PIK Report No. 27


3.1 Goals of the project

The main objective is to create a dynamic model of biosphere processes on a global scale, treating the biosphere as an entity (unitary model) and human society as its natural component (constituent element). We define the concept of an ,,ecological niche" (both local and global) for the species Homo Sapiens. In contrast to other known ,,World models", which are oriented to the calculation of concrete trajectories of development in accordance with certain scenarios, the main task of our modelling approach is, first of all, to evaluate the variants of development, which could lead either to global or to local disaster (such as the extinction of the ecological niche for Homo Sapiens). ,,Normal" development is not included in our field of interest. Therefore, the main emphasis is not on the calculation of concrete trajectories, but on the determination of stability domains (homeostasis domains) of solutions for which the ecological niche for Homo Sapiens is preserved. In the second place, the problem of bifurcations, i.e. such states of the biosphere, in the vicinity of which the future coevolution of Humans and the biosphere cannot be predicted in principle, is of interest.

3.2 Methodology to be applied

The idea of a united mechanism of functioning and the concept of the continuity (both in space and in time) of biosphere processes allow us to use systems of differential equations in partial derivatives for their description (for example, equations of continuity for the law of conservation), which should be supplemented by the equations for momentum and energy.

We consider the biosphere as a composition of five mediums: *atmosphere, *vegetation (including agricultural vegetation), *hydrosphere (ocean), *pedosphere (soils), *anthroposphere (industry). Every medium is a continuous medium, i.e. the law of matter conservation is expressed as equations of continuity for each of these mediums. In addition, these mediums are active, because an active transport of matter in possible both inside them and between them, and there is interrelation between any two points, influencing their state (for example, competition).

We should realize that in the process of modelling we will meet two types of uncertainties. Firstly, there are natural uncertainties, stipulated both by incompleteness of information about the processes under consideration, and by principal deterministic impredictability of some processes (for example, local climate or succession of vegetation communities). Secondly, there are social uncertainties, caused by the impredictable behaviour of different human societies, especially in critical situations, when the role of irrational mentality may sharply increase. Therefore the modelling approach should contain stochastic elements, in particular, the risk concept and investigation of fluctuations in the spatially distributed system describing the biosphere.

3.3 Main methodological problems of the project

The first problem. For the biosphere must be identified and analysed: former concepts and experiences, the hierarchy of time and spatial scales, elementary units and processes, specific velocities, the coordination of different-scale processes and systems, procedures of correct averaging. This is the theoretical stage. As a result, we will realize how different spatial and temporal scales are interrelated. The requirements to be fulfilled are that the submodels should not require excessive accuracy and that important dynamic factors should not be lost due to too rough averaging. In other words, we should know how to proceed correctly from the model operating at the 1 km and 1 day scale to the model operating at the 1000 km and 1 year scale.

It would be ideal to find some invariances of biosphere processes (and if we consider their dynamic description by differential equations, then the corresponding group invariances as well). Then we could formulate the criteria of similarity for biosphere processes of different scales. Still, we have to use different empirical generalizations, resulting in different classifications both in space (division of biosphere on continents and oceans, biomes, landscape units, biogeocoenosises, communities, etc.) and in time (succession: year to year changes, seasonal community changes, growth rates and chlorophyll synthesis, photosynthesis). Still there is a problem - how to combine these spatial and temporal scales?

The second problem. The problem is how to implement different scales in the description of dynamic biosphere processes, i.e. how might the averaging on time and space in the initial equations be performed for scaling up from one level to the next one? It is really a very serious problem, as non-homogeneity at the lower levels (rapid fluctuations in time and fine spatial-scale variability) would (or would not) influence slower and more large-scale dynamics at the higher level.

The third problem. The problem is the compatibility between scales of theoretical models and scales of observations. Really the network of observations at our disposal is very incomplete and is not evenly distributed over the Earth's surface. The solution of the first two problems gives us the possibility to coordinate correctly the scales of theoretical models and databases. Let us assume that this problem is also solved, and we have the hierarchical structure of coordinated spatial and temporal scales, i.e. we have a shell for the future biosphere model, and the criteria for submodel selection in accordance with their scales and for their coordination.

The fourth problem is the modelling of anthroposphere processes, in particular, the assessment of an ecological niche for Homo Sapiens. This includes demographic processes, industrial metabolism, and social uncertainties in the behaviour of different groups and decision making. This includes also risk assessment and the concept of critical levels - all the factors connected to the biosphere processes, which are quite far from our main task, which is the development of a physical-chemical-biological-mathematical model of the Biosphere.

The fifth problem. This is one of the key problems in global modelling - how to verify the model. The biosphere is different from any other natural system, being the only single unique system without any analogue system existing, and experiments with the biosphere are not possible. Besides, we have no time series of the biosphere parameters for the time periods of interest (about 100-1000 years), we have only a ,,snapshot" of this system. Paleonthologic and geologic data are too rough or have different interpretations. How can we manage to get out of this trap?

Firstly, there is the hypothesis of quasistationarity, i.e. that the current state of the biosphere is a stationary state (or close to it). Secondly, we can use certain scientific paradigms, an empirical generation of the Vernadsky concept, the paradigm of model trajectories stability and structural stability. Criteria of stability can be used for model verification and selection. The paradigm of evolution (or Darwin paradigm) can be used as well. We suppose that the current state of the biosphere is the result of evolution and the natural selection process, being one of many possible variants. Therefore, the models should have some properties of selectivity, i.e. they should be nonlinear models with many equilibrium states. Thirdly, the models should satisfy the laws of conservation (energy, matter and momentum), as the biosphere is practically a closed system (for matter) and a flowing system (for energy). This means that the biosphere is a typical dissipative structure. Fourthly, the models should not be contradictory from the thermodynamic point of view, as the biosphere is thermodynamically an open system, located far from the thermodynamic equilibrium.

The successive application of these criteria for selection and the correct mathematical methods of modelling allow to hope that such a model would adequately describe the biosphere dynamics.