Computational geometry

In recent decades, intense droughts, insect outbreaks, and wildfires have led to decreasing tree growth and increasing mortality in many temperate forests. We compared annual tree-ring width data from 1,097 populations in the coterminous United States to climate data and evaluated site-specific tree responses to climate variations throughout the 20th century. For each population, we developed a climate-driven growth equation by using climate records to predict annual ring widths. Forests within the southwestern United States appear particularly sensitive to drought and warmth. We input 21st century climate projections to the equations to predict growth responses. Our results suggest that if temperature and aridity rise as they are projected to, southwestern trees will experience substantially reduced growth during this century. As tree growth declines, mortality rates may increase at many sites. Increases in wildfires and bark-beetle outbreaks in the most recent decade are likely related to extreme drought and high temperatures during this period. Using satellite imagery and aerial survey data, we conservatively calculate that ≈2.7% of southwestern forest and woodland area experienced substantial mortality due to wildfires from 1984 to 2006, and ≈7.6% experienced mortality associated with bark beetles from 1997 to 2008. We estimate that up to ≈18% of southwestern forest area (excluding woodlands) experienced mortality due to bark beetles or wildfire during this period. Expected climatic changes will alter future forest productivity, disturbance regimes, and species ranges throughout the Southwest. Emerging knowledge of these impending transitions informs efforts to adaptively manage southwestern forests.

Forest responses to increasing aridity and warmth in the southwestern United States

Nonlinear mixed-effects crown width models for individual trees of Chinese fir (Cunninghamia lanceolata) in south-central China

Individual tree crown width models for Norway spruce and European beech in Czech Republic

Climate change has increased the need of information on amount of forest biomass. The biomass and carbon storage for larch (Larix spp.) in large geographic regions in China were failed to be accurately estimated from current biomass equations, because they were usually based on a few sample trees on local sites, generally incompatible to volume estimation, and not additive between components and total biomass. China needs reliable biomass estimation of the important species in the whole country. This study was based on the mensuration data of above- and belowground biomass from 600 and 198 destructive sample trees of larch from four regions in China, respectively. The main purpose was to develop compatible individual tree equations on both national and regional levels for above- and belowground biomass, biomass conversion factor and root-to-shoot ratio, using the nonlinear error-in-variable simultaneous equation approach. In addition, diameter at breast height (D) and tree height (H) growth models were also developed, and effects of key climate variables on biomass variation and growth process were analyzed. The results showed that mean prediction errors (MPEs) of regional aboveground biomass models were from 3.86 to 7.52%, and total relative errors (TREs) are within ±3%; and for regional belowground biomass equations, the MPEs are from 9.91 to 28.85%, and the TREs are within ±4%. The above- and belowground biomass and D- and H-growth were significantly related to mean annual temperature and mean annual precipitation. The biomass equations and growth models developed in this paper will provide good basis for estimating and predicting biomass of larch forests in China.

Individual tree biomass equations and growth models sensitive to climate variables for Larix spp. in China

Nonlinear error-in-variable models can advance the development of the systems of additive biomass equations and lead to much higher prediction accuracy of tree biomass than nonlinear seemingly unrelated regression.
 In this study, the approach of nonlinear error-in-variable models (NEIVM) was compared with nonlinear seemingly unrelated regressions (NSUR) for developing a system of nonlinear additive biomass equations using the data collected in Southern China for Pinus massoniana Lamb. Various tree variables were assessed to explore their contributions to improvement of biomass prediction using the systems of equations. It was found that diameter at breast height (D), total tree height (H) and crown width (CW) significantly contributed to the increase of prediction accuracy. The combinations of D, H, and CW led to three sets of independent variables: (1) D alone; (2) both D and H; and (3) D, H and CW together, which were used for the development of one-predictor, two-predictor and three-predictor systems of biomass equations, respectively. The results showed that both NEIVM and NSUR had high prediction accuracy of biomass for all the systems of biomass equations. For the one-predictor systems of biomass equations, both NEIVM and NSUR led to very similar predictions. However, for the two-predictor and three-predictor systems of biomass equations, the prediction accuracy of NEIVM was much higher than that of NSUR. When the two-predictor system of equations was used, in particular, NEIVM with one-step procedure, that is, by directly partitioning total tree biomass into four basic components, showed a higher accuracy of biomass prediction than NSUR for all the one-predictor, two-predictor and three-predictor systems of equations. This study implies that the NEIVM approach could provide a greater potential to develop a system of biomass equations that are dependent on the predictors with significant measurement errors.

Comparison of seemingly unrelated regressions with error-in-variable models for developing a system of nonlinear additive biomass equations

Accurate measurement of stem diameter is essential to forest inventory. As a millimeter-level measuring tool, terrestrial laser scanning (TLS) has not yet reached millimeter-level accuracy in stem diameter measurements. The objective of this study is to develop an accurate method for deriving the stem diameter from TLS data. The methodology of stem diameter measurement by diameter tape was adopted. The stem cross-section at a given height along the stem was determined. Stem points for stem diameter retrieval were extracted according to the stem cross-section. Convex hull points of the extracted stem points were calculated in a projection plane. Then, a closed smooth curve was interpolated onto the convex hull points to simulate the path of the diameter tape, and stem diameter was calculated based on the length of the simulated path. The stems of different tree species with different properties were selected to verify the presented method. Compared with the field-measured diameter, the RMSE of the method was 0.0909 cm, which satisfies the accuracy requirement for forest inventory. This study provided a method for determining the stem cross-section and an efficient and precise curve fitting method for deriving stem diameter from TLS data. The importance of the stem cross-section and convex hull points in stem diameter retrieval was demonstrated.

Precise Measurement of Stem Diameter by Simulating the Path of Diameter Tape from Terrestrial Laser Scanning Data

Quantification of forest biomass is important for practical forestry and for scientific purposes. It is fundamental to develop generic individual-tree biomass models suitable for large-scale forest biomass estimation. However, compatibility of forest biomass estimates at different scales may become a problem. We developed generic individual-tree biomass models using a mixed-effects modeling approach based on aboveground biomass data of Masson pine (Pinus massoniana Lamb.) from nine provinces in southern China. Mixed-effects modeling could provide an effective approach to solving the compatibility of forest biomass estimates at different scales. A simple allometric function requiring diameter at breast height was used as a base model to construct generic individual-tree mixed-effects biomass models. Two factors of tree origin (natural and planted forests) and geographic region (nine provinces or three subregions) were included as random effect factors in the models. The results showed that the mixed-effect...

Generic linear mixed-effects individual-tree biomass models for Pinus massoniana in southern China

Accurate estimates of forest site productivity are essential for environmental planning and forest management. In this study, we developed a new productivity index, hereafter termed basal area potential productivity index (BAPP), to estimate site productivity for irregular and complex forests characterized by multi-aged, multi-species, and multi-layer stands. We presented the biological relevance of BAPP with its computational details. We also compared BAPP against basal area realized productivity (BARP) in order to verify the practicability and reliability of BAPP. Time-series data of the national forest inventory on 1912 permanent sample plots that were located in two main forest types and consisted of oak-dominated mixed forests and other broadleaf forests in northeast China were used to demonstrate the application of BAPP. The results showed that the value of BAPP for each sample plot was larger than or equal to the corresponding BARP value for each forest type. For appropriately managed stands with relatively better site conditions, the values of both BARP and BAPP were almost identical. The values of the difference between BAPP and BARP could therefore be used to effectively assess forest site productivity. Meanwhile, BAPP also provides much reliable and valuable information that can aid decision-making in forest management.

https://www.mdpi.com/1999-4907/8/4/119/pdf

Yuancai Lei

Papers

Nonlinear mixed-effects crown width models for individual trees of Chinese fir (Cunninghamia lanceolata) in south-central China

Comparison of seemingly unrelated regressions with error-in-variable models for developing a system of nonlinear additive biomass equations

Precise Measurement of Stem Diameter by Simulating the Path of Diameter Tape from Terrestrial Laser Scanning Data

Generic linear mixed-effects individual-tree biomass models for Pinus massoniana in southern China

A Basal Area Increment-Based Approach of Site Productivity Evaluation for Multi-Aged and Mixed Forests