CN110059385B - A Grid Dynamics Scenario Simulation Method and Terminal Equipment for Coupled Allometric Growth - Google Patents

Abstract

The invention relates to a grid dynamics scenario simulation method for coupled growth at different speeds and terminal equipment, which comprises the following steps: s1: constructing a transition probability matrix P for mutual conversion among different land use types according to a Markov model; s2: predicting the newly-increased construction land area of the city according to the Markov model and the different-speed growth model respectively, and recording the area as A _m And A _a (ii) a S3: newly-added construction land area A predicted according to Markov model and different-speed growth model _m With a of _a The difference between the transition probability matrix P and the transition probability matrix P 'is corrected into P'; s4: establishing an urban cellular automaton model based on logistic regression and adding random disturbance factors and limiting factors; s5: and simulating the dynamic evolution process of the urban space according to the corrected transition probability matrix and the urban cellular automata model. The invention provides a multi-land-use cover dynamic scenario simulation model coupling a different-speed growth rule, a Markov chain and a cellular automaton, so as to predict interconversion among multiple lands and reasonable development requirements of the multiple lands.

Description

A Grid Dynamics Scenario Simulation Method and Terminal Equipment for Coupled Allometric Growth

technical field

The invention relates to the technical field of scenario simulation, in particular to a grid dynamics scenario simulation method and terminal equipment for coupled allometric growth.

Background technique

In 2018, the urbanization rate of China's permanent population was 59.58%, and some large cities and urban agglomerations were gradually formed. This land-use/land-cover change process will trigger drastic changes in the pattern, structure and process of terrestrial ecosystems, which will not only have irreversible negative impacts on ecosystem services, but also continue to increase the accumulation of ecological risks. Scenario simulation of land use/cover change is a powerful tool for analyzing the causes, processes and results of future temporal and spatial evolution of land use, supporting land use planning and predictive decision-making, and has become a powerful tool to reveal the interaction between land use/cover dynamics and terrestrial ecosystems at different scales One of the effective ways of the mechanism.

Urban cellular automata is a "bottom-up" grid dynamics model, which has the characteristics of discrete time, space and state, and can effectively simulate the spatiotemporal evolution process of the spatial pattern of complex systems. Since Tobler and Couclelis conducted pioneering research on the evolution mechanism of urban complex spatial pattern in the 1970s and 1980s, urban cellular automata has become one of the powerful process analysis tools for urban land use evolution simulation under complex resource and environmental conditions.

In view of the fact that cellular automata with spatially explicit characteristics generally cannot determine the amount of land use change, urban cellular automata are used to simulate land use dynamics, which generally include macroscopic total land use demand and microscopic land use change allocation modules, corresponding to Non-spatial attribute land demand forecast and spatially intuitive land use change allocation process. The total amount of land use change demand is often affected by the composite effect of macro factors such as social, economic and policy. Verburg et al. (2002) ^[1] considered land use demand as an important input of urban models, and its determination method varies with the study area and scenarios. Analytical needs can be tailored to include applying simple trend forecasts or coupling complex economic models. White and Engelen (2000) ^[2] combined a regional development model with cellular automata, taking into account the effects of population, employment, and distance between regions. Wu and Webster (2000) ^[3] and other coupled macroeconomic models and cellular automata, carried out research on the process of urban development, and achieved satisfactory results. Feng et al. (2011) ^[4] used the conversion threshold to control the land use conversion conditions, and obtained the dynamic land demand with the highest simulation accuracy. He et al. (2015) ^[5] and other integrated system dynamics and cellular automata, from the perspective of socio-economic systems, integrate population, economy (GDP), market regulation (food self-sufficiency rate), land policy, and technological progress ( The five factors of grain yield) simulate the land demand under different development scenarios in the future. However, the aforementioned methods are mainly used to predict the total demand of urban land or to predict the changing needs of various land types relatively independently, and it is difficult to predict the mutual conversion between various land use types and their reasonable development needs.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention provides a grid dynamics scenario simulation method and terminal equipment coupled with allometric growth, so as to predict the mutual transformation between various land use types and their reasonable development requirements.

The specific plans are as follows:

A grid dynamics scenario simulation method for coupled allometric growth, comprising the following steps:

S1: Construct the transition probability matrix P of mutual transformation between different land use types according to the Markov model;

S2: According to the Markov model and the allometric growth model, the newly added construction land area of the city is predicted, which are respectively recorded as A _m and A _a ;

S3: According to the difference between the newly added construction land area A _m and A _a predicted by the Markov model and the allometric growth model, the transition probability matrix P is revised to P′;

S4: Establish an urban cellular automata model based on logistic regression and adding random disturbance factors and limiting factors;

S5: Simulate the dynamic evolution process of urban space according to the revised transition probability matrix and the urban cellular automata model.

A grid dynamics scenario simulation terminal device coupled with allometric growth, comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, the processor executing the computer program At the same time, the steps of the above-mentioned method in the embodiment of the present invention are implemented.

The present invention adopts the above technical scheme, and has beneficial effects:

1. Apply the Markov chain to estimate the land use transition probability matrix based on historical development dynamics. In view of the significant impact of the composite driving forces such as regional population, social economy and macro policies on urban development and its uncertain characteristics, the gray model is used to predict the population growth scale , to explore the allometric growth law of urban construction land-urban population;

2. Propose a method to revise the Markov transition probability matrix based on the prediction of dominant land type mutation, so as to obtain the macro-land conversion requirements in line with regional development characteristics under different economic and social development situations and macro-control policy backgrounds;

3. Use binary logistic regression to calibrate the contribution weights of each spatial variable in the urban model, and input the land demand into cellular automata for multi-scenario evolution simulation of urban growth and land conversion.

Description of drawings

FIG. 1 is a schematic flowchart of an embodiment of the present invention.

Figure 2 shows a schematic diagram of the sampling method for logistic regression analysis.

Figure 3 shows the simulated map of land use/cover change in Xiamen in 2005 and 2015.

Figure 4 shows the simulated map of the land use/cover evolution scenario in Xiamen from 2025 to 2045.

Figure 5 shows the forecast of urban construction land growth based on allometric growth and Markov.

Figure 6 shows the land use evolution scenarios from 2025 to 2045 under different allometric scaling indices.

Detailed ways

To further illustrate the various embodiments, the present invention is provided with the accompanying drawings. These drawings are a part of the disclosure of the present invention, which are mainly used to illustrate the embodiments, and can be used in conjunction with the relevant description of the specification to explain the operation principles of the embodiments. With reference to these contents, one of ordinary skill in the art will understand other possible embodiments and advantages of the present invention.

The present invention will now be further described with reference to the accompanying drawings and specific embodiments.

Example 1

Embodiment 1 of the present invention provides a grid dynamics scenario simulation method coupled with allometric growth, which mainly includes the following contents:

The urbanization process is a major driving force affecting land use/cover changes in urban areas, and the scale of urban development is greatly affected by socio-economic policies such as population, technology, industry, and the environment. Among them, urban population size is one of the most critical determinants of urban size, which itself also reflects the influence of regional composite policy factors. However, the definition of city scale or city boundary affects whether the urban population-city size allometric growth law is established or not. Research shows that if the city size is represented by urban area, the allometric relationship between urban population and urban built-up area will appear. Growth phenomenon is ubiquitous. Therefore, under the theoretical framework of urban allometric geography, it has a feasible technical route to deduce the urban land development demand through the urban population scale. In rapidly urbanizing areas, the growth of urban area can be as high as 4-5 times in just a few decades, making urban construction land the dominant land type in regional land use dynamics. In particular, under the influence of government social and economic policies and resource and environmental constraints, the development scale of advantageous land types is prone to sudden changes. Therefore, the following problems can be solved in this embodiment:

1) If the land demand predicted by Markov is used as the benchmark, does the allometric development of urban population and urban area lead to sudden changes in the scale of urban construction land?

2) How does Markov chain predict urban land demand in the case of dominant land class mutation?

3) What characteristics will the scenario simulation of a Markov-cellular automata model with a certain dominant land type exhibit?

In conclusion, cellular automata has become a powerful tool for micro-simulation of urban land use change, while scientific prediction of regional macro-land conversion needs is still one of the bottlenecks in scenario modeling. In this example, Xiamen City, a typical area of rapid urbanization, is used as the research area, and a land use scenario evolution model is constructed by coupling the allometric growth law, Markov chain and cellular automata. First, a Markov chain is used to estimate the land use transition probability matrix based on historical development dynamics; in view of the significant impact and uncertain characteristics of the composite driving forces such as regional population, social economy and macro policies on urban development, the gray model is used to predict the scale of population growth , explore the allometric growth law of urban construction land-urban population, and further, propose a method to correct the Markov transition probability matrix based on the mutation prediction of dominant land types, so as to obtain information under different economic and social development situations and macro-control policy backgrounds , which conforms to the macroscopic land conversion demand of regional development characteristics; finally, the contribution weight of each spatial variable in the urban model is calibrated by binary logistic regression, and the land demand is input into cellular automata for multi-scenario evolution simulation of urban growth and land conversion.

1. With reference to Fig. 1, the concrete steps of the method described in this embodiment are as follows:

1.1 Coupled allometric growth model and Markov chain to predict urban land demand

A Markov chain is a special random motion process with Markov properties and discrete-time states. The random process describes the probability distribution of "no aftereffect (Markov property)" in which one state changes to another state. For the dynamic evolution process of urban spatial form with multiple land use classifications, it is appropriate to use this feature of the Markov model to predict the demand for land use change, because the spatiotemporal evolution of land use/land cover has the following Markov process nature:

1) In a specific study area, there is a mutual transformation relationship between different land use types;

2) The mutual conversion process between various land uses contains many uncertain events that are difficult to accurately describe by mathematical functions;

3) Land use change generally spans a long period of time, and the average transition state of land use structure within the study period is relatively stable, which meets the requirements of Markov chain.

Therefore, the key to using the Markov model to predict urban land demand is to construct a transition probability matrix for the mutual transformation between different land use types. The mathematical expression is as follows:

In the formula, P _ij is the transition probability that the ith land use type is transformed into the jth land use type in the process of land use type change from time T to time T+1, M is the number of land use types, and the transition probability matrix is Each element P _ij satisfies the following conditions:

Using the historical data of land use types at two time nodes, the annual transition probability of a certain type of land use type can be calculated, so as to obtain the transition probability matrix of the time period.

According to the homogeneous Markov chain and the Bayesian conditional probability formula, the Markov model for urban land demand forecast can be established: P _(n) = P _(n-1) P _ij (3)

In the formula, P _(n) is the state probability vector of the object studied by the system at any time, and P _(n-1) is the initial state probability vector of the research object.

The transition probability matrix of the Markov model objectively reflects the circulation status of various land uses, and is suitable for predicting the development trend of land use and land demand. In the process of urban development, land use change is mainly manifested in the expansion of urban land, and the dynamics of urban land use is mainly driven by social and economic factors such as population size, per capita GDP, employment status, and planning policies. However, in most studies, the estimation of the Markov probability matrix generally uses multi-year land use classification data as input, and rarely involves social and economic driving factors. Therefore, an improved Markov chain method is proposed in this embodiment, and on the premise that the growth scale of construction land is obtained by using the socio-economic model or according to the regional macro land use planning, the transition probability matrix used to predict the land conversion demand is further revised. .

The evolution process of urban spatial pattern generally follows the law of allometric growth, that is, each part of the urban system develops at different speeds, reflecting the relative growth rate of one element (such as population size) of urban development and the relative growth rate of another element (such as construction land). form a fixed proportional relationship. For the expansion of urban land, the vertical allometric model is generally used for analysis. The vertical allometric describes the dynamic process in the time evolution. The observed data are time series or corresponding sample data, and its mathematical expression is generally based on the exponential growth process: A _t =α(P _t ) ^b (4)

In the formula, t is the time series or year of historical land use data or statistical data, A _t is the urban area at time t, P _t is the urban population size at the corresponding time, α is the proportional relationship, and b is the scaling index, that is, urban construction. The ratio of the relative growth rate of land use to the relative growth rate of population size is a constant, so the parameters α and b are determined through historical data, and the area of urban construction land can be calculated from the future population size.

The population economic system is a gray system with known information and unknown information. Using the gray GM(1,1) model to predict the population data of a specific historical period requires less information and high precision, assuming the time series x ⁽⁰⁾ There are n observations x ⁽⁰⁾ = {x ⁽⁰⁾ (1), x ⁽⁰⁾ (2),..., x ⁽⁰⁾ (n)}, after accumulation, a new series x ⁽¹⁾ = {x ⁽¹⁾ (1),x ⁽¹⁾ (2),…,x ⁽¹⁾ (n)}, then the differential equation of the GM(1,1) model can be established,

为发展灰数，

为内生控制灰数，通过最小二乘法拟合可以获取前述两个待估计参数，求解微分方程，可以得到人口预测模型：in,

To develop grey numbers,

In order to control the gray number endogenously, the aforementioned two parameters to be estimated can be obtained by least squares fitting, and the differential equation can be solved to obtain the population prediction model:

Assuming that the new construction land areas predicted by the Markov model and the allometric growth model are _Am and A _a , respectively, there are often large differences between them. Although the urban expansion area that dominates urban land use changes needs to be revised, the Markov model still effectively reflects the circulation characteristics of land use in a region. If μ _j is the ratio of A _a to A _m , it can be Use μ _j to correct the transition probability of different land use types converted to urban construction land. At the same time, in order to ensure that the elements of the transition probability matrix satisfy the constraints of Equation (2), the ith land use type is converted to other land use types. The probability is modified by μ _i , and the Markov transition probability matrix modified by the allometric model can be obtained:

In the formula, _j is the element subscript of the construction land in the transition probability matrix, μ _j and _{μ i} are the correction coefficients of the aforementioned transition probability, respectively. P _jM ) has not been corrected, and the urban land renewal model can be considered in the future. At the same time, the correction coefficient can also be obtained from other dominant land types.

Further, the correction coefficient μ _i can be calculated by the following formula:

In the formula, k is the subscript of the land use type in the probability transition matrix, P _ik is the transition probability of converting the ith land use type to the kth land use type, and i is the land except for urban construction land (subscript j) subscripts of other land-use types.

1.2 Calibration transformation rules using binary logistic regression

Logistic regression is a regression analysis method used to predict the functional relationship between a dependent variable with a finite value and one or more independent variables to describe the interaction of variables. The values of the independent variables generally require continuous and independent variables. If the values of the dependent variable are determined from a finite set, there is no clear meaning of the range and order of the values. In practice, if the dependent variable has only two values, it is called binary logistic regression.

The logistic regression method is used to calibrate the cellular model. The first step is to collect sample data. Generally, by comparing the remote sensing images of two years in a specific period, randomly sample the cells with land use type changes during the period to obtain spatial variables. Or the empirical data of neighborhood factors and land use changes, and obtain a certain amount of sample data, so as to input the logistic regression model to obtain appropriate model parameters.

The assumption of variable correlation (independence) and the maximum likelihood estimation algorithm of parameters are two aspects that need special attention when applying logistic regression technology in urban models. On the one hand, according to the first law of geography proposed by Tobler, spatial Spatial effects such as correlation and spatial heterogeneity are important characteristics of urban expansion. Therefore, how to eliminate spatial dependence or effectively reduce spatial autocorrelation is the key to effectively perform logistic regression analysis. Establish a model that includes an autoregressive structure or design a Spatial sampling schemes are two feasible methods to filter out spatial autocorrelation. On the other hand, given that there is always a loss of specific information in the sample space, it is necessary to obtain enough sample points as randomly as possible to satisfy the maximum likelihood. In this method, asymptotically normal large samples are used. It is undeniable that the specific location, randomness and sample size of the sample points conflict with the above two aspects to a certain extent. Therefore, this embodiment proposes a proportional stratified randomization method. The sampling technique, as shown in Figure 2, seeks a reasonable trade-off between effectively reducing spatial autocorrelation and obtaining sufficient random sample data. Since the sample collection and analysis processes are all performed by computers, samples are collected according to 20% of the overall data. Data is available.

The specific process of the proportional stratified random sampling technique is as follows:

Set P(y=1|X) as the probability value of cell transformation, then 1-P is the probability that the cell does not change. In general multiple regression, with P as the dependent variable, the regression equation P=b ₀ +b When ₁ x ₁ +b ₂ x ₂ +...+b _k x _k is calculated, there are often cases where P>0 and P<0 are out of bounds. At this time, P/(1-P) is converted to logarithm and recorded as ln(P/(1-P)), and P is converted to unit logarithm, that is, logP=ln(P/(1-P)), Taking logP as the dependent variable, the linear regression equation is established as follows:

log P _c (S _ij =1)=b ₀ +b ₁ x ₁ +b ₂ x ₂ +…+b _k x _k (9)

In the formula, P _c represents the probability of the state transition of the cell, S _ij is the development state of the cell (i, j), b _k is the coefficient of the logistic regression model, and x _k is a set of spatial distance variables or neighborhood factors . After further transformation, there are:

In the formula, P _c,ij is the transition probability of the cell (i,j), X is the driving factor vector, X=(x ₀ , x ₁ , x ₂ ,..., x _k ), x ₀ =1, B is the parameter vector to be estimated, B=(b ₀ , b ₁ , b ₂ , . . . , b _k ).

1.3 Using cellular automata to realize micro-space allocation of land

Generating probability distribution maps of different land use/cover types is the key to the micro-space allocation of land use change. In the simulation of micro-space allocation based on cellular automata, transformation rules are the core to obtain the distribution suitability of different land use types at each location. , is generally determined by the cell state, neighborhood state and development suitability, that is, the state of the cell at time t is a function of the cell at time t-1, the state of the neighborhood at time t-1 and the corresponding transformation rules. The form is as follows:

S _ij ^t = f(S _ij ^t-1 , P _{c, ij} , Ω _ij ^t-1 , Cons, R) (11) In the formula, S _ij ^t and S _ij ^t-1 are times t and t-1 respectively The state of the cell (i, j), P _{c, ij} represents the conversion probability of the cell (i, j), that is, the land conversion potential/development suitability of the cell (i, j), Ω _ij ^t-1 is the element The distribution of specific land use/cover in the neighborhood space of cell (i, j), Cons is the constraint mechanism that restricts land use conversion, R is a random factor that simulates the dynamic uncertainty of land use, and f represents the change of cell state. A series of transformation rules.

Neighborhood interaction is one of the core components of the cell-based land use evolution model. There are complex neighborhood effects such as inertia, attraction and repulsion in the neighborhood space. Neighborhood abundance factors describe land use patterns from an empirical perspective (1 and use patterns). The neighborhood features of , become a feasible way to construct neighborhood rules:

In the formula, F _{i, k, d} is the enrichment degree of land use k on the circular molar neighborhood of radius d of the location i, n _{i, k, d} and n _{i, d} are the d neighborhood of location i, respectively On land use k and the number of all land uses, N _k and N are the land use k and the number of all land uses in the study area, respectively.

The calibrated neighborhood abundance factor curves show that there are significant neighborhood effects in the neighborhood space, and, from years to decades, the neighborhood effects and their relationships between land uses are relative. Static, therefore, the average neighborhood abundance factor observed in the study area is obtained based on the historical land use model and normalized to obtain the attenuation coefficient of the influence of land use at different distances in the neighborhood on the development of the central cell, and the average The formula for the neighborhood abundance factor is as follows,

where AF _m,k,d is the enrichment degree of land use k in the d distance neighborhood of all land use m, N _m is the number of cells of all land use m, and M is the set of all land use m.

The number of cells of each land use/cover type in the neighborhood changes dynamically with the evolution of the model. The state change of a cell is directly affected by the distribution of land use types in the neighborhood. The land use type with the largest number in the neighborhood often determines the central element. The future transformation state of the cell, using the extended Moore neighborhood (Moore) with radius d=3 as the moving window, based on the attenuation coefficient obtained above, the following neighborhood function can be constructed to reflect the neighborhood space attenuation characteristics:

In the formula, Ω _ij,k ^t-1 represents the neighborhood function value of the central cell (i,j) converted to land use k, θ _d,k represents the attenuation coefficient of land use k from the central cell d, cos( S _d,ij ^t-1 =k) represents the number of pixels of land use k on the d distance neighborhood of cell (i,j).

It is assumed that the development suitability is expressed by a local probability, and the probability value is generally affected by a series of spatial distance variables. The spatial variables considered in this embodiment include elevation, slope, distance from the city center, distance from the town center, distance from the main Distances from roads, distances from railways and distances from coastlines, distances from farmland, distances from woodlands and distances from bodies of water, etc. The parameters of the above-mentioned spatial variables are corrected by binary logistic regression, and random sampling is carried out in the remote sensing images of two years. 20% of the data were randomly stratified by sampling.

In the simulation of urban cellular automata, the cellular transition probability determines how the state of the cell is transformed between different land use types. Spatial variables such as distance, shortest distance from road, shortest distance from town center, etc. Adding random disturbance factors, limiting factors, etc., the final total distribution probability of the cell is expressed as:

表示特定大窗口邻域范围内状态为k的元胞对中心元胞(i，j)发展的影响。In the formula, t is the iterative sequence of cellular automata evolution, P _{total, k} ^t is the probability of developing a certain land use k at time t, R=(1+(-lnγ) ^α ) is the uncertainty reflecting the urban system , γ is a random number of (0-1), α is an integer between (1-10), X (X=x ₀ , x ₁ ,..., x _m ) is the influence of land use/ Covering the changing space variable vector, B _k (B=b _{0, k} , b _{1, k} ,..., b _{m, k} ) the weight vector of each space variable, Norm (Ω _{ij, k} ^t-1 ) represents the The normalized neighborhood influence, cons( ) represents the constraint function that restricts the state change of the cell.

Represents the influence of a cell with state k in the neighborhood of a particular large window on the development of the central cell (i, j).

2 Experimental results and analysis

2.1 Study area and experimental data

The study area in this example is Xiamen, and the basic data of the study include Landsat TM/ETM+ remote sensing images, traffic and cadastral data, topographic map, population and built-up area data in the study area in 1995, 2005 and 2015. Land use planning data, etc. The acquired land use data covers six types of land use: cultivated land, forest land, grassland, construction land, water area and tidal flat, with a spatial resolution of 30m × 30m. Among them, cultivated land includes paddy fields and dry land, and construction land includes urban land, rural settlements and industrial and mining sites. Land and other construction land. Traffic and cadastral data and topographic maps include DEM data of the study area, distance from urban centers at all levels, distance from traffic lines, distance from forest land, distance from cultivated land, and distance from coastline, etc. The population data comes from the Xiamen Socio-Economic Statistical Yearbook, and the population data mainly refers to the resident population. The built-up area data is obtained through the statistics of land use classification data interpreted from remote sensing images. The land use planning data is the overall planning map of Xiamen City's land use and the long-term planning data of Xiamen City from 2006 to 2020.

2.2 Parameter calibration of allometric equation and correction of transition probability matrix

Input the land use type classification map of the study area in 1995, 2005 and 2015 into the Markov chain model, and the transition probability matrix, transition area matrix and a set of conditional change probability maps can be obtained. The obtained transition probability matrix reflects the possibility of each land type being converted to any other land type. The transition probability matrix is obtained by cross-tabulating the previous and subsequent two land use classification maps, and the transition area matrix records a specific time. The mutual conversion between different land use types in the segment, and the expected future land demand is multiplied by each row of the transition probability matrix by the number of cells representing the corresponding row of land use types in the land use map of the subsequent period, and further used as the urban element. input to the cellular model.

Table 1 shows the Markov transition probability matrix between different land use types in Xiamen during 1995-2015:

Table 1

Table 1 summarizes the transition probabilities from an initial land use state to 6 land use types during 1995-2005 and 2005-2015. The results show that the probability that cultivated land remains unchanged during 1995-2005 is 0.8138, and the It will be converted to construction land with a probability of 0.1593 and forest land with a probability of 0.0106. At the same time, the forest land has a probability of 0.0103 and 0.0310, respectively, to be converted into cultivated land and construction land. During 2005-2015, there is a 0.8421 chance that cultivated land will remain unchanged, and a 0.1380 chance that it will be converted to construction land, and a 0.0094 chance that it will be converted to forest land. During this period, the forest land had 0.0078 and 0.0164 opportunities to be converted into cultivated land and construction land, respectively. The results of the transition probability matrix analysis suggest that the land use change in the study area during 1995-2015 was mainly manifested in the rapid expansion of urban construction land. tidal flats. In this embodiment, it is assumed that 10 years is a time period for calculating the transition probability matrix, and the transition probability matrix for the period from 2015 to 2025 can be obtained by raising the power of the transition probability matrix for the previous period, that is, the period from 2005 to 2015.

In order to further predict the future changes of urban land demand in the study area, it is necessary to modify the obtained transition probability matrix in combination with the socio-economic model. As mentioned above, the expansion of construction land plays a leading role in the change of land use in this area. In this example, the urban population-construction land vertical allometric growth model is used to predict the construction land demand in Xiamen from 2025 to 2045, which is used to correct the 2005 -Transition probability matrix for 2015. Two basic dimensions are used to describe the longitudinal allometric relationship between urban population and construction land. The population scale is based on the urban resident population. The data are all from the Xiamen Special Economic Zone Yearbook from 2000 to 2017. The construction land is based on Landsat TM/ETM+ remote sensing image solution The translated land use is calculated.

Table 2 lists the historical data, observed values and predicted values of resident population and construction land area.

Table 2

year(n) 1995 2005 2015 2025 2035 2045 Timing (t=n-1995) 0 10 20 30 40 50 Population (P_t)/10,000 people 156 273 386 459 545 647 Construction area (A_t)/km² 195.9 325.5 429.2 500.1 579.2 670.8

Analyzing the data in Table 2, it is found that the relationship between urban population and construction land in Xiamen from 1995 to 2015 satisfies the relationship of vertical allometric growth well. Using the sample data of three years and the least squares method, the vertical allometric growth model is fitted. The scale coefficient α=2.650 and the scaling exponent b=0.855 can be obtained. The obtained scaling exponent is very close to the theoretical prediction value of 0.85, the relative residual error is 0.0114, and the variance ratio is 0.0359. According to Xiamen's overall urban planning (2017-2035), in order to ensure the expected economic development needs, and in line with the population growth trend and resource carrying capacity of Xiamen, the long-term urban permanent population is controlled within 8 million. According to the grey GM(1,1) model of urban population growth, the 2018-2045 resident population scale of Xiamen can be predicted from the 2010-2017 resident population statistics, and the 2025-2045 data are input into the urban population-construction Based on the longitudinal allometric growth model of land use, combined with the observed values of land use/cover classification data from 2005 to 2015, the construction land areas of Xiamen in 2025, 2035 and 2045 were 500.1, 579.2 and 670.8 square kilometers, respectively. Using the Markov transition probability matrix from 2005 to 2015, it can be predicted that the area of construction land in 2025, 2035 and 2045 will be 519.1, 598.9 and 669.6 square kilometers, respectively. The two parameters μ _i and μ _j of the modified transition probability matrix are obtained as follows: As shown in Table 3, further, the transition probability matrix modified according to formula (8) is shown in Table 3.

table 3.

year(n) μ_i,farmland μ_i,forest μ_i,lawn μ_i,water μ_j,built-up μ_i,beach 2025 1.0315 1.0033 1.0065 1.0092 0.8038 1.0160 2035 1.0366 1.0038 1.0073 1.0104 0.8925 1.0181 2045 0.9979 0.9997 0.9995 0.9993 1.0047 0.9988

Combining Table 1 and Table 4, it shows that under the 2015-2025 revision scenario, the probability of cultivated land remaining unchanged is 0.8685, the probability of cultivated land conversion to construction land is revised from 0.1380 to 0.1111, and the probability of forest land conversion to construction land is revised from 0.0164 to 0.0132 , and other transition probabilities also have minor changes. For example, the probability that cultivated land is converted into water is revised from 0.0049 to 0.0051.

Further, based on the correction coefficients of the Markov transition probability matrix obtained in Table 3, the transition probabilities of the two periods of 2015-2035 and 2015-2045 can be calculated respectively (Table 4, the revised Markov transition probability of the three evolution scenarios during the period of 2025-2045). Strictly speaking, the transition probabilities of these two periods can also be characterized in the form of 2025-2035 and 2035-2045, respectively, but their essence is the same.

Table 4

2.3 Model conversion rule parameter calibration

In the process of spatiotemporal evolution of urban land use, many spatial elements are often involved, and various spatial variables required by the model can be obtained by using the analysis function of geographic information system. Studies have shown that the probability of urban land use/cover change is generally determined by a series of distance variables, the number and distribution of existing land use types in the vicinity, and the natural attributes of units. For example, when a simulated cell is close to the city center and main roads, the probability of it developing into construction land is higher; when there is a large amount of forest land in the vicinity, a cultivated land unit has a higher probability of being converted into forest land; When the ecological constraints of , the higher the probability that the cells in the area maintain the original land use/cover state. In this embodiment, 16 related spatial variables are considered, and the detailed information and acquisition methods of these variables are shown in Table 5.

table 5.

From the land use classification data of 1995, 2005 and 2015, with the help of the spatial overlay analysis function of ArcGIS, the spatial distribution of changes in each land type during the two periods of 1995-2005 and 2005-2015 can be obtained, with 1 representing the land Using the state change, 0 means no change, so as to obtain the dependent variable used to calibrate the conversion rule. At the same time, the independent variables are 10 spatial variables in Table 5, including elevation, slope, distance to the city center, distance to town center, distance to highway, distance to railway, distance to seaside, and distance to cultivated land , distance to woodland, and distance to water bodies, etc. Due to the large scope of the study area, in the case of high resolution, the number of cells of various land use categories in the cellular grid is very large and the distribution characteristics are different, so sampling needs to be performed first. In this example, Perform random stratified sampling to obtain 20% of the sample data of each spatial variable, and use binary logistic regression to extract the contribution weight of each spatial variable to each land use/cover change. Table 6 lists the 1995-2005 cropland, forest land, grassland The spatial variable parameter configuration corresponding to the four land use types of construction land.

Table 6.

From Table 6, it can be seen that the distance from the road, the slope and the distance from the railway play an important role in promoting the expansion of construction land, followed by the distance from the urban center, the elevation, and the distance from the farmland. The study area 1995-2005 During the period of 2010, the city developed from the urban center along the railway and main roads in a diffuse type, indicating that the contribution weight of the spatial variables extracted from the sample data is in line with reality. At the same time, the change of cultivated land is mainly related to the variables such as elevation, distance from farmland, and distance from grassland, while the distance from the seaside and the distance from the road contribute less to the change of land type. At the same time, the distance from the city center The distance from the urban center has a considerable impact on the change of farmland, indicating that the change of farmland during this period was continuously affected by the urbanization process. For the change of forest land, spatial variables such as the distance from the forest land and the distance from the grassland have higher weight coefficients. At the same time, the change of the grassland is mainly closely related to the distance from the forest land, indicating the changes in the three types of farmland, forest land and grassland. They are closely related to each other in spatial distribution.

2.4 Simulation results

Use ArcGIS and Matlab software to realize the data preparation and model development of the spatiotemporal evolution (Logistic-RMCA) model, in which land use/cover change, spatial variables, ecological evaluation, etc. are all completed by ArcGIS software, while the modified Markov model, spatial sampling And modules such as binary logistic regression are implemented by Matlab software. At the same time, Matlab also realizes the construction of the transformation rules of the time-space evolution model and the micro-land allocation module of cellular automata. Taking the Xiamen City Land Use Map in 1995 as the initial state, after iterative evolution, the Xiamen City land use map during 1995-2005 was used as the initial state. Using /cover change to simulate, and using the conversion rules obtained during this period, with the land use map in 2005 as the starting point, the land use /cover change in the study area during the period 2005-2015 was simulated, and the simulation of the spatiotemporal evolution model was completed. Independent verification. Figure 3 shows the actual and simulated results for 2005 and 2015, respectively, and the observational comparison shows that the simulated results are very similar to the actual ones for both simulation periods.

Further, the simulated land use maps of Xiamen in 2005 and 2015 were compared with the corresponding actual land use maps obtained from remote sensing images, and a confusion matrix was established for the analysis results to evaluate the simulation accuracy (Table 7). The results show that the overall simulation accuracy and Kappa coefficient during 1995-2005 are 85.0% and 0.81, respectively; during 2005-2015, the overall simulation accuracy and Kappa coefficient are 88.7% and 0.86, respectively. It can be seen that the simulation effect of the spatiotemporal evolution model is ideal. At the same time, the simulation accuracy of cultivated land reached 85.0% and 89.7% in the two simulation periods, and the simulation accuracy of forest land reached 86.4% and 91.5%, respectively. High prediction accuracy was obtained for the simulation of these two land types. The spatiotemporal evolution model To a certain extent, it can reflect the distribution characteristics of the spatial and temporal evolution of regional land use.

Table 7

Urban population, economic development, technological progress and stock land are the main factors that determine the demand for construction land in the future. Given that the study area is in the process of rapid urbanization, the scenario forecast does not consider the impact of urban renewal and assumes that the current economic development is maintained The speed and level of technological progress. At the same time, although the phenomenon of sea reclamation and city building occurred in the study area from 1995 to 2015, in view of the high-pressure policy adopted by government departments for marine environment and natural coastline protection at this stage, the transformation of water bodies in future scenarios is not considered. For construction land, further, using the revised Markov transition probability matrix and the number (area) of various land uses in 2015, the number of transitions between different land uses in 2015-2045 can be predicted, as the spatiotemporal evolution model. Land demand input, thus obtaining the scenario simulation results of 2025, 2035 and 2045, as shown in Figure 4.

From the resident population data from 2005 to 2017, the resident population in 2045 predicted by the grey model is 11 million, which is far more than the 8 million population planning data of Xiamen City's long-term population planning. Therefore, it is unrealistic. By analyzing the fitting curve, It is found that the growth slope after 2010 has dropped significantly, which is closely related to the sixth national census in 2010. Therefore, using the 2010-2017 resident population data as the input of the gray model, the resident population size in 2045 is 650 Wan, considering the impact of the floating population, this is consistent with the long-term planning of Xiamen City. Some studies believe that China's population growth will show a significant slowdown in the medium term and even negative growth in some areas. In this case, the study believes that gray The model is only suitable for predicting the population size in a relatively short period of time, and it is invalid for predicting the long-term population. In view of Xiamen's development orientation as a developed coastal tourist city, its net population inflow will remain at a certain level for a long period of time. Considering that compared with other large cities in China, its urban boundary and population size are significantly lower, so , assuming that the long-term population growth rate remains unchanged from 2010 to 2017. From the perspective of the development planning of the study area, this assumption is reasonable. The study shows that in the long run, the constraints or limitations of natural conditions In this case, the population growth will obey the logistic model, and in this example, it is assumed that the resident population growth of Xiamen City from 2005 to 2045 is in a certain part of the middle of the logistic curve.

Discussion of scaling parameters for allometric models:

Nordbeck (1971) ^[6] believed that people move in three-dimensional space, while urban expansion is two-dimensional plane, so the threshold of scaling index is considered to be equal to 2/3, based on the fractal characteristics of urban population and urban built-up area The American scholar Lee, through empirical research, believes that the threshold of the scaling index should be between 2/3-1, and the Chinese scholar Chen believes that the population dimension and the urban built-up area dimension are 2 and 1.7, respectively. The theoretical value is equal to 0.85, as shown in Figure 5, through the data input of the three phases of 1995, 2005 and 2015, the allometric growth curve of Xiamen's urban population-urban built-up area is obtained, and its scaling index is 0.855. This empirical study The obtained scaling index is greater than the threshold 0.85 proposed by Chen et al., indicating that there is a certain waste of urban land use efficiency. However, (only from formula (2), it is easy to understand that the threshold should be equal to 1, that is, Xiamen during 1995-2015. The urban population expansion rate is faster than the expansion rate of the built-up area, and the land is saved. The explanation for this contradiction stems from the assumption that the urban population and the built-up area are of the same dimension). Most studies believe that the dimension of the urban population may not necessarily reach 3. , Obviously, the plot ratio of new construction land has a direct impact on the dimension of the population. With the impact of technological progress, limited land and compact development policies, it can be expected that the plot ratio of new urban construction land will continue to increase, resulting in population As the dimension continues to rise, its scaling index will decrease. The research in this example shows that, according to the established allometric growth equation, the predicted built-up area area changes to the scaling index from 2025 to 2045. is extremely sensitive, as shown in Figure 6, compared with the predicted value of the allometric equation, when the scale index in 2025, 2035 and 2045 is 0.853, 0.851 and 0.848, respectively, the predicted built-up area is 494.1, 564.8 and 641.1 square kilometers.

Table 8 quantitatively analyzes the landscape structure of three evolution scenarios in 2035 from four aspects: density index, morphological index, landscape diversity and fractal dimension. The selected indices include edge density index (ED), landscape shape index (LSI), The largest patch index (LPI), area weighted average shape index (AWMSI), Shannon diversity index (SHDI), Shannon evenness index (SHEI) and area weighted average fractal dimension (FRAC_AM) 7 indicators. With the gradual downward revision of the urban expansion demand, relatively few other land types are converted into construction land, and the edge density and shape index have both changed slightly. For example, the edge density has gradually increased from 30.17 to 30.48, and the landscape shape index has increased from 42.72. The index gradually increased to 43.16, while the index of the largest patch index, the diversity and evenness index, and the fractal dimension, which reflected the more macroscopic spatial distribution of the landscape and patches, remained almost unchanged. Overall, the landscape pattern indices from different angles are highly similar, indicating that the modification of the Markov transition probability matrix produces a landscape pattern and structure that is very similar to the baseline results, indicating that the iterative simulation of cellular automata And under the same constraints, the proposed correction method can effectively preserve the circulation characteristics of regional land use and its spatial evolution trend.

Table 8

Landscape Index ED LSI LPI AWMSI SHDI SHEI FRAC_AM Logistic-MCA 30.17 42.72 37.26 11.08 1.69 0.87 1.22 Logistic-RMCA 30.42 43.09 37.26 11.14 1.69 0.87 1.22 allometric growth 30.48 43.16 37.26 10.60 1.70 0.87 1.22

The uncertainty of the spatial distribution of land use is an important feature of the urban spatio-temporal evolution dynamics, and the randomness of the revised Markov urban model has also changed. Regarding the randomness of urban cellular automata, considering only urban land, non- In the model of urban land and water body (more often only as a constraint factor), the random factor can trigger the random disturbance of urban land in the whole study area (the whole area). Similarly, in this model, the random factor is used in the calculation of specific The total cell conversion potential of the target land type to which the location is to be converted is added at the same time, and then the micro-allocation of land use is carried out according to the demand of different land types to be converted to the target land type. At the same time, this uncertainty is gradually released in the micro-land allocation process (after the demand for land use k->land use k2 is determined), because the modified Markov chain is in the process of examining land use. After the competition between them, a new conversion potential matrix is provided (the demand has changed), so theoretically the new model will also present a random perturbation distribution different from the original model. This simulation method of the dynamic uncertainty of urban land use has Different from the roulette random selection model proposed by Liu et al. 2017, in this model, the realization of micro-random allocation is based on the comprehensive comparison of the total conversion potential of various (all) target land types converted to The probability ratio is randomly determined. This random disturbance mechanism has comprehensive and one-time characteristics. At the same time, the realized microscopic land allocation demand is also dynamically adjusted based on this random disturbance compared with the determined macroscopic demand.

3 Conclusions

In the first embodiment, a spatiotemporal evolution model of urban land use coupled with asynchronous growth law, Markov chain and cellular automata is proposed. The urban population-construction land vertical allometric growth theory is used to predict the future construction land area, and it is used to correct the Markov transition probability matrix representing the characteristics of regional land use transformation, and the parameter configuration of the transformation rule is calibrated by binary logistic regression. Combined with the empirical research of this embodiment and the theoretical value of the scaling index threshold, the possible scaling index of the future allometric growth scenario is estimated. The macro-driving factors and micro-pattern evolution characteristics of land use structure changes in urban systems are analyzed, which can provide help for understanding the complex evolution mechanism of land use systems and assessing the potential ecological effects of urban land use pattern changes.

Embodiment 2

The present invention also provides a mesh dynamics scenario simulation terminal device coupled with allometric growth, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing The computer program implements the steps in the above method embodiment of the first embodiment of the present invention.

Further, as an executable solution, the terminal equipment for simulating the grid dynamics scenario of coupled allometric growth may be computing equipment such as a desktop computer, a notebook computer, a palmtop computer, and a cloud server. The terminal equipment for simulating the mesh dynamics scenario of coupled allometric growth may include, but is not limited to, a processor and a memory. Those skilled in the art can understand that the above-mentioned composition and structure of the terminal equipment for simulating the grid dynamics scenario of coupled allometric growth is only an example of the terminal equipment for simulating the grid dynamics scenario of coupled allometric growth, and does not constitute a pair of coupled allometric growth scenarios. The definition of the grid dynamics scenario simulation terminal equipment, which may include more or less components than the above, or a combination of certain components, or different components, such as the coupled allometric grid dynamics scenario simulation terminal The device may further include an input and output device, a network access device, a bus, etc., which is not limited in this embodiment of the present invention.

Further, as an executable solution, the so-called processor may be a central processing unit (Central Processing Unit, CPU), and may also be other general-purpose processors, digital signal processors (Digital Signal Processors, DSP), application specific integrated circuits (Application Specific Integrated Circuits) Integrated Circuit, ASIC), off-the-shelf Programmable Gate Array (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The processor is the control center of the coupled allometric mesh dynamics scenario simulation terminal equipment, using various interfaces And lines connect various parts of the terminal equipment throughout the coupled allometric mesh dynamics scenario simulation.

The memory can be used to store the computer program and/or module, and the processor realizes the coupling by running or executing the computer program and/or module stored in the memory and calling the data stored in the memory Allometric mesh dynamics scenarios simulate the various functions of end devices. The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system and an application program required for at least one function; the storage data area may store data created according to the use of the mobile phone, and the like. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, internal memory, plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, Flash Card, at least one magnetic disk storage device, flash memory device, or other volatile solid state storage device.

The present invention further provides a computer-readable storage medium, where a computer program is stored in the computer-readable storage medium, and when the computer program is executed by a processor, the steps of the foregoing method in the embodiment of the present invention are implemented.

If the integrated modules/units of the coupled allometric grid dynamics scenario simulation terminal equipment are implemented in the form of software functional units and sold or used as independent products, they may be stored in a computer-readable storage medium. Based on this understanding, the present invention can implement all or part of the processes in the methods of the above embodiments, and can also be completed by instructing relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer When the program is executed by the processor, the steps of the foregoing method embodiments can be implemented. Wherein, the computer program includes computer program code, and the computer program code may be in the form of source code, object code, executable file or some intermediate form, and the like. The computer-readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM, ROM, Read-Only). Memory), random access memory (RAM, Random Access Memory), and software distribution media, etc.

Although the present invention has been particularly shown and described in connection with preferred embodiments, it will be understood by those skilled in the art that changes in form and detail may be made to the present invention without departing from the spirit and scope of the invention as defined by the appended claims. Various changes are made within the protection scope of the present invention.

references:

【1】Verburg, P.H., Soepboer, W., Veldkamp, A., Limpiada, R., Espaldon, V., Mastura, S.S., 2002. Modeling the spatial dynamics of regional land use: the CLUE-S model. Environmental Management 30 (3) 391-405.

[2] White, R., Engelen, G., 2000. High-resolution integrated modelling of the spatial dynamics of urban and regional systems. Computers, environment and urban systems 24(5) 383-400.

【3】Wu, F., Webster, C.J., 2000. Simulating artificial cities in a GIS environment: urban growth under alternative regulation regimes. International Journal of Geographical Information Science 14(7) 625-648.

【4】Feng, Y., Liu, Y., Tong, X., Liu, M., Deng, S., 2011. Modeling dynamic urbangrowth using cellular automata and particle swarm optimization rules. Landscape and Urban Planning 102(3)188 -196.

【5】He, C., Zhao, Y., Huang, Q., Zhang, Q., Zhang, D., 2015. Alternative future analysis for assessing the potential impact of climate change on urbanlandscape dynamics. Science of the Total Environment 532 48-60.

[6] Nordbeck, S., 1971. Urban allometric growth. Geografiska Annaler: Series B, Human Geography 53 (1) 54-67.

Claims (6)

1. a grid dynamics scenario simulation method for coupled growth at different speeds is characterized by comprising the following steps:

s1: constructing a transition probability matrix P for mutual conversion among different land use types according to a Markov model; the transition probability matrix P is:

wherein, P _ij The transition probability of the ith land utilization type being converted into the jth land utilization type in the process from the time t to the time t +1, wherein M is the number of the land utilization types, and each element P in the transition probability matrix P _ij The following conditions are satisfied:

s2: predicting the newly added construction land area of the city according to the Markov model and the different-speed growth model respectively, and recording the newly added construction land area as A _m And A _a (ii) a The Markov model is:

P _(n) ＝P _(n-1) P _ij

wherein, P _(n) Is a state probability vector at any time, P _(n-1) Is the state probability vector at the initial time;

the different-speed growth model of the urban construction land area comprises the following steps:

A _t ＝α(P _t ) ^b

wherein, A _t Is the urban construction land area at the time of t, P _t The scale is the urban population scale at the time t, alpha is a proportionality coefficient, and b is a scale index;

s3: newly-added construction land area A predicted according to Markov model and different-speed growth model _m And A _a The difference between the two, the transition probability matrix P is corrected to P'; the modified markov transition probability matrix P' is set to:

wherein the subscript j represents a construction land, the subscript i represents a non-construction land, μ _i And mu _j All are correction coefficients;

correction coefficient mu _j The calculation formula of (c) is:

μ _j ＝A _a /A _m

correction factor mu _i The calculation formula of (2) is as follows:

s4: establishing an urban cellular automata model based on logistic regression and added with random disturbance factors and limiting factors; the urban cellular automaton model is as follows:

S _ij ^t ＝f(S _ij ^t-1 ，P _c，ij ，Ω _ij ^t-1 ，Cons，R)

wherein S is _ij ^t And S _ij ^t-1 The state of the cell (i, j) at times t and t-1, P, respectively _c，ij Denotes the transition probability, Ω, of the cell (i, j) _ij ^t-1 The distribution condition of a specific land utilization type in a neighborhood space of a cellular (i, j), cons is a limiting factor, R is a random disturbance factor, and f represents a conversion rule for determining the state change of the cellular;

s5: and simulating the dynamic evolution process of the urban space according to the corrected transition probability matrix and the urban cellular automata model.

2. The grid dynamics scenario simulation method of coupled growth at different speed of claim 1, characterized in that: the prediction process of the urban population size is as follows:

setting time series x ⁽⁰⁾ There are n observations:

x ⁽⁰⁾ ＝{x ⁽⁰⁾ (1)，x ⁽⁰⁾ (2)，...，x ⁽⁰⁾ (n)}

a new series is obtained through accumulation:

x ⁽¹⁾ ＝{x ⁽¹⁾ (1)，x ⁽¹⁾ (2)，...，x ⁽¹⁾ (n)}

differential equations for the gray GM (1, 1) model were established:

wherein,

in order to develop the ash count,

the number of the ash is controlled for the endogenesis,

obtaining by least squares fitting

And

solving a differential equation to obtain a population prediction model as follows:

and predicting the size of the urban population according to the population prediction model.

3. The grid dynamics scenario simulation method of coupled growth at different speed of claim 1, characterized in that: transition probability P of the cell _c，ij The calculation formula of (2) is as follows:

wherein X is a space variable vector influencing the land use type change, and X = (X) ₀ ，x ₁ ，x ₂ ，...，x _k )，x ₀ =1,B is the parameter vector to be estimated, B = (B) ₀ ，b ₁ ，b ₂ ，...，b _k )。

4. The grid dynamics scenario simulation method of coupled growth at different speeds of claim 1, characterized in that: cell state transition probability P of urban cell automaton model _total，k ^t The calculation formula of (2) is as follows:

wherein, P _total，k ^t Probability of conversion of land use type at time t into land use type k, R = (1 + (-ln γ) ^β ) Is a random disturbance factor, gamma is a random number of (0-1), beta is an integer, beta is more than or equal to 1and less than or equal to 10, X is a space variable vector influencing the change of land use types, B is a space variable vector _k Is a weight vector of each spatial variable, Ω _ij，k ^t-1 For neighborhood effects, norm (-) represents a normalization function, cons (-) represents a constraint function that constrains cell state changes, S _ij，k ^t-1 Indicating the state of the cell.

5. The grid dynamics scenario simulation method of coupled growth at different speed of claim 4, characterized in that: the neighborhood impact Ω _ij，k ^t-1 The calculation formula of (2) is as follows:

wherein, theta _d，k An attenuation coefficient, con (S), representing the land use type k with a distance d from the central cell (i, j) _d，ij ^t-1 = k) represents the number of pixels of land use type k in the d distance neighborhood of cell (i, j).

6. A grid dynamics scenario simulation terminal device coupled with different-speed growth is characterized in that: comprising a processor, a memory and a computer program stored in said memory and running on said processor, said processor implementing the steps of the method according to any one of claims 1 to 5 when executing said computer program.

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