Научный журнал

European Journal of Natural History

ISSN 2073-4972

ИФ РИНЦ = 0,301

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Mazurkin P.M.

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Introduction. On site http://metla.fi/ we fast have found statistical data [1, с. 51] on Fin-land wood square modification in a period of 1921-2007 years. The Finland wood statistics is rich by table models, for example in the wood program [2], and also always Q-factor of sampling is visible. However we anywhere have not found yet statistical models of dynamics, in particular, statistical models on such major landscape parameter as wood square. The biotechnical regularity examples are indicated in our books [3-6], and at that in the book [6] detailed examples on timber trade of Finland among 30 advanced countries are indicated. The mathematical modelling technology is indicated in study guide for the bachelors and magisters [7].

The article purpose - to show the biotechnical regularities of Finland wood square dy-namics in a period of 86 years, revealed by us, and also wave dynamics of oscillatory perturba-tion of the Finnish experts in wood management on an example [1, c.51]. On a ready model prognostic wood square dynamics is shown provided that in Finland the modern wood policy up to a 2100 will be continued without radical modifications. Earlier on data [8] the portrait of tim-ber this country trade [6] in a period of 1961-2005 years was composed.

Time scale. 1921 year is a beginning of coordinates t = 0 on an abscissa.

Two statistical numbers - on left t₁ and right t₂ time scale boundaries (table 1) on wood square S₁ and S₂ inclusive of different wood inventory periods were received.

If the wood parameter actualization was annual, with cyclicity of Earth rotation round the Sun one time scale would be natural.

Wood grounds. All wood parameters are subjected identification by the biotechnical law [3-7] uniformly. Let´s show two ready models of a structural type S₁=f(t₁) and S₂=f(t₂) On two scales two models of 86-year´s Finland wood square dynamics (fig. 1) were obtained.

(1)

(2)

Finland wood square dynamics 

Fig. 1. Dynamics of Finland wood square in a period of 1921-2007 years (in a right upper angle the sum of squared deviations and formula correlation coefficient are shown)

First component is the stable exponential growth law. At that this main trend shows ra-ther small growth on a comparison with the time scale beginning. And second component, with negative sign before itself, shows crisis excitation of national economy with 1925 on 2007 years and further in a period of 110 years.

Together schedules will show (fig. 2) possible scatters of data on a wood parameter.

The comparison of the schedules shows, that, since 2000 both scales begin to coincide. Therefore it is possible to make a conclusion that the national wood inventory have improved as the years go by. At that country has overcome territorial wood crisis.

Fig. 2. Dynamics of wood square on taxation periods

Crisis significance. The deal each component of a general trend (2) shows a significance of rather settlement wood square significances. The expressions  and  give from data of table 1 significance parameter dynamics (fig. 3):

 (3)

 (4)

First component (2)                 Crisis component of model (2)

Fig. 3. Dynamics of significance coefficient of Finland wood square model (2) components

Obviously, that the sum of significance coefficients of two components trend model (2) is equal 100%, that is . 

Residuals after the formula (3)           Residuals after the formula (4)

Fig. 4. Dynamics of residuals from models of significance coefficient of model (2) components

Significance coefficient k, for the formula (2) calculated as the relation k₂/k₁, ambassa-dor structural - parametrical identifications [7] has received (fig. 5) formula

 (5)

The more significance k in absolute magnitude, the activity of the given people popula-tion on use national natural riches becomes more intense. The negative sign shows crisis process. It will be stopped in Finland by a 2035 year.

The schedule of significance coefficient (5)     Dynamics of residuals after a model (5)

Fig. 5. Dynamics of adaptability of the population and Finland wood economy to wood territory

Wave perturbation. For the analysis of wave dynamics we shall accept a trend (2) S = S₂ and on its residuals shall obtain the asymmetric wavelet-function [5, 6] (fig. 6а). And after joint parametrical identification we have received trinomial dynamics model:

S = S₁ -S₂ -S₃            (6)

where S - square of woods of Finland for 86 years in dynamics in a period
of 1921-2007 years, t/ha;

S₁ - stable wood square part in a period of wood measurements, t/ha;

S₂ - critical wood square part in a period of 1925-2035 years. By a duration per 110 years a part of woods, т. Га;

S₃ - oscillatory perturbation of woods on square, which is response to a behaviour of the people, t/ha;

A - amplitude half of wave perturbation of a wood as organism, t/ha;

p - half of variable period of oscillatory perturbation of a wood on square, years. 
 
The period of oscillation in 1921 year was equal to 2⋅11,56241 ≈ 23,1 years or is approx-imately equal to two cycles of solar activity on Tchizhevsky effect [3-6]. In a period of 86 years the Finns have reduced in wood perturbation frequency increase, and this frequency in 2007 year was equal
to 1/(2⋅10,66) = 0,0469 year-1 and by a 2100 year the half cycle of wood perturbation will decrease to 10,41 years, that is all on 100⋅(11,56 - 10,41)/11,56 = 9,95%. The woods of Fin-land on square and in XXI century will change within the limits of the double cycle of solar ac-tivity till 2035 year. It means, that the interference of the Finns in life of the woods is ecological-ly responsible, and they reach an economic acceptability of wood exploitation at the expense of import of sticks [6].

Hereafter it is possible to conduct a component analysis for revealing a complex of bio-technical regularities of dynamics of woods on such parameters as geostatistical distribution of subcompartment, pfytocenosis elements, specific structure of wood trees, their age structure, vo-lumes of trunk timber, category of a sanitary state and other.

а) wave component of model (6)          b) the schedule on all triadic model (6)

Fig. 6. Finland wood square dynamics in a period of 1921-2007 years

Avareness of wood policy. The amplitude-frequency characteristic of wave component shows scientific validity forestry-based measures (fig. 7). Wood policy clearly preempts programs of timber trade, and it was visible 40 years back [2].

In the beginning XXI centuries the priorities of Finland were changed and timber trade has become active to develop. Experience of forestry management and, in particular, the reach-ings in wood statistics, can give new breathing to all wood economy sector of this wood country. In particular this experience will be useful to Russia.

Wood management dynamism. Dynamism coefficient K_д is determined as the relation of the sum of a wave model component to a class of trend parts, that is not wave model compo-nents (6), that is on expression K_Д = S₃ / (S₁  - S₂)

After identification the model (fig. of 8) of wood dynamism coefficient is obtained

.

Amplitude of oscillatory perturbation of the Finnish woods      Frequency of wave wood behaviour

Fig. 7. Dynamics of amplitude and frequency of Finland wood oscillation on square

Dynamism coefficient of the Finnish woods on (7)     Residuals after a model (7)

Fig. 8. Dynamics of Finland wood square dynamism coefficient 

From the residual schedule in a fig. 8 it is visible, that the microwaves begin since 1933 year. However, the data of wood statistics on wood farms are necessary for their identification. Models (6) and (7) are high-precision within the limits of a Finland wood square measurement error.

Dynamism of Finland wood square

The half-cycle of dynamism coefficient have a remarkable property. They in time period of 1990-2010 years almost coincide with the solar activity cycle beginnings. Finnish foresters have managed actively to use Tchizhevsky effect on 23-th cycle of solar activity in a period of 1999-2009 years, most force from measured by the astronomers. Apparently, concurrence is not casual, and quite realized. System of wood statistics and data vsk 08_01 pdf help revelation this coincidence.

Prognostic model. Under the formulas (6) and (7), and also data of table 2, the cycle of modern wood policy of Finland on a wood square parameter will be finished in a 2078 year and will proceed 148 years. Dynamism coefficient is extremely small in relation to an allowable condition K_д ≤ 1. At that it the maximum significance of wave component in the formula (6) is equal to 1,84% for 1980 year, and zero significance is achieved by
2055 year.

Therefore for an evaluation macroeconomic parameters of a wood sector it is enough to accept trend of the formula (6) for drawing up prognostic model. In an outcome is received, that the 1921 year wood square level Finland will achieve by 2020 year. Hereafter national wood can qualitative be improved without square growth. But the dynamic numbers on other wood para-meters are necessary for the analysis.

Finland wood square forecasting. When model (6) adequacy with a coefficient of cor-relation 0,9996 (see fig. 6) is high it is quite possible to accept horizon of the prognosis equal to prognosis basis length. The basis is equal to 86 years, therefore under horizon of the prognosis also in a period of 86 years the limit of all time series per 192 years or per 1921 + 192 = 2113 years is received. The schedules in a fig. 9 and fig. 10 are constructed in a period of 200 years, that is till a 2121 year.

а) schedule on all triadic model (6)  b) dynamism coefficient of wood on square

Fig. 9. Prognostic Finland wood square dynamics

Amplitude of oscillatory Finnish wood perturbation          Frequency of a wave wood behaviour

Fig. 10. Prognostic dynamics of amplitude and frequency of Finland wood oscillation on square

Conclusions. It is possible to suppose, that on other parameters of Finland woods the sta-tistical models with high adequacy to appropriate dynamic numbers accepted from wood statis-tics of this country will determined.

On wood square dynamics we formulate the following main conclusions:

1) The territorial principle is precisely executed and recovery for 86 years with 1921 for a 2007 years specifies on that. At that rather small significance crisis trend and oscillatory compo-nents of dynamics model on wood square confirms excellence of long-term wood management;

2) Adaptability of Finland to the woods is very high, at that without high society tug, and the crisis on wood square was overcome on regularity of aperiodic oscillation;

3) Small on amplitude the wave perturbations will cease in the near future, though force the microoscillations will possible at a level of separate composite of wood farms; prognostic model shows an approximation of national wood square to constant significance, and it specifies high skill Finnish foresters, and their centenary wood management experience will be distributed and to other wood countries, including Russia;

4) For revealing a full limit of growth on square and other wood parameters it is necessary to conduct a component analysis in an annual mode and on other parameters all wood sub-compartments, and also to reveal biotechnical regularities of dynamics in geostatistical distribu-tions of country territory on land cadastre categories.

References

1. Metsätilastollinen vuosikirja 2008 / vsk 08_01 pdf. - 82 p.
2. Arvasti S. Forestry and wood industry in Finland in a period of
   1970-2015 years / S. Arvasti, L. Heykinheymo, К. Кuusela. - Version № 9887. - Novosibirsk: GPNTB WITH АN USSR, 1982. - 106 p.
3. Mazurkin, P.М. Dynamics of manglings / P.М. Mazurkin, A.N. Bedertdinov, А.N. Fadeev. - Yoshcar-Ola: MarGTU, 2002. - 218 p.
4. Mazurkin, P.М. Regularities of stable development / P.М. Nazurkin. - Yoshcar-Ola: MarGTU, 2002. - 302 sp.
5. Mazurkin, P.М. A geoecology: regularities of modern natural sciences / P.М. Mazurkin. - Yoshcar-Ola: MarGTU, 2006. - 336 p.
6. Mazurkin, P.М. Wood-agrarian Russia and world dynamics of wood exploitation / P.М. Mazurkin. - Yoshcar-Ola: MarGTU, 2007. - 334 p.
7. Mazurkin, P.М. Mathematical modelling. Identification of one-factor statistical regularities: study guide / P.М. Mazurkin, A.S. Filonov. - Yoshcar-Ola: MarGTU, 2006. - 292 p.
8. Food And Agriculture Organization Of The United Nation; The FAO Statistical Database; www.fao.org < http: // www.fao.org >; www.faostat.fao.org.

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