Estimating forest parameters from top-of-atmosphere radiance data

Transcription

1 Estimating forest parameters from top-of-atmosphere radiance data V. Laurent*, W. Verhoef, J. Clevers, M. Schaepman *Contact: Guest lecture, RS course, 8 th Decembre, 2010

2 Contents Introduction Context Radiative transfer modeling Model inversion Reference data: from TOA to TOC level Comparison TOC vs TOA approaches 2 case studies Nadir case Extension to multi-angular data Methodology Simulations Local sensitivity analysis Parameter estimations Discussion Conclusion

3 Introduction

4 Context Forests are important for climate and carbon cycle parameters: LAI, Cab, fapar, Cv, Remote sensing is a great data source for monitoring forest parameters 2 approaches: Empirical: vegetation indices Physically based: radiative transfer (RT) models most general

5 Radiative transfer models Describes how the radiation interacts with the objects Physically-based models of: soil, leaf, canopy, atmosphere To estimate parameters, they need to be inverted Forest parameters Forward model Reflectance factor (%) Forest Wavelength (nm) Satellite data Model inversion

6 Inversion problem Ill posedness: Several parameter sets can give the same signature More unknowns than independent data Modeling and measurement errors 30 Regularization by: Prior information Spatial constraints Temporal constraints Model coupling Reflectance factor(%) 25 Cdm=0.01, fb=0.2, Cv= Cdm=0, fb=0.4, Cv= Wavelength(nm)

7 Reference data: Where does it come from? Radiance measured by the satellite, calibrated Correction from TOA radiance to TOC reflectance Atmospheric correction Atmosphere RT model INVERSION Look-up tables (LUT) Assume Lambertian surface Topography effect Adjacency effect Surface BRDF effect ALL THESE EFFECTS ARE INTER-RELATED!

8 Reference data vs model output Reference data HCRF ~ HDRF Compare for inversion Model output BRF Schaepman Strub, G., Schaepman, M.E., Painter, T.H., Dangel, S., & Martonchik, J.V. (2006). Reflectance quantities in optical remote sensing definitions and case studies. Remote Sensing of Environment, 103, BRF HDRF HCRF

9 TOC approach TOA approach TOA level Atmosphere LUT Lambertian surface Topography Adjacency BRDF Inversion Measured satellite radiance Atmosphere model Simulated radiance TOC level Corrected reflectance Simulated reflectance Surface BRDF Topography Adjacency Inversion Canopy Inversion Canopy model Soil level Parameter estimates Field measurements Parameter estimates

10 Benefits of the TOA approach Direct comparison with measured radiance Minimum data pre-processing Facilitate data assimilation and multi-sensor studies All surface-atmosphere effects can be included in the forward modeling More accurate Better estimations of albedo and fapar because the irradiance is available in the coupled model Better in rugged and heterogeneous scenes viewed from oblique angles

11 Nadir case study Objective: Compare the performance of the TOC and TOA approaches

12 Study area and data 3 stands of montane Norway spruce (Picea abies (L.) Karst.) CHRIS/PROBA acquisition: 12 Sept 2006 near nadir

13 Modeling set-up, TOC and TOA Top of atmosphere (TOA) MODTRAN Atmosphere Atmospheric correction 4SAIL2 Canopy Top of canopy (TOC) SLC PROSPECT Hapke Leaf Bark Soil

14 SLC demo

15 Canopy-atmosphere coupling TOA approach In the 4-stream approximation*: (no adjacency effect) Gssdorsd + Gsddordd Gsdoo + Gmultrsd L o = Lp0 + + rdo + G 1 r ρ 1 r ρ Where the gain factors can be calculated from MODTRAN outputs for 3 runs for Lambertian surface of albedo 0, 0.5, 100 (subscripts 0, 50, 100): PATH: total path radiance GSUN: sunlight ground-reflected radiance GTOT: total ground-reflected radiance dd dd dd dd ssoo r so L p 0 = PATH 0 G ssoo = GSUN 100 ρ dd = GTOT GTOT GTOT GTOT Gmult = ρ dd GSUN G G = ( 1 ρ ) GTOT GSUN sdoo dd 100 PATH100 PATH 0 sddo = G sdoo GTOT100 G ssdo PATH100 PATH = GTOT GSUN *Verhoef W. & Bach H. (2007). Coupled Soil Leaf Canopy and Atmosphere Radiative Transfer Modeling to Simulate Hyperspectral Multi Angular Surface Reflectance and Toa Radiance Data. Remote Sening of Environment. 109(2),

16 Atmospheric correction TOC approach Inverse problem Assuming Lambertian target (r t ) and background Ignoring adjacency effect Equation for atmospheric correction: r t = L G + ρ o dd L p0 ( L L 0 ) o Where: L p 0 = PATH0 p ( GTOT + PATH ) G = ( 1 ρdd ) PATH Use to compare to the TOC simulations of SLC

17 Cost function Irregular spectral coverage, bands are not equidistant Use weights: ( ) ( ) ( ) = = = i for 2 2, / n n n i i w n w w λ λ λ λ λ λ = = = n i i n i i i i i w c c r w χ Cost function r: Simulation (r so or L o ) c: CHRIS data proba.org.uk/images/chlorophyll2.gif

18 Bark Good match Simulation too high in the blue: missing pigments in PROSPECT

19 Needle Simulations are a bit high in the NIR Measured reflectances were very low

20 TOC and TOA TOC TOA Overall: good fit Slight tendency to over estimation χ values smaller at TOA due to path radiance

21 Local sensitivity analysis

22 LSA Parameter influences Jacobian matrix J r p = M r p ( λ ) r( λ ) 1 p M ( λ ) r( λ ) 1 1 n L O L p m m 1 n With: r = r so r so L r = L o ( init) o ( init) at TOC at TOA J = [ ] j i, k With: j j ( rso ( i) rso ( init) ( i) )/ rso ( init) ( i), k = at TOC p p ( init) i i, k = k ( Lo ( i) Lo ( init) ( i) )/ Lo ( init) p p ( init) k k k ( i) at TOA Parameter influence α k n w i i= 1 = n i= 1 ( j ) w i, k i 2

23 Parameter influences Influent: Cv fb needlecab needlecdm needlen Non-influent: PAI Bark Atmosphere Ignore: LIDF hot

24 LSA: Singular value decomposition Jacobian matrix r = J p transformed model output difference U t r Singular value decomposition (SVD) = SV t One-to-one relationship p J = USV Where S diagonal U, V orthonormal transformed input parameter variation t T T U U = UU = I T T V V = VV = I Rank of the estimation problem = rank of S *Verhoef W. (2007). A Bayesian Optimisation Approach for Model Inversion of Hyperspectral Multidirectional Observations: The Balance with a Priori Information. In Proc. '10th ISPMSRS' (Eds. M. Schaepman, S. Liang, N. Groot & M. Kneubühler), Intl. Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences.

25 Singular values Rank = 3

26 LSA: conclusions for parameter estimation Rank = 3 theoretical max of 3 parameters 5 influent parameters: Cv, fb, needlecab, needlecdm, needlen LUT: 4 variables: Cv, fb, needlecab, needlecdm

27 Parameter estimation

28 Parameter estimation Results are fair χ values are smaller at TOA fb estimates are better at TOA Cv and needlecab are better at TOA for only 1 stand NeedleCab and needlecdm reached the upper bound

29 Discussion

30 Discussion Good simulations were obtained at TOC and TOA levels Parameter estimation can be done from TOA radiance measurements, as good as from TOC fb was found influent in other studies (e.g. Verrelst et al) Atmosphere parameters are not very influential no obstacle to estimating forest parameters 4 parameters estimated although rank was 3 PAI/LAI is not an influential parameter for dense stands χ values were smaller at TOA because of the path radiance More stands, other land cover types

31 Conclusion

32 Conclusions Nadir case SLC provided good simulations of the stands, despite its simplicity LAI is not influential for dense forest stands cannot be estimated Jacobian matrix and SVD are very useful for local sensitivity analysis TOA approach is as good as TOC approach for estimating forest parameters

33 Multi-angular case study Objective: Investigate the potential of multi-angular data at TOA level

34 Directional effects Forest hotspot effect Sunglint effect on water surface Bright in the sun direction Dark away from the sun modis.bu.edu/brdf/images/brdfspruce.jpg

35 CHRIS multi-angular data 0 m p p nadir 90 m m Sun nadir p36 p55

36 Introduction Multi-angular data has more potential than monoangular data for estimating surface parameters Especially if the surface has strong directional properties Does this also holds at TOA level???

37 Methodology Same methods as nadir case: SLC-MODTRAN simulation Jacobian matrix SVD LUT inversion Except: extension of cost function and Jacobian matrix to multi-angular data χ = n b o Θ i= 1 w i o Θ i= 1 ( L ( λ )) n o w i i 2

38 Simulations - YOUNG Spectral signatures Angular signatures Overall: good match Good results considering the simplicity of SLC

39 LSA: Parameter importances - YOUNG Most important: fb, Cv, Cab, Cdm, Zeta, D, Cs Least important: bark, atmosphere Ignore LIDF and hot

40 Dimensionality 3 Dimensionality increases with number of images 6

41 Parameter estimation: 4-parameter LUT 4-angle combination: not the best results Max 2 best estimates together Some combinations might be better for some parameters

42 Parameter estimation: 7-parameter LUT 4-angle combination has the max number of best estimates Best estimates obtained with at least 2 angles

43 Conclusion SLC-MODTRAN provided good simulations Multi-angular data has more potential than monoangular data (increase in dimensionality), also at TOA level However, multi-angular data did not give better estimates Single solutions because of large sampling steps used

44 Further research TOA radiance image simulation Estimate atmospheric parameter using the whole image Then estimate canopy parameters per pixel Multi-sensor or multi-temporal study based on image simulation

45 Take home message The TOA approach has many advantages and is very promising!

46 Thank you! Questions? Contact: Acknowledgements: ESA/PECS project No , Institute of Systems Biology and Ecology (CZ), Petr Lukeš, Lucie Homolová, Allard de Wit (WUR) Wageningen UR