The current global warming is continuing around the globe and is apparently of anthropogenic origin. Separation of the anthropogenic component from global, including climatic, changes in the natural environment is included in the sustainable development transition strategy [1, 2]. The climate forecasts based on the scenarios of anthropogenic emissions of greenhouse gases into the atmosphere assume an increase in the average global temperature of the Earth’s surface within 1.4–5.8°C for the period of 1990–2100, which is 2–10 times greater than the warming value in the twentieth century [3]. However, the true picture far exceeds these calculations. The current warming trend will lead to an increase in the average global temperature of 4°C by 2100 [4]. Alongside with that, warming may reach 6–11°C in some Russian regions [5]. It should be noted that small external influences can cause significant global changes in the biosphere [1].

In 2015, in Paris during the Climate Conference under the UN Framework Convention on Climate Change, an agreement was reached to regulate measures to reduce carbon dioxide in the atmosphere from 2020 [6]. According to Articles 2 and 4 of the Paris Agreement, the member countries should strive to “…achieve a balance between human-generated greenhouse gases and their absorption by seas and forests by the second half of the twenty-first century,” in order to restrict the increase in the average global temperature to no higher than 1.5–2°C. The stabilization of the environment on land can be achieved through the greenhouse gas adsorption processes by natural, and primarily forest, ecosystems.

On the other hand, an important goal of the Paris Agreement is the planning of actions in the field of adaptation: “strengthening the adaptation capacity, increasing the resistance and reducing the vulnerability of ecological systems to climate change in order to ensure an adequate adaptation response in the context of the temperature goal mentioned above” (Article 7 of the Agreement). Hence, it is necessary to solve a dual-purpose task for forest ecosystems such as adsorption and adaptation to assess regulation of the carbon cycle by the forest cover to mitigate the global warming.

This report presents a regional solution of the dual-purpose problem using the example of the Oka basin (with an area of about 250 000 sq. km). We conducted a numerical experiment to assess the impact of elastic–plastic stability of forest ecosystems as an indicator of their adaptation potential, as well as the predicted climatic parameters, on the carbon balance of forests, i.e., on their adsorption capacity. The climate parameters were taken from the forecast scenarios of two global models: (1) a moderate E GISS model [7] meeting the objectives of the Paris Agreement, with its early version as GISS-1993; (2) an extreme HadCM3 model, version A2 [8], the forecast of which is compliant with the current global warming trend (see above).

The experiment was carried out with the use of the large-scale landscape–ecological survey data obtained earlier by a specially developed method at five experimental sites of the Middle and Upper Volga region [9]. Each research site characterized a certain ecoregion. The basic carbon content and climatic trends were estimated using discrete parameters of the small biological cycle: (1) skeletal tree–shrub phytomass, BS; (2) root mass, BR; (3) total green mass, BV; (4) forest cover mass, ML; (5) dead skeletal above-ground phytomass (trunk and dead wood), WD; and (6) humus mass in the organomineral soil horizon, HU. To predict these parameters, the hydrothermal ordination of their basic values was preliminarily carried out in the space of local landscape conjugations (catenas) in each ecoregion [9]. The transition from the geomass to the carbon content in it was carried out using known carbon coefficients ([10, 11], etc.).

The estimated changes in the carbon content in various biotic components and, in general, in forest biogeocenoses were obtained by the well-known forestry method [10, 12] based on the living and dead phytomass, as well as on the labile humus trends. According to the cybernetic approach implemented by [13, 14], the geomasses (carbon pools) are considered as functional parameters in the system “output,” without analyzing the metabolic processes of the “black box,” in order to represent the functional biogeosystem states as integral formations [15].

Changes in the carbon flux mass ΔС(Fa) in the soil–vegetation–atmosphere system, i.e., the carbon balance of the soil and plant assemblage for a given forecast period, were calculated using the following formula:

$$\begin{gathered} \Delta {\text{C}}({{F}_{a}}) = \Delta {\text{C}}(WD) + \Delta {\text{C}}(ML) + \Delta {\text{C}}(HU) \\ - \;\Delta {\text{C}}(BS)-\Delta {\text{C}}(BV)-\Delta {\text{C}}(BR). \\ \end{gathered} $$
(1)

∆С(Fa) was determined for each biogeocenosis group in the given ecoregion. With positive values, the first three terms on the right side of the equation yield an increase in CO2 emissions from the soil and vegetation cover into the atmosphere, and the second three terms give a decrease in this flux. With negative values of the indicated terms, the picture is reversed. Hence, the forecast ∆С(Fa) was used to estimate whether a given forest biogeocenosis would absorb additional CO2 from the atmosphere as a result of shifts in the biological cycle or, conversely, would become a source of additional emissions.

The transition from the local (analytical) level to the regional (cartographic) level was carried out using a specially developed inductive–hierarchical extrapolation [16], as well as by new geomorphometry methods [17]. For this purpose, we used the NASA satellite topographic data as matrices of the surface heights of the Earth obtained during implementation of the SRTM30 United States–Italy–Germany Project (2000).

A quantitative assessment of adaptation of the forest ecosystem to the changing climate was carried out in terms of the forest elastic–plastic stability [18] related to the forest succession–recovery potential. As is known, two processes are of key importance in the biological cycle: the relative production of green material and the velocity of its decomposition. They can be expressed with two discrete parameters of metabolism, such as the annual turnover coefficient of the aboveground phytomass (KR = PV/BL) and the forest litter–fall index (KY = PV/ML). PV is the annual production of green mass (with generative organs), BL is the total living aboveground phytomass, and ML is the forest litter mass. Using the Euclidean distance metric, the elastic–plastic stability index Ielast was calculated as a function of the indicated coefficients:

$${{I}_{{{\text{elast}}}}} = 1 - \left[ {\sqrt {{{{(\Delta KR)}}^{{2{\text{ }}}}} + {\text{ }}{{{(\Delta KY)}}^{{2{\text{ }}}}}} } \right]{\text{/}}\sqrt 2 ,$$
(2)

where

$$(\Delta KR) = (K{{R}_{{\max }}} - K{{R}_{i}}){\text{/}}(K{{R}_{{\max }}} - K{{R}_{{\min }}}),$$
$$\left( {\Delta KY} \right) = (K{{Y}_{i}} - K{{Y}_{{\min }}}){\text{/}}(K{{Y}_{{\max }}} - K{{Y}_{{\min }}}).$$

Hence, the elastic–plastic stability index is estimated in dimensionless units. In other words, it indicates a certain stability proportion of the studied ecosystem from the maximum possible in a given statistical sample.

If KRi → KRmax and KYi → 0, than Ielast → 1. Ielast of a forest ecosystem characterizes its ability to undergo recovery successions (elasticity), or to transition to a new functional stable state, while maintaining, with an acceptable probability, its primary structure (plasticity).

In practice, in the central part of the Russian Plain, Ielast can be calculated using the following empirical formulas with fairly high determination coefficients R2 [9]:

$${{I}_{{{\text{elast}}}}} = 0.715-0.0555KY;\quad {{R}^{2}} = 0.90;$$
(3)
$$\begin{gathered} KY = 0.993{{t}_{{{\text{Jan}}}}}-0.5365{{t}_{{{\text{Jul}}}}} + 0.003508{{r}_{{{\text{year}}}}}; \\ {{R}^{2}} = 0.61; \\ \end{gathered} $$
(4)
$$KY = \exp (6.453-0.2993{{t}_{{{\text{Jul}}}}});\quad {{R}^{2}} = 0.76.$$
(5)

tJan and tJul are the average temperatures of January and July, respectively (°С), and ryear is the annual precipitation (mm).

The mapped data pool was formed (more than 52 000 points) after the procedure for assigning the values of the elastic–plastic stability indices and changes in the carbon content to mesocatenas of the distribution of each plant formation. The spatial variability of the forest carbon balance in connection with the adaptation potential in the basin was studied by multiple regression methods.

Table 1 shows the obtained statistical relationships between adsorption ∆C(Fa) and adaptation Ielast of the zonal/subzonal types/subtypes of forest formations, according to the classification by [12], with a fairly high Pearson significance (P < 10–6). ∆C(Fa) represents variations in the specific CO2 flux (t/ha year) in the Earth’s surface–atmosphere system, and tJul and ryear are normalized values (in fractions of 1) of the average July temperature and annual precipitation. The generally low values of the Spearman rank coefficient Rs are due to the huge number of statistical samples: a significant “noise” effect is exerted by local geomorphological and edaphic factors that create groups of averages with opposite relationships. As is known [13], violations of the basic statistical analysis principles are inevitable when describing complex multicomponent biological systems. In particular, the principle of the predictor of linear independence is not respected and the correlation and determination coefficients are not high. Nevertheless, the general relationship trend can be taken as reliable for each equation, as evidenced by the mentioned Pearson coefficient.

Table 1. Equations describing the relationship between changes in the carbon content in the forest formations of the Oka basin, their elastic–plastic functional stability, and climatic characteristics
Full size table

Each zonal/subzonal type/subtype includes primary and derived forest communities, as well as fragmented forest lands, thus reflecting the real status of the forest cover.

Equations (3)–(11) are proposed to be included directly in the revision of the “Methodological Guidelines for Quantitative Assessment of Greenhouse Gas Absorption” approved by the Ministry of Natural Resources of Russia (Decree no. 20-r dated June 30, 2017) in relation to the boreal and nemoral forests in the central zone of European Russia. As an example, Table 2 shows the calculations (by formulas A–D2 in Table 1) of the predicted specific and total carbon balance of the zonal/subzonal types/subtypes of forest formations throughout the Oka–Volga basin in terms of the basic and predicted Ielast, as well as in terms of tJul and ryear given by two different global climate models (see above). According to the first, moderate, model, climate warming will range from 0.2–0.6°C in winter to 0.8–1.1°C in summer in the Middle Volga region by the middle of the twenty-first century. These data are consistent with the scenario proposed under the Paris Agreement. The extreme model gives an overall annual temperature increase by 2.5–4.0°C by this period. These values can be achieved at the current velocity of global warming.

Table 2. Specific and total carbon balances of forest formations in the sample area of the Volga basin, predicted for 2100 with their basic and final labile elastic stability and according to climate scenarios, based on two global forecast models: moderate GISS-93 and extreme HadCM3
Full size table

During the entire 100-year forecast period, the overall elastic–plastic stability of forest formations should increase, to the greatest extent during extreme warming. Due to this fact, we should also expect a substantial increase in the ability of boreal forests to absorb greenhouse gases and thereby mitigate the warming trend; it will mean an increase in their ecological resources by the definition of [14]. The compared carbon balance of forest formations obtained at the initial (basic) and final (end) functional stability indices yields an unambiguous picture of a considerable increase in the adsorption capacity of coniferous and mixed forests with an increase in their adaptation potential.

It was also important to take into account variations in the ecological resources of forest formations, which could be caused by their functional and structural transformations during this forecast period. These variations were ambiguous. Algebraic summing of ∆C(Fa) values for the zonal/subzonal types/subtypes of forest formations in the Volga basin was carried out (Table 2) according to the moderate climate warming scenarios (GISS-93 model). The following changes in the specific carbon balance of forests ∆[∆C(Fa)] (t/ha) were obtained: А = (+4.998), B = (–14.570), C = (+27.773), and D1 = (+10.010). In general, the potential of the ecological resources of the entire range of boreal dark coniferous and dark coniferous broad-leaved forests, as well as subtaiga broad-leaved pine forests, will remain unchanged. The adsorption capacity of purely broad-leaved forests increases noticeably (mainly due to their supposed transformation into boreal forests). Meanwhile, more than 50% of the southern taiga pine forests moving into mixed forest communities lose their ecological resources to a great extent, although their ∆C(Fa) remains positive.

In general, the data reported are indicative of the fact that the adsorption capacity of the forest cover grows in the central part of the Russian Plain with an increase in the global warming signal and a corresponding increase in the stability of the elastic–plastic ecosystem. This fact is confirmed by comparing the ∆C(Fa) values in the GISS-93 and HadCM3 models (Table 2). A decisive contribution to greenhouse gas conservation by forests is made by their growing adaptation potential. This potential plays the role of a direct environmental factor in mitigating climate fluctuations, including the current warming.

Hence, the empirical–statistical modeling of changes in the carbon balances of forest formations in the Oka–Volga basin, depending on their elastic–plastic stability, made it possible to reveal the influence of forest adaptation processes on the forest adsorption potential. Thus, we demonstrated one of the ways to solve the dual-purpose problem posed by the Paris Agreement (2015) on the need for coupled research on the adsorption capacity of forest biomes and their adaptation to the changing climate.