Modeling Height–Diameter Relationships for Mixed-Species Plantations of Fraxinus mandshurica Rupr. and Larix olgensis Henry in Northeastern China

The mixture of tree species has gradually become the focus of forest research, especially native species mixing. Mixed-species plantations of Manchurian ash (Fraxinus mandshurica Rupr.) and Changbai larch (Larix olgensis Henry) have successfully been cultivated in Northeast China. Height–diameter (H–D) models were found to be effective in designing the silvicultural planning for mixed-species plantations. Thus, this study aimed to develop a new system of H–D models for juvenile ash and larch mixed-species plantations, based on competition information and tree and stand attributes. The leave-one-out cross-validation was utilized for model validation. The result showed that the H–D relationship was affected not only by the tree attributes (i.e., tree size and competition information) but also by stand characteristics, such as site quality and species proportion of basal area. The best model explained more than 80% and 85% variation of the tree height of ash and larch, respectively. Moreover, model validation also confirmed the high accuracy of the newly developed model’s predictions. We also found that, in terms of total tree height, ash in middle rows were higher than those in side rows, while larch in the middle rows were higher in the early growth period but then became lower than those in the side rows, as the diameter increased. The newly established H–D models would be useful for forestry inventory practice and have the potential to aid decisions in mixed-species plantations of ash and larch.

Comparison of Tree Biomass Modeling Approaches for Larch (Larix olgensis Henry) Trees in Northeast China

Accurate quantification of tree biomass is critical and essential for calculating carbon storage, as well as for studying climate change, forest health, forest productivity, nutrient cycling, etc. Tree biomass is typically estimated using statistical models. Although various biomass models have been developed thus far, most of them lack a detailed investigation of the additivity properties of biomass components and inherent correlations among the components and aboveground biomass. This study compared the nonadditive and additive biomass models for larch (Larix olgensis Henry) trees in Northeast China. For the nonadditive models, the base model (BM) and mixed effects model (MEM) separately fit the aboveground and component biomass, and they ignore the inherent correlation between the aboveground and component biomass of the same tree sample. For the additive models, two aggregated model systems with one (AMS1) and no constraints (AMS2) and two disaggregated model systems without (DMS1) and with an aboveground biomass model (DMS2) were fitted simultaneously by weighted nonlinear seemingly unrelated regression (NSUR) and applied to ensure additivity properties. Following this, the six biomass modeling approaches were compared to improve the prediction accuracy of these models. The results showed that the MEM with random effects had better model fitting and performance than the BM, AMS1, AMS2, DMS1, and DMS2; however, when no subsample was available to calculate random effects, AMS1, AMS2, DMS1, and DMS2 could be recommended. There was no single biomass modeling approach to predict biomass that was best for all aboveground and component biomass except for MEM. The overall ranking of models based on the fit and validation statistics obeyed the following order: MEM > DMS1 > AMS2 > AMS1> DMS2 > BM. This article emphasized more on the methodologies and it was expected that the methods could be applied by other researchers to develop similar systems of the biomass models for other species, and to verify the differences between the aggregated and disaggregated model systems. Overall, all biomass models in this study have the benefit of being able to predict aboveground and component biomass for larch trees and to be used to predict biomass of larch plantations in Northeast China.

Dynamic Simulation of the Crown Net Photosynthetic Rate for Young Larix olgensis Henry Trees

Numerical integration of the instantaneous net photosynthetic rate (An) is a common method for calculating the long-term CO2 uptake of trees, and accurate dynamic simulation of the crown An has been receiving substantial attention. Tree characteristics are challenging to assess given their aerodynamically coarse crown properties, spatiotemporal variation in leaf functional traits and microenvironments. Therefore, the variables associated with the dynamic variations in the crown An must be identified. The relationships of leaf temperature (Tleaf), the vapor pressure deficit (VPD), leaf mass per area (LMA) and the relative depth into the crown (RDINC) with the parameters of the photosynthetic light-response (PLR) model of Larix olgensis Henry were analyzed. The LMA, RDINC and VPD were highly correlated with the maximum net photosynthetic rate (Amax). The VPD was the key variable that mainly determined the variation in the apparent quantum yield (AQY). Tleaf exhibited a significant exponential correlation with the dark respiration rate (Rd). According to the above correlations, the crown PLR model of L. olgensis trees was constructed by linking VPD, LMA and RDINC to the original PLR equation. The model performed well, with a high coefficient of determination (R2) value (0.883) and low root mean square error (RMSE) value (1.440 μmol m−2 s−1). The extinction coefficient (k) of different pseudowhorls within a crown was calculated by the Beer–Lambert equation based on the observed photosynthetically active radiation (PAR) distribution. The results showed that k was not a constant value but varied with the RDINC, solar elevation angle (ψ) and cumulative leaf area of the whole crown (CLA). Thus, we constructed a k model by reparameterizing the power function of RDINC with the ψ and CLA, and the PAR distribution within a crown was therefore well estimated (R2 = 0.698 and RMSE = 174.4 μmol m−2 s−1). Dynamic simulation of the crown An for L. olgensis trees was achieved by combining the crown PLR model and dynamic PAR distribution model. Although the models showed some weakened physiological biochemical processes during photosynthesis, they enabled the estimation of long-term CO2 uptake for an L. olgensis plantation, and the results could be easily fitted to gas-exchange measurements.

Spatial and Seasonal Variations of Standardized Photosynthetic Parameters under Different Environmental Conditions for Young Planted Larix olgensis Henry Trees

Understanding the spatial and seasonal variations in leaf physiology is critical for accurately modeling the carbon uptake, physiological processes and growth of entire canopies and stands. For a 17-year-old Larix olgensis Henry plantation, vertical whorl-by-whorl sampling and analyses of seasonally repeated measurements of major photosynthetic parameters were conducted, and the correlations between photosynthetic parameters and environmental conditions, leaf morphological traits and spatial position within the crown were analyzed. According to the correlations, the photosynthetic parameters were standardized based on the environmental conditions to avoid the influence of the changing environment on the patterns of spatial and seasonal variations of photosynthetic parameters. The results showed that the standardized light-saturated net photosynthetic rate (SPmax), standardized dark respiration (SRd) and standardized stomatal conductance under saturated light (Sgs-sat) were all negatively related to the relative depth into the crown (RDINC) throughout the growing season. However, their vertical patterns were different during the development of the phenological phase. In addition, different gradients of environmental conditions also influenced the values and the range of the vertical variation in photosynthesis. High temperature and low humidity usually resulted in smaller values and weaker vertical variations of SPmax and Sgs-sat, but larger values and more obvious vertical variations in SRd. SPmax and Sgs-sat usually exhibited a parabolic seasonal pattern in different vertical positions within the crown; however, SRd generally followed a concave pattern. These seasonal patterns were all weaker with increasing RDINC. Different environments also exhibited a significant influence on the seasonal patterns of photosynthesis. We suggested that standardization is necessary before analyzing spatial and seasonal variations. A single environmental condition could not represent the spatial and seasonal patterns under all gradients of the environment. Spatial and seasonal variations should be simultaneously analyzed because they are related to each other.