Finnish Forest Research Institute  Metla

Press release 14.8.2006

Linear programming to provide more exact information on stem characteristics

The Finnish Forest Research Institute (Metla) has developed a linear programming (LP) method for creating more accurate height/age curves by using stem analysis materials.

In a stem analysis, the stem is cut in bolts of specified length and a ring count is performed from each crosscut. Often also the width of the ring is measured. The problem with using the stem analysis results as a basis for a height/age curve is that the method only reveals the bolt where height growth ends.

In this study, a method was developed to produce more smoother height curves than those gained by previous methods. In the new method, smooth curves are obtained by minimizing the sum of absolute values of second order differences of heights. Constraints for the height curve are the known bolts where height growth has ended. The created minimization task can then be solved by linear programming. However, the height curve created as a result may be too smooth, if it removes not only artificial variation but also significant non-linear trends. To obtain a smoother curve constraints can be added based on the assumption that the crosscut occurs randomly within the annual height increment.

The LP method was tested by using simulated data. With short bolts and regular height growth the method provided better results than earlier methods. With longer bolts or less regular growth the new method remained optimal for longer with regard to estimating height growth than height. If the aim is to produce accurate estimates of height curves and especially height growth by using the stem analysis method and by cutting short bolts, the additional work necessitated by the presented LP method may be well justified. However, the new method needs empirical testing using accurately measured material to determine the most suitable bolt length for the method.

Publication: Lappi, J. 2006. Smooth height/age curves from stem analysis with linear programming. Silva Fennica 40(2): 291-301.

The study summary in Finnish was published in Metsätieteen aikakauskirja 2/2006, p. 334. (pdf)

Additional information:

Press releases in English are available at:   Metlan RSS-newsfeed
Finnish Forest Research Institute - Metla/Communications
Unioninkatu 40 A, FI-00170 HELSINKI, FINLAND. Phone +358 10 211 2000    E-mail: info @