Exergy of forest stand as a quality indicator for biological productivity tables

This paper proposes using stand exergy as an indicator for assessing the quality of biological productivity tables (BPTs). To this end, a comparative analysis was conducted on the construction of the biological productivity tables presented in the works of V. A. Usoltsev, A. Z. Shvidenko, and his co-authors. The study examines the BPTs of oak and birch stands of various quality classes across Central European Russia, the North Caucasus, the flat part of the Middle Urals, the Southern Trans-Urals, and the steppe ecoregions of southern Western Siberia (Northern Kazakhstan). The analysis is based on an ecological-physiological model (EPM) previously developed by the authors. The parameters of this model were obtained through multi-criteria optimization and have a clear physiological meaning. It has been shown that two of the four EPM parameters carry silvicultural significance. One of them is termed the quality index, while the other is referred to as the species index. The study demonstrates that the quality index equals 0.05 for forest stands of quality class I, increasing by 0.003 with each subsequent quality class. These values remain constant and are independent of the stand species. Similarly, the species index remains constant within a given species. The paper establishes that the Nash-Sutcliffe efficiency (NSE) values for the number of trees per hectare, stand phytomass, and phytomass per tree, as well as the relative errors of these variables obtained using BPTs as input empirical data, do not fully ensure an objective assessment of BPT quality. To determine the advantages of a specific BPT construction method, it is necessary to additionally calculate stand exergy based on these tables. The Nash-Sutcliffe efficiency values generally range from 0.99 and above, indicating the high quality of the applied EPM, while the mean relative deviations from the respective empirical values of the variables used range from 1 % to 5 %. Deviations exceeding this range are typically very rare. The exergy value for oak and birch stands varies from 468 kJ/g to 561 kJ/g, which allows using exergy not only as an indicator of stand quality but also as a criterion for evaluating the quality of biological productivity tables.