Bias-variance trade-off in radiative transfer model inversion drives uncertainty in leaf area index estimation

Large-scale leaf area index (LAI) retrieval from satellite observations primarily relies on inverting canopy radiative transfer models (RTMs). Despite the widespread use of various inversion methods, how and why LAI retrievals vary with the method choice remains unclear. Here, within a unified Bayesian framework, we primarily characterized four representative methods as statistical point estimators: (i) numerical optimization (OPT) method; (ii) look-up table (LUT) method; (iii) LUT method with solution averaging (LUT-mean); and (iv) neural network (NN)-based method. Differences in their statistical principles lead to distinct bias-variance trade-offs, causing LAI retrieval RMSEs to vary by 30%–35% across simulated and in situ datasets. Our findings are: (1) The OPT and LUT methods approximate the maximum a posteriori estimator, exhibiting low bias but high variance and producing funnel-shaped scatter between retrieved and reference LAIs. (2) The LUT-mean and NN-based methods reduce variance by introducing bias, leading to overestimation in the mid-LAI range and underestimation in the high-LAI range, thereby producing S-shaped scatter. These characteristics enable the LUT-mean and NN-based methods to achieve lower RMSEs, with the NN-based method approximating the posterior mean estimator and attaining the lowest RMSE. Two alternative machine learning (ML)-based methods, i.e. , random forest (RF) and Gaussian process regression (GPR), share the same statistical interpretation as the NN-based method and exhibit similar retrieval performance. Our study identifies the bias-variance trade-off of inversion methods as one important yet previously underappreciated component of uncertainty in LAI monitoring and highlights the need to consider it in future LAI product development and evaluation.