A crown ratio model for Austrian forests

Abstract A crown ratio model for individual trees is developed for all major tree species in Austria. The study is part of a comprehensive project developing a distance-independent single tree growth simulator for the full range of stand conditions in Austria. Data were obtained from the Austrian National Forest Inventory and consist of more than 42 000 trees growing on over 5000 permanent plots measured during 1981 and 1985. Crown ratio was predicted using nonlinear regression with a logistic function. The argument of the logistic was a linear combination of tree size characteristics, stand density measures, and topographic site factors. The total variation explained by the model varied from 49% for larch to 17% for the ‘other broadleaf species’. The model explained 41% of the variation in crown ratio for the principal species, Norway spruce. The model explained less than a quarter of the variation for all the broadleaf species and for stone pine. The effect of the size variables is approximately equal in importance to the variables representing competition for the major species. The set of topographic site factors explained the least amount of variation, less than 10% in all cases. Because the height/diameter ratio, the most important size variable, can also be considered to be an integrator of past competition, the crown ratio model is dominated by competition measures. A validation test using independent data from permanent research plots for the main species (Norway spruce, white fir, Scots pine, and beech) demonstrated that the models appear to be well behaved and robust for both pure even-aged and mixed uneven-aged stand types in Austria. Analyses of the residuals from permanent research plots representing a wide variety of thinning treatments indicate that the effect of management seems to be adequately represented by the model.

[1]  David Bruce.  Yield Differences between Research Plots and Managed Forests , 1977 .

[2]  Douglas A. Maguire,et al.  Constructing models for direct prediction of 5-year crown recession in southwestern Oregon Douglas-fir , 1990 .

[3]  Donald W. Marquaridt.  Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation , 1970 .

[4]  Harold E. Burkhart,et al.  Compatible crown ratio and crown height models , 1987 .

[5]  E. D. Ford,et al.  Simulation of branch growth in the Pinaceae: Interactions of morphology, phenology, foliage productivity, and the requirement for structural support, on the export of carbon† , 1990 .

[6]  Stephen R. Shifley,et al.  A generalized system of models forecasting Central States tree growth. , 1987 .

[7]  Ronald D. Snee,et al.  Some Aspects of Nonorthogonal Data Analysis: Part I. Developing Prediction Equations , 1973 .

[8]  D. Hann,et al.  A Stem Dissection Technique for Dating Branch Mortality and Reconstructing Past Crown Recession , 1987 .

[9]  H. Mayer.  Waldbau : auf soziologisch-ökologischer Grundlage , 1977 .

[10]  G. Somers,et al.  Methods for Modeling Individual Tree Growth and Stand Development in Seeded Loblolly Pine Stands , 1979 .

[11]  Harold E. Burkhart,et al.  Predicting Crown-Height Increment for Thinned and Unthinned Loblolly Pine Plantations , 1992, Forest Science.

[12]  D. Hann,et al.  Longevity and duration of radial growth in Douglas-fir branches , 1990 .

[13]  T. Kozlowski.  Growth and Development of Trees , 1971 .

[14]  Jari Hynynen,et al.  Predicting tree crown ratio for unthinned and thinned Scots pine stands , 1995 .

[15]  R. M. Newnham.  The development of a stand model for Douglas fir , 1964 .

[16]  R. Monserud,et al.  Methodology for simulating Wisconsin Northern Hardwood stand dynamics , 1980 .

[17]  A. E. Hoerl,et al.  Ridge Regression: Applications to Nonorthogonal Problems , 1970 .

[18]  Douglas A. Maguire,et al.  A sampling strategy for estimating past crown recession on temporary growth plots. , 1990 .

[19]  J. Krajícek,et al.  Crown competition-a measure of density. , 1961 .

[20]  E. David Ford,et al.  Structure and basic equations of a simulator for branch growth in the Pinaceae , 1990 .

[21]  John Neter,et al.  On the Appropriateness of the Correlation Coefficient with a 0, 1 Dependent Variable , 1970 .

[22]  William R. Wykoff,et al.  A Basal Area Increment Model for Individual Conifers in the Northern Rocky Mountains , 1990, Forest Science.

[23]  R. Monserud,et al.  A basal area increment model for individual trees growing in even- and uneven-aged forest stands in Austria , 1996 .