Optimizing LUT-Based RTM Inversion for Semiautomatic Mapping of Crop Biophysical Parameters from Sentinel-2 and -3 Data: Role of Cost Functions

Inversion of radiative transfer models (RTM) using a lookup-table (LUT) approach against satellite reflectance data can lead to concurrent retrievals of biophysical parameters such as leaf chlorophyll content $(Chl)$ and leaf area index (LAI), but optimization strategies are not consolidated yet. ESA's upcoming satellites Sentinel-2 (S2) and Sentinel-3 (S3) aim to ensure continuity of old generation satellite sensors by providing superspectral images of high spatial and temporal resolution. This unprecedented data availability leads to an urgent need for developing robust, accurate, and operational retrieval methods. For three simulated Sentinel settings (S2-10 m: 4 bands, S2-20 m: 8 bands and S3-OLCI: 19 bands) various optimization strategies in LUT-based RTM inversion have been evaluated, being the role of i) added noise, ii) multiple best solutions, iii) combined parameters $(Chl \times \hbox{LAI})$ , and iv) applied cost functions. By inverting the PROSAIL model and using data from the ESA-led field campaign SPARC (Barrax, Spain), it was demonstrated that introducing noise and opting for multiple best solutions in the inversion considerably improved retrievals. However, the widely used RMSE was not the best performing cost function. Three families of alternative cost functions were applied here: information measures, minimum contrast, and M-estimates. We found that so-called "Power divergence measure", "Trigonometric", and spectral measure with "Contrast function $K(x) = -\log(x) + x$ ", yielded more accurate results, although this also depended on the biophysical parameter. Particularly, when simultaneous retrieval of multiple biophysical parameters is the objective then "Contrast function $K(x) = -\log(x) + x$ " provided most consistent optimized estimates of leaf $Chl$ , LAI and canopy $Chl$ across the different Sentinel configurations (relative RMSE: 24–29 $\%$ ).