## 4 Discussion  
This study proposed a physically-based grassland retrieval method based on the inversion of PROSAIL model against MCD43A4 imagery. Validation showed that it could reproduce the reference  
Figure 5: Temporal profile of the estimated aboveground biomass (AGB) in our study area. The shaded area represents standard deviation of estimated AGB. The mean and standard deviation of the reference map are displayed as solid box and corresponding error bar. Figure 6: Temporal profiles of the estimated leaf area index (LAI) and dry matter content (Cm) used to calculate the aboveground biomass (AGB). AGB map, which generated by upscaling the field measurements, in terms of magnitude and spatial distribution. The estimated AGB time series also agreed reasonably well with the expected temporal dynamic trends of the grassland in our study area. Empirically-based grassland AGB retrieval methods, relying on the regression relationship between field AGB measurements and vegetation indices, are relatively mature and widely represented in literature. For example, [PERSON] et al. obtained an accuracy of 85.6% when MODIS GPP and NDVI products were used as depended variables [2]. [PERSON] et al. found that when the MODIS LAI serving as dependent variables the corresponding RMSE was 54.25 g\(\cdot\)m\({}^{-2}\)[44]. The above two studies with field measurements involved in the calibration of the retrieval method attained only very slightly better results than our physically-based method without any field information involved (RMSE = 60.06 g\(\cdot\)m\({}^{-2}\), RRMSE = 18.1%). Our method even outperforms some empirical method in accuracy, e.g., [PERSON] et al. reported a RMSE of 88.71 g\(\cdot\)m\({}^{-2}\) when empirical methods were used [11]. Many other studies confirm the conclusion that our physically-based method can achieve similar accuracy with empirical ones [5; 9; 10]. The most obvious advantage of the physical method over empirical ones does not lie in the accuracy, but in its generality [45]. Besides the time-consuming and labor-intensive nature, the empirical methods are also subject to the representativeness of the field measurement, and therefore, are time- and site-specific. However, our physically-based method is applicable for grassland nearly at anytime and anywhere, because PROSAIL model can simulate grassland reflectance in a wide range of scenarios [20; 21]. In fact, it is the very reason that the proposed method can reproduce the expected temporal dynamic trends of the grassland (see Figure 5). Direct comparison reveals that the estimated AGB is slightly over-estimated and under-estimated the reference vales when the reference vales are less than 200 g\(\cdot\)m\({}^{-2}\) and between 300 and 350 g\(\cdot\)m\({}^{-2}\), respectively. The over-estimation may be because of the unspecific parameterization of brightness coefficient which influences the retrieved results significantly when the AGB is small. This implies that the localization of the PROSAIL model would further improve the performance of our method. The under-estimation of our method for the medium AGB values may come from the neglect of non-herbaceous organs of grass, e.g., stem. The proportion of non-herbaceous organs decreases as the growth of the vegetation, and so the 'big-leaf structures' assumption of our method would not result in obvious under-estimation when the AGB is larger than 350 g\(\cdot\)m\({}^{-2}\). There is not only grass in the grassland, but also other species, so the estimated AGB will be over-estimated or under-estimated. Traditional AGB validation procedures rely on the direct comparison between the retrieved values and field measurements. Two main drawbacks exist in the direct application of field measurements: First, the granularity difference between sampling plots and MDC43A4 pixels (100 m vs. 500 m) would induce scale error [40; 41; 43]. Second, the spatially sparse nature of the field measurements makes the spatial pattern comparison between estimated and reference values impossible.