An Iterative BRDF/NDVI Inversion Algorithm Based on A Posteriori Variance Estimation of Observation Errors

Current bidirectional reflectance distribution function (BRDF) inversions using ordinary least squares (OLS) criterion can be easily contaminated by observations with residual cloud and undetected high aerosols, which leads to abrupt fluctuations in the normalized difference vegetation index (NDVI) time series. The OLS criterion assumes the noise has Gaussian distribution, which is often violated due to positive noise biases caused by clouds and high aerosols. A changing-weight iterative BRDF/NDVI inversion algorithm (CWI) based on
a posteriori
variance estimation of observation errors is presented to explicitly consider the asymmetrically distributed noise and observations with unequal accuracy in the BRDF retrieval. CWI employs
a posteriori
variance estimation and an NDVI-based indicator to iteratively adjust the weight of each observation according to its noise level. The validation results suggest CWI performs better than the Li–Gao and OLS approaches. The rmse was reduced from 0.074 to 0.028, and the relative error decreased from 13.4% to 3.8% at the U.S. Department of Agriculture Beltsville Agricultural Research Center site. Similarly, at the Harvard Forest site, the rmse was reduced from 0.086 to 0.031, and the relative error decreased from 9.5% to 2.7%. The average noise and relative noise of the CWI NDVI time series over ten EOS Land Validation Core Sites from 2003–2009 was smaller (0.028, 3.7%) than those of MOD13A2 (0.041, 5.2%), MYD13A2 (0.039, 4.9%) and MCD43B4 (0.030, 4.4%). The results demonstrate the robustness of the CWI approach in suppressing the influence of contaminated observations in BRDF retrievals by producing results that are less affected by undetected clouds and high aerosols.