Next Article in Journal
On the Use of Hedonic Price Indices to Understand Ecosystem Service Provision from Urban Green Space in Five Latin American Megacities
Previous Article in Journal
Aboveground Biomass Equations for Small Trees of Brutian Pine in Turkey to Facilitate Harvesting and Management
Article Menu
Issue 12 (December) cover image

Export Article

Open AccessArticle
Forests 2017, 8(12), 479; https://doi.org/10.3390/f8120479

A Linkage among Tree Diameter, Height, Crown Base Height, and Crown Width 4-Variate Distribution and Their Growth Models: A 4-Variate Diffusion Process Approach

1
Institute of Forest Management and Wood Sciences, Aleksandras Stulginskis University, Kaunas, LT 53361, Lithuania
2
Centre of Mathematics, Physics and Information Technologies, Aleksandras Stulginskis University, Kaunas, LT 53361, Lithuania
*
Author to whom correspondence should be addressed.
Received: 23 October 2017 / Revised: 19 November 2017 / Accepted: 1 December 2017 / Published: 4 December 2017
(This article belongs to the Section Forest Inventory, Quantitative Methods and Remote Sensing)
Full-Text   |   PDF [4107 KB, uploaded 5 December 2017]   |  

Abstract

The evolution of the 4-variate probability distribution of the diameter at the breast height, total height, crown base height, and crown width against the age in a forest stand is of great interest to forest management and the evaluation of forest resources. This paper focuses on the Vasicek type 4-variate fixed effect stochastic differential equation (SDE) to quantify the dynamic of tree size components distribution against the age. The new derived 4-variate probability density function and its marginal univariate, bivariate, trivariate, and conditional univariate distributions are applied for the modeling of stand attributes such as the mean diameter, height, crown base height, crown width, volume, and slenderness. All parameters were estimated by the maximum likelihood procedure using a dataset of 1630 Scots pine trees (12 stands). The results were validated using a dataset of 699 Scots pine trees (five stands). A newly developed 4-variate simultaneous system of SDEs incorporated covariance structure driving changes in tree size components and improved predictions in one tree size component given the other tree size components in the system. View Full-Text
Keywords: diameter; height; crown base height; crown width; mean stem volume; slenderness; 4-variate stochastic differential equation; conditional probability density function diameter; height; crown base height; crown width; mean stem volume; slenderness; 4-variate stochastic differential equation; conditional probability density function
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Rupšys, P.; Petrauskas, E. A Linkage among Tree Diameter, Height, Crown Base Height, and Crown Width 4-Variate Distribution and Their Growth Models: A 4-Variate Diffusion Process Approach. Forests 2017, 8, 479.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Forests EISSN 1999-4907 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top