An adaptive transition probability matrix with quality seeds for cellular automata models

Figures & data

Figure 1. Geographic location of Beijing, Wuhan, and the Pearl River Delta in 2000.

Table 1. Details and generalization of each spatial variable.

Data classification	Datasets	File type	Year	Grid resolution	Spatial variable	Meaning of the spatial variables
Accessibility factors	County centers	Shp	2010	/	DIS2CC	Distance from the county centers
	County Highways	Shp	2010	/	DIS2CH	Distance from the County Highways
	Metros & Light Rails	Shp	2010	/	DIS2MLR	Distance from the Metros & Light Rails
	Railways	Shp	2010	/	DIS2RW	Distance from the Railways
	Provincial Highways	Shp	2010	/	DIS2PH	Distance from the Provincial Highways
	National Highways	Shp	2010	/	DIS2NH	Distance from the National highways
	Super Highways	Shp	2010	/	DIS2SH	Distance from the Super Highways
Socio-economic factor	NDVI	Tif	2010	1km	NDVI	Distribution of NDVI
	Population	Tif	2010	1km	POP	Distribution of spatialized population
Natural factors	GDP	Tif	2010	1km	GDP	Distribution of spatialized GDP
	Rivers	Tif	2010	30m	DIS2RV	Distance from the rivers
	Elevation data	Tif	2010	30m	DEM	The elevation
	Slope	Tif	2010	30m	Slope	The slope
	Land Use and land cover	Tif	2010	30m	DIS2UL	Distance from the urban land in 2010

Figure 2. Methodological framework.

Figure 3. The architecture of the artificial neural network.

Table

Algorithm 1. The pseudo-code of the ATPMS-ANN-CA
Input: Population Size, crossover rate, mutation rate, termination condition, quality seed data (Calculated by the Markov model) Output: Global best probability matrix begin
Initial chromosomes and generation;
Population [generation]= binary to decimal (chromosomes);
FoM= ATPMS-ANN-CA (population[generation]); Compute the fitness value of each chromosome; Population (the lowest fitness) = quality seeds (the Markov model);
While is TerminationConditionMet () == false do//The difference between 5 consecutive optimal solutions does not exceed 1e-5
Parents = selectParents(population[generation]);//Extract the populations based on fitness
Population [generation + 1] = crossover(parents);
Population [generation + 1] = mutate (population [generation + 1]); Chromosomes [generation] (the lowest fitness) = chromosomes [generation − 1] (the highest fitness)
Generation++;
End loop;
Return the best solution; end

Figure 4. Spatial distribution of land transfer in the three study areas during the calibration and validation periods. Numbers 1–6 represent cropland, forest, grassland, water area, built-up land and unused land. Code “12” represents the transfer of cropland to forest, et cetera.

Table 2. Transition matrix for land use type transition (km²) in Beijing, Wuhan, and the Pearl Delta River, 2000–2010.

Study area	land use types	Cropland	Forest	Grassland	Water area	Built-up land	Unused land	Sum
Beijing	Cropland	4362.85	56.85	0.01	5.26	495.28	0.00	4920.25
	Forest	23.55	7327.48	0.25	14.72	40.65	0.00	7406.64
	Grassland	0.31	2.26	1279.53	1.33	11.09	0.00	1294.52
	Water area	15.19	0.17	4.06	469.24	25.72	0.00	514.38
	Built-up land	1.45	0.29	0.38	1.07	2245.67	0.00	2248.86
	Unused land	0.00	0.00	0.00	0.00	0.23	0.92	1.15
	Sum	4403.35	7387.06	1284.23	491.62	2818.63	0.92	16385.80
Wuhan	Cropland	4640.99	16.90	12.56	177.91	322.45	4.28	5175.08
	Forest	14.13	760.18	1.04	3.80	22.75	0.02	801.91
	Grassland	0.68	0.30	58.70	5.80	7.53	0.19	73.20
	Water area	50.66	0.72	2.44	1606.29	59.96	3.61	1723.69
	Built-up land	10.78	1.93	1.14	18.40	626.04	0.06	658.34
	Unused land	0.88	0.31	0.09	14.30	5.57	52.86	74.01
	Sum	4718.11	780.34	75.97	1826.50	1044.30	61.01	8506.23
The PRD	Cropland	11648.14	262.60	10.36	665.20	1788.83	0.23	14375.36
	Forest	207.31	28898.85	30.74	75.38	754.81	0.41	29967.51
	Grassland	14.30	76.76	899.73	12.56	63.79	0.04	1067.17
	Water area	548.01	50.67	4.31	3063.34	505.20	0.04	4171.56
	Built-up land	147.90	96.31	3.68	72.06	3936.06	0.08	4256.07
	Unused land	2.14	1.03	0.05	3.30	6.60	9.71	22.83
	Sum	12567.79	29386.22	948.85	3891.84	7055.29	10.50	53860.50

Table 3. Transition probability matrix (%) in Beijing, Wuhan, and the Pearl Delta River, 2000–2010.

Study area	land use types	Cropland	Forest	Grassland	Water area	Built-up land	Unused land
Beijing	Cropland	–	0.77	0.01	1.07	17.57	0.01
	Forest	0.53	–	0.02	2.99	1.44	0.01
	Grassland	0.01	0.03	–	0.27	0.39	0.01
	Water area	0.35	0.01	0.32	–	0.91	0.01
	Built-up land	0.03	0.01	0.03	0.22	–	0.01
	Unused land	0.01	0.01	0.01	0.01	0.01	–
Wuhan	Cropland	–	2.17	16.53	9.74	30.88	7.01
	Forest	0.30	–	1.36	0.21	2.18	0.03
	Grassland	0.01	0.04	–	0.32	0.72	0.31
	Water area	1.07	0.09	3.21	–	5.74	5.92
	Built-up land	0.23	0.25	1.50	1.01	–	0.09
	Unused land	0.02	0.04	0.12	0.78	0.53	–
The PRD	Cropland	–	0.89	1.09	17.09	25.35	2.14
	Forest	1.65	–	3.24	1.94	10.70	3.95
	Grassland	0.11	0.26	–	0.32	0.90	0.36
	Water area	4.36	0.17	0.45	–	7.16	0.39
	Built-up land	1.18	0.33	0.39	1.85	–	0.72
	Unused land	0.02	0.01	0.01	0.08	0.09	–

Figure 5. Accurate modeling results of the adaptive transition probability matrix with quality seeds for transition probability optimization are presented for Beijing (a), Wuhan (b), and the Pearl River Delta (c) during the period 2000–2010.

Table 4. Optimized transition probability matrix (%) in Beijing, Wuhan, and the PRD, 2000–2010.

Study area	land use types	Cropland	Forest	Grassland	Water area	Built-up land	Unused land
Beijing	Cropland	–	7.12	0.20	54.05	17.66	12.59
	Forest	38.05	–	6.34	0.78	3.90	28.39
	Grassland	13.17	0.88	–	0.29	50.05	9.46
	Water area	6.83	50.05	13.27	–	1.07	3.22
	Built-up land	0.10	0.10	0.10	51.41	–	0.10
	Unused land	4.29	47.32	30.63	35.12	55.71	–
Wuhan	Cropland	–	5.27	47.02	90.44	7.12	90.73
	Forest	47.90	–	98.54	10.54	72.88	84.78
	Grassland	94.44	54.34	–	92.68	74.63	72.98
	Water area	99.71	68.49	45.27	–	55.22	87.51
	Built-up land	49.76	43.51	52.49	99.80	–	64.78
	Unused land	37.95	66.24	17.17	2.63	16.00	–
The PRD	Cropland	–	0.29	21.07	73.56	75.12	53.95
	Forest	37.76	–	16.00	35.61	59.90	30.63
	Grassland	50.44	25.37	–	6.44	0.98	12.59
	Water area	6.05	10.05	12.98	–	32.10	9.85
	Built-up land	0.88	0.78	0.88	33.17	–	2.93
	Unused land	0.49	76.59	7.12	20.39	0.98	–

Table 5. Validation coefficients for three different the cellular automata models in Beijing, Wuhan, and the PRD in calibration period.

Study area	Validation coefficients	ANN-CA	Markov-ANN-CA	ATPMS-ANN-CA
Beijing	OA	0.95	0.95	0.95
	FoM	0.23	0.24	0.25
Wuhan	OA	0.91	0.91	0.92
	FoM	0.09	0.09	0.15
The PRD	OA	0.90	0.90	0.91
	FoM	0.20	0.19	0.21

Table 6. Validation coefficients for three different the cellular automata models in Beijing, Wuhan, and the PRD in validation period.

Study area	Validation coefficients	ANN-CA	Markov-ANN-CA	ATPMS-ANN-CA
Beijing	OA	0.85	0.85	0.85
	FoM	0.14	0.14	0.15
Wuhan	OA	0.91	0.91	0.91
	FoM	0.07	0.06	0.11
The PRD	OA	0.93	0.93	0.91
	FoM	0.10	0.12	0.13

Figure 6. Comparative results of landscape details of current land use status in Beijing, Wuhan and the Pearl River Delta using artificial neural networks-cellular automata, Markov-artificial neural networks-cellular automata and adaptive transfer probability matrix-artificial neural networks-cellular automata models with quality seeds during the period of calibration (2000 to 2010) and validation (2010 to 2020).