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Estimating ground water recharge and base flow from streamflow hydrographs for a small Appalachian mountain basin

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Estimating ground water recharge and base flow from streamflow hydrographs for a small Appalachian mountain basin
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Mau, David P ( David Phillip )
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English
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viii, 130 leaves : illustrations ; 29 cm

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Groundwater -- New Hampshire ( lcsh )
Groundwater flow -- New Hampshire ( lcsh )
Groundwater ( fast )
Groundwater flow ( fast )
New Hampshire ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Includes bibliographical references.
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Submitted in partial fulfillment of the requirements for the degree, Master of Science, Civil Engineering.
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Department of Civil Engineering
Statement of Responsibility:
by David Phillip Mau.

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|University of Colorado Denver
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ocm29150276
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LD1190.E53 1993m .M356 ( lcc )

Full Text
I
ESTIMATING GROUND WATER RECHARGE AND BASE FLOW
FROM STREAMFLOW HYDROGRAPHS FOR A SMALL
APPALACHIAN MOUNTAIN BASIN
by
David Phillip Mau
B.S., University of Michigan, 1983
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Civil Engineering
1993
!i -



This thesis for the Master of Science
degree by
David Phillip Mau
has been approved for the
Department of Civil Engineering
by
Aib!f3
Date


Mau, David Phillip (M.S., Civil Engineering)
Estimating Ground Water Recharge and Base Flow from Streamflow
Hydrographs for a small Appalachian Mountain Basin
Thesis directed by Professor William C. Hughes
ABSTRACT
Ground water recharge was determined from existing data for a small,
Appalachian watershed using: 1) analytical methods based on recession
characteristics of streamflow hydrographs, 2) methods based on analytical
filtering of streamflow hydrographs. The results were evaluated to test the
applicability of the methods for northern Appalachian terrain and climate.
Two streams, NW and W, representing the watershed flow into Mirror Lake,
New Hampshire. The total basin area is 0.25 square miles. Daily streamflow
data for the two streams exists for ten years. Three periods were selected
within those years representing high, intermediate, and low ground water
recharge years.
A necessary component for determining recharge was the calculation of a base
flow recession slope. Methods developed separately by Meyboom and Knisel
to determine recession slopes were performed on semilog streamflow
hydrograph plots for each stream. The average recession slopes for each stream
over a ten year period was used in the recharge analysis.
The methods used for determining ground water recharge were the manual
instantaneous recharge and constant recharge methods developed by



Rorabaugh, and the automation of Rorabaugh's instantaneous recharge method
developed by Rutledge. The results of the automated procedure for the high,
intermediate, and low water years were 22,20, and 9 inches respectively for the
NW stream and 18, 18, and 8 inches respectively for the W stream.
Streamflow partitioning methods were also used to separate the base flow
component from streamflow and calculate total base flow volume. The results
from the Rutledge automated method were slightly higher than the results
obtained using Wahl's method. The Institute of Hydrology method was
automated by Wahl and gave satisfactory results. The base flow volume results
from the Wahl method for the high, intermediate, and low water years were 15,
15, and 8 inches respectively for the NW stream and 14, 12, and 6 inches
respectively for the W stream.
Finally, digital filter methods developed by Nathan and McMahon and
modified by Chapman were analyzed for base flow volumes using streamflow
hydrographs. Base flow volumes were much lower than those calculated by the
Wahl and Rutledge methods and were not considered applicable for small,
mountainous basins.
This abstract accurately represents the content of the candidate's thesis. I
recommend its publication.
Signed
IV


ACKNOWLEDGEMENTS
This study was funded by the U.S. Geological Survey and I would like to
thank Tom Winter for his guidance and advice. His unwavering support is
deeply appreciated. Thank you also to Don Rosenberry and Renee Parkhurst for
their technical assistance and support in this thesis.
I would like to thank Dr. Hughes for his recommendations and advice during
the preparation of this thesis as well as for the outstanding lectures from the
many courses I took from him. I would also like to thank the other members of
my committee, Professors Lynn Johnson and James Guo, for their assistance.
The debt to my parents for their support and encouragement is immeasurable.
Very few people get a second chance in their careers and I am aware of how
fortunate I am. Thank you.
Finally, I would like to thank my wife, Nancy, who has stood by me during
these past three years. Her patience, understanding, and continual
encouragement kept me going during times when I thought I'd never finish.
v


CONTENTS
CHAPTER
1. INTRODUCTION............................................1
Purpose and Scope.................................... 5
2. ENVIRONMENTAL SETTING OF THE
MIRROR LAKE AREA......................................6
Location and Hydrologic Setting of the
Mirror Lake Area......................................6
Climate.............................................. 6
Soils and Vegetation..................................6
Glacial Drift.........................................9
Drainage Basin Morphology.............................9
3. METHODS . .........................................13
Streamflow Measurements..............................13
Methods of Estimating Recharge.......................13
Manual Hydrograph Analysis........................14
Meyboom and Knisel methods of
determining a recession slope..................14
Rorabaugh instantaneous ground water
recharge method................................17
Rorabaugh constant ground water
recharge method................................22
Automated Hydrograph Analysis.....................24
Rutledge automated recession curve
displacement method............................24
vi


Methods of determining the Base Row component
of Streamflow.............................................. 26
Streamflow Partitioning.....................................26
Rutledge Method.........................................29
Institute of Hydrology method...........................30
Digital Filtering...........................................31
Nathan and McMahon recursive digital
filter method...........................................31
Chapman recursive digital filter method.................32
Selection of Years for Analysis................................32
4. RESULTS..........................................................36
Determination of Recession Slope...............................36
Recharge determined by Manual Hydrograph Analysis..............41
Instantaneous recharge method of Rorabaugh..................41
Constant recharge method of Rorabaugh.......................43
Recharge determined by automation of Rorabaugh's
instantaneous recharge method..................................52
Determination of Base Flow component of Streamflow............ 54
Streamflow Partitioning method of Rutledge..................54
Streamflow Partitioning method of the Institute
of Hydrology (Wahl).....................................60
Digital filter method of Nathan and McMahon.................62
Digital filter method of Chapman............................68
Vll


5. DISCUSSION..................................................72
Determination of Recession Slopes.........................72
Comparison of Instantaneous Recharge method
and Constant Recharge method of Rorabaugh..................75
Comparison of the Automated Instantaneous
Recharge method of Rutledge with the manual
use of the Instantaneous and Constant Recharge
methods of Rorabaugh..............................82
Comparison of methods used to determine the Base Flow
Component of Streamflow...............................88
Comparison of Rutledge and Wahl Automated Streamflow
Partitioning methods..................................88
Comparison of the Digital Filter methods with the
Streamflow Partitioning methods.......................97
Comparison of methods used for determining
Recharge with those used for determining the
Base Flow component of Streamflow.....................101
6. CONCLUSIONS.................................103
APPENDIX
A. Meyboom and Knisel plots for streams NW and W..........106
B. Manual Rorabaugh Instantaneous Recharge plots for
streams NW and W......................................122
REFERENCES....................................................128
vm


CHAPTER 1
INTRODUCTION
Accurate estimates of ground water recharge are an important aspect of
many geohydrologic studies. Several methods for determining ground water
recharge have been developed, but some are considered more applicable for
specific physiographic and climatic settings than others. Methods for
determining recharge can be grouped into two categories: 1) those designed to
actively measure the recharge process, and 2) those designed to determine
recharge using existing data. Methods for determining ground water recharge
from existing data include: 1) analytical methods based on recession
characteristics of hydrographs, 2) methods based on analytical filtering of
hydrographs, 3) rainfall-runoff modeling emphasizing subsurface flow
components, and 4) numerical ground water modeling. Mirror Lake, New
Hampshire, was chosen as a study site to evaluate the applicability of the first
and second of the above methods for a northern Appalachian terrain and
climate.
Many analytical methods are based on work by Boussinesq (1877), who
described outflow from ground water to surface water as a first order
exponential decay function. Horton (1933) determined a similar analytical
expression in his studies on ground water recharge and baseflow. Barnes
(1939), recognizing that stream runoff consisted of: a) direct runoff b) interflow
and, c) base flow (ground water discharge), also developed an empirical
equation similar to Boussinesq's. He found that when the logarithm of
1


discharge was plotted against time, a linear relationship between the two
variables was obtained which represented the ground water recession. The
following equation was the result of this effort;
Qt = Q0Ktr
Kr= recession factor.
Meyboom (1961) applied this method to a basin near Calgary, Alberta, but took
it one step further and estimated ground water discharge and recharge.
Meyboom made the following assumptions that were valid for the large (460
square miles), semi-arid basins he studied: 1) straight lines connecting points of
minimum discharge represented true baseflow (ground water recession)
conditions, 2) bank storage contributed significantly to annual base flow, and 3)
rainfall was a negligible source of bank storage. These conditions are not
representative of New Hampshire, which receives abundant precipitation and
bank storage is probably negligible on Appalachian mountain streams.
Because of the dissimilarity of drainage basins, and because of water
diversions and regulations in some basins, empirical methods of hydrograph
analysis commonly are not valid. To overcome this, Rorabaugh (1960, 1964)
used theoretical concepts from heat flow and electricity to develop baseflow
recession equations in terms of ground water parameters: transmissivity,
storage coefficient, and time. Rorabaugh assumed the initial aquifer water table
was horizontal throughout the basin prior to recharge, and that recharge raised
water levels instantaneously and evenly. Rorabaugh showed that if recharge is
instantaneous, a plot of the logarithm of streamflow versus time became a
2


straight line at a point defined as critical time. Using his equation he calculated
the total volume of ground water that would drain to the stream as baseflow
from this time to a theoretical infinite time. The definition of critical time was
significant because Glover (1964) showed that at critical time approximately one
half of the water that initially recharged ground water had drained away.
Therefore, recharge could be calculated as 2 times the volume calculated by the
Rorabaugh equation for instantaneous recharge. Rutledge and Daniel (in press)
developed an automated procedure to analyze hydrographs using Rorabaugh's
instantaneous recharge method.
Rorabaugh (1964) also developed a method to determine ground water
recharge based on Jacob's solution for constant recharge (1940). This solution
requires steady state conditions and would be applicable primarily to areas that
receive large rainfalls and have high baseflows.
In addition to the above methods of analyzing streamflow hydrographs to
estimate recharge, some researchers focused on streamflow partitioning, which
is determining the baseflow component of streamflow. If it can be assumed that
on the average, near equilibrium exists between recharge and discharge,
recharge can be estimated by determining discharge (Meyboom, 1961). Many
attempts have been made to determine realistic methods of separating
hydrographs into various flow components. Pettyjohn and Henning (1979)
developed an automated, computer-based method that identified a streamflow
minimum based on the number of days after a peak that surface runoff ceased.
The Institute of Hydrology (1980a) developed an automated method that
3


searched for minimum streamflow values on a continuous record by analyzing 5
day periods. Streamflow values that were less than 0.9 of the two days at each
end of the 5 day values were considered baseflow. Rutledge's streamflow
partitioning program was similar to the Institute of Hydrology method, but
added Linsley (et. al)'s (1982) empirical relation for determining time of surface
runoff and start of baseflow. Nathan and McMahon (1990) used a recursive
digital filter, commonly used in signal analysis, to separate the baseflow
component of streamflow. Their justification was that it was just as physically
unrealistic as separating baseflow with a series of straight lines such as that
proposed by the Institute of Hydrology.
A review of the literature on analysis of streamflow hydrographs to
determine ground water recharge and baseflow indicates that the methods were
used primarily on large basins (10 750 sq. miles) in areas where rainfall is
intermittent, and there are frequent low flow periods. The effects of ground
water recharge and discharge are more evident in hydrographs of streams in
these areas. In contrast, the two watersheds comprising the Mirror Lake study
area cover only 0.25 sq. miles. These watershed basins exist on hillslope
terrain that receive frequent precipitation. Few studies using hydrograph
analysis have considered the types of watersheds associated with Mirror Lake.
Therefore, it was decided to evaluate the applicability of these methods for a
small mountain basin.
4


Purpose and Scope
The purpose of this study was to estimate ground water recharge for the
Mirror Lake, New Hampshire, basins using various streamflow hydrograph
analysis methods. The specific methods were: 1) to evaluate and compare the
manual use of Rorabaugh's instantaneous and constant recharge methods, 2) to
evaluate and compare manual use of the Rorabaugh instantaneous recharge
method with Rutledge's automated use of this method, and 3) to evaluate and
compare the Rutledge with the Wahl modified Institute of Hydrology
streamflow partitioning method, and in turn, these with the Nathan and
McMahon versus Chapman digital filter programs for determining base flow.
5


CHAPTER 2
ENVIRONMENTAL SETTING OF THE MIRROR LAKE AREA
Location and Hydrologic Setting of the Mirror Lake Area
Mirror Lake is located in the White Mountains of north central New
Hampshire, approximately fifty miles north of Concord (figure 1). The lake
lies at an altitude of about 700 feet, and the highest point in the watershed is
about 1,540 feet. The drainage basin of Mirror Lake is characterized by high
ridges and steep land slopes. The ridges consist primarily of bedrock, whereas
unconsolidated glacial drift, ranging in depth from 0 to 165 ft., can be found
overlying the bedrock in the lower portions of the basin (Winter, 1984).
Characteristics of the lake and drainage basin are given in table 1.
Climate
The general climate of Mirror Lake and the surrounding area is classified as
humid with short, cool summers and long, cold winters. The mean air
temperature in July is approximately 19C and in January, -9C. Snow depth
averages 5 feet throughout the winter, and occasionally mild midwinter
temperatures will melt the snowpack.
Soils and Vegetation
Soils in the Mirror Lake area rest on till and consist mostly of sandy loam.
The soil depth varies but averages about 1.5 ft. (Winter, 1984, p.5).
6


M MUS
Figure 1 -- Location of Mirror Lake and the Hubbard Brook Valley.
7


Table 1-Morphometric characteristics of
Mirror Lake and Drainage Basin
Location: 43 56.5 N, 70 41.5' W
Mirror Lake:
Maximum effective length, (ft.)
Maximum effective width, (ft.)
Area, (ft2)
Maximum depth, (ft.)
Average depth, (ft.)
Mirror Lake Drainage Basin:
Basin
Area (ft2)
Basin length, (ft.)
Basin width, (ft.)
Basin perimeter, (ft.)
Basin land slope
2000
1214
1.61xl06
36
19
NW W
3.98xl06 2.77xl06
2989 3320
1240 781
7851 9922
0.211 0.124
Stream
Main channel length, (ft.) 3511 4311
Main channel slope 0.224 0.129
8


The vegetation of the area consists of northern hardwoods, extending from
Nova Scotia to the Blue Ridge Mountains and westward to Lake Superior.
Deciduous species found in the area include beech, sugar maple, basswood, red
maple, red oak, and white elm. Coniferous species in the area include hemlock,
red spruce, and white pine.
Glacial Drift
Seismic geophysical surveys and test drilling at Mirror Lake indicate as
much as 80 feet of glacial drift along the northwest shore of Mirror Lake
(Winter, 1984, p. 22). With the exception of the south and southwest sides of
the lake, drift thickness in the remainder of the drainage basin is generally 20 to
40 ft. (figure 2). Composition of the glacial drift in the northwest and west
basins is silty, sandy till, containing numerous cobbles and boulders.
Drainage Basin Morphology
Three small streams flow into Mirror Lake (figure 3). Two of the streams,
NW and W, flow into the lake from the west side, whereas the third stream
enters the lake from the northeast side. Very little flow is observed and
measured in the east stream, and therefore, is not included in this study of
ground water recharge. Basins W and NW have very different morphometry
(table 1). Basin W is about 11 percent longer and 37 percent narrower than
basin NW, and its perimeter is about 26 percent larger. The main channel
9


EXPLANATION
BEDROCK OUTCROP
------------12
LINE OF EQUAL THICKNESS
OF GLACIAL DRIFT.Dashed
Figure 2 Thickness of glacial drift at Mirror Lake, NW and W basins.
10


11


slope differences indicate that the NW stream channel is 74 percent steeper than
the W channel.
12


CHAPTER 3
METHODS
The methods described in this study were used to evaluate ground water
recharge and base flow at Mirror Lake. Daily streamflow data was required for
these analyses and was collected by two flumes that were located near the
stream outlets, approximately 100 meters from the lake (figure 3).
Streamflow Measurements
Streamflow into Mirror Lake is measured using prefabricated Parshall
flumes. The throat dimension on the NW flume is 1 ft. wide by 2 ft. high, and
on the W flume is 0.75 ft. wide by 2 ft. high. To collect streamflow data
during winter months, the flumes are insulated with styrofoam and wrapped in
plastic sheets. Flameless propane catalytic heaters are hung inside the flumes to
prevent freezing. Water levels in the stilling wells are measured using strip
chart recorders.
Methods of Estimating Recharge
The two methods of estimating ground water recharge from hydrographs of
streamflow discussed herein are the instantaneous recharge method
(Rorabaugh) and the constant recharge method (Rorabaugh). The instantaneous
recharge method can be done manually, or it can be done automatically using a
computer program written by Rutledge. To use either method of Rorabaugh's a
recession slope must be determined for the stream of interest.
13


Manual Hvdrograph Analysis
Mevboom and Knisel methods of determining a recession slope. Base flow,
also known as ground water recession or ground water discharge, represents
withdrawal of ground water from the aquifer after ground water recharge has
ceased (Meyboom, 1961). The mathematical expression governing flow from
an aquifer to a fully penetrating stream was first presented by Boussinesq in
1877. The equation was nonlinear and difficult to solve, therefore it was
linearized using simplifying assumptions. The result was (Hall, 1968, p. 975);
Qt= Q0e"at (1)
where, Qt = discharge at time t
Qo = initial discharge
a = constant
From studies done on the upper Mississippi Valley, Barnes (1939)
developed an empirical equation similar to equation 1;
Qt = Q0Ktr (2)
where
Q0 = discharge at any time, cfs
Qt = discharge at t time units after Q0, cfs
Kr = daily recession constant (depletion factor)
t = time interval, days
14


Using a typical streamflow hydrograph where discharge is plotted on a log scale
on the y axis and time is plotted on a cartesian scale on the x axis, Meyboom
(1961) suggested that the ground water recession slope could be estimated by
successive points of minimum streamflow over the period of at least two
seasons.
Knisel (1963) used a correlation method for determining base flow
recessions. Again using equation 2, the recession constant, Kr was determined
by plotting Qq and Qt as abscissa and ordinate values, respectively. Stream data
that was considered to be base flow was used in the plot. The recession
constant K, is defined as the slope of the straight line drawn through the origin
and maximum value of Qt Adherence to the K-line suggested base flow,
whereas departure from the line indicated continued surface flow The data
points that plotted along the K-line were located on the stream hydrograph and a
straight line was drawn through them and extended for at least a log cycle. For
both methods base flow recessions were calculated as the number of days per
log cycle (see figure 4).
For the Mirror Lake study, base flow recessions were determined for the
northwest and west streams using both the Meyboom and Knisel methods. The
base flow recession value selected for each stream was an average of the results
derived from the two techniques. These recession slopes were used in the
following methods of estimating recharge.

15


o 40 eo 120 ISO 200
ftfsec.
Figure 4 Example of a Knisel K-line plot


Rorabaugh instantaneous ground water recharge method. Rorabaugh modified
a heat flow equation (Ingersoll, Zobel, and Ingersoll, 1948, p.125 ) to
determine ground water recession characteristics from water level data from
wells. In ground water terms, the equation was:
h = h0(l/a)E[e(-m27t2Tt/4a2S)(2a/m7t)(l-cosm7t)sin(m7tx/2a)] (3)
where, h = water level, ft.
T = transmissibility, ft2/day
S = storage coefficient, dimensionless
a = half width of aquifer, ft.
m = counter
t = time, days
Rorabaugh plotted h/hD vs Tt/a2S (Rorabaugh, 1960, figure 2), and found that
the recession curves approached straight lines when Tt/a2S > 0.2. This was
designated as critical time, the time after which water levels in a well would
decline exponentially. Rorabaugh also found that when Tt/a2S= 0.2, equation 3
reduced to:
h = h0(4/7t)e(7l2^'^a2^)sin(TCx/2a) (4)
Using equation 4, to solve for two arbitrary points on the recession curve,
Rorabaugh calculated aquifer diffusivity, T/S, as;
17


T/S = 4a22.3031og(hi/h2)/rc2(t2 ti) or simplified,
T/S = 0.933a2[log(hi/h2)]/(t2 tl) (5)
The assumptions needed to use equation 5 properly are (Rorabaugh, 1960):
1. The aquifer is thick relative to the change in water level;
2. The aquifer is wide relative to its thickness;
3. The aquifer is uniform in shape, isotropic, and homogeneous;
4. The aquifer is underlain by impermeable material, and its side
boundaries are vertical and fully penetrating;
5. The initial water level is everywhere horizontal prior to
recharge;
6. The recharge that raises the water level is instantaneous and
evenly distributed;
7. Sufficient time has passed so that the water level is declining
exponentially with time; and
8. Extraneous natural factors ( such as ET and precipitation) and
human-induced factors are not affecting the water level.
Rorabaugh recognized that because base flow is groundwater discharge, the
base flow recession of streams should behave as water level recession in wells,
that is, decline exponentially with time after critical time. Differentiating
equation 3, originally for heat flow, with respect to x (distance from stream) to
obtain the gradient dh/dx, setting x equal to zero, and multiplying by T,
Rorabaugh arrived at,
18


q = ITCVaXe^TWS) + e(-^2Tt/4a2S) +e(-25^Tt/4a2S) +
(6)
q = ground water discharge per unit of stream length at any time after
recharge ceases, cfs.
When Tt/a2S > 0.2, the logarithm of streamflow versus time becomes a straight
line and equation 6 reduces to:
q = 2T(h0/a)e(-7t2Tt/4a2S) (7)
Critical time, tc, the point where the recession curve becomes a straight line,
was computed by:
^ = 0.2a2S/T (8)
Equations 5 and 8 were combined to obtain a parameter equation that contained
T, S, and a:
T/a2S = 0.933[log(hi/h2)]/(t2 ti) (9)
If the base flow recession curve is evaluated after tc to determine the time for
streamflow to decline through one log cycle (At/log cycle), equation 9 can be
rewritten as ( Rorabaugh and Simons, 1966):
T/a2S = 0.933/(At/Log cycle) (10)
19


Finally, combining equations 8 and 10 results in:
t<, = 0.2 (At/log cycle)/0.933 (11)
Equation 11 shows that it is not necessary to know the half width of the aquifer.
Rorabaugh also determined the volume of ground water in storage that
would eventually drain to the stream if there were no more recharge
(Rorabaugh, 1964, p.440) by integrating equation 7 from t=t to t=infinity:
V = q(4a2S/7t2T) (12)
where,
V = Volume of ground water in storage that would eventually drain to
the stream after ^ ft3
If equation 10, T/a2S = 0.933/(At/log cycle), is rearranged:
At= t2-ti = 0.933 a2S/T
and knowing, 0.933 = 2.303/(tt2/4)
Substituting back into equation 12,the result is:
V = qAt/2.303 (13)
where, At = days/log cycle
Equation 13 does not require knowledge of a,S, or T.
20


To determine the volume of ground water remaining in storage in the entire
basin at tc, Bevans ( Bevans, 1986, p. 58, eq. 12 ) modified Rorabaugh's
storage calculation for one side of a stream (Rorabaugh, 1964, p. 490, eq.ll)
to include both sides and arrived at:
V = Qtc(0.933a2S/T)/2.3 (14)
V = total ground water remaining in storage at tc, ft3
Glover, in independent studies, showed that one half of the ground water in
storage from a recharge event would discharge to a stream by tc ( Glover,
1964). Because the critical time defined by Glover is the same as the critical
time defined by Rorabaugh, recharge could be calculated by multiplying
Rorabaugh's V by 2. Furthermore, by superposition of recharge events, at tc
the potential ground water discharge minus the potential ground water discharge
had the event not occurred is equal to one half of the recharge that occurred
during the event. The following equation summarizes the concept:
Recharge = 2(Q2 Qi)K/2.303 (15)
where Qj = ground water discharge at critical time, extrapolated
from the pre-event stream flow recession, cfs
Q2 = ground water discharge at critical time, extrapolated
from the post-event stream flow recession, cfs
21


Bevans provides an example of the technique along with sample calculations
(Bevans, 1986, p. 59-60).
Rorabaugh constant ground water recharge method. Rorabaugh developed an
equation for the case where a constant rate of recharge exists. Starting again
with equation 3 for the condition dh/dt = C:
q = CaS{ l-(8/7t2) [ +(1/9) e(-97t2Tt/4a2S)
+(l/25)e(257t2Tt/4a2s) +...]}. (16)
When Tt/a2S > 2.5, the bracketed term becomes very small and the flow
approaches the steady state condition (Rorabaugh, 1964, p.435):
q = CaS (17)
For the situation where constant recharge begins at time, t, and ends at some
later time, t', ground water discharge is calculated using equation 16.
Discharge, q, at time, t', is subtracted from q at time, t, resulting in:
q = CaS { (8/ji2) [ e^T^S) .^Tt^S) + (1/9) e^Tt'A^S)
-(1/9) e("9lt2Tt/4a2si...l. (18)
Plotting q/CaS against Tt/a2S and using equations 16 and 17 results in a
dimensionless type curve (Rorabaugh, 1964, p. 436, fig. 2). The upper curve
22


q/CoS
represents a constant rate of recharge in the ground water discharge-time
relationship. The downward sloping 'tails' represent ground water recessions
following the end of a recharge period (figure 5).
Figure 5 Rorabaugh dimensionless type curve of time-discharge relation
during constant rate of recharge. Lower limbs are for discharge
after cessation of recharge.
23


To use the constant recharge method, one needs to fit the type curve, which is
in dimensionless time, to a real-time hydrograph. Furthermore, it needs to be
fit starting with a point on the recession slope from the last major streamflow
event. The type curve is fit using this recession slope as a base. Starting and
ending dates need to be chosen for the constant recharge period. As an example,
when the dimensionless parameter, Tt/a2S =1.0, q/CaS=0.93 (figure 5).
Recalling the condition for the rate of constant recharge, CS = S(dh/dt), the
volume of constant recharge can be calculated from:
CS(At)= QAt/a(0.93) (19)
where,
At= length of time for recharge, days
Q= ground water discharge on ending date of recharge period, cfs
a = drainage area of basin, mi2
Automated Hvdrograph Analysis
Rutledge automated recession curve displacement method. Rutledge developed
computer programs RECESS and RORA to automatically use Rorabaugh's
instantaneous method of determining ground water recharge. The programs
were designed to consider complete calender years, and prompt the user for the
beginning and ending dates. Data gaps in streamflow are permissible.
Standard AD APS 2 and 3 card format is required.
24


In order to calculate ground water recharge, RORA needs to identify periods
of recession within the streamflow record. Manual instantaneous recharge
methods allow visual interpretation of the hydrograph and the best placement of
the recession slopes. However, Rutledge had to devise a method for the
computer to determine the beginning of the recession slope. Rutledge
accomplished this by assuming ground water discharge equals streamflow
during periods of negligible surface runoff. Using an antecedent recession
equation found in Linsley and others (1982):
N = A0-2 (20)
where, N = number of days after a peak in the hydrograph when surface
runoff ceases (time base of surface runoff)
A = drainage area, mi2
N was used to determine the time after a peak in the hydrograph when the
position of the ground water recession curve would first be measured. The
program was interactive to allow the user to change N if the calculated value
was unsatisfactory. The program then requests K, the storage delay factor.
RECESS calculates K based on equation 20, or, if the value is known, input
directly into RORA by the user when prompted. Once N and K are known,
critical time is calculated, which becomes the ending point after each peak when
the ground water recession curve is measured. Bevans' method is used to
determine total ground water recharge (Bevans, 1986). A flow chart and
25


hydrograph describing Rutledge's automation of Rorabaugh's instantaneous
recharge method are shown in figure 6 and figure 7. The flow chart
corresponds to the hydrograph in figure 7. In addition to calculating total
recharge, the program output includes a file that contains a detailed tabulation
of calculations for each peak in the hydrograph.
Methods of determining the Base Flow component of Streamflow
Streamflow Partitioning
Streamflow partitioning is a method of determining ground water discharge,
or base flow, from the streamflow hydrograph. Many different techniques have
been used to separate hydrographs into their base flow and streamflow
components. Barnes (1939) separated surface flow, interflow, and base flow
from the hydrograph. Kulandaiswamy and Seetharaman (1969) suggested
Barnes' three part technique was unreliable, but valid for separating surface
flow and base flow. The premise behind hydro graph separation is: a) ground
water discharge equals streamflow for periods of low flow, and b) during
periods of surface runoff, estimates of ground water discharge can be
determined by linear interpolation from the adjacent low flow periods. These
assumptions were adopted by Knisel and Sheridan (1983), .and
Shirmohammadi and others (1984), using an antecedent recession equation
similar to equation 20. However, Knisel and Sheridan's and Shirmohammadi's
work used antecedent precipitation as an indicator that ground water equaled
26


K
CT
1
TP(I)
C(I)
QA(I), TA(I)
QB(I),TBC(I)
QC(I),TBC(I)
dQ
dT
delQ
Explanation
Storage delay factor(time per log cycle of recession after critical time)
Critical time
Peak counterthe above calculations pertain to the present peak which is peak I
The time of occurrence of peak I
A constant (for peak I) that is used in the equation for the margin of flow due to
peak I up to the critical time after peak I
The flow and time at critical time after the last peak (1-1) that would
have occurred in the absence of all peaks subsequent to the last peak
one exception is that if 1-1, then QA(I) and TA(I) axe the flow and time on the
last day of the recession period before the first peak.
The flow and rime at critical time after the present peak(I) dial would
have occurred in the absence of the present peak and all subsequent peaks
The flow and time at critical time after the present peak(I) that would
have occurred in the absence of all peaks subsequent to the present peak.
Difference between the measured flow during the recession period after
peak I and the flow that would have occurred in the absence of peak I
Time increment between the peak and a day during the recession period
Margin of flow at critical time after peak I that occurs because of peak I only
Figure 6 Flow diagram used for Rutledge automated recession curve
displacement method.
27


8TREAMFLOW (LOGARITHMIC SCALE)
INCACASINO TIME
Figure 7 Schematic of hydrograph showing the procedures executed for.
each peak in the recession curve displacement method.

28


streamflow, whereas Rutledge used antecedent streamflow recession as the
indicator.
Rutledge method. The Rutledge streamflow partitioning program, PART, reads
daily mean streamflow data and searches for days that meet the antecedent
recession requirements in equation 20. On each of these days, ground water
(base flow) is designated equal to streamflow as long as it is not followed by a
daily decline of more than 0.1 log cycle. A daily decline of more than 0.1 log
cycle is indicative of continued surface runoff or interflow. The program reads
through the daily data again, calculating ground water discharge by linear
interpolation for the days not meeting conditions for equation 20. This is
accomplished by interpolating base flow values between 1) the log of the base
flow value of the closest preceding day meeting the conditions of equation 20
and less than 0.1 log cycle and 2) the log of the base flow value of the closest
following day meeting the conditions of equation 20 and less than 0.1 log cycle.
Total base flow volume for the year is the sum of the daily base flow values
calculated by the program. Two output files are created, OUTPART and
OUTP2. OUTPART provides basic results; mean base flow, and base flow
index (mean base flow/mean streamflow). OUTP2 provides date, streamflow,
and base flow for each day of the period analyzed. Streamflow and base flow
graphs can be constructed from this file.
29


Institute of Hydrology method. Another method for separating base flow from
streamflow was developed by the Institute of Hydrology (1980a, b). In this
technique, the year is broken into five day segments and the minimum mean
daily discharge from each segment marked on the hydrograph as potential base
flow (on semi-log paper). Each 'marked' minimum discharge value is
compared with the minimums from adjacent segments. If 90 percent of a given
minimum is less than an adjacent minimum, the marked minimum is kept as a
point defining the base flow hydrograph. These 'points' are referred to as a
turning points. The turning points are connected by straight lines to form the
base flow hydrograph.
Wahl and Wahl (1988) automated the Institute of Hydrology method. The
program operates on complete water years (Oct. 1 Sept. 30 ), and uses mean
daily streamflow data. ADAPS 2 and 3 card format is required for data input.
The program is interactive, allowing the user to change the five day segment,
used in the minimum discharge evaluation, to any time length desired. Also,
the 0.9 factor selected as an indicator of base flow can be changed to test the
sensitivity of base flow volumes to this factor. Total base flow volume, total
streamflow volume, and base flow index (BFI, ratio of total base flow volume
to total streamflow volume) are summarized in the program output. If desired,
a separate file containing turning points and dates is created for use in graphing.
30


Digital Filtering
Nathan and McMahon recursive digital filter method. Nathan and McMahon
(1990) separated base flow from streamflow using a recursive digital filter
method commonly used in signal analysis (Lyne and Hollick, 1979). The
justification for using this technique is that filtering out high frequency signals
is analagous to separating low frequency base flow from high frequency surface
runoff. According to Nathan and McMahon (1990, p.1470), the digital filter
method is no more unrealistic than separating base flow using a series of
straight lines as in the streamflow partitioning method.
The filter equation described by Nathan and McMahon is:
fk = otfk-i+ (i + 0(yk" yk-i)/2 (21)
where fj, = filtered quick response at the kth sampling instant
yk = original streamflow
a = filter paramater
Equation 21 is applied to the streamflow data, in both the forward and reverse
direction, as many times as desired. The number of times equation 21
processes the data determines the degree of smoothing in the base flow
hydrograph. The filter parameter, a, controls the degree of attenuation of f^.
The computer program developed by Nathan and McMahon was evaluated
on the Macintosh computer system. The program is interactive, asking the user
31


for both a and number of passes over the data. Program results include daily
flow values and base flow index.
Chapman Recursive Digital Filter. Chapman (1991) calculated the base flow
response using Nathan and McMahon's equation 21 and found that predicted
base flow from equation 21 would be constant when direct surface runoff was
absent. This was inconsistent with conventional recession theory, so Chapman
modified equation 21 to:
fk = {(3a l)fk_]/(3 a)} + {2(yk ay^/H a)}. (22)
Symbols are defined as in Nathan and McMahon. Chapman left Nathan and
McMahon's program intact with the exception of removing equation 21 and
replacing it with equation 22. The program output is in the same format.
Selection of Years for Analysis
The time periods for analysis were chosen by visually inspecting
continuous streamflow hydrographs. Ten hydrographs spanning one year each
were examined for periods of ground water recharge. For the New Hampshire
region, recharge generally begins in late August, with the advent of the fall
rains, and continues through the winter months and into spring, because of
snow melt and rain. The peak in recharge occurs in April and early May, which
was evident from the hydrographs. Streamflow declines by late May. Streams
lose volume due to evapotranspiration from June through August. The
32


streamflow hydrographs reached their lowest levels by August, only to begin
recharging again in late August (figures 8,9).
Selection of years for this study was based on obtaining records
representative of all possible streamflow conditions. Hydrographs were
chosen by visual inspection for high, medium, and low water years. To
minimize the effects of evapotranspiration, the periods selected for
determination of recharge were for the months of August to June. The high,
medium, and low water years selected were 1983-1984, 1989-1990, 1987-
1988 respectively (figures 8, 9).
33


Figure 8 Streamflow hydrographs of NW stream at Minor Lake.
34


Figure 9 Streamflow hydrographs of W stream at Minor Lake.
35



CHAPTER 4
RESULTS
Chapter 4 describes the application of the methods from chapter 3 to the
Mirror Lake drainage basin. Each method is used to estimate ground water
recharge and base flow and the results are tabulated for comparison.
Determination of Recession Slope
The streamflow hydrographs of streams NW and W indicate frequent
precipitation that prevents the development of long streamflow recessions.
Therefore, recession analysis is difficult. The practice of seeking periods on the
hydrograph where base flow might predominate, and plotting these on Knisel
plots did not result in many clearly identified recessions. As an example of
acceptable recessions, it was observed that base flow probably dominated the
NW stream during January 13-17, 1988, and November 7-12, 1988. When
the data points corresponding to these dates were plotted on Knisel graphs, a
straight line could be drawn through them, which would have indicated base
flow (figure 10). Straight lines drawn through the periods in January and
November on the actual hydrograph (semi-log scale) were almost identical in
slope. The recession slope for January was 110 days per log cycle compared
with 111 days per log cycle in November (figure 11).
Unfortunately, very few of the ten years examined had similar acceptable
results (Appendix A). It appeared that stream NW had greater fluctuations in
recession slope values than stream W. This may be a result of the higher
streamflows found in stream NW and the uncertainty of choosing Knisel points
36


0+1, eft
Knlsel Plot
Mirror Lake NW 1988
0, eft
Figure 10 Knisel plot of NW stream, 1988, at Mirror Lake.


oo
Figure 11 -- Meyboom and Knisel plots for NW stream, 1988, at Mirror Lake,


that actually represent base flow. Another source of error was the subjectivity
in the placement of the recession slope line. For stream NW in 1988, a slight
deviation in placement of the line on the semi log could mean differences in
days per log cycle of 15-35%.
Fitting a straight line to the spring recession using the Meyboom method
gave results very close to the Knisel technique, when the line was placed along
true ground water recessions. If the recession line was drawn through minima
too close to the peak, it could represent interflow rather than base flow. The
Meyboom recession line connected minimum points on the streamflow
hydrograph during the maximum spring recession (March June). For stream
NW in 1988, the Meyboom recession slope was 87 days per log cycle. If the
error associated with the Knisel method is accounted for, it comes close to the
Meyboom value.
An overall recession slope value unique to each stream, NW and W, was
calculated by averaging the Meyboom and Knisel methods. The average for
stream NW using eight years of values determined by the Meyboom method
was averaged with the average of eight years of values determined by the Knisel
method to arrive at 125 days per log cycle. The same averaging technique was
done on stream W to give 85 days per log cycle. The results are summarized in
table 2.


Table 2 Meyboom and Knisel values for determining recession slope.

Northwest Northwest Average West Average
Year Meyboom Knisel Knisel NW Meyboom Knisel Knisel W
days/log cycle days/log cycle days/log cycle days/log cycle days/log cycle days/log cycle
1984 96 111/82 97
1985 148 168/71 120 80 102/51 77
1986 85 93 93 83 66/58 62
1987 160 131 131 93 51/130 91
1988 87 110/111 11 104 41/60/32 44
1989 150 79/120/223 141 91 90 90
1990 151 184/165/168 172 89 93/77/67 79
1991 84 92/92 92 86 120/89/131 113
Average 124 129 90 81

Average 125 85



Recharge determined bv Manual Hvdrograph Analysis
Instantaneous Recharge Method of Rorabaugh
The beginning and ending dates of the recharge periods for the three years
were November 4 May 30 for the 1983-1984 water year, September 15 May
8 for the 1989-1990 water year and September 9 April 7 for the 1987-1988
water year. Some small differences in dates between streams NW and W in
both the 1989-1990 and 1987-1988 years were caused by differences in the
calculated critical times between the two streams. Calculated critical times for
streams NW and W were 27 and 18 days, respectively. The Rorabaugh
instantaneous recharge method determines recharge based on the critical time,
which is the elapsed time after a peak on the streamflow hydrograph when half
of the ground water resulting from the event has been discharged to the stream.
Using the same hydrograph peaks, and subsequent critical times as
measurements of time, was more important in evaluating recharge than the
julian date for quantitative comparison of the streams.
The soil type and geology of the W and NW basins are very similar.
Therefore, it would be reasonable to assume that ground water recharge would
be similar in both basins. This was not the case for the recharge determined by
the Rorabaugh instantaneous recharge method, where both 1989-1990 and
1987-1988 showed considerable differences in recharge between the two basins
(table 3). Streamflow hydrographs for 1989-1990 indicate the buildup of water
from Sept. 15 -April 30 is more significant in stream NW than in stream W.
Based on the graphs, ground water recharge would be expected to be higher in
41


Table 3 -- Summary of calculated recharge values for NW and W basins.
1 1 1 1
1007-1000
Racial!# ("1 (Diit/Orta Av| fUchary Oachama |n| IlLilMLU JuLJlLi:'
hitmUnMM IBM mmmm
Northwaal (NWI 10 3 700:11/4-5/30 10.7 235:0/15-5/8 11.9 211:9/0-4/7
wmi rwi 17.8 200:11/4-8/30 15.2 220:9/15-4/20 7.4 201:0/0-3/20

ICofiaUrtl Baclwrai IMM:
1 22.0 278 11.8 201
*2 20.4 200 18.8 220 10.0 201
11 20.4 708 17.5 220 . 11.7 201
04 20.2 200 20.4 19.4 0.2 201 10.0

m:
1 ift.e 2q0 22.0 220 12.0 201:0/0-3/20
2 18.7 200 9.7 201
3 18.0 220 7.2 201
4 20.0 200 15.0 220
ft 10.7 200:1175-5/30 17.9 10.0 93

RulMn Aataau4a4
(NW).
1 24.2 70S 73.0 731 12.4 204
*2 23.3 705 71.7 731 12.2 204
3 22.1 70S 20.0 231 8.0 204
4 20.7 205 22.1 10.8 231 20.5 7.4 204 9.2

w *
1 10.7 205 10.8 220 7.9 109
2 18.4 205 18.8 278 7.8 109
3 18.1 205 17.7 276 7.0 180
4 17.4 205 10.0 17.1 220 17.0 7.5 109 7.7

|Tatal MnnllM ((1*31 1
NH 0.57*10*0 7.04*10*8 3.68*10*8
W 5.40*10*0 4.52*10*0 2.04*10*8 1

ratal fracta. IM 30.4 209:11/4-5/30 33.7 235:9/15-5/0 20.0 211:0/9-4/7
32.0 220:9/15-4/29 20.1 201:0/0-3/20


the NW stream than the W stream. The percentage differences between NW
and W recharge values were 9% in the high water year, 1983-1984, and 80% in
the low water year, 1987-1988.
Determining which streamflow peaks to use for ground water recharge
calculations was based on peaks thought to contribute substantially to recharge.
Major peaks were selected and the recession lines were placed at the end of a
recharge event, just prior to the next major increase in discharge (figure 12;
Appendix B). The calculations involved in determining recharge using the
instantaneous recharge method, a step by step process, are shown in figure 13.
There were errors of 7 15% associated with this method that were caused by
the accuracy of reading streamflow values from the hydrograph.
Constant Recharge Method of Rorabaugh
Rorabaugh's constant recharge method relies on fitting a type curve to a
streamflow hydrograph. For the periods analyzed, a buildup in streamflow
volume could be seen on the hydrographs, and an effort was made to
characterize recharge patterns based on this streamflow buildup. The ground
water recharge type curve was built from a base line, which is a recession slope
from previous streamflow peaks determined by the Meyboom and Knisel
methods. The placement of different base lines in relation to the starting'date
had minimal effect on total recharge for the period. A sensitivity test was done
on stream NW for 1983-1984 that showed a difference of 0.2 inches, or 1
percent, of recharge from shifting the baseline (figure 14). In another
43


Figure 12 -- Peaks selected to represent recharge using Rorabaugh's instantaneous method for stream
NW, 1983-1984.


Procedure
1. Compute recession slope, K
(125 days/log cycle)
2. Compute critical time, CT
(0.2144 *K, or 27 days)
3. Locate time that is
27 days after peak
4. Extrapolate pre-event
recession (5 ft3/sec)
5. Extrapolate post-event
recession (23 ft3/sec)
6. Compute total recharge,
2*f23 51*125 davs(8640f) sec/day)
23026
4.69*106 7 ft3
Figure 13 Procedure for using the recession curve displacement method to
estimate total recharge in response to a recharge event (modified
from Bevans, 1986, fig. 5).
45


Q>cfs
4^
On

CO CO CO Tfr If Nf
oo oo oo oo oo oo oo

94 o 9-4 o 14 9 4
d o tn 9-4 d <> d 9-4 CO CO CO *o
^0.01
n
n
* S S
Figure 14 Effect on changing the baseline to calculate recharge using Rorabaugh's constant recharge
method.


sensitivity test small shifts in the curve near the endpoints affected total recharge
by as much as 4-5 inches ( 20 percent). For example, recharge calculated for
basin NW for 1989-1990 indicated values differed by as much as 4.5 inches
(trials 1-3, table 3). However, as figure 15 shows, the endpoints vary only by
0.07cfs (0.35 0.28).
Ground water recharge was less sensitive to the initial buildup of the
constant recharge curve than to the date of the end of the constant recharge
periods. Percentage differences in total ground water volume remained the
same between 5 and 226 days after the start of recharge. From Sept. 13 to
Nov. 29, 1989 (figure 15) large differences in the initial buildup resulted in
small volumetric differences in ground water recharge. Total recharge for the
NW basins varied between 6.0 and 7.5 inches for this 77 day period. Table 4
summarizes the differences for both streams during the initial buildup for the
years analyzed. It is evident from this table that small differences between
curves suggest the number of days used for constant recharge is more
influential in determining recharge than the shape of the curve during the initial
buildup phase,
The constant recharge curves that appeared most reasonable were averaged
in an effort to reduce the extremes. A new curve representing the average was
plotted, and the total ground water recharge was calculated from this curve.
The results are shown in table 3 and figure 16 and figure 17. Two constant
recharge curves are plotted in figure 17 for stream W for 1989-1990. The
hydrograph shows two periods of recharge separated by a thirty day recession
47


Q.cfi
oo
Figure IS -- Effect on total recharge from variations in initial buildup using the Rorabaugh constant
recharge method.


Table 4 Summary of effects on recharge from variations in initial buildup using the Rorabaugh
constant recharge method.

Stream Year ffDays Smallest trial recharge, in Largest trial recharge, in. Difference, In.
W 83-84 91 7.26 9.15 1.89
W 89-90 91 6.40 9.15 2.75
W 87-88 91 3.24 5.42 2.18
WV 83-84 91 8.91 8.91 0.00
mi 89-90 91 7.05 8.85 1.80
NW 87-88 91 3.71 5.26 1.55

VO


50


Figure 17 -- Average Rorabaugh constant recharge curves for the W stream
at Mirror Lake.
51


period. Rather than overestimate the total recharge from September to May
using one constant recharge curve, two were used to represent the buildup of
ground water.
Recharge determined bv automation of Rorabaugh's Instantaneous Recharge
Method
Results of using Rutledge's automation of Rorabaugh's instantaneous
recharge method are shown in table 3. The four trials listed are the results of
using four different time bases. Trial #1 is defined when the time base of
surface runoff equals one day, trial #2 equals two days, etc. From the
streamflow hydrographs and the recession slope, it is evident that the time base
of surface runoff is between two and four days. With the exception of stream
NW for 1987-1988, differences in the recharge values are 4-12%. There is a
distinct difference in the low water year, 1987-1988, for stream NW. Recharge
varies from 12.4 inches when the time base equals one day to 7.4 inches when
the time base equals four days.
To obtain recharge for the same period as that used for the manual methods,
only data representing those periods was used in the RORA input file. One of
the output files, OUTROR2, calculated recharge event by event, and printed the
results (table 5). The total recharge is a summation of the incremental
recharges. RORA tended to overestimate total recharge because the program
included streamflow peaks beyond the desired endpoint. To counter this, data
was removed until the proper final event was displayed in OUTROR2.
Calculated recharge events than agreed with the manual methods.
52


Table 5 Output from Rutledge program RORA. Example of incremental recharge for the NW stream,
1987-1988. Column headings arc explained in figure 7.
Time Base: 2 days

TP Date TS TE TA TBC OP QA GB OC C DELQ RECHARGE
5 9/13/87 7 11 4.0 31.8 0.3 0.100 0.060 0.065 0.025 0.005 0.13
12 9/20/87 14 21 31.8 38.8 0.1 0.065 0.057 0.064 0.036 0.007 0.19
22 9/30/87 24 24 38.8 48.8 0.1 0.064 0.053 0.057 0.021 0.004 0.11
26 10/4/87 28 28 48.8 52.8 0.2 0.057 0.053 0.064 0.059 0.011 0.32
29 10/7/87 31 32 52.8 55.8 0.1 0.064 0.061 0.064 0.013 0.003 0.07
33 10/11/87 35 41 55.8 59.8 0.1 0.064 0.059 0.069 0.052 0.010 0.28
43 10/21/87 45 49 59.8 69.8 0.2 0.069 0.057 0.066 0.042 0.008 0.23
50 10/28/87 52 55 69.8 76.8 0.4 0.066 0.058 0.080 0.118 0.023 0.64
56 11/3/87 58 61 76.8 82.8 0.1 0.080 0.072 0.075 0.015 0.003 0.08
62 11/9/87 64 70 82.8 88.8 0.1 0.075 0.067 0.070 0.015 0.003 0.08
71 11/18/87 73 78 88.8 97.8 0.3 0.070 0.059 0.074 0.078 0.015 0.42
79 11/26/87 81 82 97.8 105.8 0.6 0.074 0.064 0.111 0.244 0.047 1.33
83 11/30/87 85 91 105.8 109.8 1.6 0.111 0.103 0.166 0.324 0.063 1.76
92 12/9/87 94 102 109.8 118.8 0.2 0.166 0.141 0.123 0.093 0.018 -0.50
104 12/21/87 106 107 118.8 130.8 0.2 0.123 0.098 0.099 0.003 0.001 0.01
109 12/26/87 111 117 130.8 135.8 0.2 0.099 0.090 0.094 0.021 0.004 0.11
118 1/4/88 120 131 135.8 144.8 0.1 0.094 0.080 0.083 0.015 0.003 0.08
133 1/19/88 135 144 144.8 159.8 0.2 0.083 0.063 0.080 0.087 0.017 0.47
147 2/2/88 149 156 159.8 173.8 0.4 0.080 0.062 0.093 0.162 0.031 0.88
157 2/12/88 159 159 173.8 183.8 0.1 0.093 0.077 0.076 0.008 0.002 -0.04
160 2/15/88 162 162 183.8 186.8 0.1 0.076 0.072 0.074 0.011 0.002 0.06
165 2/20/88 167 179 186.8 191.8 0.2 0.074 0.067 0.081 0.068 0.013 0.37
184 3/10/88 186 189 191.8 210.8 0.2 0.081 0.057 0.077 0.103 0.020 0.56



The Rutledge automated method compares favorably with the Rorabaugh
manual methods (table 3). The Rorabaugh instantaneous recharge, constant
recharge, and Rutledge automated methods for basin NW for 1983-1984 are
within three inches of recharge of each other. The results for basin for NW
1987-1988, the low water year, also compare well among the different
techniques. The three recharge techniques used for stream W are within three
inches of recharge of each other for the three water years analyzed.
Determination of Base Row Component of Streamflow
Streamflow Partitioning Method of Rutledge
Streamflow partitioning methods are intended to separate out the base flow
component of the streamflow hydrograph. To determine the base flow volume,
Rutledge relied on an antecedent recession requirement. The antecedent
recession is the number of days following a peak in the hydrograph when the
total flow in the stream is provided by base flow. To calculate the antecedent
recession Rutledge used (Linsley et al., 1982);
N = A0-2 (20)
The values of base flow using equation 20 are shown in table 6. The values
are high compared to values determined from the other base flow techniques
such as discussed herein. This can probably be attributed to use of the Linsley
equation, which was developed for basins much larger than the Mirror Lake
basins. For basins as small as those at Mirror Lake, equation 20 calculates a
54


Table 6 Summary of calculated base flow values for the NW and W basins.
Comparison of Baaeflow volumes for same periods

1883-1984 1989-1890 1887-1888
BF Volume (in.) #Days/Date BF Volume (in.) #Davs/0ate BF Volume (in.) #Days/Date
Rutledge "PART
NW N-A-0.2 18.2 209:1 1/4-5/30 19.4 235:9/15-5/8 9.1 211:9/9-4/7
W NmA*0.2 16.7 208:11/4-5/30 15.4 226:9/15-4/29 8.2 201:9/9-3/28
Average BF(in.) Average BF(ln.) Average BF(ln.)
(NW): N-A(-0.4)
Time Base 2 17.3 18.3 9.0
3 16.7 16.9 8.3
4 15.1 16.4 15.8 17.0 8.0 8.4

(W): N-A"(-0.4)
Time Base 2 15.5 14.5 7.8
3 14.9 13.4 7.7
4 13.6 14.7 12.6 13.5 7.2 7.6

Wahl
(NW):
Time Base 2 15.6 16.7 8.9
3 14.9 14.5 8.2
4 13.9 14.8 13.6 14.9 7.1 8.1
5 13.0 13.5 6.9

(W):
Time Base 2 15.1 13.8 6.2
3 13.2 11.9 6.0
4 13.2 13.8 10.9 12.2 5.5 5.9
5 12.2 10.9 5.4

Nathan
(NW):
I-0.B50, Pass-2 14.9 15.7 7.5
f-0.850, Pass-3 13.9 14.9 7.2
1-0.850, Pass-4 12.7 13.8 6.7
t-0.850. Pass-5 12.0 13.4 13.2 14.4 6.6 7.0

(-0.925, Pass-2 13.6 14.4 6.9
1-0.925, Pass-3 12.6 13.5 6.8
f-0.925, Pass-4 11.2 12.2 6.3
1-0.925. Pass-5 10.6 12.0 11.7 13.0 6.2 6.6

1-0.950, Pass-2 12.8 13.6 6.7
1-0.950, Pass-3 11.8 12.8 6.6
1-0.950. Pass-4 10.2 11.3 6.1
f-0.950. Pass-5 9.5 11.1 10.8 12.1 6.1 6.4

(-0.975, Pass-2 10.9 12.2 6.6
(-0.975, Pass-3 9.7 11.6 6.5
(-0.975, Pass-4 7.8 9.8 6.0
f-0.975. Pass-5 7.0 8.9 9.4 10.8 5.8 6.2
55


Table 6 Continued

m.
1-0.850, Pass-2 13.9 12.6 6.1
f-0.850, Pass-3 13.1 11.8 5.8
U0.850, Pass-4 11.9 10.8 5.6
f-0.850, Pass-5 11.4 12.6 10.2 11.3 5.4 5.7

f-0.925, Pass-2 7.8 11.2 5.9
f-0.925. Pass-3 11.8 10.4 5.6
1-0.925, Pass-4 10.5 9.1 5.3
f-0.925, Pass-5 9.9 10.0 8.7 9.9 5.2 5.5

f-0.950, Pass-2 7.2 10.4 5.7
f-0.950, Pass-3 11.0 9.7 5.5
f-0.950, Pass-4 9.5 8.3 5.2
f-0.950, Pass-5 8.8 9.1 7.9 9.1 5.0 5.4

f-0.975, Pass-2 6.0 9.1 5.6
f-0.975, Pass-3 8.9 8.6 5.4
f-0.975, Pass-4 7.1 7.0 4.9
f-0.975, Pass-5 6.2 7.1 6.7 7.9 4.6 5.1

Chapman
(NW):
f-0.850, Pass-1 12.1 11.9 5.3
f-0.850, Pass-2 6.3 6.0 2.7
f-0.850, Pass-3 3.0

f-0.925, Pass-1 11.8 11.8 5.1
f-0.925, Pass-2 6.3 6.0 2.7
f-0.925, Pass-3 3.0

f-0.950, Pass-1 11.5 11.6 5.0
f-0.950, Pass-2 6.2 6.0 2.7
f-0.950, Pass-3 2.9

f-0.975, Pass-1 10.9 11.1 4.7
f-0.975, Pass-2 6.0 5.9 2.7
f-0.975. Pass-3 2.7

(W):
f-0.850. Pass-1 1 1.1 9.7 4.2
f-0.850, Pass-2 5.8 4.9 2.2

f-0.925, Pass-1 10.9 9.5 4.2
f-0.925, Pass-2 5.8 4.8 2.2

f-0.950, Pass-1 10.7 9.3 4.2
f-0.950, Pass-2 5.8 4.8 2.2
-
f-0.975, Pass-1 10.1 8.7 4.1
f-0.975, Pass-2 5.5 4.7 2.3
56


time base of surface runoff equal to one day. The streamflow recessions
indicate that a time base of two to four days is more reasonable.
A sensitivity analysis was done on the Linsley equation to determine its
effect on determination of base flow volume (table 7). Changing the Linsley
exponent from 0.2 to minus 0.40 increases the antecedent recession (or time
base), N, from 1 to 2 days in stream W for 1983-1984. Using equation 20 to
calculate the time base, N, the program determines base flow from daily
streamflow values By changing the time base from 2 to 4 days, the total base
flow volume decreases from 15.5 to 13.6 inches. The best overall value for
the exponent for this data set, with respect to base flow values calculated by the
other methods, would be approximately -0.40.
The Rutledge program "PART", used in the streamflow partitioning
method, calculates a mean base flow volume based on the time base determined
from the Linsley equation. The program determines three integer time bases
(one less than and two greater than the Linsley value) and calculates daily base
flow for each time base. Curvilinear interpolation between the three time bases
was used to calculate a mean daily and total base flow volume. One output file
from PART called OUTPART, displays the time base, mean streamflow in
cfs/year and in./year, mean base flow in in./year, and mean base flow index.
The other output file, OUTP2, provides daily streamflow and base flow values
for use in plotting graphs.
In addition to the time base requirements, Rutledge used a threshold factor
to distinguish surface flow and interflow from base flow. The premise was if
57


Table 7 Effects on base flow of varying the Linsley exponent to meet the
antecedent recession requirement
Rutledge Antecedent Rtoesiion Sanshlvttv AnaVstt
N.V*

Stream Year I N Bate flew. In.
NV 9-84 -0.75 4 16.1
5 14.2
18.6
MV 83-84 0.60 t 17.3
a 16.7
4 15.1
MV 87-88 0.60 2 9.0
3 8.3
4 6.0
MV 89-90 0.50 2 18.3
a 16.9
4 15.8
W 83-64 0.50 3 14.9
4 13.6
5 12.8
W 87-88 0.50 3 7.7
4 7.2
6 7.1
w 89-90 0.50 3 13.4
4 12.6
5 11.4
MV 63-84 0.35 1 18.1
2 17.3
3 16.7
MV 83-84 0.40 2 17.3
3 16.7
4 15.1
W 83-84 0.40 2 15.5
% 3 14.9
4 13.6
MV 87-86 0.40 2 9.0
3 8.3
4 8.0
MV 89-80 0.40 2 18.3
3 16.9
4 15.8
W 87-86 0.40 2 7.8
3 7.7
4 7.2
w 89-90 -0.40 2 14.5
a 13.4
4 12.6
MV 83-84 -0.45 2 17.3
a 16.7
4 15.1
W 83-84 -0.45 2 16.5
3 14.9
4 13.6

58


streamflow varied between days by more than 0.1 log cycle (the threshold
factor), it was considered surface flow, not base flow. The reasoning for this
is based on Barnes' ground water recession equation:
Qt=QoKr (23)
Values for Kr frequently range from 0.96 to 0.99. If 0.98 is selected as an
average recession constant, and t = 5 days, then:
Qt=Qo(0.98)5
Qt = 0.904Qo (24)
Therefore, if Qt, the discharge after 5 days, is 90% or less than the initial
discharge, Q0, then base flow conditions are possible. A sensitivity study was
done on the threshold factor, f, to determine its effect on base flow volume.
Stream NW for 1983-1984 was arbitrarily selected, and f was varied from 0.08
to 0.15. The percentage difference in total base flow volume between f of 0.08
and f of 0.1 was 3%. The difference in volumes between f of 0.08 and f of
0.15 was 9%. Therefore, altering the threshold factor, f, was not significant to
the total base flow volumes.
The base flow volumes for each year calculated by the Rutledge program are
higher in stream NW than in stream W (table 6). This is expected because
streamflows are higher in stream NW which results in higher base flows. Base
flow volume is greater in the intermediate year, 1989-1990, than in the high
59


water year, 1983-1984 (table 6). However, for those same years the base flow
volume does not respond similarily in stream W. Base flow volume for stream
W in 1989-1990 was 15.4 inches compared to 16.7 inches in 1983-1984.
Streamflow Partitioning Method of the Institute of Hydrology fWahll
The Wahl program, developed to automatically use the Institute of
Hydrology method, required data be entered for complete water years. The
program aborted if one day was missing from the daily streamflow data.
Therefore, to obtain the base flow volume for the periods desired, some of the
calculations had to be done manually. It was possible to do this because one of
the output files listed all the turning points as well as their incremental base flow
volumes.
The results of the base flow calculations for both streams NW and W were
summarized in table 6. Different time bases were evaluated to test the
sensitivity of base flow to the time base. Base flow volumes increase as the
time base of surface runoff decreases (figure 18). All of the curves follow a
gradual increase until approximately day 180, where a sharp increase in base
flow occurs. Following the sharp increase the slope of all the curves gradually
increase again. The time base of surface runoff for basins NW and W are
between two and four days, similar to that determined using Rutledge's
program. It was unclear which time base most nearly represented the basin
conditions, therefore an average base flow volume was determined by
averaging the two, three and four day values.
60


Base flow
Day
Figure 18 Effect on base flow in the Wahl program of varying the time base of surface runoff.


The base flow values determined by Wahl's program for both streams were
lower than those determined by Rutledge's base flow program. This is due, in
part, to the Linsley antecedent recession requirement used by Rutledge. Even
when the exponent in the Linsley equation (equation 20) is adjusted the
Rutledge base flow volumes are still higher than the Wahl values. Graphically
comparison of the base flow curves of the Rutledge and Wahl partitioning
programs are shown in figure 19 and figure 20. For water year 1984, and
using a time base of three days, base flow determined from the Wahl program
are very similar to those determined from the Rutledge program (figures 19 and
20). Daily base flow values from the Rutledge program are calculated using
curvilinear interpolation, whereas in the Wahl program base flow curves
connect the minimum value in each five day section of streamflow values using
linear interpolation on a semi-log scale. Although the programs appear similar,
extended days where base flow values from the Rutledge program are
consistently higher than base flow values from the Wahl program results in
higher total base flow volumes calculated using the Rutledge program.
Digital Filter Method of Nathan and McMahon
The digital filter method developed by Nathan and McMahon evaluated
streamflow data using the filter and number of passes through the data.' The
program can handle incomplete data sets so it could be restricted to specific
periods of interest. Results of this method indicate that the base flow volume
decreases as the filter constant increases (table 3). Responses to altering the
62


o\
u>
Figure 19 Comparison of Rutledge and Wahl base flow values for NW stream, 1983-1984. The
Linsley equation, N=A(0-2\ was used to establish antecedent recession.


Q, cfs
stream, 1983-1984. The Linsley equation, N=Al-2), was used to
establish antecedent recession.


filter constant as well as the effect on base flow volume of varying the number
of passes are shown in figures 21 and 22. The most troublesome aspect of the
base flow curves occur where base flow intersects the streamflow hydrograph
at a high angle. The graphs clearly show base flow controlling the stream as the
stream receives precipitation.
Averaging each filter constant for 2 to 5 passes suggests that 0.850 might be
the best overall filter constant for the Mirror Lake data. The average base flow
volume for stream NW for 1983-1984 using the Nathan and McMahon method
is 13.4 inches as compared to 14.8 inches calculated by the Wahl program for
the same period. However, at a filter constant of 0.850, the base flow curves
do not appear to be representative of actual base flow curves (figure 21). The
base flow curve at two passes and a filter constant of 0.850 shows a rapid and
high response to every streamflow peak. The base flow curves for stream NW
for 1983-1984, representing filter constants of 0.950 and 0.975, appear to
underestimate the base flow buildup from November to January.
The base flow curves shown in figure 21 and figure 22 indicate a lag in
response to peaks in the streamflow hydrograph. The digital filter approach
was the only computer program analyzed herein that simulates actual ground
water behavior using the response lag.
Comparing the Nathan and McMahon program against the Rutledge and
Wahl programs for the three different water years, 1983-1984, 1987-1988,
1989-1990, indicate similar trends in all three methods. Average base flow
volumes for stream NW are higher in 1989-1990 than in 1983-1984 for all three
65




67


programs. The average for stream W for all three programs show 1983-1984
as the high base flow year followed by 1989-1990 and 1987-1988.
Digital Filter Method of Chapman
The results of applying the Chapman filter were shown in table 6. Graphs
of the performance of the base flow curve when changes are made to the filter
constant and number of passes are shown in figure 23 and figure 24. The
graphs indicate that if more than one pass is applied, base flow falls so far
below the streamflow hydrograph that it never discharges to the stream. The
graphs also show that as the filter constant increases from 0.850 to 0.975 the
base flow curves become more attenuated. What appear to be the most
reasonable base flow curves for stream NW for 1983-1984 are filter constants
between 0.925 and 0.950 with one pass. At a filter constant of 0.925 and one
pass, the total base flow volume calculated by the Chapman filter method is
11.8 inches. This compares well with the average value of 12.0 inches
calculated by the Nathan and McMahon method, but is lower than values
calculated by both streamflow partitioning methods.
The Chapman filter method is successful in eliminating the presence of base
flow during an increase in the streamflow hydrograph. However, for stream
NW for 1983-1984, at one pass and a filter constant of 0.925 parts of the
streamflow hydrograph that are considered surface runoff or interflow are
intersected by the base flow curve. See the week of December 15 in figure 23
for an example. Other sections of the same graph show no segments where the
68


SF -Pass=2
Pms=1 Pass=3
69


Jja/im
10
10
SF -Pasa*2
Pass*=l Pass3
Figure 24 -- Results of Chapman digital filter for NW stream, 1983-1984.
70



recession slope would indicate that base flow should have a strong presence.
The weeks surrounding March 1 and March 13, in figure 23, show periods
where base flow might be contributing all of the streamflow, but this is not
evident using the Chapman method.

71


CHAPTER 5
DISCUSSION
Determination of Recession Slopes
Recession slopes initially selected varied greatly between years and within
years. Differences in recession slope within years using the Knisel approach
can be partially explained by the technique itself. The K-line which passes
through the origin and maximum streamflow value from the data sets of
potential base flow values has a potential error of 1-5 degrees, which means that
data sets that might otherwise be eliminated from consideration as base flow
were included.
The applicability of the Knisel method is questionable for streams having
greatly variable discharge for short periods of time. The 61 basins Knisel
studied were located in the south-central United States. The basins ranged in
size from 5 to 500 sq. miles and had base flow for only part of the year.
Therefore, base flow recessions were easier to identify on streamflow
hydrographs. Mountain streams such as those at Mirror Lake have frequent
precipitation events, continuous base flow, and subsequently, few and shorter
base flow recessions. In any given year, a maximum of three to four potential
base flow recessions were identified on the stream hydrograph. Of those, data
sets that met the K-line test, two to three days in each data set were identified as
true base flow. Drawing a straight line through these days on the stream
hydrograph to represent base flow recession was inexact. A slight offset in the
line could represent errors in the recession slope of 15-35%. Considering the
72


potential for error, it is surprising that the averages of the Meyboom and Knisel
values for recession slope were close to one another (table 2).
Two important assumptions underlying the Meyboom method were: 1) the
straight lines connecting successive points of minimum stream discharge are
considered to approach true base flow conditions and, 2) ground water
recession ceases as soon as one of the three base flow components is affected
by recharge. Meyboom's study focused on a 460 sq. mile basin in Calgary,
Alberta, Canada. The base flow components he was concerned with were bank
storage, contact springs and artesian leakage. The mountain terrain of New
Hampshire does not lend itself to bank storage or artesian leakage.
Meyboom's first assumption, of connecting successive points of minimum
stream discharge, is usually applied following the seasonal streamflow peak. A
definite recession is evident at Mirror lake from mid-April to late August, 1988
(figure 11). If a straight line is drawn through successive minimum stream
discharges following the early April peak, the recession slope value is very
close to the average yearly recession number determined by the Knisel method.
Base flow recessions determined by the Meyboom method are easily
reproducible but must be drawn carefully. It is easy to connect minimum
stream discharges with straight lines, but the lines may represent surface runoff
or interflow recessions rather than true base flow recessions (figure 25). A little
practice in the technique can provide reliable base flow results.
The second assumption made by Meyboom, that ground water recession
73


Q, cfs
-t*.
basin characteristics.


ceases as soon as base flow becomes affected by recharge, is supported by
inspection of the stream hydrographs (figures 8, 9). A buildup in streamflow
volume under the hydrograph indicates the presence of recharge. This occurs at
Mirror Lake from September to April followed by a recession period lasting
from May until August.
Although the basin that Meyboom studied was 460 sq. miles and had a
gentle slope, the method he developed for determining recession slopes worked
well for the mountainous terrain at Mirror Lake. With the exception of stream
W for 1988, yearly recession slopes determined by the Meyboom method
compared well with the average slopes determined by the Knisel method(table
2). The low values using the Knisel method for stream W for 1988 may be a
reflection of the method's inability to handle low flow years. The Meyboom
method was insensitive to high, medium, or low flow years and consistently
worked well.
Comparison of Instantaneous Recharge Method and Constant Recharge
Method of Rorabaugh
The instantaneous recharge method of Rorabaugh is a step by step
accounting of ground water recharge from each streamflow peak. Accounting
for each peak as a contributor to recharge would seem to overestimate total
recharge, but the results do not support this conception. Recharge values
determined from the constant recharge method are higher than those determined
from the instantaneous recharge method.
75


Ground water recharge estimates determined from Rorabaugh's methods
should not be applicable to basins such as those at Mirror Lake because of the
restrictive assumptions made by Rorabaugh that led to the development of
equation 9. Some of these are: 1) the aquifer is uniform in shape, isotropic, and
homogeneous, 2) the initial water level is everywhere horizontal prior to
recharge, 3) the stream fully penetrates the aquifer, and 4) sufficient time has
passed so that the water level is declining exponentially with time.
The basins of Mirror Lake are underlain by unconsolidated glacial drift
consisting of sandy till, sand, gravel, and numerous cobbles and boulders.
This geologic material would imply an anisotropic, nonhomogeneous aquifer
system that does not meet the assumption of 1. Assumption 2 was not valid for
Mirror lake because the land slopes of basins NW and W were 21% and 12%,
respectively, therefore the water table would not be horizontal. The streams do
not fully penetrate the aquifer, therefore assumption 3 does not apply.
However, it could apply if only the ground water system above the base level of
the stream is considered. Finally, exponentially declining water levels over time
occur infrequently at the NW and W basins. Despite the inability of the Mirror
Lake area to meet the assumptions needed to use the instantaneous recharge
method of Rorabaugh, the values of recharge obtained seem to be reasonable
and comparable to the other methods used in this study.
The eight assumptions that went into the development of the Rorabaugh
instantaneous recharge method also apply to the constant recharge method. The
76


same questions involving the validity of the assumptions for hillslope terrain
need to be addressed. The same inability to meet the assumptions exist for the
constant recharge method as for the instantaneous method. In addition,
application of the constant recharge method relies on the condition where dh/dt
= C, which requires a constant rise in the water table associated with ground
water recharge. For the periods investigated for the two basins, September -
April, the assumption of dh/dt = C was reasonable for the eight months of
recharge.
The Rorabaugh constant recharge method uses a type curve similar to those
developed by Theis, as well as by Jacob. If dh/dt = C is valid, equations 16
through 18 can be used to develop the dimensionless type curve, figure 5,
which "expresses the time-discharge relation in response to a constant rate of
recharge" (Rorabaugh, 1963, p. 435). The best test of its applicability is the
curve fit on the stream hydrograph. Figures 26 and 27 show the average curves
for both the NW and W streams, respectively. The strength of the method is
that it actually resembles the gradual ground water recharge buildup in the early
stages, as well as sustaining the recharge during the peak flow periods of March
and April. The constant recharge method smooths the streamflow peaks and
valleys to provide a recharge calculation not dependent on individual streamflow
events. The constant recharge method does not specifically consider each
streamflow peak as contributing to recharge. Instead, the rising and falling
limbs of the stream hydrograph are used to estimate the best fit curve
77


Figure 26 -- Rorabaugh constant recharge type curves for stream NW, 1987-1988.
U


-J
VO


10
Mirror Lake W
1983-1984
o.o Ur
I I - I I M I i I I
oo
CO m tn Tf
00 oo oo oo oo oo

o >4 o Ot r-4
n m n m N n

o ^4 N m
*4 ^4
^0.01
Figure 27 Rorabaugh constant recharge type curves for stream W, 1983-1984.


representing recharge.
The results from the Rorabaugh constant recharge method were comparable
to both the instantaneous method and Rutledge's automation of the
instantaneous method, which will be discussed later. Proper application of the
constant recharge technique requires more understanding of hydrology. The
curves simulating ground water recharge can differ slightly among trials,
representing significant differences in total ground water recharge. As an
example, figure 28 for trials 1 and 3 of stream W for 1989-1990 indicates
recharge values of 22.6 and 15.8 inches, respectively. However, the actual
differences in placement of the curves are not as significant as the 6.8 inch
recharge difference might suggest.
With the exception of stream W for 1989-1990, the instantaneous recharge
values were within two inches of the average constant recharge values (table 3).
The results compared well, especially for the instantaneous recharge method.
The exception to this is the 15.2 inches of recharge calculated by the
instantaneous recharge method for stream W for 1989-1990. Instant recharge
was 3.6 inches less than the average calculated by the constant recharge
method. Considering the errors associated with the methods used, a 24%
difference in the two values is within acceptable boundaries.
80


Figure 28 Rorabaugh constant recharge type curves for stream W, 1989-1990.


Comparison of the Automated Instantaneous Recharge method of Rutledge with
the manual use of the Instantaneous and Constant Recharge methods of
Rorabaugh
Rutledge automated Rorabaugh's manual instantaneous recharge method,
therefore it is of interest to compare results of the automated method with the
manual methods. For the Rutledge program to calculate recharge, an antecedent
recession, the time after a streamflow peak when ground water discharge
dominates stream flow was required. The effects on recharge of using
antecedent recession values of 1 to 4 days is shown in table 3. As would be
expected, the recharge values decrease as the number of days for surface runoff
increases. If the average recharge value from the automated method for each
stream is compared with the values from the manual method for each stream,
the differences are less than 21%. Differences in the values from the automated
versus the manual instantaneous recharge method are a result of calculation
procedures. For the automated method, the antecedent recession requirement
determines where the recession slope is placed, regardless of the size of the
streamflow peak. The manual method is more subjective, and recession slopes
are placed at the end of stream peaks considered to be contributing to recharge.
Manually interpolating discharge values from the stream hydrograph has errors
as much as 15%.
A statistical t-test was performed to test if recharge determined by the
automated approach versus the manual approach of Rorabaugh's instantaneous
recharge method are statistically similar. A t-test determines whether or not two
normally distributed populations are statistically similar (Snedecor and Cochran,
82


1971, p.60). A normal distribution within the two data sets was assumed so
that incremental recharge from the same streamflow peaks could be compared in
the two methods. An average time base, or antecedent recession, of 3 days was
used for the Rutledge automated method. The peaks used for the comparison as
well as the results from the t-test are shown in table 8. Although the sample
size is small, 15 sets of recharge values, the t-test results show that only 4.37%
of the data lie further from the center than the absolute value of 2.216.
Therefore, there is no statistically significant difference between the recharge
values determined by the automated approach of Rutledge and those determined
by the manual approach.
A linear regression was performed on the same data set (table 8) as an
additional check on the relationship between the automated and manual
approaches. The purpose of the scattergram, figure 29, was not to calculate a
manually derived recharge value from an automatically derived one, or vice
versa, but to evaluate the coefficient of determination, R2, which is another way
of appraising the similarity of the relation between two variables. Snedecor and
Cochran (1971, p. 176) describe R2 as "the proportion of the variance Y that can
be attributed to its linear regression on X". An R2 =1.0 represents a perfect
correlation between X and Y. The R2 for the Rutledge and Rorabaugh data was
0.849.
Rutledge also compared the manual use of the instantaneous method against
his automated method to test for differences in results produced by
83


Table 8 t-test for the Rorabaugh instantaneous and the Rutledge automated
recharge methods.
Manual vs. Automated t-test Comparison
Time Base = 3 days

Stream Date Automated Manual
NW 11/11/83 0.206 0.396
NW 11/16/83 0.289 0.368
NW 11/18/87 0.416 0.650
NW 2/2/88 0.849 0.765
NW 10/2/89 0.237 0.481
NW 10/11/89 0.196 0.425
NW 1/19/90 0.763 0.990
NW 2/23/90 1.096 0.990
W 11/16/83 0.304 0.526
W 11/25/83 1.240 1.220
W 11/18/87 0.420 0.747
W 3/9/88 0.716 0.498
W 1/18/90 0.361 0.470
w 1/25/90 1.482 1.490
w 2/9/90 0.599 0.550





Paired t-Test
xl automated, in.
ylrmanual, in. -

Degrees of freedom mean (x-y) Paired t value Probability (2 tail)
14 -0.093 2.216 -0.0437


84


9 .7171 .242, R-ffMr4: .141
methods.


different workers (Rutledge and Daniel, 1993). His study showed that the
variation in recharge estimates among the four workers using the manual
instantaneous method ranged from 13 to 22 percent. These differences were
considered statistically significant and reflected the subjectivity in methodology
between the workers.
The automated approach to determining recharge removes some of the
subjectivity associated with the manual approach. However, determining the
antecedent recession for hillslope basins is difficult and the automated approach
relies on the user to determine this, if the calculated value is unacceptable. The
best method for determining ground water recharge is one that provides
consistent results that can be repeated and are comparable with the other
methods of hydrograph analysis. When the pros and cons of both the
automated and manual approach to using Rorabaugh's instantaneous recharge
method are considered, the Rutledge's automated approach is probably better
because it is objective, reproducible, and fast.
Results of the manual use of the constant recharge method and Rutledge's
automated approach to the instantaneous recharge method were shown in table
3. Comparing average recharge values between methods for basin NW for each
year shows a difference less than 2 inches. The same is true for basin W.
Although the constant recharge curves logically resemble the buildup of ground
water through recharge better than the automated instantaneous method, proper
placement of the curves requires the ability to see a constant recharge pattern in
86


streamflow hydrographs.
Another method of determining ground water recharge was done through
watershed modelling. The U.S. Geological Survey model PRMS (precipitation
runoff modelling system) is a surface runoff model that incorporates ground
water recharge. The model was run on the Mirror Lake basins. Basin NW was
divided into 11 subsections and basin W into 10 subsections. The model
calculated recharge for each subsection and determined an overall recharge
based on weighted averages. The results of using PRMS are shown in table 9
(Sean Mallory, 1992, personal communication).
Table 9 Recharge determined by using PRMS for Mirror Lake
Basins NW and W.
Basin Year Recharge, in.
NW 1983-84 18.9
NW 1987-88 10.5
NW 1989-90 20.5
W 1983-84 19.4
w 1987-88 10.7
w 1989-90 21.1
There is a 10 percent margin of error associated with the recharge estimates of
the PRMS model. The model results compare well with the recharge values
shown in table 3. The recharge values determined by PRMS verify the methods
used in this study for obtaining ground water recharge from streamflow
hydrographs.
87


Comparison of Methods used to determine the Base Flow Component of
Streamflow
Evaluation of methods designed to determine the base flow component of
streamflow was done to test the assumption that ground water discharge (base
flow) is a minimum estimate of ground water recharge. Realizing that water
that recharges ground water will not all reach the stream because some will be
lost to deep ground water and some to ET. However, if evaluated for only
winter months, the losses of ET should be minimized.
Comparison of Rutledge and Wahl Automated Streamflow Partitioning
Methods
Results from the computer programs developed by Rutledge and Wahl to
calculate total base flow volume by streamflow partitioning were presented in
table 6. The base flow values calculated by the Rutledge method, calculated in
part by using the Linsley antecedent recession requirement to determine the time
base of surface runoff, equation 20, are much higher than the corresponding
base flow values determined by the Wahl program for the Institute of
Hydrology method. Equation 20 was developed for large, gently sloping
basins and does not apply as well to the mountainous terrain of New
Hampshire. Therefore, a sensitivity analysis was performed on the exponent of
equation 20 to test its' effects of the time base (antecedent recession) on
calculation of base flow. Knowing from the stream hydrographs that time of
surface runoff is between 2 and 4 days, a value of x=-0.40 (where x=exponent)
in the Rutledge program "PART" gave results closest to the other base flow
88


methods tested (table 6 and table 7). The Rutledge program calculated base
flow for the time base determined by the exponent as well as the next two days.
If x, the exponent, was greater than -0.4, base flow values for 1,2, or 3 days
were calculated. If x was less than -0.45, N was calculated for 3,4, or 5 days,
or higher. An x value of -0.4 evaluated base flow for time bases of 2,3, and 4
days for both the NW and W basins.
If the modified equation 20 is used, that is, N=A('-4), and an average time
base of 3 days is selected from table 6, the base flow values are within 2 inches
of the average values determined by the Wahl program, for all the years
investigated in the study. Figures 30 and 31 shows the relationship between
base flow values for the two different methods. Although the results of the
methods appear very similar there are fundamental differences. The Rutledge
method, as previously mentioned, determines the start of base flow based on a
calculated time base of surface runoff and threshold value. The threshold value
was held constant at 0.1 log cycle, and if exceeded was considered streamflow
or interflow. The Wahl program uses the British Institute of Hydrology method
to determine turning points, that when connected by linear interpolation become
the base flow curve. The threshold value used in the Wahl program was also
maintained at 0.1 log cycle. The Rutledge method calculates daily base flow
values that form a smoother base flow curve and tend to give total higher base
flow volumes than those calculated using the Wahl program.
To further establish the relationship between the Rutledge streamflow
89


Q, cfs
stream, 1983-1984. The Linslcy equation, N=Al"-4), was used to
establish antecedent recession.
5/30/8^


Figure 31 Comparison of Rutledge and Wahl base flow values for W
stream, 1983-1984. The Linsley equation, N=A<- 4>, was used to
establish antecedent recession.



partitioning method and the Institute of Hydrology method as programmed by
Wahl a linear regression was performed using data from stream NW for 1983-
1984. The turning points selected by the Wahl program were matched to the
Rutledge base flow values on the same dates. A total of 47 matched pairs were
found (table 10) and regressed as shown in figure 32. The coefficient of
determination is 0.985, representing a statistically significant relationship
between the two methods. A t-test was not performed because the sample size
was too large. Beyond 30 degrees of freedom the t-distribution approaches the
normal distribution, the t-multiple decreases and the t-test loses significance
(Neter and Wasserman, 1966, p. 329).
The streamflow partitioning methods of Rutledge and the Institute of
Hydrology (Wahl) both rely on finding a starting point for base flow following
a peak in the hydrograph. There is no physical basis to support the argument
that the time base of surface runoff, along with the threshold factor, consistently
indicate the beginning of base flow to the stream. If this were true, a single
linear plot representing the base flow recession slope would intersect the
hydrograph every time the time base requirement was met. The four plots
comparing the Rutledge and the Institute of Hydrology (Wahl) methods, figures
19 and 20 and figures 30 and 31, indicate base flow is frequently attributed to
periods that actually represent surface runoff or interflow. Regardless which
time base equation is used, N=A(0-2) or N=A('0-4), both programs overestimate
the base flow contribution. A week on either side of December 14, 1983, for
92