When using the unique in terms of the volumes of databases on the level of a stand of Picea and Abies spp., the trans-Eurasian additive allometric models of biomass for Eurasian forests are developed for the first time, and thereby the combined problem of model additivity and generality is solved. The additive model of forest biomass of Picea and Abies is harmonized in three levels, one of which provides the principle of additivity of biomass components, the second one is associated with the introduction of dummy independent variables localizing model for eco-regions of Eurasia, and the third one makes the biomass structure of spruce and fir compatible by means of binary variable. The model can be developed further according to the third level of harmonization, when instead of the binary variable one can include another block of dummy variables coding the membership of actual biomass data of each eco-region to basic forestforming wood species in Eurasia. This might be a subject for further research.
Introduction
In recent years, the scientific branch associated with the estimating the biological productivity of trees and stands is
the most intensely developed in two aspects: (1) in compiling the world's actual data bases on biological productivity at
the levels of forest stands and sample trees with their development through global and transcontinental patterns
[
The development of generic allometric biomass models [
Harmonization implies at least two directions: (1) designing of compatible regional models based on dummy
variables [
Additive biomass models usually are designed on the tree level, but on the stand level they are presented today with single studies [1,11,42,46,45) without any attempts of their regionalization. In our study, the first attempt of combined solution the problem of additivity and universality of biomass allometric models of forest stands on the examples of the genera of Picea sp. and Abies sp. nally, for the original components, i.e. firstly for needles and branches and secondly for stem wood and stem bark, according to their structure taken into account: lnPi = ai +bi (lnA)+ci (lnA)2+ di (lnH)+ei (lnD)+fi (lnN)+giYk + ΣhijXj, (1) where Pi is biomass of i-th component, t per ha; А is stand age, yrs; Н is the mean height of a stand, m; D is the mean diameter at breast height, сm; N is tree density, thousand trees per ha; a-h are regression coefficients; i is designation of biomass component: total (t), aboveground (a), roots (r), crown (c), stems above bark (s), needles (f), branches (b), stem wood (w) and stem bark (bk); Yk is binary variable: for spruce k = 1, for fir k = 0; j are the codes of dummy variables for ecoregions designation, from 0 to 7. After the anti-log transformation the model (1) has the form
Pi = ai AbiAci(lnA)Hdi DeiNfiegiYkeΣhijXj (2)
Approximation of the model (1) on actual biomass data gives the regression coefficients and indices of adequacy. All regression coefficients of numerical variables are significant at the level of probability P0.95, and the equations are adequate to original data.
At the second stage of the study, the structure of the additive model and its calculating algorithm proposed by
Chinese researchers [
At the third stage of the study the adequacy comparison between the additive model (Table 1) and the initial (original) equations (1). As an additive model and initial equations (1) are tabulated on actual biomass-forming indices and the calculated biomass values were compared with the actual ones using the formulas:
where Yi - actual value; Ŷi - calculated value according to the model; Ῡ - mean actual value of the all (N) plots; p = 5 – number of variables; N – total plot number, involving into calculating R2 and RMSE.
The results of comparison of the adequacy of two modeling methods are summarized in the Table 2, indicating higher adequacy of additive model compared to the original (non-additive) equations.
, (3) * Designations see equation (1).
The additive model designed (Table 1) includes four numeric independent variables. When its tabulating, the
problem occurs, which is that we can give (know) of four independent variables (A, D, H, N) only stand age, and the
remaining three variables can be entered into the table in the form of calculated values, obtained by using the system of
auxiliary recursive equations [
The results of sequential tabulation of equations 3 and 1 are the rather cumbersome table, the volume of which exceeds the format of a journal article. Therefore, a comparative analysis of the biomass structures of spruce and fir stands of different ecoregions we limit with the age 60 years (Table 4). According to the Table 4, the highest biomass values correspond to the regions with minimal index of continentality, adjacent to the Atlantic and Pacific coasts, and the lowest values to the regions of Siberia, with its maximum index of continentality. WME A. alba 21,5 23,8 0,980 47,9 20,9 27,1 52,6 206,9 186,9 20,0 ЕРR A. sibirica 15,9 16,8 1,375 27,2 11,8 15,4 28,4 114,4 103,3 11,1 Ural A. sibirica 14,1 15,6 1,091 27,8 14,3 13,5 22,9 77,6 68,5 9,1 Cau A. nordmanniana 21,7 30,9 1,131 49,4 16,7 32,6 17,4 188,4 169,8 18,6 MES A. sibirica 13,9 15,8 1,154 18,9 8,3 10,6 16,3 60,3 52,2 8,1 FE A. nephrolepis 14,2 16,8 2,537 35,9 12,8 23,1 27,9 119,6 102,9 16,7 Japan AA.. svaeicthcahliiin,eAn.sfiisr,ma 11,6 16,3 2,398 242,5 191,8 43,9 18,6 25,2 50,7 147,9 128,6 19,3 China Cunninghamia lanceolata 11,7 18,6 0,859 300,7 246,9 63,2 25,7 37,5 53,9 183,6 162,5 21,2 * Denotes of the ecoregions: WME – Western and Middle Europe; ЕРR – European part of Russia; Ural – Ural region; Cau – Caucasus; MES – Middle and Eastern Siberia; FE – Far Eastern province (Primorye).
Negative correlation of calculated indices of spruce and fir biomass with continentality index by [48,4,27) is characterized by a correlation coefficient -0.92 to total phytomass and -0.89 for aboveground ones on the probability level above P95.
Conclusion
Thus, for the first time, when using the unique in terms of volume database on the examples of the genera Picea sp. and Abies sp. the comparative analysis of biomass structure of forest stands on the territory of Eurasia is fulfilled in a new light, the result of which is the additive allometric model, harmonized on three levels, one of which provides the principle of additivity of biomass components, the second one relates to the involving dummy variables, localizing the model along to ecoregions of Eurasia, and the third one harmonizes the structure of a transcontinental model of spruce and fir stands by involving the binary variable into biomass model. It is shown that the model demonstrates differences between spruce and fir stand biomass not only for its absolute values for stem, needles, branches and roots (as is typical for trivial independent models that includes only dummy variables), but also for their ratios, i.e. the differences in the biomass structure.