V. Clark Baldwin

The relationship between Reineke's stand-density index and physical stem mechanics

Abstract Data from 358 plots from long-term, growth-and-yield studies established in loblolly pine plantations were used to test the hypothesis that the value of Reinekes stand-density index (SDI) represents the amount of bending stress generated in the stems by wind action on the canopy. By assuming constant bending stress in stems as a function of height and a linear relationship between canopy depth and mean tree spacing, SDI can be expressed in terms of foliage density (leaf area per unit volume of space, F ), mean live-crown ratio ( C r ), and canopy depth ( C d ). The equation is SDI = a [ F (1/ C r − 0.5) 0.53 C d 0.12 , where a is a constant. Foliage density was calculated as leaf area index divided by canopy depth. An initial test of the equation was conducted by fitting the model SDI = β 0 [ F (1/ C r − 0.5) β staggered1 to the growth-and-yield data. The factor C d was not included in the model because of its mathematical relationship to F . The fitted equation explained 76% of the variation in SDI and estimated β 1 as 0.51, which was not significantly different from the derived exponent, 0.53. Residuals from the fitted equation were unbiased with respect to foliage density and mean live-crown ratio. Further analysis revealed that species variation in maximum values of SDI increased linearly with decreasing wood specific gravity, providing additional evidence that density indexes are related to physical stem mechanics.

Growth in loblolly pine plantations as a function of stand density and canopy properties

Abstract Interrelationships between forest-canopy properties, stand growth, and Reinekes stand density index (SDI) were investigated for unthinned plots of a loblolly pine, growth-and-yield study. Gross, periodic-annual increment (Iv) and mean-tree, gross, periodic-annual increment (Imv) were calculated for the intervals between 17, 22, 27, 32, and 37 years of age. Data to calculate canopy variables were available only after age 22. Regression analysis indicates that a second-degree polynomial of SDI is statistically related to both growth variables during the first two measurement intervals but not the last two. The shape of the significant equations generally agreed with conventional growth-growing stock relationships, and Iv, adjusted for SDI, decreased significantly with age. Leaf area index (L) and foliage density (F) were linearly related to SDI for each measurement period. While the equations relating F and SDI were not significantly different between measurement periods, the intercepts of the fitted equations for L and SDI generally decreased with plantation age. Mean-live-crown ratio (Cr) was significantly related to SDI for all measurement periods, with the exception of age 32, and canopy depth (Cd) was statistically related to SDI only at age 22. Significant multiple-linear regression models were found between the growth variables and canopy properties with one exception. With that one exception, Iv was significantly related to L during each measurement interval and to F and Cr during the first two intervals. Mean, gross, periodic-annual increment was statistically related only to those canopy variables that described canopy structure. With the exception of F, the overall average value of the canopy variables decreased with age in these loblolly pine plantations, probably leading to the systematic reduction in Iv with age. Although growth-growing stock relations were not significant in these plantations after age 27, the relationships between canopy variables and canopy variables emphasize the importance of early density management to maintain vigorous crowns and growth rates as plantations age.

A LINKED MODEL FOR SIMULATING STAND DEVELOPMENT AND GROWTH PROCESSES OF LOBLOLLY PINE

Linking models of different scales (e.g., process, tree-stand-ecosystem) is essential for furthering our understanding of stand, climatic, and edaphic effects on tree growth and forest productivity. Moreover, linking existing models that differ in scale and levels of resolution quickly identifies knowledge gaps in information required to scale from one level to another, indentifies future research needs to fill these information gaps, and provides a test of the present state of modeling sciences for creating model systems for predicting responses to natural and human-based disturbances.

Signal-transfer modeling for regional assessment of forest responses to environmental changes in the southeastern United States

Stochastic transfer of information in a hierarchy of simulators is offered as a conceptual approach for assessing forest responses to changing climate and air quality across 13 southeastern states of the USA. This assessment approach combines geographic information system and Monte Carlo capabilities with several scales of computer modeling for southern pine species and eastern deciduous forests. Outputs, such as forest production, evapotranspiration and carbon pools, may be compared statistically for alternative equilibrium or transient scenarios providing a statistical basis for decision making in regional assessments.

Addressing multi-use issues in sustainable forest management with signal-transfer modeling

Management decisions concerning impacts of projected changes in environmental and social conditions on multi-use forest products and services, such as productivity, water supply or carbon sequestration, may be facilitated with signal-transfer modeling. This simulation method utilizes a hierarchy of simulators in which the integrated responses (signals) from smaller-scale process models are transferred and incorporated into the algorithms of larger spatial- and temporal-scale models of ecological and economic phenomena. Several innovative procedures germane to multi-issue sustainable forest management have been initiated in our signal-transfer modeling development for forests of the southeastern United States. These developments include response surface interpolation for multi-factor signal-transfer, use of loblolly pine modeling to infer the growth of other southern pines, determination of soil nutrient limitations to productivity, multivariate clustering as a spatial basis for defining land units relevant to forest management, and variance propagation through the modeling hierarchy. Algorithms for larger scale phenomena are shown to constrain the variance introduced from a smaller-scale in a simulation of ambient ozone exposure effects on loblolly pine timber yield. Outputs of forest variables are frequency distributions that may be statistically compared for alternative environmental or management scenarios.