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SUPPLEMENT ARY MATERIAL
Land use change models
Models to study LUCC can range from equation-based models (Parker et al., 2003;
Ligmann‐Zielinska et al., 2008; Abe et al., 2018), system dynamics models (Liu and
Deng, 2010), statistical models (Munroe et al., 2002; Ku, 2016; Wang et al., 2019),
expert system models (Dujmovic et al., 2009; Le et al., 2010), evolutionary models
(Glanville and Chang, 2015a), cellular automata models (Cho et al., 2007; Vliet et al.,
2009; Santé et al., 2010), and agent-based models (Ligmann-Zielinska and Jankowski,
2007; QuanLi et al., 2015) to hybrid models (Kocabas and Dragicevic, 2007; Jjumba
and Dragicevic, 2012; Pérez-Vega et al., 2012). Not only has the type of LUCC models
made for a panoply of literature, but also has the great variety of applications. Among
few of them, literature reports the analysis of patterns associated to urban growth (De
Groot et al., 2010; Nurwanda et al., 2016; Sefidi and Ghalehnoee, 2016; Zhang et al.,
2017; Huang et al., 2018), future modelling of land-use changes (Ward et al., 2000;
Singh, 2003; Al-Khatib et al., 2007; Catalán et al., 2008; Rigol-Sánchez et al., 2011;
Bussi et al., 2016; Liu et al., 2017; Traore and Watanabe, 2017; Gounaridis et al., 2019),
and the study of socio-environmental impacts derived from those changes (Lambin and
Meyfroidt, 2010; Seneviratne et al., 2010; Bajocco et al., 2012; Röder et al., 2015; Popp
et al., 2017; Gashaw et al., 2018). Although a large amount of research presents
methods and applications to study LUCC, to the authors’ knowledge, there are no
scientific publications that approach the illegal landfills matter. It is also important to
highlight that among the previously listed studies of LUCC, many have used modelling
approaches based on complex systems theory.
Complex systems modelling: cellular automata and hybrid approaches
Complex behaviours can be replicated by using simulation approaches that allow the
integration of stochasticity and spatiotemporal fluctuations. Cellular automata (CA)
models are amongst these approaches, CA models have been widely used to mimic and
study land-use cover and change dynamics, due to their capability to reproduce non-
linear processes (Wolfram, 1984; White and Engelen, 2000; Engelen, 2002; Vliet et al.,
2009). CA were developed by the mathematicians Alan Turing and John von Neumann
in the 1940s (Batty, 2005; Langlois, 2008). These approaches have been widely used to
create simulations of future scenarios ( Langlois and Phipps, 1997; Engelen, 2002;
Syphard et al., 2005; Di Traglia et al., 2011; Yu et al., 2011; Liu et al., 2014;), to study
land-use changes (Pontius et al., 2004; Nurwanda et al., 2016; Feng and Tong, 2017), as
well as for understanding complex processes that have high levels of uncertainty, such
as the appearance of ILs. CAs are composed by a matrix of cells that represent the
spatial environment under study. Each cell has a state or value that can change in time
depending on the previous state and according to the set of rules applied at a discrete
time within an specific neighbourhood (Green and Sadedin, 2005). The transition rules
are thus applied homogeneously to all cells for each discreet time step. Although
powerful, one of the main issues of using CA to simulate changes is the deterministic
nature of the rules creation. To overcome this limitation, alternative hybrid approaches
can be implemented. The combination of CA with a Markov decision process, adds
stochasticity to the model, while the combination of CA with the Logistic Regression
(LR), or Multicriteria Analysis (MA) provide an alternative way to eliminate the
determinism in the transition rules creation.
As CAs, Cellular automata – Markov (CAM) and multi-objective land allocation
(MOLA) enable the analysis of changes in terrestrial covers, detecting and locating their
future tendencies for change (Pontius et al., 2004). CAM is a combination between CA
and Markov chains (MCs). CAM recognises the spatial contiguity of each cell as well as
its spatial distribution probability based on MC analysis. This allows a transition area
matrix and a transition probability matrix to be obtained for a certain time interval. The
former enables total area (in pixels) to be obtained, which changes between any land
cover class pair. The latter indicates the probability of change for each land cover class
determined for all other categories. Hence, use of the transition probability matrix
makes it possible to obtain information about the influence of neighbouring cells on
those transitions (Eastman , 2015). Both matrixes in CAM can be used to implicitly
insert the necessary suitability maps to develop a simulation. Suitability maps in CAM
can be generated by using LR or MA approaches. LR is an extensive procedure of
statistical inference in predictive modelling of land-use changes (Feng and Tong, 2017;
Tiné et al., 2018). It consists in maximising the logarithm of a binomial probability. The
relationship between observations and prediction characteristics thus define the
response (0/1) of the i-observation by means of a logistic function. The latter represents
the probability of a binary response based on unknown regression parameters. Hence,
the probability of change of a ground cover without IL to IL and vice-versa can be
modelled, within a pre-set time interval, using the linear combination of characteristics.
Alternatively, MA is a procedure used to define the criteria that control the behaviour of
a phenomenon. There are numerous focuses for its application to resolve environmental
problems, such as direct allocation by simple appraisal (Gómez-Delgado and Barredo-
Cano, 2005), direct allocation by order (Barredo-Cano, 1996), seven-point scale
(Gómez-Delgado and Barredo-Cano, 2005), and comparison by pairs (Saaty, 1980). The
weight granted to characteristics involved in IL proliferation can be assigned using the
method of direct allocation by simple appraisal (Clark Labs, 2016). The option of
weighted linear combination can be used to produce suitability maps in the calibration
process (Hajehforooshnia et al., 2011).
On the other hand, the multi-objective land allocation (MOLA) algorithm can be used to
assign new land-use transitions and predict changes (Clark Labs, 2016). MOLA allows
the use of suitability maps based on LR and Multi-Layer Perceptron Artificial Neural
Network (ANN) to help divide the amount of change predicted by MC in the different
land cover classes. ANN is a computational model based on a large group of simple
neural units (artificial neurons) in a manner somewhat analogous to the behaviour
observed in the axons of neurons in biological brains (Tino et al., 2015). ANN uses
logical functions such as AND or OR, XOR to separate different patterns into
categories. (Tino et al., 2015). ANN can classify the entry patterns between two classes.
In our case, the behaviour of the characteristics included in the database was determined
by the ability to correctly separate the sampling into presence or absence of ILs. The
partition and assignment of covers in MOLA is an iterative process, which also allows
unequal weighting of the different sub-objectives (Eastman et al., 1995; Eastman ,
2015). MOLA supplies a procedure to resolve multi-object land allocation problems for
cases with conflicting objectives (Hajehforooshnia et al., 2011). It also determines a
trade-off that attempts to maximise suitability of lands for each objective with respect to
their assigned weights (Hajehforooshnia et al., 2011). MOLA thus permits conversion
of the simulation into a dynamic process, by recalculating in each time step (discreet
simulation) certain conditions such as the modification of distances to land uses or to
protected spaces. MOLA therefore includes not just dynamic variables but also
recognises the changes produced in the characteristics.
Model calibration
Model 1 considered the characteristics’ importance within the logistic regression
equation (see supplementary material: Table 10s and Table 11s). The transition potential
maps could furthermore be evalued using the ROC curve. Model 2, based on MCE,
calculated IL potential based on restrictions (spatial limits) and the weighting of factors.
The latter express the potential relationship of a characteristic to the IL proliferation
phenomenon (see supplementary material: Table 12s). The characteristics were thus
standardised and weighted, assigning more importance to the influence of
communication routes, slope and distances to urban areas and agricultural areas (Tasaki
et al., 2007; Biotto et al., 2009; Morales-Matos et al., 2012; Alexakis and Sarris, 2013;
Quesada-Ruiz et al., 2018). Models 3 and 4 were calibrated using a set of transition
potential maps indicating the degree of suitability of a pixel for transition to another
class. Two transition potential maps were generated in each model for the periods:
2000-2006 (used in the validation); and 2006-2012 (used in the simulation for 2018).
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Tables
Table 1s. Model
characteristics associated to change potential evaluation.
Zone A Zone B
Year Count
Interannual growth rate (%)
IL surface (ha)
Interannual growth rate (%)
CountInterannual growth rate (%)
IL Surface (ha)
Interannual growth rate (%)
2000 144 67.823 334 135.8132006 202 5.803 88.352 4.501 529 7.965 233.654 9.54622012 270 4.955 153.416 9.642 650 3.463 345.217 6.725
Table 2s. Illegal landfills by zones and periods.
Year Urban Industrial Under construction Farmin
g Green zones
2000 2 0 0 33 272006 13 6 4 31 382012 16 16 2 52 67
Interannual growth rate (%)2000-2006 41.605 -0.891 5.416
2006-2012 3.869 19.727 -11.598 9.191 10.025
Table 3s. Illegal landfill affected areas (ha) by land cover in Zone A.
Year Urban Industrial Under construction Farmin
g Green zones
2000 11 18 0 66 402006 10 19 22 82 992012 15 47 35 118 128
Interannual growth rate (%)2000-2006 -1.998 0.455 3.516 16.440
Model ProgramChange potential
map
Analysis of drivers
Expert knowledge integration
Assessment
1 CA_Markov Suitability Logistic regression No
ROC, Fuzzy Kappa
2 CA_Markov Suitability Multicriteria evaluation Yes Fuzzy
Kappa
3 MOLA Transition probability
Logistic regression No
ROC, Fuzzy Kappa
4 MOLA Transition probability
Neural networks No Fuzzy
Kappa
2006-2012 6.334 16.707 8.262 6.259 4.400
Table 4s. Illegal landfill affected areas (ha) by land cover in Zone B.
Year Urban Industrial Under construction Farmin
g Green zones
2000 12 1 1 57 362006 37 10 2 56 73
2012 63 25 3 133 126
Interannual growth rate (%)2000-2006
21.099 47.265 14.043 -0.382 12.870
2006-2012
9.440 15.725 4.101 15.484 9.351
Table 5s. Number of illegal landfills within 250 m from different land uses in Zone A.
Year Urban Industrial Under construction Farmin
g Green zones
2000 44 29 10 111 80
2006 93 75 35 189 140
2012 141 133 52 276 217
Interannual growth rate (%)2000-2006
13.094 16.933 23.278 9.226 9.769
2006-2012
7.176 10.070 6.872 6.489 7.564
Table 6s. Number of illegal landfills within 250 m from different land uses in Zone B.
Zone Model Kstandard Kno Klocation QD AD
A
1 0.991 0.993 0.995 0.002 0.0032 0.990 0.993 0.994 0.018 0.0033 0.989 0.992 0.991 0.001 0.0044 0.989 0.991 0.991 0.001 0.004
B
1 0.985 0.989 0.989 0.002 0.0052 0.986 0.989 0.990 0.002 0.0053 0.982 0.987 0.984 0.001 0.0084 0.982 0.986 0.984 0.001 0.008
Table 7s. Kappa indexes – validation results
Zone Model kno klocation kfuzzy
A1 0.991 0.652 0.6102 0.989 0.621 0.6013 0.984 0.472 0.472
4 0.990 0.460 0.464
B1 0.990 0.583 0.6322 0.989 0.583 0.6403 0.981 0.502 0.5614 0.982 0.484 0.535
Table 8s. Fuzzy Kappa validation results for illegal landfill categories.
Zone Year 2000 2006 2012
APCI 86.507 86.323 88.923AI 80.754 79.097 83.032
BPCI 86.299 87.303 88.841AI 78.835 79.913 82.531
Table 9s. Evolution of Path Cohesion Index and Aggregation Index.
2000 2006 2012ALTITU 0.0017 -0.0011 -0.0040SLOPE 0.0065 0.0070 0.0056E_COAS 0.0001 -0.0001 -0.0001
E_CLIFF -0.0008 -0.0007 0.0004
E_PRAR 0.0004 0.0002 0.0002E_CARR 0.0001 0.0001 0.0003
E_WAYS -0.0065 -0.0048 -0.0019
E_FOAR 0.0002 0.0003 0.0002
E_CUAR -0.0001 -0.0002 -0.0001
E_DUAR -0.0002 0.0001 -0.0001
E_DAAR 0.0000 0.0001 -0.0001
E_IAAR -0.0002 -0.0004 -0.0004
E_GAAR 0.0005 0.0002 0.0003
CONSTANT-
4.5263 -6.0661 -5.4791ROC 0.93 0.92 0.93
Table 10s. Logistic Regression equations for transitions maps in Zone A.
2000 2006 2012ALTITU 0.0032 -0.0029 -0.0001SLOPE 0.0029 0.0034 0.0010E_COAS 0.0000 -0.0001 0.0000E_CLIFF 0.0002 0.0001 0.0001
E_CARR 0.0011 0.0006 0.0004E_WAYS 0.0003 -0.0001 -0.0001E_HIGH 0.0002 -0.0001 -0.0002E_TSAR 0.0000 0.0000 0.0000E_GAAR 0.0002 -0.0001 -0.0001E_WVAR 0.0000 0.0002 0.0001E_FOAR 0.0003 0.0002 0.0001E_COSI 0.0007 0.0000 0.0000E_DUAR 0.0000 0.0002 -0.0001
E_CUAR -0.0001 0.0001 0.0002
E_INAR -0.0002 -0.0003 -0.0005
E_DAAR -0.0009 -0.0001 0.0001
E_IAAR 0.0000 -0.0001 0.0000
CONSTANT-
7.6273 -4.2643 -4.0272ROC 0.90 0.90 0.89
Table 11s. Logistic Regression equations for transitions maps in Zone B.
Table 12s. Assigned weights for MCE.
Characteristics WeightE_HIGH 0.140E_CLIF 0.040E_ROAD 0.070E_COAS 0.090ALTITU 0.070SLOPE 0.150E_WAYS 0.080E_FORE 0.020E_CUAR 0.100E_INAR 0.050E_IAAR 0.100E_DAAR 0.020E_COSI 0.040E_TSAR 0.010E_WVAR 0.020
FIGURES
Figure 1s. Homes built in Spain and the Canary Islands from the year 2000 to the year 2016. Based on information from the National Statistics Institute of the Government of Spain, 2017.
Figure 2s. a) Illegal landfill locations in 2000 in north-western Gran Canaria; b) illegal landfill locations in 2006 in north-western Gran Canaria; c) illegal landfill locations in 2012; d) illegal landfill locations in 2000 in eastern Gran Canaria; e) illegal landfill locations in 2006 in eastern Gran Canaria; f) illegal landfill locations in 2012 in eastern Gran Canaria.
Figure 3s. Gains and losses of illegal landfill surfaces by areas. a) North-western Gran Canaria from 2000 to 2006; b) north-western Gran Canaria from 2006 to 2012; c) eastern Gran Canaria from 2000 to 2006; d) eastern Gran Canaria from 2006 to 2012.
Figure 4s. 2012 Illegal landfill simulation model for north-western Grand Canary: a) Logistic regression CA_Markov model; B) Multicriteria evaluation CA_Markov model; c) Logistic regression MOLA; D) Neural network MOLA.
Figure 5s. 2,012 Illegal landfill simulation model for eastern Grand Canary: a) Logistic regression CA_Markov model; B) Multicriteria evaluation CA_Markov model; c) Logistic regression MOLA; D) Neural network Land Change Modeller.
Figure 6s. 2018 Illegal landfill simulation model for north-western Gran Canaria. a) Logistic regression CA_Markov model; b) multicriteria evaluation CA_Markov model; c) logistic regression MOLA; d) neural network MOLA.
Figure 7s. Gains and losses 2018. Illegal landfills – simulated model for north-western Gran Canaria. a) Logistic regression CA_Markov model; b) multicriteria evaluation CA_Markov model; c) logistic regression MOLA; d) neural network MOLA.
Figure 8s. Suitability analysis of illegal landfill occurrence in north-western Gran Canaria. a) Logistic regression CA_Markov model; b) multicriteria evaluation CA_Markov model; c) logistic regression MOLA; d) neural network MOLA.