Use of the Weibull function in estimating the basal area dbh-distribution.

Kilkki, Pekka; Maltamo, Matti; Mykkänen, Reijo; Päivinen, Risto

doi:10.14214/sf.a15550

Cited by 71 publications

(57 citation statements)

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“…These species-specific characteristics were calculated from empirical diameter distributions. The theoretical basal area diameter distributions were predicted from the calculated stand characteristics using the three-parametric approach of the Weibull function (Mykkänen 1986, Kilkki et al 1989. The heights of the sample trees obtained from the theoretical diameter distribution were predicted using Veltheim's (1987) height models.…”

Section: Generation Of True Stand-level Inventory Datamentioning

confidence: 99%

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The assessment of the uncertainty of updated stand-level inventory data

Haara¹,

Leskinen²

2009

Silva Fenn.

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Predictions of growth and yield are essential in forest management planning. Growth predictions are usually obtained by applying complex simulation systems, whose accuracy is difficult to assess. Moreover, the computerised updating of old inventory data is increasing in the management of forest planning systems. A common characteristic of prediction models is that the uncertainties involved are usually not considered in the decision-making process. In this paper, two methods for assessing the uncertainty of updated forest inventory data were studied. The considered methods were (i) the models of observed errors and (ii) the k-nearest neighbour method. The derived assessments of uncertainty were compared with the empirical estimates of uncertainty. The practical utilisation of both methods was considered as well. The uncertainty assessments of updated stand-level inventory data using both methods were found to be feasible. The main advantages of the two studied methods include that bias as well as accuracy can be assessed.

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Section: Generation Of True Stand-level Inventory Datamentioning

confidence: 99%

“…The practice in Finland is to use basal area diameter distributions instead of the stem diameter distributions (e.g. Kilkki et al 1989, Maltamo 1998. Each sample tree from the theoretical diameter distribution predicts a certain number of trees in the stand.…”

Section: Introductionmentioning

confidence: 99%

The assessment of the uncertainty of updated stand-level inventory data

Haara¹,

Leskinen²

2009

Silva Fenn.

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“…Stepwise regression analysis was used to identify a set of candidate functional forms based on a 0.01 risk level (Kilkki et al 1989). Parameter estimates for the resultant system of equations were estimated simultaneously via seemingly unrelated regression (SUR) analysis given that SUR estimation takes into account error covariances across the three equations and is asymptotically efficient in the absence of specification error (Zellner 1962).…”

Section: Discussionmentioning

confidence: 99%

A parameter recovery model for estimating black spruce diameter distributions within the context of a stand density management diagram

Newton¹,

Lei²,

Zhang³

2004

The Forestry Chronicle

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The objectives of this study were to develop and subsequently demonstrate a parameter prediction approach for estimating black spruce (Picea mariana (Mill.) BSP) diameter frequency distributions within the context of a stand density management diagram (SDMD). The approach consisted of three sequential steps: (1) obtaining maximum likelihood estimates for the location, scale and shape parameters of the Weibull probability density function for 153 empirical diameter frequency distributions; (2) developing and evaluating parameter prediction equations in which the Weibull parameter estimates were expressed as functions of stand-level variables based on stepwise regression and seemingly unrelated regression techniques; and (3) explicitly incorporating the parameter prediction equations into the SDMD modelling framework. The results indicated that the Weibull function was successful in characterizing the diameter distributions within the sample stands: the fitted distributions exhibited no significant (p ≤ 0.05) differences in relation to their corresponding observed distributions, based on the Kolmogorov-Smirnov test. The parameter prediction equations described 94, 94 and 89% of the variation in the location, scale and shape parameter estimates, respectively. Furthermore, evaluation of the recovered distributions in terms of prediction error indicated minimal biases and acceptable accuracy. As demonstrated, incorporating the parameter prediction equations into an algorithmic version of the SDMD enabled the prediction of the temporal dynamics of the diameter frequency distribution by initial density regime and site quality. Additionally, an executable version of the resultant algorithm with instructions on acquiring it via the Internet is provided.Key words: 3-parameter Weibull probability density function, stepwise and seemingly unrelated regression, predictive error, product value, algorithm, Internet Les objectifs de cette étude étaient de développer et par la suite d'utiliser une approche de récupération de paramètres pour estimer les distributions de fréquence de diamètre de l'épinette noire (Picea mariana (Mill.) BSP) dans le cadre d'un diagramme d'aménagement de la densité d'un peuplement (SDMD). L'approche comportait trois étapes séquentielles : (1) l'obtention du maximum vraisemblable d'estimés pour les paramètres du site, de l'échelle et de la forme de la fonction de probabilité de densité de Weibull pour 153 distributions empiriques de fréquence de diamètre; (2) le développement et l'évaluation des équations de récupération des paramètres dans lesquelles les estimés des paramètres selon Weibull étaient exprimés en tant que fonctions des variables du peuplement selon des techniques de régressions par étape et d'autres techniques de régression apparemment sans rapport, et (3) l'intégration explicite des équa-tions de récupération des paramètres dans le cadre du travail de modélisation SDMD. Les résultats démontrent que la fonction Weibull a réussi à représenter les caractéristiques des distributions de diam...

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“…The regeneration harvests were done as soon as the 5-year moving average of value growth percentage, or so-called v-value, of the stand was less than the interest rate chosen. To estimate the timber assortment volumes and incomes from the harvests, tree diameter distributions were constructed for each stand before the harvests, using the distribution models by [45][46][47]. The value of each diameter class was then predicted with the taper curve functions of [48] and optimal stem bucking algorithm of [49].…”

Section: Simulation Of the Sources Of Uncertaintymentioning

confidence: 99%

Uncertainty in Forest Net Present Value Estimations

Holopainen

Mäkinen

Rasinmäki³

et al. 2010

Forests

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Uncertainty related to inventory data, growth models and timber price fluctuation was investigated in the assessment of forest property net present value (NPV). The degree of uncertainty associated with inventory data was obtained from previous area-based airborne laser scanning (ALS) inventory studies. The study was performed, applying the Monte Carlo simulation, using stand-level growth and yield projection models and three alternative rates of interest (3, 4 and 5%). Timber price fluctuation was portrayed with geometric mean-reverting (GMR) price models. The analysis was conducted for four alternative forest properties having varying compartment structures: (A) a property having an even development class distribution, (B) sapling stands, (C) young thinning stands, and (D) mature stands. Simulations resulted in predicted yield value (predicted NPV) distributions at both stand and property levels. Our results showed that ALS inventory errors were the most prominent source of uncertainty, leading to a 5.1-7.5% relative deviation of property-level NPV when an interest rate of 3% was applied. Interestingly, ALS inventory led to significant biases at the property level, ranging from 8.9% to 14.1% (3% interest rate). ALS inventory-based bias was the most significant in mature stand properties. Errors related to the growth predictions led to a relative standard deviation in NPV, varying from 1.5% to 4.1%. Growth model-related uncertainty was most significant OPEN ACCESSForests 2010, 1 178 in sapling stand properties. Timber price fluctuation caused the relative standard deviations ranged from 3.4% to 6.4% (3% interest rate). The combined relative variation caused by inventory errors, growth model errors and timber price fluctuation varied, depending on the property type and applied rates of interest, from 6.4% to 12.6%. By applying the methodology described here, one may take into account the effects of various uncertainty factors in the prediction of forest yield value and to supply the output results with levels of confidence.

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Use of the Weibull function in estimating the basal area dbh-distribution.

Cited by 71 publications

References 0 publications

The assessment of the uncertainty of updated stand-level inventory data

The assessment of the uncertainty of updated stand-level inventory data

A parameter recovery model for estimating black spruce diameter distributions within the context of a stand density management diagram

Uncertainty in Forest Net Present Value Estimations

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