h'^3 7

Agriculture Handbook No.237

S.AIVI FILING ^

CODING

sr-ici

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RING FLOOD

PLAIN

DATA

Farm Economics Division • Economic Research Service

U.S. DEPARTMENT OF AGRICULTURE
FOFEWORD

This handbook reports one phase of a study of the characteristics and use

of rural flood plains conducted by the University of Chicago, under a Research

and Marketing Act contract with the Economic Research Service, U. S. Department

of Agriculture. Other phases include an analysis of types of rural occupance

of flood plains, experimentation with classification of such occupance, and

preliminary measurements of changes in occupance during the past 25 years. The

project supervisor is Gilbert F. White, Chairman of the Department of Geography,

University of Chicago. The designated representative of the Economic Research

Service for administration of the contract is Robert C. Otte, Farm Economics

Division.

Specifically, the report describes a unique field method for punchcard

coding and storing of geographic sample data to be analyzed and compared with

data from other sources. The method should be useful particularly to agencies

concerned with flood-control planning and of general interest to researchers

interested in coding and storing resource data.

CONTENTS

Page

Summary ii

Background and Objectives 1

Sampling Methods 2

Sampling units 4

Areal samples 4

Advantages of various areal samples 5

Tests of the relative efficiency of sampling systems 10

Sample size 11

Coding, Storage, and Comparative Analysis 14

Coding 15

Geographic coding 15

Storage 17

Analysis -— " ~ " 20

Comparisons with previous studies 20

Analysis through time 21

Conclusion 24

Bibliography 26

August 1962
SUM/MRY

This report attempts to develop practical methods of sampling, coding,

and storing data relating to the agricultural occupancy of flood plains in

the United States, given the problem that many objectives must be satisfied.

It appears that the most efficient sample for analysis of areal distributions,

for making estimates of the areal coverage of phenomena, and for comparative

analysis is a systematic, stratified, and unaligned point sample.

The systematic feature of such a sample facilitates an unconventional

use of punched card systems that has the invaluable property of maintaining

geographic ordering of the data. Once prepared, the punched cards provide

permanent storage in a compact format. A nominal scale is used for coding.

The card system vdth nominal coding and geographic ordering facilitates

comparative analysis of land-use, soil, slope, land-capability, flood-hazard,

or other distributions by allowing easy preparation of contingency tables

and rapid location of residuals in their geographic setting. Similarly,

studies of changes through time are facilitated.

Since the systems and operations described are simple and readily

applied, it appears that they could be undertaken directly in the field.

This has the advantage of suggesting additional questions and supplemental

observations while field workers are out in the study area, instead of later

in the office.

11
SAIBLING, CODING, AND STORING FLOOD PLAIN DATA

By

Brian J. L. Berry, Assistant Professor, Department of Geography,

University of Chicago

BACKGROUND AND OBJECTIVES

This report is concerned with methods of sampling, coding, and storing

data relating to the agricultural occupance of flood plains in the United

States. 1/ Since a properly structured national sample must await the

development of a classification of rural flood plains, we will focus on the

analysis of individual flood plains.

Several aspects of the problem can be identified: (a) Overall measurements

of land use on the flood plain, with a view to comparison with other areas and

with the same area at other times; (b) variations in use of land within the

flood plain and the adjacent area, together with changes in these uses through

time; and (c) explanations of the variations in uses and their changes in terms

of soil and slope characteristics, drainage, relative location, nature of the

flood hazard, and so forth.

These objectives are not necessarily complementary. The nature and size

of the sample and type of data storage system required are likely to differ,

depending on which of the objectives is paramount. If all interests have to

be served, as appears to be the case in studies of individual flood plains,

the sampling system used must be a compromise.

For other reasons, however, the problem becomes one of maximizing utility

for more than one purpose. Many different surveys are conducted at irregular

intervals by a variety of public agencies and private individuals, working at

different levels of inquiry and using contrasting units of observation.

Examples include watershed work plans, soil surveys, national inventories, and

censuses. The sampling and storage systems must also be designed so that

ready comparisons between the findings of these diverse studies and the flood

plain investigations are possible.

In this report we will attempt to devise methods that do no excessive

violence to any of these ends. The first part of the discussion reviews

\J Occupance, as used in this report, is defined as the process of occupying

or living in an area and the transformations of the original landscape that

result.
method«; of sa.:,pl:nq and proposes and exemplifies ways of collecting data

relating to individual flood plains. These collection methods are designed to

be directly translatable into handy storage systems. Likewise, the coding is

arranged to facilitate analysis needed in both the office and the field, and

to make subsequent comparative studies possible. Storage, coding, and analysis are the topics of the second half of the discussion.

Objectives of the flood plain sample are thus to (l) estimate land uses

in the flood plain and its adjacent borderland (both of these will be referred

to hereafter as the "flood plain"); (2) evaluate changes in these uses through

tine and space; and (3) study changes in relationships between these uses and

associated geographic features of the flood plain, considering also its relative location.

SA//1PLING Í-ETKODS

Sampling is a well-established method whereby part of a whole is selected

to reduce the cost, increase the speed and scope, and improve the accuracy of

estimates relating to the whole; see Cochran (4). 2/ For obvious reasons

such estimates are subject to error. Whether or not a sample gives results

which are representative of the whole depends on keeping sampling errors small

and the sample unbiased.

Common causes of bias include deliberate selection of "typical" cases,

"convenient" substitution of sampling units by observers, and failure to cover

the whole of a chosen sample. The only certain way to avoid bias is to see

that each member of the population under investigation has an equal chance of

being included in the sample. There is one possible exception. In studies of

change, bias will be removed from the estimates of change by using the same

sample for both "before" and "after" studies, provided the bias is constant

through time; see Goodall (7).

Given a proper sampling method, the probability of occurrence of errors

of any magnitude can be calculated from information obtained in the sample.

By extension, the relative efficiency of different sampling methods can be

obtained. If random sampling errors are large, there are several ways in

which they can be reduced. For example, the size of the sample can be

increased, since, other things being equal, random sampling error is

proportional to the square root of the number of observations. (See fig. 1.)

Alternatively, restrictions such as stratification might be imposed, to eliminate from the sampling error differences between strata. These refinements

need not be elaborated here, since excellent discussions of them are available

m standard textbooks; see Cochran (4) and Yates (21). The present discussion

must focus on special kinds of samples of observations arrayed in twodimensional space.

+ hp J^^^T^^•°^ ' ^'''^y consists of all flood plains in the United States;

the population which is sampled comprises all locations on some particular

2/ Underscored numbers in parentheses refer to Bibliography, page 27.
95% LIMITS OF PROPORTION FOR

SIMPLE RANDOM SAMPLE

NO« OF OBSERVATIONS

.005

5,000 h

95% LIMITS OF

PROPORTION

Therefore, with P =0.2

and sample n = 250, 95%

¡rrits of P with simple

random sample would be

P ±.05, or 0.15-^0.25.

,0.1 0.2 0.3 0.4 0.5

PROPORTION WITH PROPERTY

Figure 1.—This chart records the 95-percent confidence limits of a

proportion p for different sample sizes n, assuning that the population N is

large. Under such conditions these limits are given by p plus or minus 1.96 S ,

where S = (p.l-p/n)2"; Cochran, (á., Lhäii. ¿). Thus, if a random sa.mple of

size n=200 is taken, and a proportion of 0.4 of the observations has some

particular characteristic, the 95-percent limits are plus or minus 0.07, and

the true P is expected to lie between 0.33 and 0.47, although there is a 2.5-

percent chance that P is less than 0.33 and another 2.5 percent chance that

P exceeds 0.47. If the sample is increased to n=600 the limits are plus or

minus 0.04 when p is 0.4, and even with n=2400 the limits are plus or minus

0.02.

The shaded area in the lower left section includes all points which, for

the given sample size, lead to p-1.9ó S of less than zero, an impossibility.

This is therefore the area for which a sample is too small for meaningful

estimates of the possible range of P, even with a 2.5-percent risk that P will

be meaningless.
flood plain; and the sample will always consist of elements which are parts

of this flood plain.

Sampling Units

The elements, or sampling units, may be (l) points at which the presence

or absence of some characteristic is recorded, or at which a value is read

from some continuous pattern of variation; (2) lines (traverses), the length

of which lying on particular land use and related features is of interest; or

(3) small areas (guadrats) in which the quantities of occupance characteristics

present are measured.

Traverses are used for forest surveys in the United States and in the

form of the "vdndshield investigations" have been utilized in agricultural

land use investigations. The most commonly used method of timber cruising

is the so-called "10 percent strip method." In this, strips 1 chain (66')

wide and 10 chains apart are traversed. The cruiser moves down the middle of

the strip and records everything one-half chain either side of his course.

Strips are laid to run across the grain of topography, not with it. Cain and

Castro (2) record alternative methods of surveying forest, including the 10

percent strip and its variants, such as the "line-plot" method in which blocks

selected at random along the survey line are studied. They show a distinct

preference for "random plot" methods based upon quadrat or point sample,

however, because these methods are easier to use and apply.

Another type of sampling unit specifically designed for studies of flood

plains is the sample cross section, utilized by the Corps of Engineers and the

Soil Conservation Service, Schneider (16). If they are selected by a proper

method, sample cross sections provide workable methods of achieving most of

'Î^^?-?^J^^Î-^^^^ of ^he flood plain sample. They do, however, present certain

difficulties if changes through time are to be analyzed, because coding and

storage systems that are simple as well as sound are difficult to design with

cross sections as the sampling elements.

Quadrat methods are used by plant ecologists, in particular. An

excellent review of their advantages and limitations is to be found in GreigSmith (8). In general, they may be used to achieve all the objectives of the

flood plain sample, but results are subject to problems of "modifiable units."

As Duncan (5) inaicates, when sampling units vary in size, or when the choice

°-i^^K® ^u ^^'^^^^^'^y» ot^er sizes can always be taken and different results

win beobtamed. This is because local variability is averaged out as

successively larger quadrats are used as sampling units.

.hr..J^^ simplest of the alternative sampling units, points, have none of the

above problems. If points are used as units of observation, all the objec-

^iï L°-i-i\ i°°'' P^^^" "'"P^^ '^^y ^^ achieved, and both coding and storage

Joint sam leí "^''''^' ^^^ ^^^^^^^^9 discussion will deal exclusively with

Areal Samples

refeJpH ^^"^'"^ ^^°°í P^^i" s^-^Ple is of points in area. Thus, it may be

referred to as an areal sample, or alternatively as a geographic, plane, or
two-dimensional sample. Many such samples have been proposed; see Quenouille

(15), Cochran (4), Yates (21), Krumbein (12), and Greig-Smith (8). The number

of alternative areal samples is large because of the following considerations:

(a) A two-dimensional space has both latitudinal and longitudinal axes.

Any element of an areal sample may be located by a coordinate reference to

each axis. Usually, such an element is obtained by selecting sample pairs of

coordinates. Since a different sampling method may be used to provide the

coordinates on each axis, many combinations are possible.

(b) The available sampling methods for each axis include both random and

systematic sampling. In a random sample every possible coordinate value is

given an equal chance of being selected, and each value is chosen independently of other values that are obtained. «Vith a systematic sample the first

coordinate is selected at random, after v;hich the locations of all other

coordinates are determined on the basis of a regular interval.

(c) The sample may be independent or stratified. To obtain a stratified

random sample the axis is divided into several parts, and coordinates are

selected at random within these strata. For a systematic stratified sample,

separate systematic samples are taken within strata. Such systematic samples

may be aligned (as in a "square-grid" or "checkerboard" pattern) or unaligned.

(d) Sample elements may or may not be clustered, such that the location

of a single sample point detsrmines the location of a set of others, or the/

may be nierarchical (multistage), in which detailed sampling is done within

fewer, larger sampling units selected by higher order samples.

Figures 2 through 6 depict a few of the more common combinations and

describe their construction. In each of these figures point samples are

presented, but the methods apply equally to selection of quadrat samples.

Figure 7 illustrates two possible kinds of traverses, systematic and random,

v;hich are also among the alternatives discussed above.

Advantages of Various Areal Samples

Both theoretical and empirical analyses have been undertaken to determine

which of the many possible types of areal samples is to be preferred.

Quenouille (l^), after providing expressions for the variance of random and

systematic samples—both simple and stratified, and independent or aligned—

concluded that provided the autocorrelation function of successive strata is

concave upwards, not only do systematic samples provide the most precise

estimates of the mean, but that least satisfactory variance estimates are

given by simple random samples, followed by stratified random and systematic

samples in that order. Moreover, unaligned samples are more efficient than

aligned. The most efficient areal sample is, thus, the unaligned stratified

systematic.

Osborne (14) provides empirical support for upward concavity of

autocorrelation functions in land use surveys. Furthermore, in a review of

the studies which have been completed to compare alternative areal sampling

systems, Cochran (4) concludes that "systematic sampling shows a gain in
A RANDOM AREAL SAMPLE

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Figure 2.--In this sample each point is selected by entering a table of

random numbers and selecting two such numbers, one within the range of

coordinate values of the ordinate, the ether within the range of coordinate

values of the abscissa. The random ordinate and abscissa values thus obtained

locate the sample element. Note the uneven areal coverage which can emerge.

A STRATIFIED RANDOM AREAL SAMPLE

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Random x coordinates within strata

Figure 3.—In a stratified random areal sample, elements are located by

selecting random pairs of coordinates within blocks of the larger area. The

example has three points so located within each block, although variable

sampling proportions could have been used such that the number of points is

larger within more variable blocks, or within blocks which have more of the

phenomena of interest. Note that areal coverage is better than that of simple

random areal sample.
A SYSTEMATIC ALIGNED

(CHECKERBOARD) SAMPLE

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Regularly spaced x

Figure 4.—A checkerboard sample has a perfectly even spread of points,

with regular spacing on both abscissa and ordinate after point A has been

located at random. But such a selection piocedure implies that all parts of

the study area do not have an equal chance of being included in the sample.

Furthermore, if there are periodicities in the data being collected, the

regularly spaced points could hit the same point on a cycle time and again,

and give completely biased pictures of the spatial variations of phenomena

under stuay.

A STRATIFIED SYSTEMATIC

UNALIGNED SAMPLE

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Alignment on random element of marginals

Figure 5.—The preferred areal sample is the stratified systematic

unaligned sample. It is constructed as follows: First, point A is selected

at random. The x coordinate of A is then used with a new random y coordinate

to locate B, a second random y coordinate to locate E, and so on across the

top row of strata. By a similar process the y coordinate of A is used in

combination with random x coordinates tc locate point C and all successive

points in the first column of strata. The random x coordinate of C and y

coordinate of B are then used to locate D, of E and F to locate G, and so on

until all strata have sample elements. The resulting sample combines the

advantages of randomization and stratification v/ith the useful aspects of

systematic samples, while avoiding possibilities of bias because periodicities

are present.
ONE HEIRARCHICAL SAMPLE

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Random x within random blocks

Figure 6.--Blocks are selected at random with random pairs of coordinates,

and then points are selected at random within the blocks so obtained.

precision which, although modest, is worth having ... the gains are largest for

the types of data /land use, soils, etc^/ in which we would guess the variations would be nearest to continuous." In the investigations reviewed by

Cochran, the relative efficiency 3/ of unaligned systematic over stratified

random samples varied from 1.83 to 5.83.

Both Cochran (4) and Quenouille (25) therefore conclude that unaligned

systematic samples are superior to stratified random samples in studies of two

dimensional space. On the other hand, checkerboard systematic samples may be

only as good as simple random samples, and inferior to stratified random

samples, because of the effects of gradients and periodicities. Systematic

samples are both convenient to draw and execute, and can be recommended when

the autocorrelation function is concave upwards, as appears to be the case in

land use surveys.

A disadvantage is that no dependable method for estimating the variance

of the means from systematic samples is known, because systematization implies

lack of equality of opportunity of places being included in the sample. This

has led, frequently, to the assertion that systematic samples should not be

used. For example, "if sampling is systematic an estimate of the mean is

available which may ... deviate less from the true value than that given by

3/ Relative efficiency is defined as variance of the stratified random

sample divided by variance of the systematic unaligned sample. Thus, if the

^K ! r.u "^y '^ ^'°' ^^^ variance estimate of the stratified is twice

that of the systematic, or the systematic is twice as efficient.
TRAVERSES: SYSTEMATIC AND RANDOM

Figure 7.—Traverses are another variety of areal sample, often used in

forest surveys. It has been shown that unbiased estimates of the percent

coverage of various uses may be obtained from a traverse, as the percentage

of length of line.

random samples, but there is no indication of its precision and no possibility

of assessing the significance of its difference from the mean of another area,"

according to Greig-Smith (8, p. 21).

These considerations may not be absolutely insurmountable, hov;ever.

Expressions for the variance of systematic samples are suggested by both Yates

(21) and Cochran (4) and, after his theoretical analysis. Quenouille (15)

proposed three different methods of estimating the variance:

(a) By using sets of systematic samples randomly placed with respect

to each other, with the error variance calculated from the variances of the

systematic samples in each block.
(b) By using one set of systematic samples randomly placed, with the area

then broken into blocks and the error variance calculated from the variances

of the portions of the systematic samples in each block.

(c) By using one systematic sample, breaking it up into several systematic

samples of wider spacing, and calculating the error variance from the portions

of the sub-systematic samples which fall into blocks into which the area is

divided.

These three methods are increasingly accurate in their estimate of the mean,

increasingly biased in their estimate of the sample variance, and decreasingly

difficult in their practical application, so that the method of sampling may

vary according to the population and the use to which the results are to be put.

These considerations are relevant if estimates of percent of area occupied

by particular uses are of interest, or if it is desired to compare areas. When

comparisons through time are of concern, and bias is relatively constant from

one time period to the next, then accurate estimates of change can be obtained

without satisfying the requirement of unbiased estimates; see Goodall (7).

If the purpose of the sample is simply to gain an understanding of the

geographic distribution and spatial variations of any phenomenon over an area,

there is no doubt that a systematic arrangement of points is preferable;

Krumbein (12). In addition, as will be seen below, systematic patterns

facilitate storage and machine mapping.

On all counts, therefore, systematic unaligned samples appear to be most

advantageous in flood plain investigations.

Tests of the Relative Efficiency

of Sampling Systems

Tests of the relative efficiency of sampling systems were undertaken to

ascertain whether the above conclusions could be supported in practice, in

flood plain studies. One check was made in the Coon Creek intensive study

area, 4/ and another in the Montfort area, previously studied by Finch and

Platt (6). '

In the Coon Creek area (about 10 square miles) a map of land use was

available, and is shown in figure 8. Planimetered estimates of the proportions

of total area occupied by different types of land use were 40.8 percent woodland,

32.5 percent cropland, 22.5 percent pasture, 2.0 percent gallery, and 2.2 percent

other uses. Four stratified systematic unaligned samples were taken, randomly

oriented with respect to each other, as recommended by Quenouille (15). One of

An?i.i?f^^^?V" "^^^^^^ ^^' B'J^ton. in a companion study (Burton, Ian. Types of

Agricultural Occupance of Flood Plains in the United sLtes. R;search pIper

No. 75. Department of Geography, University of Chicago, 1962).

10
these is shown in figure 9. Each sample contains an average of one point per

10 acres, so that the 6ó0 points have an average spacing of one-eighth of a

mile or 660 feet. 5/

Estimates of percentage of woodland cover were 40.49, 40.96, 40.24, and

41.07 in the four samples. The mean is thus 40.69 percent and the variance is

0.17. In a simple random areal sample the expected variance for a sample of

this size is 3.66, so that the relative efficiency of the systematic sample

over the simple random is 21.5.

For a meaningful comparison of relative errors, the area was stratified

into quarter-mile square blocks, and four points were located at random in e.T.ch

block to create a stratified random areal sample. This was repeated four times.

The percent woodland coverage estimates from these four samples yielded a mean

of 41.4 percent and a variance of 0.96. The relative efficiency of the

systematic over stratified random areal samples is thus 5.65, much the same as

in the results of experiments reported by Cochran. Similarly, for pasture the

relative efficiency of systematic over stratified random samples was 2.3 and for

cropland it was 3.4. Gains in efficiency are consistent and useful. A

systematic stratified unaligned sample is to be preferred.

In the /'tontfort area a complete detailed land use survey was undertaken,

and the results published in the volume Geographic Surveys in 1933 (6). Of the

total area of 29,396 acres, 55.4 percent was in cultivated land. Relatively

small samples were taken, with-n equaling 184, or about one point to every 160

acres.

With a sample of this size, the expected variance of simple random samples

is 13.4. Four systematic unaligned samples were taken, and they yielded an

overall estimate of the mean of 54.7 percent, with a variance of 10.2. The

variance of four stratified random samples was 11.3, of four checkerboard

systematic samples 12.8, of systematic traverses 13.5 (50.5 percent, 48.7

percent, 51.4 percent, 57.2 percent), and of random traverses 11.0. Although

gains in efficiency are less impressive than in the Coon Creek case, the

systematic unaligned sample again provides the most efficient of the sampling

methods, even when compared with traverses.

Sample Size

The relative efficiency of systematic unaligned samples over stratified

random samples is greater than one, and often as high as five. This implies

that fewer observations are needed with an unaligned systematic sample than

with other methods to obtain estimates with a given variance. Let us assume

that to obtain estimates which have similar variance the systematic sample has

to be only one-fifth the size of a simple random sample. Then for a p of 0.1

5/ 660 feet was chosen as an average spacing because, as will be seen in fig.

9, a grid of that density was placed over the land use map. However, such a

spacing approximates the 1,000 feet suggested as somewhere near tlie optimum for

soil surveys by Youden and Mehlich (22).

11
COON CREEK: LAND USE

N3

Figure 2
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Figure 9
to have 95 percent limits of plus or minus 0.02, the systematic sample can be

of 180 observations rather than the 900 of the simple random sample (fig. 1).

In the Coon Creek area of 10 square miles this means 18 observations^ per

square mile rather than the 90 the simple random sample v/ould demand, .ihilp

considerable savings in field effort result, there still must be one point to

every 35 acres, with points spaced at an average of every quarter mile. To

locate and visit all such points and record their characteristics would require

more field effort than the usual field methods (consisting of traverses, with

mapping directly onto air photographs, and the preparation of complete land use

maps). 6/

It follows that, despite the savings introduced by the systematic sample,

improved methods of field work are not provided. Flood plain studies of the

character and scope of the Coon Creek investigations must still use traditional

methods of field work if one of the products of the research must be a land use

map. 7/

On the other hand, as Spurr (il) notes in his excellent manual on aerial

photography, careful combination of ground surveys and sampling studies utilizing aerial photographs can reduce markedly the number of repetitive field

studies which might otherwise be needed in analyses of changes through time.

If a land usr> map is available initially, and a point sample is laid over it,

then readings for the same points will yield a perfectly adequate measure of

change in land uses. Moreover, the use of the point sample removes the need

for the hazardous practice of drawing boundaries around presumed homogeneous

areas both on the land use map and in the aerial photographs. This eliminates

one whole range of possible human errors. Spurr also notes how quadrat and

point sampling from aerial photographs may be used to estimate percentages of

areas occupied by different land uses. In very large areas, an hierarchical

sample can also be arranged, such that one samples photographs first, and then

elements within the photographs.

The real advantages of systematic unaligned sampling therefore lie not so

much in the collection of data, whether by field work or by aerial photography

but (a) in providing quick methods of estimating percent cover, with variance

of the estimates known; (b) in facilitating studies of relationships between

distributions in space through time; and (c) in facilitating storage of data

and mapping by machine.

CODING, STORAGE, AND COf^PARATIVE ANALYSIS

After field workers have provided a series of maps of land use, soil,

flood hazard, and related variables, and corresponding compilations of field

data, there emerge problems of making summary estimates, of analyzing

o/ A fact verified in field experiments.

7/ Of course, this is not to imply that other kinds of studies, for example

where farms have to be visited and interviews made, will not benefit from use

Oí samples. These remarks apply to flood plain studies soecifically, and to

similar intensive land use analyses in oeneral.

14
distributions, of evaluating relationships between distributions, and of

storing the mapped data for subsequent comparative analysis.

A series of systematic unaligned point samples may be taken, being certain

that the grids in each case are randomly oriented. From these samples, the

percent coverage of different phenomena, with their related variances, may be

obtained in the usual manner. Coding, storage, and analysis problems remain.

Coding

Coding is the first problem to solve and depends in turn on the nature of

the data, the units of observation, and the level of measurement which has been

used. Table 1 summarizes the various possible levels of measurement or types

of scaling and their characteristics. In flood plain studies two of these

levels occur most frequently, nominal and ratio scaling.

N'o.T.inal scaling is used when the units of observation are points which

are or are not certain things (sucn as woodland or flood plain) and have or

have not seme prooerty (such as slope in excess of fifteen degrees). It is

normal to code such points 1 for presence and C for absence of the property in

question.

Ratio scaling is used when the units of observation are quadrats or

management units, or when points have associated with then readings from some

continuous surface. Various quantitative statements may be made about such

units, for example area devoted to different land uses, outputs, and inputs.

Such statements, on ratio scales, are coded in their full numeric terms. Once

coded, both types of data may be analyzed in a variety of v;ays.

Geographic Coding

A further kind of coding which is of fundamental importance to any spatial

analysis, and also to any system of storage and machine mapping, is geographic

coding. Geographic coding implies attaching to each observation a pair of

coordinates, latitudinal and longitudinal, that assign it to a unique location;

see the discussion in Tobler (19). This kind of coding is now being introduced

to Swedisli census operations on an experimental basis, using a lO-meter grid on

the 1:10,000 map series. 8/ All houses, farms, fields, etc., may be located

within five meters on this grid, in addition to being located b^ their usual

census-type designations. For a discussion with examples see Hager strand (9);

a traditional approach to locational coding is described, by contrast, in

Houseman (lO).

Once data have been coded geographically both the conventional and

unconventional storage systems described below may be used. Just as important,

the v/hole field of machine mapping and automatized analysis of geographic

distributions is available for use by the research worker, as Tobler (20) shows

8/ A special subcommittee of the Census Advisory Committee of the Association

of American Geographers is beginning preliminary feasibility studies for the

United States as well.

15
Table 1.- A classification of scales of measurement

Scale

Basic

empirical

operations

Permissible

statistics Examples

Nominal

Ordinal

Determination

of equality

Determination

of greater or

less

Number of cases

Mode

Phi and chi-square

Median

Percentiles

Order correlation

Assignment of

type, as "vVoodland"

"Flood plain"

Hardness

Grades of severity

Interval

Ratio

Determination of

the equality of

intervals or

differences

Determination of

the equality

of ratios

f'lean

Variance

Product-moment

Correlation

Geometric mean

Harmonic mean

Percent variation

Temperature)

(F or C) ) no

Potential

energy

Calendar

time

) absolute

) zeros

)

)

Length

Numeros i "cy

Density

Time

Kelvin

)

) have

) absolute

) zero

)

temperature)

Source: S. S. Stevens, "The Psychophysics of Sensory Function," The

American Scientist. 48 (l9óO), 226-53.

16
so clearly, with only one probleiTi remainir.g. If latitude and longitude are

used as coordinates, accuiaLe maos of large areas are difficult to prepare on

naciiine, because cf thv usual pioblems of representing the curved surface of

'.he earth on flat paper. It is therefore desirable lo have orthogonal twodimensioiial giids available for purposes of geographic coding, similar to the

military coordinate systeins or the British Ordnance Survey grid. In the

United States, thie State Plane Coordir.ates appear to provide such a required

framev.'ork for geographic coding of large areas, enabling local study areas to

be fitted into large regions; see Mitchell and Simmons (J^). On a world scale,

other grid systems may be constructed to achieve the desired mappings; see

Bailey (l_).

Storage

Several methods of storing data are feasible once these data have been

collected and coded. The data can be left in the form of maps or on

appropriate aerial photographs, with point sample and grid system superimposed.

Such a method has many advantages, but subsequent quantitative analysis is not

possible, and most research workers are aware of the dangers attendant upon

simple visual comparisons of maps in lieu of more sophisticated methods of

analysis.

A second v;ay to store the observations is by making conventional use of

punched cards. In such a system each observation is assigned to one or more

data cards. Recorded on the cardr are the location of the observation, both

traditional (State, county, sub-county unit, etc.) and geographic (latitude

and longitude), followed by the various bits of information (scores on

variables) available about the observation. To compare distributions when

data are coded in this manner requires a pass of the entire deck of cards

through an appropriate tabulating or computing machine. These machines may be

programmed so that they will use the locational coding information to produce

a map of any required distribution in addition to comparing distributions,

although the row-column arrangement of the printing devices attached to

computing machines means that data have to be napped in a souare-grid pattern;

see Tobler (JJ). 9/

The most efficient sample for estimating percent cover is one of points

in a systematic unaligned pattern. This sample also may be combined with

unconventional use of punched cards to provide an alternative and extremely

9/ Tobler (20) shows how, if one has observations on altitudes, for

example, these may be mapped by the machine, and then contoured in the usual

way. However, some simple processing of the altitudes will produce an equation

which represents the contoured surface, and this may be stored even more

completely. The first derivative of this equation, when mapped, yields a map

of slope; the second derivative yields curvature. Hence, once stored in

compact form, elem.entary mathematical operations produce maps of interesting

characteristics oí distributions available only at the expense of considerable

effort if appropriate cor.:pact storage methods are not used.

17
useful storage system that maintains the spatial properties of the map, yet

provides quick methods for comparative analysis of distributions both in tlie

office and the field.

A conventional storage system allocates each observation to a card, and

information relating to the standing of the observation on many variables is

stored in that card. But the card also provides a square grid (conventionally

of 12 rows--Y, X, 0, 1, 2, 3, ... 9--and 80 columns). This could well represent

960 points in a systematic point sample spread over an area.

Let us assume that each cell of the card does represent an observation.

Then if a characteristic is present at that point, the hole is punched; if not,

the cell remains untouched. Only one card is needed for each characteristic,

rather than one for each observation, with real advantages of compactness.

Observations occupy the same position on each of these cards. Of course, the

conventional system must still be used when data have been collected on

something other than a nominal scale.

One variable might be "woodland." The woodland card will have holes

punched in it when the points in the sample fall on woodland, and will be left

untouched where points fall on something other than woodland. If the card is

held up to the light, then the pattern of holes is the geographic pattern of

woodland in the study area. For example, a sample section of the Coon Creek

study area has been enclosed in figure 9. This area contains 10 x 14, or 140

sample points. The land use at these points is tabulated in figure 10.

Figure 10 shows four cards punched in the unconventional manner described

above, one of the map of woodland, one of cropland, one of pasture, and one of

flood plain. A comparison of figure 9 with figure 10 will reveal that the

only distortion introduced is that the unaligned points of the stratified

systematic sample are forced into the square grid shape of the card. The

cards are not the usual 12 x 80 cards, but 10 x 40 cards, especially scored so

that they may be punched on a simple inexpensive hand punching board 10/ while

in the field (hence only 40 columns, to maintain strength of the scored cards).

They are also labeled so that use (variable) and areas (locational identification for the standard card) may be entered at the top of the card.

It is entirely possible to prepare these storage cards while in the field.

Prior to the field survey, the coordinate reference system and the preselected

systematic point sample should be drawn on the aerial photographs and maps.

The area should then be broken into a master set of 10 x 40 units, representing

cards. These units should be given special grid designations, such as area A

Uatitude) 1 (longitude) in the top left hand corner, followed by A2 to the

right of It and Bl below it, etc. Stable base information which can be derived

irom published sources, such as slope and soil type, should be mapped and

punched into the 10 x 40 cards, which will be provided for the field workers.

%7^n r T °^'''^ '^'P' '"^° ^ ^^^^^^ pocket, is light, and costs only

rill , n^ "". """^^ ^^ °^'' thousand after initial costs of the plate have

rl'r. u '" ^^^'"''^ --^ '''-^^ prepared especially for the Department of

Ceograpny, University of Chicago, to be used in field work and field training.

18
LAND USE: COON CREEK SAMPLE

Sample Observations

2 4 6 8 10 12 14 16 18 20 22 24 26 28

0 W w w w w w c c c w w w p c

1 C

w

w

w

c

w

c

c

c

w

w

w

c

c

w

p

c

w

w

c

c

p

c

w

w

c

p

c

w

w

w

c

w

w

w

c

w

c

c

p

G

c

c

w

p

c

p

c p

2 p p

3 p p

c

p

p

p

p

4 p

p

p

5 p p c p p p c p p

6 c p p p p c p p p p p p p p

7 p p p p p

p

p

p

p

p

p

p

p

c

p p p w

w

w

w

w

c

c

c

c

8 w

w

w

w

p

p

p

p

c

w

c

w

w

9 c c w

C =Cropland G = Gallery P= Pasture W= Woodland = Flood Plain

Data Storage, Punched Cards

Area. COON CREEK ^^^| COON CREEK ^^^^^^H

CROPLAND ^^^H Type: PASTURE

í~0 0 G G G G Ö"Ö"G~Ö~1 ri~i'ä~G"

1 1 1 1 1 1 1 1 1 1 1 7 1 1 1 1 1

G G G 0 0 ^^^^^^^^1

l%ltllll211771llllllll ^^^^H 3:33132¡3illll3¡7 2 Z 3 2 2 7 ^^^^^^1

1|31|¡33||131133333I]1 3^^^^ 333|333333||||333 3 3 3 3 3 3^^^^^^^H

4|IIII<<II|4<<<<4I<<<4 4^^H 44444444444|||444 4 4 4 4 4 ^^^^^^

|SS|Si5SS|SSSSiiSSSSSÏ S^^^H Sl|3|lll|9|lll9iS S S S i b^^^^^^Ê

1 t i t i 1 E t ( ( ( ( E t s E t s G Í t s '^^^^1

3 I T 7 7 7 7 T 7 7 T 3 T 1 ) T I 7 T ' ' 3 ^^^^^|

EllllEllllllllEEE

1 1 1 1 1 1 1 1 1 I I 7 7 7 7 7 7 7 7 7 7 T^^^^^^^^^l

1 illllllllllBIIII I^^H llllllllllEEEBII G B B S e B^^^^^^^l

) S i 3 t 9 1 1 9 9 < 9 1 1 9 1 9 3 1 1 ) 9 '^^^H 9 9 1 1 1 1 9 9 9 9 9 9 9 9 9 9 9 mil ^^1

Area COON CREEK ^^H

T/pe: WOOOIAND ^^^H

—m 1 rri a firro o o « ^^^1

i i i i i I' ï 1 1 î i î " t T I ^^H

COON CKEK ^^^^^^1

Type: flOOD PtAIN

OOaOOOOOOGOOOOOOG

7 7 7 t 1 1 1 1 1 1 1 1 1 1 1 1 1 1)711 ^^^^^^^^H

lllllllllZI2i!I232I332 ^^H ! ! ! î ! ! ! ! ! ! ! ! 1 ! ! ! ! 12 2 2 2 2 ^^^^^^1

|]|33lll)333B33333S333 3^^H 3 3 3 3 3 3 3 3 3 3 113 3 3 3 3 3 3 3 3 3 3|^^^^^^|

44444||444444444444444 ^^H

S Í S S S S S S S i S 9 i S S i S S S S 9 i S ^^H

E ( S ( E t i E ( 6 6 I E S e Í i E 1 E Í ( 6 ^^^|

44444444444|||444

ilIlESlIllllllESS

llll|E|||llE|EG6(

4 4 4 4 4 ^^^^^^^^^H

5 9 5 i ^^^^^^^H

G G E E E ^^^^^^^^1

7 7 7 7 7 7 7 7 7 7 7 11)77777777 t^^| IIIIIIIIIII7 7 7 7 7 7 7 7 7 7 7 7^^^^^^|

1 > 1 I I > E • • 1 1 1 1 1 ! > 1 1 . . . i^^H EEIllllllllEIIIII S B S B B B ^^^^^^^1

* *. \ \ \l \ \\ííí \ l II l l l l l ?^^| 9 9 9 9 9 1 9 9 9 9 ) 9 9 9 9 9 9 9 9 ^^^^^H

^^ É^^H

Figure 10

19
The cards, placed in envelopes and mounted on a board in Uie Al, Dl, /\2, •••

pattern, constitute the initial storage system.

Field work proceeds in tne usual fashion, and rraps are prepared. Then,

additional cards may be made up by the field workers, one for each type of data

collected, anü the cards filed. The master maos and aerial photographs, with

coordinates, card-grid, and point sample on tiiem, plus the board and envelopes

•of cards, constitute the storage system.

Analysis

The stage is now set for cross-sectional analysis. To compare any two

geographic distributions, all that is required is to pull out the appropriate

cards and lay one over the other. A two-by-two contingency table may be

prepared in which coincident punches, coincident lack of punches, and punches

on one card but not on the other are indicated. Phi ( / ) then provides the

coefficient of correlation, indicating the degree of association of the

distributions, and chi-square ()(,") provides a test of whether the association

is significantly greater than could have arisen by chance.

For example in figure IC, woodland, pasture, cropland, and the flood plain

have been punched into appropriate storage cards. In an analysis by optical

coincidence (as suggested by Cam.pbell and Caron (3) table 2 was produced.

Forty-one out of 140 points, for example, are both pasture and flood plain.

Plii between pasture and flood plain is 0.694, which is significant at the

0.001 level. Very little flood plain land is not in pasture, so the fact that

correlation is not higher is due to the presence of pasture off the flood plain.

The storage principles are thus that each card is a variable, and each one

of its positions is a specified sample point, identifiable in the grid system

overlaying the aerial photographs and maps of the study area. The same position belongs to the same sample point on all cards prepared for a given area.

Analysis proceeds simply and quickly, by optical coincidence, using contingency

tabulations and related calculations.

Comparisons IVith Previous Studies

Other studies may provide data which can be compared with the results of

the field investigations. If these studies produce a map, as in the case of a

soil survey, the grid system may be superimposed on this map, and point sample

aata extracted. (We iiave already suggested that much of this information

could be provided in a preliminary storage system to the field worker).

Figure 11 is such a map of soil types. In figure 12 the sample points which

were used to construct figure 10 have been used to sample soil types. Table 3

lists the soil types and their letter designation, and table 4 presents all the

characteristics of these soils and the areas they occupy that could be extracted

from descriptions in the soil survey report. It is evident that comparisons

can be made between the spatial distribution of land use and such items as

physiography, terrain, drainage, depth of soil, texture and materials of soil,

and degree of acidity.

Since there is no reason why such data could not be coded and stored

Deiore embarking on field work, field workers could be the ones to compare

20
Table 2.- Correlation of pasture and flood plain land

Item Pasture

present

. Pasture

! absent

' Totals

Flood plain present

Flood plain land absent

. Points

41 a

. 17 c

Points

4 b

78 d

Points

45 C

95 D

Tnta le: 58 A ! 82 B : 140 N

/ = ad - be = 0.694

V^A B C D

7V^ - N/ = 67.4, significant at beyond 0.001 level

results of their own work with such stable or base data. Comparisons of this

kind inevitably raise questions which can only be answered in the field; hence

more penetrating field work would be fostered.

If other studies do not produce maps, but only totals or averages relating

to census areas or similar survey units, comparisons may still be made between

the coded data and these other studies. For example, if the area mapped in

figures 10 and 12 is the subject of another study, perhaps one for which a

watershed workplan records that 95 percent of the flood plain is in pasture,

the percent estimate of land in pasture may be obtained from the point sample

for that area. Then, by performing a simple test for difference between the

percentages, the similarity of the observations may be compared.

Analysis Through Time

If the stored materials and the grid system are preserved through time,

then similar point samples may be taken at later dates and the nature and

degree of land use or other changes, whatever are of interest, may be compared

by exactly the same methods described above. Similarly, if later aggregate

estimates are presented for all or part of the area, the correct point estimate

for comparative analysis may be obtained by summarizing the information for the

points lying within the area for which aggregate estimates are presented.

Comparisons are then made in the usual way. As Spurr (17) suggests, real

savings occur in studies of changes through time if appropriate combinations

of field survey, sample field check, aerial photography, and sample analysis

21
N3

COON CREEK: SOIL TYPES

V7Z:\ CS (STEEP, [JXIIO DC

RXSN DU (STEEP) ^Mi^ RG

BM

WS

w^^

^^^

Figure 11
SOIL TYPES: COON CREEK SAMPLE

Sample Observations

2 4 6 8 10 12 14 16 18 20 22 24 26 28

Rb Rb Rb Cs Du

St Rb Bm Bl Bl Rb Rb Bl B Rb

Cs

St Rb Rb Rb Du

St Cs Cs Rb Bm Br Bm Bl Gy Gy

Rb Ws Rb Du Rb Rb Rb Du Rb Br Gy Bf Gy Be

Bm Ws Rb Rb Dl Dl Rb Rb Bm Br Gy Rs Bf Be

Br Br Ws Rs Rb Ws Rb Rb Rb Br Rb Rs Rs Bf

Br Br Rb Rs Br Br Rs Gy Rs Rb Rs Rs Gy Bf

Rs Rs Rs Rs Br Br Gy Rs Rs Gy Rs Rb Ws Ws

Rs Bm Rs Rs Rs Rs Gy Rs Rs Rb Rs Rb Rb Bm

Bm Rb Bm Bf Gy Gy Bt Bf Bl Br Bm Rb Du

St Rb

Bm Rb ^^^ Bm Bm Bl Bf Rb Bl Rb Rb ^^^ Rb Br

SEE TABLE 3 FOR EXPLANATION OF CODES.

Data Storage, Punched Cards

Area: COON CREEK _

Type: TERRACE AND BENCH SOILS Br Bf Be Ws

0 0 0""0 0 D""0

) t 1 I 1 t

g 0 0 0 I 0

1 1 1 1 1 1

0 0 0 0 0

1

0 0 0

1 1

0 0

1

0

1

0 Q 0 D 0 0 0 0 0 0 D a 0

1 1 1 1 1 1 1 t 1 1 1 1 1

2 1 1 1 1 1 1 2 1 2 2 Î 2 2 2 I 2 2 2 7 2 2 2 2 2 2 2 2 2 2 2

3 1 1 1 3 1 3 1 3 3 3 Ï 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ;

1 1 < • • 4 i 4 1 4 i 4 4 d « 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4^

1 1 5 S 1 1

S Í 1 5

5 5 5 5 5 5 5 5 5 5 5 S 5 5 5 5 5 5 5 5;;.

I t t C 1 1 G E 6 6 E E G S E G 6 6 B G 6 e e G G 6 G 6 6 6 6 G G 6 6 :,

J J 7 î J î ï ?

1 I 8 1 i 1

9 9 9 ! 1 Î

1 1 )

19 9 9

8

9

8 t 8

9 9 9

8

S ;

i

9

B B S S 8 S « 8 B B 8 8 S

3 9 9 9 9 9 9 9 9 9 9 9 9

a a a B B e B

9 9 9 9 9 9 9

Areo; COON CREEK 1

Type: HIGH RIDGE SOILS Cs S. Ds

0 0 0 1 1 0 0 0 0 0 0

1 i i i i i i i' ' ? í'

0 0

1 1

0 0 0 0 0 0 0 0 0

1111)1

0 0 0 0 0

11111

2 2 : 1 2 2 2 1 1 ! I

3 3 3 3 3 3 3 3 3 3 3

44441444444

5 S 5 5 5 5 5 S 5 5 5

E G G G 6 6 E E E E E

j ; ; I I 7 j 1 7 j I

18 18 8 8 8 8 8 8 8

9 9 1 ] 9 9 9 9 9 9 9

2 2

3 3

4 4

5 5

G G

7 1

> 1

1 9

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 S 5 S S i

t G E E E G

7 7 7 7 7 7

8 8 8 8(1

9 9 9 19 9

G E G G G

8 8 8 11

9 9 9
Table 3.- Soil Types

Code

Cs Clinton Silt Loam

Cs steep Clinton Silt Loam, steep phase

Du Dubuque Silt Loam

Du steep Dubuque Silt Loam, steep phase

Rb Rough Broken Land

Bra steep Boone Loam, steep phase

Bl steep Boone Silt Loam, steep phase

B Boone Fine Sandy Loam

Ba Bates Silt Loam

Br Bertrand Silt Loam

Bf Bertrand Fine Sandy Loam

Be Bertrand Loam

Ss Sparta Sand, Brown Phase

Ws Waukesha Silt Loam

Rs Ray Silt Loam

W Wabash Silt Loam

Gy Genesee Fine Sandy Loam

M Meadow

of aerial photographs are undertaken. Taking point samples from aerial

photographs and punching the data into cards, as described above, enables

ready estimates of degrees of change to be made without encountering some of

the more subjective and unsatisfactory aspects of aerial photograph

interpretation.

COJCLUSION

The most efficient point sample for analysis of areal distributions, for

making estimates of areal coverage of phenomena, and for comparative analysis,

appears to be a stratified systematic unaligned sample. This kind of sample

is admirably suited to unconventional use of card storage systems which

maintain geographic ordering of the data. If such use of cards is made th^re

appear to be feasible additions to field work that will facilitate immediate

comparative analysis by the field workers themselves.

24
Table 4.- Soil characteristics; Coon Creek "intensive" survey 1/

: : Cs

Soil description :Cs :steep

! ¡phase

Du

Du

steep

Dhase

Rb

Bm

steep

ohase

I Bl

steep

phase

B

:

Ba :Br .Bf

:

:Be :Ss iWs

:

:Rs

Î

: H :" Gy : M

!

: :

Location : :

Hiqh ridqes : x : x X X

:

: I

:

: :

: 1

:

:

Low ridqes : : X X ;

Valley slopes : : X X X X X ;

Terraces and benches : : : X X : X : X : X ¡

First bottom lands, alonq streams and drainaqewavs : : ! X ! X ! X

Bottom lands : : X

Slope and Terrain : :

Broken land, slopes often 30 oercent : : X

:

X

Gently undulatinq or rollinq 1 x : X X X

X X X X X X X : X X

Drainaqe : :

Excessive, low water holdinq capacity, subject to drouqht—: : X X X X

:

X X X X X X X X I 1 :

Imperfect : ; ! 1 1 X I

Poor ; : : X X : X

ivj "Subject to overflow" : ¡ X : X

U1

Depth : :

:

:

:

To 3D inches : ; X : X X : X X : X : X !

To 5 feet ¡ : X : X X t

To more than 5 feet : x : x X

Texture : :

Floury soft : x : x X

.

:

Fine, friable : : X X X . X : X X : X

Mediuin : : :

Heavy : : X X X : X : X X

Materials : :

Stony : :

:

Sandy : : X X X X . : X : X

Silty : X : X X X X X X X X : X . X : X : X 1 X

Clayey : x : x X X X X :

Acidity : :

Alkali — : :

.

:

:

Neutral : : X :

X X X X X X X X X X : X X : X : X : X : X

1/ See table 3 for explanation of soil type codes.
BIBLIOGRAPHY

(1) Bailey, H. P. . r a.u c +;, 195Ó. Two Grid Systems That Divide the Entire burface of the bar.h

Into Quadrilaterals of Equal Area. Amer. Geophys. Union Trans.

37, 628-35.

(2) Cain, S. A., and G. M. de Gliveira Castro.

1%9. Manual of Vegetation Analysis. New York: Harper.

(3) Campbell, J. D., and H. 3. Caron. _

1961. Data Processing by Optical Coincidence, ocience, U-, LJöö-ö.

(4) Cochran, <V. S.

1953. Sampling Techniques. New York: Wiley.

(5) Duncan, 0. D., and others.

1960. Statistical Geography. Glencoe: The Free Press.

(6) Finch, V. C, and R. S. Platt.

1933. Geographic Surveys. Bui. 9, Chicago Geog. Soc.

(7) Goodall, D. -V.

1952. Some Considerations in the Use of Point Quadrats for the Analysis

of Vegetation. Austral. Sei. Jour., Res. Ser. B, 5, 1-61.

(8) Greig-Smith, P.

1957. Quantitative Plant Ecology. New York: Academic Press.

II

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27

Û U.S. GOVERNMENT PRINTING OFFICE ; 1962 O - 6Ó4768
Growth Through Agricultural Progress