Cincinati Thesis - Christaller

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13 March 2009

Brayden M. McLaughlin

Master of Community Planning

School of Planning, College of DAAP

Application of the Central Place TheoryIn a Modern Metropolitan Area to DetermineCurrent Centrality Patterns

Brayden M. McLaughlin

Michael C. Romanos, Ph.D.

Colleen McTague, Ph.D.

Changjoo Kim, Ph.D.

Michael C. Romanos, Ph.D.

Application of the Central Place Theory In a Modern Metropolitan Area to Determine

Current Centrality Patterns

Case Study of Cincinnati, Ohio

A thesis submitted to the

Graduate School of the University of Cincinnati

in partial fulfillment of the requirements for the degree of

Master of Community Planning

in the School of Planning of the College of Design, Architecture, Art, and Planning

by

Brayden M. McLaughlin

B. A., Geography, University of Nebraska Lincoln

August 2007 M.C.P. University of Cincinnati

June 2009

Thesis Committee

Chair: Michael Romanos, Ph. D.

Member: Colleen McTague, Ph. D.

Member: Changjoo Kim, Ph. D.

Honorary Reader: J. Clark Archer, Ph. D

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Abstract This study looks at applying the principles of Walter Christaller’s Central Place theory within a

contemporary urban area. The challenge of this is that urban areas are much more complex and less

predictable than the rural patterns studied by Christaller. Factors such as numbers of retail jobs, numbers

of stores, sales per square foot, access to highway interchanges, and more recently the internet, in the

United States has vastly altered the principles on which the Central Place Theory is based. So if we look

at the retail centers of a city, such as Cincinnati, Ohio, can we find patterns that would show that the

Central Place Theory properly explains the current locations of those same centers?

Using a set number of centers in the Cincinnati Metropolitan Area, certain characteristics were used to

determine which centers were important at which level of the local hierarchy. The center’s characteristics

were then placed in an index where a multiple regression analysis was used to find their weights or their

relative importance to each other. From here, the patterns that developed as a result were analyzed and a

complete picture of the urban effectiveness of the Central Place Theory began to take shape. The results

that were found showed that the Central Place Theory does apply, but not perfectly. This is due to many

reasons, but primarily three: the Cincinnati Metropolitan Area is not a homogeneous theoretical region,

so because of this there is not a homogenous distribution of centers; “Big Box” retail stores and locations

similar to them drastically change the nature, scale and locality of centers; and unlike a theoretical

landscape of Christaller, accessibility is not uniform and centrality is greatly affected by distance from and

vicinity to interstate highways. Because of these reasons, as well as others, this study finds that the Central

Place Theory is not entirely suited to explaining centrality patterns in urban areas.

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ACKNOWLEDGMENTS First I wish to thank Dr. J. Clark Archer of the University of Nebraska - Department of

Geography, whose work and teaching inspired me to go forward with this study to begin with. I

would also like to thank Dr. Colleen McTague from the University of Cincinnati Geography

Department for all her help and suggestions as well as being on this thesis committee. And I

would like to thank Dr. Michael Romanos for his help and guidance being my thesis Chair, and

for being a professional mentor and a good friend.

Thanks to Maria Fernanda Ramirez and Dr. Romanos for allowing me to use the Berkeley

Dataset, and for being so helpful. Special thanks also goes out to Dr. Changjoo Kim of the

University Geography Department at UC, whose skills and programs created the final study area

maps for the thesis, and to all my friends and family for putting up with me all of these years.

And finally, I would like to thank my wife Annette, for without her love, help, patience and

understanding; I do not believe I would have ever been able to complete this thesis. Thank you

all so very much.

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PREFACE I first became interested in the mechanics of the Central Place Theory back while I was still

getting my undergraduate degree in Geography. I had taken two classes with Dr. J. Clark Archer

and was fascinated by the methods and the applications of the theory and its effects on urban

geography. I eventually wrote two different papers on the subject, studying the population

redistribution of the Great Plains as a whole, and the Patterns of Centrality in Southeastern

Nebraska. When I came to the University of Cincinnati and studied the Central Place Theory

again in Dr. Michael Romanos’ class, I was excited by the idea of applying the theory to a whole

new study in the form of the Cincinnati Metropolitan Area, a place I had never even thought

about back home. This time as a graduate student, I would attempt to view the theory from a

practical viewpoint instead of merely a report on statistics and findings. So it is from this

perspective that I have reached this point, studying centrality in my new adopted city.

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Contents Acknowledgements ............................................................................................................................................ v Preface ..................................................................................................................................................................vi List of Figures .................................................................................................................................................. viii I. JUSTIFICATION AND BACKGROUND ........................................................................................... 6 1. Problem Statement ................................................................................................................................... 7 II. CENTRAL PLACE THEORY: THE CONCEPT AND ITS EVOLUTION ........................... 10

1. Introduction ............................................................................................................................................ 10 2. Origins of the Central Place Theory - Christaller .......................................................................... 10 3. Evolution of the theory – Regional Studies ..................................................................................... 17

3.1. Nested Hexagons ........................................................................................................................... 17 3.2. Administrative and Manufacturing Centers ........................................................................... 20 3.3. Market Boundaries ........................................................................................................................ 23

4. Evolution of the theory – Intraurban Studies .................................................................................. 24 4.1. Retail Centers ................................................................................................................................. 24 4.2. K Values and Center assumptions ............................................................................................. 27 4.3. Probability Geometry ................................................................................................................... 29 4.4. Intra-Urban Summary .................................................................................................................. 30

4.5. Evolution of the theory – Locational Use ............................................................................... 30 III. METHODOLOGY ................................................................................................................................. 34 1. Tasks and Objectives ............................................................................................................................. 34 1.1. Goals of the Study ......................................................................................................................... 34 1.2. A note on data ................................................................................................................................ 35 2. Tasks .......................................................................................................................................................... 36 2.1. Task 1: Explanation of Study Area ............................................................................................ 36 2.2. Task 2: Data acquisition and issues........................................................................................... 38 2.3. Task 3: Defining the central places ........................................................................................... 41 2.4. Task 4: Model Implemetation.................................................................................................... 42 2.4.1. Definition of the model ..................................................................................................... 42 2.4.2. Tests of the model .............................................................................................................. 47 IV. ANALYSIS.................................................................................................................................................. 48 1. Hierarchical Description and Maps ................................................................................................... 48 2. K Value Analysis ..................................................................................................................................... 60 V. CONCLUSIONS ....................................................................................................................................... 62 1. Limitations ............................................................................................................................................... 62 2. Findings and Discussion ....................................................................................................................... 64 VI. BIBLIOGRAPHY ..................................................................................................................................... 73 VII. APPENDIX............................................................................................................................................... 76

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LIST OF FIGURES Figure 1: Christaller’s Hexagonal Hierarchy............................................................................................. 12 Figure 2: Christaller’s K Systems ................................................................................................................. 14 Figure 3: Proposed Arrangement of Urban Centers in Ghana ............................................................ 35 Figure 4: Possible Hexagonal Arrangement of Central Places in Cincinnati ................................... 36 Figure 5: Selected Metropolitan Counties – Study area ........................................................................ 37 Figure 6: Thesis Study Area – Census Tracts and 500m Centers ....................................................... 40 Figure 7: H Centers – Hierarchical Level 1............................................................................................... 52 Figure 8: M Centers – Hierarchical Level 2 .............................................................................................. 53 Figure 9: A Centers – Hierarchical Level 3 ............................................................................................... 54 Figure 10: K Centers – Hierarchical Level 4 ............................................................................................. 55 Figure 11: B Centers – Hierarchical Level 5 ............................................................................................. 56 Figure 12: G Centers – Hierarchical Level 6 ............................................................................................ 57 Figure 13: P Centers – Hierarchical Level 7 ............................................................................................. 58 Figure 14: L Centers – Hierarchical Level 8 ............................................................................................. 59 Figure 15: Central Place Classes and Levels ............................................................................................. 48 Figure 16: Hierarchical K Values ................................................................................................................. 60 Table 1: Christaller’s Example of Radial Centrality ................................................................................ 18 Table 2: Ranking of Christaller’s Central Places...................................................................................... 19 Table 3: Losch’s Ten Smallest Market Areas ............................................................................................ 22 Table 4: Berry’s Classification of Retail Centers...................................................................................... 26 Table 5: West’s Arrangement of Stores and Centers .............................................................................. 32 Table 6: Necessary Data Variables .............................................................................................................. 38 Table 7: Place Names for the Database Central Points ......................................................................... 72 Table 8: Ranking of Local Retail Services.................................................................................................. 74 Table 9: Weights of Retail Square Footage ............................................................................................... 75 Table 10: Centrality Index ............................................................................................................................ 75 Table 11: Eliminated Points and Explanations ........................................................................................ 78 Table 12: Central Place Hierarchy Rankings ............................................................................................ 79 Table 13: Hierarchical K Values .................................................................................................................. 60 Table 14: Number of Centers at Each Hierarchical Level .................................................................... 61

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I. JUSTIFICATION AND BACKGROUND In the field of planning, much of our time and resources is used (and often wasted) trying to

predict where future growth centers are going to develop, but perhaps a new way to approach

this is to use a theory of the past to calculate the future. In 1933, German geographer Walter

Christaller created the Central Place Theory to explain the locations of rural towns and market

centers as a series of hierarchical hexagon-shaped service areas. Since then, the Central Place

Theory has been taught in many schools and universities across the United States as a

geographical theory that seeks to explain the size and spacing of human settlements. It rests on

the notion that centralization is a natural principle of order and that human settlements follow

this pattern, and the theory suggests that there are laws determining the number, size and

distribution of towns. The theory rests on focusing on cities as service centers, mainly in their

functions as markets. It has been applied quite effectively in areas such as the Great Plains and

portions of Europe, and it has been accepted as an effective theory, holding a prominent position

in many core classes. But a question has begun to rise over the last several years: in a modern-day

city, with factors such as transportation and the internet involved, does it still adequately explain

the locational patterns of centrality?

In Christaller’s day, cities were simpler, more predictable entities. However, urban changes over

the past forty of fifty years, particularly in the United States, has vastly altered the fundamental

ideas on which the Central Place Theory is based. The Central Place Theory has great value

from a theoretical standpoint, but other than being a useful concept that we read in a book, does

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this idea of nested market hexagons continue to be relevant in an urban environment completely

transformed by interstate highways, and even the internet’s function as a market. In other words,

is it still relevant from a practical application viewpoint?

So, how can we use this theory in a contemporary American city like Cincinnati? If the urban

application of the theory is still effective, then the Central Place Theory (CPT) could be used by

public officials to determine where the greatest need for services at the same time successfully

expand the city’s tax base as well as providing jobs in areas that need them most. If so this would

have a huge impact on long term community and regional planning, if we could accurately

forecast the development of future retail and commercial centers, and could prove to be relevant

for nearly every level of economic development. Imagine if planners could use the Central Place

Theory to find the vacuums of retail demand and could focus limited funds where they could be

most effective.

1. Problem Statement

The question we are asking here is this: Can planners or geographers use the Central Place Theory

to explain the current locations of retail and commercial centers of different hierarchical levels in an

urban setting, and define their market areas? If it does, does this mean that planners could use the

Central Place theory to predict future retail centers? If it does not, do we need to question if the

Central Place Theory is still a relevant urban planning methodology in the 21st Century and

beyond?

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By looking at commercial and retail areas as well as neighborhoods within Cincinnati and its

metropolitan area, can we find patterns that would show that the Central Place Theory could

explain the commercial growth of the city? Are the neighborhood centers of Cincinnati located

in such a way as to create the hexagonal approximations of local markets and fall into the

hierarchical organization suggested by Christaller? If so what are their K values? If it does

influence the city, how has it left its mark? Many of these questions are rather in depth and

cannot be fully studied in a thesis such as this. But what will be done in this study will be a

geographical analysis of the Central Place Theory on the current retail centers of present-day

Cincinnati Metropolitan Region using formulas derived from past urban studies. This will be

accomplished by using a central place dataset and formula index (which I will explain in detail in

the Methodology Chapter) and using this data in GIS to establish the patterns and hierarchies in

the most urbanized portions of the Cincinnati Metropolitan Area.

So what will be shown here is whether or not the variables and formulas of the Central Place

Theory consistently and reliably match or explain Cincinnati’s hierarchy of retail centers. Once

this has been determined, we can then see if the retail areas follow a particular pattern of

development (or a lack of one). If we have established a pattern, then we can use the CPT to

find the ‘holes’ in Cincinnati’s urban retail hierarchy and from there, determine areas of different

hierarchical levels in the Cincinnati metro area which are most likely to develop into retail

centers.

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Christaller’s study provides the base from which we can begin, but we cannot use his models

verbatim when applying it to a modern city. There are many parts of his theory that have

become obsolete over the course of time and over the last forty years, studies involving the CPT

have had to compensate for the changes in cities, regarding economic behavior and culture, so

first we will look at research that previous studies have conducted and how this has progressed

the urban model of the Central Place Theory.

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II. CENTRAL PLACE THEORY: THE CONCEPT AND ITS EVOLUTION

1. Introduction

The purpose of this literature review is to give a background on the Central Place Theory and its

evolution, the evolution of the model and formulas which have been used to test this theory, as

well as which ideas can be taken from the theory and applied to an intra-urban study. These

ideas and their authors will be basis for this thesis and will be reviewed and critiqued for their

applicability to identify central places within an urban setting. So first, I will be reviewing both

regional and urban studies of the central place theory to understand the progression of

applications from Christaller to the present day.

2. Origins of the Central Place Theory - Christaller

Christaller used the Central Place Theory as an attempt to explain the spatial arrangement, size,

and number of settlements in a particular geographical area. Christaller noticed that towns of a

certain size were roughly equidistant, and by examining and defining the functions of the

settlement structure of certain cities and the size of their hinterland, he tried to model the

pattern of settlement locations of different sized cities using geometric shapes, such as circles or

hexagons (Christaller 1966).

A central place is a center which provides one or more services, such as providing food for, or

selling fuel to the population living in and around it. Simple basic services (gas stations, grocery

stores, etc.) are called low order goods and services while specialized services (universities,

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hospitals, and airports) are higher order goods. A center possessing high order services usually

has low order goods and services around it or within it, but not the other way around (King

1984). Centers which provide low order services are called low order centers and centers that

provide high order services are called high order centers. The sphere of influence, or hinterland,

is the area under the influence of the central place (Christaller 1966).

The CPT consists of two basic concepts: the threshold population, which is the minimum

population size required to profitably maintain a certain order of a good or service, and the range

of goods or services - the average maximum distance people will travel to purchase goods and

services (Christaller 1966). From these two concepts the order (lower and upper limits) of

goods or services can be found, and with orders and limits, one can envision how central places

would be arranged in a theoretical area.

Now, if transportation costs were equal in all directions (as assumed by Christaller) each central

place would have a circular market area. However, a circular shape of the city’s market area

would result in either underserved areas or over-served areas, and to try and solve this problem,

Christaller suggested a hexagonal shape to market areas (Christaller 1966). Within a given area

there will be fewer high order cities and towns in relation to the more numerous lower order

villages and hamlets (Christaller 1966). For any given order, theoretically the settlements in

each order will be equidistance from each other, and the higher order cities will be further apart

from each other than the lower order towns, a pattern which can be seen in Figure 1. The larger

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the settlements, the fewer their number and the center’s range increases as the town’s population

increases (Christaller 1966).

So, if we view the importance of the CPT as the creation and maintenance of inter-connected

market areas, what are some of the patterns of these markets? The two main divisions of goods

and services as concerned with the CPT are convenience goods and shopping goods.

Convenience goods are products that are numerous, easy to get and easy to find, items such as

soda pop or a newspaper, or in general, low-order goods. Shopping goods are items that are

much harder to find, such as high order goods, or in particular, schools, hospitals, airports and

the like. People are much more likely to travel further distances to purchases goods and services

of this type, and are more willing to accept higher transportation costs to obtain them

(Christaller 1966).

Source: Christaller (1966)

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Christaller’s base theory provides the framework for my study and the studies that came before

it, and so I will continue to place importance on his main ideas. Christaller was mainly interested

with towns’ functions as markets and argued that population alone was not significant enough to

determine the importance of a central place. Christaller’s model proposed a hierarchical

arrangement of settlements and conceptualized the model via hexagonal arrangements. The

hexagon best equated a circle for maximum coverage and some of the problems of overlap

within circular arrangements were solved by using hexagons (Christaller 1966).

The variations in Christaller’s theory were based on transportation (mid-point) and

administration (strong central market). The marketing model is better known as the K=3

system, where a hexagonal space is envisaged with the central places serving two lower-order

places each or one-third of the lower-order neighbors surrounding them, so a total of three

places are served.

The goal in the marketing principle was to serve a maximum number of consumers from a

minimum number of centers. The hierarchy in the marketing model follows the rule of threes,

where a consumer equidistant from three higher order places would make a third of their

purchases from each, hence K=3 (Christaller 1966). In the transportation model, the goal was to

minimize the network length and maximize the connectivity of centers being served. To

minimize transportation costs, a different model of K=4 is proposed, where the hexagon is

shifted so that the settlements are located at the center point of each side, and each central place

serves a half of the surrounding hexagon so the number of places served is four. In the

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administrative model, the goal was to provide a hierarchy of controls, where the lower level

centers are completely controlled or administered by the higher order places. The administrative

model is where K=7 where six lower-order places in the hexagon are served by the central place

(Christaller 1966). All three of these geometries can be seen in Figure 2.

Source: Christaller (1966)

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Christaller treated all three models as hierarchical, with all higher order places in the hexagon

surrounded by other higher-order places to explain not only local but regional economics and

spatialization of urban centers, a hierarchy which should also occur within cities as well as

between them. But Christaller said that one of the three values will not completely triumph but

that one or another will be dominant in the day-to-day market decisions of that area (Christaller

1966).

If we change the spotlight of CPT to focus on the relationships between places such as retail

centers, it becomes easier to visualize each place in a city, from the smallest shop to the largest

business district, to be directly linked to one another. These links would be physical (roads or

railways), economic (food, resources, raw materials, etc), and administrative. What each

commercial center would produce and ultimately transport would be determined by the center’s

size and its relation to its neighbors (Christaller 1966).

How these central places would be physically linked is also important: i.e. transportation. The

shorter the distance, the better most frequently transported goods, and even people. With small

distances between settlements resulting in lower transport costs, frequent trips between towns

would increase. As the distances increase, direct (and frequent) travel between communities

becomes less and less, making the bond between any two given places only as good the

relationship between each place: the cost and the distance to travel back and forth (Berry 1967).

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Also the economics of the CPT can be explained further via the Principle of Least Effort, which

is just what it sounds like. The principle of least effort is a theory of human (or consumer)

behavior held among researchers which states that someone seeking something will tend to use

the most convenient method, using the least amount of energy and resources possible. Also this

theory takes into account the person’s previous experiences. The user will use the routes and

methods that are most familiar to them and easiest to use. The principle of least effort applies

not only in the humanist context, but also to virtually any activity. For example, if a customer is

looking for a convenience good, he or she will find the closest place that that good is available,

and will attempt to travel the most direct route to the place of purchase (Christaller 1966). The

principle of least effort can help us understand why people are not always willing to go to the

best central place, but the cheapest or the closest (King 1984).

Each of these lower order centers, which would ideally range in size from several hundred to just

over a thousand jobs, would surround a larger, central employment place, such as a CBD. Ideally

these centers would be close by, no more than a mile or two, to facilitate easy travel between

neighborhood and regional centers. The larger center itself would ideally be the home of several

thousand jobs and house some of the higher level goods, services and functions that would not

make much sense to replicate in each of the smaller business centers (Christaller 1966).

These smaller order retail centers would orbit the main employment center of the region, which

would maintain higher levels of population and job specialization, and with more connections

between the smaller centers and the CBD, allowing easier transportation of goods and people

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between places. This top ranked central place would be the administrative and economic hub for

this region and carry out top level governance and would house the most technologically

sophisticated industries. This center would also need to produce lower order goods as well as

serve as the region’s educational and cultural center, a mold which Cincinnati may fit into quite

well.

3. Evolution of the Theory – Regional Studies

The first group of studies I will focus on here are the regional or interurban models. At first

Christaller’s model was applied as existed and to large areas such as U.S. states or portions of a

country (such as Southern Germany). The two most important studies that approached CPT

from a regional viewpoint were from Christaller and August Lösch. Lösch’s ideas evolved

directly from Christaller and he used most of Christaller’s formulas when creating his own.

However, even in the mid twentieth century, other authors began looking at the Central Place

Theory, but without using Christaller’s formulas as their base, forming an alternate line of theory

evolution. Godlund’s study, which will be mentioned later, is an example of this. It is from these

dual stand points that we will approach understanding the methods behind the theory. If we

study first the regional models, we can understand which portions of those studies will apply to

this thesis, and how those studies have led to the intraurban studies as well.

3.1. Nested Hexagons - Christaller

When testing his theory, Christaller needed a model to explain the differences in centrality

between places and he first looked a concentric rings, or regions, around a central place.

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Christaller determined that one cannot determine the size of the central place merely from the

size or the population of the region (Christaller 1966). So he provided an example of an area and

its surrounding areas as seen in Table 1.

Table 1: Christaller’s Example of Radial Centrality Area(sq. km) Population Density Nucleus 80 4000 50 Ring I 100 4270 42.7 Ring II 120 4668 38.9 Ring III 160 5312 33.2 Source: Christaller (1966) So from these areas, he stated that it would be easier to define the central places importance.

Christaller’s original formula for the importance of a central area was as follows:

C = D[(2a)+1-(1/2b)+(1c)+(1/2d)] (1) Where: D = the population density, and

a, b, c and d are the areas of each ring and the numbers

for the amount of goods consumed per capita in each ring respectively

(Christaller 1966).

He then could classify each central place according to its rank (decided by the formula) and its

region. Christaller used the number of telephones in an area as the determining factor of

centrality, but any number of statistics could have been used. Using the telephones, Christaller

stated the pattern that the larger the rank and the more important the city, the fewer or them

there will be in a particular area and the greater the pull of its economic gravity. He used this

formula to define local centrality:

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C = Tc – Pc(Tr/Pr) (2)

Where: Tc = the number of phones in the central place,

Tr = the number of phones in the region,

Pc = the population of the central place, and

Pr = the population of the region.

Christaller called Tc the expected importance and Pc(Tr/Pr) the actual importance with the

difference being the real centrality. Christaller then ranked his central places in the fashion

shown in Table 2.

Table 2: Ranking of Christaller’s Central Places

Type Population Number of Phones Centrality H 800 5 to 10 0 to 0.5 M 1,200 10 to 20 0.5 to 2 A 2,000 20 to 50 2 to 4 K 4,000 50 to 150 4 to 12 B 10,000 150 to 500 12 to 30 G 30,000 500 to 2,500 30 to 150 P 100,000 2,500 to 25,000 150 to 1,200 L 500,000 25,000 to 60,000 1,200 to 3,000 T 1,000,000 60,000+ 3,000+ R 4,000,000 ? ?

Source: Christaller (1966) Christaller states that an M place has one region of a certain size, an A place has two regions, a K

place has three regions and so on. Christaller only determined areas as far as around 1,000,000,

which was about the size of Berlin at Christaller’s time, and as far as a study of Germany was

concerned, there were simply no places larger than that to study at that time (Christaller 1966).

He also attempted to analyze the specific importance of a central place:

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C = Tc(Pr/40Pc ) (3) Where: Tc = the number of telephone connections in a central place,

Pr = the number of inhabitants in the region, and

Pc = the population of the central place

Pr/40Pc is the ratio of people to phones, or, the number of inhabitants in the region divided by

the ratio of telephone connections in a region (Christaller 1966). In Christaller’s time, the

phone ratio of people to phones in southern Germany was 40:1, hence the 40Pc.

3.2. Administrative and Manufacturing Centers - Lösch

The main modifications to the principles of the Central Place Theory were made by August

Lösch, who expanded on Christaller’s K value system, and made a consumer model based on

administrative and manufacturing structure as opposed to service centers which Christaller used

(Lösch 1954). Lösch started by considering one customer, or one unit of consumption and

build up from there. In Lösch’s model, the ten smallest market areas, each with a different k-

value are plotted with each network surrounding a central place. These networks were then laid

over each other and positioned to produce the largest number of places for each k-value. This

model produced an uneven (and somewhat more realistic) pattern of city-rich and city-poor

areas around each central place, more typical of what an intra-urban system would possibly look

like (Lösch 1954).

Unlike in Christaller’s model, settlements in reality are not usually geometrically ordered, and a

hierarchical clustering tends to be a more common arrangement (Lösch 1954). To make the

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Central Place Theory work, Christaller had to assume the following factors: That the study area

(in this case the Great Plains) was flat without any geological barriers (non-existent on planet

Earth), that the population, as well as all natural resources, was an evenly distributed and that all

consumers maintained the same purchasing power, which as we can see from socioeconomic

status, they do not (Lösch 1954). No provider of goods or services could earn excessive profits,

usually impossible in a market economy and, most importantly, only one type of transport

existed and it would be equally accessible in all directions and transportation costs would be

equivalent. Needless to say, those are a lot of factors to just simply ignore (Lösch 1954). And

also, Christaller’s CPT explained urban settlement patterns that described existing conditions in

a handful of places in the world, most notably the U.S. Great Plains, but tends to come up short

in other more densely settled areas (Lösch 1954). Lösch then argues that for service centers to

truly follow the theory, balance should be the same throughout a particular market area, defining

it as thus:

Ps / Sr = (Pm / Se) (4) Where: Ps = the population the sub-center,

Pm = the population of the metropolitan area,

Sr = the size of the region, and

Se = the size of the economic landscape.

But Lösch also determined that the distance between two businesses of the same type is equal to

the distance between the settlements supplied times the square root of their number (Lösch

1954). And, along with Christaller’s K=3, K=4 and K=7 systems, Lösch argued that those were

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only the three smallest areas and he then expanded upon this and defined the ten smallest

possible market areas as he shows in Table 3.

Table 3: Losch’s Ten Smallest Market Areas

Area # n b ds

1 3 3a a

2 4 4a a

3 7 7a a

4 9 9a 3a

5 12 12a 2 a

6 13 13a 3a

7 16 16a 2 a

8 19 19a 2 a

9 21 21a 7a

10 25 25a 7a Source: Lösch (1954) Here n is the number of places supplied by the central place, or the K value, b is the distance

between supply points, ds is the shipping distance, or the threshold, and a is the distance

between the central places (Lösch 1954). Lösch also provided formulas further analyzing the

hexagons of Christaller. Lösch’s study analyzed the characteristics and volumes of the demand

areas, which he could then translate into hexagons. For the shape of a market region, he uses the

following model as a guide for translating a circular market area into a hexagonal one:

A = H - (0.608H( )) (5)

Where: H = the height of the demand cone,

r = the radius or a circle within the hexagonal area, and

R is the radius or the original circular market area

(Lösch 1954).

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3.3. Market Boundaries

Godlund was a Swedish geographer who studied centralized spheres of influence in Southern

Sweden, and he took Christaller’s notion of the hexagonal network and twisted it. He focused

on the number of shops in a central place, the size of the shops and the average accessibility to

them. He then found the boundaries of each trade area (or distorted hexagon) which he called

Umlands, and then mapped them according to the data he found (King 1984). Godlund also

argued that central places of a particular function could be upgraded or downgraded in the

hierarchy depending on the number and stability of jobs at that place.

Instead of telephones, which was Christaller’s study, Godlund used the number of shops located

in a central place, and the following formula to study centrality:

C= (6)

Where: n = the number of shops in the central place,

W = a weight factor which took into account the average size, or square footage

of the shops,

P = the population of the central place, and

Ia = an index of accessibility to retail trade for that region

So, to sum up, it is the regional interpretations of the theory which provide the backbone for the

later, and more specific intraurban studies. Why we have looked at these first is to complete our

background of the intraurban studies. The models here are the precedent for the urban and

24

locational theories and need to be touched on first to understand where later geographers

received the foundation for their studies. So first we have analyzed the regional studies which

gives us a base for more specific models, and by understanding the formulas of regional models,

it becomes easier to analyze the models at the city and neighborhood level – the intraurban

studies.

4. Evolution of the Theory – Intraurban Studies

Starting in the 1960’s an increasing number of urban geographers began to apply the principles

of the Central Place Theory to intraurban studies. Scholars started looking at the relationships

between regional centers or neighborhood centers in a much more focused geographical area,

such as Chicago instead of the Midwest. These studies are not only more recent and narrower in

focus, but they also attempt to understand the causes behind city transformation, which makes

the intraurban grouping of studies more crucial to what we are trying to learn in this paper.

4.1. Retail Centers – Brian Berry

Brian Berry has studied the Central Place Theory both in rural and intra-urban market

situations, particularly the range of goods, and it is in his study of Southwestern Iowa where he

classifies the relative importance of market centers via political, transportational and market

advantages and spatial hierarchies.

Berry expanded on the ideas of Christaller and Lösch and turned the focus of the CPT to retail

and commercial areas within cities. Berry’s most important work has explained the hierarchy of

25

business centers, highway-oriented ribbons, urban arterial commercial developments and

specialized function areas, such as automobile rows and concentrations of medical offices (Berry

1967). Focusing on Chicago, Berry and his research team defined the local commercial and

retail centers as well as smaller and major regional centers within the Chicago MSA. Berry

expanded Christaller’s model and used the following equations to define an intra-urban

hierarchy:

Pc = M(Pc+Ps) (7) Where: Pc = the center’s population,

Ps = total population served by the central place, and

M = the urban multiplier

He then moves on to apply this to Christaller’s model, but from the lowest level upwards (Berry

1967):

Prh = Pch+KPr(h-1) (8) Where: Pc = the center’s population,

Pr = the total population of the region,

h = the level of hierarchy held by the central place, and

K = the bifurcation ratio (K Value)

For his study of Chicago, Berry also provided an alternate urban classification table, based on

Christaller’s original classifications and similar to Lösch, but with added definitions used to

classify the different levels of central places, as seen in Table 4.

26

Table 4: Berry’s Classification of Retail Centers

Type of Place Classification Order

L (Highest) Central Business District Eighth P Large Regional Center Seventh G Medium Regional Center Sixth B Small Regional Center Fifth K Large Neighborhood Center Fourth A Medium Neighborhood Center Third M Small Neighborhood Center Second H (Lowest) Corner Retail First

Source: Berry (1967) Berry also used an additional formula to define the expected relationship between the

population size of a central place and the number of establishments of a chosen function, such as

retail, within it:

P = A( ) (9)

Where: P = the population of a place

Nr = the number of retail establishments

A = the center’s market area, and

M = the urban multiplier

(Berry 1967).

Berry also used Reilly’s Gravity model, or the Law of Retail Gravitation to explain the breaking

points of intra-urban market areas. This model explains the effect of greater distance on the ‘pull’

of a central place, or, its ability to attract demand for a good at that particular location, as well as

defining the distance from a central place to the break point (Berry 1967).

27

d = (10)

Where: dAB = the distance between points A and B

SizeA = the number or retail places in center A

SizeB = the number or retail places in center B

(Berry 1967).

Here, however, Berry also states that there is no absolute breaking point in metropolitan regions

due to the close proximity of the retail areas to each other, so my study will try to find the

approximate boundaries. Berry also studied Chicago and used retail square footage as another

defining characteristic of the importance of retail places as well as the hierarchy of urban

business centers within cities (Berry 1967).

4.2. K Values and Center assumptions – Parr

John Parr has studied the theoretical problems of the CPT (such as the assumptions made by

Christaller) and has followed more of an observational approach rather than an analytical one

(McCann 2002). Parr also makes some additions to the break point model using the ratio of

transportation rates, and by following the intuitions of Christaller, Parr expanded on the ideas of

Lösch, and Berry as well, and gave his model for the proportional relationship between central

places using the following formula:

28

Ph = PL (11)

Where: applied to center type h and

P = the center’s population,

PL = the population of a center’s largest market area, and

K = the bifurcation ratio (K Value)

(Parr 1973).

This formula can be expanded thus:

Ph = (A + B + 4c) (12)

Where: (A + B + 4π) means that and A center and an B center are added with

4c, where c is equal to the lowest size center.

This model can be further expanded to determine which basic centers are serviced entirely by

center h in its highest capacity with respect to the order of goods. Parr uses an equation (one

also used by Michael Dacey) for K: K = x2 + xy +y2, so that when used with the number of B

centers within an A center’s market hexagon, the K ratio can be calculated more simply than

with Lösch’s calculations (McCann 2002).

He also found the likely frequency of market centers of a particular level of the hierarchy by

using this formula:

Fh = KN-h (13)

29

Where: Fh = the frequency of centers at a specific hierarchical level

K is the k value,

h = the hierarchy level and

N = the number of basic central places. 4.3. Probability Geometry

A geographer named Michael Dacey has focused much of his research on the actual physical

geometry of the Central Place Theory and has formulated dozens of models dealing with the

shapes and sizes of the hexagonal service areas. He has also created a probability model for

finding the locational properties of central places. His formulas should be transferable to an

intra-urban study.

Dacey mainly focuses on matrices and lattice levels of the hexagonal structure of the CPT using

numerous complex models to explain the differences and variants of applying the theory to

different real-life scenarios. But his main model provides more of an economic slant to

Christaller’s hexagons (Berry and Parr 1988). Dacey used the following model to show that

there is a distinct difference between the internal and external markets of a central place:

m1 = (14)

Where: = the export component of the central place, and

= the local portion of the retail component of that place.

30

4.4. Intra-Urban Summary

There are several authors I have come across (Preston, Bell, Walter Isard, Eaton and Lipsey,

etc.) whose work has also made headway into the intra-urban aspects for metropolitan

application of the Central Place Theory, but whose focus remains too specific for the formulas to

be included in this study. This is where concepts such as demand externalities, zones of

indifference and consumer behavior can help guide the study of central places better within

urban boundaries. They also study the number of stores, types of stores as well as what causes

central places to move up and down in an urban hierarchy, i.e. how do urban centers become

more or less important. But for our purposes here, these are not as crucial to this paper as some

of the aforementioned studies are. So this is not to say that this study is a complete analysis of all

the central place models, but that many other studies have been left out for brevity.

So, following the work of Christaller, Lösch, Berry and Parr and others, could analyzing the

smaller details could the CPT explain the potential retail and commercial patterns for the

Cincinnati of the 21st century? The intraurban formulas help to flesh out the original ideas of the

CPT and apply them in a more dynamic landscape: the contemporary city. From here we can

form a more specific viewpoint and observe studies that have precisely detailed how the Central

Place Theory has been used to specifically explain urban retail locations.

4.5. Evolution of the Theory – Locational Use

Most of the intraurban studies involving Location Theory evolved from Berry’s interpretation of

Christaller’s formulas. The main direction in this part of the field was guided by Douglas West

31

and his studies of intraurban Central Place Theories in Canadian cities. West researched

agglomeration economies as well as market clustering, drawing his work directly from

Christaller. He took Christaller’s hierarchy of places and narrowed it to create a hierarchy of

retail firms, and formed a classification of types of retail stores, as well as providing a alternate

classification for highway corridors, classifications which should be important to this study as

well. This taxonomy can be found in Table 5 in the Appendix.

West also studied competition in retail gasoline prices as a yardstick of how markets and retail

centers within an urban area interact with one another and with the problem of small and

extremely local market areas. West determined four factors that most affect the location of retail

establishments:

(1) Cost-minimizing consumers will wish to engage in multipurpose shopping,

(2) Company location decisions will take into account the demand externalities which

multipurpose shopping behavior can produce,

(3) The importance of demand externalities to a particular business will depend upon the nature

of the goods which it sells,

(4) The size of the customer base necessary to support a particular company's store will depend

upon the location-specific demand for the store's products (West 1985).

From this, he also created a matrix of retail classification and hierarchy as applied to the City of

Edmonton, Alberta, seen in Table 5, and also provided a format for how stores and centers move

up or down his hierarchy.

32

Table 5: West’s Arrangement of Stores and Centers

Number of Stores and Centers by Shopping Class, Edmonton 1977

Stores Neighborhood

Centers Community

Centers Regional Centers Malls

Central Retail District

Highway Corridors

1 37 1 - - - 3 11 8 7 - - - 5 21 - 30 - 10 - - - - 31 - 40 - 2 4 1 - 1 41 - 50 - - 1 2 - - 51 - 60 - - 2 1 - - 61 - 70 - - 1 2 - - 70+ - - - 3 1 - Total Number of Centers 45 20 8 9 1 9 Mean Number of Stores 8 23 46 61 327 16

Source: West (1985) Other studies involving intraurban consumer behavior and its effect on centrality were done by

William A. Clark. Clark analyzed Lösch’s derivative of the Central Place Theory and emphasized

the sensitivity of the nearest center, studying in Christchurch, New Zealand. His main

arguments that although consumers could be closer to one center which sells a particular good,

often times the actual centers that are patronized by those consumers are completely different

than the hypothetical ones. Clark provided a formula to define the differences between the two

and explain the variances for different intraurban services.

asd = psd/Psd (15)

Where: a = the centrality accessibility of the center

s = business of a particular level of hierarchy

d = distance from consumers, or population groups to retail locations,

33

p = is the population expected to interact with the center, or the expected

theoretical centrality of a place

P = is population that could interact with other centers, the actual

centrality of the central place (Clark 1970).

According to Clark, this helps define the locations of potential retail areas not as just distance

based, but as dependent on complexity and accessibility (Clark 1970). Clark argues that

preferences on issues such as transportation, and even aesthetic characteristics affect the

location of retail establishments greatly and need to be taken into account in any study that

looks at urban locational centrality.

West, Clark, and their colleagues attempted to combine the influence of preferences with

opportunities, and to predict spatial choice patterns by applying interaction rates to retail

alternatives in any area. Here, location and accessibility become the drivers of centrality.

However, the main problem here is that much of their work is descriptive and often does not

provide a specific model, just the theoretical background. But, now that we have researched

studies with a similar to this thesis, we can analyze which parts of these methods we will use here,

and how we are going to test the Central Place Theory on Cincinnati.

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III. METHODOLOGY For the methodology portion of this study, first we establish the actual goals of this thesis, and

how they are achieved. Next, the study area is described and data collection and problems will

be, how we have actually defined the central places in the study, and finally, an explanation of the

final model used for the analysis will be provided.

1. Goals and Objectives

1.1. Goals of the Study

In this study, as mentioned, we will be determining whether or not the variables and formulas of

the Central Place Theory consistently and reliably match or explain Cincinnati’s hierarchy of

retail centers. So, from a theoretical and practical standpoint, this study hopes to find distinct

correlations between the hypothetical markets and hierarchies of the CPT and the physical

environment of the Cincinnati metro.

The main goal of this thesis is to be able to come to the conclusion that, through quantitative

study, the CPT is a useful tool for planners to be able to predict where cities and local

governments should encourage retail and commercial developments in the places where they

will be the most useful. So using the information in the database, we could view the existing

centers and their respective service areas and then determine where proposed or potential retail

centers would be most effective, much like the arrangement of urban centers in Ghana as seen in

Figure 3.

35

Figure 3: Proposed Arrangement of Urban Centers in Ghana

Source: Grove and Huszar (1964), King (1984) Now, if we were to apply the CPT to the Cincinnati metropolitan area, it will probably be easy to

see that it doesn’t fit perfectly, even using the hexagonal service areas. If we were to apply these

models we may find a hexagonal pattern similar to that seen in Figure 4.

1.2. A note on Data

For this thesis data has been used for the metropolitan area of Cincinnati, and only the

Cincinnati Metro. The variables and methods of this study have not been applied to other cities

for comparison or research as this is a study of a test of only the Cincinnati Metropolitan Area.

Only one dataset, the Berkeley/Penn Urban dataset which will be discussed shortly, is used for

each and every task, as well as the same index and study area for the methods and tasks of the

thesis.

36

Figure 4: Possible Hexagonal Arrangement of Central Places in Cincinnati

Source: King (1984), modified 29 December 2008

2. Tasks

2.1. Task 1: Definition of Study Area

Due to the changes in urbanization throughout the Cincinnati Metropolitan Area, county

boundaries were followed for the extent of the study area here, and since urban centrality is the

focus of the study, I have chosen to and leave out the more rural areas of the Cincinnati Metro.

So, for this study I have used only leaving out Brown County of Ohio, Dearborn and Ohio

Counties of Indiana, and Gallatin, Grant and Pendelton Counties of Kentucky. This will allow

me to focus on the most urbanized portion of the Cincinnati CMSA, Hamilton, Butler, Warren

37

and Clermont Counties in Ohio, and Boone, Kenton and Campbell Counties in Kentucky, seen

in Figure 5. The census tracts (and to a certain extent, the zip codes as well) within these

counties will be the basis for this study, and the data from these tracts will be used in a formula

which will be derived from centrality formulas discussed previously.

Figure 5: Selected Metropolitan Counties – Study area

Source: CAGIS 2007 Created 15 December 2008

38

2.2. Task 2: Data acquisition and issues

The data that has been collected comes from the needed variables for the thesis formula, to use

the data by inserting it into the index to find which retail centers are of which hierarchy and

which areas have grown, which areas are underserved (places where there should be a center) as

well as the pattern and location of the market polygons. Most of the data I have collected is with

regard to one or more formulas to test centrality and the main factors are as follows:

Table 6: Necessary Data Variables

Data variable Source: Number of commercial jobs UC Berkeley Number of retail jobs UC Berkeley Census tract population U.S. Census Center population U.S. Census Region population U.S. Census Number of retail establishments UC Berkeley Basic employment in a center UC Berkeley Total jobs in a center UC Berkeley Distance between places CAGIS Center retail square footage CAGIS Region retail square footage CAGIS Local accessibility Numerous sources Number of zipcode points per center UC Berkeley

Most of the data comes from the U.S. Census, or from a University of California -Berkeley study

which is explained below. Earlier, I had attempted to retrieve data using the Claritas dataset, but

I encountered several problems with this. First the data was highly expensive. It was 10 cents per

data variable times the number of study areas. So, for example, 3 variables x 4 census block

groups cost $1.20 There was a minimum data purchase price of $25 and extra data is charged as

previously mentioned. For a whole county or even just for Cincinnati proper would get

39

expensive very quickly. There was also no freedom to explore the Claritas data to determine how

relevant it would be; as I would have had to purchase the data which I would like to research

without knowing its importance to this study.

So instead, I am using for my central places a new database from the University of California

Berkeley, which has been provided to me by Michael Romanos and Maria Fernanda Ramirez of

the University of Cincinnati. This data set contains estimates of the number of jobs per zip code

based employment center in 1994 and 2003, which was generated as follows. Using the 1994

and 2003 data from the US Census Bureau's County Business Patterns series, zip code-based job

counts were estimated for every 4-digit SIC (Standard Industrial Classification) and NAIC

(North American Industry Classification) industry group by applying a series of mid-point

estimates to an establishment size frequency distribution (Penn Urban/UC Berkeley 2008).

Then the resulting job counts were summarized by major sector, then the resulting sectoral

totals were geocoded to their zip code locations (the centroid of the zip code), and finally the

job totals in zip code centroids and points within 500 meters of each other were aggregated

together to form the job centers which are the subject of the study, and which are seen in Figure

6.

40

Figure 6: Thesis Study Area – Census Tracts and 500m Centers

Source: CAGIS 2007. Created 15 December 2008

41

The biggest problem that has risen with this data as far as limitations go, is that it does not quite

narrow down the information enough for what was originally intended. Originally, I was hoping

to use economic numbers (such as income, etc) for individual types of stores such as grocery

stores but this information is only available at the census block group level, for fear of legal

repercussions, and is not available for census block groups which was my original level of study.

Also there is limited information as to exactly which zip codes are grouped in which central

places, which may hinder the results.

2.3. Task 3: Defining the central places

From a purely quantitative perspective, each central place is a centroid of combined zip codes,

and as defined from the data, each center has a certain number of commercial jobs, a certain

number of square feet of space and a certain number of individual businesses. Each point is the

sum of the number of jobs in a specific field (retail) for each zip code or combination of zip

codes. As such, to begin with they are only points on a map, but this study will become much

clearer if we are to name each center, as described in Table 7 in the appendix. This will ease our

discussion of the centrality of the different places and avoid the use of anonymous numbers

when describing the retail centers. Also the level of centers has been defined directly following

Christaller’s and Berry’s classifications which were seen in Table 4.

Table 4: Berry’s Classification of Retail Centers

Type of Place Classification Order L (Highest) Central Business District Eighth P Large Regional Center Seventh G Medium Regional Center Sixth B Small Regional Center Fifth K Large Neighborhood Center Fourth A Medium Neighborhood Center Third M Small Neighborhood Center Second H (Lowest) Corner Retail First

Source: Berry (1967)

42

The central places were ranked by the kinds of services which they provide. These retail services

were defined according to the U.S. Census 2003 NAICS classifications of Retail Trade for

individual industry selections (such as hardware stores, gas stations, computer software stores,

etc.). The services were then ranked similarly to Brian Berry’s study of Snohomish County

(Berry 1967, Berry and Garrison 1958) using their threshold sizes and then finding the lowest

common service to define the level or hierarchy. Table 8 in the Appendix contains the complete

ranking of local retail services.

2.4. Task 4: Model Implementation

In order to test this study, the index will be applied as follows: First the mathematical model will

be applied by using the data from the Berkeley/Penn Urban database and entering it into our

model for centrality, which will be defined shortly. From here we can define the hierarchical

structure and patterns of the central places and then rank each center according to its centrality

magnitude. Finally, the market areas which will be mapped should tell us where the geographical

areas are of different levels in the hierarchy where retail services are needed or lacking.

2.4.1. Definition of the model

What has been done for the mathematical model, is use a combination of factors relevant to

Cincinnati, derived from the literature we have studied, and combined into an index from which

we can find the centrality of each point. From the literature review, each model has something to

offer for our study which was why they were included. First off let us look at Christaller’s base

formulas, Formula 1 and 2. When concerning ourselves with Christaller’s variables, in the early

43

21st Century, the telephone cannot be applied. There are several problems with these formulas,

but one in particular: cellular phones. How could we use phones to determine centrality if you

are able to take your phone with you wherever you go? So unfortunately for Christaller,

technology has rendered his equations obsolete. However, the reasoning behind the formula is

still sound if we were to use a more concrete and relevant variable, such as the total number of

retail jobs in a center. Here we obtain our first factor, which we will name Rc, or the number of

retail jobs in each center, which we take from our UC Berkeley dataset. In addition, Rc will also

need to be multiplied in the index by a weight factor, a factor found by a regression analysis to

determine its importance relative to the other centrality factors which we have used. This

regression analysis will be discussed later in this section. To avoid skewing of the results toward

the largest population centers, I have replaced the actual numbers of jobs with a weight ranging

from 0 as less than 100 jobs for the lowest of our centers, to 134 for the highest number of jobs

represented by Rc. So, from Christaller’s studies we can use jobs as a replacement for telephones

as a measure of centrality. The principles from Christaller can be used but the formulas cannot.

Following from Godlund, and most importantly, from Berry, the index also looks at the amount

of retail sales per square foot, represented by the factor S. These numbers were determined by

taking the total retail sales and dividing this figure by the total retail square footage for each

center, using the 2006 NAICS U.S. Census data for each center.

44

To determine the accessibility of each center to transportation, in this case the distance from a

interstate highway interchange, a dummy variable named a has been added to show this

influence. A value of 1 is given to centers within 3000 feet from an interchange, which is the

distance at which the impact on retail drops off according to the Evidence and Policy

Implications of Highway's Influence on Metropolitan Development Study by the Brookings

Institute (2000). Centers outside of this increased demand area hold a zero, or no change

variable, for their distance from interstate influence.

From here, we observe the number of retail stores in each center, or, the factor n, as similarly

used by Godlund in Equation 6. Here the number of stores is small enough where we can keep

the actual data, although we still weigh it according to its importance. The number of retail

stores was used from the 2006 Zip Code Business Patterns by Employment Size Class data field

for each center. In the index, n will need to be multiplied by a proper weight to emphasize the

number of stores correctly in the index.

Next, we will take into account another weight factor which is called W, which summarizes the

amount of retail square footage for each of our centers, a factor used by Berry, Parr and

Godlund. This has been found by using the attributes of building footprints from CAGIS which

have been cross referenced to the retail parcel data (also from CAGIS) across the study area to

find only the retail square footage. The weight factor is scaled from 1 representing 50,000 square

feet or less to 130 which represents over 6.5 million square feet which is our largest attribute, the

scale of weight factors are also seen in Table 9 in the Appendix. As with retail jobs and the

45

number of stores, W will multiplied by a proper weight found from the regression analysis to

determine its importance in the index.

And finally, we use h as a placeholder for each center’s level within the Cincinnati hierarchy. h is

merely a variable in our index and not the deciding factor of centrality for one main reason. For

each center, the types of shops and services in each is similar but not constant, and some centers

should be at one particular level of the hierarchy but may have one or more outliers which would

skew the results of its centrality. For example, if we have a lowest level center which has four

retail establishments, three of which are level 1 types of services, but contains a service which in

our index is a level 6 retail service. If we were to use only h as our means of determining

centrality, then this center would be moved up five spots in the hierarchy based on one store. So

it makes logical sense that we use h along with other factors to determine centrality. So once

again in the index, h will need to multiplied by a weight to determine the importance of its value

amongst the other factors in the index.

All of the weight factors for each variable were created from a perspective as to which factors

were the most important to the centrality of each center. The complete version of the centrality

index can be found as Table 10 in the Appendix. But, from a formulaic viewpoint, the model of

the index is viewed as follows for each center (c):

46

C = f(Rc, Sc, a, nc, Wc, hc) (16)

Where: Rc = the number of retail jobs in each center,

Sc = the sales dollars per square foot for each center,

a = a dummy variable that indicates interstate accessibility

nc = the number of shops in the central place,

Wc = a weight factor which took into account the average size, or square

footage of the shops, and

h = the hierarchy level of the center

At this point we must determine what the proper weights for each variable need to be. So from

here we run a regression analysis to find the value of each variable. From here we modify the

formula to represent the weights:

C = x1Rc + x2Sc + x3a + x4nc + x5Wc + x6hc

At this point using the regression analysis based on equation 3 and the factors of population and

number of retail jobs, and the ratio of people to jobs (6), we find Christaller’s value c for each

center. At this point we find that after using the Data Analysis tool in Excel to run the multiple

regression analysis to determine the weights, our final weighted index appears as follows:

C = 114Rc + 1.6Sc + 200a + 3.8nc + 45Wc + 5hc

Finally, we can input each factor of centrality and discover the centrality of each center by testing

the model. From here, the Centrality Index (Table 10) was applied for each center to find its

relative centrality, or C, as an added weight to the maps in the test of the model.

47

2.4.2. Tests of the model

The market areas were mapped by first finding the Centrality of each center, or C, from the

index as described in Chapter 4.1. From here we use these numbers as our ‘mass’ for each center

which can be used as a weight, or an importance factor, when mapping the polygons in GIS.

After this, the boundaries of the market areas were found by using a version of Reilly’s Break

Point model (Formula 10) which was used by Berry in urban applications to find where the

market areas ended. This was found partially by using Thiessen polygons which show the half-

way or equidistant point between two centers. The problem with only using Thiessen polygons,

also known as a Voronoi Diagram, is that the break points found here are only equidistant and

do not take into account the masses, or in this case the weights of each point. So, I approached

Dr. Changjoo Kim from the Geography department at the University of Cincinnati, who had a

special extension program for GIS which he created. Using Dr. Kim’s mapping program the

following market area maps were created for each level of the hierarchy, which can be seen in

Figures 7 through 14 on pages 52 through 59. The purpose here is not to create hexagons – we

could do that arbitrarily on a map- but to see if they occur naturally in an urban area.

K Definitions will be our second guide to determining if the CPT does indeed apply correctly in

Cincinnati. The K value we will find by calculating the changes in the size of market area and the

size in threshold populations to determine the K for each change in hierarchical level. Then we

will see if the K value is constant for each change in hierarchy, a variable we will use as a final

measure of similarity to Christaller’s formula.

48

IV. ANALYSIS

1. Hierarchical Descriptions and Maps

We must keep in mind that these maps are of the theoretical market areas, not the absolute

market areas. There are physical boundaries and barriers that the map software does not

consider. For example the market area for Florence Mall (Center 12) is mapped as extending up

through Delhi Township in several levels when the Ohio River creates enough of a barrier where

Delhi would be much more drawn to the Western Hills center. However the mapping software

has not compensated for physical barriers, an issue which needs to be kept in mind when

analyzing these maps. For further clarification, the typology of the hierarchical centers can be

seen in Figure 15. The different levels of hierarchy were established along the lines of Brian

Berry’s ranking of urban central places which was seen in Table 4. So from those levels, this

study of Cincinnati has eight different levels of hierarchy; H to L, H being the highest level and L

the lowest level, corner retail to central business district. The complete hierarchy rankings of

each central place can be seen in the Appendix in Table 12.

Figure 15: Central Place Classes and Levels

49

In this hierarchy there are three centers in the eighth or L level of the hierarchy (the CBD size

centers), which outclass any of the other central places: Center 12 which is the highly developed

retail areas in and around Florence Mall, Center 86 mainly consisting of Kenwood Towne

Center and Center 102 which is the commercial areas of the Tri-County Mall in Springdale.

Center 44, Cincinnati’s central business district places fourth, but a distant fourth so much so

that it is not quite as dominant as the three main centers. Outside of the big three, downtown

Cincinnati is the largest of the seventh or P level of the hierarchy along with Blue Ash, the

Eastgate Mall, West Chester Township, and Fairfield. At the 6th or G level, mid size regional

centers begin to appear, such as the Western Hills area, Loveland, Milford and Hamilton in the

northern areas, and Newport and Covington in the south.

Reaching hierarchical level 5, the first main centers within Cincinnati are visible, with Hyde Park

and Oakley ranking at this level. Also at level 5, or the G Level centers, we first start to see the

formation of market areas resembling hexagons, particularly around the Westwood – Delhi

Township area with centers 47, 61 and 81. There is also the beginning of this pattern forming

around the Mason – Loveland – West Chester area. Level 5 also becomes the first time we can

see a corridor of centers stretching across the Cincinnati metro, following I-71 from Florence in

the south through Cincinnati’s central business district all the way up to Mason in the northeast.

At level 4 in the hierarchy, patterns starting to resemble hexagons appear in the Middletown –

Franklin – Lebanon area, with patterns strengthening in the Western Hills area.

50

At the bottom three levels of the hierarchy some interesting patterns occur. It is at Level 3 with

the A level centers where we first see widespread patterns of hexagons or hexagon-shaped

market areas. The areas with the strongest patterns are the northern and northeastern areas of

Hamilton County, the Western Hills area along the west side of Cincinnati and the north central

areas of Cincinnati near Oakley, Hyde Park and Norwood. Northeastern Hamilton County at

level 3 shows some of the best patterns throughout any of the hierarchical levels, with an

excellent arrangement centering on Sharonville. Sharonville (Center 97) and the centers

around it (Reading, Blue Ash, Kenwood, Springdale, Symmes Township and West Chester) all

have roughly equal sized market areas all of which resemble hexagons.

In Level 2 (M Level centers) we find a thorough semi-hexagonal network forming around the

central city areas of Cincinnati, starting in the Western Hills area stretching across town to

Oakley and Madisonville, which blends into a newly formed pattern centered around

southwestern Hamilton County, with centers 51 and 37 through 39 in the Mt. Washington –

Anderson Township – Eastgate area. Hexagonal patterns are still present in the Western Hills

area and are still strong in the Sharonville area, but at Level 2 the market areas have begun to

shift and are slightly closer to the theoretical patterns than we see in Level 3.

Finally, at the base level of the hierarchy, Level 1, we can see another rearranging of the market

areas, particularly within Cincinnati itself. Due to the closeness of each neighborhood business

center to each other and the level of services involved with H level centers, we can find a market

boundary pattern throughout the entire city and most of Hamilton County for the first time.

The market areas are not exact hexagons, but the configuration and network of market areas

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does resemble Christaller’s theory. In the older inner city centers of Cincinnati, we find market

areas with roughly equivalent areas that are contiguous to one another, much as Christaller tried

to predict. The areas around Uptown Cincinnati, northern Cincinnati and its northern suburbs,

and the inner city neighborhood centers all have a close network of connected market areas.

So, some of the patterns that we can observe here is that the suburban retail areas tend to

populate the top three or four levels of the hierarchy while the inner city centers and outlying

rural centers tend to populate the lowest three levels. The lack of retail centers in inner city

Cincinnati could be attributed to either the dominance of the CBD or lack or retail jobs and sites

in the older urban neighborhoods. The largest changes in the maps are between levels 8, 7 and 6

and get more and more similar as the hierarchical level decreases. Also, the maps and markets

appear to be much the same between levels 1 and 3 (H through A) with only minor changes in

the market areas. This could be a result of one of two factors; The local hierarchy in Cincinnati is

completely dominated by the higher level centers that smaller centers just cannot create enough

pull to counteract the large centers, or possibly this study has failed to classify the lower level

centers correctly.

The most interesting aspect of analyzing the maps of the Cincinnati area’s retail markets is that

the arrangement of market areas matches the theoretical pattern at some levels of the hierarchy

better than others. We can see cohesive networks of market areas at some levels, and at different

levels, we have areas of the metropolitan region which show a distinct hexagonal organization.

To help understand why there are such changes from one end of the hierarchy to the other, we

must turn to the analysis of the K Values for further explanation.

52

Figure 7

53

Figure 8

54

Figure 9

55

Figure 10

56

Figure 11

57

Figure 12

58

Figure 13

59

Figure 14

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2. K Value Analysis

Now that the maps have been completed we can assess the different levels of the hierarchy and

discover the changes in the K Value. The K value is simply the change in the size of the market

area as well as the change in market population from one level of the hierarchy to another. If we

describe the K value from Christaller’s perspective then the K values should be constant at every

level. However, this is not the case with Cincinnati’s Hierarchy. If we look at Figure 15 we can

see that the distribution of K values in Cincinnati is not even, and in fact follows an exponential

growth pattern from the lowest to the highest levels of the hierarchy. However, the pattern also

shows a curious match with Christaller’s K expectations: a horizontally linear arrangement with

values close to 3.

Figure 16: Hierarchical K Values – Graphic Representation Table 13: Hierarchial K Values

Numeric Values

Table 13 shows the specific K values for each change in hierarchical level. What we can observe

is that although the value of K increases somewhat exponentially across all levels of hierarchy,

the interesting part is its value between levels 1 through 6 and possibly 1 through 7. The K values

61

increase in a linear pattern in the first five hierarchical levels. What this tells us is that the number

of actual central places in each level of the existing hierarchy does not match the number of

centers which should be in each level theoretically, a pattern seen in Table 14.

Table 14: Number of Centers at Each Hierarchical Level

Theoretical Centers Actual Centers K = 3 K = 4 K = 7 K Level

8 1 1 1 3 7 3 4 7 9 6 9 16 49 22 5 27 64 343 33 4 81 256 2401 46 3 243 1024 16807 56 2 729 4096 117649 75 1 2187 16384 823543 114

However, there are portions of the hierarchy where the K Values are similar to each other, and

can be grouped together. For example, the K values for Levels 1 through 6 are all close enough to

3 and increase in such a linear fashion that they need to be grouped together as one section of

the hierarchy while Levels 7 and 8 form a second part. Level 7, with a value of 4 may be

concluded in the linear pattern, but is enough of an outlier where it could also be part of the

exponential end of the hierarchy. Level 8 is so drastically greater than the other K values that it

alone necessitates the exponential characteristic of the hierarchy. Without the distinct shift from

levels 7 to 8, the entire hierarchy could be seen as linear, and thus more compatible to

Christaller. However, these issues and characteristics of the hierarchy will be more completely

in the final chapter.

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V. CONCLUSIONS

1. Limitations

To begin with, there are several limitations with this study which could call into doubt the

validity of the results. First, the exact formula which was used by UC Berkeley to calculate the

center points is unknown, as they have been unwilling to provide it to this study, so any results

provided here will be incomplete without this bit of information.

Second, the variables of centrality as used here are by no means a complete and exclusive index.

The regression analysis eliminates subjectivity in the weights of the variables, but other variables

such as accessibility or customer preference could be added or used in place of variables that are

used here.

Third, the square footage as determined by CAGIS only takes into account the building

footprint, not multiple floors or floor areas not used by retail uses, both of which could greatly

affect the centrality of a place when the model is applied.

Fourth, the hierarchy levels are based on the thresholds as discussed in Chapter 4.2, and the level

of importance of retail services is different in different cities and regions. For our study, the

threshold was used instead of using rarity of a service in Cincinnati to rank a service. Where in

Pittsburgh or Chicago, a department store (which in Cincinnati is a Level 6, or G center) may be

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ranked a 5 or a 7, here it is a level 6 service according to its local threshold instead of in

proportion to the numbers of the other retail services available.

And finally, even though this is an urban study, rural areas within the study counties could not be

eliminated altogether. All these issues must be addressed so the context of these findings can be

kept in the proper perspective.

For the analysis, the dataset provided this study with 137 central points which as stated in the

methodology chapter, used job totals from zip code centroids and points within 500 meters of

each other were aggregated together to form the job centers which have been studied. However,

in the final analysis only 114 points were used to determine centrality, and there are several

reasons for this. The main two issues were either two centers were within a mile or less of each

other and were close enough and similar enough in composition to be considered the same

center. Second, other points were removed from the dataset which were further apart but were

in the same market area as another point in which the latter point possessed all retail population

data and the former contained no information. For further detail, the omitted points and their

reasons for elimination are explained in Table 11 in the Appendix.

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2. Findings and Discussion

So, finally after we have analyzed the market areas, the central places, and the K values does the

Central Place Theory explain the locations of retail centers in Cincinnati? To a certain extent, it

does, but not in the way one would expect. Why? There are three main reasons why the

correlation is not perfect: The Cincinnati Metropolitan Area is not a homogeneous theoretical

region and so there is not a homogenous distribution of centers; “Big Box” retail stores and

locations similar to them drastically change the nature, scale and locality of centers; and unlike a

theoretical landscape of Christaller, accessibility is not uniform and centrality is greatly affected

by distance from and vicinity to interstate highways.

First, when we analyze the hierarchies of the market areas in Cincinnati, we need to analyze their

spatial relationship. Even though the market areas are uneven, there are areas of the Cincinnati

hierarchy which do follow hexagonal patterns, especially around Sharonville at Level 3, and the

central city at the lowest levels. Even though they are not a complete arrangement of hexagons,

this does show that the theory is valid in an urban setting, and valid in a test of Cincinnati. Also,

the values of K between levels 1 and 6 indicate that at the lowest levels of the hierarchy, the

changes in the threshold population and the minimum market areas does follow a somewhat

linear course and remain close to 3, even if it is not a perfectly constant function where K would

be equal to 3 at all levels. Of course, in an imperfect urban area it would be foolish to assume that

there would be a perfect match with the theoretical market areas.

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In urban areas, with much smaller distances involved than in Christaller’s originally rural study,

market areas are much more likely to be fluid and not of a rigid equidistant structure. Market

boundaries are not as clear in cities as in rural areas, where the greater space between service

centers creates much fewer available markets and forces consumers into more predicable

patterns (Berry 1967). We also see that the older centers in the inner city areas follow the

arrangement of contiguous market areas much closer than the surrounding suburban markets.

Cincinnati, being an older American city, still has areas and centers in its urban core which were

built when Christaller’s theoretical ideas matched technology and the physical landscape much

more accurately than it does today.

However there are problems with the theory involving Cincinnati. If we were to truly have an

equidistant hexagonal hierarchy, we would see centers of higher levels not only in the outer

fringe regions of the urban areas, but also in the core areas of the central city. In Cincinnati, this

is a pattern that simply does not exist mainly due to the lack of homogeneity of its center

distribution. Because of this, at no point at any level of the hierarchy do we see the complete and

seamless blanket of equal-area hexagons as predicted by Christaller.

But it is the variation of the K Value which throws a wrench into this study. The crucial aspect of

the K value as applied by Christaller, is that it must be constant at every level of the hierarchy.

Here the K value does vary, but actually even comes close to being constant between levels 1

through 4 of the hierarchy, and particularly between the second and third. But the K values start

to increase at an exponential rate at level seven, which means that by Level 8 the centers at the

66

top of the hierarchy are so dominant, that they can pull demand for lowest level services which

under normal circumstances are provided by the lowest local centers. Also because of the much

lower urban density in the suburbs, market areas must be much bigger to serve the same number

of people in the central city. So we have values of K that tell us two things: that at the first six

levels of the hierarchy the principles of the Central Place Theory we have a arrangement of

centers and K values which matches closely with Christaller’s theoretical configuration, yet over

the complete hierarchy we have an exponential arrangement dominated by large suburban retail

centers.

The hierarchy of Cincinnati tells us what the retail landscape of the area looks like. The newer

suburban and exurban areas of Cincinnati have market area patterns which match an area of

recent urban growth with little or no history of density, with centers spread far apart and with

most retail services available in a few high order centers. Centers on the edge are separated by

wide regions of almost exclusively residential development or by leapfrogging development

resulting from Euclidean zoning with few substantial local centers outside the scope of the

neighborhood convenience store. But when we look at the landscape of centers in the older

central areas of Cincinnati, there is a much closer correlation to Christaller’s theories than in the

suburban or exurban areas. One of the main reasons for this is that these areas of the study

region were urbanized before the dominance of the automobile and were built during the time

that Christaller was forming his theories. In this area, there is also a much longer and more well

established history of public transportation use, walking, and a shorter distance to local services.

Here also are areas that were once independent of the City of Cincinnati (Clifton, Oakley, St.

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Bernard) and required their own individual retail centers. Patterns of centrality existed similar to

these areas until after the Second World War, when the slow transition to suburban patterns

began. Centers began to move futher and further apart as transportation modes became more

centered around cars, the number of local centers began to decrease, and the fewer numbers of

centers in the outlying areas became more and more diverse, providing greater quantity and

greater diversity of services in one location. Once one has reached the outer extents of the urban

area, the shift is complete and the size and distribution of retail centers bears almost no

resemblance to their urban counterparts. Here the retail landscape is totally dependent on

scarce, massive, regional centers with virtually no record of (or need for) non-automotive

transportation and a complete lack of pedestrian access.

Second is the issue is the ‘big box’ retail centers, or in this classification here, the Warehouse

Clubs and Supercenters. Centrality takes on a whole new meaning when we analyze these types

of stores. Big box stores (such as a Wal-Mart or a Sam’s Club) are in themselves higher order

centers because they combine so many different levels of services in one spot, services such as a

grocery, pharmacy, office supplies, and in some cases gas stations. The effect of this is that

consumers can go to one location for all the levels of services they need, similar to suburban

malls, which results in other centers being ignored and falling by the wayside, and in this study

the Warehouse Clubs and Supercenters were ranked at the highest level due to the enormous

threshold they possess.

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Here also, there is a problem with the true identification of the scale of services at each

hierarchical level. In this classification, Supermarkets such as a Biggs or large multifunctional

convenience stores are classified as level one services, and equal to the small corner convenience

store and the Mom-and-Pop grocery store. For there to be a more accurate picture of the

centrality of Cincinnati, distinctions must be made between true Level 1 facilities and larger

similar service stores. For example, one of the Level 1 services is the Convenience Store with Gas

Station: does a gas station with 2 gasoline pumps constitute the same level or service as a

superstation with 16 pumps and semi trailer access? Probably not. But it becomes difficult to tell

the difference between all the different service types without documentation of the scale of

stores, as they are both classified as level 1 gas stations. A scale variable of some sort is probably

needed to distinguish between a small corner grocer with a half dozen aisles and a supercenter or

hypermarket which essentially provides the same function (food) but to a much higher degree.

And the third primary reason for this variation of market areas and K Values is that accessibility

has a huge impact on centrality and greatly increases the retail ‘pull’ of centers immediately near

major highways. Current technology frees people from the friction of distance and allows them

to shop at nearly any market center they wish. For example, Kenwood Towne Center (Center

86) has a pull far beyond what the networks of Christaller would predict because of an absence

of local centers in rural Warren and Clermont Counties. Local Centers which exist and are

actually on route from far away residential areas in these counties are passed over due to the

number of shops and retail services accessible at Kenwood. Florence Mall possesses a similar

69

market area overreach due to its available services and the relative absence of those services in

Northern Kentucky.

Therefore, in an increasingly mobile society, with globalization, the internet, faster

transportation with greater ranges, and stores which encompass more than one level or

hierarchy under one roof, the accessibility of retail services has become much more important.

Location in Christaller’s day was, to put it in terms of our Centrality index in this study, weighted

far heavier than it would be today. If travel is the only way to reach a good or service, then travel

is your most important variable. But in today’s economy, where almost unlimited places can be

reached in a day’s drive by car, other factors trump distance and location as the deciding factors

of retail shopping.

As we see in the first three levels of the hierarchy and particularly at Level 1, people are much

less willing to travel to the lower orders of retail services then they are for the higher services. But

this arrangement quickly dissolves as the hierarchical level increases and the suburban high

order centers begin to take over. One result of the dominance of the high order suburban

centers is that lower order centers, small centers and centers in close vicinity to largest centers

have extremely small market areas. The pull of these highest centers is strong enough that the

large centers dominate the market areas of the smaller ones very quickly outside of the

immediate area of the small center. This causes a mapping of the small center’s market area to be

very small, explaining some of the tiny market area circles seen around some centers at different

levels of the hierarchy.

70

But the most interesting fact about Cincinnati’s hierarchy is that, with the exception of the

central business district, every center in the top two levels of the hierarchy has a suburban mall.

Eastgate, Northgate Tri-County, Florence and Kenwood malls are all at least Level 7 centers.

This mall factor also helps explain the exponential quality of the K value of levels 7 and 8.

Centers such as malls are much more likely to contain services from multiple if not all levels of

the hierarchy and create a stronger pull from a larger market area in one general location. So the

changes in K values from a neighborhood hierarchical level to a level dominated by suburban

malls are bound to be greater than K changes from neighborhood level to another.

The hierarchial level (7) of Cincinnati’s central business district is an issue as well. One would

hope that the main primary center of the region would be at the top of the hierarchy where here

it is not, but there is one main reason for this: office space. Cincinnati’s CBD holds a significant

amount, if not a majority of the specialized office services of the region, such as large banks,

corporations, and white-collar firms. This study only focused on retail services. If a new

centrality index was to be used which included the statistics of office space this would greatly

increase the importance of the central business district which would be reflected in its

hierarchical level.

One issue is that many of the individual retail centers are too close together to be truly classified

as separate, and that many small retail areas close together are not individual centers. For

example, Rookwood Commons in Norwood is only six city blocks from Oakley Square, the local

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neighborhood business district and Oakley Square is only six or seven blocks from the Center of

Cincinnati. So instead of individual retail centers, numerous centers close together should be

treated as one, a calculation that would drastically affect the number of centers, the centrality

and the general retail patterns of Cincinnati. If many of the small retail centers were combined,

many areas which have low centrality ratings could move up several levels in the hierarchy,

creating a more balanced hierarchical pattern than the one dominated by large suburban malls. If

this is taken into account Cincinnati has more along the lines of forty or fifty centers instead of

the 114 used in this study. Many of the inner city centers from levels 1 through 4 could easily be

joined together and treated as centers closer in strength and importance as some of the highest

level centers, such as the large suburban malls.

Also, we must also keep in mind that the data used in this study is from 2003 and 2006 and much

has changed in the urban economy in the years since. With the economic characteristics of 2008

and 2009, Dillards has closed at Northgate Mall in Colerain Township (Center 93) and Tri-

County Mall (Center 102) is reeling from numerous store closings, including such mainstays as

JC Penney, Barnes and Noble, Circuit City and even Wal-Mart (Cincinnati Enquirer, 13

February 2009; 3 March 2009). All the while Downtown Cincinnati, which continues to remain

stable as a high order center, could return to Level 8 in the Cincinnati hierarchy as a possible

replacement for Tri-County mall as a member of the big three centers.

So, in conclusion, would it indeed be possible to use Central Place Theory to discover the future

retail centers in Cincinnati? The answer here again, is it does, but only to a point. Different

72

studies of different American cities (or areas of cities) may find a greater or worse fit for the

CPT’s principles at all levels of centers. But from our study of Cincinnati the jury is still out:

there is just not a constant relationship even though the theory does work well at some levels.

So after all this, is Central Place Theory still a relevant methodology? As studied in rural areas, it

is still valid, but to a lesser and lesser extent due to the elimination of distance by speed and

technology. Even in rural areas, people depend progressively more on the internet for ordering

far away products instead of travelling to them. Even though the theory does not apply in full, it

may still be useful, even though we cannot use it for different time periods to find historical

changes in Cincinnati, particularly when we cannot find solid patterns using the data from only

one time period.

But there are many reasons why the CPT does not explain the locations of centers in Cincinnati,

from geographical barriers, to transportational problems, to cultural and political issues as well

as the characteristics of the different level centers themselves. The theory is still relevant, but

perhaps as an increasingly historical theory. The principles are still the foundation of other

centrality studies, but as time and technology progresses, if becomes more and more difficult to

use Christaller’s models and formulas without any modifications. The theory can be used to

observe current locations of and differences between central places, but in Cincinnati it does not

explain the differences regularly. Based on this study, the Central Place Theory is a useful tool,

but would not be recommended to consistently explain locations of central places in the

changing world of today.

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APPENDIX Table 7: Place Names for the Database Central Points

Center # Geographic Area Name 0 ZIP 41092(VERONA,KY) 4 ZIP 41094(WALTON,KY) 5 ZIP 41063(MORNING VIEW,KY) 6 ZIP 45120(FELICITY,OH) 7 ZIP 41091(UNION,KY) 8 ZIP 45153(MOSCOW,OH) 9 ZIP 41007(CALIFORNIA,KY)

10 ZIP 41001(ALEXANDRIA,KY) 11 ZIP 41051(INDEPENDENCE,KY) 12 ZIP 41042(FLORENCE,KY) 13 ZIP 45157(NEW RICHMOND,OH) 15 ZIP 41018(ERLANGER,KY) 16 ZIP 45106(BETHEL,OH) 17 ZIP 41080(PETERSBURG,KY) 18 ZIP 41005(BURLINGTON,KY) 19 ZIP 41015(LATONIA,KY) 20 ZIP 45275(CINCINNATI CVG) 21 ZIP 41017(FT MITCHELL,KY) 23 ZIP 41076(NEWPORT,KY) 24 ZIP 41099(N KY UNIVERSITY) 25 ZIP 41059(MELBOURNE,KY) 26 ZIP 41085(SILVER GROVE,KY) 27 ZIP 41048(HEBRON,KY) 28 ZIP 45102(AMELIA,OH) 29 ZIP 41014(COVINGTON,KY) 30 ZIP 41011(COVINGTON,KY) 31 ZIP 45228(CALIFORNIA) 32 ZIP 41071(NEWPORT,KY) 34 ZIP 41075(FORT THOMAS,KY) 35 ZIP 41016(COVINGTON,KY) 37 ZIP 45245(EASTGATE) 38 ZIP 45255(ANDERSON TOWNSHIP) 39 ZIP 45230(MT WASHINGTON) 40 ZIP 45233(SAYLER PARK) 41 ZIP 45204(LOWER PRICE HILL) 42 ZIP 45176(WILLIAMSBURG,OH) 43 ZIP 45203(QUEENSGATE) 44 ZIP 45202(CINCINNATI CBD) 45 ZIP 45205(PRICE HILL)

77

46 ZIP 41073(BELLEVUE,KY) 47 ZIP 45238(DELHI TOWNSHIP) 48 ZIP 45210(OVER-THE-RHINE) 49 ZIP 41074(DAYTON,KY) 50 ZIP 45001(ADDYSTON,OH) 51 ZIP 45244(NEWTOWN,OH) 52 ZIP 45103(BATAVIA,OH) 53 ZIP 45052(NORTH BEND,OH) 54 ZIP 45221(UNIV OF CINCINNATI) 55 ZIP 45226(COLUMBIA TUSCULUM) 56 ZIP 45214(WEST END - FAIRMOUNT) 57 ZIP 45206(WALNUT HILLS) 59 ZIP 45219(MT AUBURN-CUF) 60 ZIP 45225(CAMP WASHINGTON) 61 ZIP 45211(WESTWOOD) 62 ZIP 45220(CLIFTON) 63 ZIP 45208(HYDE PARK) 64 ZIP 45207(EVANSTON) 65 ZIP 45248(GREEN TOWNSHIP) 67 ZIP 45229(AVONDALE) 68 ZIP 45209(OAKLEY) 69 ZIP 45160(OWENSVILLE,OH) 70 ZIP 45212(NORWOOD) 71 ZIP 45217(ST BERNARD) 72 ZIP 45223(NORTHSIDE) 73 ZIP 45227(MADISONVILLE-MARIEMONT) 74 ZIP 45002(CLEVES,OH) 75 ZIP 45174(TERRACE PARK,OH) 76 ZIP 45232(WINTON PLACE) 77 ZIP 45213(PLEASANT RIDGE) 78 ZIP 45237(BOND HILL-ROSELAWN-AMBERLEY) 79 ZIP 45247(COLERAIN TOWNSHIP SW) 80 ZIP 45041(MIAMITOWN,OH) 81 ZIP 45239(MT AIRY-N COLLEGE HILL) 82 ZIP 45216(CARTHAGE) 83 ZIP 45224(COLLEGE HILL) 84 ZIP 45243(MADEIRA-INDIAN HILL) 85 ZIP 45150(MILFORD,OH) 86 ZIP 45236(KENWOOD) 87 ZIP 45111(CAMP DENNISON) 89 ZIP 45030(HARRISON,OH) 91 ZIP 45215(READING-WYOMING-WOODLAWN) 92 ZIP 45231(SPRINGFIELD TOWNSHIP)

78

93 ZIP 45251(COLERAIN TOWNSHIP NE) 94 ZIP 45242(MONTGOMERY-BLUE ASH) 95 ZIP 45252(COLERAIN TOWNSHIP NW) 96 ZIP 45218(GREENHILLS) 97 ZIP 45241(SHARONVILLE) 99 ZIP 45122(GOSHEN,OH)

100 ZIP 45240(FOREST PARK) 101 ZIP 45140(LOVELAND,OH) 102 ZIP 45246(TRI COUNTY SPRINGDALE) 104 ZIP 45249(SYMMES TOWNSHIP) 107 ZIP 45162(PLEASANT PLAIN,OH) 108 ZIP 45053(OKEANA,OH) 109 ZIP 45014(FAIRFIELD,OH) 111 ZIP 45039(MAINEVILLE,OH) 112 ZIP 45069(WEST CHESTER,OH) 113 ZIP 45040(MASON,OH) 114 ZIP 45015(HAMILTON,OH) 116 ZIP 45034(KINGS ISLAND) 117 ZIP 45152(MORROW,OH) 118 ZIP 45011(HAMILTON,OH) 120 ZIP 45013(HAMILTON,OH) 122 ZIP 45065(SOUTH LEBANON,OH) 124 ZIP 45050(MONROE,OH) 125 ZIP 45056(OXFORD,OH) 127 ZIP 45036(LEBANON,OH) 128 ZIP 45054(OREGONIA,OH) 129 ZIP 45067(TRENTON,OH) 131 ZIP 45044(MIDDLETOWN,OH) 133 ZIP 45042(MIDDLETOWN,OH) 135 ZIP 45068(WAYNESVILLE,OH) 136 ZIP 45005(FRANKLIN,OH) 137 ZIP 45066(SPRINGBORO,OH)

79

Table 8: Ranking of Local Retail Services

Rank Service Threshold Population

8 Warehouse clubs & supercenters 10931 7 Household appliance stores 8344 7 Musical instrument & supplies stores 7094 6 Home centers 6657 6 Department stores (expt discount dept stores) 6208 6 News dealers & newsstands 6208 6 Optical goods stores 6208 5 Floor covering stores 5879 5 Clothing stores 5156 4 Baked goods stores 4662 4 Computer & software stores 4662 4 Jewelry stores 4662 4 Office supplies & stationery stores 4662 4 Sporting goods stores 4182 4 Shoe stores 4076 3 Furniture stores 3873 3 New car dealers 3617 3 Book stores 3605 3 Nursery, garden center, & farm supply stores 2698 2 Hardware stores 1202 2 Pharmacies & drug stores 1202 2 Radio, television, & other electronics stores 1202 2 Supermarkets & other grocery (non-convenience) stores 1202 2 Used car dealers 1104 1 Automotive parts & accessories stores 223 1 Beer, wine, & liquor stores 223 1 Convenience stores 223 1 Gasoline stations with convenience stores 223

Source: U.S. Census Data 2006 NAICS Classifications Table 9: Weights of Retail Square Footage

sq foot (in thousands)

Weight (W)

1 to 50 1 50 to 100 2

100 to 150 3 150 to 200 4 200 to 250 5 250 to 300 6 300 to 350 7 350 to 400 8 400 to 450 9 450 to 500 10

500 to 550 11 550 to 600 12 600 to 650 13 650 to 700 14 700 to 750 15 750 to 800 16 800 to 850 17 850 to 900 18 900 to 950 19

950 to 1000 20 1000 to 1050 21 1050 to 1100 22

1100 to 1150 23 1150 to 1200 24 1200 to 1250 25 1250 to 1300 26 1300 to 1350 27 1350 to 1400 28 1400 to 1450 29 1450 to 1500 30 1500 to 1550 31 1550 to 1600 32 1600 to 1650 33 1650 to 1700 34

80

Table 10: Centrality Index

Center Name a Rc Sc nc Wc h C

0 ZIP 41092(VERONA,KY) 0 0 86 2 2 1 387

4 ZIP 41094(WALTON,KY) 1 9 93 13 12 3 2223

5 ZIP 41063(MORNING VIEW,KY) 0 0 76 2 1 1 327

6 ZIP 45120(FELICITY,OH) 0 0 92 5 1 1 363

7 ZIP 41091(UNION,KY) 0 3 90 6 3 1 796

8 ZIP 45153(MOSCOW,OH) 0 0 83 1 1 1 334

9 ZIP 41007(CALIFORNIA,KY) 0 0 87 2 1 1 344

10 ZIP 41001(ALEXANDRIA,KY) 0 15 140 31 1 4 2708

11 ZIP 41051(INDEPENDENCE,KY) 0 7 113 19 10 3 1959

12 ZIP 41042(FLORENCE,KY) 1 134 492 203 130 8 23910

13 ZIP 45157(NEW RICHMOND,OH) 0 2 102 8 4 2 907

15 ZIP 41018(ERLANGER,KY) 0 35 280 50 19 6 6400

16 ZIP 45106(BETHEL,OH) 0 4 99 12 4 2 1145

17 ZIP 41080(PETERSBURG,KY) 0 0 89 1 1 1 343

18 ZIP 41005(BURLINGTON,KY) 0 11 150 16 13 3 2598

19 ZIP 41015(LATONIA,KY) 1 14 170 27 13 4 3167

20 ZIP 45275(CINCINNATI CVG) 0 1 170 1 1 1 586

21 ZIP 41017(FT MITCHELL,KY) 1 41 350 63 31 6 7785

23 ZIP 41076(NEWPORT,KY) 0 22 130 31 15 6 4426

24 ZIP 41099(N KY UNIVERSITY) 0 0 124 1 1 1 399

25 ZIP 41059(MELBOURNE,KY) 0 0 93 2 1 1 354

26 ZIP 41085(SILVER GROVE,KY) 0 0 101 2 1 1 366

27 ZIP 41048(HEBRON,KY) 0 17 60 20 10 4 3172

28 ZIP 45102(AMELIA,OH) 0 15 118 40 17 5 3581

29 ZIP 41014(COVINGTON,KY) 1 1 231 8 4 2 998

30 ZIP 41011(COVINGTON,KY) 1 44 280 73 43 6 8594

31 ZIP 45228(CALIFORNIA) 1 1 101 7 1 1 499

32 ZIP 41071(NEWPORT,KY) 1 41 234 58 61 7 9084

34 ZIP 41075(FORT THOMAS,KY) 0 5 160 17 5 4 1727

35 ZIP 41016(COVINGTON,KY) 0 1 129 4 1 2 685

37 ZIP 45245(EASTGATE) 1 65 478 89 105 7 14307

38 ZIP 45255(ANDERSON TOWNSHIP) 0 48 210 63 31 6 8360

39 ZIP 45230(MT WASHINGTON) 0 21 220 29 15 5 4295

40 ZIP 45233(SAYLER PARK) 0 4 150 9 7 2 1350

41 ZIP 45204(LOWER PRICE HILL) 0 2 108 6 10 1 1026

42 ZIP 45176(WILLIAMSBURG,OH) 0 0 90 6 1 1 364

43 ZIP 45203(QUEENSGATE) 1 19 104 12 21 2 3628

81

44 ZIP 45202(CINCINNATI CBD) 1 107 401 86 92 8 18529

45 ZIP 45205(PRICE HILL) 0 7 123 22 11 4 2185

46 ZIP 41073(BELLEVUE,KY) 1 9 160 13 12 3 2329

47 ZIP 45238(DELHI TOWNSHIP) 0 51 347 83 50 7 10005

48 ZIP 45210(OVER-THE-RHINE) 1 5 134 16 28 3 2563

49 ZIP 41074(DAYTON,KY) 0 2 150 6 5 2 1020

50 ZIP 45001(ADDYSTON,OH) 0 0 92 2 1 1 352

51 ZIP 45244(NEWTOWN,OH) 0 11 230 34 9 4 2767

52 ZIP 45103(BATAVIA,OH) 0 20 126 36 20 6 4436

53 ZIP 45052(NORTH BEND,OH) 0 1 94 3 4 1 608

54 ZIP 45221(UNIV OF CINCINNATI) 0 19 231 7 1 1 2758

55 ZIP 45226(COLUMBIA TUSCULUM) 0 6 151 13 14 3 2063

56 ZIP 45214(WEST END - FAIRMOUNT) 1 0 109 26 20 4 1785

57 ZIP 45206(WALNUT HILLS) 1 10 139 20 39 4 3805

59 ZIP 45219(MT AUBURN-CUF) 1 0 186 27 25 4 2136

60 ZIP 45225(CAMP WASHINGTON) 1 8 157 13 13 3 2255

61 ZIP 45211(WESTWOOD) 0 46 208 61 28 7 8139

62 ZIP 45220(CLIFTON) 1 8 140 14 12 4 2340

63 ZIP 45208(HYDE PARK) 0 26 298 42 15 6 5192

64 ZIP 45207(EVANSTON) 1 1 148 9 6 2 960

65 ZIP 45248(GREEN TOWNSHIP) 0 15 213 26 28 4 4020

67 ZIP 45229(AVONDALE) 0 9 162 18 12 4 2505

68 ZIP 45209(OAKLEY) 1 38 280 46 18 6 6681

69 ZIP 45160(OWENSVILLE,OH) 0 1 91 5 3 1 566

70 ZIP 45212(NORWOOD) 1 23 240 34 37 5 5564

71 ZIP 45217(ST BERNARD) 1 5 118 9 5 2 1323

72 ZIP 45223(NORTHSIDE) 1 5 175 20 11 4 2032

73 ZIP 45227(MADISONVILLE-MARIEMONT) 0 26 203 27 29 5 5460

74 ZIP 45002(CLEVES,OH) 0 8 119 12 12 2 1993

75 ZIP 45174(TERRACE PARK,OH) 0 0 104 1 2 1 412

76 ZIP 45232(WINTON PLACE) 1 12 145 10 5 2 2168

77 ZIP 45213(PLEASANT RIDGE) 1 21 12 28 18 5 4095

78 ZIP 45237(BOND HILL-ROSELAWN) 0 12 240 26 41 4 4306

79 ZIP 45247(COLERAIN TOWNSHIP SW) 0 17 180 31 9 5 3513

80 ZIP 45041(MIAMITOWN,OH) 1 2 100 5 1 1 604

81 ZIP 45239(MT AIRY-N COLLEGE HILL) 0 27 290 52 34 6 6186

82 ZIP 45216(CARTHAGE) 1 10 119 35 19 4 2930

83 ZIP 45224(COLLEGE HILL) 0 9 182 22 20 4 2912

84 ZIP 45243(MADEIRA-INDIAN HILL) 0 9 140 18 14 4 2560

82

85 ZIP 45150(MILFORD,OH) 1 47 302 74 55 7 9668

86 ZIP 45236(KENWOOD) 1 127 585 189 86 8 21226

87 ZIP 45111(CAMP DENNISON) 0 0 89 3 1 1 351

89 ZIP 45030(HARRISON,OH) 1 22 159 41 28 5 4943

91 ZIP 45215(READING-WYOMING-WOODLAWN) 1 28 231 47 40 6 6457

92 ZIP 45231(SPRINGFIELD TOWNSHIP) 0 28 430 72 30 6 6419

93 ZIP 45251(COLERAIN TOWNSHIP NE) 1 67 230 83 37 7 11058

94 ZIP 45242(MONTGOMERY-BLUE ASH) 1 73 419 92 108 7 15272

95 ZIP 45252(COLERAIN TOWNSHIP NW) 0 0 112 3 3 1 478

96 ZIP 45218(GREENHILLS) 1 1 104 2 3 1 575

97 ZIP 45241(SHARONVILLE) 0 59 391 77 79 7 12269

99 ZIP 45122(GOSHEN,OH) 0 2 73 13 3 3 988

100 ZIP 45240(FOREST PARK) 1 37 290 46 66 6 8743

101 ZIP 45140(LOVELAND,OH) 0 28 269 50 19 6 5584

102 ZIP 45246(TRI COUNTY SPRINGDALE) 1 114 319 159 123 8 20871

104 ZIP 45249(SYMMES TOWNSHIP) 1 64 390 60 42 7 11107

107 ZIP 45162(PLEASANT PLAIN,OH) 0 0 81 2 1 1 334

108 ZIP 45053(OKEANA,OH) 0 0 84 3 2 1 388

109 ZIP 45014(FAIRFIELD,OH) 0 69 345 97 78 7 13367

111 ZIP 45039(MAINEVILLE,OH) 0 8 120 14 8 3 1975

112 ZIP 45069(WEST CHESTER,OH) 1 63 411 90 90 7 13301

113 ZIP 45040(MASON,OH) 0 49 251 61 69 7 10395

114 ZIP 45015(HAMILTON,OH) 0 8 164 27 15 4 2563

116 ZIP 45034(KINGS ISLAND) 1 10 241 16 10 3 2493

117 ZIP 45152(MORROW,OH) 0 1 87 5 1 1 469

118 ZIP 45011(HAMILTON,OH) 0 39 247 104 39 7 8063

120 ZIP 45013(HAMILTON,OH) 0 38 193 70 22 7 6968

122 ZIP 45065(SOUTH LEBANON,OH) 0 1 114 4 2 1 554

124 ZIP 45050(MONROE,OH) 0 8 105 12 9 2 1836

125 ZIP 45056(OXFORD,OH) 0 23 127 30 10 5 4154

127 ZIP 45036(LEBANON,OH) 0 25 128 52 20 6 5071

128 ZIP 45054(OREGONIA,OH) 0 0 90 2 1 1 349

129 ZIP 45067(TRENTON,OH) 0 3 94 13 5 3 1225

131 ZIP 45044(MIDDLETOWN,OH) 0 31 146 63 22 6 5915

133 ZIP 45042(MIDDLETOWN,OH) 0 25 131 48 23 6 5195

135 ZIP 45068(WAYNESVILLE,OH) 0 5 91 14 7 3 1542

136 ZIP 45005(FRANKLIN,OH) 0 32 132 72 19 6 5907

137 ZIP 45066(SPRINGBORO,OH) 0 21 15 33 11 5 3804

83

Table 11: Eliminated Points and Explanations Center Reason for Omission

1 Same data as Center 6 2 Same data as Center 8 3 Data in Center 5

14 No Data 22 Within 1/2 mile of Center 19 33 Same data as Center 40 36 No Data 58 Same data as Center 60 66 Same data as Center 74 88 Same data as Center 93 90 No Data 98 Within 1/2 mile of Center 99

103 Repeat Point 105 Within 1/2 mile of Center 120 106 No Data 110 Within 1/2 mile of Center 112 115 Within 1/2 mile of Center 118 119 Within 1/2 mile of Center 118 121 Within 1/2 mile of Center 120 123 Within 1/2 mile of Center 124 126 No Data 130 No Data 132 Repeat Point 134 Same data as Center 135

Table 12: Central Place Hierarchy Rankings

Center Name Rank 10 ZIP 41001(ALEXANDRIA,KY) 4 18 ZIP 41005(BURLINGTON,KY) 3

9 ZIP 41007(CALIFORNIA,KY) 1 30 ZIP 41011(COVINGTON,KY) 6 29 ZIP 41014(COVINGTON,KY) 2 19 ZIP 41015(LATONIA,KY) 4 35 ZIP 41016(COVINGTON,KY) 2 21 ZIP 41017(FT MITCHELL,KY) 6 15 ZIP 41018(ERLANGER,KY) 6 12 ZIP 41042(FLORENCE,KY) 8 27 ZIP 41048(HEBRON,KY) 4 11 ZIP 41051(INDEPENDENCE,KY) 3 25 ZIP 41059(MELBOURNE,KY) 1

84

5 ZIP 41063(MORNING VIEW,KY) 1 32 ZIP 41071(NEWPORT,KY) 7 46 ZIP 41073(BELLEVUE,KY) 3 49 ZIP 41074(DAYTON,KY) 2 34 ZIP 41075(FORT THOMAS,KY) 4 23 ZIP 41076(NEWPORT,KY) 6 17 ZIP 41080(PETERSBURG,KY) 1 26 ZIP 41085(SILVER GROVE,KY) 1 7 ZIP 41091(UNION,KY) 1 0 ZIP 41092(VERONA,KY) 1 4 ZIP 41094(WALTON,KY) 3

24 ZIP 41099(N KY UNIVERSITY) 1 50 ZIP 45001(ADDYSTON,OH) 1 74 ZIP 45002(CLEVES,OH) 2

136 ZIP 45005(FRANKLIN,OH) 6 118 ZIP 45011(HAMILTON,OH) 7 120 ZIP 45013(HAMILTON,OH) 7 109 ZIP 45014(FAIRFIELD,OH) 7 114 ZIP 45015(HAMILTON,OH) 4 89 ZIP 45030(HARRISON,OH) 5

116 ZIP 45034(KINGS ISLAND) 3 127 ZIP 45036(LEBANON,OH) 6 111 ZIP 45039(MAINEVILLE,OH) 3 113 ZIP 45040(MASON,OH) 7 80 ZIP 45041(MIAMITOWN,OH) 1

133 ZIP 45042(MIDDLETOWN,OH) 6 131 ZIP 45044(MIDDLETOWN,OH) 6 124 ZIP 45050(MONROE,OH) 2 53 ZIP 45052(NORTH BEND,OH) 1

108 ZIP 45053(OKEANA,OH) 1 128 ZIP 45054(OREGONIA,OH) 1 125 ZIP 45056(OXFORD,OH) 5 122 ZIP 45065(SOUTH LEBANON,OH) 1 137 ZIP 45066(SPRINGBORO,OH) 5 129 ZIP 45067(TRENTON,OH) 3 135 ZIP 45068(WAYNESVILLE,OH) 3 112 ZIP 45069(WEST CHESTER,OH) 7 28 ZIP 45102(AMELIA,OH) 5 52 ZIP 45103(BATAVIA,OH) 6 16 ZIP 45106(BETHEL,OH) 2 87 ZIP 45111(CAMP DENNISON) 1 6 ZIP 45120(FELICITY,OH) 1

99 ZIP 45122(GOSHEN,OH) 3

85

101 ZIP 45140(LOVELAND,OH) 6 85 ZIP 45150(MILFORD,OH) 7

117 ZIP 45152(MORROW,OH) 1 8 ZIP 45153(MOSCOW,OH) 1

13 ZIP 45157(NEW RICHMOND,OH) 2 69 ZIP 45160(OWENSVILLE,OH) 1

107 ZIP 45162(PLEASANT PLAIN,OH) 1 75 ZIP 45174(TERRACE PARK,OH) 1 42 ZIP 45176(WILLIAMSBURG,OH) 1 44 ZIP 45202(CINCINNATI CBD) 8 43 ZIP 45203(QUEENSGATE) 2 41 ZIP 45204(LOWER PRICE HILL) 1 45 ZIP 45205(PRICE HILL) 4 57 ZIP 45206(WALNUT HILLS) 4 64 ZIP 45207(EVANSTON) 2 63 ZIP 45208(HYDE PARK) 6 68 ZIP 45209(OAKLEY) 6 48 ZIP 45210(OVER-THE-RHINE) 3 61 ZIP 45211(WESTWOOD) 7 70 ZIP 45212(NORWOOD) 5 77 ZIP 45213(PLEASANT RIDGE) 5 56 ZIP 45214(WEST END - FAIRMOUNT) 4

91 ZIP 45215(READING-WYOMING-WOODLAWN) 6

82 ZIP 45216(CARTHAGE) 4 71 ZIP 45217(ST BERNARD) 2 96 ZIP 45218(GREENHILLS) 1 59 ZIP 45219(MT AUBURN-CUF) 4 62 ZIP 45220(CLIFTON) 4 54 ZIP 45221(UNIV OF CINCINNATI) 1 72 ZIP 45223(NORTHSIDE) 4 83 ZIP 45224(COLLEGE HILL) 4 60 ZIP 45225(CAMP WASHINGTON) 3 55 ZIP 45226(COLUMBIA TUSCULUM) 3 73 ZIP 45227(MADISONVILLE-MARIEMONT) 5 31 ZIP 45228(CALIFORNIA) 1 67 ZIP 45229(AVONDALE) 4 39 ZIP 45230(MT WASHINGTON) 5 92 ZIP 45231(SPRINGFIELD TOWNSHIP) 6 76 ZIP 45232(WINTON PLACE) 2 40 ZIP 45233(SAYLER PARK) 2 86 ZIP 45236(KENWOOD) 8 78 ZIP 45237(BOND HILL-ROSELAWN- 4

86

AMBERLEY) 47 ZIP 45238(DELHI TOWNSHIP) 7 81 ZIP 45239(MT AIRY-N COLLEGE HILL) 6

100 ZIP 45240(FOREST PARK) 6 97 ZIP 45241(SHARONVILLE) 7 94 ZIP 45242(MONTGOMERY-BLUE ASH) 7 84 ZIP 45243(MADEIRA-INDIAN HILL) 4 51 ZIP 45244(NEWTOWN,OH) 4 37 ZIP 45245(EASTGATE) 7

102 ZIP 45246(TRI COUNTY SPRINGDALE) 8 79 ZIP 45247(COLERAIN TOWNSHIP SW) 5 65 ZIP 45248(GREEN TOWNSHIP) 4

104 ZIP 45249(SYMMES TOWNSHIP) 7 93 ZIP 45251(COLERAIN TOWNSHIP NE) 7 95 ZIP 45252(COLERAIN TOWNSHIP NW) 1 38 ZIP 45255(ANDERSON TOWNSHIP) 6 20 ZIP 45275(CINCINNATI CVG) 1