3.4.1. Spatially Averaged Surface Temperature Regression Model

Multi-variable linear regression models were developed to predict spatially averaged surface temperature and it was found that air temperature and solar radiation are significant predictors (Figure 9). Standard least squares regression was applied to develop models that predict the surface temperature of six land use types: grass, canopy cover, parking lot (concrete), sidewalk, rooftop (composite) and road. The models had an average R<sup>2</sup> of 0.71 with the parking lot having the greatest of (0.89) and the road the lowest (0.37). The parked cars and heat shadows were clipped out as inconsistencies before analysis occurred and therefore the parking lot surface had the most homogenous distribution of temperatures. The grass model had the second greatest R<sup>2</sup> (0.84) and had a similarly homogenous distribution. Contrarily, the roadway surface had a much less homogenous distribution of temperatures and thus the road model had a low predictive power and statistical significance. This may be due in large part due to the difficulty of clipping out inconsistencies related to nonstationary objects (e.g., moving cars) combined with their impact on pavement temperatures.

The data collected in El Paso, TX was evaluated for influence and leverage and it was found that it did not have high influence or leverage in any of the six models. To evaluate influence we used Cook's D and found that the El Paso data points all fell below the threshold of 2.4 (max 0.19) to be considered high-influence points [38]. In addition, we used the hat matrix to evaluate leverage and found that no El Paso data points exhibited high leverage in the model. The agreeability of the data across the two case study areas indicates that the findings in this study may have generalizability beyond the case study locations.

**Figure 9.** Temperature prediction models of six surface types: grass (**a**), canopy cover (**b**), parking lot (**c**), sidewalk (**d**), composite rooftop (**e**) and road (**f**). UTEP datapoint is fitted in green. Note the 95% confidence intervals are in blue.

#### 3.4.2. Diurnal Prediction Model

Finally, models were developed to predict land surface temperature throughout the day based upon the air temperature and solar radiation (Equations (7)–(9)). The diurnal data was fit with a Gaussian peak distribution and it was found that the parking lot and composite rooftop had the best model fit with an R<sup>2</sup> of 0.83 and 0.78, respectively, while all other models had an R<sup>2</sup> value of 0.53 or below (Figure 10). While this approach is constrained by a limited number of data points from four flights and only four numerical x-axis variables, there are a few insights we can gain from these results. The first is that these models confirm what was found in the previous regression models: it is much easier to predict the land surface temperature of homogenous materials, such as pavements and rooftops, than it is to predict land surfaces that have a greater distribution in texture and material, such as canopy. The second is that anthropogenic variables, such as pedestrians and vehicular traffic that are difficult to quantify, may influence the ability to predict surface temperatures based upon meteorological variables. This was shown by the lower model fit in the high-traffic roadways and sidewalks as compared to the low-traffic parking lot.

**Figure 10.** Gaussian peak models of six surface types: grass (**a**), canopy cover (**b**), parking lot (**c**), sidewalk (**d**), composite rooftop (**e**) and road (**f**). Note that GRS = grass; CPY = canopy; PL = parking lot; SW = sidewalk; RTC = composite rooftop; AT = air temperature; SR = solar radiation; t = time.

#### **4. Discussion**

We have presented a case study that applied high resolution drone measurements (13 cm) to evaluate urban surface temperatures and results indicate that there is a wide variability in surface temperature behavior across urban land use types. Some of the uncertainty in land surface temperature variability may be attributable to human movement patterns, land surface properties or urban geometry. Results indicate that mean land surface temperatures can be predicted based upon solar radiation and air temperature. By elucidating some of the factors that influence land surface temperature variability, we hope to contribute to the growing body of knowledge centered around land surface temperature in the urban environment.

To this end, our findings suggest that when parameterizing models, it is important to understand the unique relationship between surface material properties, urban geometry, weather and human movement. For example, the results indicate that pedestrian or vehicular traffic may have an impact on land surface temperature variability across sidewalks, parking lots and streets. Depending on the volume of cars, either parked or moving, this can greatly impact the temperature profile of paved surfaces. Parked cars can create heat shadows which cool the surface below and our study demonstrates that when a car moves it can reveal temperatures as low as 8.3 ◦C cooler than the exposed surface.

In addition, results have identified several factors of urban geometry that affect land surface temperatures. Urban factors such as building reflectivity and surface altitude can impact solar radiation, which then influences surface temperatures in locations impacted by these effects. For example, sidewalks often lie near buildings and depending on a buildings reflectance or shadows this can make sidewalk temperatures more vulnerable to temperature fluctuations. In this study, sidewalk temperatures impacted by glass reflectance were on average 4.7 ◦C hotter that sidewalks not impacted by reflectance. Therefore, knowledge of the spatial distribution of urban geometry is important for predicting and evaluating land surface temperatures in the built environment. While addressing urban geometry or pedestrian and vehicular traffic within our prediction models is outside of the scope of this project, future work should evaluate how to incorporate these important parameters into land surface temperature predictions.

Results indicate air temperature and solar radiation are significant predictors of mean land surface temperature in both of our models and it was found this relationship holds true in both Milwaukee, WI and El Paso, TX. Because the model holds true across two different climatic regions, the models developed in this project may be generalizable beyond their case study regions. In addition, these models can also be easily applied as air temperature and solar radiation are commonly measured across the world. The generalizability of these findings also has important implications for engineering applications that use predictions of land surface temperatures. Urban land surface temperatures are often used by public health officials to mitigate the impact of the urban heat island effect on human health [2], in developing binders and mixers of pavement in roadway designs [41] or to estimate the impact of land surface temperatures on receiving stream temperatures [42–44].

This study also demonstrates several advantages and disadvantages of using drones as compared to satellite or in-situ imagery. The case studies we evaluated were restricted to the size of a city block around 46,000 m<sup>2</sup> and even though battery life would have allowed us to collect an area ten times this size, we were restricted by United States Federal Aviation Administration UAV pilot rules that restrict the flight of UAVs to within line of sight of the pilot. In an urban environment with tall buildings the line of sight may be the primary constraint on coverage area. Therefore, a disadvantage of UAVs is that flight time and legal restrictions may constrain the flight areas to small portions of a city. However, this could be overcome with fixed-wing drones that are able cover a greater area, in addition to relaxed regulations that allow flights beyond the line of sight [45]. Despite the restriction on the spatial extent of the study area, advantages of UAVs over satellites or in-situ methods are their ability to collect distributed temperature data at spatial resolutions (13 cm) that reflect small scale changes in the urban environment. In addition, satellite data is restricted to daily to weekly observations while drones can be flown on-demand, which allows them to capture temperature changes throughout the day.

Overall, this study highlights the utility of using drone observations to capture the variability of urban land surface temperatures at small spatial scales. Urban environments are spatially complex, making it difficult to capture the spatial distribution of observable phenomena outside of high-resolution remote sensing techniques. Our findings suggest that drones could also be good tools for evaluating the variability of other parameters of the urban environment that are important for environmental studies such as soil moisture, leaf area index or impervious cover. Therefore, it is important for studies such as this one that evaluate the spatial complexities of the urban environment in order to improve the methods that we use to model and understand urban systems.

#### **5. Conclusions**

The main objectives of this work were to apply drone imagery to capture land surface temperature variability and develop models to predict mean land surface temperatures. This was done through the application of high-resolution thermal imagery as a parameterizing tool for model development. The results revealed that land surface temperature variability is extensive and influenced by numerous variables related to urban environments and that air temperature and solar radiation are significant predictors of mean land surface temperature. Conclusions from this study hold true in both Milwaukee, WI and El Paso, TX, indicating they could be generalizable to regions beyond these two case study locations.

The key findings from this study were:


Overall, our findings suggest that land surface temperature variability in the urban environment can come from several sources including surface material properties, urban geometry, weather and pedestrian and vehicular traffic. This has direct implications for land surface temperature models that are used for urban environmental studies. As climate change and urbanization continue to exacerbate the SUHI, studies such as this are important for gaining a better understanding of the complexities of land surface temperatures. Ultimately this improved understanding will help to develop better methods and procedures to mitigate the impact of land surface temperatures on human and environmental health.

**Author Contributions:** J.N. provided investigation, data collection, data analysis, and writing of the original draft. W.M. contributed conceptualization, supervision, data collection and draft editing.

**Funding:** This project was funded by the Marquette OPUS College of Engineering Earl B. and Charlotte Nelson Award.

**Acknowledgments:** The authors would like to acknowledge and sincerely thank Saurav Kumar and Wissam Atwah at the University of Texas El Paso for their help in collecting data in El Paso, Tx.

**Conflicts of Interest:** The authors declare no conflict of interest.
