j - Dipartimento di Matematica - Politecnico di Torino

A mathematical procedure for the evolution of future landscape scenarios.
Authors: F. Gobattoni 1 , G. Lauro 2 , A. Leone 1 , R. Monaco 3 , R. Pelorosso 1
1 Department of Environment and Forestry, University of Tuscia, Viterbo (Italy)
2 Architecture Faculty, Second University of Naples, 81031 Aversa, (Italy)
3 Department of Mathematics, Politecnico di Torino, Torino (Italy)
Corresponding author: f.gobattoni@unitus.it
Introduction
Since the European Landscape Convention aims to encourage all European countries to define their
landscape quality objectives, a new frame of mind in management and planning of territory is
nowadays required as a point of reference for territorial government, entities and authorities, so as
to advance towards conservation and protection of landscapes providing positive impact on the
quality of life of population. Moreover, planning efficiently at the landscape scale needs a crosssector
cooperation and people involvement with planners and communities working closely in
achieving positive landscape change understanding and in characterizing the relations between
nature and society, which will integrate landscapes and their dynamics. (C. Petit et al., 2008).
The methodologies for successful landscape and environmental planning have been severely
challenged when classical concepts and models such as economic and socioeconomic development,
ecosystems preservation and sustainability have been questioned (J. E. Vermaat et al., 2005). The
actual challenge is to build transparent and flexible decision-making tools to be used in
environmental planning and to embrace a broad range of stakeholders needs together with
landscape management requirements.
Landscape-scale geographical information provides an ideal framework for developing spatial
strategies and to implement simulation models to support landscape planning identifying
opportunities for change and anticipating and comparing the results of planning decisions. Model
outputs can be used to elaborate thematic maps and visualizations of landscape scenarios as an
effective and direct way of communicating results and opportunities.
In this framework, landscapes can be defined as spatially extended heterogenous complex systems
organized hierarchically into structural arrangements determined by nonlinear interactions among
their components through flows of energy and materials (we shall use the overall term "bio-energy"
as introduced by Ingegnoli, 2002 ). Human activity has, also, strongly modified recent landscape by
means of land use and land cover changes and consuming of natural resources (Pelorosso et al.,
2009). Alterations of natural equilibriums has pointed out several consequences on landscape
capacity to furnish goods and service (Willemen et al, 2008) as biodiversity conservation
(Tscharntke et al., 2005) and regulation of water regimes (Lindborg et al., 2008).
Environmental available energy has been pointed out as a key factor in the explanation of many
ecological processes and theories (metabolic and species energy theory, biodiversity conservation)
recurring to different indeces (e.g. Net Primary Productivity, NNP, Actual Evapotraspiration, AET,
Potential Evapotraspiration, PET) (Hurlbert and Jetz, 2010; Currie, 1991; Carrara et al. 2010;
Brown at al., 2004). A more complete measure of available energy, so-called Biological Territorial
Capacity (BTC), was proposed by Ingegnoli (2002) considering a synthetic function of vegetation
metabolism. As the importance of energy exchange, although it is rare for a landscape to be in any
form of equilibrium and the landscape equilibrium concept is not yet clear (Perry, 2002; Turner et
al., 1993; Bracken and Wainwright, 2006), it’s interesting to focus on which hypothetical energetic
equilibrium state is going to be realized and the effects of human decisions on that equilibrium.
Most of mathematical models are strictly related to air dispersion, hydrology and hydrodynamics,
water quality, ground water quality, erosion and sedimentation, and so on, just taking into account
each aspect of the environmental system separately and without looking directly at landscape as a