Isolines
and Interpolation
Reading in Slocum:
Chapter 14
isolines =
isarithms
= lines of equal value
e.g.
'contour'
for elevation data only
suited to
mapping
smooth and continuous surface
x,y,z data
used
to map surface of volume
isometric:
true values at points (totals or derived values)
isoplethic:
derived from area data, show conceptual form
interpolation:
estimate data values at new positions
all places
with
particular values (e.g. isoline)
or
data
values at particular x,y positions (e.g. grid)
Interpolation by computer (examples figure 14.4)
triangulation
use
triangular
grid joining closest points
interpolate
isolines
positions in straight segments
smooth isolines
inverse
distance
intermediate
step:
interpolate to grid of values
then thread
isolines
through grid and smooth
importance decreases as distance increases
|
|
||
| estimate
of |
|
sum of (data value / distance to grid point) |
| value
at |
= |
|
| grid point |
sum of (1 / distance to
grid point) |
|
kriging
semivariogram used for weighting
|
|
||
| estimate
of value at grid point |
= |
sum of (weight*data value) for control points |
| (weights sum to 1; closer points have higher weights) | ||
Tobler's
pycnophylactic method for isopleths
preserve
volume
in each enumeration unit
evaluation
criteria
correct at
control
points
correct at
non-control
points
handling of
discontinuities
execution
time
parameter
selection
time
Design issues
contrast: lines are figure
labels: run with line, near horizontal, line up, repeat along line if long
legend: verbal statement of units and interval (e.g. contour interval is 20 feet)
line selection: choose constant interval for best surface form
enhancements:
index
, supplementary, depression lines
