# The Relationship between Urban Density and Building Energy Consumption

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## Abstract

**:**

^{2}cells were classified into five categories of settlement density using the US Geological Survey’s National Land Cover Dataset (NLCD), the US Census, and Census Block data. In the next step, linear hierarchical spatial and non-spatial models were developed and applied to building energy data in those seven metropolitan areas to explore the links between urban density (and other urban form parameters) and energy performance, using both frequentist and Bayesian statistics. Our results indicate that urban density is correlated with energy-use intensity (EUI), but its impact is not similar across different metropolitan areas. The outcomes of our analysis further show that the distance from buildings within which the influence of urban form parameters on EUI is most significant varies by city and negatively changes with urban density. Although the relationship between urban density parameters and EUI varies across cities, tree-cover area, impervious area, and neighborhood building-covered area have a more consistent impact compared to building and housing density.

## 1. Introduction

## 2. Methodology

#### 2.1. Data

^{2}land-cover datasets available through the EPA’s EnviroAtlas data portal (https://www.epa.gov/enviroatlas/enviroatlas-data-approach, accessed on 25 October 2019) were used to measure the percentage of tree canopy and impervious surface cover for each cell. Surface temperature data for 30 × 30 m

^{2}cells were extracted from Landsat 8 OLI images with less than 1% cloud cover. Atmospheric corrections were applied using ENVI for all bands, including thermal ones, and the Landsat Digital Numbers (DNs) of band 10 were converted to top-of-atmosphere (TOA) reflectance in accordance with USGS instructions (http://landsat.usgs.gov/Landsat8_Using_Product.php, accessed on 20 July 2021):

^{2}.srad.μm)), ${M}_{L}$ is the band-specific multiplicative rescaling factor from the metadata, ${A}_{L}$ is the band-specific additive rescaling factor, and ${Q}_{cal}$ is the quantized and calibrated standard product pixel value (DN). In the next step, radiance values were converted to the satellite brightness temperature:

_{1}and K

_{2}are band-specific thermal conversion constants from the metadata. In the last step, satellite brightness temperature (BT) data were normalized based on emissivity values for each land-cover class using the following equation:

^{2}(20,000 ft

^{2}) be reported by owners to the city (see Table 1 for the building-type mix by city). Every building data-point that carried energy-use data was geocoded based on longitude and latitude. All the above-mentioned layer sections were converted to raster layers at 30 × 30 m

^{2}resolution. For land-cover layers, tree canopy and impervious surface coverage information were aggregated from 1 × 1 m

^{2}to 30 × 30 m

^{2}resolutions.

#### 2.2. Analysis

^{2}. For every window, urban form composites were created using a principal component analysis (PCA) in which correlated variables were loaded into orthogonal components. The variables used to create each of the composites were the average area of the buildings, number of buildings per hectare, average tree-cover area, impervious surface area, morphological density category (1–5; 1 = low density, 5 = high density), number of housing units per hectare, and surface temperature for all of the windows. It is important to note that, ultimately, only the first three components in each PCA were technically used in evaluating the relationship between urban form and EUI (energy per area per year) since 80% or more of the variance in all windows for all the cities was explained by them.

^{2}significantly, and the additional predictive power was supposed to be the greatest of all the windows in which the first requirement was met.

## 3. Regression Results

#### 3.1. City-Specific Trends

^{2}window. Building type and urban form parameters were the major determinants of energy consumption in DC. Residential units, on average, had a lower EUI (by 18.09%) than non-residential units. The morphological density category was negatively correlated with EUI, with units located in high-density urban-core areas consuming 7.39% less than units located in medium-density areas. Finally, despite statistical significance, the impact of building coverage in the surroundings on EUI was not greater than 0.001%.

^{2}window. Some of the spatial form variables were removed due to multicollinearity. The only form variable significantly associated with energy consumption was the tree cover area in the case of Austin, with each square meter increase in tree cover associated with a 0.2% rise in EUI.

^{2}window. Building type and building count per hectare were significantly related to energy consumption. Residential units consumed on average 6.74% less energy than non-residential units. Furthermore, building count per hectare was negatively related to EUI. Each extra building was associated with a 0.14% reduction in EUI, indicating a slight negative correlation between density and EUI. Building age and the area covered by buildings were also significantly correlated with energy consumption, although negligible in magnitude.

^{2}window. Impervious area and residential density around a building were positively associated with energy consumption intensity. One square meter increase in impervious area was associated with 0.06% higher EUI. In addition, every 10% increase in the proportion of residential neighbors was associated with a 1.59% rise in energy consumption.

^{2}window. In Philadelphia, every unit of increase in building area was associated with a 10.87% rise in EUI. Also, the building count per hectare had a positive relation with energy use, with each added building leading to an increase in EUI by 2.38%.

^{2}window. The results showed lower consumption for residential units by 33.29% and, like the other cases, positive correlation between area and EUI. One unit of increase in building count per hectare led to a 1.63% increase in energy consumption, while the morphological density variable positively correlated with energy-consumption intensity. The area of units was treated as a categorical variable, with 10 categories each representing 10% of the sample. The results showed that a unit jump in unit area was associated with a 1.91% increase in EUI. One unit increase in building count per hectare was associated with an energy consumption reduction of 1.14%. Furthermore, a unit increase in the morphological density category was associated with an increase in energy-consumption intensity by 19.15%. A summary of the results for all the cities is provided in Table 4.

#### 3.2. Cities Combined

^{2}window was chosen for its higher predictive power, based on the method previously introduced for the city-specific models. The morphological density category needed to be transformed into a dichotomous variable to recognize that most of the units in the dataset came from highly dense neighborhoods. Furthermore, the types of units included in the model were reconsidered to incorporate categories that represented at least 2% of the total units in the combined dataset, giving relevance to categories such as hospitals or worship centers. Lastly, some variables were dropped due to multicollinearity.

^{2}increase in tree-cover area was associated with an increase in EUI of 0.04%; a 1 m

^{2}increase in impervious area was associated with a 0.02% increase in EUI; a one unit increase in the building count per hectare was associated with a 0.52% reduction in EUI; and, finally, a unit increase in the housing density per hectare was associated with a rise in energy consumption of 0.05%. Cooling degree days (CDD) was also significantly and positively correlated with energy use (0.02% EUI increase per CDD). The spatial error parameter was positive and significantly different from zero ($\lambda $ = 0.281, p-value < 0.001).

#### 3.3. The Bayesian Models

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Distribution of the regression coefficient for the impact of morphological density on EUI (posterior, all cities).

Austin, TX | NYC, NY | Philadelphia, PA | Seattle, WA | Chicago, IL | Washington, DC | Minneapolis, MN | |
---|---|---|---|---|---|---|---|

Hotel | 22 (7%) | 164 (4%) | 38 (3%) | 75 (2%) | 45 (3%) | 71 (6%) | 13 (5%) |

Multi-use | 19 (6%) | 114 (4%) | |||||

Warehouse | 42 (14%) | ||||||

Office | 81 (27%) | 837 (18%) | 153 (13%) | 375 (12%) | 239 (14%) | 398 (32%) | 66 (27%) |

Retail | 98 (32%) | ||||||

Residential | 3245 (70%) | 320 (28%) | 1649 (55%) | 694 (40%) | 458 (36%) | 1 (0%) | |

College | 27 (2%) | 66 (4%) | 15 (1%) | ||||

School | 176 (15%) | 134 (4%) | 320 (19%) | 117 (9%) | |||

Parking | 33 (13%) | ||||||

Other | 41 (14%) | 388 (8%) | 425 (37%) | 671 (22%) | 363 (21%) | 615 (49%) | 133 (54%) |

City | Model Type | Urban Form Impact | Selected Window |
---|---|---|---|

Austin, TX | Linear | Yes | 1950 × 1950 m^{2} |

Chicago, IL | Hierarchical | Yes | 270 × 270 m^{2} |

Washington, DC | Hierarchical | Yes | 1950 × 1950 m^{2} |

Minneapolis, MN | Linear | No | n/a |

New York City, NY | Hierarchical | Yes | 390 × 390 m^{2} |

Philadelphia, PA | Hierarchical | Yes | 510 × 510 m^{2} |

Seattle, WA | Hierarchical | Yes | 1590 × 1590 m^{2} |

Moran’s I | p-Value | |
---|---|---|

Austin, TX | 0.38 | 0.02 |

Chicago, IL | 0.07 | <0.001 |

Washington, DC | 0.00 | 0.47 |

Minneapolis, MN | NA | n/a |

New York City, NY | 0.17 | <0.001 |

Philadelphia, PA | 0.06 | <0.001 |

Seattle, WA | 0.03 | <0.001 |

**Table 4.**A summary of the impacts of urban form and density variables on energy-use intensity (gray = positive correlation; white = negative correlation; numbers provided only for the statistically significant relationships).

Austin | Chicago | DC | NYC | Philadelphia | Seattle | |
---|---|---|---|---|---|---|

Area of building coverage | 0.00% | |||||

Tree-covered area | 0.24% | 0.00% | ||||

Impervious area | n/a | 0.06% | n/a | |||

Morphological density | −7.39% | 19.15% | ||||

Housing density per hectare | n/a | |||||

Building count per hectare | −0.14% | 2.38% | −1.14% |

Estimate | Standard Error | z Value | Pr (>|z|) | |
---|---|---|---|---|

Intercept | 3.692 | 0.068 | 54.622 | <0.001 |

Philadelphia dummy | −0.026 | 0.032 | −0.810 | 0.418 |

New York City dummy | 0.282 | 0.026 | 11.005 | <0.001 |

Chicago dummy | 0.428 | 0.027 | 15.943 | <0.001 |

Residential (1 = yes) | −0.167 | 0.015 | −10.821 | <0.001 |

Office (1 = yes) | −0.001 | 0.019 | −0.031 | 0.975 |

Warehouse (1 = yes) | −0.900 | 0.038 | −23.384 | <0.001 |

Worship center (1 = yes) | −0.460 | 0.061 | −7.532 | <0.001 |

Hospital (1 = yes) | 0.870 | 0.067 | 13.017 | <0.001 |

Hotel (1 = yes) | 0.331 | 0.042 | 7.879 | <0.001 |

Property value (USD 1000) | 0.000 | 0.000 | −1.873 | 0.061 |

Area (1000 ft^{2}) | 0.000 | 0.000 | 1.640 | 0.101 |

Percentage of residential neighbors | −0.004 | 0.031 | −0.123 | 0.902 |

Tree-cover area | 0.000 | 0.000 | 3.056 | 0.002 |

Impervious area | 0.000 | 0.000 | 2.222 | 0.026 |

Area of building coverage | 0.000 | 0.000 | 0.284 | 0.776 |

Morphological density category (1 = 5) | 0.038 | 0.021 | 1.829 | 0.067 |

Building count per hectare | −0.005 | 0.001 | −3.795 | <0.001 |

Housing density per hectare | 0.001 | 0.000 | 3.541 | <0.001 |

Cooling degree days (CDD) | 0.0002 | 0.000 | 9.384 | <0.001 |

Confidence Interval | |||||
---|---|---|---|---|---|

Estimate | Standard Error | Lower Limit | Upper Limit | $\hat{\mathrm{R}}$ | |

Intercept | 3.9 | 0.2 | 3.54 | 4.29 | 1.13 |

Morphological density category | 0.05 | 0.01 | 0.02 | 0.06 | 1.03 |

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**MDPI and ACS Style**

Mostafavi, N.; Heris, M.P.; Gándara, F.; Hoque, S.
The Relationship between Urban Density and Building Energy Consumption. *Buildings* **2021**, *11*, 455.
https://doi.org/10.3390/buildings11100455

**AMA Style**

Mostafavi N, Heris MP, Gándara F, Hoque S.
The Relationship between Urban Density and Building Energy Consumption. *Buildings*. 2021; 11(10):455.
https://doi.org/10.3390/buildings11100455

**Chicago/Turabian Style**

Mostafavi, Nariman, Mehdi Pourpeikari Heris, Fernanda Gándara, and Simi Hoque.
2021. "The Relationship between Urban Density and Building Energy Consumption" *Buildings* 11, no. 10: 455.
https://doi.org/10.3390/buildings11100455