The forest growth and yield models, which are used as important decision-support tools in forest management, are commonly based on the individual tree characteristics, such as diameter at breast height (DBH), crown ratio, and height to crown base (HCB). Taking direct measurements for DBH and HCB through the ground-based methods is cumbersome and costly. The indirect method of getting such information is possible from remote sensing databases, which can be used to build DBH and HCB prediction models. The DBH and HCB of the same trees are significantly correlated, and so their inherent correlations need to be appropriately accounted for in the DBH and HCB models. However, all the existing DBH and HCB models, including models based on light detection and ranging (LiDAR) have ignored such correlations and thus failed to account for the compatibility of DBH and HCB estimates, in addition to disregarding measurement errors. To address these problems, we developed a compatible simultaneous equation system of DBH and HCB error-in-variable (EIV) models using LiDAR-derived data and ground-measurements for 510 Picea crassifolia Kom trees in northwest China. Four versatile algorithms, such as nonlinear seemingly unrelated regression (NSUR), two-stage least square (2SLS) regression, three-stage least square (3SLS) regression, and full information maximum likelihood (FIML) were evaluated for their estimating efficiencies and precisions for a simultaneous equation system of DBH and HCB EIV models. In addition, two other model structures, namely, nonlinear least squares with HCB estimation not based on the DBH (NLS and NBD) and nonlinear least squares with HCB estimation based on the DBH (NLS and BD) were also developed, and their fitting precisions with a simultaneous equation system compared. The leave-one-out cross-validation method was applied to evaluate all estimating algorithms and their resulting models. We found that only the simultaneous equation system could illustrate the effect of errors associated with the regressors on the response variables (DBH and HCB) and guaranteed the compatibility between the DBH and HCB models at an individual level. In addition, such an established system also effectively accounted for the inherent correlations between DBH with HCB. However, both the NLS and BD model and the NLS and NBD model did not show these properties. The precision of a simultaneous equation system developed using NSUR appeared the best among all the evaluated algorithms. Our equation system does not require the stand-level information as input, but it does require the information of tree height, crown width, and crown projection area, all of which can be readily derived from LiDAR imagery using the delineation algorithms and ground-based DBH measurements. Our results indicate that NSUR is a more reliable and quicker algorithm for developing DBH and HCB models using large scale LiDAR-based datasets. The novelty of this study is that the compatibility problem of the DBH model and the HCB EIV model was properly addressed, and the potential algorithms were compared to choose the most suitable one (NSUR). The presented method and algorithm will be useful for establishing similar compatible equation systems of tree DBH and HCB EIV models for other tree species.

Forest trees exhibit a large variation in the basal area increment (BAI), and the variation is attributed to the stand density, biodiversity, and stand spatial structure. Studying and quantifying the effect of these above variables on tree growth is vital for future forest management. However, the stand spatial structure based on neighboring trees has rarely been considered, especially in the mixed forests. This study adopted the random-forest (RF) algorithm to model and interpret BAI based on stand density, biodiversity, and spatial structure. Fourteen independent variables, including two stand density predictors, four biodiversity predictors, and eight spatial structure predictors, were evaluated. The RF model was trained for the whole stand, three tree species groups (gap, neutral, and shade_tolerant), and two tree species (spruce and fir). A 10-fold blocked cross-validation was then used to optimize the hyper-parameters and evaluate the models. The squared correlation coefficients (R²) for the six groups were 0.233 for the whole stand, 0.575 for fir, 0.609 for shade_tolerant, 0.622 for neutral, 0.722 for gap, and 0.730 for spruce. The Stand Density Index (SDI) was the most-important predictor, suggesting that BAI is primarily restricted by competition. BAI and species biodiversity were positively correlated for the whole stand. The stands were expected to be randomly distributed based on the relationship between the uniform angle index (W) and growth. The relationship between dominance (U) and BAI indicated that small trees should be planted around the light-demanding tree species and vice versa. Of note, these findings emphasize the need to consider the three types of variables in mixed forests, especially the spatial structure factors. This study may help make significant advances in species composition, spatial arrangement, and the sustainable development of mixed forests.

Tree height is a basic input variable in various forest models, such as growth and yield models, biomass models, and carbon budget models, which serve as very important tools for the informed decision-making in forestry. The height-diameter model is the most important component of the growth and yield models and forest simulators. We developed the nonlinear mixed-effects height-diameter model with the interaction effects of stand density and site index introduced using data from 765 Larix olgensis trees in Jingouling forest farm of the Wangqing Forest Bureau in northeast China. Among the various basic versatile functions evaluated, a simple exponential growth function fitted the data adequately well, and this was then expanded through the introduction of the variables describing the interaction effects of the stand density and site index on the height-diameter relationship. Sample plot-level random effects were included into this model through mixed-effects modeling. The results showed that the random effect of the stand density on the height-diameter relationship was substantially different at different classes of the site index, and the random effect of the site index was different for the different stand density classes. The nonlinear mixed-effects (NLME) height-diameter model coping with the interaction effects of the stand density and site index had a better performance than those of the NLME models with the random effect of the single variable of stand density or site index. To conclude, the inclusion of the interaction effects of stand density and site index could significantly improve the prediction accuracy of the height-diameter model for Larix olgensis Henry. The proposed model with the interactive random effects included can be applied for the accurate prediction of Larix olgensis tree height in northeast China.

Individual trees are characterized by various sizes and forms, such as diameter at breast height, total height (H), height to crown base (HCB), crown length (CL), crown width, and crown and stem forms. Tree characteristics are strongly related to each other, and studying their relationships is very important. The knowledge of the compatibility and additivity properties of the major tree characteristics, such as H, CL, and HCB, is essential for informed decision-making in forestry. H can be used to represent site quality and CL represents biomass and photosynthesis of crown, which is the performance of individual tree vigor and light interception, and the longer the crown length (or shorter HCB) is, the more vigorous the tree would be. However, none of the studies have uncovered their inherent relationships quantitatively. This study attempts to explore such relationships through the application of appropriate modeling approaches. We applied seemingly unrelated regression, such as nonlinear seemingly unrelated regression (NSUR), which is commonly used for exploring the compatibility and additivity properties of the variables, for the proposes. The NSUR involves the variance and covariance matrices of the sub-models that are used for the interpretation of the correlations among the variables of interest. The data set acquired from Mongolian oak forest and spruce-fir forest in the Jingouling forest farm of the Wangqing Forest Bureau in the Northeast of China were used to construct two types of model systems: a compatible model system (the model system of H, CL, and HCB can be estimated simultaneously) and an additive model system (the sum of HCB and CL is H, the form of the H sub-model equals the sum of the HCB and CL sub-models) from the individual models of H, CL, and HCB. Among the various tree-level and stand-level variables evaluated, D (diameter at breast), Dg (quadratic mean diameter), DT (dominant diameter), CW (crown width), SDI (stand density index), and BAS (basal area of stand) contributed significantly highly to the variations of the response of the variables of interest in the model systems. Modeling results showed the existence of the compatibility and additivity of H, CL, and HCB simultaneously. The additive model system exhibited better fitting performance on H and HCB but poorer fitting on CL compared with the simultaneous model system, indicating that the performance of the additive model system could be higher than that of the simultaneous model system. Model tests against the validation data set also confirmed such results. This study contributes a novel approach to solving the compatibility and additivity of the problems of H, CL, and HCB models through the application of the robust estimating method, NSUR. The results and algorithm presented will be useful for constructing similar compatible and additive model systems of multiple tree-level models for other tree species.

Spatial structure dynamics play a major role in understanding the mechanisms of forest structure and biodiversity formation. Recently, researches on the spatial structure dynamics utilizing multi-period data have been published. However, these studies only focused on comparative analyses of the spatial structure of multi-period living trees, without an in-depth analysis of the change processes. In this study, we propose a new comprehensive analysis method for dynamic change of the spatial structure at the individual level, which includes three processes (living trees’ flow, mortality process and recruitment process) that have not been considered in previous researches. Four spatial structural parameters (SSSPs, Uniform angle index, Mingling, Dominance and Crowding) and a natural spruce-fir-broadleaf mixed forest with two-phase data were taken as an example to find out the laws of the spatial structure dynamics. All types of dynamic change were named and their proportions were analyzed. The proportion of changes in the SSSPs of individuals was relatively high, even though the mean values of the stand did not change considerably. The five values (0, 0.25, 0.5, 0.75, 1) of the SSSPs are in mutual flow, and the flows are typically one-step, with three-steps and four-steps changes being uncommon. The processes of mortality and recruitment have a higher influence on the spatial structure than the flow of living trees. The dynamic change of spatial structure analysis method created in this study can capture more features not discovered in earlier approaches, as well as guiding forest management in some ways. Understanding the nuances of these changes is a critical part of reasonable spatial structure and biodiversity maintenance, and should be the focus of future research efforts.

The degradation of ecosystem services (ES) poses a significant obstacle to regional sustainable development. Land-use change is widely recognized as a pivotal factor driving the spatio-temporal dynamics of ES supply and demand. However, the future impact of land-use changes on supply–demand risks remains largely unknown. To fill this knowledge gap, we conducted a study in the Gansu section of the Yellow River Basin. By integrating Cellular Automata (CA) and an enhanced Markov model within the GeoSOS-FLUS framework, we dynamically simulated land-use changes under three scenarios—the Normal Development Scenario (NDS), Ecological Protection Scenario (EPS), and Rapid Socio-economic Development Scenario (RDS)—spanning from 2020 to 2050. Furthermore, we employed the InVEST model to analyze the spatio-temporal pattern of supply, demand, supply-to-demand ratios, and supply–demand risks for water provision, carbon storage, and soil conservation under all scenarios. Firstly, all scenarios project an increase in built-up land, primarily from unused land, shrubland, grassland, and cropland. Forest land and water bodies remain stable. Secondly, water provision increases, but demand grows faster, leading to supply–demand imbalances, with high-risk areas in the north, central, and east. Soil conservation shows balanced supply and demand with high-risk areas in the north. Carbon storage remains stable, with high-risk areas in the central and east regions. Thirdly, high-risk areas for water provision increase under all scenarios, particularly under the Rapid Socio-economic Development scenario.