# Spatio-Temporal Variation of the Urban Heat Island in Santiago, Chile during Summers 2005–2017

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## Abstract

**:**

^{2}. During the last few summer seasons, the highest extreme maximum temperatures in over 100 years have been recorded. Given the projections in temperature increase for this metropolitan region over the next 50 years, the Santiago UHI could have an important impact on the health and stress of the general population. We studied the presence and spatial variability of UHIs in Santiago during the summer seasons from 2005 to 2017 using Moderate Resolution Imaging Spectroradiometer (MODIS) satellite imagery and data from nine meteorological stations. Simple regression models, geographic weighted regression (GWR) models and geostatistical interpolations were used to find nocturnal thermal differences in UHIs of up to 9 °C, as well as increases in the magnitude and extension of the daytime heat island from summer 2014 to 2017. Understanding the behavior of the UHI of Santiago, Chile, is important for urban planners and local decision makers. Additionally, understanding the spatial pattern of the UHI could improve knowledge about how urban areas experience and could mitigate climate change.

## 1. Introduction

_{3}) [4]. All these factors can negatively impact work productivity and urban metabolism [5]. These processes consider the exchange of matter, energy and information established between an urban settlement and its natural environment. In this manner, the city is considered a living organism, incorporating measurements of technical and socio-economic processes that result from resource consumption, growth, energy production, and waste management [6,7].

^{2}[30]. Therefore, it is important to understand temperature differences and UHIs in the region and their spatial distribution and behavior over time with regards to geographic extension and movement, as well as their temperature magnitudes. The effects on mortality due to high temperatures in Santiago were studied by [31], leading to the conclusion that higher temperatures could be related to increased mortality risks, especially for the elderly population. Additionally, [32] concluded that, for Santiago, heat effects have an immediate impact on the mortality of the city‘s population.

- Determination of the relationship between air temperature and satellite-derived LST.
- Analysis of historical UHI spatio-temporal temperature behavior.

## 2. Materials

#### 2.1. Study Area

#### 2.2. Satellite Data

#### 2.3. Meteorological Data

## 3. Methods

#### 3.1. Spatially Explicit Model of the Daily Air Temperature (Day/Night)

#### 3.1.1. Linear Regression Model (LRM)

^{2}), standard error, statistical significance (p-value), and correlation coefficient (R).

#### 3.1.2. Spatially Explicit Regression Models (GWR)

_{0}, a

_{1}) from the nine equations were modeled using two independent variables: the NDVI vegetation index and altitude, given their known relationship with temperature [41]. The general GWR model can be seen in Equation (2).

_{i}, V

_{i}) are the geographic coordinates of point i and ${\beta}_{k}\left({U}_{i},{V}_{i}\right)$ is the value calculated from the continuous function ${\beta}_{k}\left(U,V\right)$ in point i [42].

#### 3.1.3. Cokriging of Coefficients

#### 3.2. Calculation and Analysis of UHIs

_{0}and a

_{1}), and a zonal statistical calculation to a commune scale level using the mean maximum NDVI during the period of analysis. The NDVI presents a high inverse correlation with thermal emissivity [36,37], which demonstrates thermal differences between rural and urban areas if the former has a higher presence of vegetation.

^{2}). The agreement index (d) ([45,46,47,48,49]) and the Akaike information criterion (AIC) ([50,51]) were also calculated.

## 4. Results

#### 4.1. Meteorological Database

#### 4.2. Spatially Explicit Model of the Daily Air Temperature (Day/Night)

^{2}range 0.643–0.853), and therefore it was much better than daytime (R

^{2}range 0.254–0.480) or nighttime (R

^{2}range 0.172–0.358) as individual data sets.

_{0}and a

_{1}were obtained and adjusted considering altitude and NDVI in the model (Equation (3)). Table 4 shows the a

_{0}and a

_{1}coefficient averages, their estimation error percentage, and general statistics for each model. The determination coefficients (R

^{2}) for both models were higher than 88%, presenting a low mean, standard error, and significance level of a p-value less than 0.001.

_{0}and a

_{1}, completing in each pixel a linear equation that estimated air temperature using LST.

#### 4.3. Calculation and Analysis of UHIs

## 5. Discussion

^{2}and a population density of 8497 people/km

^{2}. Therefore, the density of the automatic meteorological stations (AMS) network is 0.0096 AMS/km

^{2}, which is equivalent to one AMS per every 105 km

^{2}. This coverage is insufficient to carry out more detailed studies inside the city, especially for the spatial variability of air temperatures to be used in urban planning associated with the complexities of a city. In this sense, the scientific literature shows that the use of thermal satellite images improves the estimation of air temperature behavior inside the city, differentiating thermal configurations associated with the urban structure of the city [7,9,13,14].

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Study area, administrative zones (communes), and location of the meteorological station, which are part of the National Information System of Air Quality (SINCA, by its initials in Spanish) in the city of Santiago, Chile.

**Figure 2.**The methodological scheme is divided into four steps: Step 1 is in regards to linear regression models (LRM) estimating air temperature from land surface temperature. After that, it is necessary to consider the estimation of LRM parameters considering their spatial position using geographic weighted models (Step 2). In Step 3, we use bivariate interpolation models as a cokriging to estimate the air temperature for each pixel of the area. Finally (Step 4), the urban heat island (UHI) is calculated for different dates, studying its behavior in all periods.

**Figure 3.**Zonal average of maximum NDVI for each period and commune (

**a**); K-means cluster analysis on coefficients calculated from the linear models by meteorological stations (

**b**).

**Figure 4.**Daytime urban heat islands (based on daily data from 2005 to 2017). UHI is calculated from the difference between the pixels and the rural station of reference (Talagante station). The first row shows the mean monthly temperatures of December, January, and February; the central row shows the average of the maximum temperature of the same period; the last row shows the average standard deviation of temperatures. Mean: Heat increases in intensity towards the northwest zones as February approaches, while also advancing to the center of the city. Max: The maximum temperature behavior in December and February are similar, but January has the maximum higher temperature towards the west zone. SD: The standard deviation increases from southwest to northeast; this trend continues from December to February, decreasing variability towards the end of summer.

**Figure 5.**Nocturnal urban heat island (based on data from 2005 to 2017). Nocturnal UHI is calculated using images at nocturnal acquisition times (22, 23, or 24 h). The first row shows the behavior the nocturnal mean monthly temperature of December, January, and February; the central row shows the maximum nocturnal temperature average of the same period; the last row shows the average standard deviation of the nocturnal temperature. Mean: The mean night temperature is regular in its extension and intensity throughout the period and study area. Max: The maximum night temperature’s behavior is similar during the three summer months, but the intensity is greatest in February. SD: The standard deviation night temperature increases mainly in January in the city center, and stays down near the rural station of reference during the whole summer.

**Figure 6.**Average daily and nocturnal UHI for the 2005–2017 summer seasons. Each summer season considers the month of December for the prior year and January and February of the following year (e.g., S 2005–2006 means December 2005 and January and February 2006). The graph shows the mean day and night temperatures over three months. The main difference is that during the night the UHI is more intense in temperature and extent. In the day, the UHI is high only in the northwest extending to the center, but ultimately loses intensity.

**Figure 7.**Maximum daytime and nighttime UHIs for the 2005–2017 summer seasons. Each summer season considers the months of December from the previous year and January and February of the following year (e.g., S 2005–2006 means December 2005 and January and February 2006). The graph shows the maximum day and night temperatures over three months. During the maximum days in 2006–2007, there are high values mainly in the northwest, while at night during the same summer the UHI almost covers the entire city, probably due to the heat waves that occurred at that time. Conversely, during the summer days in 2015–2016 and 2016–2017, the UHI is higher than during the night.

**Figure 8.**Daily and nightly temperature dispersion of the UHI during each summer 2005–2017. Each summer season considers the months of December from the prior year and January and February of the following year (e.g., S 2005–2006 means December 2005 and January and February 2006). The graph shows the standard deviation of day and night temperatures over three summer months. There was greater dispersion in UHIs during the day than during the night (almost double), reaching the highest values in the summer of 2016–2017, followed by daytime UHIs in the summer of 2015–2016.

**Figure 9.**UHI stratified in three ranges using the natural break method and daily and nightly data for summertime periods between 2005 and 2017. This graph shows a nocturnal UHI in 2006–2007 that decreases in extension during subsequent summers. On the other hand, during the daytime from 2013 to 2014, UHIs tend to increase, reaching the entire city in the summers of 2015–2016 and 2016–17.

Station Name | Eastern Coordinates (UTM 19S) | Northern Coordinates (UTM 19S) |
---|---|---|

Parque O’Higgins | 345673 | 6296019 |

Independencia | 346488 | 6300681 |

EL Bosque | 345313 | 6286825 |

La Florida | 352504 | 6290304 |

Las Condes | 358305 | 6305906 |

Cerro Navia | 338984 | 6299360 |

Pudahuel | 337311 | 6298809 |

Puente Alto * | 352049 | 6282013 |

Talagante * | 318945 | 6272298 |

Description | Symbol | Equation | N° |
---|---|---|---|

Systematic error | BIAS | $\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}\left({O}_{i}-{P}_{i}\right)$ | (5) |

Mean absolute error | MAE | $\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}\left|{O}_{i}-{P}_{i}\right|$ | (6) |

Root mean square error | RMSE | $\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^{N}}{\left({O}_{i}-{P}_{i}\right)}^{2}}$ | (7) |

Determination Coefficient | R^{2} | $\frac{{{\displaystyle \sum}}_{i=1}^{N}{\left({P}_{i}-\overline{O}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{N}{\left({O}_{i}-\overline{O}\right)}^{2}}$ | (8) |

Agreement Index | d | $1-\frac{{{\displaystyle \sum}}_{i=1}^{N}{\left({O}_{i}-{P}_{i}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{N}{\left(\left|{P}_{i}-\overline{O}\right|+\left|{O}_{i}-\overline{O}\right|\right)}^{2}}$ | (9) |

Akaike information criterion | AIC | $2\cdot k-N\cdot \mathrm{Ln}\left(\frac{{{\displaystyle \sum}}_{i=1}^{N}{\left({O}_{i}-{P}_{i}\right)}^{2}}{N}\right)$ | (10) |

MMA * Station | Model | $\mathbf{Intercept}\text{}\left({\mathit{a}}_{\mathbf{0}}\right)$ | $\mathbf{LST}\text{}\left({\mathit{a}}_{\mathbf{1}}\right)$ | R^{2} | p-Value |
---|---|---|---|---|---|

Pudahuel | D & N | 14.3956 | 0.2745 | 0.6590 | <0.0001 |

Independencia | D & N | 14.1418 | 0.3136 | 0.6860 | <0.0001 |

La Florida | D & N | 12.7507 | 0.3359 | 0.7049 | <0.0001 |

EL Bosque | D & N | 12.2912 | 0.3490 | 0.7427 | <0.0001 |

Cerro Navia | D & N | 11.8035 | 0.3709 | 0.6434 | <0.0001 |

Parque O’Higgins | D & N | 11.6696 | 0.3576 | 0.7483 | <0.0001 |

Puente Alto | D & N | 11.4993 | 0.3235 | 0.6952 | <0.0001 |

Las Condes | D & N | 10.7222 | 0.3989 | 0.7403 | <0.0001 |

Talagante | D & N | 5.9368 | 0.5409 | 0.8531 | <0.0001 |

Statistician | a_{0} | a_{1} |
---|---|---|

$\overline{{a}_{0}}\pm {\sigma}_{{a}_{0}}{}_{}$ (%) | 11.76 ± 7.01% | |

$\overline{{a}_{1}}\pm {\sigma}_{{a}_{1}}{}_{}$ (%) | 0.36 ± 6.18% | |

AIC | 27.7247 | −35.4228 |

BIAS | −0.0737 | 0.0025 |

R^{2} | 0.8795 | 0.8846 |

Nash–Sutcliffe efficiency | 0.8082 | 0.8266 |

RMSE | 0.8491 | 0.0252 |

p-value | 0.0002 | 0.0002 |

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**MDPI and ACS Style**

Montaner-Fernández, D.; Morales-Salinas, L.; Rodriguez, J.S.; Cárdenas-Jirón, L.; Huete, A.; Fuentes-Jaque, G.; Pérez-Martínez, W.; Cabezas, J.
Spatio-Temporal Variation of the Urban Heat Island in Santiago, Chile during Summers 2005–2017. *Remote Sens.* **2020**, *12*, 3345.
https://doi.org/10.3390/rs12203345

**AMA Style**

Montaner-Fernández D, Morales-Salinas L, Rodriguez JS, Cárdenas-Jirón L, Huete A, Fuentes-Jaque G, Pérez-Martínez W, Cabezas J.
Spatio-Temporal Variation of the Urban Heat Island in Santiago, Chile during Summers 2005–2017. *Remote Sensing*. 2020; 12(20):3345.
https://doi.org/10.3390/rs12203345

**Chicago/Turabian Style**

Montaner-Fernández, Daniel, Luis Morales-Salinas, José Sobrino Rodriguez, Luz Cárdenas-Jirón, Alfredo Huete, Guillermo Fuentes-Jaque, Waldo Pérez-Martínez, and Julián Cabezas.
2020. "Spatio-Temporal Variation of the Urban Heat Island in Santiago, Chile during Summers 2005–2017" *Remote Sensing* 12, no. 20: 3345.
https://doi.org/10.3390/rs12203345