Climate impact on social systems: the risk assessment approach

A novel approach to the problem of estimating climate impact on social systems is suggested. This approach is based on a risk concept, where the notion of critical events is introduced and the probability of such events is estimated. The estimation considers both the inherent stochasticity of climatic processes and the artificial stochasticity of climate predictions due to scientific uncertainties. The method is worked out in some detail for the regional problem of crop production and the risks associated with global climate change, and illustrated by a case study (Kursk region of the FSU). In order to get local climatic characteristics (weather), a so-called statistical weather generator is used. One interesting finding is that the 3% risk level remains constant up to 1.0–1.1°C rise of mean seasonal temperature, if the variance does not change. On the other hand, the risk grows rapidly with increasing variance (even if the mean temperature rises very slowly). The risk approach is able to separate two problems: (i) assessment of global change impact, and (ii) decision making. The main task for the scientific community is to provide the politicians with different options; the choice of admissible (from the social point of view) critical events and the corresponding risk levels is the business of decision makers.     

Nonlinearities in mathematical ecology: Phenomena and models: Would we live in Volterra's world?

Presented is a critical survey of canonical nonlinear models in theoretical population ecology, namely single-species population, prey–predator, competition, migration within a metapopulation, and trophic chains. Various nonlinear effects, like hysteresis, structural instability, dissipative structures, dynamic chaos, etc., do exist in these models, but the problem how to detect these phenomena in real ecosystems is not yet solved. In the mathematics of nonlinear models, the central question is whether the simplest, i.e., Volterra-type, nonlinearity is sufficient to reproduce a variety of nonlinear phenomena in a given model or we need a more sophisticated formalism. Examples are considered where the Volterra models fail. Although fundamental physical principles, like, e.g., the mass conservation law, should work in ecology too, the ecological origin of the models often causes mathematical effects which are distinct from those in theoretical physics. For example, the trophic-chain model does reveal a kind of chaotic behaviour, but the “ecological strange attractor” occupies an intermediate position between Lorenz's and Feigenbaum's attractors; moreover, the phase volume of our system contracts, hence the system is dissipative (like a Lorenz's one) in spite of its matter conservation property. Nevertheless, when applied properly, physical concepts, like, e.g., the thermodynamic notion of exergy, give better insight both to the patterns of nonlinear ecosystem behaviour and to comparison of the patterns.     

Mathematical modelling of a fish pond ecosystem

A mathematical model is constructed for a fish breeding pond for carp, silver carp and bighead. The model is a system of ordinary differential equations describing the material transformations in the ecosystem. It allows a choice of optimal regimes of the aeration, feeding and fertilization of a pond for different climatic conditions in order to maximize the yield.     

The model for human population dynamics as a part of the global biosphere model: some aspects of modeling in a dialogue regime

"A matrix model for an age structured population with 4 groups is presented....The demography matrix is identified with data from global demographic statistics for the 1970s. When calibrating the matrix elements, a semi-formal procedure was used to calculate the dominant eigenvalue and corresponding eigenvector. This procedure was based essentially on the dialogue mode of computation provided by the programing language APL." The advantages of using APL are discussed     

“Emission game”: some applications of the theory of games to the problem of CO2 emission

If there are no doubts that we must reduce the total emission of carbon dioxide, then the problem of how much different countries should be allowed to contribute to this amount remains a serious one. We suggest this problem to be considered as a non-antagonistic game (in Germeier's sense). A game of this kind is called an “emission game”. Suppose that there are n independent actors (countries or regions), each of them releasing a certain amount of CO₂ per year (in carbon units) into the atmosphere, and that the emission would be reduced by each actor. Each actor has his own aim: to minimise the loss in the Gross Domestic Product (GDP) caused by the reduction of emissions. On the other hand, taking into account that it is impossible to estimate more or less precisely the impact of the climate change on GDP for each country today, a common strategy will be to reduce the climate change. Since one of the main leading factors in global warming is the greenhouse effect, then the common aim will be to reduce the sum of emissions. This is a typical conflict situation. How to resolve it? We can weigh the “egoistic” and “altruistic” criteria for each actor introducing the so-called “coefficients of egoism”. This coefficient is very large, if the actor uses a very egoistic strategy, and conversely, if the actor is a “super-altruist”, then the corresponding coefficient is very small. Using these coefficients we get the general solution of the game in a form of some Pareto's equilibrium. The solution is stable and efficient.     

The model of long-term evolution of the carbon cycle

The weathering processes and their role in the formation of the atmospheric carbon and, as a consequence, on the climate are considered. The model operates in the framework of “active planetary cover”, i.e. considering the interactive role of the biosphere, looking at its development as a non-linear evolutionary system of so-called “virtual biospheres”.     

Life-cycle model of terrestrial carbon exchange

We present here a terrestrial carbon cycle model based on a scheme of the phytomass change, which is continuous in time. The experimental information about net primary production, living and dead phytomass, and soil organic matter for various ecosystems is used for calibration of the model. The suggested model enables to characterize terrestrial ecosystems as carbon sources or carbon sinks and to evaluate intensity of these sources and sinks. The model is applied for the European territory of Russia as a case study. Intensity of the total exchange carbon flux for this territory is evaluated. The obtained results allow to conclude that the given territory is the sink of carbon.     

Optimisation of reduction of global CO2 emission based on a simple model of the carbon cycle

A simple model has been designed to describe the interaction of climate and biosphere. Carbon dioxide, understood as a major emitted gas, leads to a change of global climate. Economic interpretation of the model is based on the maximisation of the global CO₂ cumulative emissions. The two most important profiles of emission have been obtained: optimal and multi-exponential suboptimal profiles, each displaying different characteristics. This revised version was published online in July 2006 with corrections to the Cover Date.