Raffaele Pelorosso, Federica Gobattoni, Roberto Monaco and Antonio Leone on "A new approach for the assessment of landscape evolution scenarios: from whole to local scale"

1. Seventh International Conference on Informatics and Urban and Regional Planning
10‐12 May 2012, University of Cagliari
A new approach for the assessment of
landscape evolution scenarios: from whole to
local scale.
by Raffaele Pelorosso1, Federica Gobattoni1, Roberto Monaco2 and Antonio Leone1 .
1 DAFNE Department, University of Tuscia,
Viterbo, Italy.
2 Dipartimento Interateneo di Scienze, Progetto
e Politiche del Territorio, Politecnico di Torino,
Torino, Italy

2. Landscape Equilibrium
Landscape continuously evolves. The interactions between human actions and natural
processes are evolved together researching an equilibrium, usually precarious or
metastable, based on fundamental physics laws as the energy conservation and entropy
growing principles (Kleidon, 2010; Naveh, 1987; Pelorosso et al., 2011).
All ecosystems, as open
systems, continuously exchange
energy, nutrients and biomass
with the environment through
irreversible processes.
Ecosystems evolve developing
highly ordered, lower entropy
structures to increase the total
dissipation of energy and
maximize the “global”
production of entropy
(Gobattoni et al., 2011).
Ecosystems strive to increase
their ability to degrade
incoming solar energy, and
much of this dissipation occurs
through vegetation (Brunsel at
al., 2011).

3. Landscape is a complex system
Human actions
(infrastructures, urban
development, natural
resources exploitation
etc) behave as external
constraints imposed on
the eco‐system,
reducing flows of
energy and matter; they
alter the dynamic
flux
equilibrium affecting
landscape evolution in
terms of functionality,
biodiversity reduction,
as well as accelerated
erosion phenomena and
hydrological instability.
flux
These external
constraints represent
obstacles to the
connected fluxes of
flux
energy and matter
(barriers), leading to
local reduction of
entropy and to the
creation of organized
systems (Chakrabarti More energy exchange
and Ghosh, 2010). more landscape resilience and biodiversity are ensured

4. Introduction
Modelling the energy fluxes and variation of landscape energetic
equilibrium state, is therefore interesting because it could allow
to assess the most suitable plan strategies for natural resources
conservation management and landscape functionality
preservation.
Numerous physical and empirical models have been developed
to simulate landscape and vegetation dynamics in time in order
to explain environmental evolution and equilibrium conditions.
Although these efforts, a macroscopic theory about landscape
rules and its variables still lacks (Chakrabarti and Ghosh, 2010;
Coulthard, 2001; Jorgensen, 2004) and if some equilibrium is
observed it may only be seen at certain spatio‐temporal scales
(Pickett at al., 1994).

5. An innovative procedure, called PANDORA, Procedure for mAthematical aNalysis of
lanDscape evOlution and equilibRium scenarios Assessment, was proposed to assess the
effects of different planning strategies on final possible equilibrium states that are
energetically stable.
It provides a tool for the evaluation of landscape functionality and its resilience.
PANDORA, linking together thermodynamic concepts, mathematical equilibrium,
metabolic theory and landscape metrics, allows to model landscape evolution in time
under the impact of external constraints and giving a unique response from it in terms of
energy.
All the parameters required by the mathematical model can be obtained from GIS data,
which are usually available to land managers.
The model is proposed as a Decision Support System for choosing among possible
planning strategies following a holistic approach.
Urban sprawl
2000
2005

6. For more details:
GOBATTONI F., LAURO G., LEONE A., MONACO R., PELOROSSO R. (2010). “A mathematical
procedure for the evolution of future landscapes scenarios”. LIVING LANDSCAPE The European
Landscape Convention in research perspective.” Firenze, 18‐19 Ottobre 2010. Vol II. ISBN 978‐88‐
8341‐459‐6.
GOBATTONI F., LAURO G., LEONE A., MONACO R., PELOROSSO R. (2010). “A mathematical
procedure for the evolution of future landscapes scenarios”. La Matematica e le Sue Applicazioni n°
11. Hard copy ISSN 1974‐3041. Online ISSN 1974‐305X.
GOBATTONI F., PELOROSSO R., LAURO G., LEONE A., MONACO R. (2011). PANDORA: Procedure for
mAthematical aNalysis of lanDscape evOlution and equilibRium scenarios Assessment. EGU
General Assembly, Session ERE 5.1 Landscape functionality and conservation management, 3 ‐ 8
April 2011, Vienna, Austria. Vol. 13, EGU2011‐4023‐1, 2011.
GOBATTONI F., PELOROSSO R., LAURO G., LEONE A., MONACO R. (2011). A procedure for
mathematical analysis of landscape evolution and equilibrium scenarios assessment. Landscape
and Urban Planning, 103:289‐302.
GOBATTONI F., LAURO G., MONACO R. PELOROSSO R. (2012). Mathematical models in landscape
ecology: Stability analysis and numerical tests. SUBMITTED.

7. PANDORA: Procedure for mAthematical aNalysis of lanDscape
evOlution and equilibRium scenarios Assessment.
PANDORA model was proposed to assess the effects of different planning strategies on final
possible equilibrium states that are energetically stable. It is able to describe and assess the
environmental fragmentation due to external constrictions .
The whole model implementation procedure is constituted by 3 sequential steps :
⎡ M (t) ⎤
M ' (t ) = cM ( t )⎢1 − − k [1 − V (t )]M (t ),
⎣ M max ⎥
⎦
V ' (t ) = bT V (t )[1 − V ( t )] − h U 0V ( t ),
2) Calculation of Generalized
1) Landscape Units 3) Resolution of differential
Biological Energy and
definition equations
Landscape graph building

8. 1. Landscape Units
Identification
In this case, a Landscape Unit (LU) is
considered as an area delimited by
significant barriers to energy fluxes. LUs
were pointed out by means of holistic
classification method (Van Eetvelde and
Antrop, 2009).
Most important factors that represent the
barriers to energy fluxes were weighted
(Saaty matrix) and used to individuate
LUs.
In order of importance used barriers can be
identified as follows:
1) Main roads and railways
2) Lines of change between very different
soil types
46 Landscape Units
3) Limits between hill and mountain areas Minumun LU 0.36 Km2
Maximun LU 29.26 Km2

9. 2. Calculation of Generalized BTC, Biological Territorial Capacity, is a physical quantity measured in
Biological Energy and Mcal/m2/year, linked with the capacity of vegetation to transform solar
Landscape graph building energy. By considering the concepts of biodiversity (i.e., landscape diversity),
resistance stability and the principal ecosystem types and their metabolic
Calcolation of Generalized data (biomass, gross primary production, respiration), the BTC index seems
Biological Energy to sum up the available energy in an ecosystem.
The BTC index can assess the flux of energy that an ecological system needs
to dissipate to maintain its level of metastability, i.e., its temporaneous
stability condition
BTC, Biological Territorial Capacity
Ingegnoli (2002)
M j = (1 + K j ) ⋅ B J
Generalized Biological
Energy (GBE) or bio‐energy
of LUj
LU characteristics
(energy diversity, shape, climatic conditions,……)
Land cover K j = (K S + K P + K D + K C + K E ) /5
j j j j j
The energy flow between LUs can be derived from Biological Territorial Capacity, BTC, (Ingegnoli,
2002) through the definition of a Generalized Biological Energy as the available energy for each LU.
M is the energy available for exchange between LUs and it depends on several intrinsic
characteristics of each LU such as energetic diversity inside it, barriers in it, shape, climatic
conditions, permeabilities of the boundaries and so on.

10. 2. Calculation of Generalized
Biological Energy and
Landscape graph building
Landscape Graph building
‐Barriers with different degrees of permeability
to the flow of bio‐energy.
‐Bio‐energy (M) of each LU represented by
proportional nodes.
‐Energy exchange flux, (F), between LUs
depends on the degree of permeability of the
barriers.
‐Connections between LUs are represented by
arcs, whose thickness is proportional to the
magnitude of the energy flux between LUs
Lij pij
Mi + M j
Fij = ⋅
2 Pi + P j
Mi and Mj are the Generalized Biological Energies
correspondent to LU‐i and LU‐j, respectively, Lij is the length
of the boundary between LU‐i and LU‐j and Pi and Pj are the
perimeters of LUi and LUj, respectively. pij ∈ [0;1] is the mean
permeability index of such a boundary.

11. 3. Resolution of differential The PANDORA evolution model uses a system of two nonlinear
equations differential equations (a kind of Lotka‐Volterra model) and is based on
a balance law between a logistic growth of energy and its reduction
due to limiting factors coming from environmental constraints
Analysis of M and V variation in time t until the reaching of mathematical equilibrium (asymptotic)
⎡ M (t) ⎤ V ' (t ) = bT V (t )[1 − V ( t )] − h U 0V ( t ),
M ' (t ) = cM ( t )⎢1 − − k [1 − V (t )]M (t ),
⎣ M max ⎥
⎦
M(t)= Generalized Biological Energy of the whole system. It is derived from BTC values and intrinsic
characteristics of each LU
V(t)= fraction of the total territory occupied by areas with high values of BTC (e.g forests)
•U0 depends on urban areas (compact and sprawl)
•h depends on urban perimeters (compact and sprawl)
•k depends on global impermeability of barriers
•bt is related to mean BTC value of the system
•c is the connectivity index and depends on number and amount of fluxes

12. Beside the interesting results, the model presents some drawbacks:
1‐ parameters bT and c are time‐independent (this assumption is not realistic
since bio‐energy production and connectivity must change during environment
evolution).
2‐ relative small and/or localized modifications of landscape connectivity and
GBE could be not well assessed by the model. Indeed, the model works with
global variables for all the system and local environmental quality variations
could be balanced by the response of another portion of the studied territory.
For these reasons a new model, overcoming these simplifications, is proposed
(PANDORA2?) on the basis of the following aims:
1) To investigate the landscape evolution at the level of each LU and not only at
that of the whole environment under investigation;
2) To re‐define the connectivity index making it time‐dependent so that the
links between the LUs are updated at any time;
3) To make the dimensionless variables defined with respect to absolute
quantities.

13. The new PANDORA differential equations system:
Mi
M i = max
M = ci M i (1 − M i ) − ν i (1 − Vi ) M i
i
'
Mi
Vi
Vi = M iVi (1 − Vi ) − µiU iVi
' Vi =
Ai
where the constants νi, µi and Ui play almost the same role of h, k and U0, but this time
are referred to each LU, i = 1,….,n, so that
νi are the ratios between the sum of all the perimeters of the
impermeable barriers inside the i‐th LU and the perimeter Pi of the LU
itself;
µi are the ratios between the sum of the perimeters of all the compact
edified areas (those with lower BTC (0‐0.4)belonging to class A) inside the
i‐th LU and Pi;
Ui are the ratios between the sum of the surfaces of all the edified areas
inside the i‐th LU and Ai.

14. The connectivity indexes cik between two LUs i and k, as well as the total
connectivity index ci between the i‐LU and all its neighbors can be defined by the
following formulas:
c can be greater than one
where Ii is the set of the neighbors of the i‐th LU.
LUk LUi LUk
LUk LUk LUk
LUi LUk LUk LUk LUk
LUi
LUk LUk LUk
LUk LUk
LUi LUk
LUk LUk LUk LUk
LUk LUi

15. Once the variables Mi(t) and Vi(t) are known from the
new equations, one can recover, at each time t, the
corresponding variables at the level of the whole
environmental system; in particular the non-
dimensionless variables M and V can be computed by
whereas the dimensionless ones M and V referred to
the whole system are given by

16. Study case
Subset of 8
landscape units.
The total area
covered by urban
sprawl is about
21% of the total
Lazio Region
urban area.
Road and railway
networks are highly
developed (183.7
Km).
A new stretch of
the Orte-
Civitavecchia
freeway (dashed
line) was completed
during the year
2011 and it crosses
the LU No.26.
Scenario analysis
Scenario A without the stretch of the freeway Orte-Civitavecchia
Traponzo watershed Scenario B with the completed freeway (actual landscape)

17. RESULTS and DISCUSSION
The table shows the values of the model parameters for each simulated LU in
the initial conditions. i.e. scenario A, without the last stretch of the free-way
Orte-Civitavecchia that was completed during the year 2011. In this Table
changed values referred to scenario B are reported between brackets.
LU Vi Mi Ui µi νi
9 0.0000 0.044 0.689 1.317 1.859
13 0.0317 0.191 0.014 0.084 0.286
14 0.3895 0.423 0.013 0.222 0.835
22 0.4329 0.457 0.006 0.005 0.562
24 0.0335 0.206 0.021 0.909 0.566
26 0.1604 (0.1601) 0.257 (0.256) 0.016 (0.017) 0.347 (0.746) 1.517 (1.956)
29 0.0624 0.185 0.014 0.912 0.341
41 0.2226 0.311 0.016 0.177 1.029

18. Evolution trends of the variables V(t) and M(t) for LU n°26. a) scenario A; b) scenario B.
0.3 0.3
a) M
V
b) M
V
0.25 0.25
0.2 0.2
0.15 0.15
0.1 0.1
0.05 0.05
0 0
0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50
Evolution trends of the variables V(t) and M(t) for LU n° 24: a) scenario A; b) scenario B.
0.2
b)
0.2
a) M
V
M
V
0.18 0.18
0.16 0.16
0.14 0.14
0.12 0.12
0.1 0.1
0.08 0.08
0.06 0.06
0.04 0.04
0.02 0.02
0 0
0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50

19. Evolution trends of the variables V(t) and M(t) for the whole environmental system
in scenario A (black lines) and scenario B (grey lines)
0.7
0.7
a) M
V
0.6
0.6
0.5
0.5
0.4
0.4
PANDORA2
0.3
0.3
0.2
0.2
0.1
0.1
0
0 5 10 15 20 25 30 35 40 45 50
PANDORA2 differential equations consider the time evolution of parameters and the
feedback effects between them.
To better understand the complex mechanism of cause and effect underlying
landscape evolution dynamics, a holistic approach should be pursued, but local
critical status of landscape health can be pointed out recurring to the simulation of
the evolution of the global variables at local level, namely at the level of each LU.

20. CONCLUSIONS
PANDORA2 can provide a reliable tool to estimate the effects of actions and
strategies on the landscape equilibrium conditions not only at the whole landscape
scale but also at that of each LU.
Local critical values of the variables chosen to describe the health of the landscape
can be pointed out only recurring to the simulation of the evolution of the same
variables at local level, at the level of each Landscape Unit.
The parameters and indices of the model can suitably represent the ecological
health of the landscape and can be used alone or in combination to assess and
compare landscape scenarios.
Further effort is needed to accurately test this new dynamical model to real-life
applications assessing its sensibility in order to develop a more helpful tool for “what
if " scenarios analysis and planning strategy conception.
Raffaele Pelorosso
pelorosso@unitus.it
Thank you very much!