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1. Scale Invariance and Scaling Breaks: New Metrics for Inferring Process Signature from High Resolution LiDAR Topography ChandanaGangodagamage Department of Geography and Polar Byrd Research Center Ohio State University Colloquium series Dep. Of Geography- OSU– 11 Feb 2010 Chandana G
2. Outline Background Introduction of a New Scale Parameter New Scaling Considerations across Hillslopes and Fluvial regimes Statistical Signature of Deep-Seated Landslides Spatial heterogeneity using higher order moments Landscape complexity and discontinuous erosional processes Statistical signature of the vegetation height Modeling in spectral and wavelet domain Estimating Vegetation height from satellite based vegetation topography measurements Outline Chandana G
3. Scaling Laws “Why are scaling laws of such distinguished importance? The answer is that scaling laws never appear by accident. They always manifest a property of the phenomenon of basic importance . . This behavior should be discovered, if it exists, and its absence should also be recognized.” - Barenblatt (2003) Hillslope-valley transition Periodicvalleys Dynamic similarity Hierarchy of drainage basins Chandana G
4. New Scaling Considerations across Hillslopes and Fluvial regimes Chandana G
5. Motivation -Get away from the discreteness of stream order ω -Can indentify regime transitions from hillslope to convergent valleys to fluvial network (naturally emerges) -Can extend to higher order moments of basin attributes and understand the spatial heterogeneity of the landscape -Extend new finding to other application e.g., vegetation Chandana G
6. A new scale parameter “Directed distance from divide” Introduce a new scale parameter “directed distance from divide” and use it to study the scaling properties of drainage paths of a river basin. A drainage divide is defined as any point which has no flow accumulations from neighboring pixels. Directed distance refers to the fact that when two flow paths converge, the shortest upstream part will be eliminated and the flow distance continue along the principal path. Gangodagamage, C. et al. (2009) Revisiting river network laws……Water Resour. Res
7. River network laws 250m
8. Real networks: SF Eel -Number of streams N(l) B 2 Region-A 3 C 1 Region-B Region –C
9. Real networks: SF Eel -Number of streams N(l) B A region-B C region-C region-A C B A
10. distance from ridge line Contributing area.. B A C
11. Slope & Slope-Curvature Above are average quantities. But at every we have whole probability distribution.
12. Simulated river networks: spanning trees Gaussian flowpath P=0.5 21 No scaling break
13. Flowpath complexity Hillslope- Straight flowpaths (region-A) Complexity of flowpaths increases highly convergent flowpaths (region-B) fluvial network 22
14. Complexity of flowpaths fluvial network highly convergent flowpaths (region-B) Hc=1.8 Complexity of flowpaths increases HB=3.0 Hillslope- Straight flowpaths (region-A) HA=1.0 23
15. landslide, evacuate immediately—don't wait for an official warning!
16. Statistical signature of deep-seated landslides Gangodagamage, C. et al. (2009) Statistical signature of deep-seated landslide (200), JGR (under review) Chandana G
17. Outline – Part 2 Statistical signature of landslides (using ensemble averages) Mapping landslides Landslides and Landscape complexity
18. Landslide signature: Study area Dark Canyon (Non-landslide basins) Skunk Creek (Landslide prone basins) TR6 unnamed basin
19. Statistical signature of landslides - slope Gangodagamage, C. et al. (2009), statistical signature of deep-seated landslides, JGR in review
20. Landslide and their statistical signature
21. Statistical signature : slope-curvature
22. Statistical signature: slope-curvature 32
23. Conclusions so far … The landslide signature is recorded in the slope vs. directed distance and in the curvature vs. slope plots. Can identify whether a watershed has deep-seated landslides But how to map the exact location of these landslides?
24. Mapping landslides.. B1 B2 B3
25. Mapping landslides..
26. Mapping landslides.. 120< l <140 Gangodagamage, C. et al. (2009), Autocorrelation, Spatial (2008), Encyclopedia of geographic information science
27. Mapping landslides..
28. Can tell if landslides present in a watershed Can map location of landslides QU: Do landslides affect the spatial scaling in landscape attributes?
29. The topographic signature of landslides in higher order moments Q: Do landslide-disturbed landscapes show different statistical signature compared to undisturbed landscapes? Hypothesis: Landslides locally “smooth” the landscape and reduce its spatial heterogeneity. This is reflected in how the higher order statistics of topographic attributes (e.g., contributing area) scale with “directed distance from divide”.
30. Real networks: SF Eel – Contributing Area A( ) Scheidegger Straight flowpaths Elder fluvial RN Gaussian Elder hillslope hollows 41 Hillslope hollow flowpaths have more complex branching structure than fluvial network paths (greater spatial heterogeneity at small scales)
31. Skunk TR-6, Dark Canyon Landslides reduce the Spatial Heterogeneity in landscape Landslide disturbances reduces spatial heterogeneity in flowpath structure and shows up in higher order moments .
32. Interesting analogy Analogy: Healthy vs. unhealthy heart beat rates. Heartbeat fluctuations* of an unhealthy heart are found to exhibit less temporal heterogeneity, especially in extremes (i.e., in higher order statistical moments) 43 * Ivanov, P. Ch., Amaral, L. A. N., Goldberger, A. L., Havlin, S., Rosenblum, M. B., Struzik, Z. & Stanley, H. E. (1999) Multifractality in healthy heartbeat dynamics. Nature 399, 461-465.
33. Stress reduces the intensity and temporal heterogeneity of “bursts” in cardiac signals (heart beat) * Ivanov, P. Ch., Amaral, L. A. N., Goldberger, A. L., Havlin, S., Rosenblum, M. B., Struzik, Z. & Stanley, H. E. (1999) Multifractality in healthy heartbeat dynamics. Nature 399, 461-465.
34. Summary – part 1-2 “directed distance( )” allows to examine the detailed “statistical signature” of attributes in both unchannelized and channelized parts of the landscape. Three distinct regions emerge namely: hillslopes, valley network, and fluvial channelized area Landslides are shown to leave a distinct signature on landscape Hillslope-valley transition Periodic valleys Dynamic similarity Hierarchy of drainage basins

35. BARE EARTH DEM FROM SRTM DATA

    CG
36. Objective of the project Improve Digital Elevation Models (DEMs) from SRTM mission for hydrodynamic modeling and other applications. Obtain spatial and temporal structure of vegetation biomass. Obtain a high resolution bare-earth DEM (90m) for areas where the elevation data is not available.
37. Vegetation appears as uniformly distributed noise at some scales SRTM Data @ 30 m NED data @30 m
38. SRTM VEGETATION RESPONSE A Fundamental law of science applies to the SRTM data “ One scientist’s noise is another scientist’s signal”
39. Fourier Analysis Vege. Topo. = bare earth Topo.+ veg. ht Unknown, but at large scale bare-earth topo. Amplitude is approximately equals to the amplitude of the SRTM signal. Phase is unknown and will be resolved iteratively Unknown, but we have shown that phase of the veg. height can be obtained using SRTM signal. Amplitude can will be resolved iteratively Known from SRTM Signal We have two equations in the Fourier domain and two unknowns- can be resolved. Can be extended to the 2D
40. Fourier based approach Linearity of the Fourier transform is used. If: x1[n] + x2[n] = x3[n], then: ReX1[f] + ReX2[f] = ReX3[f] and ImX1[f] + ImX2[f] = ImX3[f].
41. Chandana Gangodagamage
42. Additively in Spectral Domain
43. Fourier Power spectrum : vegetation topography, bare-earth, and vegetation height high frequency region low frequency region Clear signature of vegetation surface Wave number –k (cycles/m)
44. Canopy topography phase VS Canopy height phase CANOPY HEIGHT PHASE CAN BE OBTAINED! AMPLITUDE CAN BE RESOLVED ITERATIVELY
45. Phase topography vs. canopy surface VEG HT PHASE OF THE BARE EARTH IS NOT CORRELATED WITH THAT OF IN THE SRTM SIGNAL. SOLVE ITERATIVELY BUT THE AMPLITUDE OF THE FOURIER TRANSFORM OF BARE EARTH CAN BE FOUND AT LARGE SCALE AND CAN BE SYNTHESIZED AT SMALL SCALES.
46. Results.. Results are obtained before solving the equation iteratively. Iterative solutions results a narrow Pro. Dis Function.
47. Conclusions: Vegetation topography leaves a clear statistical signature about the vegetation height and the bare-earth ( can be extracted using minimally used ancillary data.) A clear signature of the vegetation height data – two power law scaling regimes (i.e., low frequency and high frequency) with a scaling break at a intermediate characteristic frequency. The characteristic frequency depends on the vegetation density and the grid resolution vegetation mainly distort bare-earth power law scaling regime at the high frequency range If the objective is canopy model (hydrodynamic model) model resolution should be selected from low frequency (high frequency) range.
48. Can we improve our solution! Fourier approach can not localized spatially! Solution obtained from iterative optimization may not be always realistic. Can we integrate remotely sensed ground truth data to obtain realistic solutions We want to zoom down to vegetation patch scales and implement scale dependant interpolating approach to remove the vegetation effect/ obtain the vegetation height while preserving observed statistical properties of the bare earth
49. SCALE 1 SACLE 2 SCALE 3 SCALE 4 SCALE 5 Chandana Gangodagamage
50. You waited all this time! I thought I get enough time to play with you now !!!!!!!!!!!!!!!!! ? ChandanaG