# A New Approach for Understanding Urban Microclimate by Integrating Complementary Predictors at Different Scales in Regression and Machine Learning Models

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Lyon: A Study Area Characterized by a Considerable Urban Morphological Diversity

#### 2.2. Data Acquired by the Measuring Instruments and Selected Days

#### 2.3. Morphological Descriptors Relevant to Air Temperature Estimation

#### 2.4. The Statistical Procedure Followed

#### 2.4.1. An Explanatory Buffer Zone, Which Varies According to the Indicator

#### 2.4.2. Three Complementary Regression Methods in Modelling Use

#### 2.4.3. Quality Control on Modeling by Spatial Identification of Error Clusters

## 3. Results

#### 3.1. Multiple Linear Regression Modeling

^{2}of 0.65 and an RMSE of 1.54. The results for the sample with all measurements for the four outputs (Figure 10) show an R

^{2}of 0.65 and an RMSE of 1.54. The RMSE is logically slightly higher than for the single day models due to the larger sample of measurements and greater morphological diversity, even though the weather conditions remain similar. These results confirm the general trends observed at day scales. In particular, the cooling effect of variables such as water density (normalized coefficient of –0.35; Figure 10), densely vegetated areas (–0.11 for NDVI and –0.09 for the density of high vegetation), road embankment (–0.08 for SVF), and humidity (–0.05 for Modified Normalized Difference Water Index (MNDWI)) can be found. The presence of proximity to tourist areas can be explained by the fact that these areas are mostly made up of green spaces or historic buildings in old Lyon.

#### 3.2. Partial Least Square Regression Modeling

^{2}equal to 0.699 and an RMSE of 1.503. They also confirmed the dominant role of surface temperature. This variable had a VIP of 2.2. This is followed by the density of water areas (VIP = 1.81), the density of low vegetation (1.43), the NDVI (1.15), and the humidity indices (1.03 for the MNDWI and 1.01 for the TCT Wetness). These results are in agreement with those obtained through multiple linear regression (Section 3.1).

#### 3.3. Random Forest Regression Modeling

## 4. Discussion

#### 4.1. Implication of Important Predictors in Urban Air Temperature Modeling

#### 4.2. Spatialization of Error

#### 4.3. Grouping of Similar Errors

#### 4.4. Limits and Future Research Outlooks

## 5. Conclusions

^{2}of 0.65 and an RMSE of 1.54 °C, on a par with the PLS regression which shows an R

^{2}of 0.70 and an RMSE of 1.50 °C. The global random forest modelling based on all days, however, proposes superior results with a high R

^{2}of 0.98 and an RMSE of 0.33 °C. This modelling method is therefore the most efficient of the three tested for this study area and this sample of measurements. However, it is less accessible than the other types of multiple regressions tested and requires a greater statistical investment.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Explanatory Variables Selected to Estimate Fine-Scale Air Temperature

Data Category | Variables Used for the Input (Units) | Expected Effect of the Variable on the Model | Calculation Method | Reference |

Climatic data from remote sensing | Surface temperature (°C) | Positive | Single channel algorithm | [49,89,121,122] |

UTFVI Urban Thermal Field Variation Index) | Positive | $UTFVI=\frac{{T}_{s}-{T}_{mean}}{{T}_{S}}$ | [87,123] | |

Brightness temperatures (°C) | Positive | $Brightness=\frac{{K}_{2}}{Ln\left(\frac{{K}_{1}}{Ls+1}\right)}$ | [124,125] | |

Vegetation index | NDVI Normalized Difference Vegetation Index | Negative | $NDVI=\frac{NIR-RED}{NIR+RED}$ | [85,126,127] |

SAVI Soil Adjusted Vegetation Index | Negative | $SAVI=\frac{NIR-RED}{NIR+RED+L}\times \left(L+1\right)$ | [126] | |

EVI Enhanced Vegetation Index | Negative | $EVI=G\times \frac{NIR-RED}{NIR+{C}_{1}\times RED-{C}_{2}\times BLUE+L}$ | [126] | |

Tasseled Cap greenness or GVI | Negative | $\begin{array}{l}TCTG\\ =Blueband\times coefGr+Greenband\\ \times coefGr+Redband\times coefGr\\ +NearInfraredband\times coefGr\\ +SWIR1band\times coefGr\\ +SWIR2band\times coefGr\end{array}$ | [128] | |

Density of low vegetation | Positive | LasTool Software (LasTool: http://lastools.org/) Vegetation quantity according to different buffer size | [46,97] | |

Density of medium vegetation | Negative | LasTool Software Vegetation quantity according to different buffer size | [46,97] | |

Density of high vegetation | Negative | LasTool Software Vegetation quantity according to different buffer size | [110] | |

Water presence index | NDWI Normalized Difference Water Index | Negative | $NDWI=\frac{Green-NIR}{Green+NIR}$ | [85,126] |

MNDWI Modified Normalized Difference Water Index | Negative | $MNDWI=\frac{Green-SWIR1}{Green+SWIR1}$ | [126] | |

Moisture index | Tasseled Cap Wetness | Negative | $\begin{array}{c}\mathrm{TCT}\text{}\mathrm{W}=\text{}\mathrm{Blue}\text{}\mathrm{band}\times \mathrm{coefWr}\\ \text{\hspace{1em}\hspace{1em}}+\mathrm{Green}\text{}\mathrm{band}\text{}\\ \text{\hspace{1em}\hspace{1em}}\times \mathrm{coefWr}+\mathrm{Red}\text{}\mathrm{band}\\ \text{\hspace{1em}\hspace{1em}}\times \mathrm{coefWr}\\ \text{\hspace{1em}\hspace{1em}}+\mathrm{NearInfrared}\text{}\mathrm{band}\\ \text{\hspace{1em}\hspace{1em}}\times \mathrm{coefWr}\\ \text{\hspace{1em}\hspace{1em}}+\mathrm{SWIR}1\text{}\mathrm{band}\\ \text{\hspace{1em}\hspace{1em}}\times \mathrm{coefWr}\\ \text{\hspace{1em}\hspace{1em}}+\mathrm{SWIR}2\text{}\mathrm{band}\text{}\\ \text{\hspace{1em}\hspace{1em}}\times \mathrm{coefWr}\end{array}$ | [128] |

NDMI Normalized Difference Moisture Index | Negative | $NDMI=\frac{NIR-SWIR1}{NIR+SWIR1}$ | [86,88] | |

Bare soil index | NDBaI Normalized Difference Bareness Index | Positive | $NDBaI=\frac{SWIR1-TIRS}{SWIR1-TIRS}$ | [85,126] |

BI Bare Soil Index | Positive | $BI=\frac{\left(SWIR1+RED\right)-\left(NIR+BLUE\right)}{\left(SWIR1+RED\right)+\left(NIR+BLUE\right)}$ | [126] | |

EBBI Enhanced Built-Up and Bareness Index | Positive | $EBBI=\frac{SWIR1-NIR}{10\sqrt{SWIR1+TIRS1}}$ | [126] | |

Building index | NDBI Normalized Difference Built-Up Index | Positive | $NDBI=\frac{SWIR1-NIR}{SWIR1+NIR}$ | [85,126] |

UI Urban Index | Positive | $UI=\frac{SWIR2-NIR}{SWIR2+NIR}$ | [126] | |

IBI Index-based Built-Up Index | Positive | $IBI=\frac{NDBI-\frac{\left(SAVI+MNDWI\right)}{2}}{NDBI+\frac{SAVI+MNDWI}{2}}$ | [126] | |

Building density | Positive | LasTool Software Building quantity according to different buffer size | [46,97] | |

Topographic | Slope (%) | Depending on the context | From the DEM (RVT 1.3 Software (RVT 1.3: https://iaps.zrc-sazu.si/en/rvt#v)) | [129,130] |

Exposure (°N) | Depending on the context | From the DEM (RVT 1.3 Software) | [131] | |

Curvature | Depending on the context | From the DEM (RVT 1.3 Software) | [132,133] | |

Proximity to land occupations | Water area | Negative | Water area according to different buffer size | [134,135] |

Distance to fountains | Negative | Euclidean distance to nearest fountain | ||

Distance to subway entrances | Depending on the context | Euclidean distance to the nearest subway entrance | ||

Distance to points of tourist interest | Negative | Euclidean distance to the nearest tourist point | ||

Distance to railway tracks | Positive | Length of the railways according to different buffer size | ||

Radiation index | Spectral Radiance | Negative | ${L}_{\mathsf{\lambda}}={L}_{\mathrm{min}\left(\mathsf{\lambda}\right)}+\left({L}_{\mathrm{max}\left(\mathsf{\lambda}\right)}-{L}_{\mathrm{min}\left(\mathsf{\lambda}\right)}\right)\frac{{Q}_{dn}}{{Q}_{max}}$ | [136] |

Emissivity | Negative | $\in =\frac{{L}_{T}}{{L}_{nT}}$ | [137] | |

Tasseled Cap Brightness | Positive | $\begin{array}{c}TCTB=Blueband\times coefBr\\ \hspace{1em}+Greenband\\ \hspace{1em}\times coefBr+Redband\\ \hspace{1em}\times coefBr\\ \hspace{1em}+NearInfraredband\\ \hspace{1em}\times coefBr\\ \hspace{1em}+SWIR1band\\ \hspace{1em}\times coefBr\\ \hspace{1em}+SWIR2band\\ \hspace{1em}\times coefBr\end{array}$ | [128] | |

Urban morphology | Sky View Factor | Depending on the context | RVT 1.3 Software | [16,111,138] |

Variation in building height | Negative | Standard deviation of the building height | [97,116,139] |

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**Figure 3.**Hourly measurements of temperature (°C—red line) and humidity (%—blue dotted line) at the Météo-France Lyon-Bron station from 06/28/18 to 09/24/18.

**Figure 4.**Air temperature measurement points for 22 July 2019 (top left), 19 July 2018 (top right), 1 August 2017 (bottom left), and 30 August 2016 (bottom right—source: Data Grand Lyon).

**Figure 5.**Example of variation in the correlation (coefficient of determination) between predictor and air temperature as a function of study scale.

**Figure 9.**Modelling of air temperature in the dense urban center of Lyon on 19 July 2018 (source: Data Grand Lyon).

**Figure 11.**Evolution of the importance of the variables selected in random forest classification and regression modelling for the four study dates.

**Figure 12.**Evolution of the importance of the variables selected in random forest classification and regression modelling for the global modelling.

**Figure 13.**Box plots representation of the modeling error from multiple linear regression and random forest classification and regression.

**Figure 14.**Location of the modeled measurement error of the air temperature by multiple linear regression (left) and by random forest (right) for all the study days (source: Data Grand Lyon).

**Figure 15.**Localization of the measurement error of the air temperature modeling by multiple linear regression (source: Data Grand Lyon).

**Figure 16.**Localization of the measurement error of the air temperature modeling by random forest regression (source: Data Grand Lyon).

**Figure 17.**LISA of the differences between modelled and measured air temperatures for all study days (source: Data Grand Lyon).

**Figure 18.**Gi* of the differences between modelled and measured air temperatures for all study days (source: Data Grand Lyon).

Land Use/Land Cover | Covered Surface Area (%) |
---|---|

Continuous urban fabric | 50 |

Industrial, commercial, military, or public units | 19.5 |

Roads (main and secondary) | 14.3 |

Vegetation | 8.9 |

Water | 7.3 |

**Table 2.**Synthesis of the correlation coefficients, root mean square error (RMSE) and MSE from the different measurement instruments used in relation to the Lyon-Bron station of Météo-France.

LOG 32 n°1 | LOG 32 n°2 | EL-USB-1-RCG n°1 | EL-USB-1-RCG n°2 | |
---|---|---|---|---|

Temperature (°C) | MSE: 0.892 | MSE: 0.797 | MSE: 0.516 | MSE: 0.566 |

RMSE: 0.944 | RMSE: 0.893 | RMSE: 0.718 | RMSE: 0.752 | |

R^{2}: 0.983 | R^{2}: 0.981 | R^{2}: 0.989 | R^{2}: 0.987 | |

Humidity (%) | MSE: 12.305 | MSE: 11.970 | ||

RMSE: 3.507 | RMSE: 3.459 | |||

R^{2}: 0.977 | R^{2}: 0.978 |

**Table 3.**Meteorological parameters of the study days at the Lyon-Bron station at 12:00 noon (source: Météo-France).

Temperature (°C) | Humidity (%) | Wind Speed (m/s) | Pressure (hPa) | Wind Direction (degrees) | Start | Finish | |
---|---|---|---|---|---|---|---|

08/30/2016 | 27.7 | 46 | 9 | 1017.8 | 350 | 14:42 | 16:50 |

08/01/2017 | 29.4 | 52 | 10 | 1012.2 | 34 | 15:23 | 18:37 |

07/19/2018 | 29.8 | 42 | 5 | 1014.2 | 309 | 12:32 | 14:45 |

07/22/2019 | 30.1 | 41 | 11 | 1022 | 10 | 12:25 | 16:12 |

Mean | 29.3 | 45.3 | 8.8 | 1016.6 | 260.8 | ||

Standard deviation | 0.9 | 4.3 | 2.3 | 3.7 | 132.0 | ||

Minimum | 27.7 | 41 | 5 | 1012.2 | 34 | ||

Maximum | 30.1 | 52 | 11 | 1022 | 350 |

Variables (Units) | Acquisition Source | Variables (Units) | Acquisition Source | ||
---|---|---|---|---|---|

Climate data from remote sensing | Surface temperature (°C) | Landsat 8 | Building Index | NDBI Normalized Difference Built-Up Index | Landsat 8 |

UTFVI Urban Thermal Field Variance Index | Landsat 8 | ||||

Sunshine duration of the study day (h) | LiDAR data and modelling by ESRI ARCGIS | UI Urban Index | Landsat 8 | ||

Radiation received for the study day (WH/m^{2}) | LiDAR data and modelling by ESRI ARCGIS | IBI Index-based Built-Up Index | Landsat 8 | ||

Vegetation index | NDVI Normalized Difference Vegetation Index | Landsat 8 | Building Density | LiDAR | |

SAVI Soil Adjusted Vegetation Index | Landsat 8 | ||||

EVI Enhanced Vegetation Index | Landsat 8 | ||||

Tasseled Cap Transformation greenness (GVI) | Landsat 8 | Topographic | Slope (°) | Data Grand Lyon | |

Density of low vegetation | LiDAR | ||||

Density of medium vegetation | LiDAR | Exposure | LiDAR | ||

Density of high vegetation | LiDAR | Curvature | Data Grand Lyon | ||

Water presence index | MNDWI Modified Normalized Difference Water Index | Landsat 8 | Urban morphology | Sky View Factor | LiDAR |

NDWI Normalized Difference Water Index | Landsat 8 | Standard Deviation (STD) of Building Height (building height variation) | Data Grand Lyon | ||

Moisture index | Tasseled cap Transformation Wetness | Landsat 8 | Land use | Distance to railway tracks | Data Grand Lyon |

NDMI Normalized Difference Moisture Index | Landsat 8 | Distance to points of tourist interest | Data Grand Lyon | ||

Bare soil index | NDBaI Normalized Difference Bareness Index | Landsat 8 | Distance to subway entrances | Data Grand Lyon | |

BI Bare Soil Index | Landsat 8 | Distance to fountains | Data Grand Lyon | ||

EBBI Enhanced Built-Up and Bareness Index | Landsat 8 | Water area | Data Grand Lyon | ||

Density of bare soil | LiDAR | ||||

Radiation Index | Spectral radiance | Landsat 8 | |||

Emissivity | Landsat 8 | ||||

Tasseled Cap Transformation Brightness | Landsat 8 |

Variables (unit) | Buffer Zone (m) | Variables (unit) | Buffer Zone (m) | ||
---|---|---|---|---|---|

Climate data from remote sensing | Surface temperature (°C) | 500 | Bare soil index | NDBaI | 1000 |

UTFVI | 500 | BI | 50 | ||

Vegetation index | NDVI | 1000 | EBBI | 1000 | |

SAVI | 1000 | Density of bare soil | 50 | ||

EVI | 50 | Built index | NDBI | 1000 | |

Tasseled Cap greenness | 1000 | UI | 1000 | ||

Density of low vegetation | 200 | IBI | 500 | ||

Density of medium vegetation | 50 | Density of built-up | 5 | ||

Density of high vegetation | 100 | Urban morphology | STD Building Height | 100 | |

Water index | MNDWI | 500 | Radiation Index | Spectral radiance | 1000 |

NDWI | 500 | Emissivity | 500 | ||

Moisture index | Tasseled cap Wetness | 50 | Tasseled Cap Brightness | 1000 | |

NDMI | 1000 | Land use | Density of water area | 100 |

Variables | After Spearman Correlation Matrix and VIF | |||
---|---|---|---|---|

08/30/2016 | 08/01/2017 | 07/19/2018 | 07/22/2019 | |

Surface temperature (°C) | X | X | X | X |

UTFVI | ||||

Sunshine duration of the study day | ||||

Radiation received for the study day | X | X | X | |

NDVI | X | X | X | |

SAVI | ||||

EVI | X | X | X | X |

Tasseled Cap greenness (GVI) | X | |||

Density of low vegetation | X | X | X | X |

Density of medium vegetation | X | X | X | X |

Density of high vegetation | X | X | X | X |

MNDWI | X | X | X | X |

NDWI | X | |||

Tasseled Cap Wetness | X | X | X | X |

NDMI | X | |||

NDBaI | X | |||

BI | X | X | X | X |

EBBI | ||||

Density of bare soil | X | X | X | X |

Spectral radiance | ||||

Emissivity | X | X | ||

Tasseled Cap Brightness | X | X | X | |

NDBI | X | |||

UI | ||||

IBI | X | X | ||

Building Density | X | X | X | X |

Digital Elevation Model | X | X | X | X |

Slope (°) | X | X | X | X |

Longitude | X | |||

Exposure | X | X | X | |

Curvature | X | X | X | X |

Sky View Factor | X | X | X | X |

STD Building Height | X | X | ||

Distance to railway tracks | X | X | X | X |

Distance to points of tourist interest | X | X | X | |

Distance to subway entrances | X | X | X | |

Distance to fountains | X | X | X | |

Water area | X | X | X | X |

Final Number | 21 | 27 | 22 | 26 |

**Table 7.**Statistical parameters of the three explanatory variables used in air temperature modelling by partial least square linear regression.

Date | R^{2} | MSE | RMSE | Variables | Model Parameter in Absolute Value | Impact on the Model |
---|---|---|---|---|---|---|

08/30/2016 | 0.79 | 0.11 | 0.33 | LST | 0.0675 | Negative |

NDVI | 1.71 | Positive | ||||

MNDWI | 4.53 | Positive | ||||

08/01/2017 | 0.77 | 0.03 | 0.18 | BI | 0.58 | Positive |

NDMI | 0.51 | Negative | ||||

NDBI | 0.51 | Positive | ||||

07/19/2018 | 0.37 | 0.09 | 0.07 | Emissivity | 2.1128 | Negative |

Longitude | 1.3906 | Positive | ||||

NDBaI | 1.2262 | Positive | ||||

07/22/2019 | 0.,53 | 1.13 | 1.06 | Emissivity | 7.4782 | Positive |

BI | 3.0472 | Positive | ||||

NDBaI | 2.5931 | Positive | ||||

Mean | 0.62 | 0.34 | 0.41 |

**Table 8.**Summary of Coefficients of Determination, Out-Of-Bag Error and Root Mean Square Error of Random Forest Classification, and Regression Modeling Errors.

Date | R^{2} | Out-Of-Bag | RMSE |
---|---|---|---|

08/30/2016 | 0.98 | 0.0071 | 0.08 |

08/01/2017 | 0.96 | 0.0045 | 0.07 |

07/19/2018 | 0.95 | 0.0071 | 0.08 |

07/22/2019 | 0.92 | 0.19 | 0.44 |

Mean | 0.95 | 0.05 | 0.17 |

**Table 9.**Multiple linear regression (MLR) and random forest regression (RDF) model error descriptive statistics.

MLR | RDF | |
---|---|---|

Biggest negative error (°C) | −2.23 | −0.99 |

Biggest maximum error (°C) | 2.50 | 1.29 |

First Quartile | −0.17 | −0.05 |

Median | 0.02 | 0.002 |

Third Quartile | 0.17 | 0.05 |

Mean | 0.01 | 0.003 |

Variance | 0.19 | 0.03 |

Standard deviation | 0.44 | 0.17 |

© 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**

Alonso, L.; Renard, F. A New Approach for Understanding Urban Microclimate by Integrating Complementary Predictors at Different Scales in Regression and Machine Learning Models. *Remote Sens.* **2020**, *12*, 2434.
https://doi.org/10.3390/rs12152434

**AMA Style**

Alonso L, Renard F. A New Approach for Understanding Urban Microclimate by Integrating Complementary Predictors at Different Scales in Regression and Machine Learning Models. *Remote Sensing*. 2020; 12(15):2434.
https://doi.org/10.3390/rs12152434

**Chicago/Turabian Style**

Alonso, Lucille, and Florent Renard. 2020. "A New Approach for Understanding Urban Microclimate by Integrating Complementary Predictors at Different Scales in Regression and Machine Learning Models" *Remote Sensing* 12, no. 15: 2434.
https://doi.org/10.3390/rs12152434