# Application of a Semi-Empirical Approach to Map Maximum Urban Heat Island Intensity in Singapore

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{max}) intensities during nighttime over the city of Singapore for specific weather conditions. By adopting the methodology proposed by Theeuwes et al., but selecting meteorological and morphological parameters that affect UHI

_{max}intensity most for Singapore, evaluation of the developed equation shows good agreement with observations (RMSE = 1.13 K and IOA = 0.76). Model performance depends strongly on wind conditions and is best during weak winds when ‘ideal’ conditions for UHI development are approached (RMSE = 0.65 K and IOA = 0.85). Results using the simple equation developed to map UHI

_{max}intensities in Singapore under dry weather conditions are comparable to those obtained from more sophisticated numerical models, which demand significant computational resources, and the complex parameterizations involved require expertise to carry out the simulations. The resulting maps of the present study can be used to investigate less favorable thermal conditions and assess population vulnerability to a certain temperature excess, as well as provide insights for urban planning strategies of mitigation measures according to the land cover and morphology of a location.

## 1. Introduction

_{max}) using long-term observations in tropical Singapore. To achieve this purpose, we adapt the methodology proposed in T17 to better represent the local characteristics of Singapore. A number of past studies have already analyzed the spatial and temporal evolution of CL-UHI intensity over Singapore using observations [37,38,39] and numerical simulations [40]. However, the present study provides an alternative method to estimate spatial patterns of maximum CL-UHI intensities that is easy to apply and provides detailed spatial information on the local-scale air temperature variability under selected meteorological conditions. Section 2 provides a description of the study area, observation network, local climate, and urban morphological characteristics of Singapore. The original T17 model is applied to Singapore in Section 3. Section 4 introduces the modified model for Singapore, which is evaluated in Section 5. Maps of UHI

_{max}intensities for different weather conditions are shown in Section 6, followed by a discussion and concluding remarks in Section 7.

## 2. Study Area, Observational Data, and Urban Morphological Characteristics

^{2}[41] (Figure 1). Most of the terrain is low-lying with little change in topography across the island. The highest point is 168 m a.s.l., located in a nature reserve close to the center of the island, which is also home to several freshwater reservoirs. Regarding land cover classification, the local climate zone (LCZ) scheme is sometimes used to divide the landscape into regions of uniform surface cover, structure, material, and human activity, having a characteristic CL air temperature [42]. The LCZ map for Singapore is developed using Google Earth Engine, a cloud-based platform for planetary-scale geospatial analysis [43,44]. The procedure consists of classifying several times the training areas developed for Singapore into LCZ categories, using satellite data products within the period 2014–2016, and the final LCZ map comprises the modal category [45]. The most predominant built type region in Singapore is LCZ 4 (open high-rise), followed by LCZs 9 (sparsely built) and 8 (large low-rise), respectively (Figure 1, [45]).

_{max}magnitude is computed as the maximum difference of hourly air temperature at any urban station (${T}_{2m,urb}$) minus the air temperature at the rural reference station (${T}_{2m,rur}$) during nighttime (from 20 LT to 06 LT): UHI

_{max}= ${T}_{2m,urb}-{T}_{2m,rur}$. Here, ${T}_{2m,rur}$ is calculated as the average of stations S16 and S23 (see R22 for further explanations on the selection of the rural reference sites). R22 presents a detailed analysis of the effect of weather on CL-UHI, with the highest magnitudes observed during dry, calm, and clear nights. Using the same filtering approach for ‘ideal’ conditions as in R22 leaves only 36 nights or 3.5% of the entire dataset. This sample size is too small for rigorous analysis. Hence, the present study only filters for rainfall by excluding days with >0.2 mm rainfall measured simultaneously at the five MSS stations. The remaining dataset for further analysis comprises 303 dry days (30% of the original data).

## 3. Application of Diagnostic Equation Proposed in Theeuwes et al. [33]

^{−1})), DTR the daily temperature range (DTR (K) = ${T}_{max}-{T}_{min}$), and ${U}_{24h,av}$ the 24 h average 10 m wind speed (m s

^{−1}), all measured at a rural reference site. The SVF at the station location is estimated from building height and street width data, and ${F}_{veg}$ is the vegetation fraction within a 500 m circle centered on the urban station. Equation (1) is only valid over the parameter range for which it has been developed, which for SVF and ${F}_{veg}$ are 0.2 to 0.9 and 0 to 0.4, respectively. Hence, our stations S4, S7, S21, S32, and S47 are excluded from the evaluation. Also, since the present study did not measure ${K}_{in}$ and ${U}_{24h,av}$ at our rural sites, we use respective data from the Changi weather station (Figure 1). Given that Changi is an official WMO weather station (WMO Index Number: 48698) and considering the absence of significant topography and little variability of synoptic conditions across the relatively small size of Singapore, we assume that the Changi data is representative of regional weather and hence similar day-to-day variability is expected to that at the rural sites. Therefore, using ${K}_{in}$ and ${U}_{24h,av}$ at Changi station, DTR measured at the rural site and SVF, and ${F}_{veg}$ from Table 1, the proposed equation in T17 (Equation (1)) is applied to predict UHI

_{max}intensities at 19 urban stations for the 303 dry days of the study period. Modeled UHI

_{max}magnitudes are compared with observed UHI

_{max}intensities at the selected urban stations (Figure 2a).

_{max}is slightly overestimated, and the relationships show considerable scatter (Figure 2a).

- Different reference stations are used for the weather variables. ${K}_{in}$ and ${U}_{24h,av}$ are mainly considered in the equation to determine the seasonal variability of weather conditions within the study period. Although similar day-to-day variability is expected at Changi compared to the rural site, the magnitude, particularly for wind speed, might vary.
- The rural reference sites are characterized by different land cover types. LCZ D (low plants) is used in T17, but LCZ B (scattered trees) in the present study. DTR for the former is therefore likely larger since daytime air temperature will be higher over an open area, compared to a partially shaded area. This discrepancy could be responsible for the large scatter in Figure 2b, as compared to the strong relationship between UHI
_{max}and DTR observed in T17.

_{max}intensities for the specific local climate and urban geometry of Singapore.

## 4. Development of the Model Equation for Singapore

_{max}intensities. A set of dimensionless groups is defined from such variables through dimensionless analysis [30], from which a relationship with UHI

_{max}is determined empirically using data from 24 urban stations and 303 dry days.

#### 4.1. Selection of Independent Variables

#### 4.1.1. Land Cover and Morphological Parameters

_{max}increases with urban fraction (${F}_{urb}$) and decreases with ${F}_{veg}$, with a slightly lower correlation coefficient for the latter (Figure 3). Street geometry can be characterized by street aspect ratio (H/W) and SVF. In the present study, H/W is the average for an area within a 300 m circle centered on the station, and SVF is determined from fisheye images at the actual station location [47]. Scatter plots do not reveal a clear trend of UHI

_{max}with the local SVF (R = 0.13, Figure 3d). On the other hand, a good fit in the form of an exponential relationship is found for H/W (R = 0.77, Figure 3c). Therefore, ${F}_{urb}$ and H/W are selected as key independent variables to build our model.

#### 4.1.2. Meteorological Variables

_{max}intensity.

_{max}and ${T}_{a,ref}$ and ${T}_{d,ref}$ (Figure 4a), except for the highest magnitudes (UHI

_{max}> 6 K). The reason for this is that UHI

_{max}is at the time also affected by other meteorological variables and hence the difficulty to find an individual relationship with only one parameter. The scatter points with the highest UHI

_{max}intensities in Figure 4a occur for high ${T}_{a,ref}$ but low ${T}_{d,ref}$, which would indicate air humidity diminishes, and it also coincides with low wind speed conditions (${U}_{ref}$ < 1.5 m s

^{−1}) (Figure 4b). We therefore use ${T}_{a,ref}$, ${T}_{d,ref}$, ${U}_{ref}$, and ${K}_{in}$ as indicators of further weather variability within the 303 dry days selected.

#### 4.2. Development of the Model Equation for Singapore

^{−1}), nocturnal ${U}_{ref}$ (m s

^{−1}), ${T}_{a,ref}$ and ${T}_{d,ref}$ (K) measured at the reference Changi station, as well as land cover and morphological characteristics ${F}_{urb}$ and H/W, respectively.

_{max}magnitudes over Singapore becomes:

## 5. Model Evaluation

_{max}using the test dataset (Figure 7). Model results show an acceptable agreement with observations (IOA = 0.76) and R = 0.58 (Figure 7) and slightly improve compared to applying the model equation (Equation (1)) proposed by T17 (Figure 2). Overall, the model slightly underestimates observed UHI

_{max}and error metrics are similar to those observed in other studies using Equation (1) (Table 2).

_{max}variability across the selected stations with IOA varying between 0.59 and 0.76. The worst model agreement is obtained at S21 (LCZ 6). This is likely due to the low number of data points at the low end of ${F}_{urb}$, since only three urban stations have ${F}_{urb}$ below 0.45.

_{max}as a function of weather conditions variability. Further analysis at the individual station level reveals that scatter increases with stronger reference wind speed (not shown). Hence, further analysis is conducted to quantify model accuracy as a function of ${U}_{ref}$ (Figure 9). Absolute errors calculated as the difference between modeled and observed UHI

_{max}magnitudes for all stations confirm that the smallest differences (<1 K) are usually found when ${U}_{ref}$ is <2.5 m s

^{−1}(Figure 9). Equation (3) is mainly developed to estimate UHI

_{max}intensities according to urban parameters, whose influence on UHI development is most pronounced under calm wind conditions. The best performance of the model is therefore obtained for low reference wind speeds (Table 3), which correspond to the largest UHI

_{max}values and maximum influence from local characteristics (e.g., H/W and ${F}_{urb}$).

## 6. Mapping Spatial Patterns of UHI_{max} Intensities

_{max}intensity under dry conditions for different seasons. Figure 10 shows the spatial distribution of UHI

_{max}calculated as the mean of 36 ‘ideal’ (dry, calm, and clear) nights within the study period. The corresponding scatter plot reveals a very good correlation with observations (R = 0.85) and low prediction errors (RMSE = 0.65 K and MEAE = 0.55 K) (Table 4). These evaluation metrics confirm the better performance of the model during low wind conditions, which coincides with the maximum UHI

_{max}intensity (Figure 10b).

_{max}intensities reach 5.5–6.0 K covering around 1% of the total area and are mainly located in the densely built-up financial and business districts (LCZ 1) close to the south-central coast. Other areas with UHI

_{max}> 4.5 K can be found in high-density residential districts (LCZ 2) in the southeast and industrial areas (LCZ 8) in the southwest of Singapore. The spatial average of the modeled UHI

_{max}across built-up areas is 2.64 K, which can be interpreted as the maximum nighttime city-wide average air temperature increment caused by the presence of the city. The most frequent UHI

_{max}intensity range across the city is between 4.0 and 4.5 K, covering 16.4% of the urban area. The second most frequent range of 0.0–0.5 K covers 15.4% of the built-up area and is found next to the coast or bordering reservoirs, parks, and secondary rainforests. In addition, the gridded model results for the mean UHI

_{max}are used to analyze the spatial distribution based on the urban LCZ classification by resampling the original (100 m) map [45] to the present 300 m resolution (Figure 10c). The highest UHI

_{max}intensities are found in LCZs 2 and 1, with the highest magnitude of 6.1 K corresponding to a grid cell pixel located in the business district belonging to LCZ 1. The distribution of the spatial analysis follows the expected variability of urban–rural differences as a function of the LCZ class [42]. The present results are similar to those observed in previous studies in Singapore under ‘ideal’ heat island conditions [37,39] and support the utility of the present simple statistical modeling approach.

_{max}observed across all stations during the study period. UHI

_{max}variability across the city is low on 5 February 2012, with the most frequent UHI

_{max}magnitude band of 2.0–2.5 K covering 25.7% of the total built-up area (Figure 11a). Maximum values barely exceed 3.0 K (0.3% of the area), and the average nighttime temperature increment due to built-up areas across the city is 1.49 K. Comparison with observations shows good model performance (Table 4). February is part of the Northeast monsoon season and characterized by cloudy and rainy conditions, but the model nevertheless works well for dry periods during this otherwise wet month.

_{max}variability is much larger when values are higher, as shown by the map for 19 June 2013 (Figure 11b). Five stations recorded their highest UHI

_{max}intensity on this day, with the highest value of 7.53 K observed at S07 (LCZ 1) [39]. June coincides with the inter-monsoon period, which is characterized by calm winds and clear skies, both of which maximize heat island development and hence differences across different land covers. Unlike for February, the UHI

_{max}probability distribution shows larger magnitudes and hence larger differences across different urban areas. The most prevalent UHI

_{max}temperature bin is 6.0–6.5 K and covers 11.6% of the built-up area. Maximum intensities reach between 8.0 and 8.5 K. This is slightly higher than what was observed, but this particular range is only modeled over 0.1% of the built-up area, and 5% of the area shows UHI

_{max}values > 7.0 K as observed at five stations. This confirms that the model is able to accurately capture the peak UHI

_{max}values during these conditions. Model error metrics more generally also suggest good performance for this particular day (Table 4). The available spatial data also enable predicting the area (and population) exposed to a certain urban temperature excess, an important measure related to human thermal comfort. In the case of this particular day, 50% of the city’s built-up area, for example, was experiencing an UHI

_{max}of 4.5 K or higher.

_{max}values and variability across the city experienced in February (June) (Figure 11c,d), as a result of the particular weather conditions in each month pointed out above. The spatial distribution is similar in both months, with the highest and lowest UHI

_{max}values obtained over the more heavily built-up and greener areas, respectively. The maximum February (June) UHI

_{max}values do not exceed 4.0 (5.0) K, and the probability distribution peaks between 3.0 and 3.5 (3.5–4.0) K, with ∼50% of the built-up area experiencing UHI

_{max}values > 2.0 (2.5) K. Highest values always correspond to the south-central coast classified as LCZ 1. The mean UHI max across all built-up areas in February (June) is 1.94 (2.33) K. The model evaluated across all days of the respective month shows again good performance with a high R of 0.83 and prediction errors of between 0.52 and 1.01 K (Table 4).

## 7. Summary and Conclusions

_{max}intensities in Singapore using the dimensional analysis technique and long-term (∼3 years) observations. The main purpose is to generate a simple and fast method to map the spatial distribution of UHI

_{max}for dry weather conditions based on ${F}_{urb}$ and H/W.

_{max}and DTR [33]. We therefore develop a similar statistical model but adapted to predict UHI

_{max}intensities during dry conditions in Singapore using the methodology proposed in T17. The main results are as follows:

- Evaluation of the model adapted to Singapore (Equation (3)) shows overall good agreement with observations of daily UHI
_{max}for different dry weather conditions. - Model performance shows a strong dependency of the estimated UHI
_{max}on wind speed. Best performance is reached for low wind speed (<2.5 m s^{−1}at the reference site). During these conditions, the model provides reliable estimations of UHI_{max}with low errors (RMSE and MEAE < 1 K) and a high level of agreement with observations (R > 0.80). - Estimates for UHI
_{max}tend to underpredict observed values over open low-rise areas (LCZ 6) (R < 0.5). The paucity of stations with low ${F}_{urb}$ values (0.3–0.6), compared to the majority of stations that are placed in more densely built-up environments (${F}_{urb}$ > 0.6), is one reason why the model is less robust over these open urban landscapes. Given nevertheless significant UHI_{max}magnitudes over less developed urban spaces, we suggest increasing the placement of stations in these areas. - The low prediction errors (RMSE < 1.2 K and MEAE < 1 K) obtained at every station and for different seasons in Singapore reveal that the accuracy of this simple semi-empirical equation might be comparable to the performance for dry weather conditions of more sophisticated numerical models (e.g., WRF or uSINGV), which include complex building effect parameterizations.

_{max}intensity across the tropical city of Singapore. However, there is still potential for improvement. Although the spatial performance of the estimated UHI

_{max}is consistent with the expected results according to the LCZ classification, the model should also be evaluated at different measurement points from the locations used to build the equation in order to confirm its accuracy across the entire city. Additional improvements might be incorporated for even better performance, e.g., the inclusion of other factors known to influence the UHI, such as local anthropogenic heat fluxes. The latter would particularly improve the estimation of UHI

_{max}magnitudes in areas known to have high anthropogenic heat emissions, such as certain industrial estates or commercial centers with dense building configurations and high traffic volumes.

_{max}maps that are easy to calculate based on a few input variables. The present semi-empirical equation performs best during calm wind conditions, which coincides with maximum UHI development and highest UHI

_{max}values. This is an important result as these situations are associated with reduced outdoor thermal comfort and higher health risk. Hence, the resulting maps can be used to investigate less favorable thermal conditions and assess the population vulnerability to a certain temperature excess and thus identify risk levels of a target region [51]. Additionally, the spatial distribution of the modeled UHI

_{max}can provide insights for urban planning strategies [52], as well as for designing corresponding mitigation measures according to the land cover and morphology of a location.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Calculation of the Dimensionless Π Variables

## References

- Stewart, I.D. Why should urban heat island researchers study history? Urban Clim.
**2019**, 30, 100484. [Google Scholar] [CrossRef] - Oke, T.R.; Mills, G.; Christen, A.; Voogt, J.A. Urban Climates; Cambridge University Press: Cambridge, UK, 2017. [Google Scholar] [CrossRef]
- Rizwan, A.M.; Dennis, L.Y.; Chunho, L. A review on the generation, determination and mitigation of Urban Heat Island. J. Environ. Sci.
**2008**, 20, 120–128. [Google Scholar] [CrossRef] [PubMed] - Steeneveld, G.J.; Koopmans, S.; Heusinkveld, B.; Van Hove, L.; Holtslag, A. Quantifying urban heat island effects and human comfort for cities of variable size and urban morphology in the Netherlands. J. Geophys. Res. Atmos.
**2011**, 116, D20. [Google Scholar] [CrossRef] - Schatz, J.; Kucharik, C.J. Seasonality of the urban heat island effect in Madison, Wisconsin. J. Appl. Meteorol. Climatol.
**2014**, 53, 2371–2386. [Google Scholar] [CrossRef] - Oke, T.R. The urban energy balance. Prog. Phys. Geogr.
**1988**, 12, 471–508. [Google Scholar] [CrossRef] - Oke, T.R. Canyon geometry and the nocturnal urban heat island: Comparison of scale model and field observations. J. Climatol.
**1981**, 1, 237–254. [Google Scholar] [CrossRef] - Unger, J. Intra-urban relationship between surface geometry and urban heat island: Review and new approach. Clim. Res.
**2004**, 27, 253–264. [Google Scholar] [CrossRef] - Yuan, C.; Chen, L. Mitigating urban heat island effects in high-density cities based on sky-view factor and urban morphological understanding: A study of Hong Kong. Archit. Sci. Rev.
**2011**, 54, 305–315. [Google Scholar] [CrossRef] - Zoulia, I.; Santamouris, M.; Dimoudi, A. Monitoring the effect of urban green areas on the heat island in Athens. Environ. Monit. Assess.
**2009**, 156, 275–292. [Google Scholar] [CrossRef] - Oliveira, S.; Andrade, H.; Vaz, T. The cooling effect of green spaces as a contribution to the mitigation of urban heat: A case study in Lisbon. Build. Environ.
**2011**, 46, 2186–2194. [Google Scholar] [CrossRef] - Konarska, J.; Holmer, B.; Lindberg, F.; Thorsson, S. Influence of vegetation and building geometry on the spatial variations of air temperature and cooling rates in a high-latitude city. Int. J. Climatol.
**2016**, 36, 2379–2395. [Google Scholar] [CrossRef] - Freitas, E.D.; Rozoff, C.M.; Cotton, W.R.; Dias, P.L.S. Interactions of an urban heat island and sea-breeze circulations during winter over the metropolitan area of São Paulo, Brazil. Bound.-Layer Meteorol.
**2007**, 122, 43–65. [Google Scholar] [CrossRef] - He, B.J.; Ding, L.; Prasad, D. Relationships among local-scale urban morphology, urban ventilation, urban heat island and outdoor thermal comfort under sea breeze influence. Sustain. Cities Soc.
**2020**, 60, 102289. [Google Scholar] [CrossRef] - Skarbit, N.; Stewart, I.D.; Unger, J.; Gál, T. Employing an urban meteorological network to monitor air temperature conditions in the ‘local climate zones’ of Szeged, Hungary. Int. J. Climatol.
**2017**, 37, 582–596. [Google Scholar] [CrossRef] - Stewart, I.D. A systematic review and scientific critique of methodology in modern urban heat island literature. Int. J. Climatol.
**2011**, 31, 200–217. [Google Scholar] [CrossRef] - Arnds, D.; Böhner, J.; Bechtel, B. Spatio-temporal variance and meteorological drivers of the urban heat island in a European city. Theor. Appl. Climatol.
**2017**, 128, 43–61. [Google Scholar] [CrossRef] - Giannaros, T.M.; Melas, D.; Daglis, I.A.; Keramitsoglou, I.; Kourtidis, K. Numerical study of the urban heat island over Athens (Greece) with the WRF model. Atmos. Environ.
**2013**, 73, 103–111. [Google Scholar] [CrossRef] - Chen, F.; Yang, X.; Zhu, W. WRF simulations of urban heat island under hot-weather synoptic conditions: The case study of Hangzhou City, China. Atmos. Res.
**2014**, 138, 364–377. [Google Scholar] [CrossRef] - Yang, B.; Zhang, Y.; Qian, Y. Simulation of urban climate with high-resolution WRF model: A case study in Nanjing, China. Asia-Pac. J. Atmos. Sci.
**2012**, 48, 227–241. [Google Scholar] [CrossRef] - Salamanca, F.; Martilli, A.; Yagüe, C. A numerical study of the Urban Heat Island over Madrid during the DESIREX (2008) campaign with WRF and an evaluation of simple mitigation strategies. Int. J. Climatol.
**2012**, 32, 2372–2386. [Google Scholar] [CrossRef] - Gutiérrez, E.; González, J.E.; Martilli, A.; Bornstein, R.; Arend, M. Simulations of a heat-wave event in New York City using a multilayer urban parameterization. J. Appl. Meteorol. Climatol.
**2015**, 54, 283–301. [Google Scholar] [CrossRef] - Li, H.; Zhou, Y.; Wang, X.; Zhou, X.; Zhang, H.; Sodoudi, S. Quantifying urban heat island intensity and its physical mechanism using WRF/UCM. Sci. Total Environ.
**2019**, 650, 3110–3119. [Google Scholar] [CrossRef] [PubMed] - Kusaka, H.; Chen, F.; Tewari, M.; Dudhia, J.; Gill, D.O.; Duda, M.G.; Wang, W.; Miya, Y. Numerical simulation of urban heat island effect by the WRF model with 4-km grid increment: An inter-comparison study between the urban canopy model and slab model. J. Meteorol. Soc. Jpn.
**2012**, 90, 33–45. [Google Scholar] [CrossRef] - Sharma, A.; Fernando, H.J.; Hamlet, A.F.; Hellmann, J.J.; Barlage, M.; Chen, F. Urban meteorological modeling using WRF: A sensitivity study. Int. J. Climatol.
**2017**, 37, 1885–1900. [Google Scholar] [CrossRef] - Bottyán, Z.; Unger, J. A multiple linear statistical model for estimating the mean maximum urban heat island. Theor. Appl. Climatol.
**2003**, 75, 233–243. [Google Scholar] [CrossRef] - Hoffmann, P.; Krueger, O.; Schlünzen, K.H. A statistical model for the urban heat island and its application to a climate change scenario. Int. J. Climatol.
**2012**, 32, 1238–1248. [Google Scholar] [CrossRef] - Straub, A.; Berger, K.; Breitner, S.; Cyrys, J.; Geruschkat, U.; Jacobeit, J.; Kuehlbach, B.; Kusch, T.; Philipp, A.; Schneider, A.; et al. Statistical modelling of spatial patterns of the urban heat island intensity in the urban environment of Augsburg, Germany. Urban Clim.
**2019**, 29, 100491. [Google Scholar] [CrossRef] - Gardes, T.; Schoetter, R.; Hidalgo, J.; Long, N.; Marquès, E.; Masson, V. Statistical prediction of the nocturnal urban heat island intensity based on urban morphology and geographical factors—An investigation based on numerical model results for a large ensemble of French cities. Sci. Total Environ.
**2020**, 737, 139253. [Google Scholar] [CrossRef] [PubMed] - Buckingham, E. On Physically Similar Systems; Illustrations of the Use of Dimensional Equations. Phys. Rev.
**1914**, 4, 345–376. [Google Scholar] [CrossRef] - Hidalgo, J.; Masson, V.; Gimeno, L. Scaling the daytime urban heat island and urban-breeze circulation. J. Appl. Meteorol. Climatol.
**2010**, 49, 889–901. [Google Scholar] [CrossRef] - Lee, T.W.; Lee, J.; Wang, Z.H. Scaling of the urban heat island intensity using time-dependent energy balance. Urban Clim.
**2012**, 2, 16–24. [Google Scholar] [CrossRef] - Theeuwes, N.E.; Steeneveld, G.J.; Ronda, R.J.; Holtslag, A.A. A diagnostic equation for the daily maximum urban heat island effect for cities in northwestern Europe. Int. J. Climatol.
**2017**, 37, 443–454. [Google Scholar] [CrossRef] - Zhang, X.; Steeneveld, G.J.; Zhou, D.; Duan, C.; Holtslag, A.A. A diagnostic equation for the maximum urban heat island effect of a typical Chinese city: A case study for Xi’an. Build. Environ.
**2019**, 158, 39–50. [Google Scholar] [CrossRef] - Yao, L.; Yang, X.; Zhu, C.; Jin, T.; Peng, L.L.; Ye, Y. Evaluation of a Diagnostic equation for the daily maximum urban heat island effect. Procedia Eng.
**2017**, 205, 2863–2870. [Google Scholar] [CrossRef] - Yang, X.; Yao, L.; Peng, L.L.; Jiang, Z.; Jin, T.; Zhao, L. Evaluation of a diagnostic equation for the daily maximum urban heat island intensity and its application to building energy simulations. Energy Build.
**2019**, 193, 160–173. [Google Scholar] [CrossRef] - Chow, W.T.; Roth, M. Temporal dynamics of the urban heat island of Singapore. Int. J. Climatol. J. R. Meteorol. Soc.
**2006**, 26, 2243–2260. [Google Scholar] [CrossRef] - Jin, H.; Cui, P.; Wong, N.H.; Ignatius, M. Assessing the effects of urban morphology parameters on microclimate in Singapore to control the urban heat island effect. Sustainability
**2018**, 10, 206. [Google Scholar] [CrossRef] - Roth, M.; Sanchez, B.; Li, R.; Velasco, E. Spatial and temporal characteristics of near-surface air temperature across local climate zones in a tropical city. Int. J. Climatol.
**2022**, 42, 9730–9752. [Google Scholar] [CrossRef] - Mughal, M.O.; Li, X.X.; Yin, T.; Martilli, A.; Brousse, O.; Dissegna, M.A.; Norford, L.K. High-resolution, multilayer modeling of Singapore’s urban climate incorporating local climate zones. J. Geophys. Res. Atmos.
**2019**, 124, 7764–7785. [Google Scholar] [CrossRef] - DOS. Yearbook of Statistics Singapore 2019; Department of Statistics (DOS), Ministry of Trade & Industry: Singapore, 2019.
- Stewart, I.D.; Oke, T.R. Local climate zones for urban temperature studies. Bull. Am. Meteorol. Soc.
**2012**, 93, 1879–1900. [Google Scholar] [CrossRef] - Gorelick, N.; Hancher, M.; Dixon, M.; Ilyushchenko, S.; Thau, D.; Moore, R. Google Earth Engine: Planetary-scale geospatial analysis for everyone. Remote Sens. Environ.
**2017**, 202, 18–27. [Google Scholar] [CrossRef] - Demuzere, M.; Bechtel, B.; Mills, G. Global transferability of local climate zone models. Urban Clim.
**2019**, 27, 46–63. [Google Scholar] [CrossRef] - Middel, A.; Lukasczyk, J.; Maciejewski, R.; Demuzere, M.; Roth, M. Sky View Factor footprints for urban climate modeling. Urban Clim.
**2018**, 25, 120–134. [Google Scholar] [CrossRef] - Simón-Moral, A.; Dipankar, A.; Roth, M.; Sánchez, C.; Velasco, E.; Huang, X.Y. Application of MORUSES single-layer urban canopy model in a tropical city: Results from Singapore. Q. J. R. Meteorol. Soc.
**2020**, 146, 576–597. [Google Scholar] [CrossRef] - Li, R. Spatio-Temporal Dynamics of the Urban Heat Island in Singapore. Master’s Thesis, Department of Geography, National University of Singapore, Singapore, 2012. [Google Scholar]
- Yow, D.M. Urban heat islands: Observations, impacts, and adaptation. Geogr. Compass
**2007**, 1, 1227–1251. [Google Scholar] [CrossRef] - Runnalls, K.; Oke, T. Dynamics and controls of the near-surface heat island of Vancouver, British Columbia. Phys. Geogr.
**2000**, 21, 283–304. [Google Scholar] [CrossRef] - Sanchez, B.; Roth, M.; Simón-Moral, A.; Martilli, A.; Velasco, E. Assessment of a meteorological mesoscale model’s capability to simulate intra-urban thermal variability in a tropical city. Urban Clim.
**2021**, 40, 101006. [Google Scholar] [CrossRef] - Zhu, W.; Yuan, C. Urban heat health risk assessment in Singapore to support resilient urban design—By integrating urban heat and the distribution of the elderly population. Cities
**2023**, 132, 104103. [Google Scholar] [CrossRef] - Koopmans, S.; Ronda, R.; Steeneveld, G.J.; Holtslag, A.A.; Klein Tank, A.M. Quantifying the effect of different urban planning strategies on heat stress for current and future climates in the agglomeration of The Hague (The Netherlands). Atmosphere
**2018**, 9, 353. [Google Scholar] [CrossRef]

**Figure 1.**Location of five MSS weather stations (diamond) and 26 air temperature sensors at 2–3 m height, of which 24 are placed in urban areas (dots) and two in rural areas with scattered trees (triangle). Background image: LCZ map from Middel et al. [45].

**Figure 2.**(

**a**) Modeled UHI

_{max}applying Equation (1) against observed UHI

_{max}from 19 urban stations for dry days. (

**b**) Relationship between observed UHI

_{max}and DTR

_{rur}at Station S41 for dry days.

**Figure 3.**Observed mean UHI

_{max}at 24 urban stations for dry days against: (

**a**) urban fraction (${F}_{urb}$), (

**b**) vegetation fraction (${F}_{veg}$), (

**c**) street aspect ratio (H/W) and (

**d**) local sky-view factor (SVF). Vertical lines denote +/−1 standard deviation.

**Figure 4.**Relationship between: (

**a**) UHI

_{max}(K), ${T}_{a,ref}$ (K), and ${T}_{d,ref}$ (K), and (

**b**) ${T}_{a,ref}$ (K), ${T}_{d,ref}$ (K) and ${U}_{ref}$ (m s

^{−1}) for S41 for dry days.

**Figure 5.**Relationship between the two dimensionless groups plotted as log(${\Pi}_{2}$) against log(${\Pi}_{1}$) for two examples, stations S07 (black) and S41 (red) and the respective linear trend lines.

**Figure 6.**Scatter plots of the estimated $\alpha $ for each station i (${\alpha}_{i}$) against (

**a**) ${F}_{urb}$, (

**b**) $1-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\left(1+H/W\right)$}\right.$, and (

**c**) the function $a\xb7{F}_{urb}+b\xb7\left(1-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\left(1+H/W\right)$}\right.\right)$, where a and b are obtained using the multiple linear regression method and are 0.9 and 0.5, respectively.

**Figure 7.**Modeled (using Equation (3)) against observed UHI

_{max}for 24 stations and for the second subset of the data (91 nights). Dashed lines indicate the 1:1 relationship and the range of factor of two (FAC2).

**Figure 8.**Same as Figure 7 for S07 (LCZ 1), S13 (LCZ 2), S45 (LCZ 3), S17 (LCZ 4), S24 (LCZ 5), S21 (LCZ 6), and S25 (LCZ 8).

**Figure 9.**Absolute errors in UHI

_{max}(= $|{\mathrm{UHI}}_{\mathrm{max},\mathrm{modeled}}-{\mathrm{UHI}}_{\mathrm{max},\mathrm{observed}}|$) as a function of reference wind speed regime for the test dataset (91 nights). The box defines the interquartile range (IQR), the horizontal line is the median, whiskers extend to 1.5 times the IQR, and circles are outliers.

**Figure 10.**(

**a**) Mean UHI

_{max}map using Equation (3) applied to 300 m gridded morphological data for ideal conditions (36 nights), (

**b**) scatter plot of modeled and observed mean UHI

_{max}for the 24 urban stations, and (

**c**) spatial average of modeled mean UHI

_{max}for ideal nights according to the urban LCZ types.

**Figure 11.**Maps for the (

**a**) lowest UHI

_{max}intensity observed on 5 February 2012, (

**b**) highest UHI

_{max}observed on 19 June 2013, (

**c**) mean UHI

_{max}map for dry days in February, and (

**d**) mean UHI

_{max}map for dry days in June within the study period.

**Table 1.**Coordinates, morphological and land cover characteristics of measurement stations. SVF—sky-view factor, H/W—height-to-width ratio, ${F}_{urb}$—urban fraction, ${F}_{veg}$—vegetation fraction, LCZ—local climate zone. LCZ 1 (compact high-rise), LCZ 2 (compact midrise), LCZ 3 (compact low-rise), LCZ 4 (open high-rise), LCZ 5 (open midrise), LCZ 6 (open low-rise), LCZ 8 (large low-rise), LCZ A (dense trees), and LCZ B (scattered trees) [42].

Station ID | Lon (°) | Lat (°) | Local SVF | $\mathit{H}/\mathit{W}$ (300-m Average) | ${\mathit{F}}_{\mathit{urb}}$ (300-m Average) | ${\mathit{F}}_{\mathit{veg}}$ (300-m Average) | LCZ |
---|---|---|---|---|---|---|---|

Urban stations | |||||||

S2 | 1.4171 | 103.7485 | 0.69 | 0.41 | 0.88 | 0.10 | 8 |

S4 | 1.3167 | 103.7724 | 0.19 | 0.20 | 0.44 | 0.47 | A/4 |

S7 | 1.2837 | 103.8507 | 0.19 | 5.16 | 0.87 | 0.06 | 1 |

S8 | 1.3712 | 103.9591 | 0.37 | 0.97 | 0.64 | 0.31 | 4 |

S12 | 1.4509 | 103.8088 | 0.55 | 0.44 | 0.85 | 0.10 | 8 |

S13 | 1.3129 | 103.8833 | 0.66 | 0.96 | 0.84 | 0.13 | 2 |

S14 | 1.3549 | 103.9533 | 0.32 | 0.94 | 0.76 | 0.19 | 4 |

S15 | 1.3223 | 103.9512 | 0.67 | 0.76 | 0.75 | 0.20 | 3 |

S17 | 1.3978 | 103.9080 | 0.47 | 1.83 | 0.77 | 0.20 | 4 |

S19 | 1.3679 | 103.8649 | 0.84 | 0.77 | 0.76 | 0.19 | 3 |

S21 | 1.3160 | 103.7946 | 0.54 | 0.61 | 0.43 | 0.56 | 6 |

S22 | 1.3035 | 103.8369 | 0.24 | 2.49 | 0.82 | 0.17 | 1 |

S24 | 1.2960 | 103.8406 | 0.55 | 1.52 | 0.68 | 0.30 | 5 |

S25 | 1.3153 | 103.6734 | 0.56 | 0.39 | 0.90 | 0.07 | 8 |

S29 | 1.3001 | 103.8411 | 0.52 | 1.18 | 0.69 | 0.30 | 4 |

S31 | 1.3053 | 103.8346 | 0.70 | 2.15 | 0.82 | 0.17 | 3 |

S32 | 1.4059 | 103.8696 | 0.78 | 0.14 | 0.30 | 0.70 | 6 |

S37 | 1.3405 | 103.6997 | 0.70 | 0.99 | 0.70 | 0.25 | 4 |

S38 | 1.3432 | 103.7031 | 0.26 | 1.52 | 0.69 | 0.28 | 4 |

S40 | 1.2844 | 103.8319 | 0.44 | 0.63 | 0.70 | 0.28 | 5 |

S41 | 1.3139 | 103.9110 | 0.86 | 0.88 | 0.78 | 0.18 | 3 |

S44 | 1.2991 | 103.8525 | 0.41 | 1.84 | 0.91 | 0.09 | 1/2 |

S45 | 1.3354 | 103.7683 | 0.79 | 0.74 | 0.76 | 0.24 | 3 |

S47 | 1.2791 | 103.8490 | 0.14 | 3.81 | 0.91 | 0.09 | 1 |

Rural stations^{1} | |||||||

S16 | 1.4028 | 103.7012 | 0.66 | 0.01 | 0.08 | 0.9 | B |

S23 | 1.3939 | 103.6961 | 0.83 | 0.01 | 0.07 | 0.9 | B |

^{1}Air temperatures from S16 and S23 are averaged to calculate the rural reference air temperature.

Dataset | IOA | RMSE (K) | MEAE (K) | R |
---|---|---|---|---|

Theeuwes et al. [33]—European cities | 0.91 | 0.58 | 0.81 | |

Zhang et al. [34]—Xi’an (China) | 1.68 | 1.14 | 0.67 | |

Yang et al. [36]—Nanjing (China) | 1.00 | 0.68 | ||

Theeuwes et al. [33]—Singapore | 0.62 | 1.10 | 0.75 | 0.37 |

Equation (3) for Singapore | 0.76 | 1.13 | 0.79 | 0.58 |

**Table 3.**Model performance metrics using the test dataset (91 nights) and entire period (303 nights) for two wind speed regimes.

Wind Speed Ranges | Test Period | Entire Period | ||||||
---|---|---|---|---|---|---|---|---|

IOA | R | RMSE | MEAE | IOA | R | RMSE | MEAE | |

${U}_{ref}$ < 2.5 m s^{−1} | 0.86 | 0.76 | 0.95 | 0.64 | 0.81 | 0.66 | 0.99 | 0.68 |

${U}_{ref}$ > 2.5 m s^{−1} | 0.49 | 0.31 | 1.33 | 1.03 | 0.70 | 0.50 | 1.18 | 0.84 |

Case | IOA | R | RMSE (K) | MEAE (K) |
---|---|---|---|---|

‘Ideal’ conditions | 0.85 | 0.85 | 0.65 | 0.55 |

Lowest UHI_{max}—5 February 2012 | 0.55 | 0.80 | 0.94 | 0.84 |

Largest UHI_{max}—19 June 2013 | 0.89 | 0.86 | 0.90 | 0.52 |

mean UHI_{max} for February | 0.82 | 0.83 | 0.57 | 0.55 |

mean UHI_{max} for June | 0.72 | 0.83 | 1.01 | 0.90 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sanchez, B.; Roth, M.; Patel, P.; Simón-Moral, A.
Application of a Semi-Empirical Approach to Map Maximum Urban Heat Island Intensity in Singapore. *Sustainability* **2023**, *15*, 12834.
https://doi.org/10.3390/su151712834

**AMA Style**

Sanchez B, Roth M, Patel P, Simón-Moral A.
Application of a Semi-Empirical Approach to Map Maximum Urban Heat Island Intensity in Singapore. *Sustainability*. 2023; 15(17):12834.
https://doi.org/10.3390/su151712834

**Chicago/Turabian Style**

Sanchez, Beatriz, Matthias Roth, Pratiman Patel, and Andrés Simón-Moral.
2023. "Application of a Semi-Empirical Approach to Map Maximum Urban Heat Island Intensity in Singapore" *Sustainability* 15, no. 17: 12834.
https://doi.org/10.3390/su151712834