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Silva Fennica 1926-1997
Acta Forestalia Fennica

Articles containing the keyword 'Parameter'.

Category: Research article

article id 10220, category Research article
Arnis Gailis, Pauls Zeltiņš, Andis Purviņš, Juris Augustovs, Valts Vīndedzis, Inga Zariņa, Āris Jansons. (2020). Genetic parameters of growth and quality traits in open-pollinated silver birch progeny tests. Silva Fennica vol. 54 no. 2 article id 10220.
Highlights: Growth and stem quality traits were under strong genetic control; Weak genetic correlations between tree growth and stem quality were found; Strong age-age and type-B correlations suggest robust improvement over time and different environments; Simultaneous improvement of growth and stem quality might be applicable.

Genetic parameters of growth and stem quality traits were estimated for open-pollinated silver birch Betula pendula Roth progenies in Latvia at the age of 10 and 14 years. Tree height and stem volume were found to be under strong genetic control at both inventories (narrow-sense heritabilities varied from 0.41 to 0.66). Mainly low heritabilities were found for stem defects, yet genetic control of branch diameter, stem straightness and overall stem quality varied from low to high depending on study site. High additive genetic coefficient of variation was found for stem volume (25.3–32.5%). Genetic correlations among growth traits were strong and positive (0.90–0.99). Mainly weak genetic correlations between growth and quality traits implied simultaneous improvement. Still, strong negative correlations between branch angle and stem straightness might result in enlarged knot size for straighter logs. The genetic age-age correlations were strong. Weak genotype by environment interaction and stability of best genotypes over different sites was indicated by strong genetic correlations between trials. Each growth or quality trait alone showed substantial improvement in terms of estimated genetic gain (up to 62% over trial mean for stem volume). Therefore, selection index combining both growth and stem quality may be developed.

  • Gailis, Latvian State Forest Research Institute Silava, 111 Rigas street, Salaspils LV-2169, Latvia ORCID ID:E-mail:
  • Zeltiņš, Latvian State Forest Research Institute Silava, 111 Rigas street, Salaspils LV-2169, Latvia ORCID ID: E-mail: (email)
  • Purviņš, Latvian State Forest Research Institute Silava, 111 Rigas street, Salaspils LV-2169, Latvia ORCID ID:E-mail:
  • Augustovs, Latvian State Forest Research Institute Silava, 111 Rigas street, Salaspils LV-2169, Latvia ORCID ID:E-mail:
  • Vīndedzis, Latvian State Forest Research Institute Silava, 111 Rigas street, Salaspils LV-2169, Latvia ORCID ID:E-mail:
  • Zariņa, Latvian State Forest Research Institute Silava, 111 Rigas street, Salaspils LV-2169, Latvia ORCID ID:E-mail:
  • Jansons, Latvian State Forest Research Institute Silava, 111 Rigas street, Salaspils LV-2169, Latvia ORCID ID:E-mail:
article id 1568, category Research article
Jouni Siipilehto, Harri Lindeman, Mikko Vastaranta, Xiaowei Yu, Jori Uusitalo. (2016). Reliability of the predicted stand structure for clear-cut stands using optional methods: airborne laser scanning-based methods, smartphone-based forest inventory application Trestima and pre-harvest measurement tool EMO. Silva Fennica vol. 50 no. 3 article id 1568.
Highlights: An airborne laser scanning grid-based approach for determining stand structure enabled bi- or multimodal predicted distributions that fitted well to the ground-truth harvester data; EMO and Trestima applications needed stand-specific inventory for sample measurements or sample photos, respectively, and at their best, provided superior accuracy for predicting certain stand characteristics.

Accurate timber assortment information is required before cuttings to optimize wood allocation and logging activities. Timber assortments can be derived from diameter-height distribution that is most often predicted from the stand characteristics provided by forest inventory. The aim of this study was to assess and compare the accuracy of three different pre-harvest inventory methods in predicting the structure of mainly Scots pine-dominated, clear-cut stands. The investigated methods were an area-based approach (ABA) based on airborne laser scanning data, the smartphone-based forest inventory Trestima app and the more conventional pre-harvest inventory method called EMO. The estimates of diameter-height distributions based on each method were compared to accurate tree taper data measured and registered by the harvester’s measurement systems during the final cut. According to our results, grid-level ABA and Trestima were generally the most accurate methods for predicting diameter-height distribution. ABA provides predictions for systematic 16 m × 16 m grids from which stand-wise characteristics are aggregated. In order to enable multimodal stand-wise distributions, distributions must be predicted for each grid cell and then aggregated for the stand level, instead of predicting a distribution from the aggregated stand-level characteristics. Trestima required a sufficient sample for reliable results. EMO provided accurate results for the dominating Scots pine but, it could not capture minor admixtures. ABA seemed rather trustworthy in predicting stand characteristics and diameter distribution of standing trees prior to harvesting. Therefore, if up-to-date ABA information is available, only limited benefits can be obtained from stand-specific inventory using Trestima or EMO in mature pine or spruce-dominated forests.

  • Siipilehto, Natural Research Institute Finland (Luke), Management and Production of Renewable Resources, P.O. Box 18, FI-01301 Vantaa, Finland ORCID ID:E-mail: (email)
  • Lindeman,  Natural Research Institute Finland, Green Technology, Kaironiementie 15, 39700 Parkano ORCID ID:E-mail:
  • Vastaranta, University of Helsinki, Department of Forest Sciences, P.O. Box 62 (Viikinkaari 11), FI-00014 University of Helsinki ORCID ID:E-mail:
  • Yu, Finnish Geospatial Research Institute (FGI), Department of Remote Sensing and Photogrammetry, National Land Survey of Finland, P.O. Box 15 (Geodeetinrinne 2), FI-02431, Masala, Finland ORCID ID:E-mail:
  • Uusitalo,  Natural Research Institute Finland, Green Technology, Kaironiementie 15, 39700 Parkano ORCID ID:E-mail:
article id 1057, category Research article
Jouni Siipilehto, Lauri Mehtätalo. (2013). Parameter recovery vs. parameter prediction for the Weibull distribution validated for Scots pine stands in Finland. Silva Fennica vol. 47 no. 4 article id 1057.
Highlights: A parameter recovery method (PRM) was developed for forest stand inventories and compared with previously developed parameter prediction methods (PPM) in Finland; PRM for the 2-parameter Weibull function provided compatibility for the main stand characteristics: stem number, basal area and one of the four optional mean characteristics; PRM provided comparable and at its best, superior accuracy in volume characteristics compared with PPM.
The moment-based parameter recovery method (PRM) has not been applied in Finland since the 1930s, even after a continuation of forest stand structure modelling in the 1980s. This paper presents a general overview of PRM and some useful applications. Applied PRM provided compatibility for the included stand characteristics of stem number (N) and basal area (G) with either mean (D), basal area-weighted mean (DG), median (DM) or basal area-median (DGM) diameter at breast height (dbh). A two-parameter Weibull function was used to describe the dbh-frequency distribution of Scots pine stands in Finland. In the validation, PRM was compared with existing parameter prediction models (PPMs). In addition, existing models for stand characteristics were used for the prediction of unknown characteristics. Validation consisted of examining the performance of the predicted distributions with respect to variation in stand density and accuracy of the localised distributions, as well as accuracy in terms of bias and the RMSE in stand characteristics in the independent test data set. The validation data consisted of 467 randomly selected stands from the National Forest Inventory based plots. PRM demonstrated excellent accuracy if G and N were both known. At its best, PRM provided accuracy that was superior to any existing model in Finland – especially in young stands (mean height < 9 m), where the RMSE in total and pulp wood volumes, 3.6 and 5.7%, respectively, was reduced by one-half of the values obtained using the best performing existing PPM (8.7–11.3%). The unweighted Weibull distribution solved by PRM was found to be competitive with weighted existing PPMs for advanced stands. Therefore, using PRM, the need for a basal area weighted distribution proved unnecessary, contrary to common belief. Models for G and N were shown to be unreliable and need to be improved to obtain more reliable distributions using PRM.
  • Siipilehto, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland ORCID ID:E-mail: (email)
  • Mehtätalo, University of Eastern Finland, School of Computing, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail:
article id 271, category Research article
Patrick Insinna, Risto Jalkanen, Bernhard Götz. (2007). Climate impact on 100-year foliage chronologies of Scots pine and Ponderosa pine in the northeast lowlands of Brandenburg, Germany. Silva Fennica vol. 41 no. 4 article id 271.
Due to differences in the high-frequency signal and mean sensitivity of needle parameters in Scots pine and Ponderosa pine revealed in previous investigations, variance caused by climate factors at a dry site in the northeast lowlands of Brandenburg was investigated. Although water is the general limiting factor for both tree species, there are evident differences in the climate-driven impact on individual needle parameters. Autumn precipitation of the previous year was equally important for Scots pine and Ponderosa pine, but summer precipitation was more significant for the needle parameters of Scots pine. In contrast to precipitation, temperature seems to have a minor impact on needle parameters. Although January temperatures are significant predictors for both species, intercorrelations between needle parameters and summer temperatures were found only for Ponderosa pine. Striking correlation was also found between sun activity and needle production in Ponderosa pine, but not Scots pine, indicating possible adaptation to solar radiation.
  • Insinna, Office for Environmental Protection Liechtenstein, Climate Change Division, P.O. Box 684, FL-9490 Vaduz, Liechtenstein ORCID ID:E-mail: (email)
  • Jalkanen, Rovaniemi Research Unit, Finnish Forest Research Institute, P.O. Box 16, FI-96301 Rovaniemi, Finland ORCID ID:E-mail:
  • Götz, Eberswalde University of Applied Sciences, Department of Forestry, Forest-Botanical Gardens, D-16225 Eberswalde, Germany ORCID ID:E-mail:
article id 332, category Research article
Marc Palahí, Timo Pukkala, Antoni Trasobares. (2006). Calibrating predicted tree diameter distributions in Catalonia, Spain. Silva Fennica vol. 40 no. 3 article id 332.
Several probability density functions have been used in describing the diameter distributions of forest stands. In a case where both the stand basal area and number of stems per hectare are assessed, the fitted or predicted distribution is scaled using only one of these variables, with the result that the distribution often gives incorrect values for the other variable. Using a distribution that provides incorrect values for known characteristics means wasting information. Calibrating the distribution so that it is compatible with the additional information on stand characteristics is a way to avoid such wasting. This study examined the effect of calibration on the accuracy of the predicted diameter distributions of the main tree species of Catalonia. The distributions were calibrated with and without considering the prediction errors of the frequencies of diameter classes. When prediction errors were assumed, the calibration was done with and without making allowance for estimation errors in the stand level calibration variables. Calibrated distributions were more accurate than non-calibrated in terms of sums of different powers of diameters. The set of calibration variables that gave the most accurate results included six stand variables: number of trees per hectare, stand basal area, basal-area-weighted mean diameter, non-weighted mean diameter, median diameter, and basal area median diameter. Of the tested three-variable combinations the best was: number of trees per hectare, stand basal area, and basal-area-weighted mean diameter. Means were more useful calibration variables than medians.
  • Palahí, Centre Tecnológic Forestal de Catalunya. Passeig Lluis Companys, 23, 08010, Barcelona, Spain ORCID ID:E-mail: (email)
  • Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, 80101 Joensuu, Finland ORCID ID:E-mail:
  • Trasobares, Foreco Technologies, Av. Diagonal 416, Estudio 2, Barcelona 08037, Spain ORCID ID:E-mail:
article id 395, category Research article
Lauri Mehtätalo. (2005). Height-diameter models for Scots pine and birch in Finland. Silva Fennica vol. 39 no. 1 article id 395.
Height-Diameter (H-D) models for two shade-intolerant tree species were estimated from longitudinal data. The longitudinal character of the data was taken into account by estimating the models as random effects models using two nested levels: stand and measurement occasion level. The results show that the parameters of the H-D equation develop over time but the development rate varies between stands. Therefore the development of the parameters is not linked to the stand age but to the median diameter of the basal-area weighted diameter distribution (DGM). Models were estimated with different predictor combinations in order to produce appropriate models for different situations. The estimated models can be localized for a new stand using measured heights and diameters, presumably from different points in time, and the H-D curves can be projected into the future.
  • Mehtätalo, Finnish Forest Research Institute, Joensuu Research Centre, P.O. Box 68, FI-80101 Joensuu, Finland ORCID ID:E-mail: (email)
article id 617, category Research article
Jouni Siipilehto. (2000). A comparison of two parameter prediction methods for stand structure in Finland. Silva Fennica vol. 34 no. 4 article id 617.
The objective of this paper was to predict a model for describing stand structure of tree heights (h) and diameters at breast height (dbh). The research material consisted of data collected from 64 stands of Norway spruce (Picea abies Karst.) and 91 stands of Scots pine (Pinus sylvestris L.) located in southern Finland. Both stand types contained birch (Betula pendula Roth and B. pubescent Ehrh.) admixtures. The traditional univariate approach (Model I) of using the dbh distribution (Johnson’s SB) together with a height curve (Näslund’s function) was compared against the bivariate approaches, Johnson’s SBB distribution (Model II) and Model Ie. In Model Ie within-dbh-class h-variation was included by transforming a normally distributed homogenous error of linearized Näslund’s function to concern real heights. Basal-area-weighted distributions were estimated using the maximum likelihood (ML) method. Species-specific prediction models were derived using linear regression analysis. The models were compared with Kolmogorov-Smirnov tests for marginal distributions, accuracy of stand variables and the dbh-h relationship of individual trees. The differences in the stand characteristics between the models were marginal. Model I gave a slightly better fit for spruce, but Model II was better for pine stands. The univariate Model I resulted in clearly too narrow marginal h-distribution for pine. It is recommended applying of a constrained ML method for reasonable dbh-h relationship instead of using a pure ML method when fitting the SBB model.
  • Siipilehto, Finnish Forest Research Institute, Vantaa Research Centre, P.O. Box 18, FIN-01301 Vantaa, Finland ORCID ID:E-mail: (email)
article id 650, category Research article
Jouni Siipilehto. (1999). Improving the accuracy of predicted basal-area diameter distribution in advanced stands by determining stem number. Silva Fennica vol. 33 no. 4 article id 650.
The objective of this paper was to study to what extent the accuracy of predicted basal-area diameter distributions (DDG) could be improved by means of stem number observations in advanced (H > 10 m) stands. In the Finnish forest management planning (FMP) inventory practice, stem number is determined only in young stands; in older stands stand basal area is used. The study material consisted of sixty stands of Norway spruce (Picea abies Karst.) and ninety-one stands of Scots pine (Pinus sylvestris L.) with birch (Betula pendula Roth and B. pubescens Ehrh.) admixtures in southern and eastern Finland. For test data, 167–292 independent, National Forest Inventory-based, permanent sample plots were used. DDGs were estimated with the maximum likelihood method. Species-specific models for predicting the distribution parameters were derived using regression analysis. The two-parameter Weibull distribution was compared to the three-parameter Johnson’s SB distributions in predicting DDGs. The models were based on either predictors that are consistent with current FMP (model G), or assuming an additional stem number observation (model G+N). The predicted distributions were compared in terms of the derived stand variables: stem number, total and timber volumes. The results were similar in modelling and test data sets. Methods, based on the SB distribution obtained with model (G+N), proved to give the most accurate description of the stand structure. Differences were marginal in stand total volumes. However, the error variation in stem number was 20% to 80% lower than when applying model (G). SB and Weibull distributions gave very much the same results if model (G) was applied.
  • Siipilehto, Finnish Forest Research Institute, Vantaa Research Centre, P.O. Box 18, FIN-01301 Vantaa, Finland ORCID ID:E-mail: (email)

Category: Research note

article id 653, category Research note
Desta Fekedulegn, Mairitin P. Mac Siurtain, Jim J. Colbert. (1999). Parameter estimation of nonlinear growth models in forestry. Silva Fennica vol. 33 no. 4 article id 653.
Partial derivatives of the negative exponential, monomolecular, Mitcherlich, Gompertz, logistic, Chapman-Richards, von Bertalanffy, Weibull and the Richard’s nonlinear growth models are presented. The application of these partial derivatives in estimating the model parameters is illustrated. The parameters are estimated using the Marquardt iterative method of nonlinear regression relating top height to age of Norway spruce (Picea abies L.) from the Bowmont Norway Spruce Thinning Experiment. Formulas that provide good initial values of the parameters are specified. Clear definitions of the parameters of the nonlinear models in the context of the system being modelled are found to be critically important in the process of parameter estimation.
  • Fekedulegn, Department of Statistics, West Virginia University, Eberly College of Arts and Sciences, P.O. Box 6330, Morgantown, WV26506, USA ORCID ID:E-mail: (email)
  • Mac Siurtain, University College Dublin, Ireland ORCID ID:E-mail:
  • Colbert, USDA Forest Service, Northeastern Research Station, Morgantown, West Virginia ORCID ID:E-mail:

Category: Article

article id 5609, category Article
Matti Maltamo. (1997). Comparing basal area diameter distributions estimated by tree species and for the entire growing stock in a mixed stand. Silva Fennica vol. 31 no. 1 article id 5609.

The purpose of this study was to compare the Weibull distributions estimated for the entire growing stock of a stand and separately for Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) H. Karst.) in describing the basal area diameter distributions in mixed stands. The material for this study was obtained by measuring 553 stands located in eastern Finland. The parameters of the Weibull distribution were estimated using the method of maximum likelihood. The models for these parameters were derived using regression analysis. Also, some parameter models from previous studies were compared with the measured distribution. The obtained distributions were compared using the diameter sums of the entire growing stock, diameter sums by tree species and of the sawtimber part of the growing stock. The results showed that far more accurate results were obtained when the distributions were formed using parameter models separately for the different tree species than when using parameter models for the entire growing stock. This was already true when considering the entire growing stock of the stand and especially when the results were examined by tree species. When the models for the entire growing stock were applied by tree species in relation to basal areas, the results obtained were overestimates for Norway spruce and underestimates for Scots pine. The models from earlier studies, where parameter models were estimated separately for tree species from the National Forest Inventory data, showed good fits also in regard to the data of this study.

  • Maltamo, ORCID ID:E-mail:
article id 7197, category Article
Erik Lönnroth. (1926). Der stereometrische Bestandesmittelstamm. Acta Forestalia Fennica vol. 30 no. 2 article id 7197.
English title: The stereometric mean tree of the stand.

The mean has a great importance in statistics in general and also in forest statistical calculations. The meaning of the average tree and its characteristics is important also for the practical forest mensuration work. However, the question is how are the statistical numbers of a mean tree related to the statistical numbers of the stand.   

Study is based on the strip-wise survey of forests in southern Finland. From that information the 30 sample plots were chosen, 10 of each of most typical forest site types, MT, VT and CT. The stands are of different ages and development classes, varying from 14 to 159 years.

For the determination of the average tree are the statistical numbers of five characteristics needed: volume, basal area, diameter, height and form factor. The stereometric mean tree of the stand can be calculated with only one statistical method and that solution is absolute.

Theoretically and statistically absolute solution for the problem is the continuous solution by the mean that is weighted with the number of stems. This solution however is not very useful in practical sense.

A simple, practical and adequately exact solution for determining the average tree by approximation procedure of a certain arithmetic mean. 

  • Lönnroth, ORCID ID:E-mail:
article id 5563, category Article
Margaret Penner, Hannu Hökkä, Timo Penttilä. (1995). A method for using random parameters in analyzing permanent sample plots. Silva Fennica vol. 29 no. 4 article id 5563.

The use of random parameter models in forestry has been proposed as one method of incorporating different levels of information into prediction equations. By explicitly considering the variance-covariance structure of observations and considering some model parameters as random rather than fixed, one can incorporate more complex error structures in analysing data.

Competition indices and variance component techniques were applied to 92 Scots pine (Pinus sylvestris L.) -dominated permanent sample plots on drained peatlands in Northern Finland. By quantifying stand, plot, and tree level variation, it was possible to identify the level (stand, plot or tree) at which the explanatory variables contributed to the model. The replication of plots within stands revealed little variation among plots within a single stand but significant variation occurred at stand and tree levels. Positive and negative effects of inter-tree competition are identified by examining simple correlation statistics and the random parameter model.

  • Penner, ORCID ID:E-mail:
  • Hökkä, ORCID ID:E-mail:
  • Penttilä, ORCID ID:E-mail:
article id 5270, category Article
Pekka Kilkki, Risto Päivinen. (1986). Weibull function in the estimation of the basal area dbh-distribution. Silva Fennica vol. 20 no. 2 article id 5270.

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, ORCID ID:E-mail:
  • Päivinen, ORCID ID:E-mail:

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