotranspiration. The 1985 average discharge in Red Brook
3
for this drainage area was 3.48 cfs (0.0986 m /s), which
yields a CFSM value of 0.525 (0.00574 in SI units). The
total discharge for 1985 at this gauge was 1272 cfs (36.02
m3/s). The total baseflow was 764 cfs (21.63 m3/s), 60% of
the total discharge. This high percentage is a result of
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59
100-
Discharge
O
cfs
Red Brook Hydrograph for Water Year 1985
Discharge
Q
m3/s
0.05
Oct
Nov
Dec
Jan
Feb Mar Apr
Water Year 1985
May
Jul
Aug
Sep
Figure 11. 1985 Hydrograph for Red Brook from data
obtained by the USGS gauging station with a drainage area
of 6.63 mi2 (17.17 km2).
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60
little rainfall, which accentuated the contribution of
baseflow to Red Brook. The amount of precipitation that
becomes streamflow, calculated by multiplying the CFSM
value by the conversion 13.57 (see section II.B.I),is
7.12 inches (18.08 cm). This number along with the CFSM are
both very low compared to the long-term results in Table 2.
The difference can be explained by the small amount of
precipitation in 1985, the failure to consider ground water
recharge in the figures in Table 2, and the removal of
water from Red Brook during low flow periods by the Onset
Fire District pumping well (Appendix Figure A-l).
The 1986 hydrograph (Figure 12) shows a more well-
defined hydrograph shape. It contains a rise in baseflow in
early spring followed by a slow decline in the summer
months. The above average rainfall in July and August
(NOAA, 1986) boosted the baseflow somewhat and can be seen
as small rises in the general decline on the hydrograph.
The 1986 data for Red Brook was recorded by the gauge
installed for this study (Ad = 9.13 mi2 » 23.65 km2), and
supplemented in a few places by the USGS gauge further
upstream. The average discharge for 1986 on Red Brook at
this gauge is 8.234 cfs (0.233 m3/s), which yields a CFSM
value of 0.90 (0.0099in SI units). This is significantly
higher than the 1985 CFSM value and can be accounted for by
the additional rainfall in 1986. The amount of rainfall
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61
Discharge
Q
cfs
100-
50-
40-
30-
20-
10-
Red Brook Hydrograph for Water Year 1986
-5
-2
-1
0.5
0.4
0.3
-0.2
-0.1
-0.05
Dischan
Q
m3/s
Oct Nov Dec Jan Feb Mar Apr May Jun
Water Year 1986
Jul Aug Sep
Figure 12. 1986 hydrograph for Red Brook. Data from
the gauge installed in December 1985 with a drainage area
of 9.13 mi2 (23.65 km2) .
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62
that became streamflow in 1986 is 12.21 inches (31.02 cm).
The total discharge at this point is 3005 cfs (85.11 m /s)
with 69% of the discharge baseflow, or a total baseflow
discharge of 2084 cfs (59.02 m3/s).
The pattern of baseflow shown in the Red Brook
hydrograph also yields some insight into the surrounding
geology. Like the Herring River, Red Brook drains permeable
material. However, the baseflow curve is not as smooth as
the Herring River 1973 hydrograph. The differences may
result from the combination of geology and amount of
precipitation. As can be seen from the surficial map
(Appendix Figure A-2), Red Brook is situated almost
entirely in the finer-grained outwash. This material is
slightly less permeable than coarser, gravelly deposits
(Williams and Tasker, 1974) that yield smoother baseflow
curves. In addition, 1973 was an extremely wet year, which
produced a uniform baseflow discharge from excess
precipitation. 1986 has not been an extremely wet year, and
as a result, dry periods, when high evapotranspiration
depletes soil moisture, are accentuated by declining
baseflow discharge. The differences in the baseflow curves
of Red Brook and the Herring River can be accounted for by
the geology, but the precipitation difference between 1973
and 1986 probably overshadows any dissimilarity due to
geology.
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63
^I.C.2 Red Brook Flow Duration
Flow duration can provide additional information on
the geology of Red Brook. Table 8 and Figure 8 show the
results of 1985 and 1986 flow duration analyses for Red
Brook.
Table 8
Red Brook Flow Duration
Station USGS gauge B.
2
Drainage Area (mi )
(km2)
Data Period (water year)
Percent 99%
of 95%
Time 90%
Discharge 75%
was 70%
Equaled 50%
or 25%
Exceeded 10%
Median
Average
Standard-Deviatign
Error in SD
6.63
17.17
1985
Discharge (cfs)
1.50
1.60
1.73
2.18
2.36
2.89
3.45
4.65
2.89
3.48
0.99
4%
U. gauge
9.13
23.65
1986
3.52
3.80
4.37
6.10
6.25
7.20
8.90
10.85
7. 20
8.23
2.30
22%
***
Since these curves do exhibit a perfect shape, the
standard deviation is the average of differences between
the median and 84% and 64%, respectively. The error is the
%error between the real value and and the average standard-
deviation.
-------
64
The flow duration curves for 1985 and 1986 are
extremely similar and like the Herring River curve, they
are both very flat. This shape is to be expected because
the outwash surrounding Red Brook and Buttermilk Bay is
highly permeable and similar to outwash on Cape Cod. The
low standards of deviation and figuring errors reflect the
flat shape of the curve and the steady character of the
streamflow. The flow duration analyses imply that permeable
deposits surround Red Brook which agrees with the results
of the surficial mapping.
II.C.3 Regulation
The shape of these flow duration curves and annual
hydrographs may also reflect some of the flow regulation
practices of the cranberry farmers. In the summer, the bogs
are drained to allow the plants to grow. As a result, the
bogs do not serve as storage ponds as their predecessor,
kettle holes, do and consequently, heavy precipitation
leads to higher stream discharge than might otherwise be
expected. The high discharges in the steep section of the
curve reflect these uncharacteristic high discharges. The
bogs are flooded in the winter to protect the plants from
freezing. They are also flooded in the spring and fall to
protect the plants from frost. Some of the irregular flow
seen on the annual hydrographs may result from these bog
management practices. Low flows in the fall occur when the
-------
65
bogs are being harvested. At this time they are flooded in
order to collect the cranberries which float. During dry
weather, in the late summer and fall, the retention of
water in the bogs, may cause extremely low discharges seen
on the flow duration curves and the annual hydrographs. In
fact, the small stream that drains Nye Bog is dry much of
the late summer and early fall.
Along with regulation from the cranberry bogs, the
discharge of Red Brook will be influenced by the pumping of
the Onset Fire District water-supply well located about
120 m from the stream (Appendix Figure A-l). In the dry
periods the discharge of Red Brook will be further
decreased by abstraction from the well. In wetter periods,
the withdrawal of water from the well won't directly affect
the discharge as it will draw ground water that ordinarily
would have discharged into Red Brook, this will slightly
decrease the flow of Red Brook. In 1985, the Onset Fire
District pumped 87 million gallons from the well. This
number converts into 0.5 inches (1.27 cm) of streamflow
denied Red Brook. Without the pumping well the flow from
Red Brook in 1985 would have been 7.62 inches (19.35 cm).
This is not a significant increase.
The flow in Red Brook is also regulated by a series of
small dams with fish ladders. Periodically, the size of the
dams are changed in order maintain ample water in the pools
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66
for the fish. As a result, the stage-discharge relation for
Red Brook periodically changes in an unnatural manner.
3J.C.4 Red Brook Discharge From Regional Equations
The regional discharge equations developed above can
be used as predictive tools to estimate discharges in Red
Brook. Because the discharge record at Red Brook is very
short, the flood discharges would be impossible to predict
without these equations.
Mean annual discharge is the most useful method in
determining the freshwater input to Buttermilk Bay. Using
equation 3:
Qma = 1.64(Ad)1>03 (23)
and the USGS value for the total drainage area of Red
Brook, 9.84 mi2 (25.49 km2) (Handle and Morgan, 1984), the
mean annual discharge will be near 17.3 cfs (0.49 m /s).
2
Qma at the gauge with a drainage area of 9.13 mi
(23.65 km2) will be 16.0 cfs (0.45 m3/s) with this
equation. These values seem high when compared with the
annual average flow of 8.234 cfs (0.233 m /s) in 1986 at
this gauge. The disparity in this calculation is most
likely due to the short periods of record of many of the
gauges used in the analysis. The other source of error lies
in the homogeneity of the region. Red Brook may not be as
similar climatically and geologically as is needed to
produce accurate results. Also, the gauges in the analysis
-------
67
themselves may not be entirely homogeneous. This quality is
more difficult to determine the shorter the period of
record on the streams in an analysis.
In order to overshadow errors resulting from short
periods of record, the high and low average discharge
equations developed above can be used to predict a range of
average discharges. Using equations 5 and 6:
1 Od
Qaah = 2.36(Ad)A ' , and (24)
Qaal = 0.69(Ad)1>01 (25)
for high and low average discharge, respectively, the
2
results for the total drainage area of Red Brook (9.84 mi
2 3
or 25.49 km ) are 25.4 cfs (0.72 m /s) on the high end and
6.95 cfs (0.20 m /s) on the low end. The drainage area of
2 2
9.13 mi (23.65 km ) at the stream gauge produces values
for high and low average discharges of 23.5 cfs (0.67 m /s)
3
and 6.44 cfs (0.18 m /s), respectively. The predictions for
low average annual flow seem to be closer to the average
annual flow observed at the discharge station on Red Brook.
Although, the mean annual discharge prediction is high the
average discharge at Red Brook does fall within the range
of annual flow produced by the high and low average flow
equations. Consequently, there is some similarity between
-------
68
Buttermilk Bay and the region used to develop these
equations.
The annual flood and low flow equations (equations 10
through 23) developed above can also be used to predict
discharges on Red Brook. However/ these equations are even
more dependent on long periods of record. The results from
these equations should be used with other local
information. Many times residents near the stream can
provide good information on flood stage and drought
periods. Water markings on trees can also provide valuable
flood stage information. The predicted discharges for Red
Brook for the mean annual, 5-year, 10-year, and 25-year
floods and 10-year low flow are presented in Table 9.
The flood predictions for Red Brook (Table 9) are
extremely large. As stated previously, the short periods of
record used in the annual flood series and the annual
minimum low flow analysis, along with a possible lack of
regional homogeneity, can account for the error in these
predictions. Unfortunately, it is impossible to predict the
amount of error involved.
II.C.5 Red Brook Rating Table
In order to make use of the discharge information
available for Red Brook, a rating curve has been developed
from occasional discharge measurements at known river
stages. The major impediment, as mentioned earlier, to the
-------
69
Table 9
Red Brook Flood Discharge Predictions
Flood Equations
Total Ad
9.84 mi2
25.48 km2
Gauge Ad
9.13 mi2
23.65 km2
Q2.33
26.26(Ad)>85
Q5 = 42.06(Ad)
Q10
61.49(Ad)
.81
.78
Q25 = 74.67(Ad)
.75
Q10. . . = 0.0044(Ad)
(rain)
1.61
cfs m /s
183.4 5.19
268.0 7.59
365.9 10.36
414.9 11.75
0.175 0.005
cfs m Is
172.1 4.87
252.3 7.15
345.1 9.77
392.2 li.ll
0.155 0.0044
development of an accurate rating curve (one with many data
points) is the regulation of the height in the pools by the
small dams. When the height of a dam is changed, the stage
of the river upstream will be affected. Consequently, when
the dams below the stage recorder were changed, the stage
discharge relation was changed. Because this occurred three
times in the past year, there are three different
stage-discharge relations for Red Brook. Each relation is
only valid for the time period in which it was developed.
The chance for error is greater in these relations than if
there were a single relation for the stream. Table 10
contains the three relations and their ranges in time.
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70
Figure 13 is a graphic representation of these relations.
Unfortunately, the occurrence of the changes of the dam
height are somewhat unpredictable because, in addition to
the authorized changes/ children playing in the stream
often play on the dams and change them!
Table 10
Stage-Discharge Relations for Red Brook in 1986
Stage-Discharge Relation
St = Stage in feet
Q = Discharge in cfs
Time Range
Q = 0.845(St)5<6°
Q = 1.34(St)3'83
(26)
(27)
10/01/85 - 04/26/86
04/27/86 - 07/17/86
0.808(St)
3.94
(28)
and 09/16/86 - 09/30/86
07/18/86 - 09/15/86
Equations 24 through 26 in Table 10 can be rewritten
in SI units, where stage (St) is in meters and discharge
(Q) is in m /s, as follows:
Q = 18.55(St)5'60,
(29)
for equation 26, and
Q = 3.59(St)3'83,
(30)
for equation 27, and
Q = 2.47(St)J* ,
(31)
for equation 28.
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71
Red Brook Stage - Discharge Relations
0.040.05 0.1
Stage
St
m
0.2 0.30.40.5
100-
50-
40-
30-
20-
Discharge
Q
cfs
5
4
3
2
0.1
0.1.34(80*
Q» 0.808(St)
Q-0.845(St)»-«°
I I I T
0.2 0.30.40.5
1
Stage
St
tt
I
2
i i i
345
rl
-0.5
-0.4
_Q 3 Discharge
O
-0.2 m3/s
-0.1
-0.05
-0.04
-0.03
10
Figure 13. Rating curves for Red Brook during water
year 1985. The stage-discharge relation for Red Brook is
unsteady due to constant regulation.
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72
TTI. HATER BALANCE
The water budget methodology, conceptualized by
Thornthwaite in 1948 and further developed by Thornthwaite
and Mather in 1955, uses meteorological parameters to
estimate a climatic water balance. The budget requires the
input of precipitation and average monthly temperature in
order to calculate values of potential evapotranspiration,
actual evapotranspiration, water deficit, and water
surplus. The water deficit is a measure of the amount
additional water needed in a soil for plant growth. The
surplus indicates the amount of water each month that can
run off into streams or be recharged as ground water. The
surplus can be to estimate the amount of freshwater
discharge to Buttermilk Bay.
III.A DESCRIPTION OF METHODOLOGY
Thornthwaite and Mather, in 1957, published a series
of tables which enable the calculation of water budgets in
a variety of vegetation and soil moisture conditions. This
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73
publication also contains tables of potential
evapotranspiration at various latitudes. These tables were
constructed from the potential evapotranspiration equation
they developed in 1948. The equation reflects an empirical
relation between potential evapotranspiration and mean
normal air temperature. The assumption inherent in this
equation is that a high correlation exists not only between
potential evapotranspiration and mean normal air
temperature, but between potential evapotranspiration and
solar radiation/ atmospheric moisture, and wind
(Thornthwaite and Mather, 1948). Although these assumptions
may not always be valid, this equation is most often used
because the parameters it requires, mean normal air
temperature and latitude, are easily obtainable (Palmer and
Havens, 1958).
There are two main approaches to calculating potential
evapotranspiration. The first is the Thornthwaite approach
described above, and the second is the energy balance
approach. This approach involves balancing incoming solar
radiation, reflected solar radiation, albedo, and net
longwave radiation reflected from plants against net energy
advected to plants, energy used for evapotranspiration,
energy transferred from plants to air as heat, and changes
in energy stored in soil and plants (Dunne and Leopold,
1978). Of the several equations for potential
-------
74
evapotranspiration that have been developed using this
approach, Penman's (1948) is the most widely used. The U.S.
Soil Conservation Service (1970) developed the other most
widely used potential evapotranspiration equation, the
Blaney-Criddle Formula, using the air temperature approach,
as Thornthwaite did. However, this equation incorporates
crop roughness, advection, and net radiation at various
growth stages (Dunne and Leopold, 1978).
In response to the tables published in 1957, Palmer
and Havens (1958) produced a graphical solution for the
Thornthwaite and Mather potential evapotranspiration
equation. They have produced graphs relating potential
evapotranspiration to day length and heat index in imperial
units for using more easily with American hydrologic data
(Palmer and Haven, 1958). This method is used here to the
potential evapotranspiration values at Buttermilk Bay.
The water budget is computed by comparing the
precipitation (P) with the potential evapotranspiration
(PE). The potential evapotranspiration (PE) is the
evapotranspiration that will occur if there is no
deficiency of soil moisture for plant use at any time
(Langbein and Iseri, 1960). A positive difference between
these values (P-PE) indicates a quantity of water that is
available for soil moisture recharge and runoff. There is
only water available for runoff after the soil has reached
-------
75
its water-holding capacity (SI). When P-PE is positive and
the soil has reached its capacity/ there is a surplus (Sur)
of water/ and the actual evapotranspiration (AE) is equal
to the potential evapotranspiration (PE). A P-PE value of
zero/ a rare occurrence, means that all moisture needed for
evapotranspiration is fully/ but not excessively/ provided
for by precipitation. When (P-PE) is negative/ there is not
enough precipitation to cover the needs of the vegetations.
Consequently, the actual evapotranspiration (AE) that takes
place is equal to the amount of water supplied by
precipitation (P) plus the amount of soil moisture drawn
(AST). The amount of soil moisture used is indicated by a
change in soil moisture storage (AST). A deficit (Def)
occurs when the value for actual evapotranspiration is less
than the potential evapotranspiration. Soil moisture
storage (ST) continues to decrease until a positive (P-PE)
value occurs/ at which point/ the extra water is used to
replenish the soil moisture.
Runoff (RO) occurs when there is a moisture surplus
(Sur). However, it is assumed that only half the moisture
available for runoff in a watershed can actually runoff in
a month (Thornthwaite and Mather, 1957). The rest is
detained in the watershed and will runoff during the next
month. Any precipitation occurring when there is a mean
-------
76
monthly temperature below 30.20»F (-1.0*C) is assumed to
have fallen as snow and is stored on the watershed surface
until the temperature rises above this point. Only 10% of
t
the snowmelt stored on the surface can runoff (SMRO) during
this first month with a temperature greater than 30.20'F
(-1.0°C) . After the first month, 50% of the remaining
snowmelt runs off each month (Thornthwaite and Mather,
1957). This assumption may be invalid for Buttermilk Bay
because snow rarely accumulates (Strahler, 1972). The ,
annual total runoff (TOT RO) is the sum of the runoff (RO)
and snowmelt runoff (SMRO) for the year. Any errors in
snowmelt runoff computation, resulting from the possible
invalid assumption, will not show up in the annual total
runoff, only in the monthly totals of runoff. The sum of
the amounts of water in soil storage, in storage on the
watershed, and in storage to runoff the next month is the
amount of water detained (DT).
The amount of water drawn from soil for
evapotranspiration depends upon the dryness of the soil.
There is an exponential decay of the rate of soil moisture
decrease with respect to evapotranspiration (Thornthwaite
and Mather, 1955). Consequently, Thornthwaite and Mather
(1957) developed tables of soil moisture for different
values of negative accumulated P-PE (AP ML) and soil
storage capacities (ST) .
-------
77
III B BUTTERMILK BAY WATER BUDGETS
The input data for the Buttermilk Bay water budgets
seen in Tables 11 & 12 is data from the National Oceanic
and Atmospheric Administration meteorological recording
station at the Cranberry Experiment Station in East
Wareham. They record daily high, low and average
temperatures, as well as daily precipitation. The Natipnal
Climatic Data Center is responsible for the distribution of
the data. The soil water-holding capacity, or amount of
soil moisture storage, is an average of values for soils in
the Buttermilk Bay drainage area. The soil information was
obtained from the Soil Conservation Service (1982).
III.B.I Average Year Hater Budget
Table 11 shows the water balance for a water year with
normal temperature and precipitation. The normal values are
the longterm averages. This budget was primarily
constructed to determine the average runoff and snowmelt
runoff values, half of which will carry into the next year.
However, it will provide an average amount of freshwater
influx to Buttermilk Bay that can be used as a prediction
for the future.
-------
78
Tab].
Average Year Water Budqet Eor Buttermilk Bay
TEHP
in
OCT
NOV
DEC
JAN
FEB
NAR
APR
HAY
JUN
JUL
AUC
SEP
IKI
52.00
42.
31.
27.
28.
36.
45.
55.
65.
71.
69.
62.
30
60
40
20
00
40
60
00
10
70
20
Totals
3.
1.
0.
0.
.0.
0.
1.
4.
7.
9.
8.
6.
42
i
35
23
00
00
00
29
82
30
15
24
75
25
.38
1.
0.
0.
0.
0.
0.
1.
2.
4.
5.
4.
3.
24
PE P
in) * * ~ *
83
72
00
00
00
31
27
83
34
» *ll *
1.66
.48
.82
.23
.94
. 39
. 15
.83
. 18
31 2.86
87 4.43
25 3.80
.73 45.77
P-PE
( in )
1.83
3
4
4
3
4
2
1
-3
-2
-0
0
21
76
82
23
94
08
88
00
16
45
44
55
04
AP ML ST
( in ) ' ' ~ '
0.00
0
0
0
0
0
0
0
-3
-5
-6
0
6
00
00
00
00
00
00
00
16
61
05
00
05
t in f
2.75
3
3
7
11
3
3
3
1
0
0
0
00
00
23
17
00
00
00
01
43
37
92
-ST
( in )
1.83
0
0
0
0
0
0
0
-1
-0
-0
0
2
25
00
00
00
00
00
00
99
58
06
55
63
AE
1 in »
1.83
0
Q
0
0
o
1
2
3
3
4
3
21
72
00
00
00
31
27
83
17
44
49
25
31
Del
t ' - '
0
0
0
0
0
0
0
0
1
1
0
0
3
in t
00
00
00
00
00
00
00
00
17
87
38
00
42
Cur
< in 1
0.00
3
4
0
0
4
2
1
0
0
0
0
16
51
82
00
00
08
88
00
00
00
00
00
29
HO
(in)
0.06
1
3
1
0
2
2
1
0
0
o
0
16
78
30
65
83
45
67
83-
92
46
23
11
29
SMRO
( t n )
0.06
0.03
0.01
0.01
0.00
0.82
3.68
1.84
0.92
0.46
0.23
0. 11
8.16
TOT RO
( in >
0.11
1
3
1
0
3
6
3
1
0
0
o
24
81
32
66
83
27
34
67
84
92
46
23
45
OT
( ~ '
2
4
6
8
12
12
9
6
2
1
o
1
n I
86
81
32
89
00
81
34
67
85
35
83
15
OCT
NOV
DEC
JAN
FEB
HAR
APR
MAY
JUN
JUL
AUC
SEP
Freshwater
Influx
( cubic feet)
4752441
75072982
137365092
68644825
34173691
135431374
•b2733S51
152078104
76039052
38019526
19009763
9504881
1012825281
Fr esnwAtei
lntlux
134554
2125509
3889159
1943511
967545
3834410
7438662
4305722
2152861
1076431
538215
269108
28675687
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79
In order to calculate a value of runoff for the
average year from the previous December, an expression was
written for the December runoff in the average year in
terms of the previous December's runoff, (x). These
quantities should be equal in an average year.
Consequently, the expressions were set equal to each other.
The following equation is the result of this process:
x = (x/4096) * 2.935234375 (32)
When this equation is solved for x, the previous December's
runoff is found. Half of this value carries from December
to January in an average year. This value was then used as
the input to the water budgets at the start of the series
of years of interest.
Figure 14 depicts the average water balance
graphically. The monthly values of precipitation (P) and
evapotranspiration (AE and PE) are plotted. From the
intersections of these lines, the periods of surplus,
deficit, soil moisture use and soil moisture recharge can
be depicted. As expected, the winter months have little to
no evapotranspiration, while June, July, and August have
the most. The deficit and the soil moisture use occur
during these summer months when evapotranspiration is high
and the precipitation is somewhat lower. In the average
year the total deficit is 3.42 inches (8.69 cm) and the
total amount of soil moisture use is 2.63 inches (6.68 cm).
-------
80
Water Budget for an Average Water Year
6-
5-
in
- P - Precipitation
__ PE - Poieniial
AE - Actunl Evnpolrnnsoiinlion
. a «SMT1 - Soil Moisture Recharge
IHIIIISMU - Soil Moisli-re Use
«**« Del - Delicti
IjXV Sur - Surplus
-15
-10
-5
Uct I Nov I Uec I Jan I Feb I Mar I Apr < May I Jun ' Jul I Aug > Sep
- 0
Avt»««e Values ni n Water Year
Figure 14. Water budget for Buttermilk Bay in a year
with average temperature and precipitation.
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81
Because the rate of soil moisture decreases exponentially
with respect to evapotranspiration, the 6.05 inches
(15.37 cm) of accumulated water loss (AP WL) is not equal
to the amount of soil moisture used/ 2.63 inches (6.68 cm).
Soil moisture recharge occurs in the fall, September,
October, and November when the evapotranspiration declines,
It equals the soil moisture use. A water surplus of 24.45
inches (62.10 cm) is shown in Figure 14. This value equals
the total runoff (TOT RO) in the budget which includes the
snowmelt runoff (SMRO) and the runoff (RO). However, Table
11 shows only 16.29 inches (41.38 cm) of surplus (Sur)
because the snow stored on the watershed in January and
February, equivalent to 8.17 inches (20.75 cm) of rain, is
not included. The total runoff equals the sum of the
surplus, 16.29 inches (41.38 cm), and the rainfall
equivalent of snowfall, 8.17 inches (20.75 cm). The total
runoff (TOT RO) value of 24.45 inches (62.10 cm) is also
equal to the actual evapotranspiration (AE) of 21.31 inches
(54.13 cm) subtracted from the precipitation of 45.77
inches (116.26 cm). This result confirms the validity of
equation 1 presented earlier,
Q = P - ET. (33)
III.B.2 Mater Budgets for Hater Years 1984 - 1986
The water budgets for water years 1984, 1985, and 1986
are shown in Table 12. The first 9 months of 1983 are
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82
Table 12
Hater Budget for Buttermilk Bay 1963 -1986
JAN
FEB
1 HAR
9 APR
8 MAY
3 JUH
JUL
AUC
SEP
OCT
NOV
H DEC
Y JAM
FEB
HAR
1 APR
9 MAY
8 JUH
4 JUL
AUC
SEP
OCT
HOV
H DEC
Y JAH
FEB
MAR
1 APR
9 HAY
a JUH
5 JUL
AUC
SEP
OCT
HOV
DEC
JAH
FEB
MAR
APR
1 MAY
9 JUN
a JUL
6 AUC
SEP
TEMP
( F 1
29.70
30. 10
38.60
45.70
53. 10
65.10
71.90
70.00
65.90
52.70
45.30
33.30
27.50
37.30
33.00
45.40
56.60
67. 10
71.20
72.00
61. 30
54.30
44.20
39.00
23.70
31.60
39.80
47.70
55.90
63.10
71.40
69.40
63.40
53.30
46.80
30.80
30.50
27.70
37.20
47.00
56.00
63.10
69.40
70.39
62. 10
PE
( In)
0.00
0.00
0.31
1.27
2.83
4.34
5.31
4.87
3.25
1.83
0.72
0.00
0.00
i) 00
0.31
1.27
2-. 8 3
4.34
5.31
4.87
3.25
1.83
0.72
0.00
0.00
0.00
0.31
1.27
2.83
4.34
5.31
4.87
3.25
1.63
0.72
0.00
0.00
0.00
0.31
1.27
2.83
4.34
5.31
4.87
3.25
P
(in)
4.07
5.61
8.81
7.82
3.60
2.61
1.55
4. 10
1.76
4. 31
6.49
4.47
2.70
5.49
6.84
4.86
3.49
7.65
4.86
0.48
2.61
4. 27
1.69
3.45
1. 17
1.61
3.21
1.29
4.92
5.25
4.21
12.61
1.29
1.75
5.60
1.15
7.72
3. 12
3.73
3.25
3.26
3.31
4.93
5.13
0.88
P-PE
( in )
4.07
5.61
8.50
6.55
0.77
-1.73
-3.76
-0.77
-1.49
2.48
5.77
4.47
2.70
5.49
6.53
3.59
0.66
3.31
-0.45
-4.39
-0.64
2.44
0.97
3.45
1.17
1.61
2.90
0.02
2.09
0.91
-1. 10
7.74
-1 .96
-o.oa
4.88
1.15
7.72
3. 12
3.42
1.98
0.43
-1.03
-0. 38
0.26
-2.37
AP UL
(In)
0.00
0.00
0.00
0.00
0.00
-1.73
-5.49
-6.26
-7.75
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.45
-5.29
-5.93
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-1.10
0.00
-1.96
-2.04
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-1.03
-1.41
0.00
-2.37
ST
(ink
7.07
12.68
3.00
3.00
3.00
1.65
0.45
0.35
0.21
2.69
3.00
3.00
5.70
3.00
3.00
3.00
3.00
3.00
2.57
0.48
0. 39
2.83
3.00
3.00
4.17
3.00
3.00
3.00
3.00
3.00
2.05
3.00
1.52
1.48
3.00
3.00
3.00
6. 12
3.00
3.00
3.00
2. 10
1.85
2. 11
1. 12
-ST
1 in )
0.00
0.00
0.00
0.00
0.00
-1.35
-1.20
-0.10
-0.14
2.48
0.31
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.43
-2.09
-0.09
2.44
0.17
0.00
0.00
0.00
0.00
0.00
0.00
0.00
-0.95
0.95
-1.48
-0.04
1.52
0.00
0.00
0.00
0.00
0.00
0.00
-0.90
-0.25
0. 26
-0.79
AE
0.00
0.00
0. 31
1.27
2.83
3.96
2.75
4.20
1.90
1.83
0.72
0.00
0.00
0.00
0.31
1.27
2.83
4. 34
5.29
2.57
2.70
1.83
0.72
0.00
0.00
0.00
0. 31
1.27
2.83
4.34
5.16
4.87
2.77
1.79
0.72
O.OO
0.00
0.00
0.31
1.27
2.83
4.21
5. 18
4.87
1.67
Def
0.00
0.00
0.00
0.00
0.00
0. 38
2.56
0.67
1.35
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.02
2.30
0.55
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.15
0.00
0.48
0.04
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.13
0.13
0.00
1.58
Sur
0.00
0.00
8.50
6.55
0.77
0.00
0.00
0.00
0.00
0.00
5.46
4.47
0.00
5.49
6.53
3.59
0.66
3.31
0.00
0.00
0.00
0.00
0 80
3.45
0.00
1.61
2.90
0.02
2.09
0.91
0.00
6.79
0.00
0.00
3.36
1.15
7.72
0.00
3.42
1.98
0.43
0.00
0.00
0.00
0.00
RO
1.65
0.83
4.66
5.61
3.19
1.59
0 80
0.40
0.20
0. 10
2.78
3.62
1.81
3.65
5.09
4. 34
2.50
2.91
1.45
0.73
C. 36
0. 18
0.49
1.97
0.99
; .30
2. 10
1.06
1.57
1.24
0.62
3.71
1.85
0.93
2. 14
1.65
4.68
2.34
2. 68
2.43
1.43
0.72
0.36
0.18
0.09
SHRO
0.01
0.00
0.97
4.36
2.18
1.09
0.54
0.27
0. 14
0 07
0.03
0.02
0.01
0.27
1.22
0.61
0.30
0. 15
0.08
0 .04
0.02
0.01
0.00
0.00
0.00
0. 12
0.53
0.26
0.13
0.07
0.03
0.02
0.01
0.00
0.00
0.00
0.00
0.00
0. 31
1.40
0.70
0. 35
0.18
0.09
0.04
TOT RO OT
(in)
1.66
0.63
5.63
9.96
5. 37
2.66
1.34
0.67
0. 34
0. 17
2.81
3.64
1.82
3.93
6.31
4.95
2.60
3.06
1.53
0.76
0. 38
0. 19
0.50
1.97
0.99
1.41
2.63
1.32
1.71
1.31
0.65
3.72
1.86
0.93
2. 15
1.65
4.68
2.34
3. 19
3.63
2.13
1.07
0.53
0.27
0. 13
* i n i
8.73
13.51
16. 37
12.96
6.37
4.33
1.79
1.02
0.55
2.86
5.81
6.64
7.52
6.93
9.31
7.95
5.60
.06
.10
. 24
.77
.02
.50
.97
. 16
.41
.63
.32
.71
. 31
2.70
6.72
3.38
2.41
5. 15
4.65
7.68
8.46
6. 19
6.83
5.13
3. 17
2.38
2. 38
1.45
JAH
FEB
HAR
APR
HAY
JUH
JUL
AUC
SEP
OCT
HOV
DEC
JAH
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
HOV
DEC
JAH
FEB
HAR
APR
MAY
JUN
JUL
AUC
SEP
OCT
NOV
DEC
JAH
FEB
MAR
APR
HAY
JUN
JUL
AUC
SEP
1963
MUTER
YEAR
1964
ROtot
( in)
32. 16
1985
ROtot
1 in )
18. 26
1986
ROtot
( in)
22.91
Butterr.Uk Bay
Freshwater Discharge
i
ce/yr
1. 332E»09
( cu . n) /yr
37731100
ct/yr
756375349
( c;u . • ) / y r
21420995
ct/yr
948889589
(cu.n)/yr
26873112
Cf/BO
6945576
116556639
150857956
75428978
162603797
261283339
204995337
116167145
126638068
63319034
31659517
15829759
7914879
20526502
81717333
40858666
58596404
108746856
54787655
70680503
54187560
27093780
154176807
77088404
38544202
8BB62163
68249109
194016007
97008003
132260612
158828886
88320314
44160157
22080078
11040039
5S20020
(CU . •) /MO
196703
3300953
4272386
2136193
4605035
7399698
5805589
3289922
3586465
1793232
896616
448308
224154
581323
2314283
1157141
1659485
3079775
1551619
2001713
1534624
767312
4366378
2183189
1091594
2516629
1932855
5494648
2747324
3745698
4498128
2501283
1250642
625321
312660
I'jfc330
-------
83
included in this table because water year 1984 starts in
1983 and the bookkeeping for a water budget should be
started during a period of no evapotranspiration; in this
case January 1983. In an average year the amount of runoff
carried from one year to another is equal, as shown above.
However, in reality, the amount of runoff carried from one
year to the next can vary widely. This can be seen in the
differences between the discharges for 1985 and 1986 on the
Red Brook hydrographs (Figures 11 & 12). Consequently, in
order to obtain the most accurate runoff for any given
year, the water budgets for several previous years must be
computed as well. The average December runoff value
computed above was used as the runoff carried into January
1983 at the start of this series of water budgets.
Figure 15 is the graphic depiction of these water
budgets. As in Figure 14 above, precipitation, potential
evapotranspiration, and actual evapotranspiration were
plotted for the three water years. The intersections of
these curves, outline:
1. the areas of deficit,
2. surplus,
3. soil moisture use, and
4. soil moisture recharge
for the water years 1984 - 1986. The most striking feature
of the plot is the differences in the size of the deficits.
-------
84
Water Budget lor Water Years 1984.1985 and 1986
13-
12-
-30
— PC • r-oimii.il Ev»nnil VM' "88
Figure 15. Hater budget for Buttermilk Bay for water
years 1984, 1985, and 1986. Hater year 1985, a dry year
shows a small deficit due to the timing of the
precipitation.
-------
85
The deficit for water year 1984, 2.87 inches (7.29 cm), is
much larger than the 1985 and 1986 deficits, 0.63 inches
(1.60 cm) and 1.88 inches (4.78 cm), respectively. Although
the precipitation, 54.25 inches (137.80 cm), during water
year 1984 was large, the periods of little rain, August and
September, occurred when evapotranspiration was highest.
Even though the precipitation, 44.97 inches (114.22 cm),
water year 1985 was smaller with a dry winter period, the
deficit was significantly less because the greatest
precipitation occurred in August when evapotranspiration
was high. However, water year 1985 did have a much smaller
surplus and a smaller runoff than water year 1984. Water
year 1986 shows a small deficit for the same reasons.
The values of the important totals from the water
budgets are presented in Table 13. The amounts of
precipitation and runoff vary the most from year to year.
Water year 1985 produced very little runoff (18.26 inches
or 46.38 cm). However, the surplus, 18.57 inches
(47.17 cm), for 1985 was larger than the runoff. This
anomaly arises because, unlike the average year, the amount
of runoff (both snowmelt runoff and runoff) carried over
from the previous year is not equal to the amount of runoff
carried into the next year. Consequently, the term
"incoming and outgoing runoff difference" (RD), must be
added to the sum of the surplus and the snowfall to obtain
-------
86
Table 13
Hater Budget Totals
Water Years 1984, 1985, 1986, and the Average Year
Quantities Reported in Inches
Quantity WY-1984 WY-1985 WY-1986 Av.Yr
Total Precipitation
Snow
Rainfall
Total Potential ET
Total Actual ET
Total Surplus
Total Deficit
Soil Moisture Use
Storage Change Deficit
Total Runoff
Runoff
Snowmelt Runoff
54.25
2.70
51.55
24.73
21.86
29.51
2.87
2.61
-0.18
32.16
29.35
2.82
44.97
1.17
43.80
24.73
24. 10 '
18.57
0.63
2.43
-1.13
18.26
17.08
1.18
43.83
3.12
40.71
24.73
22.85
18.06
1.88
1.98
0.20
22.91
19.82
3.08
45.77
8.17
37.60
24.73
21.31
16.29
3.42
2.63
0.00
24.45
16.29
8.17
Incoming & Outgoing
Runoff Difference -0.05 -1.48 1.73 0.00
the total runoff. A negative runoff difference (RD)
indicates that more water is being carried over to the next
year than was carried in from the previous year. In water
year 1985, the amount of runoff
carried in from the previous year was 0.38in and the amount
of runoff carried into the next year was 1.86in.
Consequently, the runoff difference (RD) term is -1.48in.
Similarly, the runoff difference (RD) and another term
must be added to equation 1, Q = P - ET, to validate the
equation. A soil moisture shortage along with a runoff
-------
87
difference may be carried from one year to another. The
term, Storage Change Deficit (SD), reflects a soil moisture
shortage carried in from the previous year. This term is
computed by totaling the (*ST) for a particular year. These
terms can then be added to form the equation:
Q = P - ET + SD + RD. (34)
For example, in water year 1985, the amount of
precipitation (44.97 inches or 114.22 'cm) less the amount
of actual evapotranspiration (24.10 inches or 61.21 cm) is
equal to 20.87 inches (53.01 cm). However with the addition
of the storage change deficit (SO) (-1.13 inches or
-2.87 cm) and the runoff difference (RD) (-1.48 inches or
-3.76 cm) Q is equal to 18.26 inches (46.38 cm), the amount
of runoff in water year 1985.
III.C COMPARISON WITH MEASURED STREAMFLOW
III.C.I Theoretical Considerations
Theoretically, the amount of runoff obtained in the
water budget should equal the amount of runoff measured in
the field (Thornthwaite and Mather, 1955). However, in
practice the numbers can vary greatly. The 1985 Red Brook
CFSM value, 0.525 multiplied by the conversion factor 13.57
yields 7.12 inches (18.08 cm) of streamflow resulting from
-------
88
precipitation. With the addition of the water from the
Onset Fire District pumping well, that value is 7.63 inches
(19.38 cm). The amount of runoff for water year 1985
calculated in the water budget was 18.26 inches (46.38 cm).
Similarly, the amount of precipitation becoming streamflow
for water 1986 is 12.24 inches (31.09 cm), as measured in
Red Brook. The large discrepancies are due to errors in the
water budget calculations and its failure to consider
ground water recharge, in addition to errors in Red Brook
discharge measurements.
III.C.2 Sources of Error
The first source of error in the water budget is in
the calculation of potential evapotranspiration. The
empirical equation developed by Thornthwaite (p_p cit).
although the easiest to use, may not be the most accurate
(Palmer and Havens, 1958). Secondly, the relation between
water surplus and runoff may differ from that used in the
water budget. The runoff in the water budget was computed
by allowing half the water surplus from one month to run
off in that month, and half to be detained until the next
month. Thirdly, the actual amount of snow may be different
than that used in the water budget (i.e. the total
precipitation for a month with an average temperature below
30.20°F CO.l'C}). Lastly, the water budget does not provide
for any groundwater recharge. Presumably, the soil and the
-------
89
underlying aquifer are hydraulically connected. As a
result, some of the surplus water from precipitation must
recharge the groundwater, runoff into the streams, and
d: -charge into the Bay directly, without appearing as
baseflow in a stream.
Errors in the stage-discharge relation (the rating
curve) of a stream will have a significant affect on the
calculation of the CFSM value because the discharge of the
stream is computed from the stage-discharge relation.
Consequently, the discharge and CFSM value are dependent on
the accuracy of the discharge measurements. In Red Brook
especially, the stage-discharge relations are suspect. This
may account for the large discrepancy in runoff values. The
stage-discharge relation changed often over the course of
the year for reasons enumerated above.
III.C.3 Summary
Using temperature and precipitation records, and one
of the several methods of calculating potential
evapotranspiration, discharge can be obtained easily from
the water budget. The Thornthwaite mean air temperature
equation is the most straightforward method of calculating
potential evapotranspiration. However, the assumptions
inherent in the method may not be entirely accurate.
Runoff results from the amount of water leftover from
evapotranspiration. For water years 1985 and 1986, the
-------
90
calculated amount of runoff for Red Brook, was significantly
greater than the observed runoff. The discrepancy is most
likely due to the failure of the water budget to account
the ground water ra^h-arge. Tnis is a serious drawback to
its without field data for stream discharge. However, the
water budget does provide a reasonable picture of discharge
timing. Periods of high runoff, low evapotranspiration
and/or high precipitation can be seen on the water budgets
for 1984-1986 and on the water budget for the average year.
Knowledge of the timing of the runoff may aid in
determining when pollutant loading from septic systems is
greatest and consequently, when nutrient loading to the Bay
is greatest.
-------
91
IV. BUTTERMILK BAY GROUND HATER
Freshwater entering Buttermilk Bay comes from ground
water discharge as well as surface water discharge. Just as
ground water seeps into streambeds and contributes to
streamflow in the form of baseflow, ground water discharges
to The Bay along its perimeter. Evidence for this can be
seen especially well in several places along the north side
of the bay. At low tide, ground water can be seen seeping
out at the low tide terrace (intertidal zone). Because the
material surrounding the Bay is extremely permeable, as
discussed above, the ground water contributes a significant
amount of freshwater directly to the Bay. In order to study
the ground water discharge, peizometers were monitored, a
water table map was constructed, and a pump test was
analyzed.
IV.A PEI20METER DATA
Twelve peizometers were measured approximately monthly
to determine the elevation of the water table and its
change in elevation over time. Eight of the peizometers
-------
92
were originally installed by Sam Pollock for the USGS Route
25 road salt study (Pollock, 1984). The locations of these
peizometers are shown in Appendix Figure A-l and labeled as
USGS. The rest of the peizometers were installed
surrounding Buzzards Bay Pumping Station 2 by D.W. Caldwell
for his 1971 road salt study (Caldwell, 1971). These are
Table 14
Water Table Elevation at Buttermilk Bay
Date
in 1986
A8
02/13
02/19
02/24
03/25
05/08
06/02
06/12
06/30
07/15
07/25
08/19
09/08
10/01
10/30
27.
27.
27.
27.
27.
27.
27.
27.
27.
27.
26.
26.
26.
25.
Geological Survey Well Elevations
A12 A13 B5 B6 Cl
04
10
17
51
56
48
46
41
29
02
88
60
28
84
26
26
26
27
27
27
27
26
26
26
26
26
25
25
.66
.66
.78
.13
.17
.01
.03
.95
.84
.73
.44
.20
.84
.43
26.
26.
27.
27.
27.
27.
27.
27.
27.
27.
26.
26.
26.
25.
88
96
06
41
46
32
32
23
11
01
73
44
14
72
17.01
17.24
17.03
16.83
16.75
16.61
16.50
16.43
16.26
16.11
15.89
15.67
17.34
17.48
17.32
17.09
16.99
16.88
16.78
16.68
16.34
16.17
16.08
15.92
17.46
17.26
17. 17
17.03
16.92
16.85
16.60
16.41
16.15
15.79
in feet
Dll D12
25.34
25.55
25.84
26.07
26.06
26.01
26. 31
25.86
25.53
25.22
25.12
24.86
24.49
24.06
25.37
25.57
25.73
26. 10
26.07
26.03
26. 30
25.86
25.53
25.22
25.13
24.88
24.49
24.07
Difference between Maximum and Minimum
1.72 1.74 1.74 1.57 1.56 1.67 2.00 2.00
-------
93
Table 15
Water Table Elevation at Buttermilk Bay
Date
in 1986
02/13
02/19
02/24
03/25
05/08
06/02
06/12
06/30
07/15
07/25
08/19
09/08
10/01
10/30
BUA2
5-72
5.85
5.12
5.89
5.92
4.92
4.41
4.55
4.57
4.66
4.64
4.41
4.26
4.43
BU Well Elevations
BUB1
4.72
4.79
4.28
4.93
4.70
4.02
3.62
3.66
3.69
3.77
3.75
3.43
3.40
3.49
in feet
BUB 2
4.27
4.31
4.11
4.58
4.21
3.83
3.52
3.45
3.45
3.52
3.46
3.27
3.11
3.11
BUC1
5.70
5.91
5.32
6.07
6.09
5. 19
4.66
4.76
4.78
4.89
4.86
4.57
4.49
4.54
Difference between Maximum and Minimum
1.66 1.53 1.47 1.60
identified in Appendix Figure A-l and labeled as BU. The
measured elevations of the water table at each well appear
in Tables 14 & 15. The water table elevations for each well
are shown in Figures 16, 17 and 18. The annual
fluctuations, or the differences between the minimum and
the maximum elevations, in each well are similar. This
yearly water table fluctuation is due to seasonal
-------
94
Water Table Elevation Above Mean Sea Level
29-
28-
H 27-
'••'26-
25-
24-
23
SQSA12
F«b ' Mtr Apr May Jun Jul Aug 8»p Ocl No«
1986
-8.5
-8
m*t«r«
- 7.5
Figure 16. Water table fluctuations during 1986 for
USGS wells A8, A12, A13, Oil, and 012. The latter two show
greater fluctuation because they are close to Buzzards Bay
Pumping Station 1.
-------
95
Water Table Elevation Above Mean Sea Level
7-
6 -
H 5
f««t 4 —
3 -
2 -
B.UA2
F«b Mar Apr May Jun Jul Aug 8«p Oel ' Nov
1986
>- 2
H
-1.5
m«l »r t
- 1
-0.5
Figure 17. Water table fluctuation in the four BU
wells that surround Buzzards Bay Pumping Station 2. The
large fluctuations in these wells show that they are
influenced dramatically by the pumping schedule.
-------
96
Water Table Elevation Above Mean Sea Level
H
(••l
19 -
18-
17-
18-
15 -
14 -
13
SQ8C1
USQ9B6
-6
h-5.5 .
-5
m«t«r t
-4.5
-4
i 1 IT I I i I | i r
F«b Mar Apr May Jun Jul Aug 3«p Oel Nov
1986
Figure 18. Water table fluctuation in the USGS wells
located on Tarkiln Hill on the western border of the
drainage area. These wells are isolated and show a smooth
decline in the water table.
-------
97
differences in ground water recharge rates while ground
water discharges at a constant rate (Frimpter,1980). The
changes in ground water recharge rates are due to changes
in the amount of evapotranspiration. In the summer when
evapotranspiration is high, there is little or no ground
water recharge. Most wells will show a steady decline from
the annual maximum sometime in late winter or early spring
(Frimpter, 1980). These wells show an annual Maximum in
late March or April, as do 57% wells on Cape Cod (Frimpter,
1980).
The average fluctuation is 1.69 feet. However, the
wells nearer the eastern side of Buttermilk Bay, USGSD11,
USGSD12, have somewhat larger fluctuations than the wells
on the northern and western edges of the bay. This apparent
larger fluctuation is most likely due to their proximity to
Buzzard's Bay Pumping Station 1 (Appendix Figure A-l),
rather than any difference in aquifer material. The four BU
wells are within the radius of influence of Pumping Station
2 and demonstrate especially well the irregular pattern of
the fluctuations of the water table around a pumping
station.
Although there are differences in the amounts of
annual fluctuation, all the wells exhibit an unusually
small fluctuation. Most wells in Massachusetts have an
annual fluctuation of several feet each year, depending on
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98
climate, topography, and aquifer characteristics (Frimpter,
1980). However, wells near a constant head boundary, such
as Buttermilk Bay, tend to fluctuate the least (Frimpter,
1980). Other wells in the Buttermilk Bay area exhibit this
small fluctuation as well (Church, personal communication,
1986).
IV.B MATER TABLE MAP
The peizometers were useful not only in determining
the especially constant elevation of the water table, but
also in constructing the water table map (Appendix Figure
A-3). The small fluctuation of the water table elevation
means that the position of the water table contours will
change very little on a seasonal basis. At the scale of
this map, these changes are not detectable.
The contours of the water table were constructed using
surface water elevation data seen on the USGS topographic
maps, surface water elevations from Caldwell, 1971, and the
above peizometric data. The water table elevation coincides
with the land surface elevation where it is discharging
into streams and ponds. The pond surfaces may have a slight
hydraulic gradient in the direction of the regional
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99
hydraulic gradient (Frimpter, personal communication,
1986).
The obvious hydraulic gradient seen in the map is
toward Buttermilk Bay from all directions. It is steeper on
the northern side of the bay and less steep on the eastern
and western sides of the bay nearer the Buzzards Bay
shoreline (Onset Bay) and the Cape Cod Canal, respectively,
where the groundwater divides begin.. The groundwater
divides roughly parallel the surface water divides.
However, because overland flow occurs only rarely
(Strahler, 1972) the surface water divides are less
important in the determination of the zone of freshwater
contribution to Buttermilk Bay.
The aquifer is greater than 50 feet below mean sea
level in most of the drainage area (Williams and Tasker,
1974). This may imply a deep southeastward regional ground
water flow toward Cape Cod, at least in the northerly
portions of the study area.
The ground water discharge into Buttermilk Bay can be
estimated using the water table map and estimates of
hydraulic conductivity from Williams and Tasker (1974) and
other sources discussed below.
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100
IV.C HYDRAULIC COMDUCTIVITV AMD GROUND HATER DISCHARGE
The amount of ground water discharge around the edges
of the Bay is difficult to measure directly. However, it
can be calculated using Darcy's Law:
Q = K A J, (35)
where Q is th= amount of ground water discharge (volume per
time), K is the hydraulic conductivity or coefficient of
permeability (length per time), A is the cross-sectional
area (length squared), and J is the hydraulic gradient
(length per length, or dimensionless). Several assumptions
that may not necessarily be valid (Bear, 1979), are
inherent in this equation. They are:
1. The aquifer is homogeneous, isotropic, and infinite
in areal extent.
2. Water is removed instantaneously from storage upon
a decline in head due to pumpage.
3. The aquifer bottom is horizontal.
4. The water table, before any pumpage is horizontal.
5. Flow to a discharging well and to the Bay is
horizontal.
6. Flow is laminar.
In order to use Darcy's law, the hydraulic conductivity
must be estimated. Values of hydraulic conductivity have
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101
been calculated by two methods and have been obtained from
two other sources.
^V.C.l Published Hydraulic Conductivity
Two ground water studies in or near the Buttermilk Bay
watershed have published hydraulic conductivities useful
for determining the freshwater flux into Buttermilk Bay.
Williams and Tasker (1974) in Hydrologic Atlas 507, made a
general surficial map covering the entire Uareham Outwash
Plain, along with the part of the Carver Outwash Plain. The
map also contains estimates of hydraulic conductivity for
the materials they describe. The Buttermilk Bay area is
shown as coarse to fine sand with a hydraulic conductivity
of 10 to 100 ft/day. In the areas underlain by finer
sediment, the range is from 10 to 40 ft/day and in the
areas underlain by coarser sediment, from 40 to 100 ft/day.
In the more northern areas of the outwash plains, where
there are more gravelly deposits, they have estimated the
hydraulic conductivities to be from 100 to 150 ft/day.
Healy (1986) analyzed both pump and slug tests
performed at the Cranberry Experiment Station in East
Uareham, as well as grain sizes in order to determine
hydraulic conductivities. The Cranberry Experiment Station,
adjacent to the Buttermilk Bay drainage area (Appendix
Figure A-l), is geologically and hydrologically similar to
the Bay. Consequently, the values for hydraulic
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102
conductivity determined by Healy (1986) should be good
estimates for the hydraulic conductivities of the materials
in this study area. The conductivities he calculated from
the three slug permeability tests are 37.5 ft/day
(11.4 m/day), 145 ft/day (44.2 m/day), and 91.25 ft/day
(27.8 m/day). His grain size analyses yielded a hydraulic
conductivity value of 31.2 ft/day (9.5 m/day). The
horizontal conductivity determined from the pump tests is
130.5 ft/day and the vertical conductivity is 28.0 ft/day
(8.5 m/day). The average specific yield, which is the ratio
of the volume of water that drains from a saturated rock
due to gravity to the total volume of the rock (Fetter,
1980), was determined to be 0.14. Healy (1986) also
2
reported an average transmissivity of 4530 ft /day (421
2
m /day). The transmissivity (T) is equal to the hydraulic
conductivity (K) times the aquifer thickness (b),
T = Kb. (36)
Using a--hydraulic conductivity of 87.1 ft/day (the average
of Healy's (1986) horizontal conductivities), and the
transmissivity shown above in equation , the aquifer
thickness is calculated to be 52.0 ft (15.9 m). This value
agrees with the depth to bedrock map published in
Hydrologic Atlas 507 by Williams and Tasker (1974).
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103
^V.C.2 Hydraulic Conductivity from Red Brook Discharge Data
Hydraulic conductivity (K) can be estimated from the
baseflow discharge of a stream. It is preferable to use a
long term average, or mean annual discharge value for this
calculation. However, for Red Brook this is not available.
Instead, the hydraulic conductivity, or the coefficient of
permeability, is calculated from the average baseflow
discharge for water years 1985 and 1986. Darcy's Law is
employed in the form:
K = Q / (AJ), (37)
using the average baseflow for Q, the stream length (w) to
the point of measurement, times the thickness of the
aquifer (b) for A, where A = wb, and the average hydraulic
gradient near the stream for J. The stream length was
measured from the topographic map and the hydraulic
conductivity from the water table map. The aquifer depth
was obtained from Williams and Tasker (1974). Table 16 has
the values used for these quantities.
The values calculated for hydraulic conductivity for
water years 1985 and 1986 are within the range presented by
Tasker and Williams (1974) and also agree closely with
those values presented by Healy (1986). The large
difference between the calculated hydraulic conductivities
for water years 1985 and 1986 can be accounted for by the
difference in yearly average baseflow at each station. The
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104
Table 16
Input Values and Results
of Hydraulic Conductivity Calculation
from Red Brook Discharge Data
Water Year
1985
Water Year
1986
Baseflow Discharge (Q, cfs)
Stream Length (w, ft)
Aquifer Depth (b, ft)
Hydraulic Gradient (J)
2.09
14833
75
0.00433
5.57
18229
75
0.00433
Hydraulic
Conductivity (K, ft/s)
Hydraulic
Conductivity (K, ft/d)
Hydraulic
Conductivity (K, m/d)
4.34 x 10-4
37.5
11.4
9.41 x 10-4
81.3
24.8
1985 data is from the USGS gauge and the 1986 data is from
the gauge used during the present study. The CFSM value and
the percentage of streamflow due to baseflow were different
for each gauge and for each year. Consequently, differences
in calculations made with those data are expected. Other
errors in the calculations could arise from the depth to
bedrock figure and the measured quantities/ stream length
and hydraulic gradient. Overall/ the numbers are quite
close and in agreement with others presented.
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105
jV.C.3 Ground Water Modeling
The ground water flow model PLASM (Prickett and
Lonnquist, 1971) was also used to determine the hydraulic
conductivity of the aquifer underlying Buttermilk Bay
drainage area. The program is a two-dimensional,
finite-difference, non-steady flow model for heterogeneous,
water table, non-leaky artesian, or leaky artesian
conditions. Variable pumpage, artificial or natural
recharge, water exchange between surface and ground water
reservoirs, ground water evapotranspiration, and conversion
from artesian to water table conditions can all be
simulated with this model (Prickett and Lonnquist, 1971).
A pump test performed by D.W. Caldwell in 1971 was the
calibration data for the model. A map containing the area
included in the model appears in Figure 19. The area of the
portion of the aquirer contained in the model is 3,325,536
2 2
square feet (1,013,623 m ) or 0.12 square miles (0.31 km ).
The peizometers, including all the BU wells described
above, were installed in lines 120° apart with wells
positioned from 100 to 1000 feet (30.5 m to 305.8 m) away
from the pumping well in the center. Table 17 summarizes
the drawdown in each well after 4 days of pumping at
3
approximately 184 gal/min (0.41 cfs or 0.012 m /s).
Prior to modeling, the Jacob straight-line method of
determining aquifer transmissivity (T) and specific yield
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106
Observation Wells'"and Drawdown '«
4-day Pump Test. Octotjer 1971 s
- f* "^^ A*
.»*
400 ft
100 m
Drawdown in feet
• 92
Observation Wells
37
V V
40
Figure 19. Inset from Appendix Figure A-2 showing map
of Buzzards Bay Pumping Station 2 where 1971 pump test was
performed. After Caldwell (1971).
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107
Table 17
Drawdown Data for 1971 Pump Test
at Buzzard's Bay Pumping Station 2
Well
31
32
33
34
35
37
39
40
Line 30
s r
(ft) (ft)
0
0
0
0
0
0
0
0
.95
.57
.30
.21
. 16
.00
.00
.00
100
200
292
436
500
692
900
1000
Well
41
42
43 -
45
47
50
Line 4C
s r
(ft) (ft)
1.
0.
0.
0.
0.
0.
77
80
38
19
11
00
100
200
300
500
700
1000
Line
Well
(
51
52
53
55
57
60
1
0
0
0
0
0
50
s
ft)
.07
.55
.38
.10
.00
.00
r
(ft)
100
200
300
450
700
1000
s = the amount of drawdown (feet) observed after four days
of pumping at about 184 gal/min
r = the distance from the pumping well to the peizometer in
feet.
(Sy) was applied to each line of wells (Cooper and Jacob,
1946). The distances (r) of the peizometers from the
pumping well against their drawdowns (s) for each line were
plotted on semilog paper with the distances on the log
scale and the drawdowns on the arithmetic scale (Figure
20). The following equations developed by Cooper and Jacob
(1946) were then employed:
T = 528 Q/(h -h), and (38)
o
Sy = Tt/(4790rQ2), (39)
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108
0.9-
Drawdown
In feet 1.0-
Jacob Straght-Une Method
for October 1971 Test
at Pumping Station 2
Distance from Pumping Well in meters
2345 10 2343 100 2349 1000 2 3
-0.1
ro.2
hO.3
Drawdown
In meters
hO.4
-0.5
-0.8
i i i i i iiii i i i i i i i i i i i
2346 10 2 349 100 2349 1.000 2 349 10.000
Distance from Pumping .Well In feet
Figure 20. Jacob Straight Line Method of solution for
1971 pump test. Solutions were obtained for each line of
wells.
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109
where T is transmissivity in gallons per day per foot; Q is
a constant pumping rate in.gallons per minute; (h -h) is
the drawdown per log cycle of distance in feet; t is the
time since pumping began in minutes; and r is the
intercept of the straight line with the zero drawdown axis.
The assumptions stated above for the use of Darcy's Law are
applicable here as well. A constant pumping rate of 184
gallons per minute, an average of the actual four daily
pumping rates in the test, was used in the equation. Table
18 contains the results for each line and an estimate of
hydraulic conductivity based on an aquifer thickness of
70 ft (21.3 m). The elevation of the bedrock surface is
approximately 65 ft (19.8 m) below mean sea level (M.S.L.)
-(Williams and Tasker, 1974) and the average water table
elevation is approximately 5 ft (1.52 m) above M.S.L. as
measured in the previously mentioned peizometers.
The conductivity and transmissivity values obtained
using the Jacob approximations are all somewhat higher than
those estimates made using the other methods described
above. The most obvious explanation for the discrepancy
lies in t'-a validity of the assumptions inherent in the
Jacob method. The discharge (Q) in the actual test varied
over the four day period. The aquifer is not homogeneous
and isotropic. However, it can be considered infinite in
areal extent and probably exhibits Darcian, or laminar,
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110
Table 18
Results of the Jacob Straight-Line Method
Applied to the Pump Test at Pumping Station 2
Line 30 Line 40 Line 50
Transmissivity
gal/day/ft
ft2/day
2
m /day
Specific Yield
Hydraulic Conductivity
gal/day/ft
ft/day
m/day
85,975
11,494
1,068
0.238
1,228
164
50.0
57,486
7,685
714
0.123
821
110
33.5
75,312
10,068
936
0. 247
1,076
144
43.9
flow. The aquifer bottom is not horizontal and the water
table is not horizontal before pumpage as well. Along with
the stated contradictions to the inherent assumptions,the
Jacob approximations do not account for dewatering of the
water table, which causes the saturated thickness and in
turn the transmissivity to decrease. In other words, after
dewatering, the aquifer can transmit less water
horizontally through the entire saturated thickness. This
last source of error may be the most important one, since
the Jacob approximations were originally developed for
confined situations, as were most ground water equations.
Corrections for dewatering can be made with additional
-------
Ill
aquifer information. The high specific yield values can be
accounted for by these explanations as well.
The modeling of this pump test with the PLASM program
should provide more accurate results than the Jacob
straight-line method, because it can reduce the error
caused by some of the assumptions in the Jacob method.
Initial, steady-state, aquifer conditions can be set up
with the model allowing a sloped water table to be
simulated. This is done by assigning head values for the
constant head boundaries, those boundaries perpendicular to
the direction of flow, and allowing the model to iterate
for a long time period. The initial conditions generated
can then be compared with a water table map of the area for
accuracy. The hydraulic heads generated in this manner are
then reentered into the data file to be used in the pumping
simulation. Figure 21 is a computer-generated, water-table
map of the initial conditions of the area to be modeled.
This map compares favorably with water table map in
Appendix Figure A-3.
Once the initial hydraulic heads are found, the
pumping rates can be entered. The model allows for variable
pumping rates. In this pump test, a different pumping rate
was used on each day. They are 285790 gal/day, 291180
gal/day, 251810 gal/day, and 231950 gal/day, respectively
for each of the four days (Frank, 1972).
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112
Jrutial Condtions for
Use in Pump Test Analysis
5.0 5.5 6.0
\
400 ft
» i
100 m
Elevation of Water Table in feet
. Observation Wells
• 32
Figure 21. Computer-generated contour map of the
initial hydraulic heads entered into the model. A map of
the water table prior to pumping.
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113
After the variable pumping rates are entered, the
hydraulic conductivity and the thickness of the aquifer at
each node can be entered and the model calibrated. The
calibration process is simply running the model unti] the
computed drawdowns match the observed drawdowns. The
hydraulic conductivities are changed in each run until the
optimum set is found empirically. The aquifer is considered
to be isotropic. Consequently, the vertical and horizontal
conductivities are the same. Presumably, the aquifer bottom
is not horizontal in this case. However, there is not
enough information available to construct its structure in
an area this small. For this reason, a horizontal aquifer
bottom at 65 feet below M.S.L. is assumed.
The calibrated drawdowns resulting from this model
appear in Table 19. Figure 22 is a contoured plot of the
drawdowns generated in the computer simulation of this pump
test. The distribution of hydraulic conductivities used is
shown in Figure 22. The conductivities are shown in ft/day
and convert into 40.8 m/day, 20.4 m/day, and 8.1 m/day from
134 ft/day, 66.8 ft/day and 26.7 ft/day, respectively.
Unfortunately, the final step in the modeling process could
not be accomplished with this pump test. The last step is
using the calibrated model to match results of another pump
test done at the same site.
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114
Calibrated Water Table Map
After 4-day Pump Test
Pump/ngNSfat/on 2
400 ft
100 m
_ Elevation of Water Table In feet
Observation Wells
Hydraulic Conductivities *32
11 26.7 ft/d .
D 66.8 ft/d
E3 134 ft/d
Figure 22. Computer-generated contour map of Buzzards
Bay Pumping Station 2 after four days of pumping. Locations
of hydraulic conductivities used in model are shown.
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115
Table 19
Drawdowns at Pumping Station Two
Generated by Computer Model
Well
31
32
33
34
35
37
39
40
Line 30
s
(ft)
0.99
0.52
0.31
0. 14
0.09
0.02
0.01
0.01
r •.
(ft)
100
200
292
436
500
692
900
1000
Well
41
42
43
45
47
50
Line 40
s
(ft)
1.58
0.83
0.48
0.13
0.00
-0.04
r
(ft)
100
200
300
500
700
1000
Wei
51
52
53
55
57
60
Line 50
1 s
(ft)
1.13
0.62
0.33
0.08
-0.08
-0.12
r
( ft)
100
200
.300
450
700-
1000
s = the amount of drawdown (feet) observed after four days .
of pumping
r = the distance from the pumping well to the peizometer in
feet.
The computed heads do not match the observed drawdowns
exactly. This brings to focus a particular problem of the
PLASM model. The trial and error procedure is random and
time-consuming. Consequently, to complete a problem in a
reasonable amount of time is almost impossible for the
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116
inexperienced modeler and unnecessary error is added to the
results. The other possible sources of error in the model
are due primarily to false assumptions and conditions
entered. The aquifer is probably not isotropic as was
assumed in this model. The input conditions may have been
slightly inaccurate as well. Additionally, the pumping well
may not have fully penetrated the aquifer. However, this
partial penetration would cause only the computed drawdowns
in the close (100 ft) (30.5 m) peizome'ters to be incorrect.
The hydraulic conductivities calculated with the model
do seem to agree with the conductivities from the
previously mentioned sources. However, these results are
too specific to be applied throughout the drainage area.
The average of the three conductivities may be more
applicable to the drainage area or at least to the
collapsed outwash (see Appendix Figure A-2) in which the
pumping station is located, because it encompasses the
probable range of conductivities possible in this material.
The average is 567 gal/day/ft2, or 75.8 ft/day
(23.1 m/day). '
The hydraulic conductivities found in the literature
and determined from ground water modeling and from
streamflow will be used in a stream tube analysis to
calculate the total freshwater influx to Buttermilk Bay.
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117
V. FRESHWATER INFLUX TO BUTTERMILK BAY
The goal of all the work presented here is to
calculate the influx of freshwater to Buttermilk Bay. This
calculation is needed to determine the concentration of the
influx of nutrients and coliform bearing water into the
Bay. The concentrations will then be used to identify the
sources of pollution in Buttermilk Bay. The following are
the four different methods that will be used to calculate
the total amount of freshwater Influx to the Bay:
1. the regional equation (3) for mean annual
discharge,
Qma = 1.64(Ad)1<03, (40)
will be applied to the total Buttermilk Bay drainage area,
2. the Red Brook CFSM values for water years 1985 and
1986, 0.525 and 0.90, respectively will be applied to the
total Buttermilk Bay drainage area,
3. the number of inches of runoff from the water
budgets will be converted into the amount of runoff in the
Buttermilk Bay drainage area, and
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118
4. the hydraulic conductivities will be used in a
stream tube analysis with the Dupuit equation (Fetter,
1980) to calculate the amount of ground water discharge to
the bay.
V.A REGIONAL EQUATION METHOD (#1)
The regional equation for mean annual discharge (Qma)
can be used to predict the amount of discharge in an
ungauged area with similar geological and hydrological
characteristics. Using equation (3):
Qma = 1.64(Ad)1>03, (41)
2
with the drainage area of Buttermilk Bay/ 17.83 mi
2 7
(46.18 km ), then multiplying the answer by 3.1536 x 10 ,
the number of seconds in a year, the freshwater influx to
Buttermilk Bay is 1,005,394,114 ft3/year, or 2,754,504
3 3
ft /day. These values convert to 28,473,354 m /yr and
78,009 m /day, respectively. Sources of error in using this
method are the same as those mentioned above for the use of
this equation in predicting the mean annual discharge in
Red Brook.
In order to dampen the effects of short periods of
record, the high and low average discharge equations,
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119
(5 & 6), discussed earlier can also be used to calculate
the Buttermilk Bay freshwater influx. These equations are:
Qaah = 2.36(Ad)1'04 and (42)
Qaal = 0.69(Ad)1>01, (43)
for high and low average discharges, respectively. The
equation for the high average discharge, Qaah, yields a
value of 1,489,073,061 ft3/year (42,171,426 m3/yr) or
4,079,652 ft3/day (115,538 m3/day) for the amount of
freshwater discharge to Buttermilk Bay. The low average
discharge equation produces discharges of
399,377,694 ft3/year (11,310,612 m3/yr) or
1,094,021 ft3/day (30,983 m3/day) for the freshwater influx
to Buttermilk Bay.
V.B RED BROOK STREAMFLOW METHOD (#2)
The CFSM, or amount of discharge per square mile,
values obtained from the discharge records of Red Brook
streamflow in water years 1985 and 1986 can be used to
predict the amount of discharge to Buttermilk Bay. In
this case, the equation is:
Q = 0.525(Ad) (44)
for water year 1985 and
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120
Q = 0.90(Ad) (45)
for water year 1986, where Q is discharge in cfs, and Ad is
2
drainage area in mi . The freshwater influx to Buttermilk
Bay from the 1985 and 1986 equations is 295,200,612
ft3/year (8,360,255 m3/yr) and 506,058,192 ft3/year
(14,331,866 m /yr), respectively. These values convert to
808,769 ft3/day (22,905 m3/day) and 1,386,461 ft3/day
(39,265 m /day) from the 1985 and 1986 equations,
respectively. As expected, these values are as different
from each other as the CFSM values were from year to year
and neither one can be used as a long term average number.
However, the influx calculated with the low average
discharge equation used above agrees with the values
calculated by this method.
V.C MATER BUDGET METHOD (t3)
The number of inches of runoff found in the water
budgets is a one-dimensional unit that can be converted to
a volume by multiplying it by the total drainage area
(17.83 mi2) (46.18 km2). The amount of runoff in the
average year was 24.45 inches (62.10 cm). This average
runoff converts into a total freshwater discharge to
Buttermilk Bay of 1,012,783,939 ft3/year (28,682,638
m3/yr), or 2,774,751 ft3/day (78,583 m3/day). Similarly,
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121
the water year 1985 value of runoff (18.26 inches)
(46.38 cm) converts to 756,377,699 ft3/year (21,421,062
m3/yr) or 2,072,268 ft3/day (58,688 m3/day) of freshwater
dischai-^t: to Buttermilk Bay. Finally, the 1986 value of
runoff (22.91 inche)s (58.19 cm) yields values of
948,993,049 ft3/year (26,876,042 m3/yr) or
2,599,981 ft3/day (73,633 m3/day) for the freshwater influx
to the Bay. The freshwater influx computed by this method
is slightly more than double the influx calculated from the
CFSM values for water years 1985 and 1986. However, the
average year value for freshwater influx is nearly
identical to the influx calculated with the regional
equation.
V.D STREAM TUBE ANALYSIS (#4)
A stream tube analysis is a method for determining the
ground water flux through a certain area. A stream tube is
bounded on either side by no-flow boundaries, which are
lines drawn in the direction of discharge (Q).
Equipotential lines, or lines of equal water table
elevation as seen in the water table map, are perpendicular
to these flow lines. Together, the equipotential lines and
the no-flow boundaries form a flow net comprised of stream
tubes with their long axes in the direction of discharge.
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122
The amount of discharge in a stream tube can be calculated
with a ground water flow equation. The flow net used to
calculated the influx of freshwater to Buttermilk Bay is
shown in Figure 23. There are 38 stream tubes shown.
In the case of a water table aquifer, as this is,
Darcy's law is not completely applicable as a flow equation
because the surface of the water table is not flat. The
Dupuit equation,
Q = -.5Kw(h22-h12)/L, (46)
where Q equals ground water discharge, K is the hydraulic
conductivity, w is the width of the stream tube, h is the
saturated thickness of the water table (elevation of the
water table plus the depth of the aquifer below M.S.L.) was
developed by Dupuit in 1863 and accounts for this change in
saturated thickness in a water table aquifer in the
direction of flow.
The Dupuit equation was used with the flow net shown
in Figure 23 to calculated the ground water influx to
Buttermilk Bay. The dimensions of each stream tube and
their individual discharges can be seen in Appendix C. A
hydraulic conductivity of 60 ft/day (18.3 m/day) was chosen
for this calculation because it is the average of all the
conductivities presented earlier, excluding those computed
with the Jacob approximations because of the considerable
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123
Streamtubes for Determining Ground Water Influx
fftd
flroo*—-"*"/
Wat«r Table Elevations
Q-KAJ
width (A)
gradient (J)
Figure 23. Streamtubes used with the Dupuit equation
to calculate the freshwater discharge to Buttermilk Bay.
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124
error in that calculation. The total ground water influx to.
Buttermilk Bay using this method is 345,801,932 ft /year
(9,793,314 m3/yr) or 953,080 ft3/day (26,992 m3/day). As
can be seen from the discharges shown in Appendix B, the
greatest amount groundwater is discharged along the north
edge of the Bay where the hydraulic gradient is steepest,
and lesser amounts along the east and west sides of the Bay
where the ground water divides are located and the
hydraulic gradient is considerably less steep. The value of
freshwater discharge calculated here is similar to that
calculated using the CFSM values for Red Brook.
-------
125
VI. SUMMARY AND CONCLUSIONS
Calculation of freshwater discharge to Buttermilk Bay
is necessary in order to compute the pollutant loading to
the Bay. Coliforms and nutrients are discharged to the Bay
via both surface and ground water. Consequently, both must
be considered in the methods of calculation. However, since
the aquifer material in the Buttermilk Bay area is
extremely permeable, the surface and ground water are
closely linked hydrologically, and can be considered
together in the methods of freshwater influx calculation
presented.
The methods of freshwater discharge calculation:
1. regional equations,
2. Red Brook CFSM values,
3. the water budget, and
4. a ground water streamtube analysis,
produced .discharge values within an order of magnitude. The
largest discharge values were from the water budget
3
analyses, slightly greater than 1 billion ft /year (28.3
million m /yr), and the smallest from the streamtube
analyses, 345 million ft /day (9.77 million m /yr). The
most reliable analyses are probably the calculations from
the Red Brook CFSM values and the streamtube analyses
-------
126
because they are based on field measurements in Buttermilk
Bay. The major drawback with the water budget approach is
that it does not account for groundwater recharge. The
downfall of the first method, using regional hydrologic
equations, is the problem with similarity between the
region, southeastern Massachusetts, and the point of
interest. Red Brook, as well as the homogeneity of with in
the region.
In addition to the methods used above, a fifth method
performed by the Boston University Marine Biology Program,
was used to calculate the freshwater discharge. It involved
measuring the salinity of the ebb and flood tides over a
tidal cycle. From the difference in salinity between the
ebb and flood tides, the volume of freshwater needed for
the dilution was calculated. This yields a value of
2,045,959,182 ft3/year (57,942,769 m3/yr) or
5,605,368 ft3/day (158,747 m3/day) (J. Costa, personal
communication, 1986). The values are considerably higher
than the discharge values obtained above. Most likely, this
discrepancy arises because the results are based on a
single day of measurement. These values can not be
considered as accurate as the methods used above.
These methods for computing freshwater discharge can
be applied to other coastal areas with pollution problems.
However, modification of some of the methodology should be
-------
127
made and the assumptions reviewed. For example, the
streamtube analysis cannot be used alone in areas where the
ground and surface water are not hydraulically connected.
Several hydrologic analyses have been used to
calculate the freshwater influx to Buttermilk. Bay. In doing
so, a general methodology for determining discharge to
coastal embayments has been created.
-------
128
Appendix A
Figures
Appendix Figure A-l Map of Buttermilk Bay Drainage Area
Appendix Figure A-2 Surficial Geology of Buttermilk Bay
Appendix Figure A-3 Water Table Hap of Buttermilk Bay
-------
129
Appendix B
Annual Flood Series
-------
130
Adamsville Brook at Adamsville, Rhode Island
Drainage Area 7.91 square miles
Magnitude Date Annual Maximum Recurrence
Discharge Interval
cfs
1 12/27/69 316 39.00
2 9/20/60 273 19.50
3 9/12/54 269 13.00
4 8/08/46 241 9.75
5 3/16/53 239 7.80
6 6/19/72 231 6.50
7 1/26/78 231 5.57
8 3/18/68 221 4.88
9 4/07/58 217 4.33
10 12/17/73 213 3.90
11 1/07/62 207 3.55
12 6/13/75 202 3.25
13 11/30/44 201 3.00
14 4/15/64 198 2.79
15 3/06/63 184 2.60
16 4/06/57 182 2.44
17 3/26/69 179 2.29
18 2/03/73 176 2.17
19 12/27/75 175 2.05
20 5/26/67 173 1.95
21 2/14/71 173 1.86
22 3/12/52 157 1.77
23 2/08/41 154 1.70
24 4/17/61 154 1.63
25 4/06/77 149 1.56
26 6/01/48 146 1.50
27 10/17/56 132 1.44
28 3/03/47 130 1.39
29 4/25/44 121 1.34
30 3/07/59 119 1-30
31 12/31/42 119 1-26
32 2/08/42 117 1.22
33 3/24/50 103 1.82
34 4/04/51 90 1.15
35 8/20/55 87 1.11
36 4/07/49 85 1.08
37 2/14/66 74 1.05
38 12/29/64 66 1.03
-------
131
UNITED STATU DCPAMTMINT Of THC INTW10*
(•.. 747)
Su. No..
Annual Flood
at AdMfyillv^Jlhpda.
-• • - "-T(~- -j^i 1-^.rT.. —-i——..3— ;. -'t-J—..-.|..-..'77^._^.._
Flood Diicti*r|» Q in
i No «<
CPO «4t-MI
-------
132
Dorchester Broolc near Brocicton Massachusetts
Brainage Area 4.67 square miles
Date Annual Maximum Recurrence
Magnitude Date AnDiscnarge Interval
cfs
1 3/18/68 359 13-00
2 12/27/69 276 6.50
3 3/25/69 212 4.JJ
4 10/07/62 130 3.25
4.ft'<" "? :
*w,\\
o
!'?«<«« II 1.3*0
56
12 2/26/65 55
10 12/07/72
11 2/14/66 56 1.J2
-------
133
UNITED STATU DCrftMTMCNT Of THC INTCWOft
•tO.OVOU.MVrr
Su. tic..
Annu.1 riood
ne«r Brockton. Miss«chu««tts
•f «^ T •' [* 1 J ' ~~^"' I'_ ' -
dziztrtr:
t-L.. i !._'—-1 L
rttr-rh-
Flood Discharge Q la cfs
-------
134
Herring River at North Harwich. Massachusetts
Drainage Area 9.40 square miles
Magnitude Date Annual Maximum Recurrence
Discharge Interval
cfs
1 2/12/83 75 19.00
2 9/3/72 59 9.50
3 8/07/78 59 6.33
4 6/06/87 54 4.75
5 6/02/84 52 3.80
6 3/31/68 44 3.17
7 5/26/79 40 2.71
8 9/02/81 40 2.38
9 10/03/73 40 2.11
10 9/09/69 39 ' 1.90
11 6/30/76 37 1.73
12 1/11/70 35 1.58
13 8/22/77 34 1.46
14 12/07/72 32 1.36
15 5/24/71 28 1.27
16 6/20/81 28 1.19
17 3/22/80 24 1.12
18 6/06/75 24 1.06
-------
135
l*t <•*• •'•»
M7)
UNITU STATU OtFAHTKCNT Of THE INTHUOK
Su. No.
MrM,,M»MM«c,^ Annu«l Flood
•c North_Haryic6,.M«tf«chu§«tt« _
Flood Disebctt* Q in ef*
l He •(.
-------
136
Indian Head River at Hanover, Massachusetts
Drainage Area 30.20 square miles
Magnitude
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Date
3/18/68
12/27/69
6/07/82
3/26/69
1/28/76
1/27/78
6/01/84
5/26/77
12/17/73
3/03/83
1/25/79
3/03/72
2/26/81
5/10/77
2/14/71
12/07/72
2/25/75
4/10/80
Annual Maximum
Discharge
cfs
1390
980
973
924
885
847
827
788
718
716
686
601
571
524
478
428
358
344
Recurrence
Interval
19.00
50
33
4.75
3,
3,
80
17
2.71
2.38
2.11
1.90
1.73
1.
1.
1,
1.
1,
1
58
46
36
27
19
12
1.06
-------
*«« •*•«
137
UNITED STATES DEPARTMENT Of THE INTEKIOft
S». No.
Annual Flood
•c Hanover, Maatachuaatts
,« Indian ttaad Rivtr
DrWM» «M 30.20 M. M. NnM 18 JK*»ri
"*
S
Flood Discharge Q In efs
-------
138
Jones River at Kingston, Massachusetts
Drainage Area 15.70 square miles
Magnitude Date Annual Maximum Recurrence
Discharge Interval
cfs
1 3/19/68 575 19.00
2 9/04/72 378 9.50
3 12/27/69 363 6.33
4 5/26/67 358 4.75
5 3/25/69 325 3.80
6 6/07/82 320 3.17
7 3/12/83 266 2.71
8 12/18/73 254 2.38
9 1/26/78 225 2.11
10 3/20/84 222 1.90
11 6/30/73 217 1.73
12 8/04/79 205 1.58
13 2/26/81 186 1.46
14 1/28/76 176 1.36
15 3/16/80 172 1.27
16 3/28/71 139 1.19
17 5/10/77 131 1.12
18 2/25/75 89 1.06
-------
139
».\rn
< Uf <«
UNITED STATU DEPARTMENT OF THE INTERIOR
MOLMKM,
S». No.
Annual Flood
ac King*ton, M«a»«chu«etts
w.Jones Riy«r
.. (*••»•• wu . 15 *1Q to. mt Nrwl 18 Y*Aia.
Flood DUchsrgc Q In efi
-------
140
Moshassuck River at Providence, Rhode Island
Drainage Area 23.10 square miles
Magnitude
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Date
3/18/68
3/25/69
7/30/76
1/21/79
1/26/78
4/10/83
8/01/67
2/02/73
8/17/74
2/25/65
2/01/82
4/03/75
10/20/76
8/23/66
10/10/71
4/10/80
11/29/63
8/20/71
4/02/70
10/25/80
Annual Maximum
Discharge
cfs
2390
2000
1650
1480
1200
1110
1110
980
978
952
941
872
815
802
785
774
662
607
596
294
Recurrence
Interval
21.00
10.50
00
35
20
50
00
63
2.33
2.10
1.91
1.75
1.
1,
1,
1,
1,
1
1,
62
50
40
31
24
17
11
1.05
-------
141
•«*••• >•* 4M«
(P., 7.47)
UNITED STATCS OCTMTTMCNT Of THC INTCRIOK
MOlOHCU. KW*f1
S<>. No.
Moihatsuk Rlver_
. 21_Y«ar*
ac Providence. Rho&t liUnd
s
flood Dischtrg* Q la ef(
No •(
ere ««i-Ml
-------
142
Potowomut River near East Greenwich, Rhode Island
Drainage Area 23.00 square miles
Magnitude Date Annual Maximum Recurrence
Discharge Interval
cfs
1 6/06/82 1020 44.00
2 4/11/83 968 22.00
3 1/26/78 899 14.67
4 3/18/68 866 11.00
5 1/21/79 804 8.80
6 3/22/80 646 7.33
7 4/03/70 644 6.29
8 1/07/62 482 5.50
9 l/28'76 471 4.89
10 • 5/2L/67 460 4.40
11 3/06/63 457 4.00
12 - 9/12/54 450 3.67
13 2/03/73 433 3.38
14 3/25/69 410 3.14
15 4/17/61 396 2.93
16 8/08/46 392 2.75
17 12/17/73 378 2.59
18 2/08/41 377 2.44
19 4/03/75 377 2.32
20 3/06/59 375 2.20
21 3/16/53 368 2.10
22 2/28/58 350 2.00
23 10/17/55 347 1.91
24 3/26/65 347 1.83
25 12/21/51 328 1.76
26 5/31/48 328 1.69
27 4/15/64 326 1.63
28 5/10/57 305 1.57
29 6/19/72 305 1.52
30 11/30/44 304 1.47
31 2/14/71 297 1.42
32 3/03/47 294 1.38
33 3/23/77 291 1.33
34 12/31/42 285 1.29
35 2/26/60 276 1.26
36 2/17/42 272 1.22
37 3/24/50 269 1.19
38 2/12/55 269 1.16
39 2/14/66 265 1.13
40 4/06/49 233 1.10
41 4/03/51 227 1.07
42 4/25/44 177 1.05
43 2/25/81 114 1-02
-------
143
UNITED STATES DEPARTMENT OF THE INTEKIOft
•^ 747)
Su. No.
Annual Flood
near E«at Greenwich. Rhode liland
i .EotoyoiKLt. Rlyer
S
£
tt
3s
ESE
-rt rll —t
s
Flood Discharge Q la cfs
I N. •(.
-------
144
Segreganset River near Dighton, Massachusetts
Drainage Area 10.60 square miles
Magnitude Date Annual Maximum Recurrence
Discharge Interval
cfs
1 3/18/68 867 18.00
2 4/11/83 655 9.00
3 1/26/78 552 6.00
4 12/27/69 536 4.50
5 1/26/79 514 3.60
6 5/26/67 513 3.00
7 1/28/76 445 2.57
8 2/01/82 422 2.25
9 3/26/69 417 2.00
10 12/18/73 392 1.80
11 3/04/77 388 1.64
12 4/11/80 306 1.50
13 2/14/71 282 1.38
14 3/18/72 269 1.29
15 2/03/73 231 1.20
16 2/25/75 220 1.13
17 2/26/81 163 1.06
-------
145
UNITED STATU DEPARTMENT Of THE INTENtO*
m .-._8r*8*nlec
MMMblM U
-------
146
Taunton River at State Farm near Bridgewater, Massachusetts
Drainage Area 260.00 square miles
Magnitude
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Date
3/21/68
3/27/69
8/21/55
12/28/69
12/19/73
1/29/76
12/08/45
4/14/35
5/18/54
3/14/36
4/05/33
1/08/62
10/09/62
11/07/55
5/28/67
4/14/40
12/13/36
4/16/64
2/27/61
3/18/48
7/25/38
12/08/72
3/13/52
3/07/34
3/19/72
6/12/31
4/01/53
2/15/71
4/06/60
3/07/45
2/09/41
3/18/42
4/21/39
4/13/58
4/07/57
3/30/32
2/26/75
3/08/59
10/27/48
2/14/30
2/10/51
5/05/47
3/08/43
Annual Maximum
Discharge
cfs
4980
4080
4010
3820
3330
3230
3080
3060
3040 .
3020
2990
2940
2880
2860
2800
2650
2590
2540
2520
2480
2480
2470
2460
2460
2450
2430
2320
2240
2240
2230
2080
2080
2040
2020
1950
1920
1850
1760
1740
1580
1580
1550
1540
Recurrence
Interval
48.00
24.00
16.00
12.00
9.60
8.00
6.86
6
5,
4,
4
4
3
2.
2.
2.
2.
2.
1.
1.
1,
1.
1,
1,
1,
1,
1
00
33
80
36
00
69
3.43
3.20
3.00
2.82
2.67
2.53
40
29
18
09
00
92
85
78
71
66
60
55
50
45
1.41
37
33
30
26
23
20
17
14
1.12
-------
147
Taunton River continued
Magnitude Date Annual Maximum Recurrence
Discharge Interval
cfs
44 2/15/66 1450 1.09
45 4/26/44 1430 1.07
46 2/26/65 1380 1.04
47 3/25/50 1250 1.02
-------
148
»• l«f <•!• •<•*
»_ 7.47)
UNITED STATES DEPARTMENT Of THE INTERIOR
S«t.
Annual Flood
• t State. FAlTlL.aft*r-fltidg*w«t»t, HA »•*.§•• ru
Flood Diteharg* Q in eft
SPO •«!
-------
149
Threemile River at North Dighton, Massachusetts
Drainage Area 84.30 square miles
Magnitude
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Date
3/19/68
6/02/84
1/26/79
1/27/78
12/28/69
4/12/83
3/26/69
5/27/67
6/07/82
1/29/76
12/19/73
3/18/72
4/11/80
3/24/77
12/07/72
2/15/71
4/05/75
2/27/81
Annual Maximum
Discharge
cfs
2490
1740
1730
1680
1600
1560
1440
1340
1330
1310
1090
1060
1060
969
955
637
610
487
Recurrence
Interval
19.00
9
6
1,
1,
1,
1,
1
1,
50
33
4.75
3.80
3.17
2.71
2. 38
2.11
1.90
1.73
58
46
36
27
19
12
1.06
-------
150
*«•••• !
UNITED STATES DEPARTMENT OF TMt INTERIOR
Su. No..
mlhrtialle Riv.tt
Norch Dighton. H«««achugett«
Flood Diseharg* to ef«
-------
151
Wading River near Norton, Massachusetts
Drainage Area 43.30 square miles
Magnitude
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Date
3/19/68
8/20/55
3/12/36
1/26/79
1/27/78
6/01/84
6/11/31
4/11/83
3/26/69
12/28/69
7/25/38
5/10/54
12/08/46
4/13/33
6/07/82
3/17/48
9/06/56
1/28/76
5/27/67
12/18/73
1/26/58
4/03/72
4/11/80
3/06/34
3/07/29
3/29/32
2/26/61
12/21/36
3/16/53
4/14/35
3/16/40
3/10/42
1/08/62
1/26/64
3/12/52
3/23/77
12/07/72
12/31/42
12/01/44
3/07/59
10/07/62
2/14/71
4/07/39
Annual Maximum
Discharge
cfs
1460
1170
1030
951
915
900
843
825
819
779
714
698
682
646
640
619
616
615
574
527
521
517
510
506
505
503
492
487
486
480
472
472
467
464
454
440
431
406
391
380
364
363
361
Recurrence
Interval
60.00
30.00
20.00
15.00
12.00
10.00
8.57
7.50
6.67
6.00
5.45
5.00
4.62
4.29
4.00
3.75
3.53
3.33
3.16
3.00
2.86
2.73
2.61
50
40
2. 31
2.22
2.14
2.07
2.00
1.94
1.88
1.82
1.76
1.71
1.67
1.62
1,
1,
1,
1
1
58
54
50
46
43
1.40
-------
152
Wading River continued
Magnitude Date Annual Maximum Recurrence
Discharge Interval
cfs
44 2/14/30 358 1.36
45 4/06/60 354 1.33
46 3/08/26 350 1.30
47 4/04/51 344 1.28
48 2/08/41 339 1.25
49 5/04/47 325 1.22
50 9/02/27 322 1-20
51 4/26/44 319 1.18
52 4/04/75 314 1-15
53 4/07/57 313 ' 1.13
54 2/26/65 290 1.11
55 2/27/81 278 1.09
56 12/09/27 270 1.07
57 3/24/50 256 1.05
58 2/14/66 254 1.03
59 4/07/49 200 1.02
-------
153
UNITES STATU OCPARTMCNT Of THK INTCMOK
(•_
Su. No.
at .Norton»-ilaaaacUu*etL9
""" ~ "*^ LT" :. i. ' "*^~~J \ i^ ^H
-
Flood Dlseliarg* Q In cf»
-------
154
Wading River at West Mansfield, Massachusetts
Drainage Area 19.50 square miles
Magnitude Date Annual Maximum Recurrence
Discharge Interval
cfs
1 3/19/68 541 32.00
2 8/20/55 519 16.00
3 1/26/79 375 10.67
4 6/03/84 368 8.00
5 1/27/78 306 6.40
6 3/26/69 260 5.33
7 11/07/55 248 4.57
8 12/27/69 229 4.00
9 6/07/82 227 3.56
10 4/25/83 225 3.20
11 1/28/76 201 2.91
12 5/27/67 189 2.67
13 5/09/54 188 2.46
14 1/28/58 180 2.29
15 4/05/72 174 2.13
16 12/07/72 167 2.00
17 3/10/61 167 1.88
18 12/18/73 162 1.78
19 3/23/77 152 1.68
20 4/11/80 148 1.60
21 3/04/60 145 1.52
22 3/07/59 132 1.45
23 10/08/62 122 1.39
24 9/09/57 120 1.33
25 3/04/71 115 1.28
26 1/14/75 113 1.23
27 4/02/62 105 1.19
28 4/17/64 102 1.14
29 3/01/81 94 1.10
30 2/27/65 91 1.07
31 3/07/66 89 1.03
-------
155
UNITtO STATE* DCPMTKCHT Of TMC INTUllO*
M*f»Rv«•««ra*»w»•»-Annual Flood —
«t W««t Mamfield. M««a«rhii««tr«
31
±±1
^^S-X-trr—Ltir.}—-r-
rr—-r-rM.' i • i——t-—
-*——4-t-e-t-i--t" —-->
Flood Diich«rg« Q In cfi
IN* «f
-------
156
Appendix C
Streamtube Calculations
-------
157
Stream Tube Dimensions
Stream Tube
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
Distance
between
Equi-
potentials
(ft)
2083
1771
1458
896
708
1042
2083
2146
1208
896
792
729
583
292
188
313
396
417
354
271
146
62.5
146
458
667
604
375
271
250
230
188
230
230
230
417
1021
2292
2688
Width
of
Stream
Tube
(ft)
979
854
625
417
271
354
313
521
625
583
458
479
333
313
479
500
333
333
313
333
167
208
292
292
146
250
375
333
458
375
396
604
354
563
1417
1292
1333
1792
Depth
of Aquifer
Below
M.S.L.
(ft)
90
90
90
90
90
90
90
85
85
85
85
80
80
80
75
75
75
75
75
75
75
70
70
65
65
60
60
55
55
50
50
50
50
50
55
65
75
100
Discharge
(ft3/day)
13,747
14,105
12,539
13,613
11,196
9,937
4,395
6,737
14,357
18,056
16,047
17,248
14,994
28,138
63,060
39,537
20,813
19,764
21,833
30,412
28,310
77,376
46,500
13,867
4,761
8,382
20,250
23,040
34,350
28,125
36,335
45,300
26,550
42,225
63,714
27,523
14,394
21,500
Total Influx in ft°/day
345,8701,932
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158
Appendix D
Conversion Tables
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159
Length
1 inch (in) =2.54 centimeters (cm)
1 centimeter (cm) = 0.394 inches (in)
1 foot (ft) = 0.3048 meters (m)
1 meter (m) = 3.281 feet (ft)
1 mile (mi) = 5280 feet (ft)
1 mile (mi) = 1.609 kilometers (km)
1 kilometer (km) = 0.6214 miles (mi)
Area
2 2
1 square mile (mi ) = 2.590 square kilometers (km )
2 2
1 square kilometer (km ) = 0.3861 square miles (mi )
Discharge
1 cubic foot per second (cfs) = 0.0283 cubic meters
per second (m /s)
1 cubic meter per second (m /s) = 35.32 cubic feet per
second (cfs)
Temperature
°C = 5/9 (°F - 32)
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160
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