## 4 Results and Discussion
### Validation with Observed PAR Data  
Figure 8 shows the differences between observed and inversed APAR. The observed APAR is the sum of vegetation canopy absorption PAR and soil absorption PAR; inversed APAR includes only vegetation canopy absorption PAR. Therefore, the observed APAR should be larger than the inversed value. In the period of vegetation ridge covered, the vegetation FPAR was larger, and the two APAR values were close to each other. However, when FPAR was smaller, the difference between the two APAR values was relatively larger. This occurred because the contribution of soil absorption PAR increased. Therefore, if precise verification of vegetation absorption PAR using observed APAR data is needed, the soil absorption part must be removed. This kind of observed data is obtained in the period of the vegetation ridge covered. Figure 8: Scatterplots of inversed and observed APAR with an underlying surface of: (**a**) cropland; (**b**) meadowland.4.4. Validation with the MODIS FPAR Product  
Figure 7: Differences among the three kinds of models based on simulated data: (**a**) with visibility of 5 km; (**b**) with visibility of 30 km. SAIL, scattering by arbitrarily-inclined leaves; DnD, direct and diffuse radiation. The MODIS FPAR product is primary data input for calculating GPP. In this paper, the MODIS LAI product was used as an important input to calculate FPAR. Therefore, for various vegetation types, a comparative analysis of the MODIS FPAR product and the FPAR product calculated in this research was performed (Figure 9). Because the MODIS LAI and surface albedo products were used to calculate FPAR in this study, the inversion results and the MODIS FPAR product were highly correlated. Values from the MODIS FPAR product were higher than those from the inversion product, but the biggest RMSE was 0.06 for the evergreen needleleaf vegetation type. Many previous studies have pointed out the accuracy of the MODIS FPAR product. [PERSON] _et al._ compared four global FPAR datasets over northern Eurasia for 2000, namely MODIS, CYCLOPES (Carbon Cycle and Change in Land Observational Products from an Ensemble of Satellites), JRC (Joint Research Center) and GLOBCARBON [39]. The results showed that both the MODIS and CYCLOPES datasets recorded on average similar, but substantially higher values than the JRC and GLOBCARBON datasets. [PERSON] _et al._ compared MODIS FPAR data with site-measured data [40]. The MODIS FPAR values were overestimated by 0.06-0.15 (approximately 8%-20%). [PERSON] _et al._ examined MODIS and JRC FPAR products over a site in eastern Russia. MODIS grossly overestimated the values for deciduous needleleaf larch forest [41]. These conclusions are consistent with the comparison results reported above. Figure 9: Scatterplots of inversion FPAR and MODIS FPAR for various vegetation types: **(a)** shrubs; **(b)** herbaceous; **(c)** evergreen needleleaf; **(d)** deciduous needleleaf. For the comparison of the variability of the inversed FPAR by the DnD model and the MODIS FPAR product, a method for the comparison of three kinds of multitemporal FPAR products in a previous study was used. The agreement coefficient (AC) was calculated, and the spatial agreement and temporal agreement were analyzed. AC is used to assess the agreement between two images, non-dimensional, bounded (0-1 for no to perfect agreement) and symmetric (no preference for one dataset). \(AC=1-(SSD/SPOD)\), where \(SSD\) is the sum of squared differences and \(SPOD\) is the sum of potential differences [42]:  
\[SSD\ =\ \sum_{i=1}^{n}\left(X_{i}-Y_{i}\right)^{2},SPOD\ =\ \sum_{i=1}^{n} \left(\left|\vec{X}-\vec{Y}\right|+\left|X_{i}-\vec{X}\right|\right)\left( \left|\vec{X}-\vec{Y}\right|+\left|Y_{i}-\vec{Y}\right|\right) \tag{27}\]  
To be able to compare, the total daily inversed FPAR in the Heihe River Basin was averaged for eight days. The analysis is performed on the full year of 2012. The analysis of the temporal evolution of selected spatial metrics aims to highlight specific periods of spatial disagreement [42].