Height-diameter models for mixed-species forests consisting of spruce, fir, and beech

Height-diameter models define the general relationship between the tree height and diameter at each growth stage of the forest stand. This paper presents generalized height-diameter models for mixed-species forest stands consisting of Norway spruce (Picea abies Karst.), Silver fir (Abies alba L.), and European beech (Fagus sylvatica L.) from Slovakia. The models were derived using two growth functions from the exponential family: the two-parameter Michailoff and three-parameter Korf functions. Generalized height-diameter functions must normally be constrained to pass through the mean stand diameter and height, and then the final growth model has only one or two parameters to be estimated. These "free" parameters are then expressed over the quadratic mean diameter, height and stand age and the final mathematical form of the model is obtained. The study material included 50 long-term experimental plots located in the Western Carpathians. The plots were established 40–50 years ago and have been repeatedly measured at 5 to 10-year intervals. The dataset includes 7,950 height measurements of spruce, 21,661 of fir and 5,794 of beech. As many as 9 regression models were derived for each species. Although the "goodness of fit" of all models showed that they were generally well suited for the data, the best results were obtained for silver fir. The coefficient of determination ranged from 0.946 to 0.948, RMSE (m) was in the interval 1.94–1.97 and the bias (m) was –0.031 to 0.063. Although slightly imprecise parameter estimation was established for spruce, the estimations of the regression parameters obtained for beech were quite less precise. The coefficient of determination for beech was 0.854–0.860, RMSE (m) 2.67–2.72, and the bias (m) ranged from –0.144 to –0.056. The majority of models using Korf's formula produced slightly better estimations than Michailoff's, and it proved immaterial which estimated parameter was fixed and which parameters were free. This record was migrated from the OpenDepot repository service in June, 2017 before shutting down

Credit Risk Modelling for Insurance Solvency Purposes

In this work we study credit risk pricing models from an information based pespective. This perspective implies that to distinguish which model is applicable, structural or reduced form, one needs to understand what information is available to the modeler. We also deal with a new information-based framework for credit risk modelling that is concerned with how to model the market ltration by use of the concept of partial information. This framework avoids the use of inaccesible stopping times. The pricing of several credit risk derivatives is discussed in an information-based framework. Applications of the information-based approach to insurance claims reserves and credit portfolio risk are discussed as well

Changes in growth caused by climate change and other limiting factors in time affect the optimal equilibrium of close-to-nature forest management

Historical radial increment data based on tree ring analyses from the close-to-nature experimental forest management unit Smolnícka Osada in Central Slovakia were used for retrospective modelling of changes in forest dynamics to estimate the sensitivity of management planning goals under climate change. Four example years representing historical periods with typically different species-specific patterns of radial increment in mixed beech-fir-spruce forest (1910, 1950, 1980, and 2014) served as virtual starting points for the modelling. An advanced density-dependent matrix transition model was utilised for modelling stand dynamics. An integrated tool for nonlinear financial optimisation searched for an optimal management equilibrium. In addition to transition probabilities adjusted from increment data, some assumptions for changes in ingrowth and mortality related to the increment, as well as a case study concerning the reduced ingrowth changed by game browsing intensity, were tested for modelling more realistic historical ecological conditions. The sensitivity study revealed changes in the optimal management equilibrium represented by optimal basal area, tree species composition, diameter distribution and target harvest diameter over time due to the adapted ecological modelling. The main lesson of the past for the future is to avoid placing too much trust in the simple extrapolation of current trends, such as the observed continual decline in spruce related to climate change, but to be aware of temporal and possibly reversible processes, such as the observed extensive fir recovery after the reduction of air pollution. Tree species diversity appears to be the best option for the uncertain future