# Progress in Remote Sensing of Photosynthetic Activity over the Amazon Basin
## 4 Case Study of Seasonal Variation in Light-Use Efficiency and SIF across the Amazon Basin  
### Data Retrieval  
#### 4.1.1 Photochemical Reflectance Index  
Satellite retrieval of PRI depends on Aerosol Optical Thickness (AOT), Surface Reflectance (SR) and bi-directional reflectance. Aerosols artificially enhance backscattering over vegetated (dark) surfaces and attenuate the surface directional reflectance depending on the path length. Conventional, pixel-based algorithms designed to correct for varying atmospheric properties produce a single measurement over both vegetated and non-vegetated landscapes with unknown AOT and SR; consequently, the surface reflectance is difficult to calculate without knowledge of the land cover. The standard MODIS surface reflectance algorithm (MOD09) [29] uses a version of the dark target aerosol retrieval algorithm [30; 31], relating surface reflectance in the visible (blue and red) spectral bands with MODIS Band 7 (2.1 \(\upmu\)m) reflectance with a prescribed Spectral Regression Coefficient (SRC). A Lambertian surface model is then used for aerosol retrievals and atmospheric correction. Although it simplifies processing, the Lambertian assumption reduces the anisotropy of derived surface reflectance introducing errors dependent on view geometry (e.g., [32; 33]). The use of a Lambertian assumption is likely to reduce the accuracy in the PRI detection band, as the dependency of this band on shadow fractions is stronger than that of the reference band [19]. The MAIAC algorithm, in contrast, is based on a rigorous radiative transfer model [34; 35] fully coupled with the Li-Sparse Ross-Thick (LSRT) model of surface BRDF [36]. It simultaneously retrieves AOT, SRC and surface BRDF using three to 16 days of calibrated and geo-located Level 1B (L1B) MODIS data, gridded to a resolution of 1 km. These multi-day acquisitions provide the basis toderive spectral reflectance coefficients in the blue (0.466 \(\upmu\)m) and shortwave IR (2.13 \(\upmu\)m) required for aerosol corrections [37] and to characterize the distribution of the surface Bi-Directional Reflectance Distribution Function (BRDF) for all of the MODIS reflective bands [38]. Based on time-series analysis, MAIAC has demonstrated the ability to distinguish stable surface features from those associated with random variation and changing fields of clouds [39]. For this project, we used MODIS Collection 6 Level 1B (calibrated and geometrically corrected) data, which removed the effects of major errors in sensor calibration present in earlier collections. Detailed descriptions of MAIAC and quality testing are provided elsewhere [37; 38; 40; 41]. MAIAC observations were used to obtain cloud-free, multi-angle surface reflectance in MODIS Bands 11 and 12 (526 to 536 nm and 546 to 536 nm, respectively) from the Terra and Aqua platforms to derive PRI across the Amazon Basin. The underlying assumption in this application of multi-angle MODIS data is that the xanthophyll status of the vegetation remains the same between Terra and Aqua overpasses. This assumption is reasonable considering that the equatorial location of the Amazon limits the time between overpasses to approximately 3 h.  
We modified the spectral definition of PRI (in Equation (1)) by substituting MODIS Band 12, centered at 551 nm rather than 570 nm, because MODIS lacks the latter band [42; 43]. Thus, to calculate the Photochemical Reflectance Index:  
\[\text{PRI}=(\rho_{11}-\rho_{12})/(\rho_{11}+\rho_{12}), \tag{3}\]  
where \(\rho_{11}\) and \(\rho_{12}\) are the reflectance at MODIS Bands 11 and 12, respectively. For our analysis, we focused on the MAIAC monthly composite of MODIS Terra and Aqua observations at different viewing geometries for the years 2000 to 2012. The general location of the study area and type of data analyzed are presented in Figure 3.  
Variation in the viewing geometry changes the fraction of sunlit and shaded canopy.