Measuring landscape
scale with ALSM data
J. Taylor Perron, James Kirchner
and William Dietrich
Dept. of Earth and Planetary Science
University of California, Berkeley
perron@eps.berkeley.edu
NCALM
NSF-Supported Center for Airborne Laser Mapping
Problem


Landscapes are often
strongly periodic at
multiple scales
Explaining this
phenomenon requires
that we quantify it
200m
Gabilan Mesa, Salinas Valley, CA
5m
Zabriskie Point, Death Valley
Applications (Why measure scale?)

Extract features of
interest

Model testing
?
2-D Fourier transforms
Elev (m)
-3
-2
-1
0
1
PSD (m^4)
2
3
0
20000
40000
60000
0.04
200
7
100
x 10
0.02
4
0
6
-0.02
5
0
100
4
200 m
-0.04 -0.02
2
1
0
0
0.02 0.04
Frequency (1/m)
3
PSD (m4)
0
-0.04
0
0.02
0.04
Frequency (1/m)
ALSM data: Gabilan Mesa, CA
Acquired & processed in collaboration with NCALM staff at U. Florida
~175m
~500m
24 km
0
500
1000 m
Collapsed power spectrum
~500m
~175m
Collapsed power spectrum
Landscape
is smooth
Normalization technique
Testing significance
99% Significance Level
Testing significance
99% Significance Level
Normalizing 2D spectra
0.01
PSD
(m 4 )
20
Wavelength: 174 ± 13 m
0.005
Orientation: 47°
Significance level: 99.7%
15
0
10
-0.005
-0.01
-0.01
0
500
1000 m
Wavelength: 480 ± 166 m
Orientation: 141°
Significance level: >> 99%
-0.005
0
0.005
Frequency (1/m)
5
0.01
0
Application: filtering by significance
0%
Application: filtering by significance
5%
Application: filtering by significance
25%
Application: filtering by significance
50%
Application: filtering by significance
75%
Application: filtering by significance
90%
Application: filtering by significance
95%
Application: filtering by significance
99%
Application: Filtering by scale
Application: Filtering by scale
Application: Filtering by scale
Application: Filtering by scale
Local Relief
10m 20m 30m 40m 50m 60m
Application 2: Model testing
Wavelength: 200 ± 11 m
Orientation: 171°
Significance level: 91%
Wavelength: 480 ± 30 m
Orientation: 90°
Significance level: >> 99%
Conclusions


2D spectral analysis is an objective means of
identifying & analyzing periodic topographic
features
ALSM provides spectral resolution & accuracy
necessary to identify limit of landscape
dissection
Conclusions
Applications:

Filtering by scale,
orientation,
periodicity


Model testing
Storage of large
topographic datasets
100% of spectrum
7% of spectrum