Mathematical Tools

Huge amounts of data become available in large-scale diagnostics. Networks of functional systems, sub-systems and supra-systems are emerging. The methods described in Sects. 2.2-2.5 reveal spatiotemporal pattern formation. We deal with multidimensional problems, which have to be summarized numerically or graphically and must be cast into a comprehensive presentation. This may possibly constitute the most important bottleneck. Hobbs and Mooney (1990) conclude their book on remote sensing of the biosphere functions with the statement, that even without the intensive further development of new sensors, the currently available technologies offer so much that the capacity for interpretation and application has been surpassed. The major problems do not appear to be with collection but with analysis and understanding of data.

The data mountains piling up require hardware and software technologies for storage and organization. Special statistical and mathematical procedures are essential to reduce the relevant information from the mass of data to an interpretable form, and the analysis of data needs the development of new mathematical approaches (Hütt 2001). Special geographic information systems with multi factorial mapping are designed to provide surveys related to space (Wallace and Campbell 1990). Image analyses use the concept pf cellular automata and nearest neighbour algorithms to unravel spatiotemporal structures of patterns (Hütt and Lüttge 2002, 2005).

A particular problem of great fascination is the non-linear dynamics of all the ecosystems studied. In phytosociology unpredictability, e.g. in occupation of new habitats by species, is often readily interpreted as demonstrating that the distribution of plants and the development of diversity is stochastic. Taking the term stochastic in its strict mathematical meaning, this is by no means so simple. Stochastic white noise in empirical data time series can not readily be distinguished from the so-called deterministic chaos, which follows strict mathematical rules. A distinction between the two can only be made via sophisticated theoretical analyses requiring very detailed sets of time series data. These are rarely available, and hence, it is hard to prove whether deterministic chaos or stochastic noise predominate.

Fig. 2.15A-C Comparisons A

of predictability in (A) random, (B) regular and (C) chaotic motion. (Modified after Schuster 1995)

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Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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