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This is to certify that the

thesis entitled

MORPHOLOGIC AND LITHOLOGIC INFLUENCES
ON RECHARGE IN A GLACIATED BASIN

presented by

Mark Alan Petrie

has been accepted towards fulfillment
of the requirements for

Masters degree in Geological Sciences

M:ogfl A '~ Apt/1’6”“

MM'Or professor

Date @952]; /?57

0-7639

MS U is an Affirmative Action/Equal Opportunity Institution

 

MSU

 

 

 

RETURNING MATERIALS:
Place in book drop to

umumas remove this checkout from

.—c—- your record. FINES will
be charged if book is
returned after the date
stamped below.

 

3 13927199;
SEP 2 0 200

CD

 

 

 

 

 

MORPHOLOGIC AND LITHOLOGIC INFLUENCES
ON RECHARGE IN A GLACIATED BASIN

By

Mark Alan Petrie

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Geological Sciences

l98h

ABSTRACT

MORPHOLOGIC AND LITHOLOGIC INFLUENCES
ON RECHARGE IN A GLACIATED BASIN

BY

Mark Alan Petrie

Estimates of recharge to the drift are calculated for several
sub-basins of the Upper Grand River Basin, using four methods of
hydrograph separation. Comparrison with flow duration ratios reveals
that the method in which all peak flows are separated out as surface
runoff provides the best estimate of recharge. The resulting recharge
values range from 3.95 to 5.50 in/yr for a water year of near normal
precipitation, and from 2.l0 to 8.32 in/yr for all extremes of yearly

precipitation.

The above recharge estimates were compared with several
morphologic parameters and with basin permeability estimates derived
from bore hole data. The comparrisons indicate that basin recharge
amounts depend primarily upon surface relief and permeability within

the upper five feet of the drift.

ACKNOWLEDGEMENTS

I would like to thank my committee members for their suggestions and
criticisms; Dr. Dave Long for reading my work despite the lack of
chemical data, and especially Dr. Del Mokma, for making the it to the
defense the day after his daughter Rebecca Ann was born. I owe a
great debt to Grahame for his patience and sacrifice (taking valuable
time out from sabbatical is no small concession), and for providing
support when my enthusiasm waned. Thank you, Billy, for leading me
(by the nose) through the abyss of the computer world. And special
thanks to Cathy, for helping me maintain my sanity in a world too
often conspiring to drive a poor boy wild.

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

INTRODUCTION

THE UPPER GRAND RIVER BASIN

BASIN RECHARGE

PRECIPITATION

RECHARGE VERSUS FLOW DURATION .

FACTORS INFLUENCING BASIN RECHARGE

BASIN MORPHOLOGY

AVERAGE DRIFT PERMEABILITY

VEGETATION

PRECIPITATION .

RELATION BETWEEN BASIN RECHARGE AND BASIN PARAMETERS

BASIN MORPHOLOGY

AVERAGE DRIFT PERMEABILITY

CONCLUSIONS

FURTHER WORK

APPENDICES

APPENDIX A -- MORPHOLOGIC PARAMETERS .

APPENDIX B -- SURFACE AREA RATIO ALGORITHM

APPENDIX C -- SOIL MANAGEMENT GROUP VALUES

BIBLIOGRAPHY . . . . . . . . . . . .

. 3]

.35

Figure
Figure

Figure

Figure

LIST OF FIGURES

Study Area
Bore Hole Locations

Soil Management Group Versus Average
Permeability. 0 - 5 Feet

(a) Circularity Ratio vs. Basin Recharge.

(b) Basin Permeability, 0 - 5 Feet vs.
Basin Recharge . . . .

. 23

LIST OF TABLES

Table l. Recharge (in/yr)
And Flow Duration Ratios

Table 2. Correlation Coefficients; Recharge Rates
Versus Flow Duration Ratios for
Water Year l956-57

Table 3. Recharge Rates, Morphologic And Permeability
Parameters . . . . . . . . . . . .

Table A. I958 Data on Land Use in Michigan .

Table 5. Coefficients of Correlation Between Each
Parameter and Basin Recharge

Table A. Stream Orders For The Sub-basins . .

INTRODUCTION

Long term recharge to groundwater systems depends on several
environmental and physical parameters. These include: I) amount and
type of precipitation (Mls, I980), 2) drainage characteristics of the
soil (Powell 8 Kirkham, l97h; Baker 5 Mace, I976; Corbett, I979),
3) vegetation cover (Coleman, I953: Bosch 8 Hewlett, I982), A) basin
morphology (Gupta, Waymire 8 Wang, I980). and 5) regional geology
(Walton, I970; p. 370). The relative influence that these parameters
have on recharge, however, is generally poorly understood and has been
especially difficult to evaluate for heterogeneous glaciated basins

(Walton, I965).

The purposes of this paper are; I) to estimate the recharge
occurring within several small glaciated basins in south-central
Michigan, 2) to quantify two major basin parameters (basin morphology
and permeability) for each of these basins, and 3) to determine which

of the two parameters has the greater influence on basin recharge.

THE UPPER GRAND RIVER BASIN

The Upper Grand River Basin lies in the south-central portion of
Michigan‘s lower penninsula and covers approximately 2,8h0 square
miles (7,356 square km). It is composed of nine sub-basins (Figure
I), each of which has slightly varying physical characteristics. In
general, the surficial material throughout the Upper Grand River Basin
range from nearly flat, clay rich glacial-lake sediments in the north
to more hilly morainic and outwash deposits in the south (Martin,
I955). The thickness of the drift ranges from 0-50 feet (O-l5 m) in
the southern part of the basin to 350-b00 feet (l07-l22 m) in the

northern part (Michigan Water Resources Commission, I96I).

The uppermost bedrock unit underlying the drift is predominantly
the Saginaw Formation (Pennsylvanian: Vanlier et al., I973). It is
composed chiefly of interbedded sandstone and shale, with occasional
thin beds of limestone and coal. It's thickness ranges from 0 feet in
the south to over 500 feet (I52 m) in the north. In the northern half
of the basin, low areas on the Saginaw surface contain younger
Pennsylvanian sandstones and shales of the Grand River Formation which
are up to l25 feet (38 m) thick in places (Kelly, I936). In most
areas both the Saginaw and Grand.River Formations are hydraulically
connected and act as a single aquifer (Vanlier et al., I973). Near
the southern and eastern borders of the basin the Saginaw is
completely eroded away, exposing older Mississippian limestones,

sandstones and shales.

 
 
  
   
 
  
  

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BASIN RECHARGE

Since changes in groundwater storage tend to be nearly zero
(”insignifigant”) when calculated over the course of an entire water
year, recharge to an aquifer can be found by separating groundwater
runoff (”discharge to the stream”) from total runoff for a water year
(Walton, I970; p. I83). This was done for each sub-basin of the Upper
Grand River Basin for water years of below-, near- and above normal
precipitation (U.S. Dept. Comm., I950-I980). Choosing three years of
different inputs to the system allows observation of its response to

all extremes.

The estimates of recharge were achieved using four different
methods of hydrograph separation. The first three, Local Minima (L0),
Fixed Interval (FI) and Sliding Interval (SL) are described by
Pettyjohn 8 Henning (I979). The fourth, Hand Separation (HA), is
based upon a method described by Walton (I970). In all four methods a
groundwater runoff curve is drawn under the discharge hydrograph
curve: the volume below this line is groundwater runoff and the

remainder above it is surface runoff.

The results of each hydrograph separation are presented in Table
I, together with flow duration ratios calculated for each of the

sub-basins. These ratios were obtained using the equations:

Q10 5 Q25 ‘1'
Q10/90 = -——- Q25/75 = -—-
Q90 Q75
where Q10, Q25, Q75 and Q90 are the discharges equalled or exceeded 10,

25, 7S and 90 percent of the time, respectively.
PRECIPITATION

The calculated recharge for the 9 sub-basins and the overall
basin derived from the four separation techniques are shown in Table I
for the water years of below-, near-, and above normal precipitation.
It is evident fran the data that the recharge estimates vary least
among the different separation techniques for the water year of normal
precipitation (1956-57). In contrast, the variations IFI recharge
estimates for the sub-basins are greatest for both the above- and below

normal precipitation years (1955-56 and 1961-62).

As expected, recharge values tend to be greatest for the year of
above normal precipitation, 1955-1956 (Table I), and are generally
least for the year of below normal precipitation (1961-62). In several
sub-basins (Jackson, Eaton Rapids, Sloan Creek, Deer Creek, Red Cedar,
Lansing and Portland), however, the recharge values from some of the
separation techniques are less in the year (fl: normal precipitation
(1956-57) than those for the year of below normal precipitation (1961-
62). This may be the result of soil moisture deficit affecting
infiltration rates during periods of low precipitation (Bouma, I980;

Rao, Tao 8 Rukvichai, 1980).

TABLE I. RECHARGE (IN/YR) AND FLOW DURATION RATIOS

 

 

 

WATER SEPARATION METHOD RATIOS
BASIN YEAR LO FI SL HA 010/90 025/75
l955-56 8.21 8.67 8.70 8.30 2.96 1.63
JACKSON l956-57 9.85 5.90 5.99 5.38 2.06 1.56
1961-62 9.89 5.59 5.61 5.98 2.11 1.50
1955-56 8.32 9.32 9.28 8.99 2.85 1.66
EATON I956-57 9.87 5.59 5.59 5.12 2.32 1.72
RAPIDS 1961-62 5.59 5.78 5.88 5.12 2.60 1.57
1955-56 5.33 5.63 5.98 5.27 9.57 2.11
DEER l956-57 3.09 3.72 3.72 9.19 9.21 2.58
CREEK 1961-62 3.86 9.95 9.99 9.79 9.26 2.07
1955-56 9.60 5.08 9.89 9.81 9.79 3.03
SLOAN l956-57 2.98 3.32 3.90 3.91 6.69 3.90
CREEK 1961-62 2.89 3.53 3.96 3.88 5.61 2.29
1955-56 5.56 7.39 7.33 6.68 9.21 2.01
RED 1956-57 3.95 9.87 9.96 9.72 3.13 2.02
CEDAR 1961-62 9.07 9.28 9.97 9.18 2.62 1.60
1955-56 6.95 8.98 8.92 7.10 3.36 1.78
LANSING 1956-57 9.56 5.99 5.98 9.99 2.67 1.92
1961-62 5.12 5.27 5.90 9.83 2.61 1.55
1955-56 7.29 8.70 8.72 7.99 3.19 1.72
PORTLAND 1956-57 9.77 5.65 5.67 9.98 2.73 1.87
1961-62 5.92 5.61 5.71 5.10 2.95 1.95
1955-56 6.13 8.17 8.23 8.15 3.86 1.90
LOOKING- 1956-57 5.21 6.95 6.92 6.28 3.10 2.09
GLASS 1961-62 9.70 9.85 9.96 9.91 3.79 1.61
1955-56 5.88 8.90 8.98 8.99 5.99 2.58
MAPLE 1956-57 9.35 5.56 5.56 5.99 3.86 2.79
RAPIDS 1961-62 2.10 5.06 5.00 9.91 5.99 1.93
1955-56 7.16 9.09 9.18 7.37 3.59 1.68
IONIA 1956-57 5.50 6.39 6.39 5.19 2.88 1.88
1961-62 9.79 5.90 5.96 9.81 2.71 1.93

Note: l955-56 is the above normal-, I956-57 near normal-,
and l96l-62 below normal precipitation year.

 

Because of these inconsistancies, recharge values for the years
of above- and below normal precipitation were not used in this
investigation to define the general relationship between sub-basin
physical parameters and sub-basin recharge. Only the water year
I956-57 was used in the analysis, because fewer interferences are

active during years of near-normal precipitation.

RECHARGE VERSUS FLOW DURATION

Chow (1969; p. 19-92 to 19-99) has shown that both the discharge
hydrograph and the flow duration curve of a basin are closely related.
It can be concluded, therefore, that the separation method which is in
closest agreement with the flow duration characteristics of a stream
probably best reflects the recharge characteristics of a basin. Table
2 lists the correlation coefficients of recharge (in/yr) versus the
flow duration ratios 010/90 and 025/75 for all of the sub-basins in
the Upper Grand River Basin. It is evident from Table 2 that the
recharge values obtained using subroutine L0 correlate much better
with flow duration ratios than do the values obtained using the other
subroutines. This would suggest that recharge calculated by L0
probably provides the best estimate for recharge within each of the

sub-basins.

In Table 3, both the amount of groundwater runoff as percent of
total runoff and the recharge rate calculated by L0 are shown, for
each of the nine sub-basins as well as the whole basin. The basin
areas and mean daily discharges are also given. From the data it is

evident that Jackson, Eaton Rapids, Lookingglass and lonia sub-basins

have generally high recharge rates (9.85 to 5.50 in/yr), while Sloan
Creek, Deer Creek and Red Cedar sub-basins have generally low recharge

rates (2.98 to 3.95 in/yr).

TABLE 2.

CORRELATION COEFFICIENTS;
RECHARGE RATES VERSUS FLOW DURATION RATIOS
FOR WATER YEAR l956-57

 

SEPARATION
RATIO METHOD
L0 Fl SL HA
010/90 -.893 -.755 -.761 -.679
025/75 -.811 —.697 -.706 —.589

It appears that the very small drainage areas of Deer Creek and
Sloan Creek sub-basins (16.3 and 9.39 sq.mi.) result in artifically
low recharge estimates. This is probably because most precipitation
enters into the stream channel before it has time to infiltrate.
Excluding these two sub-basins, the calculated recharge values in the
eight remaining sub-basins range from 3.95 to 5.50 in/yr. Previous
investigations have reported similar recharge values: Firouzian (1963)
used flow net analysis to calculate an average recharge rate of
9.8 in/yr for the drift in Ingham County (the Lansing metropolitan
area lies in the NW corner of the county in Figure I); based on an
analog model, Vanlier et al. (1973) estimated 9.0 in/yr of recharge to
the drift in Ingham, Eaton and Clinton Counties (these three counties

surround the Lansing metropolitan area).

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FACTORS INFLUENCING BASIN RECHARGE

BASIN MORPHOLOGY

The following morphologic parameters were determined for each
sub-basin in the Upper Grand River Basin following the methods
described by Morrisawa (I968): stream frequency (Fs), bifurcation
ratio (Rb), form ratio (Rf), circularity ratio (Rc), elongation ratio
(Re) and relief ratio (Rr). The first two parameters quantify the
sub-basin drainage characteristics while the others define the shape.
The methods of quantification are briefly discussed in appendix A, and
the values of these parameters are shown in Table 3. Note that no
stream frequencies or bifurcation ratios are reported for the two
smallest sub-basins, Deer Creek and Sloan Creek. 0n the base map
scale (Figure l) these sub-basins have no tributaries, which makes
these two ratios meaningless. In addition to these, surface roughness
was quantified by calculating the ”surface area ratio” (Rs), following

the procedure presented in appendix B.

While no clear pattern is evident in the morphologic data shown
in Table 3, there are some general trends. Stream frequencies are
fairly consistant among the sub-basins except for Maple Rapids, which
has an unusually high value. Jackson and Red Cedar sub-basins, on the

other hand, have relatively low values. The bifurcation ratios also

are about the same for each of the sub-basins except for the low value
for Jackson sub-basin. In the case of Jackson sub-basin, the low
stream frequency value and bifurcation ratio may be related to a high

water table which is evidenced by large areas of marshland (Figure l).

The high stream frequency value for Maple Rapids sub-basin is
probably due to the local low relief (surface area ratio of 1.21),
while the low stream frequency for Red Cedar sub-basin probably
reflects the trellis drainage pattern related to the parallel

Charlotte and Lansing moraines (Martin, 1955).

In general, the highest shape parameter values occur in Jackson
sub-basin and the lowest in Lookingglass sub-basin. The Portland
sub-basin, not the Lookingglass, has the lowest circularity ratio
(Rc), which is probably due to the sharp westward bend of the
sub-basin boundary near the gaging station at Portland. If this bend
were less sharp the Portland sub-basin Rc value would probably
increase signifigantly. The surface area ratios (Rs), however, do not
follow the same general trend of the shape parameters. The Ionia and
Portland sub-basins have high Rs values while the two smallest

sub-basins, Deer Creek and Sloan Creek, have the lowest values.

AVERAGE DRIFT PERMEABILITY

The permeability of the drift underlying each sub-basin in the
study area was estimated using the data set of water- and oil well
logs shown in Figure 2. This data set is part of a computer file
established for the National Coal Resources Data System (NCRDS, 1980),

and includes information on thickness- and texture of each drift and

11

 
  

UPPER GRAND RIVER BASIN

   

       

SUB-BASIN BOUNDARY

 

JACKSON 1m 9“,”
EA'ON EAP‘DS Em — — _
DEER CREEK ’DCI —
SLOAN :REH vs" —
ED CEDAR RC1 —...._...._
\ANSI c .a; - _____
annrgann Ian __ __
‘DO'INGSLA‘SS O I ................
MAPLE RADIOS may —
DNIA ‘Dl __

STATUTE MILES
5 0

 

S I .5
”- Tad—In" _
5 a I 20 25

10 as
KILOHETERS

Figure 2. Bore Hole Locations.

12

bedrock unit penetrated.

The drift permeability was estimated from the Iithologies
reported in the first 5-, IO- and 15 feet as well as the whole drift
thickness reported for each drill hole. Drift Iithologies were
grouped into three categories and were assigned a correponding value
for permeability; 7.0 in/yr for clay, 38.5 in/yr for sand and clay,
and 70.0 in/yr for sand and gravel. These values are based on
permeability values used in a finite element model of recharge through
the drift in the Lansing metropolitan area (Kehers et al., 1983).

This area lies near the center of the Upper Grand River Basin (Figure

l).

A weighted average permeability for each point was produced by
multiplying the thickness of each drift unit in a well by the
appropriate permeability value, then adding the results and dividing
by the sum of the thicknesses. The resultant values were then summed
and divided by the number of wells in the sub-basin to achieve an
average sub-basin permeability. The results of these calculations are

shown in Table 3 above.

To test the validity of the above calculations, county- and
township-wide average permeabilities compiled from well data were
compared with county- and tdwnship-wide average Soil Management Group
(SMG) values. In theory, there should be a definite correlation
between these values since SMG reflects soil permeability (Mokma 8
Robertson, 1976). These comparrisons are presented in Figure 3, and

the data are tabluated in appendix C.

13

SMG (WITH MUCK)

SMG (WITHOUT MUCK)

4.0

35

3O

25

40

35

10

25

 

O OMMnth.

A Eoton Co.

0 Ingham Co.

E] Jackson Co.

‘7 Shiowouoo Co.

 

 

 

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+
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+
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+ + +
+
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+ +
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11’} 1 fl 1 T 1 1
20 30 40 50 60

AVERAGE PERMEABILITY, 0-5 FEET

Figure 3.

Average Permeability, 0 - S

(a) Coefficient of Correlation
(b) Coefficient of Correlation

(INCHES /YEAR)

19

Soil Management Group Versus

Feet.

+0.653
+0.796

It is evident from the correlation coefficient in Figure 3
(0.653) that the permeability values calculated from well logs are
fairly reliable indicators of actual basin permeability. Using the
average SMG values which exclude muck soils provides an even better
correlation coefficient (0.796). This is probably because none of the
wells used to calculate permeability are located in muck soils. Given
this good correlation, the lack of data coverage in Figure 2 can be
considered insignifigant, because the soil associations reported in
county soil surveys are continuous across the boundaries from
adequately to inadequately covered areas. This suggests that the
calculated permeabilities for these sub-basins (Red Cedar, Lansing,
Portland, Maple Rapids and Ionia) represent fairly accurately the

whole sub-basin values.

VEGETATION

There is currently no compiled data on vegetation distribution in
the Upper Grand River Basin. However, a qualitative survey of areal
photographs of the 9 counties that lie either totally or partially
within the Upper Grand River Basin (Table 9) reveals a generally even
distribution of forest and pasture. It is therefore reasonable to
assume that the broad divisions of vegetation in Table 9 can be

extended to the sub-basins.

From the data in Table 9 it is evident that, in each of the
counties (and thus in each sub-basin), 2/3 of the area is generally
cropland, 1/9 is forest and pasture, and the remainder is urban land,

water, marsh land and others (U.S. Soil Conservation Service, 1968).

Although Montcalm and Ionia counties show slightly more than 25%
forest and pasture, most of this occurs outside the study area. It
appears, therefore, that vegetation, being generally similar among
sub-basins, has little effect on basin recharge and can be considered

insignifigant in this study.

PRECIPITATION

The recharge rates estimated by hydrograph separation seem to
indicate that recharge and precipitation vary directly. As was
previously noted, however (page 5), there are several inconsistancies
in the data (Table I) that make an assessment of the true relationship
between precipitation and recharge difficult to accomplish with any

degree of certainty.

TABLE 9. 1958 DATA ON LAND USE IN MICHIGAN*

 

(1) PERCENT OF COUNTY TOTAL

THOUSANDS FOREST, (2) (3)
COUNTY OF ACRES CROP PASTURE URBAN OTHER
Clinton “365.99 72.0 16.6 9.1 7.3
Eaton 362.88 63.2 23.2 5.5 8.1
Gratiot 362.29 70.5 20.9 3.0 5.6
Ingham 357.76 61.6 15.9 10.8 11.7
Ionia 368.00 55.9 32.0 3.1 9.5
Jackson 951.20 99.3 20.0 9.8 20.9
Livingston 365.99 98.9 23.9 6.9 21.3
Montcalm 955.68 56.9 36.1 1.6 5.9
Shiawassee 395.60 69.7 18.9 5.5 6.9

* After The Michigan Conservation Needs Inventory Of
1968 (U.S. Soil Conservation Service, 1968).

Notes:

I. The acreage listed excludes water bodies in excess
of 90 acres and river reaches over 1/8 mile wide.

2. Includes cities and built-up areas, roads and
highways.

3. Includes rural homesteads, farmsteads, farm roads,
feed lots, ditches and banks, fence and hedge
rows, small water bodies (see no. I above),
marshes, strip mines, gravel pits, borrow land,
etc.

17

RELATION BETWEEN BASIN RECHARGE AND BASIN PARAMETERS

The correlation coefficients between basin recharge and the
various basin parameters discussed below are presented in Table 5.
All the correlations were made both including and excluding the data
for Jackson sub-basin, because of the anomalous behavior exhibited by
that sub-basin. This odd behavior is probably due to a high water
table in the sub-basin (Figure I), which acts as an impermeable layer
near the surface. Because the high water table modifies the stream
hydrograph to a shape normally associated with “flashy“ streams, the
hydrograph separations result in estimates of base flow that are lower

than the probable actual amounts.

A combination of two factors are proposed to maintain this high
water table. First, the hydraulic gradient in this sub-basin is
probably directed from the Saginaw sandstone into the overlying more
permeable sand and gravel drift (Michigan Water Resources Commission,
1961). In addition, the locally thin drift cover further limits the

amount of infiltration into the drift aquifer.

BASIN MORPHOLOGY

The correlation coefficients between morphologic parameters and
recharge, listed in Table 5, are extremely low for all but the the

circularity ratios (-.856 and -.918) and surface area ratios (0.859

18

TABLE 5.
COEFFICIENTS OF CORRELATION BETWEEN
EACH PARAMETER AND BASIN RECHARGE

 

 

 

WITH WITHOUT

PARAMETER JACKSON VALUES JACKSON VALUES
STREAM FREQUENCY 0.169 0.229
BIFURCATION RATIO 0.118 0.220
FORM RATIO -.185 0.075
CIRCULARITY RATIO -.856 -.918
ELONGATION RATIO -.119 0.021
RELIEF RATIO -.905 0.310
SURFACE AREA RATIO 0.859 0.859
AVERAGE PERMEABILITY

0 - 5 FEET 0.568 0.728
AVERAGE PERMEABILITY

0 - 10 FEET 0.509 0.665
AVERAGE PERMEABILITY

0 - 15 FEET 0.399 0.989
AVERAGE PERMEABILITY

WHOLE DRIFT 0.205 0.103

19

and 0.859). This suggests that none of the morphologic parameters
except these two influence sub-basin recharge to any appreciable
degree. This is to be expected, since the surface glacial deposits in
the study area are too young (13,000 - 15,000 years old; Farrand 8
Eschman, 1979) for an equilibrium to have been established in the

drainage system (Leopold et al., 1969; p. 923-926).

The nearly perfect relationship between sub-basin values of
circularity ratio (Rc) and recharge, however, seems anomalous when
compared with the poor correlations between recharge and the other
shape parameters. A low Rc value can result from either an elongated
(less circular) basin shape, or an irregular (highly incised) basin
perimeter, or both. If the low Rc is due more to elongation, basin
recharge would be relatively low, because the short overland travel
path from the perimeter to the stream channel would allow less time
for water to infiltrate before reaching the stream. The exact
opposite is seen in the sub-basin values; as Rc decreases, recharge
increases. Basin shape, therefore, can not be the cause of the good
correlation between Rc and recharge. This conclusion is also
supported by the lack of any clear relation between the other shape
parameters and recharge, especially the elongation ratios, which show

coefficients of correlation with recharge of -.119 and +.021.

The ratio Rs measures surface irregularity, not the general
surface slope. Thus the correlation between Rs and recharge is
positive: as relief increases, opportunities for ponding of water
increase, causing increased recharge. In addition, as surface

irregularity increases the basin perimeter should become more

20

irregular, resulting in lower Rc values. Comparrison of Rs with Rc
shows correlation coefficients of -0.625 and -0.699. which seems to

support this contention.

It is sub-basin relief, therefore, not sub-basin shape that
causes the strong relationship between sub-basin circularity ratios
and sub-basin recharge. This means that the relief ratios, which show
a poor correlation with recharge (-.905 and +.3IO), do not accurately
indicate the sub-basin surface relief at all. Rather, they indicate
only the general slope from sub-basin perimeter to the sub-basin
outlet. It is the surface area ratio that quantifies sub-basin relief

in this area, and, to some extent, the circularity ratio.

A third morphologic parameter, sub-basin size, also appears to
influence recharge rates. In the case of the two smallest sub-basins,
Deer Creek and Sloan Creek, the calculated recharge values are
considerably lower than the value for Red Cedar sub-basin, in which
they both lie. Precipitation falling on these small sub-basins
reaches the stream channel very quickly, both over the surface and as
interflow through the soil, and so has less time to infiltrate. It is
possible that the lower than expected recharge value estimated for
Jackson sub-basin is due, not to the high water table, but to a
relatively small sub-basin area. This does not seem likely, however,
since the next largest sub-basin, the Lookingglass, is essentially the

same size, yet it has the second highest recharge rate (Table 3).

21

Figure 9. (a) Circularity Ratio vs. Basin Recharge.
(b) Basin Permeability, 0 - 5 Feet vs. Basin Recharge.

(JK is the Jackson sub-basin value.)

(a) Coefficient of Correlation = -0.856
with JK, -0.9l8 without JK.

(b) Coefficient of Correlation = +0.568
with JK, +0.728 without JK.

22

+Jk

116

I4

 

T
O_._.<m >HE<JDUEU

A A «I. _ Al _
0.. ad md NO $6 0.0 to md

2

 

+Jk

1 d . d i 1 1

O

n O? on O
kwmm mIO .>._._.:m<w2mwa

L
A

I I I
3 4
BASIN RECHARGE,

i!

 

N

INCHES/ YEAR

Figure 9.

23

AVERAGE DRIFT PERMEABILITY

In Figure 9b, the surface permeabilities calculated for the first
5 feet of drift in each sub-basin are plotted against sub-basin
recharge. The permeability in the first 5 feet is used because, as
the correlation coefficients (Table 5) indicate, the best estimate of
sub-basin permeability is achieved in the first 5 feet of the drift,
as opposed to the first 10 feet, the first 15 feet, or the whole drift

thickness.

The correlation between sub-basin permeability and recharge is
not as high as that between sub-basin circularity ratio and recharge
(Figure 9). If the values for Jackson sub-basin are omitted, however,
the permeability-recharge relation improves signifigantly, with the
correlation coefficient rising from 0.568 to 0.728. The circularity
ratio-recharge correlation coefficient also improves, from -.856 to
-.9l8, while the surface area ratio-recharge correlation changes very
little, from 0.859 to 0.859. This seems to indicate that discarding
the data for Jackson sub-basin is indeed justified; the high water
table in the sub-basin, acting as an impermeable layer near the
surface, causes the hydrograph separation to yield anomalously low

recharge rates.

29

CONCLUSIONS

Recharge to the drift, always a difficult parameter to quantify,
has been calculated using the best of four different hydrograph
separation techniques, as determined by comparrison with the related
hydrologic parameter -- flow duration ratio. The resulting values for
sub-basin recharge range from 3.95 in/yr to 5.50 in/yr in a water year
of near normal precipitation (excluding the values for the two
sub-basins with extremely small areas). The recharge estimates for
below- and above normal precipitation years range from 2.10 to
5.59 in/Yr and 5.56 to 8.32 in/yr, respectively. All of these values

agree with those reported for the area in previous studies.

Comparrison of sub-basin recharge values with various physical
sub-basin parameters yielded the following results: 1) Surface relief
correlated positively with recharge (0.859). This relationship was
also evident in the strong negative correlation between circularity
ratio and recharge (-.9l8). 2) Correlation between recharge and drift
permeability in the first 5 feet (0.782) was the highest of all
permeability-recharge correlations. 3) Recharge generally increased
as precipitation increased. 9) Sub-basin shape and drainage

characteristics showed no appreciable influence on recharge.

From the above observations, it is evident that recharge

25

estimates by hydrograph separation vary directly with surface relief
and soil permeability, and that surface ruggedness (high relief) has a
greater effect on recharge than soil permeability. By allowing more
infiltration due to longer holding time, the degree of surface
irregularity seems to override the influence of soil texture on

recharge rates.

One surprising result is that the best estimate of base flow is
achieved using the simplest of the four separation methods tested.
The goal of any separation is to model the actual conditions as
accurately as possible, while remaining easy to use. The method which
Walton (1970) describes as most accurately representing actual bank
storage-discharge conditions serves as the basis for the subroutine
"hand separation” (HA), the most complex of the four. The fact that
this method resulted in the poorest correlation with flow duration
parameters suggests that future modelling efforts should strive for

simplicity, rather than sophistication.

26

FURTHER WORK

Additional support for the recharge estimates could be provided
by chemical analysis of the stream waters on a daily basis, concurrent
with streamflow measurements. The resulting data should show a
general decrease in total dissolved solids as stream discharge
increases, due to the diluting of the groundwater runoff by relatively

”clean” surface runoff.

27

APPENDICES

APPENDIX A

APPENDIX A

MORPHOLOGIC PARAMETERS

STREAM FREQUENCY (Fs) -- Stream frequency is the total number of
streams of all orders divided by the basin area. Stream order was
determined by the method of Strahler (1957), in which each headwater
stream is first order, two first order streams join to form a second
order stream, two second order streams join to form a third order
stream, and so on. When two streams of different orders join, the
downstream reach is given the higher of the two orders. Table A
contains the number of streams of each order for all basins taken from

the base map.

Table A. Stream Orders For The Sub-basins

NUMBER OF STREAMS

 

 

OF EACH ORDER TOTAL N0.

BASIN I 2 3 9 5 OF STREAMS
Jackson 11 2 l - - l9
Eaton Rapids 70 I7 5 l - 93
Deer Creek 1 - - - - 1
Sloan Creek 1 - - - - . I
Red Cedar 26 6 I - - 33
Lansing 110 29 6 l - 191
Portland 122 27 7 l - 157
Lookingglass 28 9 l - - 33
Maple Rapids 62 I9 3 I - 85
Ionia 395 83 I9 2 l 950

28

BIFURCATION RATIO (Rb) -- This value was found by averaging the

following ratios:

 

N(x)
Rsb - -
N(x+l)
where N(x) = the number of streams of order x, N(x+l) = number of

streams of the next higher order, and Rsb 8 the bifurcation ratio for
each stream order x. For example, Jackson basin has 11 first-, 2
second- and 1 third order streams (Table A), and thus has a

bifurcation ratio of:

11 2
Rb = -——- + --— /2 I (5.50 + 2.001/2 E 3.75
2 1

Both the bifurcaton ratio and stream frequency values define the
basin's drainage pattern: the remaining parameters quantify the

basin's physical shape.

FORM RATIO (Rf) -- The form ratio was found by dividing the basin
area by the square of the basin's long axis. Basin length was
measured on the base map, area was assumed to be correct as reported

in the USGS Surface Water Records (1956, I957, I962).

CIRCULARITY RATIO (Rc) -- This was caluculated by dividing the
basin area by the area of a circle with the same perimeter as the
basin. The value for any circle, regardless of size, is 0.785, thus

basin values drop from 0.785 as the perimeter becomes less and less

29

circular. Basin perimeters were measured on the base map, basin areas

were taken from the USGS Surface Water Records (1956, I957, I962).

ELONGATION RATIO (Re) -- Somewhat similar to the circularity
ratio, this parameter is the ratio between the diameter of a circle of
area equal to the basin, divided by the basin length. As in the form
ratio, basin length was measured on the base map, basin area was taken

from the USGS Surface Water Records (1956, I957, I962).

RELIEF RATIO (Rr) -- This parameter quantifies the overall slope

of the basin. The ratio is calculated by the equation:

Ep - Eg

Rr=————-

Lb

where Ep is the highest elevation on the basin perimeter, E9 is the
elevation of the stream.gaging station, and Lb is the length of the
basin. The perimeter and gage elevations, in feet above mean sea
level, were taken from topographic maps (USGS 7.5 minute series), and

the basin length was measured on the base map.

30

APPENDIX B

APPENDIX 8

SURFACE AREA RATIO ALGORITHM

The surface area ratio was calculated by first reducing the bore

hole data points to an X - Y - Z grid using the program SURFACE ll

(Sampson, 1978). Each grid calculation was performed with the
following parameters:

1) Node spacing - 0.075 units of data X-Y values. The data are

located in inches from the SW corner of the state, on a scale of

1:250,000.

2) Initial search radius of 0.25, to a max of 0.75. in steps of
0.25, looking for a minimum of 9 points and a maximum of 8.

3) Nearest neighbor search. Duplicate data points averaged.
These grid nodes were then read into the program which calculated the

area of the X - Y - Z surface as follows:

I) Z is the only variable (elevation). X and Y are defined as
constants, the distance between columns and between rows,
respectively.

The distances LX and LY are calculated by:

Lx - SQRT((ABS(Z(I) - 2(2))**2) + x**2)
LY . SQRT((ABS(Z(I) - Z(3))**2) + Y**2)

where: SQRT 3 Square Root 0f...
ABS 8 Absolute Value Of...
**2 = Quantity Squared
Z(l) = Lower Left Corner Node
2(2) = Upper Left Corner Node
Z(3) = Lower Right Corner Node

2) The area of the triangle formed by these three grid nodes is
then:

AREA = (0.5*LX*LY)

31

3) Next, the adjoining triangle's area is found by:

9)

LX = SQRT((ABS(Z(9) - 2(2))**2) + x**2)
LY . SQRT((ABS(Z(9) - z(3))**2) + Y**2)
AREA - (0.5*LX*LY)

where: Z(9) = Upper Right Corner Node

These areas are summed for each set of four nodes throughout the
file. Since X and Y are constant, the areas of the X-Y-Z
triangles projected onto a flat surface are a constant, equal to
I/2 X times Y. The sum of the X-Y-Z areas is then divided by the
product of the constant projected area times the number of
triangle areas calculated in steps 2 and 3 above. This ratio is
the final result, the ”surface area ratio”. As the value of Rs
increases, the surface is becoming more irregular.

32

APPENDIX C

APPENDIX C

SOIL MANAGEMENT GROUP VALUES

Table B.
County And Township Values of
Average Soil Management Group (SMG)
And Average Permeability, 0 - 5 Feet

AVERAGE SMG
WITH WITHOUT AVERAGE PERMEABILITY

 

 

 

COUNTY MUCK MUCK O - 5 FEET
Clinton 2.55 2.60 23.02
Eaton 2.55 2.65 20.36
Ingham 2.50 2.50 25.98
Jackson 2.97 3.18 38.93
Shiawassee 2.61 2.76 29.63
Jackson Co.
Townships
T15 R3W 2.62 2.77 90.60
T15 RZW 3.25 3.38 36.72
T15 RIW 2.97 3.09 31.19
T15 RIE 2.97 3.09 39.86
T15 R2E 2.53 3.39 90.57
T25 R3W 2.88 2.93 30.18
T25 R2W 2.99 2.99 23.38
T25 RIW 2.82 2.87 29.65
Tzs RIE 3.08 3.88 99.98
T25 RZE 2.86 3.09 99.95
T35 R3W 2.90 2.96 33.72
T35 RZW 2.65 2.65 26.81
T35 RIW 3.17 3.23 39.92
T35 RIE 3.90 3.59 53.97
T35 R2E 3.53 3.99 55.16
T95 R3W 2.78 3.00 91.35
T95 R2W 2.83 2.88 36.75
T95 RIW 2.99 3.06 35.93
T95 RIE 3.32 3.61 95.25
T95 RZE 2.97 3.15 51.56

33

SMG values were estimated on a township scale from the published
soils maps (U.S.D.A., 1979, I978, I978, I979, 1981). Township values
were then averaged to yield county-wide values. The values for
average SMG with muck include all muck soils, whether drained or not.
A non-drained muck soil is assigned an SMG value of 1.0. Drained muck
soils are assigned an SMG value according to the permeability of the
sub-soil under the surface organic layer. The values for average SMG

without muck exclude all non-drained muck soils.

39

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38

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