Abstract title: Improving the performance of urban expansion models through a coupled cellularautomata and Agent-Based approach: a Hybrid Urban Expansion Model (HUEM)
Authors: Ahmed M Mustafaa, Ismail Saadia, Mario Coolsa, Jacques Tellera
Affiliation: aLEMA, University of Liège, Chemin des Chevreuils 1, Bât B.52/3, 4000 Liège,
Belgium
Keywords: logistic regression; cellular automata; agent-based; urban expansion; Wallonia.
Several statistical and geospatial approaches have been proposed to model urban expansion,
including logistic regression models (logit) (e.g. Hu and Lo, 2007; Mustafa et al., 2015;
Vermeiren et al., 2012), cellular automata (CA) (e.g. Al-Ahmadi et al., 2009; Mitsova et al.,
2011; Mustafa et al., 2014) and agent-based models (AB) (e.g. Hosseinali et al., 2013; Ralha et
al., 2013; Zhang et al., 2010), among others. Statistical models enable us to predict the outcome
of a categorical variable using a set of quantitative and/or qualitative predictors. CA models
address the change in space as state changes and simulate the state changes through immediately
neighboring cells (Wu, 2002). Both models are based on an extrapolation of past observations
using spatial inferences; they are based on the implicit assumption that people's behaviors would
be maintained over time. AB models are modelling agents as goal-oriented entities capable of
responding to their environment and taking autonomous action, where these agents may
represent households, firms, etc. ABs have the potential to model urban expansion not only as a
regular entity, but also allow to simulate the effect of macro-level policy intervention and
constraints, such as updating zoning plan or increasing built-up density per land unit.
This study presents an innovative hybrid urban expansion model (HUEM) that integrates logistic
regression, cellular automata and agent-based approaches to simulate the expected future urban
expansion. The main contribution of this paper is to highlight the added-value of using HUEM
model in terms of the model accuracy. Accuracy will be here measured through a traditional
overlaying method, and also through landscape ecology metrics.
The main components of HUEM model are highlighted in Fig. 1. The model’s space consists of a
2D array of cells of the same dimensions. The number of agents included in the model are of
three groups: developers (DevA) represents firms, households and some farmers who decided to
stop being farmers; farmers (FarmA) and government (GovA). In HUEM model, the
development of non-urban cells is done by DevA and controlled by GovA. FarmA, owning
undeveloped agriculture-related cells, will decide to keep or to sell their own cells. The
constraints are restrictive cases for urban development. Such constraints could include but are
not limited to, zoning plan and flood-prone areas. These constraints can measure the impacts of
different planning regulations on the future urban expansions.
HUEM is based on two modules: a demand module and an allocation module. The demand
module calculates the new requested urban lands at each time-step whereas the allocation
module spatially distributes the new urban lands over the study area. Once the estimated required
urban lands are reached, the model stops the allocation process. HUEM can either be fed with the
quantity of urban land change or computes this quantity based on a past trend using the Markov
chain model (MC). The model is first calibrated and validated with real observed data of at least
two time frames and it is then used to project possible future urban expansion scenarios at
specific time horizons.
Fig.1: HUEM framework
A non-urban cell is only prone to develop if the profitability of urbanization by the DevA is high,
provided that the GovA allows construction in this cell. A quantitative approach is introduced
here to parametrize the decision-making criteria of agents. When DevA has the opportunity to
make a decision regarding land-use, the agent first forms an urban development expected value
for each non-urban cell. This expected value represents the profitability score that the agent
expects to obtain from a non-urban cell. DevA tries to select cells with the best urbanization
score at each time-step using a utility function as follows:
scoret  (nt  g t ) R
(1)
ci , j
ci , j
ci , j
t
where score is the profitability score of urban development assigned to cell ci,j at time t, nt is
ci , j
ci , j
t
the local urbanization probability according to cell neighbors on the cell, g is the global
ci , j
urbanization probability according to geo-physical and socio-economic factors and R is a
stochastic perturbation component. Including R makes it possible to consider uncertainty due to
global and local factors and it can be calculated as follows:
R  1  ( ln(rand ))
(2)
where R is a scalable random perturbation term, rand is a uniform random variable varying
between 0 and 1, and α is a parameter that controls the size of the perturbation introduced in the
model.
When DevA selects an agricultural-related cell to develop, FarmA will make a decision to sell or
maintain it. FarmA aims to maintain or increase his profitability, and to keep or even expand
cropped area. Ordinarily, FarmA imitates the land-use of neighbors and therefore he is highly
affected by his urban neighbors. We assumed that the FarmA cell is negatively and positively
impacted, in terms of agriculture profits, by spatial externalities generated by urban cells and
other land-uses respectively. These externalities result in a loss or gain in FarmA profitability ω.
If a FarmA’s profitability drops below the profitability score of urban development, he must exit
farming at time t+1 as follows:
(3)
When DevA determined which cells to develop, they have to ask for a permission from GovA.
GovA considers that zoning of land is not always strictly enforced. If a cell is located in a
permitted or in a forbidden zone, GovA will instantaneously grant or reject the permission
respectively. Otherwise, if the cell is located in a restricted zone, a sort of competition will be
carried out to determine the winner. The winner of the competition depends on the number of
times that GovA has lost cells in the previous competitions. Consequently, GovA will give
permissions for a percentage of the amount of required cells to be developed within the restricted
zones as the follows:
(4)
where GovADecisiont 1 is the GovA decision in a restricted zone, LR is the loss rate and AR is the
ci , j
allowed rate. To set the allowed rate, an iteration process to generate several values based on an
increment of 1% will be performed to identify the optimal rate.
Three criterion layers, namely nt ,  t and g t have been generated. The nt and  t are developed
ci , j
ci , j
ci , j
ci , j
ci , j
t
using CA model whereas g is developed using logit model. The interaction among agents is
ci , j
governed by a series of different possible behaviors, which are themselves variable over time.
To demonstrate the feasibility of HUEM model, Wallonia, Belgium is taken as an example
application. The model first simulates urban expansion between 1990 and 2000 and then it is
calibrated and validated against a real 2000 urban expansion. The calibrated model will be
employed to simulate a 2030 business-as-usual urban expansion scenario.
To evaluate the added-value of HUEM model for simulating urban expansion, a number of urban
expansion simulations are developed based on: (1) logit model, (2) CA model, (3) logit-CA
model and (4) HUEM model. The outcome of each model will be validated under the same
conditions in order to assess the performance of each model.
To validate the simulated urban maps, we applied two scientifically rigorous statistical
techniques of map comparison: (i) cell-to-cell location agreement (CTC) and (ii) evaluating the
structure of new urban pattern in terms of landscape compactness and complexity. Two matrices
measuring fragmentation (number of patches-NP-, mean patch area-MPA-), one matrix
measuring the complexity (area-weighted mean shape index-AWMSI-) and one matrix
measuring dispersion (patch cohesion index-PCI-) were selected to evaluate the model’s
outcome landscape pattern.
The results clearly show that the performance of HUEM is better than other models, table 1. In
addition, the performance of HUEM is quite well in terms of landscape structural conformity,
Fig. 2.
Table 1. CTC agreement (%) for newly urban cells between 1990 and 2000 (simulation vs. real)
Model HUEM Logit-CA CA
Logit
CTC 37.15 32.62
31.14 23.05
Fig. 2. Spatial matrices outcomes for newly urban cells between 1990 and 2000 (simulation vs.
real). RC: real changes; HL: HUEM; LCA: Logit-CA; LG: Logit.
The case study points out that the spatial pattern of recent urban expansion (1990–2000) is
related to the presence of roads, existing built-up area and the distance from the major cities.
This findings offer tools to steer urban expansion based on various planning visions. However,
different scenarios can be integrated into HUEM and offer guidance in taking planning decisions
and evaluate the implications of such decisions.
Fig.2 demonstrates the 2030 business-as-usual urban expansion scenario.
Fig.3: the 2030 Wallonia urban expansion simulation.
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