| Abstract |
- Soils are 3-dimensional bodies that make up natural landscapes.
In addition to the morphological properties used to characterize
soils, soil bodies also have the properties of size and shape. Soil
maps are made in an effort to provide information on the spatial
distribution of different kinds of soils. Soil mappers draw to
scale, as accurately as possible, the sizes and shapes of the
different kinds of soil bodies they observe in the landscape. Beyond
that, however, very little quantitative information relative to size
and shape is provided to soil map users.
Quantitative shape characterization presents several
opportunities to learn about soil genesis and soil interpretations
for land use. Intriguing questions include "Why does a soil body
have the particular shape it has?", "Does each map unit possess an
intrinsic shape or range of shapes?", "Do existing map unit
interpretations apply equally to delineations of different size and
shape?", "How can shape data for individual delineations be
aggregated into an overall description of soil patterns in different
geographic areas?", "What effects do soil patterns have on land
use?".
None of these questions can be answered without first having an
appropriate technique for characterizing the shapes of individual
delineations. The objective of this research, therefore, was to
examine several possible shape indexes and isolate those few which
had the greatest utility for characterizing shape. These few were
then used to examine shape distributions within a few selected map
units and compare shapes between map units.
Data were collected by digitizing 452 delineations sampled from
13 different kinds of soil bodies identified in the soil survey of
Benton County. For each delineation, 43 potential indexes were
calculated. These included primary measurements, such as area and
perimeter, and figure attribute ratios such as Horton's form ratio,
Miller's circularity index, Schumm's elongation ratio, and Fridland's
coefficient of dissection. A convex hull was circumscribed around
each delineation, and the same primary measurements and attribute
ratios were calculated for the convex hull. Additional indexes were
calculated by comparing values determined for a delineation and
corresponding values for it's convex hull.
One additional technique used was to fit each polygon and convex
hull with a 22-sided vertex lag polygon. Calculation of distances
between vertices of this polygon leads to the derivation of a vertex
lag index of shape. Variations on the vertex lag theme provided
several additional indexes.
Correlation analysis showed that the set of 43 indexes was
highly intercorrelated. In order to reduce this set to a smaller set
of minimally correlated indexes, the entire data set was subjected to
a factor analysis. The result was a set of three dominant factors,
which together accounted for 86.1% of the total variance in the data
set. Each factor was interpreted by considering the nature of the
shape indexes that loaded heavily on it, and a single index was
selected to represent each factor on the basis of maximum
interpretability.
The first factor was interpreted as a measure of the complexity,
or irregularity, of a delineation. The vertex lag index for the
delineation was selected as the best single index to represent this
attribute of shape. The second factor included all of the primary
measurements. Though not a measure of shape per se, primary
measurement data were viewed as significant elements in the spatial
description of soil map delineations. Polygon area was taken as the
best index to represent the effects of primary measurements. The
third factor was interpreted as a measure of form. In this case,
Schumm's elongation ratio, as measured on the convex hull, was found
to be the most interpretable index of form.
These three attributes, size, form, and complexity, provided the
best quantitative description of shape. The indexes that represent
them were found to be minimally correlated and maximally
interpretable.
Each of the 13 kinds of soil bodies sampled was characterized in
terms of the three aspects of shape using descriptive statistics and
frequency histograms. Comparisons between samples were evaluated
using the Mann-Whitney U test. The data suggested that delineations
belonging to a single soil mapping unit do have distinctive
distributions of size, form, and complexity. Shape differences
between mapping units were most evident when comparing soils on
different landforms, parent materials, and slope gradients.
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