## 5 Conclusions  
Data gaps are a common problem in forestry modeling. In this paper, combined with the existing data parameterizing the 3-PG model, the stand diameter and biomass data were successfully filled using the monthly scale simulation results. The LSTM is trained based on the augmented data, and the 3 PG-MT-LSTM model is constructed by adding MTL and compatibility rules. In contrast to the conventional LSTM architecture, the coupling model demonstrates enhanced precision in biomass estimation following thinning operations while also circumventing the accumulation of errors across individual components. There is no significant difference in the applicability of the model when it is applied to spruce forest stands in different regions and forest ages, and the generalization ability has improved. Utilizing the hybrid model, the present study showcases the impact of diverse thinning techniques on the growth of Norway spruce trees situated at the Bily Kriz location in light of anticipated climate change scenarios. According to our analysis, the periodic light-to-moderate thinning of Norway spruce stands at intervals of 10 to 15 years had a favorable impact on the accumulation of biomass over an extended period.  
The heavy thinning technique is deemed more appropriate to produce timber with large diameters. Additionally, thinning management during the young-aged stages of forest growth is imperative for any production objective. The decision to implement additional management practices during the middle-aged stage of forest growth can be appropriately modified based on the current condition of the stand. The application of a hybrid model can help managers balance large-diameter timber production with economic benefits. The carbon sink value of a stand is determined through comprehensive research to provide scientific guidance for sustainable forest development. In conclusion, the in-depth application of deep learning presents an opportunity for the field of forestry management, but it also poses new challenges for forest managers.  
Conceptualization, J.Q. and X.S.; methodology, J.Q.; validation, J.Q., X.S. and M.M.; formal analysis, J.Q.; data curation, Y.Z.; writing--original draft preparation, J.Q.; writing--review and editing, X.S. and B.W.; visualization, J.Q., M.M. and X.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant number 32101516.  
Not applicable for studies not involving humans or animals.  
Not applicable for studies not involving humans.  
The data that support the findings of this study are openly available in the \"PROFOUND database\" ([[https://doi.org/10.5880/PIK_2020.006](https://doi.org/10.5880/PIK_2020.006)]([https://doi.org/10.5880/PIK_2020.006](https://doi.org/10.5880/PIK_2020.006)), accessed on 12 December 2022) and \"The Coupled Model Intercomparison Project Phase 6\" ([[https://esgf-node.llnl.gov/projects/cmip6/](https://esgf-node.llnl.gov/projects/cmip6/)]([https://esgf-node.llnl.gov/projects/cmip6/](https://esgf-node.llnl.gov/projects/cmip6/)), accessed on 14 February 2023).  
We thank the makers of the PROFOUND database for providing free access to their data. We acknowledge the World Climate Research Program's Working Group on Coupled Modeling, which is responsible for CMIP6, and thank the climate modeling groups for producing and making available their model outputs. We also thank the anonymous reviewers for their valuable suggestions.  
The authors declare no conflict of interest.