Silva Fennica : quarterly issues : 41(4) : sa414671.htm

Lauri Korhonen, Kari T. Korhonen, Pauline Stenberg, Matti Maltamo & Miina Rautiainen. 2007.

Local models for forest canopy cover with beta regression

Silva Fennica 41(4): 671–685

Accurate field measurement of the forest canopy cover is too laborious to be used in extensive forest inventories. A possible alternative to the separate canopy cover measurements is to utilize the correlations between the percent canopy cover and easier-to-measure forest variables, especially the basal area. A fairly new analysis technique, the beta regression, is specially designed for modelling percentages. As an extension to the generalized linear models, the beta regression takes into account the distribution of the model residuals, and uses a logistic link function to ensure logical predictions. In this study, the beta regression method was found to perform well in conifer dominated study area located in central Finland. The same model shape, with basal area, tree height and an additional predictor (Scots pine: site fertility, Norway spruce: percentage of hardwoods) as independent variables, produced good results for both pine and spruce dominated sites. The models had reasonably high pseudo R-squared values (pine: 0.91, spruce: 0.87) and low standard errors (pine: 6.3%, spruce: 5.9%) for the fitting data, and also performed well in a cross validation test. The models were also tested on separate test plots located in a different geographical area, where the prediction errors were slightly larger (pine: 8.8%, spruce: 7.4%). In pine plots, the model fit was further improved by introducing additional predictors such as stand age and density. This improved also the performance of the models in the cross validation test, but weakened the results for the external data set. Our results indicated that the beta regression method offers a noteworthy alternative to separate canopy cover measurements, especially if time is limited and the models can be applied in the same region where the modelling data were collected.

beta regression, canopy cover, forest canopy

L. Korhonen and Maltamo, University of Joensuu, Faculty of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland; K.T. Korhonen, Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 68, FI-80101 Joensuu, Finland; Stenberg and Rautiainen, Univ. of Helsinki, Dept of Forest Resource Management, P.O. BOX 27, FI-00014 University of Helsinki, Finland. E-mail

Received 15 May 2007 Revised 13.9.2007 Accepted 4 October 2007
ISSN 0037-5330

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