Sensitivity analysis and accuracy assessment of the land transformation model using cellular automata

Figures & data

Figure 1. Study areas (false color images of Landsat 8 for the year 2014).

Table 1. Variables used for urban growth simulation.

Variables (Tehran, 1985)	Range	Mean	Variable (Isfahan, 1994)	Range	Mean
Distance to agricultural land (m)	0–16,030	1650	Distance to built-up areas (m)	0–6638	831
Distance to open land (m)	0–2468	164	Distance to agricultural land (m)	0–4968	308
Distance to built-up areas (m)	0–8750	1168	Distance to open land (m)	0–5528	815
Distance to green spaces (m)	0–8361	732	Distance to nearest road (m)	0–5209	517
Distance to nearest road (m)	0–15,944	2150	Distance to salt marsh (m)	0–24,282	8912
Height (m)	956–2119	1199	Height (m)	1512–2391	1939
Slope (°)	0–45	2.36	Slope (°)	0–72	4.5
Northing parameter (m)	3,926,423–3,965,063	3,943,571	Northing parameter (m)	3,600,872–3,630,842	3,615,857
Easting parameter (m)	505,846–555,466	531,411	Easting parameter (m)	551,011–580,981	565,996

Figure 2. Workflow showing the LTM-based urban change simulation using a top-down approach and cellular automata.

Table 2. Spatial metrics used for model evaluation (Pontius et al. 2008).

Metrics	Formula	Description
Figure of merit (FOM)	$\mathrm{F}\mathrm{o}\mathrm{M}=\frac{\mathrm{B}}{\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}}$	FOM is the intersection of the observed and predicted change divided by the union of the observed and predicted change
Producer accuracy (PA)	$PA=\frac{B}{A+B+C}$	PA indicates the proportion of pixels that the model predicts accurately as change, given that the reference maps indicate observed change
Overall accuracy (OA)	$OA=\frac{B+E}{A+B+C+D+E}$	OA provides the overall agreement between the reference and predicted maps

Figure 3. Error maps for Tehran (a) LTM-CA with a 3 × 3 neighborhood size, (b) LTM-CA with a 5 × 5 neighborhood size, (c) LTM-CA with a 7 × 7 neighborhood size, (d) LTM-CA with a 9 × 9 neighborhood size, and (e) LTM with a top-down approach. The maps show the levels of agreement and disagreement between the simulated and reference maps.

Figure 4. Error maps for Isfahan (a) LTM-CA with a 3 × 3 neighborhood size, (b) LTM-CA with a 5 × 5 neighborhood size, (c) LTM-CA with a 7 × 7 neighborhood size, (d) LTM-CA with a 9 × 9 neighborhood size, and (e) LTM with a top-down approach. The maps show the levels of agreement and disagreement between the simulated and reference maps.

Figure 5. The difference between the LTM with a top-down approach (a, A1, B1, C1, D1, and E1) and LTM-CA with 7 × 7 neighborhood size (b, A2, B2, C2, D2, and E2) for Tehran.

Figure 6. The difference between the LTM with a top-down approach (a, A1, B1, C1, D1, and E1) and LTM-CA with 7 × 7 neighborhood size (b, A2, B2, C2, D2, and E2) for Isfahan.

Table 3. Accuracy assessment of the models indicated by the FOM, OA, and PA.

Tehran	PA	OA	FOM	Isfahan	PA	OA	FOM
LTM	57.98	82.92	40.82	LTM	38.92	70.49	24.19
LTM-CA 3 × 3	59.87	84.14	42.72	LTM-CA 3 × 3	41.56	71.77	26.26
LTM-CA 5 × 5	60.78	84.73	43.66	LTM-CA 5 × 5	42.54	72.24	27.05
LTM-CA 7 × 7	60.84	84.76	43.72	LTM-CA 7 × 7	42.69	72.31	27.16
LTM-CA 9 × 9	60.78	84.73	43.66	LTM-CA 9 × 9	42.17	72.06	26.74

Pontius, R. Jr, G. W. Boersma, J.-C. Castella, K. Clarke, T. De Nijs, C. Dietzel, Z. Duan, et al. 2008. “Comparing the Input, Output, and Validation Maps for Several Models of Land Change.” The Annals of Regional Science 42 (1): 11–37. doi:10.1007/s00168-007-0138-2.

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