Replication of Agroecological Models on Map Grids in Visual Studio .NET

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is typical of numerical solutions of hyperbolic partial differential equations [6,7]
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REPLICATION OF AGROECOLOGICAL MODELS ON MAP GRIDS 7-15 A Geographical Information System The SAMT (Spatial Analysis and Modeling Tool) program package developed by R Wieland [10,11] is a simple geographical information system for description and manipulation of ecological data SAMT declares and stores arrays of numerical landscape-feature values for a specified grid of geographical locations Examples of landscape features are geographical coordinates for each grid point (x, y, altitude) physical data such as temperature, soil moisture, and species counts at each grid point SAMT can assign and calculate functions that relate different landscape features at any one grid point, say
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q1 = q2 + q3 q1= cos(q2) q1 = calc(q2, q3, )
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Functions such as calc(q2, q3, ) are either numerical expressions or regression functions previously created by simple neural-network or fuzzy-set models [11] SAMT can also assign and store grid-point data values that depend on data at other grid points, such as the distance of the current grid point from another grid point, say, from a city or from a bird s nest; or the shortest distance to a river or road SAMT can, moreover, accumulate statistics such as averages and statistical relative frequencies for an entire set of grid points Last but not least, SAMT can draw maps showing grid-point data values in different colors, or showing contour lines for different landscape features (Fig 7-10) 7-16 Modeling the Evolution of Landscape Features The original SAMT database described a landscape at coarsely spaced sampling times t (eg, once per day, per month, and per year), but the program did not relate landscape features at different sampling times In contrast, DESIRE uses small time steps DT to simulate continuous changes A combination of SAMT and DESIRE can model changes of landscape features at each separate grid point with differential equations and/or difference equations SAMT/DESIRE runs under both Linux and Windows (Figs 7-11 and 7-12)
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FIGURE 7-10 A map of relative vegetation density produced by the SAMT geographical information system [12] The original display was in color
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FIGURE 7-11 A self-scaling SAMT/DESIRE graphics window Three-dimensional graphs can also be displayed
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References
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FIGURE 7-12 SAMT/DESIRE dual-monitor display under Microsoft WindowsTM To simplify interactive modeling for nontechnical users, SAMT/DESIRE simulations are programmed and run from a special editor window designed by R Wieland and X Holtmann [12] A clickable program-selection directory is on the left
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Some landscape features will be state variables with specified initial values Other landscape features, such as intermediate results and data transferred to and from the SAMT data base, are defined variables, as described in Sections 1-2 and 2-1 One might, for example, have a differential-equation system modeling competition between local predator and prey populations (Section 1-12) at each grid point Local crop growth is another promising application [15]
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REFERENCES 1 F Breitenecker and I Husinsky, Results of the EUROSIM comparison Lithium Cluster Dynamics, Proceedings of EUROSIM, Vienna, 1995 2 G A Korn, Interactive Dynamic System Simulation with Microsoft Windows, Francis and Taylor, London, 1998 3 B Kosko, Neural Networks and Fuzzy Systems, Prentice-Hall, Englewood Cliffs, NJ, 1991 4 G A Korn, Neural Networks and Fuzzy-logic Control on Personal Computers and Workstations, MIT Press, Cambridge, MA, 1995
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5 G A Korn, Simulating a fuzzy-logic-controlled nonlinear servomechanism, SAMS, 34, 1999, pp 35 52 6 W E Schiesser, The Numerical Method of Lines, Academic Press, New York, 1991 7 W E Schiesser and C A Silebi, Computational Transport Phenomena, Cambridge University Press, Cambridge, 1997 8 A Tveito and R Winther, Introduction to Partial Differential Equations, Springer, New York, 1998 9 G A Korn, Interactive solution of partial differential equations by the method of lines, Math and Computers in Simulation, 1644, 1999, 1 10 10 G A Korn, Using a runtime simulation-language compiler to solve partial differential equations by the method of lines, SAMS, 37, 2000, pp 141 149 11 R Wieland, Spatial Analysis and Modeling Tool, Report, ZALF Institut fur Landschaftsystemanalyse, Muencheberg, Germany 12 G A Korn and X Holtmann, Spatial analysis and modeling tool a new software package for landscape analysis, Simulation News Europe, December 2005 13 G A Korn, Simplified function generators based on fuzzy-logic interpolation, Simulation Practice and Theory, 7, 2000, pp 709 717 14 M Wang and J M Mendel, Fuzzy basis functions, IEEE Trans Neural Networks, 3, 1992, pp 807 818 15 R Wieland and M Voss, Spatial analysis and modeling tool possibilities and applications, Proc IAST Conference on Environmental Modeling and ED Simulation, November 2004
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