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Modeling individual tree height to diameter ratio for Norway spruce and European beech in Czech Republic

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The purposed spatially explicit and spatially non-explicit height to diameter ratio models can be useful to evaluate the stability of trees and stands for Norway spruce and European beech forests.

Abstract

Height to diameter ratio (HDR) is an individual tree index, also known as slenderness coefficient, and commonly used to evaluate stability of trees and stands. We developed both spatially explicit and spatially non-explicit HDR models for Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) using a large dataset collected from fully stem-mapped permanent research plots in various parts of the Czech Republic. Various tree and stand characteristics were evaluated for their potential contributions to the the HDR models. In addition to diameter at breast height (DBH), other highly significant predictor variables identified are dominant height (HDOM) (site quality measure), dominant diameter (DDOM) and quadratic mean diameter (QMD) (spatially non-explicit competition measures), and Hegyi’s index (spatially explicit competition index, CI). A simple exponential decay function was chosen as a base function to include these predictor variables. Both spatially explicit and spatially non-explicit models described large parts of the HDR variations [R 2adj  = 0.66 (Norway spruce), 0.72 (European beech)] without any systematic deviation of the residuals across the observed data range. Unlike for European beech, spatially explicit model for Norway spruce better described HDR variations than its spatially non-explicit counterpart. After DBH, HDOM provided the largest contribution to each model type, followed by DDOM and QMD or CI for both species. The HDR increased with increasing HDOM and CI, but it decreased with increasing DDOM and QMD, suggesting there were significantly large effects of site quality and stand density on HDR. Because of a little difference between the fit statistics and graphical displays of the two model types, spatially non-explicit model is recommended for prediction of HDR for both species as this model does not require spatially explicit CI, which is computationally much more complex than spatially non-explicit competition measures. The proposed HDR models may be applicable to assess stability of trees and stands, and to regulate stand densities.

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Acknowledgments

This study was Supported by the projects Optimization of Agriculture Land Afforestation in Relation to Increase of Landscape Retention Potential (Project No. QJ1320122) and Internal Grant Agency (IGA No. B08/15), Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague. We thank two anonymous reviewers for their constructive comments and suggestions that helped improve the manuscript.

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  1. Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague, Kamýcká 129, 16521, Praha 6-Suchdol, Prague, Czech Republic

    Ram P. Sharma, Zdeněk Vacek & Stanislav Vacek

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  1. Ram P. Sharma
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Sharma, R.P., Vacek, Z. & Vacek, S. Modeling individual tree height to diameter ratio for Norway spruce and European beech in Czech Republic. Trees 30, 1969–1982 (2016). https://doi.org/10.1007/s00468-016-1425-2

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