4.2 Uncertainty estimation of remote sensing predictions and its application in data assimilation
Like with the regression performance of GPR for leaf-level traits like specific leaf weight (Wang et al., 2019) and chlorophyll content (Verrelst et al., 2013a), our results showed high predictive performance for the traits W leaf,N leaf and LAI, at canopy level, not only in the training dataset (R 2 > 0.95), but also in the testing dataset (R 2 > 0.81) (Fig. 4). Agreeing with the threshold proposed by Global Climate Observing System for the ecological application of remote sensing observations (GCOS, 2011), the relative uncertainties of predicted leaf traits in our results were below 20% (Fig. 5). The predicted low uncertainty was in line with other related GPR research (Verrelst et al., 2016; Wang et al., 2019). Similar to the results of Wang et al. (2019), relatively high uncertainty always came with high N addition in the vegetative phase (Fig. 5a-c). We also found that the uncertainty tended to increase after entering the reproductive phase, especially for the treatments with low N input, caused by early leaf senescence (Fig. 5d-e). Meanwhile, as GPR captured temporal and spatial variations in crop growth well, DArs performed better than DAfm (Fig. 7), which agrees with the results of yield forecasting by assimilating LAI into the APSIM-Wheat model (Zhang et al., 2021b). The estimated uncertainty of remote sensing predictions likely affected inflation factor estimation as well, as the inflation factor is determined from the updated posteriors based on the observation errors (Whitaker and Hamill, 2012). The contribution of the GPR model should be further evaluated given that the uncertainty of remote sensing observations is commonly overlooked in DA (Huang et al., 2019) and arbitrarily set based on a general guess (e.g., Kang and Özdoğan (2019); Ines et al. (2013); Fig. 8b).