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Published on January 17, 2008

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Application of Stochastic Radiative Transfer to Remote Sensing of Vegetation:  Application of Stochastic Radiative Transfer to Remote Sensing of Vegetation Dissertation Committee Ranga B. Myneni Yuri Knyazikhin Alan H. Strahler Crystal B. Schaaf Alexander L. Marshak Ph.D. Dissertation Defense by Nikolay V. Shabanov Research Objectives:  Research Objectives To develop stochastic radiative transfer theory for modeling the radiation regime of heterogeneous vegetation canopies. To apply this theory for interpretation of satellite data: Validate the radiative transfer principles of the MODIS LAI/FPAR algorithm. Document and explain the observed variations in AVHRR NDVI and channel reflectances time series data in terms of RT theory. To support additional research (not discussed here).... Research Objectives (Contd.):  Research Objectives (Contd.) Kaufmann, R.K., Zhou, L., Knyazikhin, Y., Shabanov, N.V., Myneni, R.B., and Tucker, C.J. (2000), Effect of orbital drift and sensor changes on the time series of AVHRR vegetation index data. IEEE Trans. Geosci. Remote Sens., 38(6): 2,584-2,597. Zhang, Y., Shabanov, N.V., Knyazikhin, Y., Myneni, R.B., Assessing the information content of multiangle satellite data for mapping biomes. II: Theory, Remote Sens., accepted for publication. Zhou, L., Tucker, C.J., Kaufmann, R.K., Slayback, D., Shabanov, N.V., and Myneni, R.B. (2001). Variations in northern vegetation activity inferred from satellite data of vegetation index during 1981 to 1999, J. Geophys. Res., 106(D17): 20,069-20,083. Tian, Y., Woodcock, C.E., Wang, Y., Privette, J.L., Shabanov, N.V., Zhou, L., Buermann, W., Dong, J., Veikkanen, B., Hame, T., Ozdogan, M., Knyazikhin, Y., Myneni, R.B., Multiscale analysis and validation of the MODIS LAI product over Maun, Botswana, Remote Sens. Environ., submitted for publication. Contents:  Contents Part 1: Development of a stochastic radiative transfer model Part 2: Validation of the radiative transfer principles of the MODIS LAI/FPAR algorithm with data from Harvard Forest Part 3: Radiative transfer based analysis of global AVHRR NDVI and channel reflectances time series data Part 4: Summary of the main results Part 5: Future directions Part 1: Development of a Stochastic RT Model:  Part 1: Development of a Stochastic RT Model Classical radiative transfer (RT) theory is a physically based tool for study of the radiation transfer in vegetation canopies and to retrieve biophysical information about the vegetation. However, the major limitation of this approach is that it is applicable to homogeneous canopies (grasses, crops), and not to natural vegetation which exhibits spatial heterogeneity. Part 1: Objectives:  To develop a stochastic radiative transfer approach for modeling the radiation regime of natural vegetation which exhibits spatial heterogeneity. To construct a model with flexible parameterization for analysis of satellite data. To quantify, both numerically and analytically, the influence of gaps on the energy fluxes in vegetation canopies. Part 1: Objectives Basic Concepts of Stochastic RT Theory:  Basic Concepts of Stochastic RT Theory Mean radiance over the vegetation: Mean radiance over the whole space: Horizontal density of vegetation: Correlation of vegetation at two levels: Stochastic vs. Classical RT:  Stochastic vs. Classical RT The stochastic RT theory is a more general form of the classical formulation for describing the radiation regime of heterogeneous vegetation canopies. Stochastic equations collapse to classical 1-D equations when This allows flexibility in the use of the model depending on the availability of parameters. Validation of the Stochastic RT Model:  Validation of the Stochastic RT Model Sources of Validation: Similar RT models ( 1-D and 3-D) Ray-traced model of a maize canopy (featuring 3-D dynamic architecture of maize) Data from the Jornada PROVE field campaign (CIMEL sunphotometer data) Validated: Dependence of reflectance, absorptance, transmittance on LAI, Solar Zenith Angle (SZA); directional reflectance in the principal plane. Validation of the Stochastic RT Model (Contd.):  Validation of the Stochastic RT Model (Contd.) Example: Comparison of hemispherical reflectance for direct radiation (DHR) simulated by the stochastic RT model and the ray-traced model of maize canopy for “dry” and “wet” soil cases. Fifty values of DHR were compared in the case of “dry” soil and thirty values for “wet” soil. Effect of Gaps on the Energy Balance in Vegetation:  Effect of Gaps on the Energy Balance in Vegetation Numerical Analysis: The influence of gaps on the energy fluxes as a function of LAI was evaluated. The calculations were performed for three types of horizontal density of vegetation: (i) p=1.0; (ii) p=0.75; (iii) p=0.5. Analytical Results: A new formula for absorptance was derived which extends the formulation for a homogeneous medium: Part 1: Conclusions:  Part 1: Conclusions The tool for satellite data analysis, “Stochastic RT”, was implemented and tested. Key features of the model include statistical moments of parameters characterizing discontinuities in a vegetation canopy, and the parameterization of the effect of soil reflectance. Influence of gaps on the energy fluxes was quantified both analytically and numerically. Reference: Shabanov et al., (2000), Stochastic modeling of radiation regime in discontinuous vegetation canopies. Remote Sens. Environ., 74: 125-144. Slide13:  Part 2: Validation of the Radiative Transfer Principles of the MODIS LAI/FPAR Algorithm with Data from Harvard Forest A synergistic radiative transfer based MODIS LAI/FPAR algorithm was developed and prototyped with available AVHRR, Landsat TM and SeaWiFS data. Currently, MODIS is in orbit and LAI/FPAR data are operationally being produced since June 2000. Validation of the product and the theoretical assumptions with field data is needed. Slide14:  To further develop the theoretical assumptions of the algorithm: Improve the theoretical description of uncollided radiation in a heterogeneous forest based on stochastic theory. Assess the spectral invariance of certain entries of the Look-up Tables of the algorithm. To validate the MODIS LAI and FPAR products: Utilize multi-resolution data sources (field data and ETM+). Assess product uncertainties and the causes specific to a broadleaf forest. Part 2: Objectives Sampling Strategy:  Sampling Strategy Site: Harvard Forest, MA. Two Field Data Sources: 225x225 m grid site of the BU Climate and Vegetation Research Group (data utilized in the validation of the theoretical basis of the algorithm). July 21-25, 2000. 5x5 km area of the BigFoot nested sampling of LAI & FPAR (data utilized in the validation of the output of the algorithm). June 18 and August 4, 2000. Data:  Data Field Measurements: ASD-spectroradiometer (canopy spectral transmittance). LAI-2000 plant canopy analyzer (LAI, directional gap fractions). LI-1800 Spectroradiometer (leaf spectral properties). Accupar ceptometers (incident PAR). Satellite Imagery: Tiles of ETM+ surface reflectances (resolution 30 m), and MOD15 A2 product (resolution 1 km). Features of the MODIS LAI/FPAR Algorithm:  Features of the MODIS LAI/FPAR Algorithm The algorithm is radiative transfer based and model independent. The solution is dependent on the vegetation type (6 biome types). The retrievals are based on multiple bands (current version uses red and near-infrared bands only). The algorithm is optimized for searching solutions using Look-up Tables. The product consists of 8-day maximum FPAR composites of global LAI/FPAR fields (available since June 2000). Study of the Theoretical Assumptions of the Algorithm:  Definitions: The radiation arriving at the bottom of a vegetation canopy, t, is the sum of the uncollided and collided components. The uncollided radiation (q_t-parameter), is radiation arriving at the bottom of the vegetation without suffering any collision. The collided radiation is the radiation which experienced at least one collision (t - q_t). Study of the Theoretical Assumptions of the Algorithm Slide19:  Spectral invariant p_t (p_t-parameter) and the leaf albedo, w, define the portion of collided radiation (t-q_t) in total transmitted radiation, The MODIS LAI/FPAR algorithm utilizes special properties of p_t and q_t- parameters, i.e. their spectral invariance (wavelength independence). This section is devoted to the study of the p_t-parameter; the q_t-parameter. Study of the Theoretical Assumptions of the Algorithm (Contd.) Estimation of the p_t-parameter:  Estimation of the p_t-parameter The retrieval of p_t and its dependence on LAI. A comparison was made with entries stored in the LUTs of the algorithm. The retrieved p_t is approaching p_t for the case of diffuse radiation in the LUTs. Slide21:  Estimation of the p-parameter (Contd.) How to decrease the noise associated with retrievals of p_t? Take one wavelength at RED and another at NIR. Take both wavelengths where the spectra change significantly. Modeling the q_t-parameter:  Modeling the q_t-parameter or with LAI-2000 gap fraction data, Stochastic equations were used to provide a better agreement with the experiment. The q_t-parameter can be estimated from ASD and LI-1800 measurements, Validation of the MODIS LAI Retrievals:  Validation of the MODIS LAI Retrievals LAI: MODIS data ETM+ data Quality Flag: Validation of the MODIS FPAR Retrievals:  Validation of the MODIS FPAR Retrievals Quality Flag: FPAR: MODIS data ETM+ data Histograms of LAI and FPAR for Field, MODIS and ETM+ Data Sources:  Histograms of LAI and FPAR for Field, MODIS and ETM+ Data Sources The figure to the right shows LAI histograms. The disagreement between the field and the MODIS retrievals equals 11% (product specification allows 20%). The figure to the left shows FPAR histograms. The disagreement between the field and the MODIS retrievals equals 4.5% (product specification allows 10%). Part 2: Conclusions:  Part 2: Conclusions Stochastic RT theory facilitates accurate parameterization of uncollided radiation at Harvard Forest. An empirical method to improve uncertainties in the estimation of the p_t-parameter is proposed. The LAI and FPAR fields from MODIS agree within an allowable level of uncertainties with the corresponding field estimates. The major source of uncertainties is the low sensitivity of surface reflectances to LAI in dense forests. Reference: Shabanov et al., Validation of the radiative transfer principles of the MODIS LAI/FPAR algorithm with data from Harvard Forest. Remote Sens. Environ., submitted for publication. Part 3: Radiative Transfer Based Analysis of Global AVHRR Time Series Data:  Part 3: Radiative Transfer Based Analysis of Global AVHRR Time Series Data An increase in northern high latitude vegetation activity (extension of the growing season) was reported by Myneni et al. (1998). Regression statistics with NDVI time series were used in this analysis. What structural changes in the vegetation or understory caused this trend? Channel reflectance data and RT theory can provide insight into the problem. Slide28:  To document the variation in the Pathfinder AVHRR Land (PAL) Red and Near-Infrared channel reflectances during the 1982-1991 time period responsible for the observed NDVI trend. To explain the interannual variation in NDVI and channel reflectances in terms of RT theory. Part 3: Objectives Selection of the Study Area:  Selection of the Study Area The red pixels indicate the mask for the PAL data analysis. In these regions, spring period (March to May) NDVI>0.1 and increased by at least 25% between 1982 and 1991, and the correlation between spring time NDVI and temperature was at least 0.5. Two biomes were studied separately: cool grasses and needle forests. Data Sources: PAL NDVI and channel data. BU PAL corrected NDVI. NASA GISS temperature data. 6-Biome classification map. Northern Latitude Greening Trends:  Northern Latitude Greening Trends Our analysis shows that during the years 1981 through 1994 for the Northern high latitudes NDVI averaged over boreal growing season months of May to September increased by about 10%, the timing of spring green-up advanced by about 6 days. Observed Interannual Variations in Spectral Space:  Observed Interannual Variations in Spectral Space Grasses Needle forests Consider a vector of interannual variations, defined separately for March, April or May as Grasses have two signatures: (1) increase of near-infrared; (2) decrease in red and near-infrared. Needle forests have only one signature: decrease in red and near-infrared. These variations can be explained by RT theory considering trajectories in the spectral space. The channel data are generated by regression. The distribution of this variation is biome dependent. Comparison of Interannual and Seasonal Variation of PAL Channel Data:  Comparison of Interannual and Seasonal Variation of PAL Channel Data Vector fields of the interannual (1982-1991) and seasonal (March to May of 1982 and 1989) changes in the spectral space were compared separately for two biomes: Panels to the left present the interannual (top) and the seasonal (bottom) variations for grasses. Panels to the right present similar results, but for needle forests Grasses Needle forests Trajectories in the Spectral Space:  Trajectories in the Spectral Space Stochastic model was used to construct the vegetation reflectance at nadir in the red and near-infrared spectral space. Soil isoline: background reflectance constant + LAI changing. LAI isolines: LAI is constant + background reflectance changing. Soil line: LAI=0 + background reflectance changing Convergence point: LAI=infinity. Can Variations in NDVI be Attributed to Background Reflectance Variations?:  Can Variations in NDVI be Attributed to Background Reflectance Variations? The sensitivity of NDVI to background reflectance variations is The unknown sensitivity of the channel reflectance to variations in the background reflectance can be obtained from conventional RT soil parameterization, Sensitivity of NDVI to Background Reflectance Variations (Contd.):  Sensitivity of NDVI to Background Reflectance Variations (Contd.) The general rule of sensitivity of NDVI to background reflectance variations is: Example: If T (red)>0.7, a background reflectance decrease of < 40% will explain the observed NDVI change. Reflectance change could be due to replacement of snow by soil or vegetation. Part 3: Conclusions:  Part 3: Conclusions Empirical analysis of PAL data over the northern high latitudes indicates that the interannual changes in the spectral space are similar to the seasonal changes in the spring time period when the green leaf area increases. This presents an empirical argument in support of the interannual greening trend. The theoretical arguments in support of this hypothesis are constructed by modeling the trajectories of vegetation dynamics in the spectral space and by a RT based analysis of the sensitivity of NDVI to background reflectance variation. Reference: Shabanov et al., (2001), Analysis of Interannual Changes in Northern Vegetation Activity Observed in AVHRR Data during 1981 to 1994. IEEE Trans. Geosci. Remote Sens., accepted for publication. Part 4: Summary of the Main Results:  Part 4: Summary of the Main Results A stochastic approach to radiative transfer was introduced to parameterize the effect of spatial heterogeneity on the energy fluxes in natural vegetation. The new model enhances the ability of the RT approach for analysis of satellite imagery. The theoretical basis of the MODIS LAI/FPAR algorithm was extended using a stochastic parameterization of the uncollided radiation. The uncertainties in the MODIS LAI and FPAR retrievals were evaluated with field data from Harvard Forest. The interannual and seasonal variations in PAL NDVI and channel data were explained using temporal trajectories in the spectral space according to the RT theory. Part 5: Future Directions:  Part 5: Future Directions This research demonstrated the utility of stochastic radiative transfer for remote sensing of natural vegetation. However… Only the influence of the first moment of the spatial heterogeneity (horizontal density of the vegetation) on the radiation field was studied. Detailed analysis of the influence of correlation of vegetation elements on the radiation field is needed. Improved quality of data from TERRA instruments (especially MODIS and MISR) together with field measurements of vegetation structural characteristics will facilitate an accurate assessment of global vegetation dynamics in the future.

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