1. 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.eduNCALM NSF-Supported Center for Airborne Laser Mapping

2. Problem Landscapes are often strongly periodic at multiple scales Landscapes are often strongly periodic at multiple scales Explaining this phenomenon requires that we quantify it Explaining this phenomenon requires that we quantify it Gabilan Mesa, Salinas Valley, CA Zabriskie Point, Death Valley 5m 200m

3. Applications (Why measure scale?) Extract features of interest Extract features of interest Model testing Model testing ?

4. Why not use drainage density? Drainage density ≡ Drainage density ≡ Problems: Problems: Need to know where channels are Need to know where channels are Non-unique Non-unique No topographic info (structure, amplitude, periodicity…) No topographic info (structure, amplitude, periodicity…)  (channel length)/area

5. 2-D Fourier transforms Frequency (1/m) PSD (m 4 )

6. 4 km ALSM data: Gabilan Mesa, CA 2 km ~500m~175m Acquired & processed in collaboration with NCALM staff at U. Florida

7. Collapsed power spectrum ~500m ~175m

8. Landscape is smooth

9. Normalization technique

10. Testing significance 99% Significance Level

11. Testing significance 99% Significance Level

12. Normalizing 2D spectra Wavelength: 480 ± 166 m Orientation: 141°Significance level: >> 99% Wavelength: 174 ± 13 m Orientation: 47° Significance level: 99.7%

13. Application: filtering by significance 0%

14. Application: filtering by significance 1%

15. Application: filtering by significance 5%

16. Application: filtering by significance 25%

17. Application: filtering by significance 50%

18. Application: filtering by significance 75%

19. Application: filtering by significance 90%

20. Application: filtering by significance 95%

21. Application: filtering by significance 99%

22. Application: filtering by significance 99.9%

23. Application: Filtering by scale

26. Local Relief

27. Application 2: Model testing Wavelength: 480 ± 30 m Orientation: 90°Significance level: >> 99% Wavelength: 200 ± 11 m Orientation: 171° Significance level: 91%

28. Conclusions 2D spectral analysis is an objective means of identifying & analyzing periodic topographic features 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 ALSM provides spectral resolution & accuracy necessary to identify limit of landscape dissection

29. Conclusions Applications: Storage of large topographic datasets Storage of large topographic datasets Model testing Model testing Filtering by scale, orientation, periodicity Filtering by scale, orientation, periodicity 100% of spectrum7% of spectrum