In the Finnish compartmentwise inventory systems, growing stock is described with means and sums of tree characteristics, such as mean height and basal area, by tree species. In the calculations, growing stock is described in a treewise manner using a diameter distribution predicted from stand variables. The treewise description is needed for several reasons, e.g., for predicting log volumes or stand growth and for analyzing the forest structure. In this study, methods for predicting the basal area diameter distribution based on the k-nearest neighbor (k-nn) regression are compared with methods based on parametric distributions. In the k-nn method, the predicted values for interesting variables are obtained as weighted averages of the values of neighboring observations. Using k-nn based methods, the basal area diameter distribution of a stand is predicted with a weighted average of the distributions of k-nearest neighbors. The methods tested in this study include weighted averages of (i)Weibull distributions of k-nearest neighbors, (ii)distributions of k-nearest neighbors smoothed with the kernel method, and (iii)empirical distributions of the k-nearest neighbors. These methods are compared for the accuracy of stand volume estimation, stand structure description, and stand growth prediction. Methods based on the k-nn regression proved to give a more accurate description of the stand than the parametric methods.
Diameter distribution of the growing stock is essential in many forest management planning problems. The diameter distribution is the basis for predicting, for example, timber assortments of a stand. Usually the predicted diameter distribution is scaled so that the stem number (or basal area) corresponds to the measured value (or predicted future value), but it may be difficult to obtain a distribution that gives correct estimates for all known variables. Diameter distributions that are compatible with all available information can be obtained using an approach adopted from sampling theory, the calibration estimation. In calibration estimation, the original predicted frequencies are modified so that they respect a set of constraints, the calibration equations. In this paper, an example of utilizing diameter distributions in growth and yield predictions is presented. The example is based on individual tree growth models of Scots pine (Pinus sylvestris L.). Calibration estimation was utilized in predicting the diameter distribution at the beginning of the simulation period. Then, trees were picked from the distribution and their development was predicted with individual tree models. In predicting the current stand characteristics, calibrated diameter distributions proved to be efficient. However, in predicting future yields, calibration estimation did not significantly improve the accuracy of the results.Résumé : La distribution diamétrale du matériel ligneux sur pied est une information essentielle pour plusieurs problè-mes de planification en aménagement forestier. C'est par exemple la base pour prédire les assortiments de bois dans un peuplement. La distribution diamétrale prédite est généralement ajustée pour faire correspondre le nombre de tige (ou la surface terrière) aux valeurs mesurées (ou projetées). Mais une distribution qui donne les estimés exacts pour toutes les variables connues peut être difficile à obtenir. Des distributions diamétrales compatibles avec toute l'information disponible peuvent être obtenues par une approche empruntée à la théorie d'échantillonnage et appelée estimation par calibration. Dans cette approche, les fréquences prédites initialement sont modifiées pour respecter une série de contraintes définies par les équations de calibration. Cet article présente un exemple d'utilisation des distributions diamé-trales pour prédire la croissance et le rendement. L'exemple est basé sur les modèles de croissance d'arbre individuel pour le pin sylvestre (Pinus sylvestris L.). L'estimation par calibration a été utilisée pour prédire la distribution diamé-trale au début de la période de simulation. Ensuite, les arbres ont été extraits de la distribution et leur croissance a été prédite par les modèles de croissance d'arbre individuel. Les distributions diamétrales calibrées s'avèrent efficaces pour prédire les caractéristiques actuelles du peuplement, mais elles n'améliorent pas de façon significative la précision des prédictions dans le cas des rendements futurs.[Traduit par la Rédaction] Kan...
Information about diameter distribution is used for predicting stand total volume, timber volume and stand growth for forest management planning. Often, the diameter distribution is obtained by predicting the parameters of some probability density function, using means and sums of tree characters as predictors. However, the results have not always been satisfactory: the predicted distributions practically always have a similar shape. Also, multimodal distributions cannot be obtained. However, diameter distribution can also be predicted using distribution-free methods. In the percentile method, the diameters at certain percentiles of the distribution are predicted with models. The empirical diameter distribution function is then obtained by interpolating between the predicted diameters. In this paper, models for diameters at 12 percentiles of stand basal area are presented for Scots pine, Norway spruce and birch species. Two sets of models are estimated: a set with and one without number of stems as a predictor. Including the number of stems as a predictor improved the volume and saw timber volume estimates for all species, but the improvements were especially high for number of stems estimates obtained from the predicted distribution. The use of number of stems as predictor in models is based on the possibility of including this characteristic to measured stand variables.
Highlights• Airborne laser scanning (ALS) and digital aerial photogrammetry (DAP) are nearly equally valuable for harvest scheduling decisions even though ALS data is more precise.• Large underestimates of stand volume are most dangerous errors for forest owner because of missed cutting probabilities.• Relative RMSE of stand volume and the mean volume in a test area explain 77% of the variation between the expected losses due to errors in the data in the published studies.• Increasing the relative RMSE of volume by 1 unit, increased the losses in average by 4.4 € ha -1 . AbstractAirborne laser scanning (ALS) has been the main method for acquiring data for forest management planning in Finland and Norway in the last decade. Recently, digital aerial photogrammetry (DAP) has provided an interesting alternative, as the accuracy of stand-based estimates has been quite close to that of ALS while the costs are markedly smaller. Thus, it is important to know if the better accuracy of ALS is worth the higher costs for forest owners. In many recent studies, the value of forest inventory information in the harvest scheduling has been examined, for instance through cost-plus-loss analysis. Cost-plus-loss means that the quality of the data is accounted for in monetary terms through calculating the losses due to errors in the data in the forest management planning context. These costs are added to the inventory costs. In the current study, we compared the losses of ALS and DAP at plot level. According to the results, the data produced using DAP are as good as data produced using ALS from a decision making point of view, even though ALS is slightly more accurate. ALS is better than DAP only if the data will be used for more than 15 years before acquiring new data, and even then the difference is quite small. Thus, the increased errors in DAP do not significantly affect the results from a decision making point of view, and ALS and DAP data can be equally well recommended to the forest owners for management planning. The decision of which data to acquire, can thus be made based on the availability of the data on first hand and the costs of acquiring it on the second hand.
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