Epsilon Archive for Student Projects

Abstract

Growth models are very useful tools for forestry to predict growth and yield. With growth models and optimising tools you can manage forest stands in a way that maximize benefit and income. There are three major types of growth models. Stand models; stage structured models and single-tree models. The most advanced models give the most accurate forecasts. But they also require a high amount of input data, which can be expensive. Therefore it is important to make a cost benefit analyse when you are deciding what kind of model you need.

Single-tree models are the most common growth models in Sweden today. There are models that include all profitable species in different conditions. The interest in Sweden for stage-structured models is low, though there are several models developed in other countries. For example, Kolström (1992) in Finland and Solberg and Haight (1992) in Norway. There are some advantages of stage structured models compared to single-tree models. Single-tree models can be very complex and include many variables, which can be a problem when using the models in optimisations. A stage-structured model includes few variables and may be easier to understand. The purpose of this paper is to develop a stage-structured, diameter-class model. Some restrictions have been made to make it possible. The most important is that the model only includes Norway spruce and stands with high site productivity.

The model is based on material from the Swedish National Forest Inventory. Approximately 11 400 trees distributed on 660 sample plots are included in the material. The sample plots have been inventoried twice with a time interval of five years. The difference in diameter for each tree is the growth. Other variables in the model are also given by this inventory. Stand variables are age, basal area, site index, basal area weighted mean diameter and a variable that indicates thinning within ten years before the inventory. Diameter is the only class variable.

The model in this paper has its roots in Leslie and Lewis's growth models. Their model was constructed to study animal populations. It consists of vectors that describe state while a matrix describes transitions from state to state. In this model there are three transition probabilities for each class: a, the probability that trees in the class will be in the same class in five years, b, the probability that trees in the class will be found in the class above and c, the probability that trees will have grown two classes or more. Logistic regression was applied to get these transition probabilities.

The model was tested against the material to see if there were any systematically errors. The result shows that the model follows the material fairly well. It overestimates the growth with approximately ten percent. To see how it functions in a longer time-perspective, six long-term research stands were used. Rather large over- or underestimates is found in four stands, whereas in two stands the model shows a good result. The deviations of predicted growth from actual growth seems rather to have to do with the general growth level while the thinning response appears to be reflected fairly well by the model.

There are likely several reasons that could explain the growth prediction errors of the model. The most important is probably that no correction for different yearly growth due to climate was done to the diameter. It is usually done in growth models and it was a mistake that it was not done in this paper. Another thing that could have made the result better is if there would have been administrative tools available during the work with the logistic regression. This made it difficult to revise the model and introduce improvements. However, the result shows that it should be possible to make good stage-structured, diameter class models with the proposed improvements and the experience from this paper.