Articles by Pekka Kilkki

This paper is a review on the development of sustainable forest management and what has been meant with the term in different times. The article summarises the birth of sustainable use of forests in the world and in Finland, and discusses sustainability in forest management, for instance from the point of view of one forest holding, large clearcuttings performed in Lapland, biological sustainability, business economics and overall planning.

• Kilkki, E-mail: pk@mm.unknown

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 paper demonstrates the possibility of using data from small relascope sample plots in the derivation of the regression models which predict the Weibull function parameters for the dbh-distribution. The Weibull parameters describing the basal area dbh-distribution were estimated for relascope sample plots from the Finnish National Forest Inventory. In the first stage of the estimation nonlinear regression analysis was employed to derive initial parameter estimates for the second stage, in which the maximum likelihood method was used. The parameter estimates were employed as dependent variables for the derivation of the regression models; the independent variables comprised of the compartment-wise stand variables generally estimated in ocular inventories.

The PDF includes an abstract in Finnish.

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

Thinning models are generally based on the density of the stand measured by the average basal area per hectare, for instance. These models are handicapped by the uneven structure of the stands. In uneven stands the averages are inadequate indicators for the need and amount of thinnings.

Small relascope plots were tested in the measurement of the spatial distribution of trees and in the determination of the need and amount of thinnings. The thinning quantity was determined as the difference between the actual distribution of the relascope plots into basal area classes and the ideal distribution after thinning. Sequential sampling was used in the derivation of the decision equations. A respective BASIC-program for a programmable pocket calculator is given.

The PDF includes a summary in English.

• Kilkki, E-mail: pk@mm.unknown
• Pohjola, E-mail: tp@mm.unknown
• Pohtila, E-mail: ep@mm.unknown

This article is a book review on German textbook 'Forstinventur' by Fritz Zöher that handles forest inventory.

• Kilkki, E-mail: pk@mm.unknown

This paper presents the principles of a unified data processing system suitable for derivation of the most variables of interest in forest mensuration. The precedence (succedence) relations between the tree and forest stand variables are analysed and a block-wise simultaneous recursive multi-equation model is suggested to describe these relations. Regression analysis is used in the estimation of the model parameters and Taylor’s series and Monte Carlo simulation are available in the derivation of the unbiased results.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown

In the original set of equations derived by regression analysis, relative-height diameters (endogenous variables) are presented as nonlinear functions of the other relative-height diameters and of the height of the tree (an exogenous variable). Any of the original equations can be replaced by an interpolation formula which links a measured diameter to the four closest relative-height diameters. The solution of the simultaneous equation model yields 10 relative-height diameters. Intermediate values are obtained to avoid biases due to the nonlinearity of the simultaneous model equations.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Varmola, E-mail: mv@mm.unknown

A simultaneous equation model to determine taper curve for Scots pine is presented. The diameters at relative heights are endogenous variables and height an exogenous variable. Any equations may be substituted by the measured value of diameter. Solution of the system of equations yields 11 diameters at relative heights. Intermediate values are obtained by interpolation. Interpolation allows the use of diameters measured at absolute heights, too.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Saramäki, E-mail: ms@mm.unknown
• Varmola, E-mail: mv@mm.unknown

The planning of timber production in a forestry unit is divisible into two phases. In the first phase, planning provides the decision-maker with a number of possible timber production policies; these policies define the production possibility boundary. After the decision-maker has chosen one of these policies, planning moves to the second phase, in which a detailed programme is prepared with a view to meeting the requirements of the timber production policy accepted. The paper indicates one possibility of solving these two tasks simultaneously. In the first phase, the solution of the primal linear programming problem is employed and in the second phase the respective dual or shadow price solution.

The PDF includes a summary in English.

• Kilkki, E-mail: pk@mm.unknown
• Pökälä, E-mail: rp@mm.unknown
• Siitonen, E-mail: ms@mm.unknown

This paper is a book review of a book Beståndsvård och productionsekonomi by Kunglig Skogstyrelsen from Sweden.

• Kilkki, E-mail: pk@mm.unknown

The aim of this paper was that of studying the optimum growing schedules of forest stands, with the classic Faustmann formula as starting point. The study is mainly theoretical in nature. The study shows that the net present-value of the future revenues from a forest stand can be calculated, not only by means of the harvesting revenues, but also by a more theoretical concept, here termed the current gross soil rent. The current gross soil rent represents the difference between the current value growth and the rent of the growing stock.

By use of the concepts described here, it is theoretically possible to find the growing schedule for the stand which maximizes the net present-value of the stand. To make the formulae simpler, a one-year period has been adopted for discussion of the concepts involved in determination of the optimum structure and density of the growing stock, and the financial maturity. However, these concepts can be extended to cover periods of any length.

The method for determination of the optimum growing schedule for a forest stand can be summarized as follows: Thin the stand as the internal rate of return on the marginal increase in ’timber capital’ falls below the guiding rate of interest. Clear-cut and regenerate the stand as the internal rate of return on the sum of the ’timber and soil capital’ falls below the guiding rate of interest.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown

This paper reports on tests made for the study of alternative methods in forest survey. Data were acquired by measurements in five areas in Finland and in Mexico, varying in size from 20 to 900 ha. The principal characteristics used in the analysis was the entire volume. By the combination of neighbouring plots, the variation could be studied for different plot sizes and survey strips. Variable (relascope) plots could be compared.

A starting point for the comparison of different sampling methods, calculations were made of the coefficients of variation for each plot type; total and within the strata. The amount of decrease of variation with an increasing plot size could be established. Comparisons have been made of the following sampling methods: simple random, stratified random, simple systematic, and stratified systematic sampling.

On comparisons of the standard error of sample mean it was found that in both stratified sampling and different types of systematic sampling there is, with increasing size and diminishing interval of sample plots, an increase in the relative improvement of the result against simple random sampling. Only in exceptional cases did systematic surveys give results which were less precise than those derived by other methods.

In discussion of some methods for determination of the precision of systematic sampling, possibilities of theoretical determination of the degree of precision was considered. An empirical study was made of the behaviour of some equations based on the sample itself. The larger the plot size and the shorter the plot interval, the more the equations overestimated in general the variance of sample mean.

As none of the equations studied gave reliable results, regression equations were calculated for the relative standard error on the basis of the data measured. The independent variables were plot size, plot or strip interval, area of survey unit and mean volume. The results arrived at are based mainly on the complete measurement of one area only. To enable extension of the scope of application, more material is needed with a complete enumeration of trees.

The PDF includes a summary in Finnish.

• Nyyssönen, E-mail: an@mm.unknown
• Kilkki, E-mail: pk@mm.unknown
• Mikkola, E-mail: em@mm.unknown

Highest degree of precision in determining the areas of different strata in forest survey is achieved when the areas are measured from a map. However, in practice the stratum-areas usually need to be determined on the basis of samples taken in the field or from aerial photographs. The goal of the present investigation was to determine the precision in stratum-area estimation on the application of different sampling methods.

Three sampling methods were used: 1. sampling with random plots, 2. uniform systematic plot sampling, and 3. sampling with equidistant lines.

The dependence of the standard error of stratum-areas in systematic line and plot sampling was examined by regression analysis. The models for regression equations were derived from random sampling formulae. It appears that the characteristics of these formulae were applicable as variables in the regression equations for systematic samples. Also, some characteristics of the distribution of the stratum was found, which seem to influence the error in sampling with equidistant lines.

The results as regards uniform systematic plot sampling indicate that the use of random sampling formulae leads to considerable over-estimation of the standard error. Nonetheless, unless relatively short intervals between sample plots are used in the forest survey made on the ground, it is of advantage to study the division of the area into strata by measuring the distribution of the survey lines in these strata.

The results can be used in two ways: for estimation of the precision in a survey already made, or to predetermine the sample size in a survey to be made. The results may be applicable to areas ranging from 100 to 1,000 ha in size, as well as to larger areas.

• Nyyssönen, E-mail: an@mm.unknown
• Kilkki, E-mail: pk@mm.unknown

The purpose of this paper is to review tests made on the basis of Finnish material with regard to the efficiency of the 10-point cluster in sampling a stand in forest inventory. Currently, this system is applied in field work in the national forest surveys in the United States of America. The paper reports on tests, made on the basis of Finnish material, for comparison of the 10-point cluster of variable plots with 13 other designs in sampling a stand in forest survey. The research material consists of 12 stands, with Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) H. Karst.) as the main species.

The main results are concerned with the ability of different designs to provide gross volume estimates. As a measure of efficiency, three alternative series of variances were used, adjusted by three alternatives of time. The results are applicable, for instance, in double-sampling with photo and field classifications. In the comparisons, no attention was paid to the possibility of systematic errors in various designs.

For inventory volume, the 10-point cluster proved to be about 10 per cent less efficient than the best design of each alternative. The use of a single circular plot of 1,000 m² can be recommended under the conditions of this test; furthermore, one or two 500 m² plots were more efficient than any combination of variable plots.

The reason for the use of the 10-point cluster in forest surveying has been the ability of the design to provide simultaneous information on area condition classes. Among the designs tested, the 10-point cluster seems to be the only one capable of application in the estimation of condition classes.

Most of the information obtained by means of the 10-point cluster can be gained through ocular estimation, and from the sample trees to be measured in any design, but a cluster of several points appears to offer good means of estimation, for instance, of the presence of clumps and gasps in a stand.

• Nyyssönen, E-mail: an@mm.unknown
• Kilkki, E-mail: pk@mm.unknown

The objective of this study has been to discover some of the basic principles on which an increment for a large forest area might be forecast. Because the stands in a large forest area vary considerably in density and are subject to different kinds of treatment, the main interest falls on the stand characteristics which determine the increment percentage in such forest conditions as these. The material used in the study has been published earlier, it consisted of sample plots of Scots pine (Pinus sylvestris L.) stands (Nyyssönen 1954).

Increment functions are of great importance in the increment forecast for cutting budget. Because 60-80% of the variation in the increment percentage can be explained by stand characteristics in circumstances where the age of the stand is 40-130 years and the volume vary with a coefficient of variation 0.6-0.7, regression equations for increment percentage may be based on a number of sample plots smaller than in a growing stock inventory in the same conditions. It is possible to get accurate results with relatively small number of sample plots. Furthermore, the smaller amount of increment sample plots makes it possible to develop measurement techniques.

The increment functions enable study of increment as a biological process. However, conclusions about biological process on the basis of regression equations should be made with caution. Still, regression analysis is a powerful tool in yield studies.

The PDF includes a summary in Finnish.

• Kuusela, E-mail: kk@mm.unknown
• Kilkki, E-mail: pk@mm.unknown

Analysis of sample tree data showed that the major part of the residual variation of the stem volume estimates occurs within the forest stands. The division of the residual variation into the variation within and between populations is the basis for the mean-square error formulae of the volume estimators. Efficiency of different sample tree measurement combinations has been studied by comparing the errors of the volume estimates to the sampling costs. The measurement of the upper diameter (d6) is of less value than is generally suggested.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown

Taper curve models based on simultaneous equations were derived. The data consisted of 492 Scots pines (Pinus sylvestris L.) from Southern Finland. Two systems of simultaneous equations were constructed, one without the crown ratio and the other with the crown ratio as an exogenous variable. The endogenous variables consisted of 24 relative-height diameters and the height of the tree. The parameters of the model were derived by the ordinary least squares method.

In most applications, the height of the tree was exogenised. The logarithmically linear relationships between the relative-height diameters were utilized in the solution algorithm. The algorithm included both standard matrix operations and an iterative part in which the taper curve was fitted to any measured diameters by the natural cubic spline interpolation formula.

The models were applied to the derivation of taper curves, stem volumes, timber assortment percentages, and stem values. An experiment was also made to derive diameter and height increments from the taper curve model.

The reliability of the models was tested on the original data.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Varmola, E-mail: mv@mm.unknown

The purpose of this study was that of providing a long-term timber production model (Kilkki and Pökkälä 1975) with growing stock models. The paper is divided into two parts; the first is concerned with generation of the stand data through Monte-Carlo simulation. The growing stock of each stand was described by a DBH-height distribution. The necessary information on the relationships between the stand characteristics was derived from sample plots measured in the national forest inventory of Finland. A total of 1,500 Scots pine (Pinus sylvestris L.), Norway spruce (Picea abies (L.) H. Karst), and birch (Betula sp.) stands, each comprising 100 trees were provided by simulation.

In the second part, models predicting the form factor, timber assortment distribution, and value of the growing stock were derived through regression analysis for each species of tree. The predicting variables included the form factor of the basal area median tree, basal area median diameter, and height in the form factor models. In the timber assortment and value models, the only predicting variable was the volume of the basal area median tree. The Matchcurve-technique (Jensen 1973) was employed in derivation of the regression models.

The PDF includes a summary in English.

• Kilkki, E-mail: pk@mm.unknown
• Siitonen, E-mail: ms@mm.unknown

A long-term timber production model was developed. The model is based upon numerical simulation and it is viewed only as a means of providing the decision-maker with values of the predicting variables in his utility function. Special attention was paid to the development of automatic cutting decision rules. The model was applied to the area of 2,752,000 hectares of forest land in Central Finland. The measurement data were extracted from the Sixth National Forest Inventory, which was made in 1973. Utilities from a hypothetical utility function were attained to a number of feasible timber production policies. The Bayes and maximin criteria were employed to evaluate these policies.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Pökälä, E-mail: rp@mm.unknown

Production of timber in forest stands is described by a production function. The variable inputs of the function are land and growing stock and the output is the annual value growth. The partial derivatives of this production function express the marginal productivity of the land and of auction function express the marginal productivity of the land and of the growing stock. These marginal productivities can be utilized for determination of the need of regeneration and thinning. The stand should be regenerated when the marginal productivity of the land falls below the annual rent of a unit area of open land and thinned when the marginal productivity of the growing stock falls below the annual rent of one unit of growing stock.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown

Emphasis was laid on the finding of regression equations to indicate the dependence of standard error upon various variables in systematic sampling. As a result, the size of sample for a given precision could be computed, under varying alternatives of sample plot size and type. Another task was that of examining inventory costs by means of time studies. On combination of the results in regard to the sample size and survey time, the relative efficiency of different alternatives could be discussed, with a view to the precision of the total volume of growing stock.

The PDF includes a summary in Finnish.

• Nyyssönen, E-mail: an@mm.unknown
• Roiko-Jokela, E-mail: pr@mm.unknown
• Kilkki, E-mail: pk@mm.unknown

The purpose of this study was determining the optimum cutting program for forest stands by the application of dynamic programming. Calculations have been made for even-aged Scots pine (Pinus sylvestris L.) stands in Southern Finland, aged 50-100 years. Three logging cost levels, thinning from below and from above, and rates of interest of 1, 2, 3, 4, and 5% was applied. Both optimum routes and the economic results of different cutting programs was analysed.

According to the results, the higher the rate of interest is, the lower the density remains, and shorter the rotation is. The starting level of the growing stock may influence the treatment of the stand for tens of years. If logging costs change, so that harvesting small wood becomes relatively more expensive in the future, the density of growing stock will increase. However, heavy thinnings today are recommendable, to avoid expensive thinnings in the future.

The density of the growing stock should be higher if thinning from above is applied, instead of thinning from below. The growth of the stands thinned from below needs to be greater than the growth of stands thinned from above, to justify thinnings from below. Too high density often results in larger losses than do too low a density or the wrong rotation. Thinnings seem to be profitable even at much higher logging costs than those of today. The maturity of the stand is determined both by the age and the density of the growing stock. The stand may be mature because of great age, high density combined with a relatively high age, or because the growing stock is too low in density.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Väisänen, E-mail: uv@mm.unknown

The aim of this study was to develop cutting budget methods for a forest undertaking. Cutting budget provides information on the future income from the forest undertaking, and on the development of the forest.

Two cutting budget models have been developed, by the application of simulation and linear programming. Both of the models are deterministic in nature, i.e. there is only one possible outcome once the stated input information has been given. To make the models simpler, it has been assumed that thinning and clear cutting with reforestation are the only activities that can occur in the forest. The models are directly applicable only to forests consisting of even-aged Scots pine stands at three different forest types. However, they can easily be extended to cover forests comprising several tree species and more sites.

In the light of this study, simulation seems today to be more appropriate than linear programming in the preparation of cutting budgets. However, the increasing capacity of computers may even in the near future make linear programming quite competitive, especially as if it is borne in mind that the theoretical basis of linear programming is much firmer than that of simulation. The most advisable cutting budget method might consist of a combination of simulation and linear programming. Simulation could be employed to find a rough cutting schedule, and linear programming to test and improve the solution.

The PDF includes a summary in Finnish.

• Kilkki, E-mail: pk@mm.unknown