By Ralf Seppelt
Seppelt (computer technology, geographic info structures, and theoretical ecological and numerical environmental modeling, Technical U., Brunswick) explains the mathematical basics of computer-based environmental administration, targeting major matters: the combination of alternative modeling ways and the applying of optimization and optimal keep watch over idea. Sections hide the next themes: phrases, methodologies, and an summary; a translation of conceptual versions into equations; a dialogue of the implications bought within the context of meta modeling and medical idea; functions of hybrid versions in biology; an environmental review document; the mathematical foundations of the integrating modeling suggestion; the applying of environmental types in optimization; and functions of suggestions.
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Extra resources for Computer-Based Environmental Management (2003)(en)(300s)
2 Agroecological processes on different time scales and the modeling approaches. : ODE: ordinary differential equation; DAE: difference algebraic equation; DDE: delay differential equation; PDE: partial differential equation. Process Variables Characteristic time Mathematical model Growth of microbial populations Nitrification, denitrification Degradation, volatilization of agrochemicals Populations dynamics Biomass, Nitrogen content, activity NH+4 , NO−3 , N2 O, N2 , microbial activity Concentration in liquid and solute phase 30 minutes ODE 1 day to 1 week System of ODE Minutes to weeks System of ODE Weeks to vegetation periods Month Matrix equations, DAE, DDE (Systems of) ODE Vegetation period DAE 1 hour PDE Large spectrum PDE coupled ODE systems PDE coupled ODE systems Crop growth Population dynamics of weed Water transport in unsaturated soil zone Solute transport in unsaturated soil zone Solute transport in aquifer Density of eggs, juveniles, larvae, adults Organ biomass, nitrogen content, leaf area index Seed dispersal, coverage level Water content Concentration in liquid and solute phase Concentration in liquid and solute phase up to several years with with spatially explicit data requires the choice of an appropriate data model.
Complexity Characterization of the spatial or temporal scale is related to the definition of a certain degree of complexity or simply complexity. Complexity of systems systems are characterized by four topics (Wu & Marceau, 2002). Complex systems: • are thermodynamically open, they exchange energy, mass or information with their environment; • are composed of a large number of of diverse components; • have systems components that interact in a nonlinear way; • exhibit a high degree of heterogeneity in time and space.
Additionally, the matrix model is an intermediate format to translate between different conceptual models, see Chapter 4. Matrix conceptualization or matrix models are a tool for model description and analysis as well as an additional conceptualization methodology. 2 Properties: Granularity, Extent and Scale Modeling environmental systems requires selection of a problem-specific set of processes, that is — as mentioned above — albeit and subjective. This focus is defined by the problem to be solved.
Computer-Based Environmental Management (2003)(en)(300s) by Ralf Seppelt