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A Longitudinal Analysis of Height/Diameter Curves

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The paper describes a simultaneous statistical analysis of height/diameter curves in data consisting of several temporal and permanent plots. Two jack pine data sets, one from planted stands and the other from naturally regenerated stands, were analyzed using the same model structure. Parameters of a logarithmic height/diameter curve at a given age in a given stand were decomposed into a trend (an age-dependent population mean), a random stand effect, and a random time effect. The deviation of an observed height from the stand and age specific height/diameter curve was decomposed into a random tree effect and a random residual error which have nonhomogeneous variances. Trend functions for the parameters of the height/diameter curve were estimated using least squares estimates of parameters as dependent variables (generalized least squares would lead to inconsistent estimates). The trend equations describe most of the variation in the height curve parameters. Other stand variables (in addition to age) can explain the variation further, but development over time cannot then be predicted. A less stable description of the height/diameter curves is obtained in terms of dominant height. In applications, height/diameter curves can be calibrated by predicting the random stand and time effects using any combination of height measurements. A simultaneously estimated set of curves will be logical also when there are so few measurements that ordinary least squares curves show erratic fluctuations. For. Sci. 43(4):555-570.

Keywords: Dominant height; random parameters; simultaneous estimation; site index; variance components

Document Type: Journal Article

Affiliations: Finnish Forest Research Institute, Suonenjoki Research Station, FIN-77600 Suonenjoki, Finland., Fax: 358-17-513068

Publication date: 1997-11-01

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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