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Accurate estimate of tree biomass is essential for forest management. In recent years, several climate-sensitive allometric biomass models with diameter at breast height (D) as a predictor have been proposed for various tree species and climate zones to estimate tree aboveground biomass (AGB). But the allometric models only account for the potential effects of climate on tree biomass and do not simultaneously explain the influence of climate on D growth. In this study, based on the AGB data from 256 destructively sampled trees of three larch species randomly distributed across the five secondary climate zones in northeastern and northern China, we first developed a climate-sensitive AGB base model and a climate-sensitive D growth base model using a nonlinear least square regression separately. A compatible simultaneous model system was then developed with the climate-sensitive AGB and D growth models using a nonlinear seemingly unrelated regression. The potential effects of several temperature and precipitation variables on AGB and D growth were evaluated. The fitting results of climatic sensitive base models were compared against those of their compatible simultaneous model system. It was found that a decreased isothermality ([mean of monthly (maximum temperature-minimum temperature)]/(Maximum temperature of the warmest month-Minimum temperature of the coldest month)) and total growing season precipitation, and increased annual precipitation significantly increased the values of AGB; an increase of temperature seasonality (a standard deviation of the mean monthly temperature) and precipitation seasonality (a standard deviation of the mean monthly precipitation) could lead to the increase of D. The differences of the model fitting results between the compatible simultaneous system with the consideration of climate effects on both AGB and D growth and its corresponding climate-sensitive AGB and D growth base models were very small and insignificant (p > 0. 0 5). Compared to the base models, the inherent correlation of AGB with D was taken into account effectively by the proposed compatible model system developed with the climate-sensitive AGB and D growth models. In addition, the compatible properties of the estimated AGB and D were also addressed substantially in the proposed model system. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]