A shifting algorithm to simulate thinnings from below and above

Thinning is a silvicultural practice to improve tree growth and health. Thinning from below for the even-aged silviculture and thinning from above for the uneven-aged silviculture are the two mainly applied thinning practices. In forest management simulations, algorithms that describe which individual trees to be removed from a forest have developed in five growth simulators (Söderbergh and Ledermann, 2003). We have developed a shifting algorithm that determines the proportion of trees to be thinned from different diameter classes to complement the individual tree selection algorithms. Sampled (or mapped) tree diameters are grouped into diameter classes. Given the target thinning volume, the algorithm automatically computes the thinning rate in each of the diameter classes using the three-parameter Weibull distribution. The thinning rate is obtained by shifting the location parameter of an estimated Weibull distribution either to the right or to the left for thinnings from below and above, respectively. A modified bisection method is used to search for the new location parameter that yields the desired thinning volume. The proposed algorithm is demonstrated in examples by using experimental forest datasets. A stand-alone program called Weibull_thinning is downloadable at http://www.it.abo.fi/suswood/weibull_thinning/.