# Predicting Near-Future Built-Settlement Expansion Using Relative Changes in Small Area Populations

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Areas and Data

#### 2.1.1. Built-Settlement Data

#### 2.1.2. Population Data

#### 2.1.3. OpenStreetMap Data

^{2}area (rectangular bounds: 7.8606508° 46.2779033°; 8.0224478°, 46.3298123°) had a 2015 combined mid-year population of approximately 32,430 [58]. It contained 8,083 buildings manually delineated by OSM contributors, of which we contributed over an additional 1,700 buildings in an effort to have near 100 percent coverage of permanent vertical structures covered by the definition of BS. We inspected all building footprints in the area for accuracy and temporal coincidence with true colour imagery in 2015. The resource intensive nature of manually delineating and checking building footprints precluded us from carrying out more widespread validations of this nature during this study. The building footprints are provided in the linked data repository (https://data.mendeley.com/datasets/cm6bnzvzfj/1).

#### 2.2. Built-Settlement Growth Model extrapolation (BSGMe)

#### 2.2.1. Overview

_{ESA}).

- Create gridded population maps for each year in the input TS, following Stevens et al. [54].
- For all years in the TS, extract the unit-specific population sum that is coincident with the year’s corresponding BS extents and derive the unit-average BS population density
- Independently for each unit, and using a rolling origin validation, select the single best fitting model for BS population and, separately, unit-average BS population density from three classes of models:
- Auto-Regressive Integrated Moving Average (ARIMA),
- Error, Trend, Seasonality (ETS), and
- Generalized Linear Model (GLM) given log-transformed inputs.

- For each unit, use the final selected model for BS population and for unit-average BS population density to predict short-term annual BS population and annual unit-average BS population density starting with year t1+1 and ending with year t1+h, where in this case 1 ≤ h ≤ 5 and represents the projection horizon, in numbers of years.
- Use these estimates to derive the unit-specific annual quantity demand of non-BS-to-BS transitions by dividing the BS population by the BS population density.
- Create a transition probability surface using a Random Forest (RF) based upon the observed transitions between t0 and t1 of the input time-series and covariates corresponding to t0.
- Take the fit relationships between the occurrence of transitions and the predictive covariates, contained in the final RF model, and predict the future non-BS-to-BS transition probability surface using the same covariates, but corresponding to year t1, as the input.
- For each unit and iteratively for all years t1+1 through t1+h, spatially disaggregate the predicted annual unit-level transitions (steps 1–5) using the base transition probability surface (steps 5–6) and, if available, unit-relative weights derived from changes in lights-at-night brightness, similar to Nieves et al. [16].

#### 2.2.2. Demand Quantification

#### Built-Settlement Population Estimation

#### Time-Series Model Fitting and Built-Settlement Population Projections

_{ts}= 11) and our projection horizon between one and five years (1 ≤ h ≤ 5), we utilized a maximum horizon of five years in the model fitting too. This meant the model classes were iteratively fit with between six (i.e. 2000–2005) and ten (i.e. 2000–2009) input observations, with all other observations withheld, and then predicted between one and five years, respectively, forward of the last input year of the given iteration sample. Each iteration produced a set of annual absolute percent errors for the projected years, of which the median was recorded. The sum of MDAPE values across all iterations represents the total error of each model class for the given unit. Written mathematically, for a given unit i, maximum horizon length h, and a being the index of the given set of iterations, the MDAPE sum within the rolling origin framework can be written as

_{ts}= t1 + a – h and the set of projected years within an iteration are calculated for each year k that takes on values between ${n}_{ts+1},\dots ,{n}_{ts+h}$, e.g., for h = 3 and a = 3 the models are fit on years 1 to 8 with a set of predictions made for $\left\{{\widehat{y}}_{{n}_{ts}+1},{\widehat{y}}_{{n}_{ts}+2},{\widehat{y}}_{{n}_{ts}+3}\right\}$. After the rolling origin framework finished, for each unit, we selected the best model between model classes based upon the lowest $MDAP{E}_{i}{}_{sum}$ and fit the selected model class on the entire available time series. Normally, using the entire time series is cause for concern of model over fitting. However, our larger concern was that excluding later observations in the extremely short time series could lead to excluding important information late in the series. Therefore, we assumed that fitting only on a subset of the time-series would be as harmful, or more so, than potentially overfitting any given unit. After the refitting, and independently for each unit, we predicted the final outcome of interest through our projection horizon, in this case 2011–2015. Full process diagram of this sub-procedure is provided in Appendix A, Figure A2.

#### 2.2.3. Spatial Allocation

#### Projecting non-Built-Settlement (BS)-to-BS Transition Probabilities Surface

#### Annually Adjusting non-BS-to-BS Transition Probabilities

^{th}highest annually adjusted probabilities, and transitioned them from non-BS-to-BS. This is in line with Nieves et al. [16], Tayyebi et al. [77], Linard et al. [28] and others where it is assumed that pixels with higher transition probabilities are more likely to transition than pixels with lower probabilities. We repeated this process for all years in the projection period, using the previously projected year as the prior BS extents to expand upon, and output the union of the prior extents and the new projected transition as the next year’s BS extents (Figure 1). All resulting and derived data are provided in the linked data repository (https://data.mendeley.com/datasets/cm6bnzvzfj/1).

#### 2.3. Analysis

#### Validation and Comparison Metrics

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Full process diagram for the Built-Settlement Growth Model—extrapolation (BSGMe) as broken down into the “Demand Quantification” procedure and the “Spatial Allocation Procedure”. For details on the “Spatial Transition Disaggregation Procedure”, readers are referred to Nieves et al. [16]. For details on the “Subnational Temporal Model Fitting and Prediction Procedure”, readers are referred to Appendix A, Figure A2.

**Figure A2.**Full process diagram of the “Subnational Temporal Model Fitting and Prediction Procedure” referenced in Appendix A, Figure A1. Readers are directed to the main text for acronym references and details on the rolling origin framework.

**Table A1.**Table of time specific, or assumed temporally invariant, covariates used in the modelling of the population surfaces following the procedure from Stevens et al. [55].

Covariate | Time Point(s)^{a} | Original Source | Source Resolution |
---|---|---|---|

DTE Cultivated landcover | 2000–2010 | ESA CCI Landcover [36] classes 10–30 | 10 arc seconds |

DTE Woody, Herbaceous, Shrub landcover | 2000–2010 | ESA CCI Landcover [36] classes 40–120 | 10 arc seconds |

DTE Grassland landcover | 2000–2010 | ESA CCI Landcover [36] class 130 | 10 arc seconds |

DTE Lichens and Mosses landcover | 2000–2010 | ESA CCI Landcover [36] class 140 | 10 arc seconds |

DTE Sparse Vegetation landcover | 2000–2010 | ESA CCI Landcover [36] classes 150–153 | 10 arc seconds |

DTE Aquatic Vegetation landcover | 2000–2010 | ESA CCI Landcover [36] classes 160–180 | 10 arc seconds |

DTE Bare Areas | 2000–2010 | ESA CCI Landcover [36] class 200 | 10 arc seconds |

DTE Built-settlement | 2000–2010 | ESA CCI Landcover [36] class 190 | |

Distance to Inland Water Bodies | 2015, assumed invariant | MERIS-based water bodies [39] | 5 arc seconds |

Distance to Roads | Downloaded 2017, assumed invariant as temporally specific road data unavailable | OpenStreetMap [44] | Vector |

Distance to Rivers | Downloaded 2017, assumed invariant | OpenStreetMap [44] | Vector |

Distance to Coastline | Based upon boundaries of GPWv4, assumed invariant | CIESIN GPWv4 [40] | Vector |

Slope | 2000, assumed invariant | World Wildlife Fund Void-filled Hydrosheds [37] | 3 arc seconds |

Elevation | 2000, assumed invariant | World Wildlife Fund Void-filled Hydrosheds [37] | 3 arc seconds |

DTE: Distance To nearest Edge a Note, for any covariate derived from land cover or built-settlement, only one year-specific covariate was used corresponding to the desired population surface (e.g., for a 2000 population surface only covariates corresponding to 2000, or those assumed temporally invariant, were used as covariates). |

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**Figure 1.**High-level generalization of the Built-Settlement Growth Model extrapolation (BSGMe) modelling framework when predicting for short-term Built-Settlement (BS) expansion. Note, example maps and numbers are not to scale. Figure modified from [16].

**Figure 2.**Unit-level model fitting process for fitting and selecting the final model, between three classes of models, used to predict short-term future BS population and future unit-average BS population density. Here we employ a rolling origin framework, with the final model selected based upon the smallest sum of the Median Absolute Percent Error (MDAPE).

**Figure 3.**Boxplots of unit-level F1 scores across countries and years in the projection period and divided by the input time series to the BSGMe framework. All F1 scores were calculated by comparing pixel-level agreement/disagreement with withheld annual European Space Agency (ESA) Remote Sensing (RS)-derived extents. The median is indicated by the black line and outliers (outside of 1.5*the interquartile range) are given by grey circles.

**Figure 4.**Boxplots of unit-level recall scores across countries and years in the projection period and divided by the input time series to the BSGMe framework. All recall values were calculated by comparing pixel-level agreement/disagreement with withheld annual ESA RS-derived extents. The median is indicated by the black line and outliers (outside of 1.5*the interquartile range) are given by grey circles.

**Figure 5.**Boxplots of unit-level precision scores across countries and years in the projection period and divided by the input time series to the BSGMe framework. All precision values were calculated by comparing pixel-level agreement/disagreement with withheld annual ESA RS-derived extents. The median is indicated by the black line and outliers (outside of 1.5*the interquartile range) are given by grey circles.

**Figure 6.**Map of select areas from the study countries and the projection period showing the predicted extents derived from the BSGMe (red) as well as the withheld ESA observed extents (blue). Areas where the BSGMe-derived extents and the ESA RS-derived extents agreed are shown in yellow.

**Figure 7.**The 2015 BSGMe-derived extents (red), the 2015 ESA RS-derived extents (blue), and the 2010 ESA RS-derived extents (transparent black areas) of BS overlain on 2015 true color imagery via Google Earth. Map Imagery: Google, Maxar Technologies, Centre National D’ Etudes Spatiales CNES/Airbus.

**Figure 8.**Validation maps of 2015 Open Street Maps (OSM) and manually delineated building footprints of the Visp and Brig area of Switzerland as compared to the ESA RS-derived extents (top left), the BSGMe TS

_{ESA}predicted extents (bottom left) along with their corresponding confusion matrices and select classification metrics (right side).

**Table 1.**Summary of built-settlement transition data by country and period. Areal units here are pixels (~ 100m) as that is the unit handled by the model, which looks at relative areal changes as opposed to absolute areal changes. Adapted from Nieves et al. [16].

Country | Average Spatial Resolution ^{a} | Period | Initial Non-Built Area (pixels) | Period Transition Prevalence ^{b} |
---|---|---|---|---|

Panama | 10.9 km | 2000–2010 | 8,901,004 | 0.12 % |

2010–2015 | 8,890,339 | 0.75 % | ||

Switzerland | 3.9 km | 2000–2010 | 6,816,510 | 1.64 % |

2010–2015 | 6,704,973 | 0.01 % | ||

Uganda | 12.2 km | 2000–2010 | 28,231,555 | 0.11 % |

2010–2015 | 28,200,084 | 0.04 % | ||

Vietnam | 21.7 km | 2000–2010 | 40,108,425 | 0.11 % |

2010–2015 | 39,990,858 | 0.29 % | ||

a Average spatial resolution is the square root of the average subnational area, in km, and can be thought of as analogous to pixel resolution with smaller values indicating finer areal data and vice versa [35] b Note: the Switzerland data suffered from disproportionate, relative to manually interpreted 30cm true-color imagery, amounts of growth as indicated by the European Space Agency (ESA) Remote Sensing (RS)-derived extents between 2000–2005 and is thought by Nieves et al. [16] to be due to the 2003–2004 shift from delineating land cover changes at 300m to using imagery to dilenate at 150m, in conjunction with the highly variable terrain in Switzerland compounding classification attempts. |

**Table 2.**Data used for estimating the annual number of non- Built-Settlement (BS) to BS transitions at the unit level (i.e. demand quantification), predicting the pixel level probability surface of those transitions, and performing the spatial allocation procedures of the model. Adapted from Nieves et al. [16].

Covariate | Description | Use ^{b, d} | Time Point(s) | Original Spatial Resolution | DataSource(s) |
---|---|---|---|---|---|

Built-settlement ^{b} | Binary BS extents | Demand QuantificationSpatial Allocation | 2000–2010 | 10 arc sec | [36] |

Distance To nearest Edge (DTE) of Built-settlement | Distance to the nearest BS edge | Spatial Allocation ^{c} | 2000, 2010 | 10 arc sec | [36] |

Proportion Built-settlement 1,5,10,15 | Proportion of pixels that are BS within 1,5,10, or 15-pixel radius | Spatial Allocation ^{c} | 2000,2010 | 10 arc sec | [36] |

Elevation | Elevation of terrain | Spatial Allocation ^{c} | 2000; Time Invariant | 3 arc sec | [37] |

Slope | Slope of terrain | Spatial Allocation ^{c} | 2000; Time Invariant | 3 arc sec | [37] |

DTE Protected Areas Category 1 | Distance to the nearest level 1 protected area edge | Spatial Allocation ^{c} | 2010 | Vector | [34,38] |

Water | Areas of water | Restrictive Mask | 5 arc sec | [34,39] | |

Subnational Population | Annual population by sub-national units | Demand Quantification | 2000–2020 | Vector | [40] |

Weighted Lights-at-Night (LAN) ^{d} | Annual lagged and sub-national unit normalised LAN | Spatial Allocation ^{d} | 2000–2016 | 30 arc sec (2000-011)15 arc sec (2012-016) | DMSP [34,41] VIIRS [34,42] |

Travel Time 50k | Travel time to the nearest city centre containing at least 50,000 people | Spatial Allocation ^{c} | 2000 | 30 arc sec | [34,43] |

ESA CCI Land Cover (LC) Class ^{a} | Distance to nearest edge of individual land cover classes | Spatial Allocation ^{c} | 2000, 2010 | 10 arc sec | [34,36] |

Distance to OpenStreetMap (OSM) Rivers | Distance to nearest OSM river feature | Spatial Allocation ^{c} | 2017 | Vector | [34,44] |

Distance to OpenStreetMap (OSM) Roads | Distance to nearest OSM road feature | Spatial Allocation ^{c} | 2017 | Vector | [34,44] |

Average Precipitation | Mean Precipitation | Spatial Allocation ^{c} | 1950–2000 | 30 arc sec | [34,45] |

Average Temperature | Mean temperature | Spatial Allocation ^{c} | 1950–2000 | 30 arc sec | [34,45] |

a Some land cover classes were collapsed prior to calculating distance to edge: 10–30 → 11; 40–120 → 40; 150–153 → 150; 160–180 → 160 (Sorichetta et al>, 2015) b Covariates involved in Demand Quantification were used to determine the demand for non-BS to BS transitions at the subnational unit level for every given year. Covariates involved in Spatial Allocation were either used as predictive covariates in the random forest calculated probabilities of transition (see c) or as a post-random forest year specific weight on those probabilities and the spatial allocation of transitions within each given unit area. Covariates used as restrictive masks prevented transitions from being allocated to these areas. c Used as predictive covariates in the random forest calculated probabilities of transition d See Nieves et al. [16] for details on the construction of weighted LAN |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Nieves, J.J.; Bondarenko, M.; Sorichetta, A.; Steele, J.E.; Kerr, D.; Carioli, A.; Stevens, F.R.; Gaughan, A.E.; Tatem, A.J.
Predicting Near-Future Built-Settlement Expansion Using Relative Changes in Small Area Populations. *Remote Sens.* **2020**, *12*, 1545.
https://doi.org/10.3390/rs12101545

**AMA Style**

Nieves JJ, Bondarenko M, Sorichetta A, Steele JE, Kerr D, Carioli A, Stevens FR, Gaughan AE, Tatem AJ.
Predicting Near-Future Built-Settlement Expansion Using Relative Changes in Small Area Populations. *Remote Sensing*. 2020; 12(10):1545.
https://doi.org/10.3390/rs12101545

**Chicago/Turabian Style**

Nieves, Jeremiah J., Maksym Bondarenko, Alessandro Sorichetta, Jessica E. Steele, David Kerr, Alessandra Carioli, Forrest R. Stevens, Andrea E. Gaughan, and Andrew J. Tatem.
2020. "Predicting Near-Future Built-Settlement Expansion Using Relative Changes in Small Area Populations" *Remote Sensing* 12, no. 10: 1545.
https://doi.org/10.3390/rs12101545