FLOOD01751

• County: Fremont
• Community: Canon City
• Stream Name: Arkansas River
• Title: Canon City Community File
• Date: 1/1/2001
• Prepared For: CWCB
• Prepared By: CWCB
• Floodplain - Doc Type: Community File

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14

PRACTICAL INTERPRETATION OF MAP AC0IRACY SPECIFICATIONS

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Figure l.--Large apparent error caused by mis-
identifica~ion of test point.. .

to catch the ~i5takes ~nd exercise common sense
.1n dealing ~lt:h them. \lith respect- to the applica-
tion of test-satvey"data, my polnt- 1s this: test
data ~.be unlmpea~hable, but they aren't.
Results that are appa~ently unfavorable should be
carefully scrutinized before costly resurveys
are undertaken. . .

STATISTICA1. EXPRESSION OF MAP ACCU!\ACY

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There is nQ~ Yidespread agreement on the
desirability of using standard error (or root-Dean-
square error) to express ~ap accuracy. At the
moment, there is a difference of opinion as to
whether correct. statistical theory has been used
in the literature. Briefly, the nub of the debate
15 yhether position error is a univariate (as
previ~us literature assumes) or a bivariate
(meaning that it Is composed of two variables.
x and y). If the bivariate theory is correct,
then the allowable standard horizontal error .for
a 1:24.000 map is theoretically 19 feet instead
of 24 feet. I am not enough of an expert in
statistics to debate this point, but 1 have made
an em~irical check to see~which conforms more
closely with actual experience, remembering that
the objective is to retain an accuracy standard
that is equal in value .to the tr9C7. within 40
feet" expression.

Figure 2 1~ a histogram showing the dis-
. tribution of root-mean~square-error values
derived from horizontal accuracy tests carried
out by the Ceological Survey on 110 mapping
projects involving 3623 test points in 1964-65.
The data shoy that the root-~ean-square-error
value giving results that conform most closely
~lth th~ 9~~-uithin-1/5C-inch result is 28 feet.
The 90t criterion was met Cor 927. of the tests.

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The th~oretical RMSE. based on the univariate
approach 1s 24 feet. and this was ~et for 767. of
the tests. Based on the bivariate approach. the
theoreticai RMSE is 19 feet and this vas Dat for
only 497. of the tests. If a 4-foot leeway vere
allowed for th~ bivariate approach (to match the
~lfference between 24 and 28). the criterion
vouId be 23 feet, vhich was.~et for 737. of the
tests;.

. If we c.an. judge by. these t~sts (and 1 would
certairlly Relcome it if Bomeone would present a
core extenslv~ experienee), ve have to conelude
that a praetical value for the allowable &~E
. . cannot confo~ strictly to theory, vhether we
consider position error to be a univariate or a
bivariate. _.1 am sure that no one who has ,ad- ';, .
voca~ed th~ use of statistical .terminology has
intended to tighten the exl~ting specifications
thereby. I submit, therefore, that if the degree
. of horizontal a.ccuracy inherent in. the existing
"9C7." specifications is to be ll'l8intained, a value
of 2~ ~eet as the allowable root-mean-square error
for mapp~ng at 1:24.COO should be adopted.

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One can scarcely accept this adoption of an
empirical criterion without wondering Yhy the
value does. not conform.more closely to theory.
One of the obvious reaso~s jor this nonconformity
is. the oft-observed failure of the errors to
follow a normal distribution pattern. There is'~
. a strong likelihood that the abnormal distribution '.
has.a greater effect o~ the'practical result than
the. difference between the univariate and the .
bivariate approaches to the position error. Another-
factor contributlna to the discrepancy is the
effect of ~rrors in'the accuracy-test survey; such.
errors und~ubtedly have a different effect on ,
the l'go-or-no"8011 data derived under the, 907. rule
than they do on root-mean-square-error_data.
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TESTIh'G VERTICAL ACCURACY

!n the past, there has been some advocacy
of a formula for evaluating vertical accuracy
which would take the form.

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allowable root-mean-square err~r
in elevation

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contour interval

b .. th~ allowable t~orizontal shlrt~

" t .. tangent of the angle of slope of ..
the ground.

This formula Is acceptable in theory, b~t
in practice it can be applied only vhen the
ground slope ~s 'uniform over the entIre area of

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