## 3 Results and Discussion
### Evaluation of the 30-Year Trends in NDVI and Modeled GPP  
The terrestrial biosphere models suggest increasing GPP in Asia from 1982 to 2011, which is mostly consistent with the satellite-based NDVI trends. The Biome-BGC and LPJ models exhibited significant increasing GPP trends in all nine regions. Moreover, the BEAMS and TRIFFID models showed significant increasing GPP trends in eight regions (Table 1). The consistency between models and the NDVI is highest for the BEAMS model because the model uses satellite-based LAI and FPAR as inputs; only the Tropical Asia South region did not exhibit a difference in the trend significance (e.g., the BEAMS model predicts statistically significant increases in GPP, whereas the NDVI does not) likely due to uncertainties in the solar radiation data used for BEAMS models. In both the Boreal Eurasia North West region and the Tropical Asia South region, the prognostic terrestrial biosphere models (Biome-BGC, LPJ, and TRIFFID) suggest significant increases in GPP. However, a similar trend is not detected for the NDVI. The interannual variations in the NDVI and modeled GPP were highly consistent in temperate and boreal regions and weakly consistent in tropical regions (Table 2 and Figure 4). We found that the BEAMS-based GPP, in which GPP was calculated using satellite-based LAI and FPAR data, was highly consistent with the satellite-based NDVI (e.g., \(\tau=0.67-0.83\) for boreal and temperate regions). The results from the prognostic biosphere models also showed good agreement with the satellite-based NDVI data regarding interannual variations in GPP (e.g., averages of \(\tau\) in all boreal and temperate regions are \(\tau=0.48\), \(0.50\) and \(0.43\) for Biome-BGC, LPJ, and TRIFFID, respectively). However, we found large deviations between the models and the satellite-based NDVI in tropical forest regions (e.g., \(\tau<0.3\) for most tropical regions). The consistency of interannual variability and 30-year trends in boreal and temperate regions between the NDVI and modeled GPP indicates that these increases are robust for the different methodologies, that is, terrestrial biosphere models and satellite-based observations. Therefore, we can use the models to perform a process-based analysis on the underlying mechanisms. As exceptions, disagreement between the model and the NDVI data was detected in several regions and specific years. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Region** & **BEAMS** & **Biome-BGC** & **LPJ** & **TRIFFID** \\ \hline Boreal Eurasia North West & \(0.67^{**}\) & \(0.31^{*}\) & \(0.50^{**}\) & \(0.33^{*}\) \\ Boreal Eurasia North East & \(0.72^{**}\) & \(0.70^{**}\) & \(0.66^{**}\) & \(0.68^{**}\) \\ Boreal Eurasia South West & \(0.80^{**}\) & \(0.40^{**}\) & \(0.37^{**}\) & \(0.16\) \\ Boreal Eurasia South East & \(0.71^{**}\) & \(0.45^{**}\) & \(0.46^{**}\) & \(0.37^{**}\) \\ Temperate Asia North West & \(0.83^{**}\) & \(0.49^{**}\) & \(0.51^{**}\) & \(0.57^{**}\) \\ Temperate Asia North East & \(0.76^{**}\) & \(0.44^{**}\) & \(0.44^{**}\) & \(0.39^{**}\) \\ Temperate Asia South East & \(0.74^{**}\) & \(0.54^{**}\) & \(0.55^{**}\) & \(0.48^{**}\) \\ Tropical Asia North & \(0.58^{**}\) & \(0.27^{*}\) & \(0.23\) & \(0.20\) \\ Tropical Asia South & \(0.17\) & \(0.26^{*}\) & \(0.16\) & \(0.17\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation coefficients between the NDVI and GPP from each terrestrial biosphere model. Correlation coefficients were calculated based on [PERSON]’s rank correlation coefficients (Kendall’s \(\tau\)). For example, in the Boreal Eurasia North West region, mainly during the 2007-2010 period (Figure 4a), the satellite-based NDVI had negative anomalies for this period, whereas the GPPs in the prognostic models (Biome-BGC, LPJ, and TRIFFID) had positive anomalies for this period. Another distinct difference was found in the Temperate Asia North West over the period 1996-2001.