ûO-
James Michael McCluskey. SELECTED MORPHOMETRIC CHARACTERISTICS AND
THEIR RELATIONSHIP TO THE GENETIC PROVINCES OF THE SOUTHERN
APPALACHIAN HIGHLANDS. (Under the direction of Richard A. Stephenson)
Department of Geography, October, 1980.
Small scale, space-order studies using the quantifiable aspects
of drainage basins to differentiate the earth's surface have proven
to be viable. Generic regionalizations that are continental in scope
would be comparisons of drainage basins having similar morphometric
parameters. In this study, multiple discriminant analysis tests the
hypothesis that drainage basins defined by their morphometric char-
acteristics will group in fashions reflective of their genetic pro-
vinces. The results of statistical tests support the null hypothesis.
Interpretation of the test statistics indicates results which differ
from previous literature as to the importance of certain morphometric
parameters.
3r. y. JÜÏNK?. libeaky:
EAST CAROUNA UNIVERSI’^’T
SELECTED MORPHOMETRIC CHARACTERISTICS AND
THEIR RELATIONSHIP TO THE GENETIC PROVINCES OF THE
SOUTHERN APPALACHIAN HIGHLANDS
A Thesis
Presented to
the Faculty of the Department of Geography
East Carolina University
In Partial Fulfillment
of the Requirements for the Degree
Master of Arts in Geography
by
James Michael McCluskey
October 1980
SELECTED MORPHOMETRIC CHARACTERISTICS AND
THEIR RELATIONSHIP TO THE GENETIC PROVINCES
OF THE SOUTHERN APPALACHIAN HIGHLANDS
by
James M. McCluskey
APPROVED BY:
DIRECTOR OF THESIS
Richard A. Yen son
CHAIRMAN OF THE DEPARTMENT OF GEOGRAPHY
ACKNOWLEDGEMENTS
Each member of my thesis committee has imparted to me more than
a mere acknowledgement on this page can suggest. Dr. Janet Petterson
first introduced me to geography. Dr. Donald Steila convinced me that
I could be a serious student. Dr. Richard A. Stephenson taught me to
be a professional. Dr. Ennis Chestang gave me faith in myself. Dr.
Jean Lowry showed me that hard work and being a geomorphologist go
hand in hand. Of these individuals, however, I must extend an addi-
tional very personal and heartfelt thanks to Dr. Stephenson for his
constant encouragement, support, and guidance both as my thesis advisor
and as a friend.
TABLE OF CONTENTS
PAGE
LIST OF TABLES iv
LIST OF FIGURES v
CHAPTER I. INTRODUCTION 1
Statement of Problem 1
Significance of Research 2
CHAPTER II. A COMPARISON OF THE THEORETICAL FRAMEWORKS
OF GENETIC AND GENERIC LAND FORM CLASSIFICATION
SYSTEMS 4
Introduction 4
Genetic Studies and Closed Systems Analysis 4
Generic Studies and Open Systems Analysis 6
A Comparison of Open and Closed Systems 12
Summary 13
CHAPTER III. A REVIEW OF GENETIC AND GENERIC REGIONALIZATIONS.. 16
Genetic Regionalizations 16
Generic Regionalizations 20
CHAPTER IV. THE STUDY AREA 25
Introduction 25
Delineation of the Study Area 25
Description of the Study Area 27
Interpretation of the Erosional History of the
Southern Appalachians 31
CHAPTER V. HYPOTHESES AND MODEL FORMULATION 34
Hypothesis Formulation 34
Model Formulation 35
Model Assumptions 40
Summary 44
CHAPTER VI. THE MORPHOMETRIC VARIABLES 45
Bifurcation Ratio 45
Stream Length Ratio 47
Basin Elongation Ratio 47
TABLE OF CONTENTS
(Continued)
PAGE
Drainage Density 48
Basin Relief 50
Elevation-Rel ief Ratio 51
Mean Ground Slope 52
CHAPTER VII. RESULTS OF HYPOTHESES TESTING 53
Satisfaction of Model Assumptions 53
Results of Multiple Discriminant Analysis 54
Interpretation of Test Statistics 63
CHAPTER VIII. CONCLUSIONS 69
BIBLIOGRAPHY 72
APPENDIX A 79
APPENDIX B 81
APPENDIX C 88
LIST OF TABLES
TABLE PAGE
1. THE STATUS OF BASIN VARIABLES DURING TIME SPANS
OF DECREASING DURATION 14
2. EXPLANATORY REGIONALIZATIONS AT THE STATE LEVEL
AND THE STATED BASIS FOR DIVISION 17
3. GENERALIZED SQUARED DISTANCE BETWEEN GROUPS 55
4. POSTERIOR PROBABILITY OF MEMBERSHIP IN DIFFERENT GROUPS 56
5. POSTERIOR PROBABILITY OF CLASSIFICATION IN DIFFERENT GROUPS. 60
6. CHARACTERISTIC VALUES OF THE FIRST CANONICAL VECTOR 61
7. CHARACTERISTIC VALUES OF THE SECOND CANONICAL VECTOR 62
LIST OF FIGURES
FIGURE PAGE
1. STRAHLER'S METHOD OF STREAM-ORDERING 9
2. THE STUDY AREA 26
3. TOPOGRAPHIC CROSS-SECTION OF THE STUDY AREA 28
4. PLOT OF CANONICAL VARIABLES IN P DIMENSIONAL SPACE 59
CHAPTER I
INTRODUCTION
Statement of Problem
American geomorphologists have developed two distinct methodologies
to analyze land forms. These are the genetic and generic approaches
(Zakrzewska, 1967). The genetic approach is qualitative and uses verbal
descriptions to portray landscapes in an evolutionary context. The
generic approach is statistical and uses numerical data to analyze
surface forms of the earth. The theoretical framework upon which genetic
studies are based is related to closed systems analysis, while generic
studies are linked to open systems analysis. The two systems are com-
parable through general systems theory (Strahler, 1952A).
Geographers during the past century have used both approaches to
regionalize land forms. Genetic regionalizations reached their peak
in the first half of the twentieth century. They are typified by studies
that are continental in scope, such as Fenneman's (1916, 1928, 1931,
1938) delineation of the physiographic provinces of the United States.
Generic regionalizations are more recent. They normally examine small
geographic areas such as the study by Eyles (1971) of West Malaysian
drainage basins or the work of Mather and Doornkamp (1970) in Uganda.
There has been a lack of research which tests the conformity of
the spatial organization of landscapes when they are defined according
to the different modes of land form analysis. The purpose of this in-
vestigation is to test for such conformity. A comparison is made
2
between an established genetic regionalization and a generic analysis
of the same terrain.
Significance of Research
Numerous geographers have expressed the need for generic land form
studies. Kesseli (1946) criticized the genetic approach. He stated
that too much concern was placed upon the origin of the land instead
of upon numerical analysis which can render an accurate portrait of the
land surface. Russell (1949) suggested that geomorphology really be-
comes geographical when it ascertains what is actually present in the
landscape and where each form may be found. Strahler (1954A) noted
that genetic methods of land form interpretation are devices adequate
to teach general principles in introductory courses, but are not suf-
ficient to meet the needs of research specialists. Salisbury (1971: 6),
while tracing the quantitative thread for the descriptive analysis of
land forms, summarized numerous criticisms of the genetic approach and
offered a rationale for numerical analysis. He stated that:
... the thread found its roots in the dissatisfaction
of geographers with an historical-genetic geomorphology
that concentrated its efforts upon the search for.pene-
plains and gave forth laborious accounts of the evolution
of landscapes. It is possible to explain any spatial
distribution by tracing its evolution, of course. Thus
in explaining the population of the Middle West we might
examine the surge of immigration across the land, con-
sider the actual origin of the immigrants, and concern
ourselves with the details of birth and death rates on a
decennial basis. But this is an inefficient intellectual
device for the development of laws and generalizations,
particularly so if the examination of genesis is confined
by imaginary regional boundaries.
3
Geographers needed data about the land that
could be used in studies of man-land relationships,
or where land was simply one more variable in a
more complex mix. To be useful, the information
required should be more descriptive than were
traditional references to this or that peneplain.
The call for a more descriptive landform study
came before the advent of the "quantitative revo-
lution" in geography, but the answer to that call
developed in full stride with the methodological
swing to numbers.
The work of Eyles (1971) and Mather and Doornkamp (1970) in rela-
tively small geographic areas points to the validity of generic
regionalizations in concept. However, the development of a macroscale
generic regionalization has not yet been undertaken. Such a task would
be similar to the efforts of geographers to develop world climatic
classifications.
The present investigation differs from previous work in that
hypotheses are developed and tested comparing the spatial organization
of a landscape defined generically to an established genetic regiona-
lization. The area chosen to test the hypotheses is the southern
Appalachian Highlands. The desirability of such an endeavor is twofold.
First, if the spatial organization of landscapes defined by generic
methods reflects an established genetic regionalization, then the use-
fulness of the genetic method will be reinforced. Second, if this is
not the case, then possible alternatives for a generic land form classi-
fication can be considered.
CHAPTER II
A COMPARISON OF THE THEORETICAL
FRAMEWORKS OF GENETIC AND GENERIC
LAND FORM CLASSIFICATION SYSTEMS
Introduction
In order to test the conformity in the spatial organization of
land forms as defined by the genetic and generic approaches of land
form classification, a comparison must be made between their theoreti-
cal frameworks to determine the appropriate variables to be used in
the analytical model. Strahler (1952A) suggested that this can be
done in terms of general systems theory. Hall and Fagan (1956: 18)
defined a system as "a set of objects together with relationships
between their attributes." Genetic studies with their evolutionary
orientation are linked to "closed systems", while generic studies with
their quantitative considerations are related to "open systems".
Genetic Studies and Closed Systems Analysis
Von Bertalanffy (1956) defined a closed system as one in which no
import or export of energy occurs. Davis (1899) provided an early
approach to a closed system study of land forms. His approach formed
the basis for the majority of the genetic regionalizations. These
include: Fenneman (1916, 1928, 1931, 1938), Atwood (1940), Lobeck
(1950), Thornbury (1965), and Hunt (1974).
In the Davisian approach to landscape development, the concept of
stage or length of time is stressed. Davis (1899) postulated that
5
after the initial uplift of the land the interaction of geomorphic
processes and structures would produce sequential landscapes. The
sequential landscapes are identified as the stages of youth, maturity,
and old age. As the land evolves through time, there is a continuous
volumetric reduction in the surface of the earth ending in a state of
peneplanation. Davis defined a peneplain as a condition where a feature-
less plain is developed through the processes of subaerial erosion. The
various stages of Davis' "geographical cycle" are not of the same time
duration, and the process of evolution can be reinitiated if there is
another uplift of the land. Davis thought that landscapes could be
regionalized according to the various stages of his geographical cycle
(Bryan, 1941).
Davis (1899) formulated his cyclical theory of landscape evolution
primarily for humid environments, where fluvial processes dominate.
However, he also considered the implications in arid and glaciated
areas.
Davis' cyclical viewpoint of landscape evolution is associated
with the concept of "entropy" as it is related to closed systems.
Entropy has been defined as the degree to which energy has become un-
able to perform work; an increase in entropy denotes a trend towards
minimum free energy (Von Bertalanffy, 1956). Therefore, in closed
systems there is a tendency to level down existing differentiation
within the system or toward a progressive degradation of energy to
its lowest form. This situation is analogous to the volumetric re-
duction of the land surface from its initial uplift to the state of
6
peneplanation (Chorley, 1962). The uplift of the land provides the
initial potential energy to the system, while the degradation of the
land through the processes of subaerial erosion constitutes the ten-
dency towards entropy. Entropy is maximized in the peneplanation state.
The state of any closed system is largely dependent on the amount
of time that has elapsed since its inception. Thus, closed systems may
be thought of as being time-dependent, since the basis for their study
is the historical evolution of the surface of the earth.
The closed system approach formed the basis for numerous land form
regionalizations. Davis' (1899) geographical cycle was the dominant
guide in their formulation. Other similar theories of landscape deve-
lopment are Penck's (1953) theorem of parallel slope retreat and King's
(1953) "epigene cycle of erosion".
Generic Studies and Open Systems Analysis
Generic regionalizations have only recently appeared in the litera-
ture. They are linked to open systems analysis. Open systems contrast
sharply with closed systems. In the open system, there are exchanges of
energy and materials with outside environments (Von Bertalanffy, 1950).
A balance exists between the rates of import and export of energy and
material (Doornkamp and King, 1970). This balance acts as a steady
state (Strahler, 1952A). Once equilibrium is established, an open
system becomes time-independent because of its self-regulating mechanism
(Strahler, 1952).
Hack (1965: 5) formulated these ideas in relation to the develop-
ment of landscapes in his principle of "dynamic equilibrium".
7
He stated that:
As applied to the landscape, the principle of dynamic
equilibrium states that when in equilibrium a landscape
may be considered a part of.an open system in a steady
state of balance.in which every slope and every form
is adjusted to every other. Changes in topographic
form take place as equilibrium conditions change, but
no particular cycle or succession of changes occurs
through which.the forms inevitably evolve, as was
assumed by Davis and most later workers in geomor-
phology. Differences in form from place to place
are explained by differences in the bedrock or in
processes acting upon the bedrock. Changes which
take place through time are a consequence of climatic
or diastrophic changes in the environment or of changes
in the pattern and the structure of the bedrock as the
erosion surface is lowered.
Numerous geomorphologists view a drainage basin as an open system.
These include Chorley (1962), Strahler (1964), Schumm and Lichty (1965),
and Morisawa (1968). Strahler (1964) reviewed the application of open
systems analysis to the drainage basin. He stated that in a graded
drainage basin equilibrium manifests itself in the development of cer-
tain topographic forms which are time-independent. Over a long time
span, however, there are continuous readjustments in components as
relief lowers and available energy decreases. Topographic forms show
a correspondingly slow evolution. Validity for the drainage basin
acting as an open system depends on the principle that: when a given
intensity of erosion acts upon a mass of given physical properties,
conditions of surface relief, slope, and channel configuration exist
within a steady state. The morphologies of these forms are adjusted
to transmit through the system the quantity of debris and excess water
which is characteristically produced under the controlling regime of
climate. Changes in the controlling factors of climate and geology
8
upset steady state conditions. If this is the case, a rapid series
of readjustments will take place to reestablish a steady state. New
values of basin geometry are then developed.
Systems of Stream Ordering
A concept that is basic to any numerical analysis of drainage
basin characteristics is a system of stream ordering. One such system
was proposed by Gravelius (1914), but it was not until the work of
Horton (1945) that the use of stream ordering systems became widely
used in geomorphology. The system that is most widely used today is
Strahler's (1952B) modification of the Horton method. According to
Strahler, all unbranched tributaries are first-order streams. The
joining of two first-order streams forms a second-order stream and so
on. Increases in stream order occur only when two streams of the same
magnitude join together. The head of a second-order stream is at the
junction of two first-order streams. This is also true for streams of
successively higher orders.
Strahler's system differs from that of Horton in that the Hortonian
method extends the second-order designation back to the head of the
longest first-order tributary and likewise for streams of higher orders
(see Figure 1). Other stream ordering systems have been advanced by
Scheidegger (1965), Woldenburg (1966), and Shreeve (1967). They at-
tempt to account for the total magnitude of all tributaries within a
given system. These methods of stream ordering are not widely used.
Figure 1: Strahler's method of stream-ordering.
10
Laws of Drainage Basin Composition
Horton proposed three laws of drainage basin composition which
relate stream order to the number, length and slope of streams in any
given system. The first of these is the law of stream numbers. Horton
(1945: 287) stated:
The number of streams of different orders in a given
drainage basin tends to approximate an inverse series
in which the first term is unity and the ratio is the
bifurcation ratio.
This means that within a given drainage basin there is a decrease
in the number of streams at correspondingly higher orders. The geo-
metric series may be demonstrated by plotting the number of streams
on a logarithmic scale against stream order on an arithmetic scale.
The validity of this relationship has been demonstrated in field studies
conducted by Strahler (1952B; 1957) and Leopold and Miller (1956). Some
researchers including Shreeve (1963), Bowden and Wallis (1964), and
Milton (1966) have stated that the law may be a statistical relation-
ship rather than due to the random development of drainage networks.
Other researchers such as Shreeve (1966), Smart (1967), and Scheidegger
(1968) have explored the theoretical relationship between stream order
and stream number.
Horton's second law of drainage composition denotes the relation-
ship between stream order and stream length. Horton (1945: 287) stated:
The average length of streams of each of the dif-
ferent orders in a drainage basin tend to closely
approximate a direct geometric series in which
the first term is the average length of streams
of the 1st order.
11
This law states as stream order increases so does stream length.
Again this relationship may be demonstrated by plotting mean stream
length on a logarithmic scale against stream order plotted on an arith-
metic scale. Melton (1957) and Maxwell (1960) question the validity of
the law of stream lengths when the Strahler ordering system is used
rather than the Horton method. Broscoe (1959) proposed a modification
of the stream length law for use with the Strahler system. Cumulative
stream length would be substituted for Horton's mean stream length.
The improvement of Broscoe, however, fits Horton's definition of length
better than Strahler's uncumulated mean lengths (Bowden and Wallis,
1964). Milton (1966) suggested that the law of stream lengths is a
statistical probability function similar to the law of stream numbers.
Horton's third law of drainage basin composition relates stream
order to stream slope. Horton (1945: 295) stated:
...there is a fairly definite relationship between
slope of streams and stream order, which can be
expressed by an inverse geometric-series law.
This law states that as there is an increase in the order of streams
there will be a decrease in stream slope. It may be demonstrated like
Horton's other laws of drainage composition by plotting the logarithmic
mean stream slope against stream order. Morisawa (1962) found in the
Appalachian Plateau that all drainage basins do not have straightline
plots when stream slope is related to stream order. It was felt that
the anomalies were caused by differential resistance to erosion and
rejuvenation. Broscoe (1959) restated this law to conform to the
Strahler ordering system by substituting cumulative mean slope for
12
Horton's average slope. Bowden and Wallis (1964) have substantiated
Broscoe's use of cumulative mean slope.
Two other laws regarding drainage basin composition have been
formulated. A law of basin areas inferred by Horton was formalized
by Schunrn (1956: 606). He stated:
...the mean drainage basin areas of streams of
each other tend to approximate closely a direct
geometric series in which the first term is the
mean of the first-order basins.
Field studies by Morisawa (1959) and Leopold and Miller (1956) have
substantiated this law.
Morisawa (1962: 1035) formulated a law for basin relief. She
noted that:
...the average relief of basins of each order forms
a direct geometric series in which the first term
is average relief of the first order.
Fok (1971) used Horton's laws of stream lengths and stream slopes to
derive a law which is similar to that of Morisawa. This was substan-
tiated from field data from drainage basins of the third-order and
higher.
A Comparison of Open and Closed Systems
Schumm and Lichty (1965: 115) considered the comparability of
open and closed systems with regard to the study of land forms. They
stated:
Landscapes can be considered...either as a result
of past events or as a result of modern erosional
agents. Depending upon one's viewpoint the land-
form is one stage of the erosional cycle of erosion
or a feature in dynamic equilibrium with the forces
13
operative. These views are not mutually exclusive.
It is just the more specific we become the shorter
is the time span with which we deal and the smaller
is the space we consider. Conversely when dealing
with geologic time we generalize. The steady state
concept can fit into the cycle of erosion when it
is realized that the steady state can be maintained
for a fraction of the total time involved.
Schumm and Lichty (1965) also considered the status of drainage
basin variables during time spans of decreasing duration. They de-
signated variables as being independent, dependent, or not relevant.
Variables are arranged in a hierarchy approximating increasing degrees
of dependence. For example, over the long span of cyclical time,
geology, initial relief, climate, and time are independent variables.
Time, simply the duration since the inception of the erosiona! cycle,
perhaps is the most important variable in the cyclical time span. It
determines the accomplishments of the erosional agents, and therefore,
the progressive morphological changes within the system. The graded
time span refers to a short span of cyclical time where conditions
of dynamic equilibrium exist. There are continuous adjustments between
elements within the system and negative feedback and self-regulation
dominate. From the viewpoint of graded time, time and initial relief
are not considered to be relevant variables. There are no restrictions
placed on space or area because the graded time span considers com-
ponents of the landscape in smaller units (see Table I).
Summary
When viewing the theoretical frameworks by which genetic and
generic regionalizations are formulated, it is seen that one of the
14
Table I
The Status of Basin Variables
During Time Spans of Decreasing Duration
Drainage Basin Variables Status of Variables During
Designated Time Spans
Cyclic Graded
1. Time Independent Not relevant
2. Initial Relief Independent Not relevant
3. Geology (lithology and Independent Independent
structure)
4. Climate Independent Independent
5. Vegetation Dependent Independent
6. Relief or volume of Dependent Independent
system above base level
7. Hydrology (runoff and Dependent Independent
sediment yield per unit
area within system)
8. Drainage network morphology Dependent Dependent
9. Hillslope morphology Dependent Dependent
10. Hydrology (discharge of Dependent Dependent
water and sediment
from system)
Source: Schumm, S.A. and R.W. Lichty 1965. Time, space, and
causality in geomorphology. American Journal of
Science, 263, 110-119.
15
fundamental differences is the consideration of time. Genetic studies,
such as that of Fenneman, are based upon the closed system Davisian
approach where broad expanses of land are designated according to stage.
Generic regionalizations use Hortonian analysis and relate the quanti-
fiable forms of the drainage basin to the processes by which they form
while holding time constant.
Open systems are considered to be a special case of the closed
systems, since the transport of material and energy into and from the
system becomes zero (Von Bertalanffy, 1956). Therefore, there should
be similar spatial organizations of the landscape when the dependent
variables of drainage network and hillslope morphology are considered.
This similarity is based on the fact that while genetic regionalize-
tions designate specific areas according to their stage in the evolu-
tionary cycle and generic regionalizations have no such cyclical re-
ference, both classify land forms according to the resultant form which
occurs through the interaction of geomorphic structures and processes.
CHAPTER III
A REVIEW OF GENETIC AND
GENERIC REGIONALIZATIONS
Genetic Regionalizations
The first attempt at a regional classification of the United States
was made by Powell (1896). The basis for his regionalization was the
common history by which geomorphic features developed. Physiographic
provinces were defined by map and verbal description. In the twenty
years following Powell, numerous other attempts were made at a regional
classification of the United States. Thornbury (1965) outlined these
studies which included: Davis in 1899, Brooks in 1906, Bov;man in 1911,
Blackwelder and Dryer in 1912, Fair and Von Engelen in 1913, and Fenne-
man in 1916. Some studies were based on physiographic considerations,
while others were based on combinations of physiography, soils, climate,
vegetation, and other factors. Thornbury (1965) also considered the
numerous regionalizations made at the state level and identified the
basis for each (see Table II).
Fenneman's (1916, 1928, 1931, 1938) classification of the United
States into physiographic provinces is the most widely known of the
genetic studies. It was officially accepted by the United States
Geological Survey after its initial presentation at the 1919 meeting of
the Association of American Geographers. The system has three categories
or levels of differentiation for classifying geomorphic provinces. The
division is the most general category, followed by increasing levels of
17
Table II
Explanatory Regionalizations at
the State level and the Stated
Basis for Division
Date Author State Basis for Division
1896 Marbut Missouri Principally geologic
structure
1898 Salisbury New Jersey Geologic structure,
and topography
1899 Abbe Maryland Geology and topography
1900 Hill Texas Soil, climate, geologic
structure, drainage,
and human culture
1902 Tarr New York No clear statement
1916 Martin Wisconsin Constrasting topographic
form
1922 Mai lot Indiana Altitude, relief, and
type and relationships
of land forms
1925 La Force, Georgia Altitude and relief,
et al. grouping of the features
or relief patterns, size
and scale of features,
nature of surface
1952 Hinds California Geologic history
Source: Thornbury, W.D. 1965. Regional Geomorphology of the
United States, New York: John Wiley and Sons.
18
differentiation, by the province and section. The dominant features
of topography are explained by Davis' theoretical considerations of
process, structure, and stage (Fenneman, 1928).
Other classifications similar to that of Fenneman are Loomis
(1937) and Atwood (1940). Later researchers such as Thornbury (1965)
and Hunt (1974) departed from the Davisian concept of Stage by sub-
stituting the idea of length of time as it relates to the evolution
of landscapes.
Murphy's (1967; 1968) classification of land forms on a world
scale combines the genetic and generic approaches. He used three
levels or categories of information to regionalize land forms. Struc-
tural regions identified a landscape in terms of its geologic origin
and rock composition. Topographic regions, using numerical observa-
tions for elevation, denoted the surface configuration of the earth.
The means by which landscapes were formed are regionalized in terms
of various erosional and depositional processes. Structure and process
regions are defined genetically, while topographic regions are defined
generically. When the three regional types are superimposed, a land-
scape may be considered in terms of process, structure, and stage as
well as by differences in surface configuration.
Other classifications which combine aspects of the genetic and
generic methods of terrain evaluation are the land-systems approaches
(Cooke and Doornkamp, 1977). For example, the model developed by the
Commonwealth Scientific and Industrial and Industrial Research Organi-
zation (CSIRO) of Australia is physiographic in nature and considers
19
the genetically interrelated components of the land surface which in-
elude vegetation, soils, bedrock, and slope. The hierarchy of units
within the classification are similar to those of Fenneman; however, a
more refined level of detail is reached. The CSIRO method developed
as a rapid method of reconnaissance survey of unmapped or poorly mapped
areas. The method has been adopted by the Land Resource Division (LRD)
of the Overseas Development Administration, Foreign and Commonwealth
Office in Britain. Reports have been produced for parts or all of the
countries of Bechuanaland, Tanzania, Nigeria, Lesotho, Botswana, and
Gambia (Ministry of Overseas Development, 1970). Similar mapping
techniques were put forward by Hunt (1950) as applicable to military
purposes for assessing the difficulties of passing across different
types of ground. In the United States, the Soil Conservation Service
of the Department of Agriculture formalized a land-capability classifi-
cation for agriculture which resembles the land-systems method. The
United States system recognizes a threefold hierarchy from smaller to
larger groupings of 1) capability units, 2) capability subclasses, and
3) capability classes (Klingebiel and Montgomery, 1961).
Mabbutt (1968: 12) outlined the considerations that support the
genetic framework and the reasons for its relative dominance. He stated
1) It is a logical breakdown, and similarities between
widely separated areas should be predictable when the
basic controls are similar. 2) It offers a rational
hierarchy and should allow further investigation and
subdivision within the framework. 3) It has the pro-
mise of universality.
20
Generic Regionalizations
The advent of the "quantitative revolution" in geography of the
1950's ushered in a new era of land form analysis. Hammond (1962:
71-72) emphasized the need for a shift in geographic geomorphology
from the previously dominant genetic approach. He stated that:
System in any expository presentation requires the
use of some organizing principle, but genesis is
not the only such device available. Function, for
example, is an equally valid one. Another is to
hold inherent characteristics, resolving the com-
plexity of the phenomenon into elements, component
parts or attributes that can be characterized
separately. This is a familiar scheme, regularly
utilized, for example, in the description of cli-
mates, plants, and to an increasingly exclusive
degree of soils. Indeed at the moment land form
description stands alone in its stubborn adherence
to a genetic rather than a component-characteristic
organization. Possibly this slowness to venture
into empirical description stems in part from the
fact land form data are not normally assembled in
specific numerical form, element by element.
Kesseli (1954: 220) summarized the form that such a component-
characteristic organization in geographic geomorphology should take.
He stated:
...a) that this desired geomorphology need not con-
cern itself with the origin of landforms; b) that
this geographic geomorphology.should divorce itself
from an explanatory descriptive terminology instead;
c) that this geomorphology could be developed by
recognizing and defining landform types, a procedure
which would follow the methods applied in the investi-
gation of climate, vegetation, and soils; d) that
the landforms themselves should be mapped by use of
appropriate symbols, following methods used by
European geomorphologists in constructing morphometric
maps; e) that physical as well as human geographers
could contribute to this desired geographic geomor-
phology.
21
The earliest studies to follow these lines differentiated between
aspects of slope or relative relief. Studies were often of small geo-
graphic areas, such as those conducted by Wentworth (1930), Smith (1935),
Raisz and Henry (1937), and Calef and Newcomb (1954). In contrast to
these studies on a small scale, Hammond (1964) produced a map of land-
surface form for the United States based upon aspects of slope. He
considered three aspects: 1) amplitude of relief, 2) percent of near
level land, and 3) profile type.
The majority of empirical regionalizations concentrate upon the
differentiation of fluvially eroded topography. The drainage basin
came to be considered the logical unit of analysis, since streams are
integrated and thus orderly (Scheidegger, 1961). Doornkamp and King
(1971: 3) gave a rationale for the use of drainage basins in the regiona-
lization of landscapes. They stated:
The analysis of drainage basins, either as single
units or as a group of basins which, taken together
comprise a distinct morphological region, has
particular relevance to geomorphology. Fluvially
eroded landscapes are comprised of drainage basins,
and these provide convenient units into which an
area can be subdivided. The development of a land-
scape is equal to the sum total of each individual
drainage basin of which it is composed. The fact
that morphological regions can be recognized suggests
not only within each region the drainage basins have
forms similar to each other but also that the basins
are evolving in a similar way to each other. Thus,
by analyzing the development of each drainage basin,
greater understanding of the landscape as a whole
may be achieved. This is possible if there are
definable relationships between the form of the
drainage basin and the processes at work within it.
22
The pioneering work of Horton (1945) concerning the development
of drainage basins and the resulting basin forms led others to follow
in this vein. Strahler (1952A, 1952B, 1954B, 1957, 1958; 1964) en-
larged upon the work of Horton. Others such as Schumm (1956), Smith
(1950), and Miller (1953) also contributed. Their basic research has
been used for the comparison and regionalization of land forms using
drainage basin morphometry.
Early studies which used aspects of drainage basin morphometry
to compare land forms in different regions were important building
blocks in the body of theory and techniques eventually used in generic
regionalizations. A complete review of all the comparative studies
is beyond the scope of this investigation, since the primary concern
is with the regionalization of land forms. However, a few specific
examples are given. Chorley (1957) compared the morphometry of the
Exmoor region of England, north central Pennsylvania, and northern
Alabama. Melton (1958) analyzed the differences in drainage density
in the American southwest. Chorley and Morgan (1962) compared the
morphometric characteristics of the Unaka Mountains of North Carolina
and Tennessee with the Dartmoor region of England. Woodruff (1964)
compared the mean values of five morphometric variables for four geo-
graphically separate regions of the United States. Milling and Tuttle
(1965) conducted a study of two east-flowing tributaries of the Iowa
River. Woldenburg (1971) expanded upon the work of Milling and Tuttle.
Folsom and Winters (1970) analyzed the spatial variation of basin pro-
perties in the southern shoreline of Michigan. Stephenson (1971)
23
considered the previous classifications of stream types in the Des
Moines River basin using five channel response variables. These com-
parative studies added to the knov/ledge about spatial differences in
drainage basin morphometry and permitted regionalizations in such
terms.
Landscape regionalization using aspects of morphometry share two
common characteristics. First, drainage basins are all of the same
order or dimensionless parameters are used for purposes of standardiza-
tion. Second, some form of multivariate analysis is used for classifi-
cation purposes. Three studies are used to demonstrate this regional iza-
tion process: 1) Mather and Doornkamp (1970), 2) Eyles (1971), and 3)
Giles (1974). Similar studies were conducted by Lewis (1969) and
Gardner (1972).
Mather and Doornkamp (1970) in their study of 130 third-order
Ugandan drainage basins used cluster analysis as the method of classi-
fication. They identified five distinct drainage basin types based
upon eight morphometric variables which were shown to be significant
by factor analysis. The eight morphometric variables are: 1) relative
relief, 2) drainage density, 3) stream frequency, 4) relief ratio, 5)
basin area, 6) total stream length, 7) number of streams, and 8) bi-
furcation ratios. The five morphometric groups were in contrast to
eight morphological regions which had been subjectively defined by the
authors prior to their research. The strength of their classification
scheme was tested by discriminant analysis.
24
Eyles (1971) also used cluster analysis in his classification of
a random sample of fourth-order West Malaysian drainage basins. He
used five morphometric variables for purposes of differentiation.
These included: 1) the hypsometric integral, 2) average slope, 3)
basin relief, 4) drainage density, and 5) basin area. The identifi-
cation of six distinct drainage basin types by multivariate analysis
was said to decrease the degree of subjectivity found in earlier studies.
Giles (1974) used factor analysis to regionalize the Coastal Plain
of North Carolina. He used a sample of 170 third-order drainage basins
and twenty-eight morphometric variables for purposes of classification.
He found similarities in the grouping of drainage basins and the inci-
dence of marine terraces.
CHAPTER IV
THE STUDY AREA
Introduction
The study area chosen for this investigation is the southern
Appalachian Highlands which includes the physiographic provinces of
the Piedmont, the Blue Ridge Mountains, the Ridge and Valley, and the
Appalachian Plateau. This area was selected because: 1) the topo-
graphy of the area is largely the result of fluvial processes; 2) there
are several distinct geomorphic units within a compact geographic area;
and 3) the dominant climatic controls are relatively uniform.
Delineation of the Study Area
A linear transect roughly parallel to the northern borders of
North Carolina and Tennessee is used to take a systematic sample of
fifty third-order drainage basins. The 560 kilometer transect extends
along 36° 3' 45" North latitude between 79° and 85° West longitude.
The eastern margin of the transect is the Durham Triassic basin and
the western margin is the Highland Rim of Tennessee (see Figure 2).
The sample drainage basins are taken from 7.5 minute series topographic
quadrangles, which conform to national map accuracy standards (United
States Geological Survey, 1976). One third-order drainage basin is
selected from an area which corresponds to the center of each of the
quadrangles (see Appendix A).
Figure 2; The study area.
ro
CTi
27
Third-order drainage basins are used because they are large enough
to demonstrate relationships between morphometric parameters and small
enough not to become unwieldly for data collection. Also, it is useful
to have all drainage basins of the same magnitude for purposes of uni-
formity.
Description of the Study Area
Since both genetic and generic regionalizations concentrate upon
geologic structure, local lithology, and topographic expression to
classify land forms, the study area is described in such terms. Ap-
pendix B lists the percentage of rock types found in each of the drain-
age basins, while Figure 3 shows the topographic cross-section of the
study area.
The Piedmont Province
The Piedmont Province attains its maximum width of 200 kilometers
near the North Carolina - Virginia border. It is the least mountainous
of the southern Appalachian provinces. The surface of the Piedmont
is undulating. Relief may be increased locally by low knobs. Small
areas of downfaulted Triassic sedimentary rocks give rise to lowland
tracts. Structural and lithologic controls of drainage is observed
locally, but regionally it is lacking.
Except for the sediments of the Triassic basins. Piedmont rocks
are predominantly metamorphic (schists, gneisses, quartzites, and
slates) or plutonio (granites, granodiorites, gabbros, and dunites).
The metamorphic and plutonio rocks of the Piedmont have a highly complex
(mELEeVtAeTIrOsN)
DISTANCE ALONG CROSS-SECTION (km)
Figure 3: Topographic cross-section of the study area
29
structure. The latest episode of regional metamorphism in the Pied-
mont dates from the early Paleozoic. Plutonic rocks were emplaced at
intervals ranging from the early Precambrian to the late Paleozoic.
The Triassic sediments are mainly continental red sandstones, shales,
and conglomerates, which accumulated in down faulted troughs with di-
mensions somewhat greater than their present outcrop areas.
The Blue Ridge Mountain Provinces
The Blue Ridge Mountain Province attains its maximum width of
130 kilometers in North Carolina. Massive mountains and high peaks
characterize the southern portion of this province. Several peaks
exceed 1800 meters in elevation. Angularity and lineation of topo-
graphy are lacking. Mountain tops which have grassy or heath summits
are known as balds. They are common in the Great Smoky and Unaka
Mountains. The eastern front of the Blue Ridge escarpment is the most
striking feature of the region. The eastern continental drainage di-
vide is very near the eastern edge of this portion of the Blue Ridge
province. Streams flowing into the Piedmont are short and steep com-
pared to those with a westward flow. Stream piracy is common.
The Blue Ridge is underlain by Lower Cambrian sedimentary rocks.
Upper Precambrian sedimentary and metamorphic rocks, and a Precambrian
basement complex. The sedimentary rocks are of the Precambrian Ocoee
series and the Lower Cambrian Chilhowee series. These rocks are pre-
dominantly elastics which have undergone varying degrees of metamorphism.
Metasedimentary rocks are found on the western side of the province.
East of these are basement rocks similar to those found in the Piedmont,
30
but the Paleozoic igneous plutons of the Piedmont are not found in the
Blue Ridge. A series of overthrust faults separates the western Blue
Ridge from the Ridge and Valley.
The Ridge and Valley Province
A series of weak and strong rocks controls the topography of this
province. Less resistant limestones and shales form the valleys, while
more resistant sandstones, shales, cherts, and dolomites compose the
ridges. Varying degrees of karst development occur within the lime-
stone valleys.
The structure of the Ridge and Valley province varies from south
to north. In the southern section folds are compressed, overturned,
and often broken by thrust faults, which themselves have been folded.
Except for the Blue Ridge border faults, the thrusts are shallow and do
not involve the basement complex. In the northern section, steep folds
with minor amounts of faulting are characteristic.
Due to the differential erosion of folded structures, the Ridge
and Valley Province is marked by several geomorphic features. The most
outstanding of these are: 1) a marked parallelism of ridges and valleys
having a northeast-southwest orientation; 2) a few major streams with
the notable development of subsequent streams forming a trellis drainage
pattern; 3) numerous ridges displaying accordant summit levels; and 4)
hundreds of water gaps through hard rock ridges and an equal number of
wind gaps, testifying to stream diversion.
The Appalachian Plateaus Province
The southern section of the Appalachian Plateaus Province is known
31
as the Cumberland. Altitudes there are not as high as in the southern
Blue Ridge. The province is essentially a broad syncline of rocks of
Pennsylvanian and Mississippian age. Rocks of the plateau are mostly
clastic in nature: conglomerates, sandstones, shales; with some lime-
stones and some interbedded coal seams. The Appalachian Plateaus have
not been subjected to the intense deformation which has occurred in
the other provinces. In the eastern portion of the province there are
local gentle folds contrasting with the steep folds of the Ridge and
Valley Province. The plateau is bounded on all sides by outfacing
escarpments. Most of the region has undergone extreme dissection. This
is so great in the eastern portion of the province that locally the up-
land surface of the plateau has been reduced to narrow interfluves so
that the terrain is designated as mountainous.
Interpretation of the Erosional History of the Southern Appalachians
There is a wide diversity of opinion as to the age and the number
of erosional surfaces found in the Appalachians. Bascom (1921) believed
that there are as many as five peneplains, with an equal number of
strath terraces below the youngest peneplain. She suggested ages
ranging from the Jurassic to the Pleistocene for these erosion surfaces.
Ashley (1935) thought that only one peneplain is present and that
the other topographic surfaces which have been called peneplains are
the result of the differential lowering of the one peneplain upon rocks
of varying resistance, local baseleveling of areas of weak rocks, or
the stripping of areas of less resistant rocks.
32
Hack (1960, 1965) questioned the existence of any remnants of
surfaces having cyclical significance within the Appalachians. He
believed that it is not necessary to postulate a Mesozoic or Cenozoic
history of the Appalachian region to explain the existing topographic
forms. Present topography is explained as the result of recent pro-
cesses acting on rocks of unequal resistance.
The conventional interpretation of the geomorphic history of the
Appalachians acknowledges the remnants of two erosional surfaces (Thorn-
bury, 1965). These are known as the Schooley and Harrisburg peneplains.
The Schooley peneplain is now thought to date from the early to middle
Tertiary, while the Harrisburg peneplain is believed to date from the
late Tertiary. Evidence for the Schooley peneplain is not strongly
convincing. The accordance and subaccordance of numerous ridge crests
in the Ridge and Valley province are offered to explain its existence.
It is argued that similarities in ridge crest altitudes may be the re-
suit of the uniform downwasting of rocks of unequal resistance. Evi-
dence for the Harrisburg peneplain is more convincing. In the Piedmont
there are extensive tracts of rolling topography having deeply weathered
soils which conform to Davis' initial conception of a peneplain.
The Harrisburg surface is thought to be represented in the Ridge
and Valley Province strath terraces in the Great Valley at the east
side of the province. Some geomorphologists feel that there has been
a subcycle following the Harrisburg cycle that is represented locally
by straths given local names. Another interpretation of these surfaces
is that they represent areas lower than the typical Harrisburg surface
33
which developed on belts of weak rocks. However, if they do represent
local post-Harrisburg erosional surfaces then their age is very late
Pliocene or early Pleistocene.
CHAPTER V
HYPOTHESIS AND MODEL FORMULATION
Hypothesis Formulation
The Fenneman (1938) regionalization of land forms is an estab-
lished genetic classification scheme. The problem is to test if such
a regionalization has conformity in its spatial organization when the
morphometric variables of drainage basins are used as distinguishing
characteristics.
The working hypothesis of this investigation is that when drain-
age basins are defined on the basis of their morphometric parameters
they will group in a similar fashion to an a priori genetic regionali-
zation. The rationale for this statement is that morphometric para-
meters reflect geomorphic processes acting differentially upon varied
structures and lithologies, and need not be tied to any particular time
element, whether cyclic or graded.
Drainage basins are initially assigned to one of Fenneman's four
physiographic provinces of the southern Appalachian Highlands. They
are defined by a set of morphometric parameters which are measurements
of the drainage basin as an open system. Appropriate statistical tests
are made which test hypotheses concerning similarities in the spatial
organization of drainage basins when they are defined according to the
two modes of landform analysis.
35
Model Formulation
Discriminant analysis is employed for a set of observations which
are already classified in some manner. The technique was originally
developed to allocate new observations to a set of pre-established
classes on the basis of certain characteristics. Its most common use
in geography has been as an aid for the classification of variables
(King, 1970).
In discriminant analysis the term allocation is used to refer to
some aspects of the discrimination problem which focus on the assign-
ment of individuals to populations and the related issues of the pro-
babilities of wrong assignment. By contrast, the classification pro-
blem concerns itself with deciding how observation units fall into
groups, how many groups are needed for proper classification, and the
delimitation of groups.
Kendall (1966) suggests three situations which give rise to the
statistical discrimination problem. These are: 1) where there are
missing or lost data such that it is impossible to choose between dif-
ferent populations precisely, 2) where it is essential for some decision
to be made as to the nature of the condition of certain observed symp-
toms, and 3) where certain problems of prediction need to be approached
by means of discriminating between particular conditions before they
actually occur. This investigation concerns itself with the second of
Kendall's situations and the related allocation problems of the assign-
ment of individuals to populations and the probabilities of wrong
assignment.
36
The allocation problem is handled within the framework of the
theory of statistical decision functions. Rao (1965) noted that a
decision rule may be nonrandomized or randomized. The sample space
of the former case is divided into mutually exclusive k regions with
X measurements allocated to the one region.
w^, if X2:w^ (1)
Using the randomized rule, the observation is allocated to population
i with a probability
}\ i(x), i = 1, 2, . . . k (2)
The nonrandomized rule would be for those which
Y = 0 (3)
Any allocation problem has numerous alternative hypotheses, where
k is the number of populations. Using either of the allocation rules,
there is a loss associated with an incorrect hypothesis. For each rule
there is a loss vector
(L^. L^, . . . L^) (4)
corresponding to the alternative hypotheses. The problem is choosing
between the different decision rules with respect to their loss vectors.
A decision rule 5i is admissable if in comparison to any other decision
rule ^2 when
i 1, 2, . . . k (5)
37
for at least one i,
(6)
Not all decision rules, however, are directly comparable and the
class for admission may be large. The class is complete if for any
rule outside the class there is a better one in the class. A minimal
complete class implies that the class contains no complete subsets.
The selection of a decision rule is straightforward when the a
priori probabilities of the k populations are known (King, 1970). The
optimum solution is one which allocates the observations to populations
such that the a posteriori risk is minimized. This is the case with
the present study. The groups of drainage basins in each of the physi-
ographic provinces are assumed to be non-randomized complete populations
with known a priori probabilities.
The multiple discriminant analysis procedure computes a set of
linear functions for the purpose of allocating observations into several
groups or populations. The input data consist of a set of observations
for a set of variables, and each observation contains a value for each
of the variables.
The allocation criterion developed is determined by a measure of
generalized squared distance (Barr et al, 1976). It is based upon the
within group covariance matrices. The generalized squared distance is
Dt (X) = g^ (X, t) + (X, t) (7)
where
38
1
(X,t) = (X 0-1- S'" (X - X^) + logg (8)
and
g2 (X, t) = -2 log (prior probability for e group t) (9)
with
A subscript to distinguish groups,
The covariance matrix for observations within group t.
^t The determinant of S^,
X A vector of values of the variables being analyzed,
The vector of means of the variables being analyzed.
The posterior probability of membership in group u for a vector
of values x based upon the expected probabilities of assignment (exp)
was formulated by Barr et ai (1976) such that
exp (-0.5 (X)) (10)
sum (exp (-0.5 D? (X)))
t ^
In the case of k groups a maximum of (k-1) discriminant axes is
necessary. Fewer than (k-1) axes may suffice if they account for a
higher proportion of the total intergroup differences, or if p, the
number variables, is less than k, the number of groups, in which case
a maximum of p discriminant axes will be required irrespective of the
number of groups. The first discriminant axis is the line of closest
fit to the means of the k groups in p dimensional space defined by
the variables. The second discriminant axis is orthogonal to the first
39
and subsequent discriminant axes.
The coefficients which define the discriminant axes are termed
canonical vectors. The canonical vectors are eigenvectors of the matrix
W"^A, where W‘^ is the inverse of the pooled within groups sums of squares
and cross products matrix of the k groups and A is the between groups
sums of squares and cross products matrix. The matrix W”^A is a ratio
of the within groups to between groups sums of squares and cross pro-
ducts. The first canonical vector maximizes the ratio, while the second
canonical axis minimizes the ratio being orthogonal to the first.
The discriminating power of each eigenvector is given by the cor-
responding eigenvalue. The eigenvalue, /^'^is the square of the canon-
ical correlation coefficient r. The results are expressed as a percent-
age.
The relative contribution of each variable in the separation be-
tween groups is determined by scaling their characteristic values
associated with each of the eigenvectors. The variables are scaled in
such a manner that the largest value is equal to one. If the value
assigned to a variable approaches one, then its relative contribution
in separating between groups is large. There is a range of values
associated with each of the k-1 eigenvectors.
The null hypothesis that the discriminating power of the canonical
vectors above the gth group is due to chance may be tested. The Chi
square test of the null hypothesis is
= -N - 0.5 (p + k) - 1 log^ A (11)
40
where
j = g + 1 (12)
with
d.f. = (p - g) (k - g - 1) (13)
If the calculated Chi square exceeds the selected significance level
then the null hypothesis is not accepted. The test is repeated with
g incremented by 1 until all n functions have been tested or until
Chi square is not significant.
A plot of the separation of the k groups in p dimensional space
can be derived based upon the canonical variables. The separation
between groups as well as areas of overlap between groups may be ob-
served.
Model Assumptions
The main assumptions of discriminant analysis are; 1) that each
of the k samples are drawn from separate populations; 2) that the
variables upon which the measurements are made are normally distributed;
3) that the multivariate means of the k populations are not equal; and
4) that the within group variance-covariance matrices of the k popula-
tions are equal (Mather, 1976).
Satisfaction of the first assumption of discriminant analysis,
that each of the samples are drawn from distinct populations, is met by
41
a systematic sampling of third-order drainage basins from each of the
four physiographic provinces. Drainage basins selected are located at
approximately 11.0 kilometer intervals.
In order to test the second assumption of discriminant analysis,
that the variables are normally distributed, a Kolmogrov-Smirnov test
is employed. The null hypothesis that the sample data come from a
population that is normally distributed.
The Kolmogrov-Smirnov test concentrates upon the greatest dif-
ference between frequencies of a given class interval. Cummulative
frequency distributions are produced for both the observed data and the
heights of ordinates on the normal curve. By inspection, the largest
difference in frequency, for a given class, between the two distribu-
tions is
D = maximum (F-j (x^) - (x^-)) (14)
where F-j is the frequency of heights of ordinates on the normal curve,
F2 is the frequency of the observed data, and i is the class for which
D is a maximum. With the null hypothesis, D follows Chi square with
two degrees of freedom, such that
D >* 1.36 n-j + n2 ^ (15)
Successive applications are made using various data transformations
until normality is attained (Till, 1974).
42
The third assumption of discriminant analysis, that the multivari-
ate means of the k populations are not equal is tested by the Hotelling-
Lawley trace statistic
= TR (E"^ X H) (16)
in comparison to an approximation of Fisher's F, such that
F = 2(S X N + 11 X TR (E"^ x H) (17)
(S X S (2M + S + 1))
with F having degrees of freedom
S (2M + S + 1) (18)
and
2 (S X N + 1) (19)
where
TR is a trace of the addition of eigenvalues along the
diagonal of the multivariate matrix
E is the error associated with the sum of squares and
cross products of the within group matrix
H is the between group sum of squares and cross-products
matrix
S is the minimum (P,Q)
M equals 0.5 (ABS (P - Q) - 1)
N equals 0.5 (NE - P - 1)
and
43
P is the number of dependent variables
Q is the degrees of freedom specified by the hypothesis
NE is the degrees of freedom associated with E.
2
If the F approximation exceeds T , the the null hypothesis that the
multivariate means of the k populations are equal is rejected (Mather,
1976).
The final assumption of discriminant analysis, that the within
group variance-covariance matrices of the k populations are equal is
tested using the null hypothesis that
-2.0 RHO loq„ V (20)
^—N--PNni72-
is distributed approximately as Chi square with
d.f. = 0.5 (K - 1) P (P + 1) (21)
where
K is the number of groups
P is the number of dependent variables
N is the total number of observations
N(I) is the number of observations in the Ith group
with
V = (within $S matrix (I))*^^^^^^ (22)
(pooled SS matrix)^^^
44
and
1 - 1 2P^ + 3P - 1
RHO 1.0 (23)= - sum
N(i) - 1 rnn< 6 (P+i) ( k--n-y
If the Chi square is small then the null hypothesis that the within
group variances and covariances are unequal is not accepted. If the
Chi Square is greater than the tabled value at the appropriate signi-
ficance level, then either or both the following conclusions apply: 1)
the variances and covariances are truly unequal, or 2) the distributions
are not normal (Barr et al., 1976).
Summary
The application of discriminant analysis to the present problem
allows for the direct comparison of the spatial organization of land-
scapes when they are defined according to the different modes of land
form analysis. The hypotheses that are tested give insight into the
relationships of the two methodologies. The technique also permits
the analysis of the relative contribution of the various morphometric
variables in the allocation procedure.
CHAPTER VI
THE MORPHOMETRIC VARIABLES
The four types of morphometric variables used in this study are:
1) measurements of the drainage network; 2) the basin geometry; 3) the
intensity of dissection; and 4) those involving height. Morphometric
variables fall into several distinct groups. Some, such as lengths,
are measured directly from maps, while others, such as ratios, are de-
rived from several direct measurements. Variables also differ in their
dimensions. Stream length, for example, is a one-dimensional measure-
ment, while basin area is a two-dimensional measurement. Drainage
density is the reciprocal of a one-dimensional measure, and variables
involving length and area in their denominator are considered dimen-
sionless. The seven morphometric variables used in this study are:
1) the bifurcation ratio; 2) the stream length ratio; 3) the basin
elongation ratio; 4) drainage density; 5) basin relief; 6) the elevation-
relief ratio; and 7) the mean ground slope.
Bifurcation Ratio
Horton (1945: 286) defined the bifurcation ratio (R|^) as being
the "ratio of the average number of branchings or bifurcations of streams
of a given order to that of streams of the next higher order." Several
methods may be used to determine the bifurcation ratio. It can be com-
puted for pairs of stream orders using the formula
Rb = N„ / Nu+1 (24)
46
where is the bifurcation ratio and is the number of streams of
a given order. The average mean bifurcation ratio can be calculated
from all individual bifurcation ratios within a basin. The geometric
mean bifurcation ratio may be determined from the slope of a line pass-
ing through the two end points on a Horton diagram (Shreeve, 1966).
A weighted mean bifurcation ratio can be determined by multiplying
each individual bifurcation ratio by the total number of streams of
each order involved in the ratio and taking the mean sum of these values
(Schumm, 1956). Also, the antilog of a regression line relating log
number of streams to stream order may be used (Maxwell, 1955). This
study uses the bifurcation ratio between the number of first-order
streams and second-order streams.
The minimum bifurcation ratio is 2.0. Normally the ratio ranges
between 3.0 and 5.0 where geologic structures do not distort the drain-
age pattern. Because the bifurcation ratio is a dimensionless para-
meter, and because drainage systems of homogeneous materials display
geometrical similarity, the ratio usually shows only a small variation
from region to region. High bifurcation ratios can be expected in areas
of steeply dipping strata where narrow strike valleys are confined be-
tween hogback ridges (Strahler, 1964).
The rationale for using the bifurcation ratio as a variable is that
it is a measurement of Horton's first law of drainage composition, the
law of stream numbers. The bifurcation ratio should show where the
drainage patterns are structurally such as in the Ridge and Valley pro-
vince. Additionally, it has been used in a positive manner in several
47
generic studies of land forms such as by Woodruff (1964), Mather and
Doornkamp (1970), and Giles (1974).
Stream Length Ratio
The stream length ratio was formulated by Horton (1945: 286-287)
as the "...ratio of the average length of streams of a given order to
that of streams of the next lower order." The formula is
(25)
where R-j is the stream length ratio and is the mean length of stream
segments of a given order. This study uses the stream length ratio be-
tween second-order and first-order streams as a variable.
The stream length ratio is selected as a variable because it is a
measurement of Horton's second law of drainage composition, the law of
stream lengths. It is expected that the stream length ratio will vary
regionally, dependent upon local structures and lithologies. Giles
(1974) used the stream length ratio successfully to distinguish fluvially
eroded terrain in the North Carolina Coastal Plain.
Basin Elongation Ratio
The basin elongation ratio is a measurement of basin shape pro-
posed by Schumm (1956). The basin elongation ratio (R^) is defined as
the ratio of a circle equal to the perimeter of the drainage basin to
the maximum basin length. This is formulated
48
(26)
where is the elongation ratio, is the circumference of a circle
equal to the perimeter of the drainage basin, and is the maximum basin
length.
This dimensionless parameter varies between 0.6 and 1.0 over a wide
variety of climatic and geologic types. Values near 1.0 are common to
areas of very low relief. Values in the range of 0.6 to 0.8 are associated
with regions of steep ground slopes (Strahler, 1964). Morisawa (1958)
found the basin elongation ratio to be a good measure of basin outline
form in the Appalachian Plateau.
The basin elongation ratio is used as a variable because it is an
indicator of drainage basin shape. Morisawa (1959) and Stephenson (1967)
related the importance of drainage basin shape to runoff conditions.
Woodruff (1964), Mather and Doornkamp (1970), and Giles (1974) success-
fully used the basin elongation ratio as a variable in generic land form
regionalizations.
Drainage Density
Horton (1945) used drainage density (D^) in his landmark hydrologic
study. Defined simply, it is the ratio of the total channel-segment
length cumulated for all orders within a drainage basin to the drainage
basin area. The formula for drainage density is
k n
/ A,u (271
49
where is drainage density, is the stream lengths of channels of
a given order, and is the area of the drainage basin.
Several measurements of drainage density have been made over a wide
area of the United States. The lowest observed values, 4.8 and 6.4
p
(km. / km. ), are found to occur in the resistant sandstone strata of
the Appalachian Plateau province (Smith, 1950 and Morisawa, 1959).
Values ranging from 12.9 to 25.7 are typical in the humid regions of the
central and eastern United States where rocks are of a moderate resis-
tance and exist under a deciduous forest cover (Strahler, 1952; Coates,
1958; and Stephenson, 1967). Similar values are found in the Rocky
Mountain region, but in the drier portions of this area they may range
from 80.5 to 160.9 (Melton, 1957). The strongly fractured and deeply
weathered igneous and metamorphic rocks under the dry climate of the
coast ranges of Southern California exhibit drainage densities in the
range of 32.2 to 48.3; however, where Pleistocene sediments have been
exposed drainage densities range from 48.3 to 64.4 (Smith, 1950;
Strahler, 1952; and Maxwell, 1960). The highest values which have been
observed for drainage density are found in badlands topography, which
are developed on weak clays barren of vegetation. Smith (1950) encoun-
tered densities ranging from 321.9 to 643.7 in the badlands national
monument of South Dakota, while Schumm (1956) found values as high as
1,609.3 to 2,092.1 in the badlands at Perth Amboy, New Jersey. Generally,
a low drainage density is associated with areas of highly resistant or
highly permeable subsoil materials, under a dense vegetation cover where
relief is low. A high drainage density is indicative of regions of weak
50
or impermeable subsurface materials, sparse vegetation, and mountainous
relief (Strahler, 1964). Drainage densities may be related to the re-
lative term "texture", the spacing of drainage lines. A low drainage
density indicates a coarse texture, while a high drainage density indi-
cates a fine texture (Strahler, 1964).
Drainage density is selected as a variable because it is an impor-
tant indicator of the intensity of dissection within the drainage basin.
It is expected that drainage densities will vary across the study area
depending upon local lithologies and structures. The generic land form
regionalizations of Mather and Doornkamp (1970), Eyles (1971), and Giles
(1974) demonstrated the primary importance of drainage density for the
differentiation of fluvially eroded topography.
Basin Relief
Basin relief (H) is obtained by finding the difference between the
highest and lowest points within the drainage basin. This is formulated
H = Z - z (28)
where H is the basin relief, Z is the highest elevation within the drain-
age basin, and z is the lowest elevation in the drainage basin.
The rationale for using basin relief as a variable is twofold.
First, it is a quantified expression of altitudinal differences used in
several genetic studies such as Fenneman. Second, it is a measurement
suggested by Morisawa's law of basin relief. The highest values are
expected in mountainous terrain. Woodruff (1964), Eyles (1971), and Giles
(1974) successfully used basin relief to differentiate stream eroded topo-
graphy.
51
Elevation-Relief Ratio
The elevation-relief ratio (E) was derived by Wood and Snell (1960)
It is an expression of the relative proportion of upland to lowland
within a sample region. The ratio is formulated
P^ "_ mean elevation - minimum elevation (29)maximum elevation - minimum elevation
High values indicate broad, level surfaces occasionally broken by de-
pressions, while low values characterize isolated relief features stand-
ing above extensive level surfaces.
Pike and Wilson (1971) demonstrated that the elevation-relief ratio
is mathematically identical to the hypsometric integral developed by
Strahler (1952B). Calculation of the hypsometric integral is a lengthy
process due to the planimetry required for its derivation. Despite
simplified procedures which have been developed to approximate the hypso
metric integral (Chorley and Morley, 1959), the elevation-relief ratio
is the more practical of the two since it can be calculated rapidly and
with greater ease.
The elevation-relief ratio is selected as a variable because it is
a quantified expression of the degree of erosion within the drainage
basin. Strahler (1958), using the hypsometric integrals, suggested that
drainage basins may be designated as youthful, mature, or old depending
upon their characteristic curves. Eyles (1971) and Giles (1974) used
such altitude-to-area measurements to successfully distinguish fluvially
eroded terrain.
52
Mean Ground Slope
Random point smapling of drainage basin ground slope can yield
essentially the same information as that obtained from a slope map
(Strahler, 1956). Salisbury (1957) suggests that a minimum of five
2
sample points be selected for every 1.6 km of area. Mean ground slope
may be calculated as
n
Sg = f_i / L) (100). / n (30)
where 0 is mean ground slope expressed in percent, H is the elevation
y
difference between the highest and lowest points on a line orthogonal
to the contour where the sample point is found, and n is the size of
the sample.
Mean ground slope is selected as a variable because it depicts the
important aspect of grade within the drainage basin. Although mean
ground slopes are higher than stream slopes, it can be used as a surro-
I gate measure for that parameter. Hence, it also serves to demonstrate
aspects of Horton's law of stream slopes. The highest mean ground slopes
are expected to be found in the more mountainous areas. Eyles (1971)
and Giles (1974) used mean ground slope in a positive manner in generic
regionalizations.
CHAPTER VII
RESULTS OF HYPOTHESES TESTING
Satisfaction of Model Assumptions
The multiple discriminant analysis model has four major assump-
tions: 1) that each of the k samples are drawn from separate popula-
tions; 2) that the variables upon which the measurements are made are
normally distributed; 3) that the multivariate means of the k popula-
tions are not equal; and 4) that the within group variance-covariance
matrices of the k populations are equal (Mather, 1976).
The first assumption of multiple discriminant analysis is satisfied
by the nature of the sampling procedure. A systematic sample of third-
order drainage basins was taken from each of the four physiographic pro-
Vinces. Drainage basins within each province are assumed to belong to
k mutually exclusive populations as defined by Fenneman (1938).
The second assumption of multiple discriminant analysis, that the
variables are normally distributed, was verified by the use of the
Kolmogrov Smirnov test. The selected alpha level for acceptance of the
null hypothesis that the variables are normally distributed was 0.05.
This same significance level is used in all subsequent tests.
It was found that the distributions of bifurcation ratios, stream
length ratios, basin elongation ratios, elevation-relief ratios, and
drainage densities were normally distributed in their original forms.
The distributions of mean ground slopes and basin reliefs were found to
be normal upon transformation to log -jq distributions (Eq. 14 and 15).
54
The third assumption of multiple discriminant analysis, that the
multivariate means of the k populations are not equal, was tested by the
Hotel 1ing-Lawley trace statistic. The null hypothesis that the multi-
variate means of the k populations are equal was rejected. It was found
that the multivariate means of the k populations were unequal at Fq
with 21 and 116 degrees of freedom (Eq. 16, 17, 18, and 19).
The fourth assumption of multiple discriminant analysis, that the
within group variance-covariance matrices are equal, was tested using
the Box test for homogeneity. The null hypothesis that the within group
variance-covariance matrices were unequal was rejected. It was found
that 2the within group variance-covariance matrices were equal at X q
with 84 degrees of freedom (Eq. 20, 21, 22, and 23).
Results of Multiple Discriminant Analysis
The multiple discriminant analysis procedure reallocated drainage
basins to different groups based upon the generalized squared distance
between groups (Eq. 7, 8, and 9). The generalized squared distance be-
tv;een groups is given in Table III. Along the diagonal, there are similar
distances to the centroids for each group. The relatively large values,
such as between the Ridge and Valley province and the Appalachian Pla-
teau province, indicate the distinct nature of the two groups from one
another. The posterior probability of membership in each group indicated
that five drainage basins were significantly different from the groups
to which they were initially assigned (Eq. 10). This is shown in Table
IV. Two drainage basins from the Piedmont province were reassigned, while
three drainage basins from the Ridge and Valley province were reassigned.
55
Table III
Generalized Squared Distance Between Groups
From ID Generalized Squared Distance to ID
12 3 4
1 -13.826 75.596 - 3.833 858.456
2 4.770 -15.274 29.641 145.012
3 - 9.165 50.990 -11.837 401.548
4 - 5.495 9.382 6.962 -17.429
ID 1 = Piedmont Province
ID 2 = Blue Ridge Mountain Province
ID 3 = Ridge and Valley Province
ID 4 = Appalachian Plateaus Province
56
Table IV
Posterior Probability of Membership to Different Groups
Observation ID To ID 1 2 3 4
Piedmont
Province
1 1 1 1.0000 0.0000 0.0000 0.0000
2 1 1 1.0000 0.0000 0.0000 0.0000
3 1 1 1.0000 0.0000 0.0000 0.0000
4 1 1 1.0000 0.0000 0.0000 0.0000
5 1 1 1.0000 0.0000 0.0000 0.0000
6 1 1 1.0000 0.0000 0.0000 0.0000
7 1 1 1.0000 0.0000 0.0000 0.0000
8 1 1 1.0000 0.0000 0.0000 0.0000
9 1 1 0.9827 0.0000 0.0173 0.0000
10 1 1 0.9995 0.0000 0.0005 0.0000
11 1 1 0.9738 0.0000 0.0262 0.0000
12 1 1 0.9411 0.0000 0.0589 0.0000
13 1 1 0.9936 0.0000 0.0064 0.0000
14 1 1 0.9854 0.0000 0.0146 0.0000
15 1 1 019948 0.0000 0.0052 0.0000
16 1 3* 0.2297 0.0000 0.7703 0.0000
17 1 4* 0.0317 0.1083 0.0000 0.8600
18 1 1 1.0000 0.0000 0.0000 0.0000
19 1 1 0.8011 0.0000 0.1989 0.0000
Blue Ridge Mountain
Province
20 2 2 0.0234 0.9666 0.0000 0.0000
21 2 2 0.0025 0.9974 0.0000 0.0000
22 2 2 0.0000 1.0000 0.0000 0.0000
23 2 2 0.0004 0.9996 0.0000 0.0000
24 2 2 0.0117 0.9883 0.0000 0.0000
25 2 2 0.0051 0.9949 0.0000 0.0000
26 2 2 0.0155 0.9845 0.0000 0.0000
27 2 2 0.0000 1.0000 0.0000 0.0000
28 2 2 0.0000 1.0000 0.0000 0.0000
29 2 2 0.0000 1.0000 0.0000 0.0000
30 2 2 0.0000 1.0000 0.0000 0.0000
57
Table IV
(Continued)
Observation ID To ID 1 2 3 4
Ridge and Valley
Province
31 3 3 0.0000 0.0000 1.0000 0.0000
32 3 3 0.0058 0.0000 0.9942 0.0000
33 3 3 0.0000 0.0000 1.0000 0.0000
34 3 3 0.0000 0.0000 1.0000 0.0000
35 3 1* 0.8427 0.0000 0.1573 0.0000
36 3 1* 0.8701 0.0000 0.1299 0.0000
37 3 3 0.0221 0.0000 0.9779 0.0000
38 3 3 0.0028 0.0000 0.9972 0.0000
39 3 1* 0.7449 0.0000 0.2551 0.0000
40 3 3 0.0161 0.0000 0.9839 0.0000
41 3 3 0.1784 0.0000 0.8216 0.0000
42 3 3 0.0590 0.0000 0.9410 0.0000
Appalachian Plateau
Province
43 4 4 0.0002 0.0000 0.0000 0.9998
44 4 4 0.0080 0.0127 0.0000 0.9794
45 4 4 0.0000 0.0271 0.0000 0.9721
46 4 4 0.0149 0.0047 0.0000 0.9805
47 4 4 0.0003 0.0000 0.0000 0.9997
48 4 4 0.0031 0.0000 0.0000 0.9969
49 4 4 0.0000 0.0000 0.0000 1.0000
50 4 4 0.0719 0.0000 0.0000 0.9281
ID 1 = Piedmont Province
ID 2 = Blue Ridge Mountain Province
ID 3 = Ridge and Valley Province
ID 4 = Appalachian Plateau Province
An * indicates a drainage basin which has been reassigned.
58
There was no change in the prior probabilities for the Blue Ridge Moun-
tain and Appalachian Plateau provinces (see Table V).
The relative dispersion of drainage basins before reallocation in
p dimensional space may be seen by plotting the first two canonical
vectors or variables (see Figure 4). It was found that the first canon-
ical vector with an associated eigenvalue of 0.8765 explained 76.83 per-
2
cent of the overall discriminating power of the model with X q qqq-j at
21 degrees of freedom (Eq. 11, 12, and 13). The second canonical vector
with an associated eigenvalue of 0.6014 accounted for 36.17 percent of
the total discriminating power of the model with X q q281 degrees
of freedom. A third canonical vector was calculated, but it was found
2
not to be significant in the model formulation with X q g234 ^ degrees
of freedom (Eq. 11, 12, and 13).
The relative contribution of each variable in the separation of groups
is seen by the scaling of their characteristic values associated with
each of the eigenvectors. The scaling is accomplished by dividing the
score of all of the values by the score of the largest value. The rank
of each value then determines its relative contribution in the overall
separation between groups. The higher a rank that a variable holds, then
the greater its importance. The range between the highest and lowest
values is important in determining the causation of the separation in p
dimensional space of the different groups. Each canonical vector has a
set of characteristic values associated with each variable. The rank
and scaled value for the first two canonical vectors is seen in Tables
VI and VII. It is seen that for the first two canonical vectors that the
1.1 • PIEDMONT
© BLUE RIDGE
1.0 o RIDGE AND VALLEY ^
? PLATEAU
0.9
e ?
0.8 ?
VC2AENCTO 0.7 ?o ©o o ? © ©ONICARL 0.6 ? © ©©0.5 • ?
© ©
0.4 a
o
?
0.3
Lj I I I I I I I I I I I I—
1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65
CANONICAL VECTOR 1
Figure 4: Plot of canonical variables in P dimensional space. Ln140
60
Table V
Posterior Probability of Classification
into Different Groups
From Group Into Group
Piedmont Blue Ridge Ridge and Appalachian Total
Mountains Valley Plateau
Piedmont 89.47 0.00 5.26 5.26 100.00
(17) (0) (1) (1) (19)
Blue Ridge 0.00 100.00 0.00 0.00 100.00
Mountains (0) (11) (0) (0) (11)
Ridge and 25.00 0.00 75.00 0.00 100.00
Valley (3) (0) (9) (0) (12)
Appalachian 0.00 0.00 0.00 100.00 100.00
Plateau (0) (0) (0) (8) (8)
Total 40.00 22.00 20.00 18.00 100.00
(20) (11) (10) (9) (50)
61
Table VI
Characteristic Values of the First Canonical Vector
Variable Scaled Rank
Value
Bifurcation ratio 0.0379 5
Stream length ratio 0.0015 6
Basin elongation ratio 0.2104 3
Drainage density -0.0119 7
Relative basin relief 0.2268 2
Elevation-relief ratio 1.0000 1
Mean ground slope 0.0687 4
62
Tablé VII
Characteristic Values of the Second Canonical Vector
Variable Scaled Rank
Value
Bifurcation ratio 0.0275
Stream length ratio -0.0548
Basin elongation ratio -0.1080
Drainage density -0.0065
Relative basin relief 0.1069
Elevation-relief ratio 1.0000
Mean ground slope -0.1532 7
63
elevation-relief ratio and relative relief are the most important dis-
tinguishing variables. The lowest value for the first canonical vector
is drainage density, while for the second canonical vector the lowest
value is mean ground slope.
Interpretation of Test Statistics
The working hypothesis for the present study is that when drainage
basins are defined on the basis of their morphometric parameters they
will group in a similar fashion to an a priori genetic regionalization.
The results of the discriminant analysis model must be interpreted in
such a manner that it may be related back to the working hypothesis
and the applicable theory.
It was found that 90.0 percent of all the drainage basins were in
accord with their initial assignments. This high degree of spatial co-
hesion supports the premise of the working hypothesis; however, five
anomalous drainage basins were identified. These drainage basins were
more aligned with the new groups to which they were allocated. Inspec-
tion of the posterior probabilities of membership to different groups
by province illuminates the results of the multiple discriminant analysis
model.
Piedmont Province
Sixteen of the nineteen Piedmont drainage basins, on the basis of
their generic characteristics, had posterior probabilities of greater
than 0.9400 of being classified as Piedmont types. The first eight
drainage basins within the eastern portion of the transect had posterior
64
probabilities of belonging to that group of 1.000, a fact that indi-
cates a high degree of spatial conformity. The far western Piedmont
drainage basin had a lower posterior probability of membership of 0.8011.
This lower probability was expected, since the basin is at the boundary
with the Blue Ridge Mountain province.
Two of the Piedmont drainage basins were reallocated to different
groups. These are the Osborn Creek drainage basin of the Osbornville
quadrangle and an unnamed third-order drainage basin of the Gilreath
quadrangle. Both of these drainage basins are in the Brushy Mountains
of North Carolina. Fenneman fl938) identified the Brushy Mountains as
being genetically similar to the Piedmont, but as being dissimilar in
terrain characteristics.
Osborn Creek is underlain by a Precambrian mica gneiss complex.
The drainage basin was found to have similar morphometric characteristics
to the drainage basins of the Ridge and Valley province. However, there
is a dissimilarity between the metamorphic rocks of this basin and the
overall sedimentary structures of the Ridge and Valley province. The
similarity is seen to exist in the overall topographic form of the drain-
age basin. Several resistant ridges increase the relative relief of the
drainage basin to 160 meters, which is well above the mean for the Pied-
mont province as a whole but is very similar to that of the Ridge and
Valley province fsee Appendix C). Additionally, the elevation-relief
ratio for the basin is 37.0 percent, well below the mean of the Piedmont
province, but very near to the mean of 36,5 percent of the Ridge and
Valley province. Since the elevation-relief ratio and the relative
65
relief of drainage basins were found to be the two most important para-
meters in the distinguishing of groups, such findings are reasonable.
A similar situation exists with the unnamed third-order drainage
basin of the Gilreath quadrangle. This basin is underlain by a granitic
complex, which is unlike the overall sedimentary structures of the Appa-
lachian Plateau province with which the drainage basin has greater
similarities. Again the explanation is seen in the overall topographic
expression of the drainage basin. The drainage basin is highly dissected
in a manner similar to that of the basins of the eastern portion of the
Appalachian Plateau province. The mean relative relief of the drainage
basin is 347 meters which is very close to the mean relative relief of
the Plateau province of 312 meters. The elevation-relief ratio of the
drainage basin being 53.0 percent is also similar to the elevation-relief
ratio for the Plateau province as a whole of 52.8 percent.
The difference in the lithologies of the two drainage basins from
the predominant lithologies of the provinces with which they are similar,
may be accounted for by the fact that despite the difference in rock
types the erodibility of the structures are similar.
The identification of these two drainage basins as anomalies illu-
strates the classic dichotomy of the two systems of land form classifi-
cation. Genetically the two basins are related to the Piedmont, but
there are dissimilarities in their terrain characteristics with the
province as a whole. This factor, however, was pointed out by Fenneman
(1938) more than forty years ago.
66
Blue Ridge Mountain Province
The drainage basins of the Blue Ridge Mountain province exhibited a
high degree of similarity between being classified by the two modes of
land form analysis. Each drainage basin had a posterior probability of
membership to the Blue Ridge Mountain group of greater than 0.9500. Five
drainage basins of the total eleven had posterior probabilities of 1.0000.
The distinct nature of the physiographic province predicates such con-
formity between the two classification schemes.
Ridge and Valley Province
The Ridge and Valley Province showed the greatest disparity in the
comparison of the two classification schemes. Three of the twelve sam-
pie drainage basins were reallocated. In each instance the reallocation
was from the Ridge and Valley province type drainage basin to Piedmont
type drainage basins. However, eight drainage basins did have posterior
probabilities of membership to the Ridge and Valley Province of greater
than 0.9400 and three of these drainage basins had probabilities of
1.0000.
The three Ridge and Valley drainage basins that were reallocated
were the Leadville Creek drainage basin of the White Pine quadrangle, the
Goose Creek drainage basin of the Jefferson City quadrangle, and the Legg
Creek drainage basin of the John Sevier quadrangle.
The Leadville Creek drainage basin of the White Pine quadrangle is
underlain by Knox dolomite and Sevier shale. The sedimentary structure
of this drainage basin is dissimilar to the metamorphic and igneous
structures of the Piedmont, but since these sedimentary structures are
67
massive similar erodibility functions are thought to exist with the
lithologies of the Piedmont province. The elevation-relief ratio of the
drainage basin is 46.0 percent which is very close to the mean of 49.0
percent of the Piedmont province. Additionally the 70 meter relative
relief of the drainage basin is equal to the relative relief of the Pied-
mont province.
The Goose Creek drainage basin of the Jefferson City quadrangle is
completely underlain by Knox dolomite, which is dissimilar to the meta-
morphic and igneous structure of many Piedmont drainage basins. However,
since Knox dolomite is a massive structure, it is felt that the erodibi-
lity of the formation will be less and of similar nature to those rock
types found within the Piedmont province. The causative factor of this
drainage basin being reallocated to the Piedmont type group is its
elevation-relief ratio of 52.0 percent, which is comparable to the mean
of the Piedmont of 49.0 percent.
The Legg Creek drainage basin is underlain by shales, limestones,
and dolomites. The upper portion of the drainage basin at MacNally Ridge
is composed of shales. The middle portion of the drainage basin is lime-
stone, while the lower portion of the drainage basin is composed of
dolomite. The main third-order stream traverses MacNally Ridge. Again
the rock types of this drainage basin have similar erodibility to those
rock types of the Piedmont. The only common link which was found between
this drainage basin and those of the Piedmont was a similarity in drain-
age densities. The drainage density for Legg Creek is 2.37, while the
mean drainage density for the Piedmont province is 2.40.
68
Appalachian Plateau Province
The Appalachian Plateau Province like the Blue Ridge Province showed
complete conformity according to the two different systems of terrain
evaluation. Seven of the eight sample drainage basins of the Appalachian
Plateau Province had posterior probabilities of membership of belonging
to the group of greater than 0.9700. One drainage basin had a probabi-
lity of 0.9200.
CHAPTER VIII
f
CONCLUSIONS
Several conclusions can be drawn from the results of this study:
1) that the classification of terrain by either genetic or generic
schemes will yield similar results; 2) that a simplified generic approach
can be applied to terrain analysis that incorporates the essential ele-
ments of both systems; and 3) that morphometric studies are pertinent
to more applied geomorphic analyses.
The classification of terrain by either the genetic or generic ap-
proaches has been shown to have similar results spatially. Ninety per-
cent of the sample drainage basins fell within the original groups to
which they were assigned. The five drainage basins which were reallocated
had differences in their morphometric characteristics. The two Piedmont
drainage basins which were reallocated are in the Brushy Mountains of
North Carolina. This area, an outlier of the Blue Ridge Mountain pro-
vince, was noted by Fenneman (1938) as being dissimilar from the rest of
the Piedmont province. This anomaly judged qualitatively by Fenneman has
been confirmed quantitatively here. The remaining drainage basins that
were reallocated are in the Ridge and Valley province. This highly com-
plex geologic area, while unified genetically, has great diversity in the
individual topographic expression of drainage basins due to varied struc-
tures and lithologies. When the scale of morphometric analysis used for
individual drainage basins is considered, the work of Fenneman stands as
an example of the thoroughness of an earlier generation of American geo-
morphologists. The point of view taken by Schumm and Lichty (1965) that
70
open and closed systems analysis focus on different variables but can
yield similar results is confirmed.
The drainage basin as a unit of study offers the advantage of a more
complex picture of the essential elements of terrain. However, multi-
variate studies thus far have been complicated in procedure and have not
been duplicable in other areas. It is suggested that the elevation-
relief ratio and basin relief offer the simplest means of classifying
terrain, since these variables were found to be of predominant importance.
These variables, while being quantitative in nature, are expressions of
Davis' concept of stage and of elements of topographic form. The use of
these two variables in future studies would combine the best attributes
of the two approaches to land form analysis.
While it was found that mean ground slopes and drainage density as
variables did not play a key role in the grouping of drainage basins,
the value of these parameters as well as other morphometric variables has
not been undermined. Such morphometric parameters are of extreme impor-
tance to applied geomorphic studies where the specific information which
they yield can be applied directly to problem solving.
Since it has been demonstrated that genetic regionalizations are
more than adequate in defining the surface features of the earth into
spatial groupings, large scale generic regionalizations aimed in the same
vein might very well be fruitless endeavors. However, it is stressed
that before such a conclusion can be reached, studies similar to the pre-
sent one must be conducted in different regions. Additionally, such
studies could be used to determine the geographic significance of the
71
several morphometric parameters as well as their role in the spatial
ordering of landscapes.
72
BIBLIOGRAPHY
Ashley, G.H. 1935. Studies in Appalachian Mountain Structure.
Geological Society of America Bulletin 46: 1935-1436.
Atwood, W.W. 1940. The Physiographic Provinces of North America.
New York: Ginn and Co.
Barr, A.J. et £]_. 1976. A User's Guide to SAS 76. Raleigh: SAS
Institute.
Bascom, F. 1921. Cycles of erosion in the Piedmont province of
Pennsylvania. Journal of Geology 29: 540-549.
Bowden, K.L., and Wallis, J.R. 2964. Effects of stream-ordering on
Horton's laws of drainage composition. Geological Society of
America Bulletin 75: 767-774.
Broscoe, A.J. 1959. Quantitative analysis of longitudinal stream pro-
files of small watersheds. ONR, Geog. Branch, Project NR 389-042,
Tech. Rept. 18.
Bryan, K. 1941. Physiography. Geological Society of America Bulletin
50: 3-15.
Calef, W., and Newcomb, R. 1953. An average slope map of Illinois.
Annals of the Association of American Geographers 43: 305-316.
Chorley, R.J. 1957. Climate and morphometry. Journal of Geology 65:
628-638.
1962. Gepmorphology and general systems theory. United States
Geological Survey Professional Paper 500-B, p. 1-10.
Chorley, R.J., and Morgan, M.A. 1962. Comparison of morphometric fea-
tures, Unaka Mountains Tennessee and North Carolina, and Dartmoor,
England. Geological Society of America Bulletin 73: 14-34.
Chorley, R.J., and Morley, L.S.D. 1959. A simplified approximation of
the hypsometric interval. Journal of Geology 67- 566-571
Coates, D.R. 1958. Quantitative geomorphology of small drainage basins
of Southern Indiana. Columbia University, Department of Geology,
Tech. Rept. 10.
Cooke, R.U., and Doornkamp, J.C. 1977. Geomorphology in Environmental
Management. Oxford: Clarendon Press.
73
Davis, W.M. 1899. The Geographical Cycle. Geographical Journal 14:
481-504.
Doornkamp, J.C., and King, C.A.M. 1971. Numerical Analysis in Geo-
morphology. New York: St. Martins Press.
Eyles, R.J. 1971. A classification of West Malaysian drainage basins.
Annals of the Association of American Geographers 61: 460-467.
Fenneman, N.M. 1916. Physiographic divisions of the United States.
Annals of the Association of American Geographers 6: 19-98.
1928. Physiographic divisions of the United States. Annals
oT the Association of American Geographers 18: 261-353.
. 1931. Physiography of Western United States. New York:
McGraw-Hill Book Co.
. 1938. Physiography of Eastern United States. New York:
McGraw-Hill Book Co.
Fok, Y.S. 1971. Law of stream relief in Horton's stream morphological
system. Water Resources Research 7: 201-203.
Folsom, N.M., and Winters, H.A. 1970. Drainage orders in Michigan.
Michigan Academician 2: 79-91.
Gardner, J.V. 1972. A quantitative geomorphic study in the Lehigh
River-Delaware River section of the Great Valley of Pennsylvania.
Illinois Geog. Society Bulletin 14: 3-16.
Gilbert, G.K. 1877. Report on the geology of the Henry Mountains.
U.S. Geographic and Geological Survey of the Rocky Mountain Region.
Giles, B.E. 1974. Spatial Organization of Morphometric Characteristics
of the North CaFolina Coastal Plain. Unpublished Masters Thesis,
Department of Geogrpahy, East Carolina University.
Gravelius, H. 1914. Flusskunde: Goschensche Verlagshandlung. Berlin.
Hack, J.T. 1960. Interpretation of erosional topography in humid tern-
perate regions. American Journal of Science 258-A; 80-97.
. 1965. Geomorphology of the Shenandoah Valley, Virginia and
West Virginia, and origin of residual ore deposits. U.S. Geological
Survey Professional Paper 484.
Hall, A.D., and Fagan, R.E. 1956. Definition of systems. General
Systems Yearbook VI, Ann Arbor, Michigan, p. 18-28.
74
Hammond, E.H. 1962. Landform geography and landform description,
The California Geographer 3: 69-75.
1964. Classes of land-surface form in the forty-eight states,
DTS.A. Annals of the Association of American Geographers (Map
Supplement 4) 54i
Horton, R.E. 1945. Erosional development of streams and their drain-
age basins, hydrophysical approach to quantitative morphology.
Geological Society of America Bulletin 56: 275-370.
Hunt, C.B. 1950. Military geography. Application of Geology to
Engineering Practice. (Geological Society of America, Berkey
Volume), 295-327.
1974. Natural Regions of the United States and Canada. San
Francisco: W.H. Freeman Co.
Kendall, M.G. 1966. Discrimination and classification in Multivariate
Analysis, P.R. Krishnaiah (ed.). New York: Academic Press, l6'5-l85.
Kesseli, J.E, 1946. A neglected field: geomorphogeography. Annals
of the Association of American Geographers 36: 93.
1950. A geomorphology suited for the needs of geographers.
Mnals of the Association of American Geographers 44: 220-221.
King, L.C. 1953. Cannons of landscape evolution. Geological Society
of America Bulletin 64: 721-751.
King, L.J. 1970. Discriminant analysis: a review of recent theoreti-
cal contributions and applications. Economic Geography 46: 366-
378.
Klingebiel, A,A., and Montgomery, P.H.. 1961. Land-capability classi-
fication. Soils Conservation Service, U.S. Department of Agri-
culture. Agricultural Handbook 210.
Lobeck, A.K, 1950. Physiographic diagram of North America. Maplewood,
New Jersey: The Geographical Press.
Leopold, L.B., and Miller, J.P. 1956. Ephemeral streams - hydraulic
factors and their relation to the drainage net. United States
Geological Survey Professional Paper 282-A, p. l-TT^
Lewis, L.A. 1969. Analysis of surficial landform properties -- the
regionalization of Indiana into units of landform similarity.
Proceedings Indiana Academy of Science 78: 317-328.
75
Loomis, F.K. 1937. Physiography of the United States. New York:
Doubleday and Doran Co.
Mabbutt, J.A. 1968. Review and concepts of land classification in
Land Evaluations, G.A. Stewart (ed.). Papers of a CSIRO Symposium,
DNrSC'OV p". 12-28.
Mather, P.M. 1976. Computational Methods of Multivariate Analysis in
Physical GeograpTiy^ New York: John Wiley and Sons.
Mather, P.M., and Doornkamp, J.C. 1970. Multivariate analysis in geo-
graphy with particular reference to drainage basin morphometry.
Transactions, Institute of British Geographers 51: 163-187.
Maxwell, J.C. 1955. The bifurcation ratio in Horton's law of stream
numbers. Transactions, American Geophysical Union 36: 520.
1960. Quantitative geomorphology of the San Dimas experimental
forest, California. ONR, Geography Branch, Project NR 389-042,
Tech. Rept. 19.
Melton, M.A. 1957. An analysis of the relations among elements of
climate, surface properties, and geomorphology. ONR, Geography
Branch, Project NR 389-042, Tech. Rept. 11.
1958. Correlation structure of morphometric properties of
drainage systems and their controlling agents. Journal of Geology
66: 442-460.
Miller, V.C. 1953. A guantitative geomorphic study of drainage basin
characteristics in the Clinch Mountain area, Virginia and Tennessee.
ONR, Geography Branch, Project 389-042, Tech. Rept. 3.
Milling, M.E., and Tuttle, S.D. 1965. Morphometric study of two drain-
age basins near Iowa City, Iowa. Proceedings, Iowa Academy of
Science 71: 304-309.
Milton, L.E. 1966. The geomorphic irrelevance of some drainage net
laws. Australian Geog. Studies 4: 89-95.
Ministry of Overseas Development. 1970. The Work of the Land Resources
Division. Tolworth, England.
Morisawa, M.E. 1958. Measurement of drainage basin outline form.
Journal of Geology 66: 587-591.
1959. Relation of quantitative geomorphology to stream flow
in representative watersheds of the Appalachian Plateau province.
ONR, Geography Branch, Project 389-042, Tech. Rept. 20.
76
1962. Quantitative geomorphology of some watersheds in the
?^palachian Plateau. Geological Society of America Bulletin 73:
1025-1046.
1968. Streams, Their Dynamics and Morphology. New York:
RcGraw-Hill.
Murphy, R.E. 1967. A spatial classification of landforms based on
both genetic and empirical factors - a revision. Annals of the
Association of American Geographers 57: 185-186.
1968. Landforms of the world. Annals of the Association
ÔT American Geographers (Map Supplement 9) 58.
Penck, W. 1953. Morphological Analysis of Landforms. Translated and
edited by Helia Czeck and K.C. Boswell, London: Macmillan.
Pike, R.J., and Wilson, S. 1971. Elevation-relief, hypsometric inte-
gral, and geomorphic area-altitude analysis. Geological Society
of America Bulletin 82: 1079-1084.
Powell, J.W. et al. 1896. The Physiography of the United States.
American Book Co.
Raisz, E., and Henry, J. 1937. An average slope map of southern New
England. Geographical Review 27: 467-472.
Rao, C.R. 1965. Linear Statistical Inference and Its Applications.
New York: John Wiley and Sons.
Russell, R.J. 1949. Geographical geomorphology. Annals of the
Association of American Geographers 39: 1-11.
Salisbury, N.E. 1957. A Generic Classification of Landforms of
Minnesota. Unpublished Ph.D. Dissertation. University of
Minnesota.
1971. Threads of inquiry in quantitative geomorphology
in Quantitative Geomorphology: Some Aspects.and Appiications,
Publications in Geomorphology, The State University of New
York, Binghamton, New York, p. 9-60.
Scheidegger, A.S. 1961. Theoretical Geomorphology. Englewood Cliffs,
New Jersey: Prentice-Hal1.
1965. The algebra of stream-order numbers. United States
^ological Survey Professional Paper 525-B, p. 187-189.
77
1968. Horton's law of stream numbers. Water Resources
ïïësearch 4: 655-658.
Schumm, S.A. 1956. Evolution of drainage systems and slopes in bad-
lands at Perth Amboy, New Jersey. Geological Society of America
Bulletin 67: 597-646.
Schumm, S.A., and Lichty, R.W. 1965. Time, space, and causality in
geomorphology. American Journal of Science 253: 110-119.
Shreeve, R.L. 1963. Horton's law of stream numbers for topologically
random drainage networks. Transactions, American Geophysical Union
44: 44-45.
. 1966. Statistical law of stream numbers. Journal of Geology
74: 17-37.
. 1967. Infinite topologically random channel networks. Jour-
nal of Geology 75: 178-186.
Smart, J.S. 1967. A comment on Horton's law of stream numbers. Water
Resources Research 3: 773-776.
Smith, G.H. 1935. The relative relief of Ohio. Geographical Review
25: 272-284.
Smith, K.G. 1950. Standards of grading texture of erosional topography.
American Journal of Science 248: 655-668.
Stephenson, R.A. 1967. The Spatial Variation of Stream Flow and Re-
lated Hydrologic Characteristics in Selected Basins of the Southern
Blue Ridge Mountains. Unpublished Ph.D'. Dissertation, Department
of Geography, University of Iowa.
. 1971. Stream types in the Des Moines River basin. Water
ïïësources Bulletin 7: 1172-1179.
Strahler, A.N. 1952A. Dynamic basis for geomorphology. Geological
Society of America Bulletin 63: 923-938.
. 1952B. Hypsometric (area-altitude) analysis of erosional
topography. Geological Society of America Bulletin 63: 1117-1142.
. 1954A. Empirical and explanatory methods in physical geo-
graphy. The Professional Geographer 6: 4-8.
. 1954B. Statistical analysis in geomorphic research. Jour-
nal of Geology 62: 1-25.
78
. 1956. Quantitative slope analysis. Geological Society of
Mer ica Bulletin 67: 571-596.
1957. Quantitative analysis of water shed geomorphology.
Transactions, American Geophysical Union 38: 913-920.
1958. Dimensional analysis applied to fluvially eroded land-
forms. Geological Society of America Bulletin 69: 279-300.
. 1964. Quantitative geomorphology of drainage basins and chan-
nel networks in Handbook of Applied Hydrology, V.J. Chow (ed.).
New York: McGraw-Hill Book Co.
Thornbury, W.D. 1965. Regional Geomorphology of the United States.
New York: John Wiley and Sons.
Till, R. 1974. Statistical Methods for the Earth Scientist. New York:
John Wiley and Sons.
‘United States Geological Survey. 1976. Topographic Maps. Washington,
D.C.: United States Government Printing Off ice.
Von Bertanlanffy, L. 1956. General systems theory. General Systems
Yearbook VI, Ann Arbor, Michigan, p. 1-10.
Wentworth, C.K. 1930. A simplified method of determining the average
slope of land surfaces. American Journal of Science 20: 184-194.
Wodlenberg, M. 1966. Horton's laws justified in terms of allometric
growth and steady state in an open system. Geological Society of
America Bulletin 77: 431-434.
. 1971. The two dimensional spatial organization of Clear Creek
and Old Man Creek, Iowa. Harvard Papers in Theoretical Geography
No. 43, p. 1-34.
Wood, W.F., and Snell, J.B. 1960. A quantitative system for classify-
ing landforms. U.S. Army Natick Laboratory, Natick, Massachusetts,
Tech. Rept. EP-124, p. 1-20.
Woodruff, J.F. 1964. A comparative analysis of selected drainage basins.
The Professional Geographer 26: 15-19.
Zakrzewska, B. 1967. Trends and methods in land form geography. Annals
of the Association of American Geographers 57: 128-165.
79
APPENDIX A
Quadrangle State Basin Section Area (KM^)
Piedmont Province:
Hillsborough NC Little Creek N 3.52
Efland NC No Name C 4.86
Mebane NC No Name C 7.82
Burlington• NC No Name w 3.28
Gibsonvi1 le NC No Name c 2.35
McLeansvilie NC No Name NE 11.12
Greensboro NC No Name NW 6.34
Guilford NC Long Branch C 5.62
Kernersville NC No Name C 5.36
Winston-Salem East NC Soakas Creek SW 7.77
Winston-Salem West NC Side Branch SE 1.62
Clemmons NC Ellison Creek C 8.22
Farmington NC No Name C 12.66
Lone Hickory NC Fisher Creek C 4.86
Brooks Crossroads NC Walkers Branch W 4.01
Osbornvilie NC Osborn Creek NE 8.51
GiIreath NC No Name C 6.44
Moravian Falls NC Moravian Creek c 10.22
Boomer NC Little Warrior Creek c 9.65
Blue Ridge Mountain Province:
Grand in NC No Name w 9.70
Buffalo Cove NC Green Park Branch SE 3.11
Globe NC Johns River N 7.21
Grandfather Mtn. NC Wilson Creek N 5.91
Newland NC No Name C 6.45
Carvers Gap NC/TN Henson Creek S 8.74
Bakersvilie NC/TN Sweet Creek S 5.21
Huntdale NC/TN Brummett Creek E 3.23
Chestoa NC/TN No Name C 1.71
Flag Pond NC/TN Big Branch C 3.09
Greystone NC/TN No Name C 1.51
Ridge and Valley Province:
Davey Crockett Lake NC/TN Flag Branch C 2.74
Cedar Creek TN Gregg Creek C 3.77
Parrotsvi lie TN Sinking Creek C 1.75
Rankin TN McCowan Creek C 4.26
White Pine TN Leadvosle Creek NE 3.67
80
APPENDIX A (Continued)
Quadrangle State Basin Section Area (KM )
Ridge and Valley Province (Continued):
Jefferson City TN Goose Creek S 4.05
New Market TN Dance Branch SE 2.40
Mascot TN Clift Creek S 6.31
John Sevier TN Legg Creek c 5.20
Fountain City TN Cox Creek E 5.97
Powel1 TN Patt Branch W 2.65
Cl inton TN No Name C 5.28
Appalachian Plateau Province:
Wind Rock TN Hoskins Creek C 5.28
Petros TN Middle Creek E 2.49
Camp Austin TN Hall Branch C 4.41
Lancing TN Rock Creek C 4.97
Hebbertsburg TN Hawn Spring Branch NW 1.77
Fox Creek TN South Fork NW 5.26
Isoline TN Scott Creek E 12.08
Campbell Junction TW Clear Creek E 10.15
81
APPENDIX B
Geologic Formations
Hillsborough (Little Creek)
Carolina Slate Belt: chiefly acid tuffs, breccias, and flows, in part
of sedimentary origin; also mafic fragmentais and flow materials and
lenses of bedded slate (Precambrian or Lower Paleozoic).
Efland (Unnamed)
Carolina Slate Belt: chiefly basic tuffs, breccias, and flows, in part
of sedimentary origin; also felsic fragmental and flow materials and
lenses of bedded slate (Precambrian or Lower Paleozoic).
Mebane (Unnamed)
Carolina Slate Belt: chiefly acid tuffs, breccias, and flows, in part
of sedimentary origin; also mafic fragmentais and flow materials and
lenses of bedded slate (Precambrian or Lower Paleozoic).
Burlington (Unnamed)
Massive to weakly foliated even-grained to porphyritic granitic rocks
(Paleozoic).
Gibsonville (Unnamed)
Carolina Slate Belt: chiefly basic tuffs, breccias, and flows, in part
of sedimentary origin; also mafic fragmentais and flow materials and
lenses of bedded slate (Precambrian or Lower Paleozoic).
McLeansville (Unnamed)
Massive to weakly foliated even-grained to porphyritic granitic rocks
(Paleozoic).
Greensboro (Unnamed)
Massive to weakly foliated even-grained to porphyritic granitic rocks
(Paleozoic).
82
APPENDIX B
(Continued)
Guilford (Long Branch)
Carolina Slate Belt; chiefly basic tuffs, breccias, and flows, in part
of sedimentary origin; also felsic fragmental and flow materials and
lenses of bedded slate (Precambrian or Lower Paleozoic).
Kernersville (Unnamed)
Massive to weakly foliated even grained to porphyritic granitic rocks
(Paleozoic).
Winston-Salem East (Sokas Creek)
Chiefly mica gneiss; includes mica schist and a wide variety of other
gneisses and schists (Precambrian).
Winston-Salem West (Side Branch)
Chiefly mica gneiss; includes mica schist and a wide variety of other
gneisses and schists (Precambrian).
Clemmons (Ellison Creek)
Diorite-Gabbro: massive to weakly foliated; gray to dark greenish gray
rocks, composed mostly of plagioclase, hornblende, and pyroxene (Paleozoic)
Farmington (Unnamed)
Diorite-Gabbro: massive to weakly foliated; gray to greenish gray rocks,
composed mostly of plagioclase, hornblende, and pyroxene (Paleozoic).
Lone Hickory (Fisher Creek)
Chiefly mica gneiss, includes mica schist and a wide variety of other
gneisses and schists (Precambrian).
Brooks Crossroads (Walkers Branch)
Chiefly mica gneiss, includes mica schist and a wide variety of other
gneisses and schists (Precambrian).
83
APPENDIX B
(Continued)
Osbornville (Osborn Creek)
Chiefly mica gneiss, includes mica schist and a wide variety of other
gneisses and schists (Precambrian).
Gilreath (Unnamed)
Massive to weakly foliated, even grained to porphyritic granitic rocks
(Paleozoic).
Moravian Falls (Moravian Creek)
Chiefly mica schist, includes mica gneiss and a wide variety of other
gneisses and schists (Precambrian).
Boomer (Little Warrior Creek)
Cheifly mica gneiss, includes mica schist and a wide variety of other
gneisses and schists (Precambrian).
Grandin (Unnamed)
Chiefly mica gneiss, includes mica schist and a wide variety of other
gneisses and schists (Precambrian).
Buffalo Cove (Green Park Branch)
Chiefly mica gneiss, includes mica schist and a wide variety of other
gneisses and schists (Precambrian).
Globe (Johns River)
Light reddish, coarse or porphyritic granite gneiss (Precambrian).
Grandfather Mtn. (Wilson Creek)
Unicoi: feldspathic sandstone and conglomerate; some siltstone and
shale (Lower Cambrian).
84
APPENDIX B
(Continued)
Newland (Unnamed)
Cranberry; granite gneiss of varying colors and textures containing
lenses of hornblende gneiss, mica gneiss, and mica schist (Precambrian).
Carvers Gap (Henson Creek)
Precambrian crystalline complex: granite and gneissic rocks with indu-
sions of mica and hornblende schist (Precambrian).
Bakersville (Sweet Creek)
Precambrian crystalline complex: granitic and gneissic rocks with indu-
sions of mica and hornblende schist (Precambrian).
Huntdale (Brummett Creek)
Snowbird: shale, siltstone, arkose, and comglomerate (Precambrian).
Chestoa (Unnamed)
Unicoi: feldspathic sandstone and conglomerate; some siltstone and
shale (Lower Cambrian).
Flag Pond (Big Branch)
Precambrian crystalline complex: granitic and gneissic rocks with indu-
sions of mica and hornblende schist (Precambrian).
Greystone (Unnamed)
Unicoi; feldspathic sandstone and conglomerate; some siltstone and
shale (Lower Cambrian).
Davy Crockett Lake (Flag Branch)
Conococheague: blue limestone ribboned with dolomite (Upper Cambrian).
Cedar Creek (Gregg Creek)
Knox: siliceous dolomite (Lower Ordivician).
85
APPENDIX B
(Continued)
Parrotsville (Sinking Creek)
Sevier: blueish calcareous shale with sandstone beds and blue limestone
at base (Middle Ordivician).
Rankin (McCowan Creek)
Sevier: blueish calcareous shale with sandstone beds and blue limestone
at base (Middle Ordivician).
White Pine (Leadvale Creek)
Sevier: blueish calcareous shale with sandstone beds and blue limestone
at base (Middle Ordivician).
Knox: siliceous dolomite (Lower Ordivician).
Jefferson City (Goose Creek)
Knox: siliceous dolomite (Lower Ordivician).
New Market (Dance Branch)
Copper Ridge: dark crystalline siliceous dolomite (Upper Cambrian).
Chepultepic: siliceous dolomite and sandstone beds near base (Lower
Ordivician).
Mascot (Clift Creek)
Holston: red crystalline limestone (marble), quartzose crystalline
limestone, and limy sandstone (Middle Ordivician).
Lenoir: limestone (Ordivician).
John Sevier (Legg Creek)
Pumpkin Valley: greenish silty shale (Middle Cambrian).
Rutledge, Rogersville; Maryville: blue limestone with middle shale units
(Middle Cambrian).
86
APPENDIX B
(Continued)
John Sevier (Legg Creek cont.)
Conasauga: limestone and dolomite above and shale below (Upper Cambrian).
Copper Ridge: dary crystalline siliceous dolomite (Upper Cambrian).
Chepultepec: siliceous dolomite with sandstone beds near base (Lower
Ordivician).
Longview: very siliceous dolomite with limestone beds near top (Lower
Ordivician).
Kingsport: siliceous dolomite with thick limestone bed near base (Lower
OrdiVician ).
Mascot: siliceous dolomite (Lower Ordivician).
Fountain City fCox Creek!
Copper Ridge: dary crystalline siliceous dolomite (Upper Cambrian).
Conasauga: shale with some limestone (Middle Cambrian).
Rome: varicolored shale, siltstone, and sandstone; some dolomite and
limestone layers (Lower Cambrian).
Powell (Patt Branch)
Rome: varicolored shale, siltstone, and sandstone; some dolomite and
limestone layers ('Lower Cambrian).
Chickamauga: blue limestone of several kinds and yellow silty limestone
(Middle Ordivician).
Cl inton(Unnamed)
Knox: siliceous dolomite (Lower Ordivician).
Windrock (Hoskins Creek)
Undifferentiated sandstones and shale with coal beds (Pennsylvanian).
87
APPENDIX B
(Continued)
Petros (Middle Creek)
Undifferentiated sandstones and shale with coal beds (Pennsylvanian).
Camp Austin (Hall Branch)
Undifferentiated sandstones and shale with coal beds (Pennsylvanian),
Lancing (Rock Creek)
Undifferentiated sandstones and shale with coal beds (Pennsylvanian).
Hebbertsburg (Hawn Spring Branch)
Undifferentiated sandstones and shale with coal beds ^Pennsylvanian).
Fox Creek (South Creek)
Undifferentiated sandstones and shale with coal beds (Pennsylvanian).
Isoline (Scott Creek)
Undifferentiated sandstones and shale with coal beds (Pennsylvanian).
Campbell Junction (Clear Creek)
Undifferentiated sandstones and shales with coal beds (Pennsylvanian).
Sources: Geologic Map of North Carolina compiled by the North Carolina
Department of Conservation and Development, Division of Mineral
Resources in 1958 at a scale of 1:500,000.
Geologic Map of East Tennessee compiled by the Tennessee
Department of Conservation, Division of Geology in 1952 at
a scale of 1:125,000.
APPENDIX C
Summary of Morphometric Variables
Quadrangle Drainage Basin «b «1 ''e “d H E CD
Piedmont:
Mil Is borough Little Creek 3.50 1.98 0.90 2.53 55 0.67 5.22
Efland No Name 6.00 2.45 0.94 3.19 52 0.54 4.52
Me bane No Name 2.00 1.39 0.76 4.86 58 0.60 6.08
Burlington No Name 3.00 2.24 0.77 2.04 49 0.54 6.36
Gibsonvilie No Name 3.00 1.55 0.77 1.46 40 0.42 5.68
McLeansvi1 le No Name 4.75 1.62 0.86 6.91 55 0.62 5.83
Greens boro No Name 5.50 4.63 0.97 3.94 55 0.50 8.24
Guilford No Name 4.00 2.98 0.76 3.49 58 0.59 6.38
Kernersvi1 le No Name 4.50 0.85 0.85 3.33 46 0.49 7.92
Winston-Salem
East Sokas Creek 5.00 0.28 0.61 4.83 64 0.51 9.12
Winston-Salem
West Side Branch 2.50 0.63 0.79 1.02 55 0.48 9.17
Clemmons Ellison Branch 4.33 1.39 0.79 5.11 83 0.46 11.04
Farmington No Name 6.33 2.69 0.70 7.87 80 0.45 8.02
Lone Hickory Fisher Creek 3.00 0.92 0.70 3.02 82 0.55 13.37
Brooks
Crossroads Walkers Branch 2.50 1.40 0.71 2.49 85 0.55 10.06
Osbornvi 11e Osborn Creek 3.25 1.24 0.84 5.29 158 0.37 9.34
Guilreath No Name 3.00 1.09 0.83 4.00 347 0.53 31.90
Moravian Falls Moravian Creek 2.60 0.76 0.81 6.35 469 0.32 31.58
Boomer Little Warrior Creek 3.25 1.74 0.85 6.00 246 0.29 20.07
X 3.79 1.68 0.80 4.09 112 0.50 11.05
s 1.26 1.01 0.09 1.87 117 0.10 8.10 00
00
APPENDIX C
(Continued)
Quadrangle Drainage Basin «b Re “d H E Qg
Blue Ridge Mountains;
Grandin No Name 4.50 1.81 0.74 1.78 472 0.48 37.98
Buffalo Cove Green Park Branch 2.00 1.49 0.85 1.95 427 0.57 47.50
Globe Johns River 6.50 2.84 0.84 2.62 658 0.43 45.74
Grandfather Mtn. Wilson Creek 2.50 0.69 0.77 2.19 963 0.47 41.60
Newland No Name 3.50 0.94 0.94 1.50 372 0.42 20.93
Carvers Gap Hanson Creek 3.00 0.73 0.92 2.01 785 0.39 41.28
Bakersvil le Sweet Creek 4.50 2.21 0.98 2.26 399 0.33 33.12
Huntdale Brummett Creek 6.33 2.91 0.82 4.28 561 0.38 65.42
Chestoa No Name 5.00 3.44 0.74 5.42 732 0.50 21.88
Flag Pond Big Branch 5.20 1.62 0.74 5.28 764 0.47 50.00
Greystone No Name 3.50 3.39 0.70 3.77 524 0.52 50.00
X 4.23 2.01 0.82 3.01 605 0.45 42.31
s 1.48 1.02 0.09 1.43 190 0.07 11.59
Ridge and Valley:
Davy Crockett
Lake Flag Branch 4.50 3.58 0.78 3.21 259 0.27 17.71
Cedar Creek Gregg Creek 7.00 1.71 0.82 3.45 116 0.29 11.41
Rankin McCowan Creek 6.00 3.15 0.95 3.67 125 0.35 32.22
Parrotsville Sinking Creek 3.17 1.20 0.84 5.10 88 0.53 41.25
White Pine Leadvale Creek 3.50 1.82 0.89 2.24 69 0.46 10.42
Jefferson City Goose Creek 3.00 1.23 0.88 2.12 139 0.52 15.31
New Market Dance Branch 2.00 1.27 0.74 3.31 163 0.43 11.50
APPENDIX C
(Continued)
Quadrangle Drainage Basin “d H E
Mascot Clift Creek 7.00 1.86 0.70 2.45 126 0.23 17.04
John Sevier Legg Creek 3.00 0.68 0.87 2.37 200 0.36 15.36
Fountain City Cox Creek 5.00 3.24 0.66 1.71 152 0.30 14.90
Powell Patt Branch 2.33 1.60 0.95 2.89 119 0.30 13.27
Clinton No Name 3.00 0.86 0.89 1.95 119 0.34 14.79
X 4.13 1.85 0.83 2.87 140 0.37 17.93
s 1.75 0.96 0.09 0.95 51 0.10 9.26
Appalachian Plateau:
Windrock Hoskins Creek 5.00 0.45 0.75 3.03 600 0.27 45.63
Petros Middle Creek 2.00 0.71 0.80 2.92 506 0.44 37.08
Camp Austin Hall Branch 6.00 0.91 0.95 3.70 521 0.35 32.05
Lancing Rock Creek 3.00 0.85 0.85 2.93 323 0.54 27.38
Hebbertsburg Hawn Spring Branch 2.50 2.35 0.94 2.46 119 0.66 20.00
Fox Creek South Fork 6.00 2.46 0.71 2.69 no 0.58 9.80
Isoline Scott Creek 6.00 2.07 0.86 2.09 165 0.75 12.03
Camp bel 1
Junction Clear Creek 4.60 0.85 0.80 2.90 84 0.64 11.13
X 4.39 1.33 0.83 2.84 304 0.53 24.39
s 1.67 0.82 0.08 0.47 212 0.16 13.31
lO
o