Urban-scale air temperature estimation: development of an empirical model based on mobile transects

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Elsevier in Sustainable Cities and Society, Vol. 63, on December 2020, , available at: https://doi.org/10.1016/j.scs.2020.102471 © 2020 Elsevier. En idUS Licencia Creative Commons CC BY-NC-ND 1 Urban-scale air temperature estimation: development of an empirical model based on mobile transects Abstract The urban microclimate is influenced by many factors which trigger the well-known Urban Heat Island (UHI) phenomenon. Different approaches have been developed in the literature for estimating urban temperatures, but a compromise is always needed, either spatial or temporal. To solve this issue, this work presents a new way for estimating urban temperatures with a fine spatial resolution (even specific streets) while also keeping a high temporal resolution (hourly time-steps) for prolonged periods. This is done by developing an empirical model, based on the measurements of a reference weather station and data taken from mobile transects. The proposed method was tested in Seville (Spain). The validation was done comparing the prediction of the model with the measurements of a fixed temperature sensor, from the 7th of June 2019 until the 7th of December 2019 (4390 hours). The results showed a high R2 coefficient of 0.976 and a low RMSE of 1.21, improving the accuracy of previous literature for estimating urban temperatures. The methodology is applicable for any geographical location around the world, with different climates or population densities. In addition, it offers a precise way to verify the real impact of UHI mitigation strategies and concentrate climate change mitigation efforts. Keywords: Urban climate, Urban Heat Island, Microclimate, Mobile transects, GIS, Temperature forecasting. 1 Introduction 1.1 Background The current rate of growth of population and use of resources is endangering the sustainable development of mankind and its environment, which are exposed to many factors. One of these factors is the outdoor air temperature, closely related to climate change and particularly important in urban areas. In this regard, the Urban Heat Island (UHI) effect is distinguished by higher temperatures in urban areas compared to the surrounding rural areas (Oke, Mills, Christen, & Voogt, 2017). The main reasons for this effect are population growth and the rapid increase of urbanization, which may cause an accumulation of warm air, as well as warmer surface temperatures. The urban microclimate is important for pedestrians’ health, but it also affects air quality, citizen well-being, urban sustainability and the energy use of buildings (Wang, Berardi, & Akbari, 2015). 2 Urban Heat Islands may be distinguished as either atmospheric (Canopy Layer UHI or Boundary Layer UHI) or surface UHI. Surface UHI refers to the increased warmth of urban surfaces, measured by using thermal infrared data from remote sensors in satellites or aircrafts, and whose effect is usually greater during the day due to the influence of solar radiation on surface temperatures. However, satellites are only able to measure land surface temperatures and not canopy air temperatures (although there are estimation models, as will be explained later), with the latter being the key parameter in UHI investigations (Azevedo, Chapman, & Muller, 2016). As just mentioned, atmospheric UHI may refer to the canopy layer, which is the layer of air contained within city surfaces (approximately up to the height of its buildings), or the boundary layer, which is located above the canopy layer and forms a dome of warmer air. Canopy layer heat islands are the ones directly related to human exposure and they are weak during the day and stronger after sunset, due to the released heat from the built environment (Rajkovich & Larsen, 2016). This is also caused by the differences in the cooling rates of rural and urban areas. The present study will focus on the canopy layer where the UHI Intensity (UHII) varies in both space and time. The UHII is defined as the difference between the urban temperature and the temperature of the reference weather station, located in a rural area in the surroundings of the study domain. There are many factors that affect the heat island phenomenon, contributing to its occurrence and intensity. Among them, the most important are: a) Climate characteristics, particularly solar radiation, wind and clouds. Research studies agree that wind and clouds diminish the heat island effect, while clear conditions and calm winds increase it (Oke, Mills, Christen, & Voogt, 2017). The main reason is that during clear days more solar energy reaches the earth’s surface. Also, light winds reduce the heat convected into the atmosphere (Oke, Mills, Christen, & Voogt, 2017). b) Season and time of day, which affect the frequency and magnitude of the heat island effect (Oke, Mills, Christen, & Voogt, 2017). Higher cooling rates in rural areas compared to urban areas increase their temperature difference, particularly during the night. c) Characteristics of the city. a. Use of materials that reduce surface reflectivity (absorbing more solar radiation), reduce water evaporation and increase heat storage. Impervious surfaces such as roads of concrete or asphalt are very frequent in urban areas. b. Vegetation and green spaces, which have low surface temperatures, increase evapotranspiration and may be used to mitigate heat islands (Oke, Mills, Christen, & Voogt, 2017). c. Urban morphology: building sizes, materials and spacing. d. Anthropogenic heat: metabolic heat from humans, traffic, and heat released from buildings. 3 Since all the previously mentioned characteristics influence the magnitude of the urban heat island and may even have opposing effects, achieving an accurate urban-scale assessment of the UHII is extremely complex. This is why many different approaches have been proposed in recent years. However, previous studies present several drawbacks for achieving accurate UHI analyses at an urban scale for extended periods. The next section will present a literature review of the approaches followed by previous studies, highlighting the existing knowledge gaps. Then, Section 1.3 will outline the main research questions and key contributions of the present study to fill those gaps. 1.2 Literature review 1.2.1 UHI estimation methods Achieving an accurate assessment of the urban microclimate is paramount for designing the most suitable solutions regarding urban heat island mitigation strategies in any location. The spatial and temporal patterns of air temperatures within a city may be very different due to the variations of its characteristics: proportion of buildings and street area, pavement type, traffic, presence of parks or trees and many other factors, as described in the previous section. In the case of Spain the UHI is a very important issue, due to the particularly warm climatic conditions in several parts of the country such as Seville. Due to this, several studies focus on the UHI effects on health in Spanish cities (such as (Royé, Codesido, Tobías, & Taracido, 2020) or (Royé, Íñiguez, & Tobías, 2020). Some of the most frequently used tools for UHI analyses are based on microclimate simulation models, in which urban areas are often represented by prototypes that are simulated using software such as ENVI-met. However, even though building and microclimate models have high resolutions in the urban canopy layer, they cannot cover entire cities due to their computational costs and complexity (Mirzaei, 2015). In fact, in many microclimate models the airflow patterns around and within buildings are resolved through the use of Computational Fluid Dynamics (CFD), but their weakness is their domain size due to the extensive computational costs. Therefore, the UHI cannot be effectively evaluated for the city scale by using this method, since there are many complex phenomena involved and unrealistic assumptions and intensive computational calculations should be avoided (Mirzaei, 2015). On the other hand, the urban heat island phenomenon may also be estimated by using experimental data. The main experimental methods to evaluate air temperatures in the urban context are: remote sensing (indirect estimation), using a network of meteorological stations, and mobile transects. Remote sensing allows to estimate Land Surface Temperatures (LST), also used to assess the UHI effect. However, the presence of clouds or the overpass times might make it unfeasible to obtain accurate estimations. From the point of view of the authors of this study, remote sensing is therefore suitable for regional scales, but not for identifying key areas of vulnerability at smaller urban scales. In addition, with remote sensing it is not possible to obtain continuous temperature data for prolonged periods. 4 Conversely, meteorological stations have traditionally been used to measure air temperatures. Data are available for extended periods in this way. However, they do not have enough spatial density to be useful in the urban context, where all environments should be represented for an accurate assessment at the district level. One attempt to do so with several weather stations is the study given in (Chen et al., 2019), which employed a high-density street level air temperature observation network with a total of 100 measurement points in various urban areas. Nevertheless, such a study is rather costly and might be unfeasible in cases with budgetary constraints. The last of the three experimental approaches for UHI estimations is the use of mobile transects. Mobile measurement systems were developed as an effective method to analyze the temperature distributions within the urban canopy layer, due to the strong influence of local urban parameters. In this way, it is possible to better understand the temperature distributions across urban areas at fine spatial resolutions (Tsin et al., 2016). This method involves mobile surveys with moving equipment (mostly done by car or bicycle), following a route designed beforehand, named “transect”. For instance, the work presented in (Pigliautile & Pisello, 2019) analyses the intra-urban microclimate diversification using cluster analysis of environmental data gathered through mobile transects. Furthermore, in (Pigliautile & Pisello, 2018), a new wearable system was developed for microclimate assessments and pedestrian thermal comfort evaluations, using mobile transects carried out on foot for their purpose. Bicycles are also an affordable and effective alternative, which is why they present an ideal solution for UHI analyses on a global scale. More information about studies based on mobile transects is given in the previous work developed by the authors of the present study, shown in (Romero Rodríguez, Sánchez Ramos, Sánchez de la Flor, & Álvarez Domínguez, 2020). Nevertheless, even though a high spatial resolution may be obtained through the mobile transects’ approach, the main problem is that the air temperature data recorded are only valid for the measurement period. If data are needed for long periods of time, continuous transects would be needed, which is unfeasible. As just seen, UHI evaluations may be performed through different approaches. However, each of them presents drawbacks when performing UHI analyses at an urban scale for prolonged periods such as days, weeks or even years. An overview of the main advantages and disadvantages of the different approaches is presented in Table 1. 5 Table 1: Advantages and disadvantages of UHI estimation approaches. Approach Advantages Disadvantages Simulation models High spatial resolution. Prototypes, not real measurements. High temporal resolution. Reduced domain size due to computational costs. Capable of identifying key areas of vulnerability. Evaluation of different UHI mitigation alternatives. Remote sensing Allows an easy collection of data for various applications. Subject to meteorological conditions. Suitable for covering large domain sizes. Low temporal resolution. Data unavailable for prolonged periods. Low spatial resolution. Meteorological stations High temporal resolution. Low spatial resolution, only valid for the location of the station. Data available for prolonged periods. Unable to identify key areas of vulnerability. Mobile transects High spatial resolution. Low temporal resolution, only valid during the measurement period. Capable of identifying key areas of vulnerability. Reduced domain size, depending on the distances covered. 1.2.2 Urban-scale heat island modelling In order to solve the issues mentioned in the previous section, several studies suggested the development of air temperature prediction models. Being able to predict urbanscale temperatures is very useful for different purposes. For instance, hourly temperature forecasts are important for electrical load forecasting and other applications in the industry, agriculture and the environment (Abdel-Aal, 2004). In addition, having a way of estimating urban-scale temperatures for extended periods would be very useful for achieving accurate energy consumption evaluations at the district (neighbourhood) scale, or if it is required to verify the impacts achieved by UHI mitigation strategies. The complexity of the UHI phenomenon, the urban details required and the increased costs and computational time of analytical modelling approaches has led to the exploration of various modelling methods to estimate urban temperatures, such as the use of statistical models or neural networks (Gobakis et al., 2011). As summarized in Table 2, different models have been proposed in the literature. Most of them derive air temperatures using statistical models that relate satellite information with air temperature measurements. To evaluate the accuracy of the proposed models, the coefficient of determination (R2) and the RMSE (Root Mean Square Error) coefficients are often calculated. These coefficients are extremely important to determine whether the applied methodology was accurate to estimate the air temperatures or not. The higher the R2 and the lower the RMSE, the better the accuracy of the estimations. 6 Table 2: Studies for UHI estimation using numerical models. Study Methodology (Mathew, Sreekumar, Khandelwal, & Kumar, 2019) Created a Support Vector Regression (SVR) model using remote sensing data from the MODIS sensor to predict LSTs. (Lazzarini, Marpu, Eissa, & Ghedira, 2014) or (Schuch, Marpu, Masri, & Afshari, 2017) Derived a correlation between air temperatures measured at ground weather stations and LSTs estimated using remotely sensed thermal infrared data. (Bechtel, Zakšek, Oßenbrügge, Kaveckis, & Böhner, 2017) Estimated air temperatures from satellite data using LSTs as predictors, using empirical models. (Janatian et al., 2017) Proposed a statistical approach using the air temperature-LST relationship, developing a model capable of estimating average air temperatures with RMSE of 2.3 °C and 1.8 °C at daily and weekly scales respectively. (Rhee & Im, 2014) Used MODIS data to estimate air temperatures for regions with limited in situ data, using observed data and artificial intelligence to derive relationships between air temperature and other variables. (Nieto, Sandholt, Aguado, Chuvieco, & Stisen, 2011) Approach based on the correlation between LST and spectral vegetation index measurements, assuming that the temperature of a full cover canopy approaches the temperature of the air within the canopy. (Hrisko, Ramamurthy, Yu, Yu, & Meleciovázquez, 2019) Presented an urban air temperature model by fitting its difference against satellite LST using a Gaussian function. (Meyer, Schmidt, Detsch, & Nauss, 2019) Developed an hourly gridded air temperature data set using MSG SEVIRI data to relate it to air temperatures measured by 78 weather stations, obtaining a prediction of air temperatures with a RMSE of 2.61 °C and a R2 of 0.89. Nevertheless, even though the previous studies perform quite well, most of them are directed at larger scales and are therefore not capable of capturing the UHI spatial and temporal differences on an hourly basis at the urban scale, which is what the present study intends. Other studies follow a more appropriate approach in this regard. An example is the study developed by (Papantoniou & Kolokotsa, 2016), which presents the development and evaluation of neural network-based identification algorithms for predicting outdoor air temperatures using the latest acquired data from local 7 meteorological weather stations, obtaining a R2 greater than 0.9 in specific locations. The study in (Abdel-Aal, 2004) also proposed using modern machine learning techniques, using the abductive networks approach for hourly temperature forecasting. Also, (Pioppi, Pigliautile, Piselli, & Pisello, 2019) coupled field monitoring with a numerical model to identify indoor and outdoor critical conditions at the present time and in the future, according to climate change forecast scenarios. Last of all, the study in (Bueno, Roth, Norford, & Li, 2014) developed a model for predicting canopy level urban air temperatures using meteorological information measured at a reference weather station located in an open area outside the city. In their case, the model is based on an energy balance at the soil surface, with transient heat diffusion equations. An analytical model for predicting diurnal air temperature variations inside an urban wooded site is also presented in (Shashua-Bar & Hoffman, 2002), based on the same principles as the Cluster Thermal Time Constant model with the addition of vegetation effects. 1.3 Aim of the study The review of existing studies shows an undeniable fact: the urban heat island is a very complex phenomenon, affected by both weather conditions and the urban context. High-density temporal and spatial data are needed so as to evaluate the UHI effect precisely in an urban scale, and also to verify the effects of mitigation strategies in an accurate way. However, achieving high spatial and temporal resolutions are conflicting interests, which is why a compromise was always needed in previous approaches. New ways for trying to overcome this issue should therefore be explored, so that urban-scale temperature data may be available for extended time periods with both high spatial resolution (estimations even for specific streets) and high temporal resolution (at least hourly). In addition, the literature lacks a comprehensive and easily replicable methodology that may be applied for this purpose in any geographical location regardless of its characteristics. As a novel approach, the present work aims to propose a new methodology for estimating urban air temperatures. This is done through the development of an empirical model based on mobile transects and a reference rural weather station. This model is capable of estimating urban-scale air temperatures with both high spatial and temporal resolutions. As far as the authors know, this is the first attempt to develop an empirical model for urban air temperature estimations based on discrete measurements taken during mobile transects. The advantages of the methodology that is going to be proposed are:  High spatial resolution (meters).  Capable of identifying key areas of vulnerability.  High temporal resolution (hourly time-steps or even less).  Accurate estimations for prolonged periods using a reference weather station.  Capable of evaluating the real impact of UHI mitigation alternatives.  Applicable for any geographical location around the world, with varying climates and population densities. 8 The present work illustrates the application of the proposed methodology in the city center of Seville (Spain). Once the optimal mobile transect is found for the area under study, the route is repeated 56 times during two weeks, at different times of the day. Linking the data of the mobile transects with the data taken by the reference weather station during the previous hours, an empirical model is obtained. The model is capable of estimating the hourly evolution of urban temperatures, based only on data from the reference weather station (air temperatures, wind speed and global horizontal radiation). Additionally, a new approach will be proposed for the estimation of the direct and diffuse solar radiation components, which will be also considered. The study is focused on the hourly temporal scale and the neighborhood or city scale, while keeping a high spatial resolution. In Section 2, the methodology will be discussed together with an explanation of the models that will be considered and the gathered data. Then, Section 3 will test the different possibilities for developing empirical models so as to find the optimal one, including a proposal to estimate the direct and diffuse solar radiations. Last of all, Section 4 will present the conclusions of this work as well as suggest potential applications of the methodology. 2 Data and methods 2.1 Selection of the optimal mobile transect The primary foundation of the present study is the consideration of mobile transects as a means of estimating urban temperatures in the long term. The work shown in (Romero Rodríguez, Sánchez Ramos, Sánchez de la Flor, & Álvarez Domínguez, 2020), written by the authors of the present study, suggested a novel methodology for designing the optimal mobile transect that should be carried out in any region. This methodology was tested and validated in the city of Seville, Spain, and is based on experimental measurements as opposed to previous studies which traditionally designed the routes of the mobile transects based on land use characteristics. Due to its geographical location in the southern part of the country, Seville has a Hot-summer Mediterranean climate according to the Köppen–Geiger climate classification system. Very high temperatures (over 40 degrees Celsius) are reached during summer, which justifies the importance of evaluating accurately the UHI effect in the area. As a first step of the methodology, an intensive mobile transect (named supertransect) should be performed in order to cover as much as possible of the study domain. The route is carried out by using a bicycle, an air temperature sensor, and a smartphone with an App to record the GPS coordinates. Then, a spatial interpolation is performed using Geographic Information Systems (GIS) to obtain continuous values for the whole region. Last of all, the average temperature of each grid cell into which the region is divided is calculated, the grid cells are classified regarding their UHII, and a route is designed to cover all the representative zones. This methodology described in the previous study is summarized in Figure 1, supplemented by the development of empirical models for predicting urban temperatures, as proposed in the present study. 15 Table 7: R2 coefficients when comparing the estimated and real hourly urban temperatures for each month. Month R2 6 0.917 7 0.955 8 0.936 9 0.934 10 0.922 11 0.868 Table 8: RMSE coefficients of daily and hourly estimations for each month. RMSE (6 months) RMSE Jun RMSE Jul RMSE Aug RMSE Sept RMSE Oct RMSE Nov Max. Daily temp. 1.25 1.04 1.19 0.82 0.57 1.47 1.74 Min Daily temp. 1.31 1.16 1.10 0.90 1.11 1.28 1.91 Average daily temp. 0.94 0.73 0.80 0.84 0.86 0.90 1.30 Hourly temp. 1.43 1.31 1.26 1.38 1.27 1.46 1.64 3.2 Amount of data required from the mobile transects Another interesting issue that should be discussed, is the number of times that the optimal mobile transect should be carried out so as to obtain a precise model. Also, it is important to figure out whether the times when they are carried out are also decisive. In this section, we will maintain the model with 12 air temperature coefficients and 2 coefficients for the wind speed and the solar radiation measured by the reference weather station, but the number of mobile transects used for training the model will be changed. The results of the models will be tested when considering 14, 28, 42 and 56 transects, and two additional models will be obtained by using only the transects performed from 14h to 22h (in the afternoons) and from 8h to 22h (during daylight hours). Table 9 and Figure 6 show the results. As may be seen, performing only 14 mobile transects would result in a very erratic model, with a very weak correlation between the estimated and the real urban air temperatures, as well as high RMSEs. Considering 28 mobile transects increases the accuracy in a great way, reaching a R2 coefficient of 0.926. However, the RMSE values are still quite high. Once 42 mobile transects are carried out, the quality of the model begins to be acceptable, since a R2 value of 0.946 and an RMSE of 1.773 are achieved. The model with 56 mobile transects throws the best results. On the other hand, as previously commented it would also be important to know whether the times when the mobile transects are carried out are decisive or not in order to obtain an accurate model. The results show that, if the mobile transects had only been carried out from 14h to 22h (29 mobile transects in total), the outcomes of the model would be very inaccurate. Particularly, the daily minimum temperature RMSE is very high. The reason for this is that the minimum daily temperature in the area under 16 study is achieved around 7h-8h, so if no mobile transects are carried out around this time, the model is not capable of estimating the minimum temperatures in a precise way. Last of all, if the mobile transects were carried out from 8h to 22h (a total of 34 transects are considered in this case), the results regarding minimum temperatures would greatly improve compared to the previous case due to the mentioned reasons. However, the results are still worse than the case with 56 mobile transects, since no routes are performed after 23:00. Since the UHI effect is stronger after sunset, this means that for instance the maximum temperatures would not be estimated so well. The main conclusion is therefore that the higher the number of mobile transects the better, performed at as many different times as possible so as to be capable of capturing the shape of the hourly curve. Table 9: Results of the model when modifying the number of mobile transects used to obtain the model. R2 RMSE Daily Max. Temp. Daily Min. Temp. Daily Average Temp. Hourly temp. Daily Max. Temp. Daily Min. Temp. Daily Average Temp. Hourly temp. 14 TRANSECTS 0.765 0.696 0.943 0.555 5.473 5.088 1.512 4.012 28 TRANSECTS 0.954 0.893 0.984 0.926 3.128 2.750 0.938 2.278 42 TRANSECTS 0.965 0.914 0.984 0.946 1.638 2.217 0.922 1.773 56 TRANSECTS 0.978 0.944 0.983 0.960 1.254 1.306 0.940 1.428 From 14h to 22h 0.883 0.691 0.966 0.688 3.178 5.229 1.021 4.176 From 8h to 22h 0.962 0.897 0.983 0.921 2.041 2.324 1.359 2.310 17 Figure 6: Correlations of the model when modifying the number of mobile transects used to obtain the model. 3.3 Improving the model Once an optimal number of temperature coefficients has been found and the amount of data needed has been discussed, the present section aims to further improve the model and solve the issue mentioned at the end of Section 3.1 regarding the amount of solar radiation absorbed by the urban canopy layer throughout the year. Thus, this section will maintain the model with data from the 56 mobile transects, 12 air temperature coefficients and 2 coefficients for the wind speed, but a different approach will be followed to account for the solar radiation. 3.3.1 Decomposition of the global horizontal radiation Although most weather stations are capable of providing hourly values of the global solar radiation on a horizontal surface, the proportions of direct and diffuse radiation, which are very important due to their influence regarding the solar gains in the urban 18 canopy layer, are frequently unavailable. The present section describes a novel procedure to carry out this decomposition, based on standard weather files. The State Meteorology Agency in Spain (AEMET) provides weather files with typical hourly climatic values of every province in Spain. Among the available data, the values of direct and diffuse horizontal radiation are known, as well as the azimuth and solar height for every hour of the year determined as a function of the latitude and longitude of the location. Therefore, it is possible to know the solar position at any time. The process which is going to be described below will be fed by the data of those standard files, so that the real measurements may be compared with the data of the reference climate for the area under study. First of all, a reference weather file with all the necessary hourly data is found for the study domain: outdoor temperature, direct and diffuse radiation, azimuth, zenith and so on are thus known. Using this reference weather file which contains all the necessary variables, the daily global radiation is then calculated for every day of the year. The same is done for the measured global radiation, which is available from the reference weather station. Then, a comparison is made between the measured daily global radiation and the daily global radiation of the previous and the following 15 days of the reference weather file. Having a sample of 30 days, the two most similar days of the reference weather file are chosen. Then, the proportion of direct/global radiation of these two days is calculated for every hour of the standard file. Finally, the decomposition of the real direct and diffuse radiations is made by considering the average proportions of direct/diffuse radiations of those two days of the standard file, for every hour. In this way, the proposed procedure is capable of linking the measurements with days of similar cloud conditions in the reference climate. The process is summarized in Figure 7. The estimated direct and diffuse hourly radiations of the real measurements are thus calculated by keeping the direct/global and diffuse/global average proportions of the two most similar days of the reference weather file, for each hour independently. Figure 7: Process followed for the decomposition of the global horizontal solar radiation. 19 The results of the proposed approach were validated using data of a weather station in Madrid (Spain) which also measured the direct and diffuse components. Using only the global horizontal radiation, the direct and diffuse solar radiations were estimated with the proposed procedure and then compared with the real measurements. An example of this comparison may be seen in Figure 8 for the direct radiation in the months of January and July, showing satisfactory results for the estimation. The comparison of the total daily direct radiation is also shown in Figure 9. Figure 8: Hourly comparison of the measured and estimated direct radiation in January (up) and July (down). Figure 9: Comparison of the daily measured and estimated direct radiation in the whole year. 3.3.2 Optimal model for urban temperatures estimation through mobile transects Having a way to estimate the hourly direct and diffuse solar radiations, the question that now arises is whether these data may be helpful in order to improve the results of the proposed model. This is due to the fact that the position of the sun throughout the year influences the amount of solar radiation that may be absorbed by the urban canopy 20 layer, and the direct and diffuse solar radiations offer an insight into these solar absorption fluctuations. The procedure described in the previous section was followed in order to estimate the hourly direct and diffuse solar radiations in our case study, using the global horizontal radiation measured at the reference weather station and a standard weather file of the province of Seville. An example of the obtained decomposition is shown in Figure 10 for the 7th of December, and the monthly ratios of direct and diffuse radiation are shown in Figure 11. Figure 10: Decomposition of the measured global radiation for the 7th of December 2019. Figure 11: Ratios of direct and diffuse solar radiation for each month. This decomposition allows us to study the impact of the monthly direct and diffuse ratios on the R2 that was obtained by model 12 in Section 3.1. As it may be seen in Figure 12, the higher the ratio of diffuse radiation the lower the R2 obtained by that model, which only considered global horizontal solar radiation data. Thus, the importance of considering the direct and diffuse components is evident. 21 Figure 12: Comparison of the monthly R2 obtained by model 12 depending on the monthly ratios of diffuse solar radiation. Several variations of model 12 were therefore tested, considering different numbers of coefficients for the direct, diffuse and global solar radiation and also for the ratio of diffuse radiation. After doing so, the optimal model was found, which involved using 3 coefficients for the direct solar radiation and 3 coefficients for the ratio of diffuse radiation. Therefore, the coefficients of this model (shown in Equation 1) are: 12 coefficients for the air temperature, 2 for the wind speed, 3 for the direct radiation and 3 for the proportion of diffuse radiation. The results of this optimal model are described below in detail. 𝑇𝑢𝑟𝑏𝑎𝑛 = 𝑇𝑟𝑒𝑓𝑡−1 · 𝑐1+ … + 𝑇𝑟𝑒𝑓𝑡−12 · 𝑐12 + 𝑊𝑡−1 · 𝑐13 + 𝑊𝑡−2 · 𝑐14 + 𝑅𝐷𝐼𝑅−1 · 𝑐15 + 𝑅𝐷𝐼𝑅−2 · 𝑐16 + 𝑅𝐷𝐼𝑅−3 · 𝑐17 + 𝑃𝐷𝐼𝐹−1 · 𝑐18 + 𝑃𝐷𝐼𝐹−2 · 𝑐18 + 𝑃𝐷𝐼𝐹−3 · 𝑐20 Equation 1: Coefficients of the optimal model. Tref is the temperature recorded by the reference weather station, W is the wind speed, RDIR the direct solar radiation, and PDIF is the proportion of diffuse solar radiation. First of all, Figure 13 shows the comparison between the hourly temperatures estimated by the model and the measurements of the fixed temperature sensor, during the two weeks when the optimal mobile transect was carried out. The average temperatures recorded by the mobile transects are also shown. As it may be seen, the prediction made by the model during this period is very accurate, following the same patterns as the hourly curve of the fixed temperature sensor. It can also be observed how the temperatures of the weather station differ from the urban temperatures: during the day the temperatures are very similar, but after sunset the cooling rate of rural areas is much higher (due to the higher sky view factors or the lack of stored heat among other circumstances). This is why the highest UHII values are achieved during the night, particularly just before sunrise. 22 Figure 13: Comparison between the hourly temperatures estimated by the model and the measurements of the fixed temperature sensor. The measurements of the mobile transects and the reference weather station are also shown. On the other hand, the scatter plot in Figure 14 shows the strength of the relationship between the hourly urban temperature predicted by the model and the real measurements recorded by the fixed temperature sensor, for the whole period of six months where data was available for validation. As is apparent, the estimates are quite accurate, with a R2 coefficient of 0.976. Figure 14 (right) also shows the distribution of hourly temperature differences between the real and the estimated values. For instance, 37% of the data has a temperature difference between -1 °C and 0 °C, and high errors are rather infrequent. Table 10 shows that the model is capable of estimating 84 % of the hourly urban temperatures during the whole period of 6 months with errors lower than 10 %. Even higher percentages are achieved for daily estimates. Figure 14: Relationship between estimated and real hourly urban temperatures. Table 10: Percentages of error when estimating the urban tempeature through the developed model. Error percentage <2 % <5% <10% Max. Daily temp. 41% 82% 92% Min Daily temp. 28% 57% 78% Average daily temp. 33% 77% 92% Hourly temp. 28% 65% 84% 23 Regarding the results of the R2 coefficient for the hourly temperature estimations of each month, Table 11 (results for the improved model with direct and diffuse solar radiation data) shows values always above 0.942. Comparing these outcomes with the ones of model 12 (shown in Section 3.1), which didn’t consider the direct and diffuse components, it may be seen that the results are greatly improved (see Figure 15). Table 11: R2 coefficients when comparing the estimated and real hourly urban temperatures for each month. Month R2 6 0.957 7 0.952 8 0.970 9 0.951 10 0.944 11 0.942 Figure 15: Comparison of the previous model (Table 7) and the improved model with direct and diffuse components (Table 11). Also, Table 12 shows that the RMSE for the whole 6 months has been reduced from 1.42 to 1.21, and the R2 increased from 0.96 to almost 0.98. In particular, the hourly results for November for instance, which had very different climatic conditions than the ones measured during the mobile transects, greatly improved: the RMSE decreased from 1.64 to 1.18, and the R2 coefficient increased from 0.868 to 0.942. This proves that having direct and diffuse solar radiation data (or at least estimations) offers an optimal way to improve the estimations of the proposed empirical model. Table 12: RMSE coefficients of daily and hourly estimations for each month. RMSE (6 months) RMSE Jun RMSE Jul RMSE Aug RMSE Sept RMSE Oct RMSE Nov Max. Daily temp. 0.94 0.87 0.79 0.86 1.17 0.97 0.95 Min Daily temp. 1.24 1.30 1.13 0.85 1.18 1.47 1.38 Average daily temp. 0.83 0.82 0.86 0.67 0.77 0.86 0.94 Hourly temp. 1.21 1.11 1.16 1.02 1.17 1.31 1.18 24 3.4 UHI intensity Once an empirical model has been obtained to estimate the urban air temperatures of a certain location, the UHII may be easily inferred by comparing these temperatures with those of the reference weather station at the same times. As an example, Figure 16 shows the evolution of the UHII estimated by the optimal model during 5 days of June 2019. Note that the UHII may be evaluated for as many locations as desired. The estimations are only limited by the domain size covered during the supertransect, which is used to link each location with the most similar UHII category. Then, an empirical model may be obtained for each UHII category, with the same amount of mobile transects. This will be further discussed in the next section. Figure 16: Estimated UHII evolution during 5 days in June 2019. 3.5 Development of the model for different areas The most immediate possibility of the proposed methodology is the development of a single model which would estimate the most representative urban temperature of the region under study, feeding the model with the average temperature recorded during each mobile transect. However, it would be possible to develop as many models as the number of different areas that may be found in the region under study. This is done by performing the same amount of mobile transects as for one single model, since the designed route, as explained in Section 2.1, is capable of going through all the representative areas of the region under study. Eventually, it would be even possible to develop the model for a specific street, since GIS allow to compute the average temperature in any specific area thanks to the availability of GPS coordinates. In order to illustrate this possibility, Figure 17 shows the results when obtaining 2 models with 12 temperature coefficients, but this time only considering the temperatures recorded in grid cells 32 and 55 (the coldest and warmest categories respectively, as shown in (Romero Rodríguez, Sánchez Ramos, Sánchez de la Flor, & Álvarez Domínguez, 2020)). 56 air temperature values are therefore used for training each model. As it may be seen, in this case the hourly estimated temperatures are similar during the night, but very different during daylight hours. This is due to the different characteristics of the two grid cells, which differ for instance regarding their anthropogenic heat: a value of 8.9 W/m2 was estimated for grid cell 32, while a value of 16.2 W/m2 was found for grid cell 55.