3.1.

Introduction of SLEUTH

Urban dynamics are simulated by four growth rules in SLEUTH: spontaneous growth, new spreading center growth, edge growth, and road-influenced growth. Spontaneous growth simulates the random urbanization phenomenon. New spreading center growth is oriented to the generation of new urban centers, which results in further growth. Edge growth characterizes the tendency of cities to expand outward while experiencing infilling growth. Road-influenced growth simulates the tendency of urbanization to occur next to and along transportation lines. Each growth rule is controlled by the five model coefficients of diffusion, breed, spread, road gravity, and slope resistance. All five parameters are represented by integers ranging from 0 to 100 and are dimensionless. With the exception of slope resistance, each of the parameters reflects the relative contribution to urban growth. The last important rule of SLEUTH is the self-modification rule for parameter adjustment. According to the rule, the model parameters will be multiplied by a value (BOOM) $>1$ when the simulation growth rate of an urban area is greater than the threshold CRITICAL_HIGH, and the model parameters will be multiplied by a value (BUST) $<1$ when the simulation growth rate is lower than the threshold CRITICAL_LOW. Without the self-modification rule, SLEUTH would produce only linear or exponential growth.¹⁴

SLEUTH uses a brute-force method, making attempts on sufficient combinations of model parameters to perform a calibration and derive a set of parameters that can best capture the historic growth trend of a study area. The calibration procedure includes three phases: coarse, fine, and final. Each phase includes several Monte Carlo iterations to ensure the robustness of the resulting parameters. During the three-level calibration, the value ranges of the parameters are narrowed level by level, and the calibration accuracy is improved step by step.

Thirteen indices can be used to assess the calibration results of SLEUTH modeling. All indices range from 0 to 1. The greater an index, the higher the calibration accuracy. Indices $\text{pop}\text{-}{r}^2$, $\text{edges}\text{-}{r}^2$, $\text{clusters}\text{-}{r}^2$, and leesalee were chosen for this study, with leesalee used as the metric to measure calibration accuracy. Pop is the amount of urbanized cells, and $\text{pop}\text{-}{r}^2$ is the least square regression score of the modeled urban area compared with the actual urban area for the control years. The same is true for $\text{edges}\text{-}{r}^2$ and $\text{clusters}\text{-}{r}^2$, the total number of edges and urban clusters. Leesalee is a shape index that measures the spatial fitness between the modeled growth and the known urban extent for control years and can be formulated as

3.2.

Model Input and Macro Factors

3.3.

Improvements to SLEUTH

3.3.2.

Introduction of subregional calibration

SLEUTH uses only one set of parameters for a whole study area, which may be suitable for cities with a single core. For multicore cities, however, in which each core region may have different natural conditions and macro driving factors, the subregions have distinct urban growth rates. The aim of subregional calibration is to produce multiple sets of parameters for multicore cities, making the calibration of SLEUTH zone-based. It is also important to introduce a zoning mechanism for single-core cities, since there exists spatial heterogeneity in their urban growth rates as well.

The zoning mechanism used here does not actually divide an entire study area into several subareas and then run SLEUTH subarea by subarea. Specifically, the zoning was achieved by addition of a new input data, the subarea layer (Fig. 2). Multiple sets of optimal parameters for different subregions were obtained by having ACO employ multiple groups of ants, meaning that one group was in charge of one subregion.

Fig. 2

Regional division of Tangshan study area.

The study area was divided into four subregions according to administrative boundaries (Fig. 2): urban center (UC), Fengrun District (FRD), Fengnan District (FND), and suburban area (referred to as SA, which is the sum of Luan County and Luannan County).

3.4.

Scenario Predictions to 2020

Scenario prediction takes into account a range of factors that restrict future urban development, and it predicts the corresponding urban morphologies that result from those diverse backgrounds. Specific influencing factors include resources (water, land), policies, topography, geological environment, ecosystem protection, and urban planning.

Two different scenarios were developed for Tangshan. The first scenario, the inertia trend scenario, assumed no change in the exclusion layer. The second scenario, the policy-adjusted scenario, took account of another three constrained factors for Tangshan: the reservoir’s protected buffer zone, a polluted industry and mining area that had little appeal for urbanization, and a fragile area around the 1976 earthquake center. Changes were added to the exclusion layer to reflect these factors. For the modified exclusion layer, the middle and northern parts of a 5-km buffer zone around the largest reservoir of Tangshan was given a value of 50 considering the reservoir’s great importance as a clean water source for the city. The contaminated area and a 10-km buffer zone around the historic earthquake center were both set to 20 due to their equivalent lower appeal for urbanization. A comparison between the original and modified exclusion layer can be seen in Fig. 3.

Fig. 3

Exclusion layers for two prediction scenarios. (a) Exclusion layer for the inertia scenario. (b) Exclusion layer for the policy-adjusted scenario.

Two scenarios were run on two improved versions of SLEUTH: one improved by ACO and subregional calibration (referred to as AS), the other improved by ACO, subregional calibration, and the introduction of macro factors (referred to as ASM), making a total of four scenario prediction results for Tangshan.

4.1.

Performance of Calibration Algorithms

4.1.3.

Comparison between ACO and brute force

For calibration accuracy, ACO is slightly better than the brute-force method, as shown in Tables 2 and 5. In fact, ACO also outperforms brute force in terms of calibration efficiency. This better performance is demonstrated in two ways. First, Figs. 4 and 5 show that the five parameters and the consequent leesalee converged to their limits at the 15th of a total of 100 runs; that is, it took approximately 2 days and 6 h to obtain the final parameters by ACO. Second, the time cost of the subregional calibration by ACO, shown in Table 6, is less than 2 days and 4 h, also proving the advantage of ACO.

Fig. 4

Variation of calibration accuracy, leesalee index with ACO.

Fig. 5

Variations of the five model parameters with ACO calibration. Diff, Brd, Sprd, Slp, and RG are the abbreviations of diffusion, breed, spread, slope, and road gravity, respectively.

Table 6

Subregional calibration results by ACO and run information of ACO.

ACO information
$\text{Monte Carlo}\text{iterations}=10$	$\text{Run no.}=60$	$\text{Ants pop}=40$	$\text{Time}=02\mathrm{d}:03\mathrm{h}:51\mathrm{m}:42\mathrm{s}$	$\text{leesalee}\_\text{all}=0.48067$
Subregion	Parameter	Optimum	leesalee
SA	Diffusion	1	0.38260
	Breed	26
	Spread	15
	Slope	24
	Road gravity	44
UC	Diffusion	1	0.567833
	Breed	16
	Spread	29
	Slope	2
	Road gravity	10
FRD	Diffusion	2	0.495857
	Breed	6
	Spread	21
	Slope	28
	Road gravity	36
FND	Diffusion	1	0.396705
	Breed	27
	Spread	18
	Slope	42
	Road gravity	22

Note: leesaleeall is leesalee for the whole study area.

4.2.

Subregional Calibration

The calibration results from the zoning mechanism are illustrated in Table 6. As shown in the table, each subregion has distinct parameters and acquires different calibration accuracies. The leesalee for the whole study area is 0.48067, which is a slight improvement compared with Table 5. The total calibration time taken with 60 runs is just under 2 days and 4 h.

The convergence process of the parameters and leesalees of the four subregions can be seen in Fig. 6. The figure shows that, with the exception of UC, the parameters of the subregions converge to limits in 60 runs.

Fig. 6

Variations of the five model parameters and leesalee for the four subregions. Diff, Brd, Sprd, Slp, and RG are the abbreviations of diffusion, breed, spread, slope, and road gravity, respectively.

Simulated urban forms of the control years were also produced by the improved SLEUTH, with parameter initialization for four subregions. Table 3 (subregional part) shows the simulation result statistics. Compared with ACO, the pop index is somewhat greater for each year than that shown in ACO; the leesalee is also greater than or equal to the leesalee in ACO. The derived statistics are $\text{edge}\text{-}{r}^2=0.200$, $\text{clusters}\text{-}{r}^2=0.978$, and $\text{pop}\text{-}{r}^2=0.980$.

4.3.

Calibration of Modified Self-Modification Rule

Another calibration experiment was conducted using the modified self-modification rule with macro factors. Table 7 shows the calibration result. As is seen from the table, UC maintains the greatest spread value, in line with Table 6, but all subregional leesalees, except FND, are less than what is shown in Table 6. Consequently, the leesalee for the entire study area is not improved as expected. The accuracy difference is not significant, however, suggesting a need for further experiments with parameters BOOM and BUST to achieve confidence regarding the modified self-modification rule.

Table 7

Calibration results with modified self-modification rule and run information.

Urban extent for the control years was simulated using the additional improvements to SLEUTH, and the statistical metrics for the simulation results are shown in Table 3 (modified self-modification part). As shown, the pop index in the self-modification part is approximately equal to that in the subregional part for each year, and the leesalee is the same as that shown in the subregional part. The derived statistics are $\text{edge}\text{-}{r}^2=0.250$, $\text{clusters}\text{-}{r}^2=0.976$, and $\text{pop}\text{-}{r}^2=0.982$.

A comparison between the simulated and corresponding observed urban extent is illustrated in Fig. 7. The red color in Fig. 7 represents area in which SLEUTH failed to simulate the actual growth. Green represents the common set of the observed and simulated urban extent. Blue represents commission errors by SLEUTH. To assess the simulation accuracy, the traditional image classification accuracy metric was adopted: the resultant overall accuracy is 75.3%, 73.7%, and 75.2% for 1999, 2005, and 2009, respectively, and the corresponding $\kappa$ coefficients are 0.53, 0.49, and 0.52. The figure shows that the simulated result of each control year has a more compact internal form than the observed. In addition, the simulations of 2005 and 2009 maintain the shape of 1999, with infill at the urban center and no directional differences in urban growth. These SLEUTH simulation results are largely determined by the edge-growth rule.

Fig. 7

Comparison between simulated and observed growth of Tangshan for control years 1999, 2005, and 2009.

4.4.

Urban Growth Forecasts for Tangshan to 2020

4.4.1.

Forecasts of inertia trend scenario

The inertia trend scenario was run on two versions of the improved SLEUTH, AS and ASM, to compare their simulation results. Using the urban extent of 2009 as the basis, forecasts from 2010 to 2020 were generated by the two improved SLEUTHs. The simulated urban forms of 2015 and 2020 were used to establish a comparison, as shown in Table 8 (inertia scenario part). As seen in the table, the urban area predicted by AS for 2015 will be 1.19 times that for 2009, and that of 2020 will be 1.35 times that of 2009. Correspondingly, for ASM, 2015 and 2020 will be 1.20 and 1.38 times, respectively. The introduction of macro factors produces a slight increase in urban growth.

Table 8

Morphological indices of simulated urban forms of 2015 and 2020.

Metric	Inertia scenario				Policy-adjusted scenario
	AS		ASM		AS		ASM
	2015	2020	2015	2020	2015	2020	2015	2020
Edges	359395	357551	359303	354546	359257	359438	359430	357423
Clusters	26582	26696	25115	23504	26748	27098	25406	24085
Pop	1065990	1209481	1077347	1238644	1052662	1186125	1062618	1212749

Note: Inertia scenario for Sec. 4.4.1, policy-adjusted scenario for Sec. 4.4.2.

Comparisons of urban growth from 2010 to 2020 can be seen in Fig. 8. The figure shows that for all prediction years the annual urban growth rate is higher for ASM than AS, leading to a greater slope for ASM pop. At the same time, the urban growth rate for both ASM and AS decreases from 2010 to 2020. Despite the incorporation of macro factors for ASM, the predicted urban growth maintains a linear trend.

Fig. 8

Comparisons of urban growth of Tangshan from 2010 to 2020 for the inertia scenario, where pop is the population of urban pixels, and grw_rate is the annual growth rate of urban area.

4.4.2.

Forecasts of the policy-adjusted scenario

Two types of urban growth forecasts were produced by AS and ASM. Table 8 (policy-adjusted scenario part) shows the statistical metrics of the simulation for 2015 and 2020. The pop index in the policy-adjusted scenario is slightly lower than that in the inertia scenario for both reference years, indicating an insignificant influence on urban growth caused by the policies tested in this study.

Detailed results of the two series of forecasts are shown in Fig. 9. There are no significant differences between Figs. 8 and 9. Urban extents for 2015 and 2020 as predicted by AS and ASM are shown in Fig. 10.

Fig. 9

Comparisons of urban growth of Tangshan from 2010 to 2020 for the policy-adjusted scenario, where pop is the population of urban pixels, and grw_rate is the annual growth rate of urban area.

Fig. 10

Forecasts of urban extent for 2015 and 2020 under the policy-adjusted scenario. (a) Forecasts by AS SLEUTH. (b) Forecasts by ASM SLEUTH.

5.1.

Calibration Efficiency

Two aspects require further study: the calibration algorithms and the model rules. This study tested the former for SLEUTH. Jantz et al.¹² attempted an alternate method to improve the road-search algorithm for the road-influenced growth rule of SLEUTH, resulting in a significant efficiency improvement for calibration. In terms of the algorithms, the ACO employed could be further improved, specifically regarding ways to achieve massively parallel processing.

5.2.

Accuracy Improvement

Model rules contribute significantly to model performance. The simulation produced by SLEUTH is characterized by edge growth and infill growth, which makes the city morphology more compact. These characteristics are determined by the edge-growth rule of SLEUTH. Suggested improvements to this rule should address two issues: how to control compact growth and how to reflect the direction difference of growth; an alternative solution for the latter is to take spatial autocorrelation into consideration.

5.3.

Sensitivity Analysis of Parameters

In addition to the five basic parameters for controlling growth rules, SLEUTH has several other parameters, such as the upper bound of the urban growth rate (CRITICAL_HIGH), the lower bound of the urban growth rate (CRITICAL_LOW), the influence threshold of slope (CRITICAL_SLOPE), and BOOM and BUST in the self-modification rule. These additional parameters also contribute to the model accuracy, and the significance of their influence and the determination of a method to calibrate them need to be addressed.

5.4.

Approaches to Incorporating Macro Factors

At present, there are two methods for combining urban growth models with macro factors. In the first, urban models are loosely coupled with models of macro information, establishing the quantitative relationship between the amount of urban growth and the macro factors (the early urban models of system dynamics);^26,27 in the second, macro factors are spatialized to become inputs of urban CA models.²⁸ The first method involves a one-way interaction between macro factors and urban growth, where macro factors control urban growth. In fact, urban growth counteracts macro factors, thus creating the need to establish feedback mechanisms between the factors and urban growth. The second method is challenging because of the limited availability of high-resolution macro data, which means that spatialized macro inputs are usually calculated by a spatial distribution model, and the resultant macro layers generally have the feature of spatial symmetry. For this reason, the introduction of isotropic macro factors cannot provide valuable changes to the CA simulation results.

Aside from the general questions discussed above, four issues remain. First, for subdivisions of the Tangshan study area produced by administrative boundaries, it is preferable to divide the area along borders with gravity equilibrium among different urban cores, according to the law of universal gravitation. The term mass of the law can be replaced by an economic indicator, such as regional GDP. Second, for the modified self-modification rule, on one hand, SLEUTH is more sensitive to the adjustment of $C_1$ when simulating the urbanization of Tangshan because the growth rate is maintained at a high level, leading to BOOM growing faster or maintaining its maximum, which gives positive feedback to the growth rate in return. The higher the BOOM value, the larger the $C_1$ and the poorer the simulation accuracy will be. The same condition may hold true for $C_2$ if simulation growth rate remains low. The issue is when to meet the condition to transform the growth state from BOOM to BUST. On the other hand, the trial-and-error selection of constants $C_1$ and $C_2$ is complex, so automated calibration would be a good option for determining them. Third, again related to the modified self-modification rule, because the relationship between the macro factors and model parameters was bridged by a hyperbolic function, it is likely that this function did not match the practical situation of the urban growth trend due to the function’s fast convergence rate. Other mapping functions should be the subject of further study. Fourth, the influence of the scenario prediction strategy on urban simulation in SLEUTH is static. Different exclusion layer inputs play the role of scenarios whose ultimate goal is to decrease the amount of nonurban land. If the percent ratio between the current available nonurban land and urban land is far beyond CRITICAL_HIGH, then exclusion will have no impact on the simulation regardless of any exclusion values. If the percent ratio is lower than CRITICAL_LOW, the simulation will enter the BUST or stagnation state; if neither, the simulation state may first be intermediate between BOOM and BUST and then BUST, or it may keep BUST.