# Improving a Process-Based Model to Simulate Forest Carbon Allocation under Varied Stand Density
## 1 Introduction  
Forests are important carbon sinks that contribute to slowing global climate change. Stand density regulation is a key forest management measure that affects the carbon cycle [1]. Stand density regulation is widely used to improve the growth environment of planted trees [2]. Changes in competition conditions affect the carbon and nitrogenallocation modes of stands [3]. It is necessary to conduct a modeling study to explore the impact of stand density on carbon allocation and stand growth, so as to develop planted forest managing techniques to improve ecological function and wood production. Functional balance is commonly used to explain carbon allocation [4]. If growth is limited by underground resources, such as water and nutrients, plants allocate more carbon to their root systems to absorb more resources [5]. In contrast, if growth is limited by above-ground resources (such as light and spots), plants allocate more carbon to aboveground parts [5], especially the foliage [3]. A meta-analysis on the responses of even-aged mono-specific stands to population density revealed that with an increase in stand density, the mean size of the individuals decreased, but the tree height remained similar [6]. Through studying five sets of premature and mature pine stands, [PERSON] et al. [3] found that stand density only affected branch allocation and had no effect on the stems and foliage. In current studies, the experimental design, choice of research object, and calculation method of the selected variables led to different results [3; 5]. Few studies could explain the influence of stand density on carbon allocation, as carbon allocation is a dynamic process, and biomass partitioning could not fully explain the flux allocation at planting density trails. In addition, the research duration in previous studies was generally short [4], and there are a lack of studies on long-term carbon allocation dynamics. Modelling studies can be conducted to study carbon allocation at different climate and soil conditions. In general, because of a lack mechanistic understanding regarding carbon allocation at an individual or stand level, models use either a static or a dynamic allocation scheme [7; 8]. Static allocation models such as CABLE [9] and CLM4 [10] are practically unable to capture the changes in allocation with changing water and nutrient availability at seasonal to interannual timescales. Some models such as ED [11], LPJ-GUESS [12], and ISAM [13] use a dynamic allocation scheme to regulate carbon allocation, owing to functional relationships and resource limitations, which can change allocation coefficients based on individual development, the environment, and resource availability [4]. [PERSON] et al. [14] developed an optimization-based model to explore a leaf allocation strategy and to explain the patterns in leaf allocation across CO\({}_{2}\) fertilization. [PERSON] et al. [8] analyzed 31 contrasting models to identify the major forest carbon allocation modeling approaches and provided examples regarding how to improve C allocation modelling in the context of climate change. Using the 3-PG model with GIS, [PERSON] et al. [15] predicted the biomass of poplars under different management and climate conditions in the Pacific Northwest of the United States. To evaluate the importance of the modulations of tree carbon allocation by water and low-temperature stress for the prediction of forest growth, a new carbon allocation scheme was implemented in the CASTANEA model, which accounted for lagged and directed environmental controls of carbon allocation [16]. The coupled eco-hydroological model based on the process model was applied to study the change in forest carbon under different allocation methods, which indicated that the influence of uncertainty regarding the allocation strategy or parameters on carbon estimation varies depending on location [17].