## 5 Conclusions  
1. The parameter optimization method of coupling Biome-BGC with the differential evolution (DE) algorithm was used for model parameter calibration and validation. Through validation and the adaptability test, it was demonstrated that the Biome-BGC model had great adaptability and high model accuracy in simulating the gross primary productivity of typical vegetation types in the Yellow River Basin. This model can be applied to carbon flux simulation studies for historical periods in the Yellow River Basin.
2. From 2000 to 2021, the average gross primary productivity in the Yellow River Basin for the past 22 years was 741.90 g C m\({}^{-2}\) y\({}^{-1}\), with a range of 681.61 g C m\({}^{-2}\) y\({}^{-1}\)-785.51 g C m\({}^{-2}\) y\({}^{-1}\). On the whole, the change trend of the GPP was not significant, showing a fluctuating trend. The annual GPP of evergreen needle leaf forests and shrubs showed a significant increasing trend, while the annual GPP of deciduous broad leaf forests and alpine meadows exhibited a significant decreasing trend. On the other hand, the annual GPP variations for crops and temperate grasses were not significant. The annual change in the GPP in the Yellow River Basin showed mainly a single peak change pattern, while only the GPP of one crop a year showed a double peak change pattern.
3. From 2000 to 2021, the spatial distribution of the annual average GPP in the Yellow River Basin had the following characteristics: The annual average GPP of the Yellow River Basin had a great spatial difference because of different vegetation coverage. The annual average GPP values in the westernmost region were comparatively the lowest among the other areas. Beyond this region, the distribution of the annual average GPP presented a distinct pattern with higher values in the southern parts, lower values in the northern parts, higher values in the eastern and western parts, and lower values in the central area. The GPP in most regions of the Yellow River Basin showed an increasing trend, accounting for approximately 59.91% of the total area.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline  & \multicolumn{2}{c}{**Multi-Year Average GPP**} & \\  & \multicolumn{2}{c}{**(g C m\({}^{-2}\) y\({}^{-1}\))**} & \\ \hline
**Vegetation Type** & **Simulation of This Study** & **Simulation of Other Studies** & **Reference** \\ \hline Evergreen Needle Leaf Forest & 1715.90 & 1325.0 & [45] \\  & & 1319.0–1924.0 & [50] \\ \hline Deciduous Broad Leaf Forest & 1267.77 & 1355.0 & [45] \\  & & 1122.0–1507.0 & [50] \\ \hline One Crop A year & 1068.85 & 1101–1396 & [50] \\ \hline Two Crops A year & 1541.31 & 1471 & [50] \\  & & 1604 & [43] \\ \hline \hline \end{tabular}
\end{table}
Table 3: _Cont._  
**Author Contributions**: Conceptualization, L.J. and B.Z.; methodology, B.Z.; software, L.J.; investigation, L.J. and B.Z.; writing--original draft preparation, L.J.; writing--review and editing, B.Z.; visualization, L.J. and B.Z.; funding acquisition, B.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Fundamental Research Funds for the Inner Mongolia Normal University (2022 JBQN065).  
**Data Availability Statement**: Data is contained within the article.  
**Acknowledgments:** We are very grateful to the relevant programs for funding, and we are very grateful to the editors and reviewers for their constructive comments on this study.  
**Conflicts of Interest:** The authors declare no conflicts of interest.