Articles containing the keyword 'Weibull function'

The paper continues an earlier study by Kilkki and Päivinen concerning the use of the Weibull function in modelling the diameter distribution. The data consists of spruces (Picea abies (L.) H. Karst.) measured on angle count sample points of the National Forest Inventory of Finland. First, maximum likelihood estimation method was used to derive the Weibull parameters. Then, regression models to predict the values of these parameters with stand characteristics were calculated. Several methods to describe the Weibull function by a tree sample were tested. It is more efficient to sample the trees at equal frequency intervals than at equal diameter intervals. It also pays to take separate samples for pulpwood and saw timber.

The PDF includes an abstract in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Maltamo, E-mail: mm@mm.unknown
• Mykkänen, E-mail: rm@mm.unknown
• Päivinen, E-mail: rp@mm.unknown

The study presents a growth and yield prediction model for a Pinus kesiya (Royle ex Gordon) stand by diameter classes. The material consists of temporary sample plots taken from a plantation inventory, of permanent sample plots established in commercial compartments and of an espacement trial. The mean basal area of the stand, variance and skewness of the diameter distribution are predicted. From these variables the parameters of the Weibull function are derived. Site class is assumed to be known or is calculated from measured information. Mortality is also predicted by estimating the number and mean size of dead trees. Thinnings are defined by the number of trees removed and by their relative size. If measured tree level data at the initial situation is available it can be utilized in the predictions, however, simulations can also be performed with stand level information. The minimum information needed for the prediction is planting density, site class as well as the times and removals of thinnings.

The calculations show that by decreasing the planting density of P. Kesiya from the present 1,330 stems/ha or by conducting early precommercial thinning both the relative and absolute amount of large sawlogs in the total production increase. An increase in the present planting density only slightly increases total yield. It is obvious that the presently recommended rotation of 25 years is too short for producing large sawlogs, especially on poor sites. This rotation period is suitable for small sawlog production while for pulpwood regimes shorter rotation periods can be used. If thinnings are done before the maximum current annual growth is reached stands will react well, but later on the ability to respond to thinnings decreases rapidly. Thinnings from below accelerates the production of large sawlogs more than thinning from above or systematic thinning. If all sawlog sizes are considered no great differences between thinning type exist. The study recommends different thinning regimes according to site class. Separate programs are recommended for the production of sawlogs and pulpwood.

The used thinning reaction model needs refinement and further studies with annual measured thinning trial material.

The PDF includes a summary in Finnish.

• Saramäki, E-mail: js@mm.unknown

This study examined a theoretical model for stand structures from the volumes of pulpwood and saw logs of clear-cut stands. The average stem size was used to estimate the number of cut trees. The distribution was solved using nonlinear derivative-free optimization. The truncated 2-parameter Weibull distribution was used to describe the stand structure of the commercial stems. This method was first tested with harvester data collected from seven clear-cut stands in southern Finland. Validation included reliability in the stand characteristics and goodness-of-fit of the species-specific distributions. The distributions provided unbiased estimates for the saw log volume, while the bias in the estimated pulpwood volume was 2%. The standard stand characteristics from the Weibull distributions corresponded notably well with the harvester data. A Kolmogorov-Smirnov (KS) test rejected two distributions out of 21 cases, when the accurate input variables were available for the theoretical model. The results of the study suggest that the presented method is a relevant option for predicting the stand structure. In practice, the reliability of the presented method was dependent on the quality of the information available from the stand prior to cutting. With a timber trade data set, the solution for the distribution for a clear-cut section was found. The goodness-of-fit was dependent on the accuracy of the visually assessed timber trade variables. Especially the average stem size proved difficult to assess due to high number of understorey pulpwood stems. Due to overestimated average stem sizes, the solved number of harvested trees was underestimated. Less than 50% of the distributions predicted for clear-cut sections passed the KS test.

• Siipilehto, Natural Resources Institute Finland (Luke), Latokartanonkaari 9, P.O. Box 2, FI-00790 Helsinki, Finland E-mail: jouni.siipilehto@luke.fi
• Rajala, Metsä Group, Revontulenpuisto 2, P.O. Box 10, 02020 METSÄ, FI-02100 Espoo, Finland E-mail: miika.rajala@metsagroup.com

• Palahí, Centre Tecnológic Forestal de Catalunya. Passeig Lluis Companys, 23, 08010, Barcelona, Spain E-mail: marc.palahi@ctfc.es
• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, 80101 Joensuu, Finland E-mail: tp@nn.fi
• Trasobares, Foreco Technologies, Av. Diagonal 416, Estudio 2, Barcelona 08037, Spain E-mail: at@nn.es

• Siipilehto, Finnish Forest Research Institute, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: jouni.siipilehto@metla.fi

• Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail: annika.kangas@metla.fi
• Maltamo, Finnish Forest Research Institute, Joensuu Research Station, P.O. Box 68, FIN-80101 Joensuu, Finland E-mail: mm@nn.fi