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.