j - Dipartimento di Matematica - Politecnico di Torino

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unique system and without understanding its intrinsic evolution mechanisms. All decision making involves an implicit (if not explicit) use of models, since the decision maker invariably has a causal relationship in mind when he makes a decision. So mathematical models able to explain the landscape evolution and to compare the effects of future scenarios on its evolution and equilibrium in time, are really needed not also to understand environmental system mechanism and behaviour but above all to better plan strategies for natural resources conservation management and landscape preservation. The environment is here considered as composed by several Landscape Units (LU) delimited by natural and/or anthropic barriers. An integrated GIS (Geographic Information System)-based approach was developed (G. Lauro, R. Monaco, 2008) combining an ecological graph model for the analysis of the relationship between spatial pattern and ecological fluxes and a mathematical model, based on a system of two nonlinear differential equations. These equations are mainly based on a balance law between a logistic growth of bio-energy and its reduction due to limiting factors coming from environmental constraints. The energy exchange among them will be more or less strong depending on the degree of permeability of the barriers which can obstruct the energy passage from each LU to the other. A GIS-based mathematical model, based on the ecological graph and on the cited two differential equations, is presented and discussed here. A study case in Central Italy is introduced and discussed here just to show the importance of a such mathematical procedure to figure out planning strategies and environmental conservation and management actions with the support of rigorous methods able to fix and compare the effects of anthropic decisions on landscape. Study area description The study area (Fig. 1) for the model development, is Traponzo River catchment; Traponzo River is located in the northern part of Lazio Region and its watershed covers part of nine municipalities, lying completely in the Province of Viterbo. This stream originates in Monti Cimini relief and flows into Marta river so that Traponzo catchment, as a sub-basin of Marta river, has a total area of 475 Km 2 , with a mean elevation of 526 m a.s.l. and a maximum of 979 m a.s.l.. The climate of this area is quite Mediterranean with a mean annual temperature of about 15°C and a mean annual precipitation of about 970 mm. The total area covered by urban sprawl is about 2.23 km 2 that is about 10% of the total urban area. Land cover class Area (km 2 ) % Urban 21.02 4.4 Forest 126.36 26.6 Non irrigated crops 203.04 42.8 Pasture 22.01 4.6 Orchards 88.17 18.6 Irrigated crops 2.49 0.5 Hedges 11.77 2.5 Water bodies 0.02 0 Total area 474.89 100 Table 1.
Fig.1. Study area
Page 1 and 2: hard copy ISSN 1974-3041 on-line IS
Page 3: A mathematical procedure for the ev
Page 7 and 8: in other words M max is the maximum
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Page 11: References Bracken L. J and Wainwri

j - Dipartimento di Matematica - Politecnico di Torino

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