# Spatiotemporal Modeling of Urban Growth Using Machine Learning

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Input Variables

#### 2.2. Data Pre-Processing

- Using images from Landsat missions to obtain a set of initial estimates of the urban footprint in RGB color and the binary urban footprint. This is covered in Section 2.2.1.
- Performing a content-aware spatial resampling of all input variables for getting digital images with a common coordinate reference system, geographic extent, and spatial resolution. This is explained in Section 2.2.2.
- Applying a first-order temporal interpolation to the population distribution for getting annual estimates, and optionally if available, applying an adjustment of the annual population distribution estimates to match the total population defined by the corresponding National Bureau of Statistics (see Section 2.2.3). Notice that, if the official population values are only available for a subset of the years of interest, then a temporal regression is applied to estimate the values in missing years.
- Estimating the binary urban footprint for missing years by harmonizing it with the historical population distribution. This process is detailed in Section 2.2.4;
- Using a semantic-inpainting algorithm for estimating the urban footprint in RGB color for missing years. The block in this pre-processing stage is the same to the one explained in Section 2.6.
- Applying a zero-order hold to get annual estimates of the other input variables in missing years.

#### 2.2.1. Pre-Processing of Landsat Images

#### 2.2.2. Content-Aware Spatial Resampling of Images

#### 2.2.3. Temporal Interpolation of the Population Distribution and Official Adjustment

#### 2.2.4. Harmonization Between the Binary Urban Footprint and the Population Distribution

#### 2.3. Urban Growth Model

#### 2.4. Spatiotemporal Regression Model for the Population Distribution

#### 2.5. Binary Urban Footprint Estimation

#### 2.6. Urban Footprint Estimation

#### 2.7. Training, Model Selection, and Testing Strategies

#### 2.8. Implementation Details

#### 2.9. Case Studies

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

GHSL | Global human settlement layer |

BUF | Binary urban footprint |

POP | Population distribution |

SAD | Sum of absolute differences |

SSD | Sum of square differences |

FP | False positive |

ZNCC | Zero-mean normalized cross correlation |

IoU | Intersection over Union |

KDE | Kernel density estimation |

Probability density function | |

LAC | Latin American cities |

ML | Machine learning |

## Appendix A. Saturation Functions for the Population Distribution

## References

- United Nations. World Population Prospects 2019: Data Booket. ST/ESA/SER.A/424; Technical Report; United Nations, Department of Economic and Social Affairs, Population Division: New York, NY, USA, 2019. Available online: https://population.un.org/wpp/Publications/Files/WPP2019_DataBooklet.pdf (accessed on 30 November 2019).
- United Nations. Population Facts; Technical Report 4; United Nations, Department of Economic and Social Affairs: New York, NY, USA, 2019. Available online: https://www.un.org/en/development/desa/population/migration/publications/populationfacts/docs/MigrationStock2019_PopFacts_2019-04.pdf (accessed on 30 November 2019).
- United Nations. International Migration Report 2017: Highlights (ST/ESA/SER.A/404); Technical Report; United Nations, Department of Economic and Social Affairs: New York, NY, USA, 2017. Available online: https://www.un.org/en/development/desa/population/migration/publications/migrationreport/docs/MigrationReport2017_Highlights.pdf (accessed on 30 November 2019).
- Grant, U. Spatial Inequality and Urban Poverty Traps; Technical Report; Overseas Development Institute: London, UK, 2010; Available online: https://www.odi.org/publications/4526-spatial-inequality-and-urban-poverty-traps (accessed on 30 November 2019).
- Moore, M.; Gould, P.; Keary, B.S. Global urbanization and impact on health. Int. J. Hygiene Environ. Health
**2003**, 206, 269–278. [Google Scholar] [CrossRef] [PubMed] - Huang, W.; Huang, Y.; Lin, S.; Chen, Z.; Gao, B.; Cui, S. Changing urban cement metabolism under rapid urbanization—A flow and stock perspective. J. Clean. Prod.
**2018**, 173, 197–206. [Google Scholar] [CrossRef] - Flörke, M.; Schneider, C.; McDonald, R.I. Water competition between cities and agriculture driven by climate change and urban growth. Nat. Sustain.
**2018**, 1, 51. [Google Scholar] [CrossRef] - DeFries, R.S.; Rudel, T.; Uriarte, M.; Hansen, M. Deforestation driven by urban population growth and agricultural trade in the twenty-first century. Nat. Geosci.
**2010**, 3, 178. [Google Scholar] [CrossRef] - Panagopoulos, T.; González Duque, J.A.; Bostenaru Dan, M. Urban planning with respect to environmental quality and human well-being. Environ. Pollut.
**2016**, 208, 137–144. [Google Scholar] [CrossRef] [PubMed][Green Version] - Chen, S.; Chen, B.; Fath, B.D. Urban ecosystem modeling and global change: Potential for rational urban management and emissions mitigation. Environ. Pollut.
**2014**, 190, 139–149. [Google Scholar] [CrossRef] - Fang, C.; Wang, S.; Li, G. Changing urban forms and carbon dioxide emissions in China: A case study of 30 provincial capital cities. Appl. Energy
**2015**, 158, 519–531. [Google Scholar] [CrossRef] - Seto, K.C.; Pandey, B. Urban Land Use: Central to Building a Sustainable Future. ONE Earth
**2019**, 1, 168–170. [Google Scholar] [CrossRef][Green Version] - Ahrend, R.; Farchy, E.; Kaplanis, I.; Lembcke, A.C. What Makes Cities More Productive? Evidence on the Role of Urban Governance from Five OECD Countries. OECD Reg. Dev. Work. Papers
**2014**, 5, 1–33. [Google Scholar] [CrossRef] - Potere, D. Mapping the World’s cities: An Examination of Global Urban Maps And Their Implications for Conservation Planning. Ph.D. Thesis, Princeton University, Princeton, NJ, USA, 2009. [Google Scholar]
- Glaeser, E.L. Are Cities Dying? J. Econ. Perspect.
**1998**, 12, 139–160. [Google Scholar] [CrossRef][Green Version] - Jaffe, A.B.; Trajtenberg, M.; Henderson, R. Geographic Localization of Knowledge Spillovers as Evidenced by Patent Citations. Q. J. Econ.
**1993**, 108, 577–598. Available online: http://oup.prod.sis.lan/qje/article-pdf/108/3/577/5318741/108-3-577.pdf (accessed on 30 November 2019). [CrossRef] - Lynch, K. A Theory of Good City Form; MIT Press: Cambridge, MA, USA; London, UK, 1981. [Google Scholar]
- Colsaet, A.; Laurans, Y.; Levrel, H. What drives land take and urban land expansion? A systematic review. Land Use Policy
**2018**, 79, 339–349. [Google Scholar] [CrossRef] - He, Q.; He, W.; Song, Y.; Wu, J.; Yin, C.; Mou, Y. The impact of urban growth patterns on urban vitality in newly built-up areas based on an association rules analysis using geographical ‘big data’. Land Use Policy
**2018**, 78, 726–738. [Google Scholar] [CrossRef] - Khanal, N.; Uddin, K.; Matin, M.; Tenneson, K. Automatic Detection of Spatiotemporal Urban Expansion Patterns by Fusing OSM and Landsat Data in Kathmandu. Remote Sens.
**2019**, 11, 2296. [Google Scholar] [CrossRef][Green Version] - Goldstein, N.C.; Candau, J.; Clarke, K. Approaches to simulating the “March of Bricks and Mortar”. Comput. Environ. Urban Syst.
**2004**, 28, 125–147. [Google Scholar] [CrossRef] - Barredo, J.I.; Demicheli, L. Urban sustainability in developing countries’ megacities: Modelling and predicting future urban growth in Lagos. Cities
**2003**, 20, 297–310. [Google Scholar] [CrossRef] - Duwal, S.; Amer, S.; Kuffer, M. Modelling urban growth in the Kathmandu Valley, Nepal. In Gis in Sustainable Urban Planning and Management: A Golbal Perspective, 1st ed.; van Maarseveen, M., Martinez, J., Flacke, J., Eds.; CRC Press: Boca Raton, MA, USA, 2018; Chapter 12; pp. 205–223. [Google Scholar] [CrossRef]
- Weng, Q. Remote sensing of impervious surfaces in the urban areas: Requirements, methods, and trends. Remote Sens. Environ.
**2012**, 117, 34–49. [Google Scholar] [CrossRef] - Al-Darwish, Y.; Ayad, H.; Taha, D.; Saadallah, D. Predicting the future urban growth and it’s impacts on the surrounding environment using urban simulation models: Case study of Ibb city—Yemen. Alexandria Eng. J.
**2018**, 57. [Google Scholar] [CrossRef] - Pérez-Molina, E.; Sliuzas, R.; Flacke, J.; Jetten, V. Developing a cellular automata model of urban growth to inform spatial policy for flood mitigation: A case study in Kampala, Uganda. Comput. Environ. Urban Syst.
**2017**, 65, 53–65. [Google Scholar] [CrossRef] - Xia, C.; Zhang, A.; Wang, H.; Liu, J. Land Use Policy Delineating early warning zones in rapidly growing metropolitan areas by integrating a multiscale urban growth model with biogeography-based optimization. Land Use Policy
**2019**, 90, 104332. [Google Scholar] [CrossRef] - Cosentino, C.; Amato, F.; Murgante, B. Population-based simulation of urban growth: The Italian case study. Sustainability
**2018**, 10, 4838. [Google Scholar] [CrossRef][Green Version] - Gounaridis, D.; Chorianopoulos, I.; Koukoulas, S. Exploring prospective urban growth trends under different economic outlooks and land-use planning scenarios: The case of Athens. Appl. Geogr.
**2018**, 90, 134–144. [Google Scholar] [CrossRef] - Zhang, C.; Miao, C.; Zhang, W.; Chen, X. Spatiotemporal patterns of urban sprawl and its relationship with economic development in China during 1990–2010. Habit. Int.
**2018**, 79, 51–60. [Google Scholar] [CrossRef] - Aghion, P.; Durlauf, S. Handbook of Economic Growth, 1st ed.; Elsevier: Amsterdam, The Netherlands, 2005; Volume 2. [Google Scholar]
- Lung, T.; Lübker, T.; Ngochoch, J.K.; Schaab, G. Human population distribution modelling at regional level using very high resolution satellite imagery. Appl. Geogr.
**2013**, 41, 36–45. [Google Scholar] [CrossRef] - Bhowmick, A.R.; Sardar, T.; Bhattacharya, S. Estimation of growth regulation in natural populations by extended family of growth curve models with fractional order derivative: Case studies from the global population dynamics database. Ecol. Inform.
**2019**, 53, 100980. [Google Scholar] [CrossRef] - Wu, J.; Li, R.; Ding, R.; Li, T.; Sun, H. City expansion model based on population diffusion and road growth. Appl. Math. Model.
**2017**, 43, 1–14. [Google Scholar] [CrossRef] - Tobler, W.R. A computer movie simulating urban growth in the Detroit region. Economic Geography
**1970**, 46, 234–240. [Google Scholar] [CrossRef] - Nduwayezu, G.; Sliuzas, R.; Kuffer, M. Modeling urban growth in Kigali city Rwanda. Rwanda J.
**2017**, 1. [Google Scholar] [CrossRef][Green Version] - Herold, M.; Goldstein, N.C.; Clarke, K.C. The spatiotemporal form of urban growth: Measurement, analysis and modeling. Remote Sens. Environ.
**2003**, 86, 286–302. [Google Scholar] [CrossRef] - Ayazli, I.E.; Kilic, F.; Lauf, S.; Demir, H.; Kleinschmit, B. Simulating urban growth driven by transportation networks: A case study of the Istanbul third bridge. Land Use Policy
**2015**, 49, 332–340. [Google Scholar] [CrossRef] - Thapa, R.B.; Murayama, Y. Scenario based urban growth allocation in Kathmandu Valley, Nepal. Landscape Urban Plan.
**2012**, 105, 140–148. [Google Scholar] [CrossRef] - Makse, H.A.; Havlin, S.; Stanley, H.E. Modelling urban growth patterns. Nature
**1995**, 377, 608. [Google Scholar] [CrossRef] - Tobler, W.R. Geographical filters and their inverses. Geogr. Anal.
**1969**, 1, 234–253. [Google Scholar] [CrossRef] - Hu, Z.; Lo, C. Modeling urban growth in Atlanta using logistic regression. Comput. Environ. Urban Syst.
**2007**, 31, 667–688. [Google Scholar] [CrossRef] - Clarke, K.C.; Hoppen, S.; Gaydos, L. A self-modifying cellular automaton model of historical urbanization in the San Francisco Bay area. Environ. Plan. B Plan. Des.
**1997**, 24, 247–261. [Google Scholar] [CrossRef][Green Version] - Clarke, K.C.; Gaydos, L.J. Loose-coupling a cellular automaton model and GIS: Long-term urban growth prediction for San Francisco and Washington/Baltimore. Int. J. Geogr. Inform. Sci.
**1998**, 12, 699–714. [Google Scholar] [CrossRef][Green Version] - Schiavina, M.; Freire, S.; MacManus, K. GHS Population Grid Multitemporal (1975, 1990, 2000, 2015) R2019A; Technical Report; European Commission, Joint Research Centre (JRC): Brussels, Belgium, 2019; Available online: http://data.europa.eu/89h/0c6b9751-a71f-4062-830b-43c9f432370f (accessed on 30 November 2019).
- Florczyk, A.J.; Melchiorri, M.; Corbane, C.; Schiavina, M.; Maffenini, M.; Pesaresi, M.; Politis, P.; Sabo, S.; Freire, S.; Ehrlich, D.; et al. Description of the GHS Urban Centre Database 2015, Public Release 2019, Version 1.0; Technical Report; Publications Office of the European Union: Luxembourg, 2019. [Google Scholar] [CrossRef]
- NASA; U.S. Geological Survey. Landsat Missions; Technical Report; NASA; U.S. Geological Survey: Reston, VA, USA, 2019. Available online: https://www.usgs.gov/land-resources/nli/landsat (accessed on 30 November 2019).
- DANE. Estimation and Projection of the Total National, Departmental, and Municipal Population by Area 1985–2020; Technical Report; National Administrative Department of Statistics (DANE): Bogotá, Colombia, 2019. Available online: https://www.dane.gov.co/index.php/estadisticas-por-tema/demografia-y-poblacion/proyecciones-de-poblacion (accessed on 30 November 2019).
- Rionegro Town Hall. Master Plan of Rionegro; Technical Report; Rionegro Town Hall: Rionegro, Colombia, 2018. Available online: https://www.rionegro.gov.co/Paginas/plan-de-ordenamiento-territorial.aspx (accessed on 30 November 2019).
- Valledupar Town Hall. Master Plan of Valledupar; Technical Report; Valledupar Town Hall: Valledupar, Colombia, 2013. Available online: https://sites.google.com/a/valledupar-cesar.gov.co/pot_valledupar/batx-2-1 (accessed on 30 November 2019).
- Corbane, C.; Florczyk, A.; Pesaresi, M.; Politis, P.; Syrris, V. GHS Built-Up Grid, Derived from Landsat, Multitemporal (1975-1990-2000-2014), R2018A; Technical Report; European Commission, Joint Research Centre (JRC): Brussels, Belgium, 2018; Available online: http://data.europa.eu/89h/jrc-ghsl-10007 (accessed on 30 November 2019). [CrossRef]
- Jarvis, A.; Reuter, H.I.; Nelson, A.; Guevara, E. Hole-Filled SRTM for the Globe Version 4; Technical Report; International Centre for Tropical Agriculture (CIAT): Palmira, Colombia, 2008; Available online: http://srtm.csi.cgiar.org (accessed on 30 November 2019).
- OpenStreetMap Contributors. 2017. Planet OSM. Available online: https://planet.osm.org (accessed on 30 November 2019).
- IGAC. Open Data Cartography and Geography; Technical Report; Agustín Codazzi Geographic Institute: Bogotá, Colombia, 2019. Available online: https://geoportal.igac.gov.co/contenido/datos-abiertos-cartografia-y-geografia (accessed on 30 November 2019).
- UNEP-WCMC; IUCN. Protected Planet: The World Database on Protected Areas (WDPA); Technical Report; UNEP-WCMC; IUCN: Cambridge, UK, 2019; Available online: www.protectedplanet.net (accessed on 30 November 2019).
- Young, N.E.; Anderson, R.S.; Chignell, S.M.; Vorster, A.G.; Lawrence, R.; Evangelista, P.H. A survival guide to Landsat preprocessing. Ecology
**2017**, 98, 920–932. [Google Scholar] [CrossRef][Green Version] - Goslee, S.C. Analyzing remote sensing data in R: The landsat package. J. Stat. Softw.
**2011**, 43, 1–25. [Google Scholar] [CrossRef][Green Version] - Cao, Z.; Wu, Z.; Kuang, Y.; Huang, N.; Wang, M. Coupling an intercalibration of radiance-calibrated nighttime light images and land use/cover data for modeling and analyzing the distribution of GDP in Guangdong, China. Sustainability
**2016**, 8, 108. [Google Scholar] [CrossRef][Green Version] - Liu, F.T.; Ting, K.M.; Zhou, Z.H. Isolation-Based Anomaly Detection. ACM Trans. Knowl. Discov. Data
**2012**, 6, 3:1–3:39. [Google Scholar] [CrossRef] - Breunig, M.; Kriegel, H.P.; Ng, R.; Sander, J. LOF: Identifying Density-Based Local Outliers. ACM Sigmod Record
**2000**, 29, 93–104. [Google Scholar] [CrossRef] - Bak, P.; Tang, C.; Wiesenfeld, K. Self-organized criticality. Phys. Rev. A
**1988**, 38, 364–374. Available online: https://link.aps.org/doi/10.1103/PhysRevA.38.364 (accessed on 30 November 2019). [CrossRef] [PubMed] - Telea, A. An image inpainting technique based on the fast marching method. J. Graph. Tools
**2004**, 9, 23–34. [Google Scholar] [CrossRef] - Bertalmio, M.; Bertozzi, A.L.; Sapiro, G. Navier-stokes, fluid dynamics, and image and video inpainting. In Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2001, Kauai, HI, USA, 8–14 December 2001; Volume 1. [Google Scholar]
- Damelin, S.B.; Hoang, N.S. On Surface Completion and Image Inpainting by Biharmonic Functions: Numerical Aspects. Int. J. Math. Math. Sci.
**2018**, 2018, 3950312. [Google Scholar] [CrossRef][Green Version] - Hastie, T.; Tibshirani, R.; Friedman, J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction; Springer: New York, NY, USA, 2009. [Google Scholar]
- Nakhmani, A.; Tannenbaum, A. A new distance measure based on generalized image normalized cross-correlation for robust video tracking and image recognition. Pattern Recognit. Lett.
**2013**, 34, 315–321. [Google Scholar] [CrossRef][Green Version] - Di Stefano, L.; Mattoccia, S.; Tombari, F. ZNCC-based template matching using bounded partial correlation. Pattern Recognit. Lett.
**2005**, 26, 2129–2134. [Google Scholar] [CrossRef] - DANE. Results From National Population and Housing Census 2018 for Valledupar, Cesar; Techreport; National Administrative Department of Statistics (DANE): Bogotá, Colombia, 2019. Available online: https://www.dane.gov.co/files/censo2018/informacion-tecnica/presentaciones-territorio/050919-CNPV-presentacion-Cesar.pdf (accessed on 30 November 2019).
- Angel, S.; Arango Franco, S.; Liu, Y.; Blei, A.M. The shape compactness of urban footprints. Progress Plan.
**2018**, in press. [Google Scholar] [CrossRef] - DANE. Results From National Population and Housing Census 2018 For Antioquia; Techreport; National Administrative Department of Statistics (DANE): Bogotá, Colombia, 2019. Available online: https://www.dane.gov.co/files/censo2018/informacion-tecnica/presentaciones-territorio/190719-CNPV-presentacion-Antioquia-2.pdf (accessed on 30 November 2019).
- Duque, J.C.; Lozano-Gracia, N.; Patino, J.E.; Restrepo, P.; Velasquez, W.A. Spatiotemporal Dynamics of Urban Growth in Latin American Cities: An Analysis Using Nighttime Lights Imagery. Landsc. Urban Plan.
**2019**, 191, 103640. [Google Scholar] [CrossRef] - Inostroza, L.; Baur, R.; Csaplovics, E. Urban sprawl and fragmentation in Latin America: A dynamic quantification and characterization of spatial patterns. J. Environ. Manag.
**2013**, 115, 87–97. [Google Scholar] [CrossRef] - Berrigan, D.; Tatalovich, Z.; Pickle, L.W.; Ewing, R.; Ballard-Barbash, R. Urban sprawl, obesity, and cancer mortality in the United States: Cross-sectional analysis and methodological challenges. Int. J. Health Geogr.
**2014**, 13, 1–14. [Google Scholar] [CrossRef][Green Version] - Ewing, R.; Hamidi, S.; Grace, J.B.; Wei, Y.D. Does urban sprawl hold down upward mobility? Landsc. Urban Plan.
**2016**, 148, 80–88. [Google Scholar] [CrossRef][Green Version] - Fallah, B.N.; Partridge, M.D.; Olfert, M.R. Urban sprawl and productivity: Evidence from US metropolitan areas. Papers Reg. Sci.
**2011**, 90, 451–472. [Google Scholar] [CrossRef] - Marconcini, M.; Metz-Marconcini, A.; Üreyen, S.; Palacios-Lopez, D.; Hanke, W.; Bachofer, F.; Zeidler, J.; Esch, T.; Gorelick, N.; Kakarla, A.; et al. Outlining where humans live—The World Settlement Footprint 2015. arXiv
**2019**, arXiv:1910.12707. [Google Scholar] - Liu, G.; Reda, F.A.; Shih, K.J.; Wang, T.C.; Tao, A.; Catanzaro, B. Image Inpainting for Irregular Holes Using Partial Convolutions. arXiv
**2018**, arXiv:cs.CV/1804.07723. [Google Scholar]

**Figure 1.**The urban growth framework predicts population distribution, binary urban footprint, and urban footprint in color from these and other spatially distributed variables, if they are available.

**Figure 2.**A high-level overview of the data pre-processing applied to all the input variables of the urban growth framework.

**Figure 3.**Flow diagram with the pre-processing of Landsat images. There are three main stages highlighted in distinct colors in the diagram. The first stage removes clouds and NoData values and applies the result to the other two stages in parallel. The second stage extracts the urban footprint in RGB color for selected years. The third stage uses classification processes and morphological operations to obtain the binary urban footprint for available years.

**Figure 6.**Flow diagram with the harmonization process of the binary urban footprint using the population distribution. It has three main sub-processes that have been color-coded. The first sub-process finds the optimal threshold after which an area is considered urban. The second sub-process estimates the binary urban footprint for missing years using available information, a temporal correction, and the optimal threshold. The third sub-process cleans the binary urban footprint and only leaves urban pixels that are likely to be part of a city.

**Figure 7.**Interaction among the three key variables of the urban growth framework: population distribution, binary urban footprint, and urban footprint.

**Figure 8.**Example of required data for modeling a multiple input single output spatio-temporal dynamic system of a selected city, assuming a temporal lag of two years for the input variables, and selecting the population distribution as the output variable. These data can be seen as part of a single temporal window of a larger dataset.

**Figure 9.**Automated training, validation, and testing of the regression model to estimate the population distribution.

**Figure 11.**Tested functions for saturating the predicted population given a maximum population capacity.

**Figure 12.**Converting population distribution predictions into estimates of binary urban footprint during inference.

**Figure 13.**Semantic inpainting to estimate the urban footprint in color at a final time from the value at an initial time and the the binary urban footprints at the initial and final times.

**Figure 14.**Left: location of Valledupar and Rionegro in Colombia. Right: administrative divisions within the selected geographic extents for Valledupar and Rionegro.

**Figure 15.**Results of the classification process of Landsat images of Valledupar and Rionegro into urban and non-urban areas for the year 2015. The yellow regions highlight the urban classification results.

**Figure 16.**Estimated probability density function of a population threshold after which a non-urban pixel becomes urban in Valledupar.

**Figure 17.**Estimated probability density function of a population threshold after which a non-urban pixel becomes urban in Rionegro.

**Figure 19.**Diagnostic graphs of the geographic area of interest masked by the administrative division of Valledupar. (

**Left**) total urban population. (

**Center**) total urban area. (

**Right**) urban density.

**Figure 20.**Diagnostic graphs of the geographic area of interest masked by the administrative division of Rionegro. (

**Left**) total urban population. (

**Center**) total urban area. (

**Right**) urban density.

**Figure 21.**Estimated probability density functions of the mean square error in the spatiotemporal regression of the population distribution for different families of models as returned by the autotuning program in Valledupar.

**Figure 22.**Estimated probability density functions of the mean square error in the spatiotemporal regression of the population distribution for different families of models as returned by the autotuning program in Rionegro.

**Figure 23.**Framework performance in the geographic areas of interest. From left to right, the columns correspond to: (1) population distribution error (i.e., real value - predicted value); (2) histogram of the population distribution error; (3) binary urban footprint error (i.e., real value - predicted value); (4) histogram of the binary urban footprint error. POP = predicted population distributions; BUF = binary urban footprints; ZNCC = zero-mean normalized cross-correlation; SAD = sum of absolute differences; SSD = sum of squared differences.

**Figure 24.**Assessment of the urban predictions in the geographic area of interest masked by the administrative division of Valledupar with the test set.

**Figure 25.**Assessment of the urban predictions in the geographic area of interest masked by the administrative division of Rionegro with the test set.

**Table 1.**Examples of variables that the urban-growth framework can handle. GHSL = Global Human Settlement Layer; SRTM = Shuttle Radar Topography Mission; OSM = Open Street Map; IGAC = Agustín Codazzi Geographic Institute; WDPA = World Database on Protected Areas.

Variable Name | Data Source | Digital Format | Resolution | Availability | Importance |
---|---|---|---|---|---|

Population distribution. | GHSL pop [45]. | Raster. | 250 m × 250 m. | Global. | Essential. |

Urban footprint. | Landsat [47]. | Raster. | 30 m × 30 m. | Global. | Essential. |

Binary urban footprint. | Derived from the urban footprint through a binary classifier. | Raster. | 30 m × 30 m. | Global. | Essential. |

Official population projections. | National Bureau of Statistics [48]. | Tabular. | Administrative units. | National. | Optional. |

Maximum population capacity. | Master plan [49,50]. | Vector. | - | Local. | Optional. |

Land use (residential, industrial, commercial, official, and special). | Master plan [49,50]. | Vector. | - | Local. | Optional. |

Built-up urban ratio. | GHSL built-up [51]. | Raster. | 250 m × 250 m. | Global. | Optional. |

Terrain slope. | SRTM [52]. | Raster. | 90 m × 90 m. | Global. | Optional. |

Distances to nearest populated towns. | Derived from binary urban footprint. | Raster. | 30 m × 30 m. | Global. | Optional. |

Roads. | OSM [53], IGAC [54]. | Vector. | - | Global, National. | Optional. |

Natural hazard (flooding, landslide, fire, volcanic eruption, earthquake.). | Master plan [49,50]. | Vector. | - | Local. | Optional. |

Water bodies. | Master plan [49,50], IGAC [54]. | Vector. | - | Local. | Optional. |

Protected areas. | Master plan [49,50], WDPA [55]. | Vector. | - | Global, Local. | Optional. |

Urban development projects. | Master plan [49,50], others. | Vector. | - | Local. | Optional. |

Variables | Description |
---|---|

t | Time in years. |

r | Number of consecutive years of historical data records available for training. |

$x,y$ | Spatial coordinates along the East and North directions, respectively. |

$w,h$ | Width and height of the spatial extent under study in meters. |

${\Delta}_{x},{\Delta}_{y}$ | Spatial sampling period in meters along the x and y directions, respectively. |

$m,n$ | Number of rows and columns of each digital image. |

$i,j,k,l$ | Auxiliary variables. |

$pop$ | Population distribution. |

$buf$ | Binary urban footprint (black and white). |

$uf$ | Urban footprint (color). |

${v}_{i}$ | i-th input variable. |

${p}_{i},{q}_{i}$ | Number of rows and columns of the spatial window for ${v}_{i}$. |

${\varphi}_{i}$ | Number of consecutive temporal lags in years for ${v}_{i}$. |

${f}_{i}$ | Mathematical function applied to each possible spatial window of $\left(\right)$ pixels in ${v}_{i}$. In the naïve feature sampling, it corresponds to a reshape operation to convert the data dimensions from $\left(\right)$ to $\left(\right)$. In other scenarios it can be a spatial-filtering function that processes and reduces the number of features (e.g., an element-wise multiplication of the spatial window by a fixed spatial kernel of the same dimensions followed by a sum of its elements). |

${\eta}_{tw}$ | Number of temporal windows that can be extracted from the historical data records for all variables given the maximum consecutive temporal lag in the regression model. |

${m}_{o},{n}_{f}$ | Number of rows (i.e., observations) and columns (i.e., input features) of the resulting tabular dataset for training the population distribution growth model based on machine learning. |

$\gamma $ | Population threshold after which a region can be considered as urbanized. |

**Table 3.**Confusion matrices for the classification process of Landsat images in Valledupar. The top table corresponds to the initial classification process of pixels into four categories, and the bottom table corresponds to the final re-classification process into two categories.

Predicted Class | |||||
---|---|---|---|---|---|

built-up | bare soil | vegetation | water | ||

True class | built-up | 2094 | 45 | 3 | 0 |

bare soil | 28 | 9339 | 7 | 0 | |

vegetation | 0 | 24 | 17,504 | 6 | |

water | 0 | 6 | 43 | 89 | |

Predicted Class | |||||

urban | non-urban | ||||

True class | urban | 2094 | 48 | ||

non-urban | 28 | 27,018 |

**Table 4.**Confusion matrices for the classification process of Landsat images in Rionegro. The top table corresponds to the initial classification process of pixels into four categories and the bottom table corresponds to the final re-classification process into two categories.

Predicted Class | |||||
---|---|---|---|---|---|

built-up | bare soil | vegetation | water | ||

True class | built-up | 1355 | 29 | 11 | 1 |

bare soil | 61 | 535 | 15 | 1 | |

vegetation | 0 | 10 | 5557 | 0 | |

water | 1 | 7 | 3 | 73 | |

Predicted Class | |||||

urban | non-urban | ||||

True class | urban | 1355 | 41 | ||

non-urban | 62 | 6201 |

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**MDPI and ACS Style**

Gómez, J.A.; Patiño, J.E.; Duque, J.C.; Passos, S.
Spatiotemporal Modeling of Urban Growth Using Machine Learning. *Remote Sens.* **2020**, *12*, 109.
https://doi.org/10.3390/rs12010109

**AMA Style**

Gómez JA, Patiño JE, Duque JC, Passos S.
Spatiotemporal Modeling of Urban Growth Using Machine Learning. *Remote Sensing*. 2020; 12(1):109.
https://doi.org/10.3390/rs12010109

**Chicago/Turabian Style**

Gómez, Jairo A., Jorge E. Patiño, Juan C. Duque, and Santiago Passos.
2020. "Spatiotemporal Modeling of Urban Growth Using Machine Learning" *Remote Sensing* 12, no. 1: 109.
https://doi.org/10.3390/rs12010109