In the model all land territory is divided to into cells of the size 0.5x0.5^o of a geographical grid. It is supposed that in each cell there is a vegetation of one type according to the chosen classification. Two kinds of classification of types are used: 1. N.I. Bazilevich and L.E. Rodin and 2. J.S. Olson. The model is described by system of ordinary nonlinear differential equations. The model variables are quantities of carbon in the atmosphere, in live plants, and in soil humus in each cell. A time unit accepted in the model is one year.
     We consider that annual production of vegetation in each cell depends on atmospheric CO₂ concentration, on temperature and precipitation in a given cell and does not depend on the ecosystem type. Three kinds of annual production dependencies were applied. The first one (A.M. Tarko) expresses in a tabulated form the dependence of annual production on temperature and precipitation. The next is the dependence of  H. Leith, the third is the dependence of M.V. Kuznetsova.
    The dependence of humus decomposition rate on temperature and precipitation in a given cell was also taken into account.
     Annual air temperature and precipitation characterize the climate in a given cell. Air CO₂ concentration is considered to be equal in all the cells. The values of temperature and precipitation for each cell depending on atmospheric CO₂ concentration (the greenhouse effect) are taken from the calculations at General Circulation Models (GCM).
     We assume that in the absence of anthropogenic CO₂ emissions to the atmosphere the quantity of carbon in the biosphere is constant. Prior to the beginning of anthropogenic influences the system was in a steady state (usually 1860 is accepted as the year when the industrial era began).
     Dividing the territory into cells allowed allocating all countries of the world with size larger than 50x50 km.
    A computer program complex was developed to make calculations on the model. It works under the control of Windows 95/98/NT.

       We take into consideration the following anthropogenic impacts on the biosphere resulting in CO₂ growth in atmosphere: fossil fuel burning (industrial releases), cutting down the forests, soil erosion resulting from wrong land use.
     Dynamics of the biosphere during 1860-2050 was simulated. Let us see the following scenario. The anthropogenic CO₂ input to the atmosphere is a result of industrial releases, deforestation, and soil erosion. After 1996, the industrial emissions grew at the same rate as during the previous decade.
     The main effect of deforestation takes place in tropical forests. According to the scenario during 1950-2050 there is a deforestation and subsequent destruction of tropical forests. During this period, tropical forests  decreases each year by 0.6%.
     The soil erosion begins in 1860 and increases by 0.15 % per year. The ecosystem types are set where erosion takes place.
     Calculated dynamics of biosphere parameters is shown in a figure. Atmospheric CO₂ quantity, annual production of plants, and plants biomass are increasing. The humus quantity is decreasing for a long time . Then, because of the annual production growth resulting from CO₂ concentration and temperature increase, humus also begins to increase. Animated maps of plants and humus (see below) show spatial distribution of biosphere dynamics. Both the biosphere and ocean absorb about 50% of industrial releases of carbon dioxide. So anthropogenic actions are partly compensated and biosphere controls its stability. Problem of biosphere stability is considered from the point of view of  Le Chatellier principle: how does biosphere weaken anthropogenic impacts.
 
 

     Animated maps of plants biomass and humus changes  in 1860-2050 are shown below.

     Consideration of the zonal distribution of CO₂ exchange between the terrestrial ecosystems and the atmosphere during the industrial period shows that ecosystems of middle and high latitudes of the Northern hemisphere absorbed CO₂ and ecosystems in the equatorial zone  released CO₂ . The greatest absorption occurred in middle latitudes of the Northern hemisphere where plentiful forest ecosystems are concentrated. Move from the middle latitudes to the equator, the closer the ecosystem or the country to are to the equator, the lesser is the degree of CO₂ absorbing. And ecosystems of the equatorial zone  were CO₂ sinks. All ecosystems for this period absorbed more CO₂ than they released.

     The whole territory of Russia during 1860-1995 was a CO₂ sink though some ecosystems released CO₂. Forest ecosystems were most powerful CO₂ absorbers. Grasslands were CO₂ sinks but at some territories were sources. Phytomass was increased at all ecosystem types. Humus decreased at some grassland ecosystems. Calculations show that now and in a future at the Russian territory it will be increasing the annual plants production and phytomass. Russian territory will absorb CO₂ emissions. Quantity of humus will be mainly increased. But at some territories which allocated at agricultural zones mainly of southern regions humus will be decreased (see animated map of humus changes).
 
 

      A comparison of carbon budget of ecosystems in countries which are the greatest CO₂ "producers" (annual production minus humus decomposition, minus deforestation, minus soil erosion) and the appropriate industrial releases in 1995 are shown in a figure. That year ecosystems of the whole the world and in each of the analyzed countries absorbed CO₂ . The greatest industrial emissions were from territory of USA, China and Russia. The greatest CO₂ absorption occurred in territories of Russia, Canada and the USA. In the majority of the countries industrial emissions exceeded ecosystem absorption. The exceptions were Canada, Australia, and Brazil where ecosystem CO₂ absorption was more than industrial releases. It could be due to the rather large territory of the country and relatively small industrial releases.

 Calculations show that the CO₂ flows balance of in the world in 1995 was as follows.

      In accordance to the Kyoto protocol (1997) to the UN Framework Convention on climate change all the countries should reduce the emissions of  greenhouse gases by 2010  to a level of industrial CO₂ emissions in 1990. We will consider the effects of various restrictions on reduction of CO₂ emissions. The following scenarios were considered: 1. Above mentioned scenario of anthropogenic influences. 2. Scenario 1, but, after 2020, the industrial CO₂ emissions become constant and equal to the value which was in 1990. 3. Scenario 1, but after 2010 industrial CO₂ emissions become constant and equal to the value in 1990 (it corresponds to the Kyoto protocol). 4. Scenario 1, but after 2000 industrial CO₂ emissions become constant and equal to the value in 1990 5. Scenario 1, but after 2000 industrial CO₂ emissions stop. 6. Scenario 1, but after 1990 deforestation and erosion stop.

     We see that emissions restrictions are effective. According to scenario 1 CO₂ concentration in atmosphere will be raised by 1.82 times by 2050 in comparison with 1860. According to scenarios 2, 3, and 4 increases of CO₂ concentration will be significantly less: the CO₂ growth will be 1.56, 1.47 and 1.42 times. It is obviously that the delay of beginning to implement the Kyoto protocol for 10 years does not result in significant change in 2050.
     The termination of deforestation and soil erosion does not lead to significant effect. CO₂ growth reduction in this case is the least in comparison with other scenarios. The effect of reduction of deforestation and erosion gives weaker effect than reduction of industrial emissions. Total termination of emissions will result in CO₂ decrease in the atmosphere.

     Investigating the anthropogenic influences on the biosphere, it is important to establish not only what consequences of this or that economic strategy will be, but also what will be "a price" if we want to provide accepted values of biosphere parameters. Let us consider a task to set constant level of atmospheric CO₂ after a given year. We are to determine what values of CO₂ industrial emissions must be set to provide steady state of the atmospheric CO₂. This was done using  the control theory methods . Results of calculation show that in order to provide constant level of CO₂ in the atmosphere it is necessary to significantly decrease amount of emissions.

      The models of global biosphere processes can be compared with some kind of "universal recipient", since they combine the approaches of many sciences: physics, chemistry, ecology, soil science, geography, geochemistry, climatology, economy etc. However these models are far from being "universal donor ". In other sciences, the amount of consumers of global modeling results it is small. Results received by using the global models enrich a science but practical application of global models can be found among the decision-makers. Application of the results of modeling is also possible in economic and social sciences. So, V.S. Golubev (Institute of  Lithosphere, Russian Academy of Sciences) used the biosphere parameters calculated here to investigated indices of social and natural development of various countries.