## 4 Discussion
It is worth noting that the reference map per se is also with uncertainty. The quantification of the uncertainty involved in the upscaling procedure is challenging because of the lack of \"true\" map [46]. The choice of reference values (field measurements or upscaled map) for AGB validation depends on the tradeoff between uncertainties from scale difference and upscaling procedure. Coarse resolution pixels are often characterized by high degree of heterogeneity, resulting in obvious scale error during validation. This is also the reason why CEOS WGCV recommended using reference maps to validate coarse resolution remote sensing products [42]. Therefore, we argue that uncertainty from scale difference would outweigh that from upscaling procedure, and employed the reference map as benchmark to validate the estimated AGB. It is worth noting that the estimated temporal evolution of Cm is shaky, especially in the dormancy and senescence periods (Figure 6). However, the realistic variation of Cm would not be so shaky. In fact, this fake variation is caused by the lack of information content of MODIS bands to estimate Cm. For example, [PERSON] et al. [24] found that a narrow-band, normalized index combining two distinct wavebands centered at 1649 nm and 1722 nm was needed to estimate Cm, and [PERSON] et al. found that reflectance at 1500 nm is also critical for estimating Cm [25]. Yet MODIS sensor cannot collect reflectance at the above three key bands (see Table 1). More advanced sensors with dedicated band configuration are needed to further improve Cm retrieval accuracy in future. The greatest improvement of our method over other physically-based methods is that our method is fully physical, i.e., no empirical variable or relationship is needed. Existing physically-based methods are also needed to support the field measurements. For example, [PERSON] et al. [22] transformed estimated LAI to AGB through a constant Cm which is estimated through the regression of field measured LAI and AGB. [PERSON] et al. [23] parameterize the PROSAIL model based on an empirical relationship between leaf equivalent water thickness and Cm. However, the ratio between them is temporally variational, which is the main driver causing the temporal variation of Cm (see Figure 6). Therefore, field measurements are also the prerequisite in [PERSON]'s [22] and [PERSON]'s [23] method for calibration. Conversely, the fully physical nature of our method makes it feasible for other grassland areas. Besides the calibration procedure, the data sources are also different between our method and other physically-based methods: MODIS was employed rather than Landsat or Sentinel data as in [22; 23], respectively. We selected MODIS because of two following reasons: (1) it has a high revisiting frequency, making the spatiotemporally continuous AGB monitoring possible after the temporal compositing; (2) the incidence angle of the MCD43A4 product has been normalized to local solar noon of the day [31], and therefore the range of sun-view geometries is limited, reducing the size of the LUT. The temporal variation of Cm is very limited, ranging from 0.0065 to 0.0075 g:cm\({}^{-2}\) (see Figure 6). This is inconsistent with many other foliar scale studies, which finds that the variation in Cm of leaves can cover obviously wider range [47]. This inconsistence may come from the scale difference (foliar vs. canopy). The canopy consists of many leaves and even different species, the difference of leaves in Cm may be smoothed, resulting in a relative constant Cm. The relatively constant Cm at canopy scale was also reported by [PERSON] et al. [22]. In fact, the canopy scale constant Cm assumption is the basis of their method. The two main advantages of our method are due to its fully physical nature: (1) the small temporal variation of Cm was accounted for; (2) the Cm can be estimated from remote sensing data without the support of field measurement.