Mixed-cell cellular automata: A new approach for simulating the spatio-temporal dynamics of mixed land use structures

Highlights

• A mixed-cell CA (MCCA) is proposed to simulate the structural change of land use.

• The cell state, lattice, and neighborhood of CA is re-designed based on mixed cells.

• Continuous and quantitative change of multiple land use components can be simulated.

• MCCA enables mixed land use studies to leap from static analysis to dynamic simulation.

Abstract

When used for land use change modeling, Cellular Automata (CA) usually assume that each cell has only one land use type at each time step, ignoring the mixed land use structures that are often found in land units. Mixed cells, composed of cover proportions of multiple land use types, provide a new perspective for modeling the spatio-temporal dynamics of mixed land use structures. Simulating land use change with mixed cells is challenging because mixed-cell CAs are fundamentally different from conventional CAs. This study develops a mixed-cell CA (MCCA). The structure of the CA is re-designed based on the cover proportion of land uses, including the representations of cell state, lattice, and neighborhood. The transition rules are automatically constructed by random-forest regression using historical data and a competition mechanism among multiple land use types at the sub-cell scale is proposed. In addition, a mixed-cell figure of merit (mcFoM) accuracy measure is proposed to validate the MCCA. The MCCA was applied to the Wuhan metropolitan area in China, and the results show that the MCCA was able to simulate the subtle changes of land use proportions within land units. The MCCA represents a new breed of geospatial CA models for spatio-temporal dynamics of mixed land use structures, which enables mixed land use research to leap from static analysis to dynamic simulation. The software for MCCA has been made available at https://github.com/HPSCIL/Mixed_Cell_Cellullar_Automata.

Introduction

Forecasts of land use and land cover (LULC) are needed to analyze the impacts of LULC change for a wide variety of socioeconomic and ecological processes, including population growth, economic development, carbon cycling, landscape dynamics, surface hydrology and climate change (Li et al., 2017, Pontius et al., 2011, Sohl et al., 2010). Land use modeling can therefore help understand the dynamics of the land use system and project future land use change in planning practices to achieve more sustainable development and help retain ecological security (Huang, 2014, Sohl et al., 2014, Verburg et al., 2002). Cellular automata (CA) have been widely used for simulating land use change at multiple scales (Basse et al., 2014, Dong et al., 2018, Liang et al., 2020), as they are simple and naturally spatio-temporally dynamic (Chaudhuri and Clarke, 2013, White et al., 1997, He et al., 2020).

Traditionally, geospatial CA models assume each cell within the system to be of a uniform land use type and assign a discrete state label at each time step (Chen et al., 2013, Pontius et al., 2007, Yeh and Li, 2002, Zhai et al., 2020). In other words, the cell state of conventional CA models is pure and discrete (Clarke and Gaydos, 1998, Pijanowski et al., 2006). However, because of the complexity of land use patterns, especially in cities, a piece of land is usually a mixture of multiple land use types, serving multiple functions (Abdullahi, Pradhan, Mansor, & Shariff, 2015). Therefore, at the commonly used scales of CA models (e.g., 30 m × 30 m and coarser), the land space of a cell often contains various land use types with different cover proportions, which means the lattice (also termed cell space) of a CA model is not only composed of pure cells, but also a large number of mixed cells with multiple land use structures (Foody, 1996). For example, a single urban commercial cell may contain government offices and residences, and an agricultural cell may contain roads, houses and ponds. It is worth noting that although the term ‘mixed cell’ was first mentioned by Hu and Li (2004), their ‘mixed cell’ meant a mixture of points, polylines and polygons, different from the concept of ‘mixed cell’ in this study that represents a mixture of multiple land use types within a cell.

The mixed structures inside land units are one of the key concerns of planning strategies (Song & Knaap, 2004), as they are closely related to human mobility and energy consumption (Abdullahi et al., 2015), and so affect the environmental sustainability and the functions of land units (Liu et al., 2018, Yue et al., 2017). Previous studies concentrated on the identification, measurement and change analysis of mixed land uses (Shi & Yang, 2015), and only a few studies have focused on the simulation of the dynamics of mixed land use (Charif et al., 2017, Omrani et al., 2015). Understanding the dynamics can provide rich information for understanding the interactions between mixed land use and driving factors, and for making scientifically sound land use plans for a sustainable future. A new modeling approach is therefore needed to simulate the spatio-temporal dynamics of land use structures that cover proportions of land use categories within mixed land units. Given the success of CA in land use modeling, CA models with mixed cells appear to be a promising approach to achieve this purpose.

Simulating the change of land use structures based on mixed cells is a challenge, because mixed-cell CAs are fundamentally different from conventional pure-cell CAs. CA models are composed of five basic elements: cell, lattice (or cell space), neighborhood, a set of initial states and transition rules. All these basic elements must be re-designed for a CA with mixed cells. In addition, the evaluation methods must be re-designed since the commonly used methods were primarily designed for pure-cell CAs.

Each cell in a geospatial CA represents a land unit, and a state is associated with every cell representing the attribute/status of the land unit. In pure-cell CA models, a discrete state label from a finite set is assigned to a cell, representing the uniform land use type of the land unit (Li & Yeh, 2000). Unlike a pure cell, the state of a mixed cell is made up by an array of continuously measured components, each representing the cover proportion of a certain land use type (Fig. 1). By changing the state of each cell (i.e., changing the cover proportions of land use types within a cell) along time steps, a mixed-cell CA model is able to simulate the continuous structural change of land use mixture within each land unit, while pure-cell CA models can only simulate the discrete change of the whole cell (Li et al., 2011, Liu and Phinn, 2003, Seto et al., 2012).

Usually, the lattice of a geospatial CA is composed of a group of cells arranged in a 2D space, representing the whole region of interest. Along time steps, the cells within the lattice change their states individually, hence to collectively simulate the spatio-temporal dynamics of a phenomenon (e.g., land use and/or land cover) in the region. With a discrete state label for each cell, a pure-cell CA model has only one layer of lattice for the target phenomenon, besides other layers of driving factors (Wu & Webster, 1998). As the state of a mixed cell is composed of an array of land use components (i.e., cover proportions of land use types), the lattice of a mixed-cell CA is a multi-layer structure, each layer representing the distribution of cover proportion of a certain land use type over the region.

Neighborhood effects are essential to CA models (Li & Yeh, 2002). With pure cells, CA models often use the numbers of cells of various land use types within the neighborhood (i.e., moving window) around a certain cell to represent the neighborhood condition (Chen et al., 2013, Shu et al., 2017, Wu, 2002). Therefore, the variability of land use states within a neighborhood is limited by its size. For example, when using a 3 × 3 window, there are no more than 8 (3 × 3–1) land use types in the neighborhood (Chen, Li, Liu, Ai, & Li, 2016). With the continuously measured cover proportions of multiple land use types as the states of mixed cells, the land use structure of the neighborhood can be represented in more detail (Fig. 1).

The transition rules of mixed-cell CA models are different from those of pure-CA models in two major ways. First, pure-cell CA models simulate land use change through competition among different land use types at the cell scale (Yang, Su, Chen, Xie, & Ge, 2016). However, mixed-cell CA models must estimate the proportion changes of land use types through competition among the land use components inside each cell. The transition rules of mixed-cell CA models must consider not only the effects at the cell scale (e.g., the influences of driving factors at the locations of cells), the neighborhood scale (e.g., neighborhood conditions) and the regional scale (e.g., land demands) as pure-cell CA models (Verburg & Overmars, 2009), but also sub-cell scale competition among multiple land use components. Second, compared with pure-cell CA models that simulate the qualitative change of land use for each cell, mixed-cell CA models simulate the quantitative changes among land use components inside each cell. This characteristic determines that the construction of transition rules of mixed-cell CA models should be based on the quantitative analysis of historical land use transitions. Thus, the prospect of mixed-cell CA models is of great significance for the move of CA models from qualitative simulation to quantitative simulation at the sub-cell scale when simulating the land use change of multiple land use types.

Finally, the simulation results of mixed-cell CA models are the distributions of cover proportions of multiple land use types (i.e., the multi-layer lattice in Fig. 1). The conventional evaluation methods, such as the ‘confusion matrix’ (Congalton, 1991) and ‘figure of merit’ (Pontius & Cheuk, 2006) are designed for discrete simulation results of pure-cell CA, and are unable to evaluate the continuous and multidimensional simulation results of mixed-cell CA models. Thus, evaluation of the accuracy of a mixed-cell CA model is an issue to be dealt with. The cell state of a mixed cell is a multi-dimensional array, representing the land use structure of the corresponding land unit. Therefore, the similarity of land use structure between simulation results and ground truth is an important part of the performance assessment of mixed-cell CA models. A thorough mixed-cell simulation framework needs reasonable and reliable evaluation methods, which can assess the accuracy of continuous and multidimensional distribution, the structural similarity of mixed land use between simulation results and ground truth, and even the change accuracy of mixed-cell simulation.

Some scholars have been aware of the importance of simulating the dynamics of mixed urban land structures. For example, Li and Yeh (2000) proposed a grey-CA that can represent the percentages of urban within cells. Yeh and Li (2002) presented a CA model that incorporates density gradient in the simulation of urban development. Liu and Phinn (2003) developed a fuzzy-set CA to simulate the change of degree of membership of urban land in each cell. Sunde, He, Zhou, Hubbart, and Spicci (2014) proposed an I-CAT model that can provide quantitative information on impervious surfaces within each cell. Recently, Liu et al. (2018a) developed a gradient-CA model, which can express the temporal evolution characteristics of different urbanization stages. Mustafa et al. (2018) also developed a cellular automaton based on multinomial logistic regression and a genetic algorithm to simulate the densification change of urban land. However, these studies only focused on the growth of the urban fraction, and are not applicable to the simulation of the structural change of multiple land use types. Ching and S., Milne, G (2003) developed an Epidemic CA (ECA) model that includes population densities and mobility in each cell, and Tovar, Patel, Niebur, Sen, and Renaud (2006) also proposed a Hybrid CA model (HCA) for topology optimization in mechanical design. The cell states of ECA and HCA are composed of a set of variables, which are similar to the mixed cell in this study. However, because of the differences in research fields and modeling theories, the ECA and HCA models cannot be used in the field of geospatial studies to simulate the structural change of mixed land use.

It is worth mentioning that Omrani et al. (2015) introduced the multi-label (ML) concept, where each spatial unit can belong to multiple classes simultaneously. Omrani, Tayyebi, and Pijanowski (2017) also simulated multi-label land use change with an ML-CA-LTM model, which was a great stride forward in simulating the dynamics of mixed land use. Charif et al. (2017) uses a multi-label learning method-a multi-label support vector machine, Rank-SVM-to define the transition rules of ML-CA that significantly improved the simulation accuracy. However, the multi-label land use data used in the ML-CA series model does not include the cover proportion of land use types in each cell. Therefore, a mixed-cell CA model, specifically designed to simulate the continuous and quantitative changes of cover proportions of multiple land use components within cells, is still missing.

The performance of CA largely depends on the transition rules (Yang, Liu, Li, Li, & Ge, 2018). In geospatial studies, and especially in land use change studies, the transition rules of CAs are often derived using one of two approaches: (1) transition rules are set by model designers, and the parameters/coefficients are then calibrated using historical data. Typical examples include the DUEM (Batty, Xie, & Sun, 1999), SLEUTH (Clarke & Gaydos, 1998) and multi-criteria evaluation (Yang et al., 2016) models; or (2) transition rules are automatically constructed by a data mining model/algorithm using historical data (Hagenauer, Omrani, & Helbich, 2019). In recent years, a large number of CA models have been developed using the second approach, as it makes fewer subjective assumptions and is more flexible. For example, the Artificial Neural Network (ANN) model (Liang et al., 2018, Yang et al., 2019, Yeh and Li, 2002), Random Forest (RF) model (Kamusoko and Gamba, 2015, Zhang et al., 2019), and cuckoo search algorithm (Cao, Tang, Shen, & Wang, 2015) have been used to derive the relationships between land use types/changes and their driving factors. Given the discrete state label of pure-cell CAs, previous studies usually regard the mining of transition rules as a classification problem. The transition rules output a discrete land use type (i.e., label) for a certain cell under the influences of driving factors. Such a classification approach can only obtain qualitative and ad hoc transition rules.

Different from conventional CA models, mixed-cell CA models are concerned with the continuous and quantitative changes of multiple land use components in each cell. Therefore, instead of classification, the construction of transition rules of mixed-cell CAs should be regarded as a regression problem, to discover the relationships between the quantitative changes of land use components and the driving factors. Regression methods have been used in CA models. For example, Liu et al. (2018a) employed Support Vector Regression (SVR) to mine the relationship between urban growth and its driving factors. However, this study only simulated the continuous change of one land use type (i.e., impervious surface), which cannot be used in the simulation of the more complex mutual transitions among multiple land use components (i.e., the structural change) inside mixed cells. Thus, previous studies lack a mining framework for quantitative transition rules of mixed-cell CA models.

In summary, mixed-cell CA models are fundamentally different from conventional CA models in many important ways, including the cell state, lattice, neighborhood, transition rules, and the evaluation methods. Previous methods are unable to simulate the structural changes of multiple land use components inside mixed cells. This study aims to develop a mixed-cell CA framework for land use structural change simulation, which includes a mining method for constructing quantitative transition rules based on a regression approach, a CA model for simulating mutual changes of land use components inside mixed cells, as well as ways to validate the simulation accuracy of mixed-cell CA models. The development and evaluation of mixed-cell CA models are important advances in land use models, which can provide an effective simulation method and important support for planners and researchers for regional policy making, as well as for exploring the causes and consequences of land use change.