The accuracy of estimates of basal area in beech stands using sample plots

The paper presents the results of the research on the accuracy of estimates of basal area in beech stands using sample plots. The accuracy of estimates of the analysed characteristic was evaluated on the basis of variation coefficient value of the sums of tree basal areas on sample plots. The coefficient value was empirically determined for sample plots of various size, as well as for the secondary populations differing in plot number. The research was conducted in three beech stands of age class III, IV and VI growing in the territory of the Krzeszowice Forest District

Generalized height-diameter model for black alder (Alnus glutinosa (L.) Gaertn.) in the western part of the Sandomierz Basin

The study shows that the accuracy of tree height approximation by means of investigated functions is not modified by the age or site conditions of the analysed alder stands. The widest range of tree height variability was explained by Schnute (M5) function. Higher values of adjusted coefficient of determination (R²adj) are usually obtained when the height of black alder stands in the western part of the Sandomierz Basin is determined with M2 height−diameter curve

The impact of initial soil properties on the growth of scots pine (Pinus sylvestris L.) on reclaimed surface of spoil bank kwb "Bełchatów"

W pracy podjęto próbę odpowiedzi na pytanie, które właściwości inicjalnych gleb wpływają pozytywnie lub negatywnie na wzrost sosny zwyczajnej wzrastającej na wierzchowinach zwałowisk KWB "Bełchatów". Badania wykazały, że dodatnio na przeciętny roczny przyrost wysokości sosny na powierzchniach badawczych wpływa przede wszystkim: wyższe pH, większa zawartość kationów zasadowych oraz większa zawartość frakcji pyłu (0,05-0,002 mm) w substracie glebowym. Negatywnie na przyrost drzew wpływa natomiast wzrost udziału frakcji piasku, a w głównej mierze kwasowości hydrolitycznnej substratu glebowego.This paper concerns the relationships between the properties of soil-substrate and growth of Scots pine planted on the plateaus of spoil bank KWB "Bełchatów". Studies have shown that growth of Scots pine in the research plots is primarily positively affected by: higher pH, contents of base cations and percentage of silt-sized (0.05-0.002 mm) fractions in soil substrate. In the other hand, negative influence on the average tree height growth on the study plots had the content of sand fraction, as well as the hydrolytic acidity in the soil substrate

Bandwidth of kernel estimator of DBH distribution in black alder (Alnus glutinosa (L.) Gaertn.) stands from west part of the Sandomierz Basin

Set of ‘nonparametric’ methods, that don’t make a priori assumption about functional form of empirical distribution was developed as an alternative to the parametric distribution modeling. The kernel estimators are one of such methods, that can be used to describe the frequency of data representing for example DBH records. Kernel smoothing requires the choice of weighting function and bandwidth also called as smoothing parameter or window. The lack of comprehensive analysis on the applicability of particular bandwidth selection methods to model DBH structure gave an impulse to present investigation aimed at determining value and variability of smoothing parameter in black alder stands. The optimal bandwidth was obtained according to six different variants of plug−in method proposed by Altman and Léger. Presented investigations were based on DBH measurements collected in 163 managed black alder stands aged from 6 to 89 years, growing in the west part of the Sandomierz Basin (S Poland). We measured in total 22,530 black alders, from 48 to 359 in individual stand. Stands were characterized by: age, quadratic mean diameter, basal area, mean height, Reineke’s stand density index and standard deviation of DBH. Smoothing parameter was obtained by means of plug−in method with the pilot bandwidth selected by: Silverman’s rule of thumb (nrd0), Scott’s method (nrd), unbiased cross−validation (ucv), biased cross−validation (bcv), method of Sheather and Jones (sj) and one−stage method of Wand and Jones (onestage). The bandwidth was first obtained to real data, then to 100 bootstrap samples of 5, 10, 15 ... and 100 trees from each stand. Smoothing parameters were characterized by mean and variance. Relationship between values of smoothing parameter and stand characteristics was determined. Finally the influence of sample size on value and variability of bandwidth was assessed. Value and variability of smoothing parameter in black alder stands are determined by stand age, sample size and method of bandwidth choice. There is a close relationship between bandwidth and the mean height (r from 0.75 to 0.83), quadratic mean diameter (r from 0.79 to 0.88) and standard deviation of DBH (r from 0.84 to 0.93). Potentially these stand features can be used to predict smoothing parameter values. Minor changes of bandwidth for samples containing above 50 trees together with persistence of standard error give an objective grounds for defining optimal number of diameters, that are necessary to kernel estimation of DBH distribution

Accuracy of empirical formulas for determining aboveground biomass of black alder (Alnus glutinosa (L.) Gaertn.)

The study investigated the accuracy of thirty equations formulated in England, Sweden, Turkey, Lithuania and Spain and which aim to determine the aboveground biomass of black alder. The reference constituted of bark, timber, stem, branches and leaves dry biomass of 168 sample trees aged 6−96 from 56 alder stands located in the western part of Kotlina Sandomierska (south−eastern Poland). The analysed formulas, considering local conditions, resulted in biased biomass calculations. The evaluation of such components as leaves, branches, trunk timber or trunk bark is subject to systematic errors larger than a dozen or so per cent, and in certain ranges of breast height diameters − up to even a couple of dozens or a few hundred per cent. Only three out of 30 formulas may be considered useful for estimating aboveground biomass of black alder in Poland

Diameter structure of selected pine stands growing on post-mining sites reclaimed for forestry

The paper presents the results of the research on tree diameter structure in Scots pine (Pinus sylvestris L.) stands growing on mine dumps and pits reclaimed for forestry. The diameter structure of stands was characterised using statistical concentration and dispersion measures and compared with five theoretical distributions: beta, gamma, logarithmic−normal, normal and Weibull's. The studies were conducted in eight pine stands in age classes I (below 20) and II (21−40) age classes growing on the rehabilitated areas of the Bełchatów, Piaseczno, Szczakowa and Smolnica mines

Evaluation of usefulness of selected functions for modeling distribution of breast height diameter in black alder stands (Alnus glutinosa (L.) Gaertn.)

We evaluated the usefulness of ten theoretical probability density functions for the approximation of the breast height diameter distributions in managed alder stands growing in the western part of the Sandomierz Basin (southern Poland). The study material consisted of measurement results for 22,530 alders obtained for 844 circular sample plots, established in 163 stands aged 6−89. In the area of particular stands, from 2 to 10 age−dependent circular sample plots sized 0.01−0.10 ha were systematically arranged. We evaluated the following theoretical probability distributions: normal (N), double normal (P−N), Johnson SB (J), Weibull (W), beta (B), Burr (Bu), gamma (G), log−normal (L−N), log−logistic (L−L) and Birnbaum−Saunders (B−S). Additionally the usefulness of the W, B, Bu, G, L−N, L−L and B−S distributions with omitted location parameter was tested. The goodness−of−fit of each probability density function was assessed based on the Kolmogorov−Smirnov statistic, the root mean square error and ranks established on their basis. It was found that DBH distribution of majority stands is characterized by right−sided asymmetry and negative kurtosis. It was showed that the best distribution for the breast height diameter structure approximation of alder stands is the Johnson SB (J) distribution. To describe the frequency of thickness, normal (N) and log−logistic (L−L) distribution should not be used. Elimination of location parameter significantly affects usefulness of probability density functions to modeling empirical distributions of breast height diameter. Gamma and Burr distributions with omitted location parameter gave the best results in description the frequency of breast height diameter. In certain situations, these distributions can also be used to describe the structure of breast height diameter of alder stands

Accuracy of the uniform height curves for black alder (Alnus glutinosa (L.) Gaertn.) stands

The study presents the assessment of the accuracy of two generalized height−diameter models, such as skwB [Bruchwald et al. 2001] and skwO [Orzeł et al. 2014], developed in Poland for black alder (Alnus glutinosa (L.) Gaertn.) stands. Verification of these models was conducted on empirical material that was collected in 127 alder stands located in the western part of Sandomierz Basin (southern Poland). Selected alder stands aged 6−89 years, while average breast height diameter ranged from 4.5 to 43.0 cm and average height from 6.3 to 32.7 m. The stand density varied from 222 to 4360 trees/ha. The accuracy assessment for uniform height−diameter curves was based on the analysis of single tree absolute error distributions. Synthetic indicators of goodness−of−fit, such as: average and standard errors, coefficients of variation and determination were calculated based on absolute errors. The final evaluation of the compared uniform height−diameter models results from the structure of the goodness−of−fit measures that was observed within all analyzed stands and within age classes of 20 years. The efficiency of uniform height−diameter models was also compared with stand height−diameter curve, which was developed based on the Näslund function. General height−diameter models overestimated height in alder stands on average from 0.26 (1.67) to 0.19 m (1.39%), based on skwB and skwO models, respectively. Bias depended on the age of stand and decreases from almost 3% in I age class to nearly 0.5% in IV and V age class. For both analyzed models, a positive systematic error was observed for the standardized breast height diameter. Bias in estimating the height of single stand depended on the accuracy of stand height estimations. In case of estimation based on the measurements of three trees height, bias in single stand can range from –13% to +14%. Due to the range and nature of observed systematic errors, uniform height curves should be applied to groups of stands that have different age and breast height diameter structure, as it allows for partial reduction of the error