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BARE EARTH DEM FROM SRTM DATA CG Slide 2 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. Slide 3 LiDAR 1m vegetation appears as point clouds Slide 4 Sensor dependence and data smoothing: LiDAR at 30 m Slide 5 Sensor dependence: Vegetation appears as uniformly distributed noise at some scales at SRTM 30 m SRTM Data @ 30 m NED data @30 m Slide 6 SRTM VEGETATION RESPONSE A Fundamental law of science applies to the SRTM data One scientists noise is another scientists signal Slide 7 Fourier Analysis Vege. Topo. = bare earth Topo.+ veg. ht Known from SRTM Signal 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 We have two equations in the Fourier domain and two unknowns- can be resolved. Can be extended to the 2D Slide 8 frequency domain Spatial domain Real part Imaginary part Slide 9 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]. Slide 10 Additively in Spectral Domain: proposed model Fourier AmplitudeFourier Phase Slide 11 model. For bare-earth Slide 12 Study Area: SF Eel River Slide 13 Fourier Power spectrum : vegetation topography, bare-earth, and vegetation height- SF Eel LiDAR data Slide 14 Study area 2 Slide 15 Study area 3: Tenderfoot Creek Vegetation fractional cover ~ 90 Vertical profiles Slide 16 Tendorfoot Creek: Slide 17 Vegetation effect on SRTM: Slide 18 SRTM and ASTER Slide 19 A Simple approach: Low frequency content of the vegetation topography is coming from bare-earth topography High frequency content of the vegetation topography is coming from the vegetation height. Two regions are separated by a scale break at frequency f c Slide 20 Approach. High frequency content~ vegetation height low frequency content~ bare- earth topo. Slide 21 Model parameters-Amplitudes of the bare-earth and vegetation topography: LiDAR data at low frequencies Slide 22 Model parameters-phase of the bare-earth and vegetation topography: at low frequencies Slide 23 Canopy topography phase VS Canopy height phase CANOPY HEIGHT PHASE CAN BE OBTAINED! AMPLITUDE CAN BE RESOLVED ITERATIVELY Slide 24 For bare-earth = and = The low frequency content is obtained using model eqn. The high frequency information of the bare-earth is obtained by Fourier interpolations Back to the model equations.. Slide 25 model. For vegetation height = and = High frequency contact is obtained from the model eqn. The low frequency information of the bare-earth is obtained by Fourier interpolations Slide 26 Results.. Slide 27 Model vegetation height Slide 28 Slide 29 Vegetation height: model vs. LiDAR Slide 30 Results: A comparison of Model topo. and LiDAR bare-earth: It preserves the second order moments Slide 31 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 the canopy model (hydrodynamic model) model resolution should be selected from low frequency (high frequency) range. Slide 32 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 Slide 33 Slide 34 Chandana Gangodagamage SCALE 1 SACLE 2 SCALE 3 SCALE 4 SCALE 5 Slide 35 FUSION OF DIFFERENT SENSOR DATA ASTER and SRTM Slide 36 Slide 37 Comparison of ASTER-SRTM-LiDAR data elevation Slide 38 Slide 39 Tf Tg Tv Af Ag Av eq1= 'Af/(1+(tan(Tf))^2)=Ag/(1+(tan(Tg))^2)+Av/(1+(tan(Tv))^2)' eq2= 'Af/(1+(tan(Tf))^2)*tan(Tf)=Ag/(1+(tan(Tg))^2)*tan(Tg)+Av/(1+(tan(Tv))^2)*tan(Tv)' [Tg Av]=solve(eq1 eq2,Tg,Av) [Tg Av]=solve(eq1, eq2,Tg, Av) Tg = (tan(Tf)+tan(Tf)*tan(Tv)^2-1/2/(- Af*tan(Tv)+Af*tan(Tf))*(Ag+Ag*tan(Tf)^2+(Ag^2+2*Ag^2*tan(Tf)^2+Ag^2*tan(Tf)^4+4*Af*tan(Tv)^2*Ag*tan(Tf)^2- 4*Af^2*tan(Tv)^2+4*Af*tan(Tv)^2*Ag+8*Af^2*tan(Tv)*tan(Tf)-4*Af*tan(Tf)^3*Ag*tan(Tv)- 4*Af*tan(Tf)*Ag*tan(Tv)-4*Af^2*tan(Tf)^2)^(1/2))-1/2/(- Af*tan(Tv)+Af*tan(Tf))*(Ag+Ag*tan(Tf)^2+(Ag^2+2*Ag^2*tan(Tf)^2+Ag^2*tan(Tf)^4+4*Af*tan(Tv)^2*Ag*tan(Tf)^2- 4*Af^2*tan(Tv)^2+4*Af*tan(Tv)^2*Ag+8*Af^2*tan(Tv)*tan(Tf)-4*Af*tan(Tf)^3*Ag*tan(Tv)- 4*Af*tan(Tf)*Ag*tan(Tv)-4*Af^2*tan(Tf)^2)^(1/2))*tan(Tv)^2)*Af/(-1/2/(- Af*tan(Tv)+Af*tan(Tf))*(Ag+Ag*tan(Tf)^2+(Ag^2+2*Ag^2*tan(Tf)^2+Ag^2*tan(Tf)^4+4*Af*tan(Tv)^2*Ag*tan(Tf)^2- 4*Af^2*tan(Tv)^2+4*Af*tan(Tv)^2*Ag+8*Af^2*tan(Tv)*tan(Tf)-4*Af*tan(Tf)^3*Ag*tan(Tv)- 4*Af*tan(Tf)*Ag*tan(Tv)-4*Af^2*tan(Tf)^2)^(1/2))-1/2/(- Af*tan(Tv)+Af*tan(Tf))*(Ag+Ag*tan(Tf)^2+(Ag^2+2*Ag^2*tan(Tf)^2+Ag^2*tan(Tf)^4+4*Af*tan(Tv)^2*Ag*tan(Tf)^2- 4*Af^2*tan(Tv)^2+4*Af*tan(Tv)^2*Ag+8*Af^2*tan(Tv)*tan(Tf)-4*Af*tan(Tf)^3*Ag*tan(Tv)- 4*Af*tan(Tf)*Ag*tan(Tv)-4*Af^2*tan(Tf)^2)^(1/2))*tan(Tf)^2+tan(Tv)*tan(Tf)^2+tan(Tv)) (tan(Tf)+tan(Tf)*tan(Tv)^2-1/2/(-Af*tan(Tv)+Af*tan(Tf))*(Ag+Ag*tan(Tf)^2- (Ag^2+2*Ag^2*tan(Tf)^2+Ag^2*tan(Tf)^4+4*Af*tan(Tv)^2*Ag*tan(Tf)^2- 4*Af^2*tan(Tv)^2+4*Af*tan(Tv)^2*Ag+8*Af^2*tan(Tv)*tan(Tf)-4*Af*tan(Tf)^3*Ag*tan(Tv)- 4*Af*tan(Tf)*Ag*tan(Tv)-4*Af^2*tan(Tf)^2)^(1/2))-1/2/(-Af*tan(Tv)+Af*tan(Tf))*(Ag+Ag*tan(Tf)^2- (Ag^2+2*Ag^2*tan(Tf)^2+Ag^2*tan(Tf)^4+4*Af*tan(Tv)^2*Ag*tan(Tf)^2- 4*Af^2*tan(Tv)^2+4*Af*tan(Tv)^2*Ag+8*Af^2*tan(Tv)*tan(Tf)-4*Af*tan(Tf)^3*Ag*tan(Tv)- 4*Af*tan(Tf)*Ag*tan(Tv)-4*Af^2*tan(Tf)^2)^(1/2))*tan(Tv)^2)*Af/(-1/2/(- Af*tan(Tv)+Af*tan(Tf))*(Ag+Ag*tan(Tf)^2-(Ag^2+2*Ag^2*tan(Tf)^2+Ag^2*tan(Tf)^4+4*Af*tan(Tv)^2*Ag*tan(Tf)^2- 4*Af^2*tan(Tv)^2+4*Af*tan(Tv)^2*Ag+8*Af^2*tan(Tv)*tan(Tf)-4*Af*tan(Tf)^3*Ag*tan(Tv)- 4*Af*tan(Tf)*Ag*tan(Tv)-4*Af^2*tan(Tf)^2)^(1/2))-1/2/(-Af*tan(Tv)+Af*tan(Tf))*(Ag+Ag*tan(Tf)^2- (Ag^2+2*Ag^2*tan(Tf)^2+Ag^2*tan(Tf)^4+4*Af*tan(Tv)^2*Ag*tan(Tf)^2- 4*Af^2*tan(Tv)^2+4*Af*tan(Tv)^2*Ag+8*Af^2*tan(Tv)*tan(Tf)-4*Af*tan(Tf)^3*Ag*tan(Tv)- 4*Af*tan(Tf)*Ag*tan(Tv)-4*Af^2*tan(Tf)^2)^(1/2))*tan(Tf)^2+tan(Tv)*tan(Tf)^2+tan(Tv)) Slide 40 Av = atan(1/2/(- Af*tan(Tv)+Af*tan(Tf))*(Ag+Ag*tan(Tf)^2+(Ag^2+2*Ag^2*tan(Tf)^2+A g^2*tan(Tf)^4+4*Af*tan(Tv)^2*Ag*tan(Tf)^2- 4*Af^2*tan(Tv)^2+4*Af*tan(Tv)^2*Ag+8*Af^2*tan(Tv)*tan(Tf)- 4*Af*tan(Tf)^3*Ag*tan(Tv)-4*Af*tan(Tf)*Ag*tan(Tv)- 4*Af^2*tan(Tf)^2)^(1/2))) atan(1/2/(-Af*tan(Tv)+Af*tan(Tf))*(Ag+Ag*tan(Tf)^2- (Ag^2+2*Ag^2*tan(Tf)^2+Ag^2*tan(Tf)^4+4*Af*tan(Tv)^2*Ag*tan(Tf)^ 2-4*Af^2*tan(Tv)^2+4*Af*tan(Tv)^2*Ag+8*Af^2*tan(Tv)*tan(Tf)- 4*Af*tan(Tf)^3*Ag*tan(Tv)-4*Af*tan(Tf)*Ag*tan(Tv)- 4*Af^2*tan(Tf)^2)^( 1/2))) Slide 41 Chandana G You waited all this time! I thought I get enough time to play with you now !!!!!!!!!!!!!!!!! ? Slide 42 Phase topography vs. canopy surface 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. VEG HT Slide 43 Results.. Results are obtained before solving the equation iteratively. Iterative solutions results a narrow Pro. Dis Function.