Geography Reference
In-Depth Information
The Mercator projection of the sphere
S
2
R
or of the ellipsoid-
of-revolution
E
A
1
,A
2
is, amongst conformality, characterized
by the equidistant mapping of the equator. In contrast, the
transverse Mercator projection is conformal and maps
the transverse meta-equator, the meridian-of-reference,
equidistantly. Accordingly, the Mercator projection is very
well suited to regions which extend East-West along the
equator, while the transverse Mercator projection fits well
to those regions which have a South-North extension. For
geographic regions which are centered along lines neither
equatorial, parallel circles, nor meridians, the oblique Mer-
cator projection according to
Engels and Grafarend
(
1995
)
is the conformal mapping which has to be preferred.
A typical feature of the Universal Transverse Mercator Projection (UTM) is the equidistant
mapping of the central meridian of a zone except for a dilatation factor
ρ
which is determined by
an optimality criterion. As outlined in
Grafarend
(
1995
), the Airy criterion of a minimal average
distortion over the zone leads to an optimal value of the dilatation factor
ρ
depending on the strip
width. An Airy optimal dilatation factor
ρ
, in addition, sets the average areal distortion over the
zone to zero, which is quite a welcome result of an optimal map projection. Here we aim at a
similar result for the Universal Mercator Projection (UM) and for the Universal Polycylindric
Projection (UPC): the classical Mercator projection is designed Airy optimal for a finite zone
along the equator. The equator is equidistantly mapped except for an Airy optimal dilatation
factor. In particular, we analyze the Airy optimal dilatation factor as a function of the strip
width. The UM strip is bounded by a southern as well as a northern parallel circle. While UM
with an Airy optimal dilatation factor is well suited for geographic regions along the equator, the
Airy optimal UPC has its merits for those territories which extend along a parallel circle - as a
case study, Indonesia has been chosen. For such a conformal projection, a chosen parallel circle is
equidistantly mapped except for a dilatation factor
ρ
0
which is designed Airy optimal for a zone
bounded by a southern as well as a northern parallel circle. For both types of optimal mapping,
namely UM and UPC, the Airy criterion of a minimal average distortion over the zone produces
zero average areal distortion, too.
Section I-1.
A
1
,A
2
with respect to the WGS 84. Figure
I.1
displays the Airy optimal dilatation factor as a function of
the strip width, while Table
I.1
lists various optimal dilatation factors for the given strip widths
3
◦
,
6
◦
,
12
◦
,
20
◦
.
In detail, Sect.
I-1
focuses on the optimal Mercator projection of the ellipsoid-of-revolution
E
Section I-2.
In contrast, Sect.
I-2
presents the optimal polycylindric projection of conformal type. Figure
I.2
displays various Airy optimal dilatation factors for given parallel circles-of-reference parameterized
by the ellipsoidal latitude
Φ
0
and the strip width
Φ
N
−
Φ
S
of northern and southern boundaries.
Tables
I.2
and
I.3
are detailed lists of various optimal dilatation factors in different zones sorted
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