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Measuring Measuring landscape scale landscape scale with ALSM datawith ALSM data
J. Taylor Perron, James J. Taylor Perron, James Kirchner and William Kirchner and William
DietrichDietrich
Dept. of Earth and Planetary Dept. of Earth and Planetary ScienceScience
University of California, University of California, BerkeleyBerkeley
[email protected]@eps.berkeley.edu
NCALNCALMM
NSF-Supported Center for Airborne Laser NSF-Supported Center for Airborne Laser MappingMapping
ProblemProblem
Landscapes are Landscapes are often strongly often strongly periodic at periodic at multiple scalesmultiple scales
Explaining this Explaining this phenomenon phenomenon requires that we requires that we quantify itquantify it
Gabilan Mesa, Salinas Valley, CA
Zabriskie Point, Death Valley 5m
200m
Applications (Why measure Applications (Why measure scale?)scale?)
Extract features Extract features of interestof interest
Model testingModel testing
??
2-D Fourier transforms2-D Fourier transforms
0 100 2000
100
200
-3 -2 -1 0 1 2 3
-0.04 -0.02 0 0.02 0.04
Frequency (1/m )
-0.04
-0.02
0
0.02
0.04
0 20000 40000 60000
Elev (m) PSD (m^4)
m
0 0.02 0.040
1
2
3
4
5
6
7x 10
4
Frequency (1/m)
PS
D (
m4 )
4 km4 km
ALSM data: Gabilan ALSM data: Gabilan Mesa, CAMesa, CA
2 km2 km
0 500 1000 m
~500m~500m
~175m~175m
Acquired & processed in collaboration with NCALM staff at U. Florida
Collapsed power Collapsed power spectrumspectrum
~500m~500m~175m~175m
Collapsed power Collapsed power spectrumspectrum
LandscaLandscape is pe is smoothsmooth
Normalization techniqueNormalization technique
Testing significanceTesting significance
99% Significance 99% Significance LevelLevel
Testing significanceTesting significance
99% Significance 99% Significance LevelLevel
-0.01 -0.005 0 0.005 0.01
Frequency (1/m)
-0.01
-0.005
0
0.005
0.01
0 500 1000 m
0
5
10
15
20
PSD(m )4
Normalizing 2D spectraNormalizing 2D spectra
Wavelength: 480 ± 166 mOrientation: 141°Significance level: >> 99%
Wavelength: 174 ± 13 mOrientation: 47°Significance level: 99.7%
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
1 0 m 2 0 m 3 0 m 4 0 m 5 0 m 6 0 m
Local ReliefLocal Relief
Application 2: Model Application 2: Model testingtesting
-0.006 -0.002 0.002 0.006
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
0 4 8 12 16 20 24 28
PSD (m^4)
Frequency (1/m)
Wavelength: 480 ± 30 mOrientation: 90°Significance level: >> 99%
Wavelength: 200 ± 11 mOrientation: 171°Significance level: 91%
ConclusionsConclusions
2D spectral analysis is an objective 2D spectral analysis is an objective means of identifying & analyzing means of identifying & analyzing periodic topographic featuresperiodic topographic features
ALSM provides spectral resolution & ALSM provides spectral resolution & accuracy necessary to identify limit accuracy necessary to identify limit of landscape dissectionof landscape dissection
ConclusionsConclusionsApplications:Applications:
0 500 1000
Storage of large Storage of large topographic topographic datasetsdatasets
Model testingModel testing
Filtering by scale, Filtering by scale, orientation, orientation, periodicityperiodicity
100% of spectrum
7% of spectrum
