Study on the Spatial Pattern of an Extreme Heat Event by Remote Sensing: A Case Study of the 2013 Extreme Heat Event in the Yangtze River Delta, China

The intensity and frequency of extreme heat events are increasing globally, which has a great impact on resident health, social life, and ecosystems. Detailed knowledge of the spatial heat pattern during extreme heat events is important for coping with heat disasters. This study aimed to monitor the characteristics of the spatial pattern during the 2013 heat wave in the Yangtze River Delta (YRD), China, based on the remote sensing estimated gridded air temperature (Ta). Based on the land surface temperature (Ts), normalized difference vegetation index (NDVI), built-up area, and elevation derived from multi-source satellite data, the daily maximum air temperature (Ta_max) during the heat wave was mapped by the random forest (RF) algorithm. Based on the remotely sensed Ta, heat intensity index (HII) was calculated to measure the spatial pattern of heat during this heat wave. Results indicated that most areas in the YRD suffered from extreme heat, and the heat pattern also exhibited obvious spatial heterogeneity. Cities located in the Taihu Plain and the Hangjiahu Plain generally had high HII values. The northern plain in the YRD showed relatively lower HII values, and mountains in the southern YRD showed the lowest HII values. Heat proportion index (HPI) was calculated to qualify the overall heat intensity of each city in the YRD. Wuxi, Changzhou, and Shanghai showed the highest HPI values, indicating that the overall heat intensities in these cities were higher than others. Yancheng, Zhoushan, and Anqing ranked last. This study provides a good reference for understanding the pattern of heat during heat waves in the YRD, which is valuable for heat wave disaster prevention.


Introduction
Against the background of global warming, the intensity and frequency of extreme climate events are increasing [1]. One of the most prominent manifestations of extreme climate events is extreme heat event, also known as heat wave. Extreme heat events usually refer to high air temperature and long duration, causing continuous extreme heat disasters in which people, animals, and plants cannot adapt to the environment [2]. Continuous extreme heat events will not only negatively affect the ecosystem but also pose serious challenges to industrial and agricultural production [3], social economy, and resident health [4,5]. The major issues caused by extreme heat events include increased mortality and morbidity [6][7][8], water shortage as well as power pressure [9].
As the determining factor, air temperature (Ta) plays a particularly significant role in the study of extreme heat events. Ta is operationally observed by meteorological stations, and the station observed Ta has been widely used in the studies of extreme heat events. Most of these papers concentrated on the duration, intensity, overall magnitude, impacts, and formation reasons of extreme heat events [10][11][12]. characterized by the subtropical monsoon climate, with four distinct seasons and seasonal changes in precipitation. It is greatly affected by the Western Pacific Subtropical High in summer; hence, extreme heat events are more common than other regions in China. From 22 July to 21 August in the summer of 2013, an extraordinary heat event occurred in the YRD [47]. In this extreme heat event, due to the impact of the urban microclimate, observed Ta data broke the local historical records of many sites, especially in large metropolitan areas [48]. This extreme heat event also led to dozens of deaths and huge economic costs.

Study Area
The Yangtze River Delta (YRD) is situated in the east of China, ranging from 32.56° N-29.33° N and 115.76° E-123.41° E (Figure 1). The YRD belongs to the six largest urban agglomerations around the world. It is the region with the most developed economy and the highest urbanization in China. The total area of the YRD is 211,700 km 2 , and the total population is about 150 million. This region is characterized by the subtropical monsoon climate, with four distinct seasons and seasonal changes in precipitation. It is greatly affected by the Western Pacific Subtropical High in summer; hence, extreme heat events are more common than other regions in China. From 22 July to 21 August in the summer of 2013, an extraordinary heat event occurred in the YRD [47]. In this extreme heat event, due to the impact of the urban microclimate, observed Ta data broke the local historical records of many sites, especially in large metropolitan areas [48]. This extreme heat event also led to dozens of deaths and huge economic costs.

Land Surface Temperature
The land surface temperature (Ts) data comes from the MODIS (Moderate Resolution Imaging Spectroradiometer) daily surface temperature data products provided by NASA (National Aeronautics and Space Administration), including MOD11A1 and MYD11A1. The products provide daily daytime and nighttime Ts with a spatial resolution of 1 km. MOD11A1 is the Ts product derived from TERRA/MODIS, whose overpass times were~10:30 (daytime) and~22:30 (nighttime) local time, respectively. MYD11A1 is the Ts product derived from AQUA/MODIS, whose overpass times werẽ 13:30 (daytime) and~1:30 (nighttime) local time, respectively. This study selected the MOD11A1 and MYD11A1 data from 22 July to 21 August in 2013, and the Ts of four overpass times were all involved in the Ta estimation model as a potential independent variable. The MODIS Ts data were preprocessed by the MODIS Reprojection Tool (MRT), including mosaicing and reprojection.

Normalized Difference Vegetation Index
The normalized different vegetation index (NDVI) data come from the MODIS vegetation product MOD13A3. It was provided by NASA. MOD13A3 is a monthly composite vegetation index product, which is generated from the 16-day composite vegetation index product by using a temporal compositing algorithm based on a weighted average scheme to reconstruct a calendar-month composite [49]. MOD13A3 contains monthly NDVI, monthly Enhance Vegetation Index (EVI), quality assurance, and other auxiliary datasets. The monthly NDVI on 1 August 2013 was derived from the MOD13A3 to depict the vegetation condition of the YRD. The NDVI data were also mosaicked and reprojected by MRT.

Global Human Settlement Layer
The Global Human Settlement Layer (GHSL) was released by the JRC (Joint Research Centre) and the DG REGIO (DG for Regional and Urban Policy) of the European Commission. It provides global geographical information on human presence and built-up infrastructures. The GHSL information layers mostly derive from Landsat image collections. The GHSL data set mainly includes three data layers: built-up area layer, population layer, and settlement layer. In this study, the built-up area in 2014 was derived from the GHSL data with a spatial resolution of 1 km. Its value is expressed by the proportion of building surface area in each pixel [50]. Its value ranges from 0 to 1, where 0 represents the absence of built-up area in the pixel and 1 represents the fully built-up pixel.

Digital Elevation Model (DEM)
The DEM data comes from the ASTER GDEM (Global Digital Elevation Model) version 3. The ASTER GDEM provides a global digital elevation model (DEM) of land area, which was derived from the 1.88 million ASTER Level-1A scenes acquired between 2000 and 2013 [51]. It has a global coverage between 83 • N and 83 • S and a spatial resolution of 30 m. The GDEM version is the newest version, which has an improved accuracy compared with version 2.
The DEM data were resampled to 1 km, coinciding with other spatial variables.

Observation Data
Daily air temperature observation data were provided from the China Meteorological Administration, which have been homogenized to reduce non-climatic errors. A total of 155 meteorological stations in the YRD were chosen in this study ( Figure 1). The daily Ta_max from 22 July to 21 August in 2013 was derived from the meteorological dataset, which had a total of 4805 records. According to the cloud mask information in MODIS Ts products, the corresponding station observation data under cloudy conditions were removed. Therefore, the daily Ta_max observation data under clear sky conditions were obtained. Due to the different cloud cover at different MODIS overpass times, the numbers of remaining cloud-free samples for TERRA daytime, AQUA daytime, TERRA nighttime, and AQUA nighttime were 2241, 1930, 2224, and 2640, respectively.

Temperature Estimation by Remote Sensing
Previous studies showed that Ta and Ts have strong correlations [18,52]. Ts was selected as the important independent variable for Ta estimation. The relationship between Ts and Ta is also influenced by environmental variables [46]. Therefore, other spatial variables, including NDVI, built-up area, and altitude were also selected to develop models for Ta estimation.
The random forest (RF) algorithm is a machine learning algorithm that combines the ideas of Bagging and feature subspace. The RF algorithm is not sensitive to outliers and can remove the interference of outliers during the modeling process, thereby improving the prediction accuracy [53,54]. It also has the advantages of high efficiency, strong randomness, and avoiding over-fitting. In this study, the RF algorithm was employed to estimate daily Ta_max from satellite data.
There are three important parameters in the RF model: the number of decision trees (Ntree), the number of split node features (Mtry), and the number of leaf node samples (Nodesize). Generally, higher Ntree tends to provide better fitting performance. However, the complexity of building the RF model is proportional to Ntree [55]. In this study, Ntree is tuned to develop a model with good accuracy and low complexity. When the sample size is not too large, Mtry and Nodesize have less effect on accuracy [56,57]. Given the relatively small sample size in this study, both Mtry and Nodesize were set as default. The importance of independent variables was assessed by the index, which was based on the percentage increase in mean squared error (%IncMSE) from the RF model.
Considering that there are four overpass times (TERRA daytime, AQUA daytime, TERRA nighttime, and AQUA nighttime) of MODIS Ts data during a day, Ts of these four overpass times were used to develop RF models separately, with the other three variables (NDVI, built-up area, and altitude). And the daily Ta_max was used as the dependent variable to fit models. Table 1 shows the summary of the four models: The accuracies of these four RF models were compared to determinate the best model for daily Ta_max estimation. To develop and validate RF models, 3/4 of the samples were selected as the training set randomly, and the remaining 1/4 of the samples were treated as the test set. The correlation coefficient R, mean absolute error (MAE), and root mean square error (RMSE) were figured as the accuracy indicators. The flow chart of Ta estimation is given in Figure 2.

Indicators of Extreme Heat
The China Meteorological Administration stipulates that the daily Ta_max ≥ 35 °C is a hot day. Hence this paper used 35 °C as the threshold of extreme heat, and the heat intensity index (HII) is calculated based on the Equation (1).

Indicators of Extreme Heat
The China Meteorological Administration stipulates that the daily Ta_max ≥ 35 • C is a hot day. Hence this paper used 35 • C as the threshold of extreme heat, and the heat intensity index (HII) is calculated based on the Equation (1).
where, HII is the heat intensity index, and Ta is the daily maximum temperature. Based on the intensity of high temperature, HII is divided into 7 levels using the equal interval density division method ( Table 2). Table 2. Heat intensity index levels.

Level
Heat In order to measure the intensity and spatial extent of extreme heat in various cities, using the heat island proportion index in heat island studies [29] as a reference, heat proportion index (HPI) is calculated (Equation (2)): where, HPI is heat proportion index, m is the heat intensity level (Table 2), m = 7; n is defined as the number of levels where the pixel temperature is above 35 • C, n = 6; i represents the rank number of the pixel temperature higher than 35 • C; W i is the heat intensity level i at each pixel; and P i is the proportion of the i level in each city. The HPI value ranges from 0 to 1. It characterizes the influence of extreme heat, which can quantitatively measure the overall intensity and area of extreme heat of a city or a region. The larger the HPI value, the more obvious the extreme heat event.

Validation of Remotely Sensed Air Temperature
Based on the training set, four RF models were fitted based on Ts at four overpass times (TERRA daytime, AQUA daytime, TERRA nighttime, and AQUA nighttime), Ts, NDVI, built-up area and altitude, and then validated using test samples. The scatter plots between the observed and estimated daily Ta_max from four models are given in Figure 3. The R ranged from 0.48 to 0.67, and the MAE ranged from 1.56 to 1.90 • C. Among the four models, Model 2 based on AQUA daytime Ts achieved the best performance, with a MAE of 1.56 • C. From Figure 3b, it can be seen that most samples were concentrated near the 1:1 line, indicating that the model could estimate the daily Ta_max well. Ta value of most samples was relatively high, and quite a few samples exhibited low temperature, which led to an unsatisfactory fitting effect in low temperature regions. Considering that this study focused on the regions with high temperature, the relatively high errors in low temperature regions had little effect. achieved the best performance, with a MAE of 1.56 °C. From Figure 3b, it can be seen that most samples were concentrated near the 1:1 line, indicating that the model could estimate the daily Ta_max well. Ta value of most samples was relatively high, and quite a few samples exhibited low temperature, which led to an unsatisfactory fitting effect in low temperature regions. Considering that this study focused on the regions with high temperature, the relatively high errors in low temperature regions had little effect.   Table 3 gives the importance of four independent variables in Model 2. Ts had the most significant influence on the estimation accuracy (%IncMSE = 49.48), followed by NDVI, built-up area, and altitude. The result suggests that Ts has the most crucial influence on the estimation model, which can be attributed to the high correlation between Ts and Ta. In addition, other environmental variables also should be considered because of their notable influence on the estimation accuracy of Ta. To analyze the spatial variations of the estimation error, the MAE of each meteorological station was calculated (Figure 4). It could be found that the estimation error gradually increased from north to south in details of the spatial pattern. The estimation errors in the northern part of the YRD were similar, Sustainability 2020, 12, 4415 8 of 16 indicating small spatial difference. However, the estimation error in the southern mountainous areas was quite different. Some meteorological stations had high MAE values exceeding 2 • C, while some stations had MAE values lower than 1.6 • C, which could be attributed to the complex terrain in the region. In the central YRD, the MAE values of meteorological stations gradually decreased from coast to inland, and the stations near the coast had higher MAE values than those of inland areas. The spatial variation of error indicates that the topography and the distance from the coastline have obvious influence on the model accuracy. To analyze the spatial variations of the estimation error, the MAE of each meteorological station was calculated (Figure 4). It could be found that the estimation error gradually increased from north to south in details of the spatial pattern. The estimation errors in the northern part of the YRD were similar, indicating small spatial difference. However, the estimation error in the southern mountainous areas was quite different. Some meteorological stations had high MAE values exceeding 2 °C, while some stations had MAE values lower than 1.6 °C, which could be attributed to the complex terrain in the region. In the central YRD, the MAE values of meteorological stations gradually decreased from coast to inland, and the stations near the coast had higher MAE values than those of inland areas. The spatial variation of error indicates that the topography and the distance from the coastline have obvious influence on the model accuracy.  The daily Ta_max during the heat wave over the YRD was mapped by the developed Model 2. Considering there were a lot of data gaps caused by cloud cover, the valid daily Ta_max was temporally averaged to generate a cloud-free temperature map. To validate the reliability of this composite Ta_max data, the observed daily Ta_max was also temporally averaged for comparison. Figure 5 shows the scatterplot between them. Compared with the daily temperature, the temporally averaged remotely sensed temperature showed an improved consistence with the station observed temperature. The distribution of samples was more concentrated near the 1:1 line, achieving a MAE = 0.94 • C and a R of 0.69. The good accuracy indicates that the remotely sensed Ta_max can well describe the heat environment of the YRD during the heat wave. composite Ta_max data, the observed daily Ta_max was also temporally averaged for comparison. Figure 5 shows the scatterplot between them. Compared with the daily temperature, the temporally averaged remotely sensed temperature showed an improved consistence with the station observed temperature. The distribution of samples was more concentrated near the 1:1 line, achieving a MAE = 0.94 °C and a R of 0.69. The good accuracy indicates that the remotely sensed Ta_max can well describe the heat environment of the YRD during the heat wave.

Spatial Pattern of the Extreme Heat Event
Based on the temporally averaged remotely sensed Ta_max, the heat intensity index (HII) during the 2013 extreme heat event in the YRD was calculated ( Figure 6). Generally, most areas in the YRD experienced extraordinary heat, with the HII level higher than 1. The temperature pattern also exhibited obvious spatial difference. The central YRD generally showed high HII levels (>5), which formed a sharp color difference with other areas. This region is characterized by a highly developed economy, high population density, and high urbanization level, leading to a higher temperature than other regions in the YRD. Shanghai, Suzhou, Wuxi, Changzhou, Nanjing, Hangzhou, and Ningbo, which developed along the Yangtze River and the Shanghai-Hangzhou-Ningbo corridor, formed a Z-shaped city belt and therefore a Z-shaped extreme heat belt. With the fast urbanization, the administrative boundaries between the cities in this belt had become blurred, and the extreme heat areas in different cities tended to merge into a very large heat area. In the northern YRD, the HII level generally ranged from 2 to 3, indicating a relatively low heat intensity and spatial difference. This region is mostly plains, and the economy is not well developed. The urbanization area in this region is much smaller than that in the central YRD. Urban areas exhibited obviously higher HII levels than surrounding areas, suggesting a

Spatial Pattern of the Extreme Heat Event
Based on the temporally averaged remotely sensed Ta_max, the heat intensity index (HII) during the 2013 extreme heat event in the YRD was calculated ( Figure 6). Generally, most areas in the YRD experienced extraordinary heat, with the HII level higher than 1. The temperature pattern also exhibited obvious spatial difference. The central YRD generally showed high HII levels (>5), which formed a sharp color difference with other areas. This region is characterized by a highly developed economy, high population density, and high urbanization level, leading to a higher temperature than other regions in the YRD. Shanghai, Suzhou, Wuxi, Changzhou, Nanjing, Hangzhou, and Ningbo, which developed along the Yangtze River and the Shanghai-Hangzhou-Ningbo corridor, formed a Z-shaped city belt and therefore a Z-shaped extreme heat belt. With the fast urbanization, the administrative boundaries between the cities in this belt had become blurred, and the extreme heat areas in different cities tended to merge into a very large heat area. In the northern YRD, the HII level generally ranged from 2 to 3, indicating a relatively low heat intensity and spatial difference. This region is mostly plains, and the economy is not well developed. The urbanization area in this region is much smaller than that in the central YRD. Urban areas exhibited obviously higher HII levels than surrounding areas, suggesting a distinct urban heat island (UHI) effect. In contrast, the central YRD showed a relatively weak UHI effect because its urbanization level is quite high. In the southern YRD, there are mostly mountains and valleys. The high altitude and high forest coverage resulted in an overall low HII level, and complex terrain led to a high spatial heterogeneity. In the mountainous areas covered with forest, the HII level was generally 1, suggesting that the Ta_max was lower than 35 • C. In the cities located in valleys, the HII level was quite high and even reached the highest level (level 7). distinct urban heat island (UHI) effect. In contrast, the central YRD showed a relatively weak UHI effect because its urbanization level is quite high. In the southern YRD, there are mostly mountains and valleys. The high altitude and high forest coverage resulted in an overall low HII level, and complex terrain led to a high spatial heterogeneity. In the mountainous areas covered with forest, the HII level was generally 1, suggesting that the Ta_max was lower than 35 °C. In the cities located in valleys, the HII level was quite high and even reached the highest level (level 7). To assess the overall heat intensity of each city, the heat proportion index (HPI) of the 26 cities in the YRD was calculated (Figure 7). The overall HPI value of the YRD was 0.57. The HPI values of Wuxi, Changzhou, and Shanghai were the highest, reaching 0.75, 0.74, and 0.73, respectively, which suggests that these cities had higher heat intensities as a whole than others. Yancheng and Zhoushan had the lowest HPI values, which meant that the overall heat intensities of these cities were quite low. From Figure 6, it could be found that the extreme heat areas in some cities were large, and the HPI values in these cities were also high. However, some other cities had large extreme heat areas, while their HPI values were not high. For the purpose of better understanding spatial patterns of different cities, the relationship between the HPI and the strong heat area (HII > 5) needs to be analyzed. To assess the overall heat intensity of each city, the heat proportion index (HPI) of the 26 cities in the YRD was calculated (Figure 7). The overall HPI value of the YRD was 0.57. The HPI values of Wuxi, Changzhou, and Shanghai were the highest, reaching 0.75, 0.74, and 0.73, respectively, which suggests that these cities had higher heat intensities as a whole than others. Yancheng and Zhoushan had the lowest HPI values, which meant that the overall heat intensities of these cities were quite low. From Figure 6, it could be found that the extreme heat areas in some cities were large, and the HPI values in these cities were also high. However, some other cities had large extreme heat areas, while their HPI values were not high. For the purpose of better understanding spatial patterns of different cities, the relationship between the HPI and the strong heat area (HII > 5) needs to be analyzed. Figure 8 shows the scatterplot between the HPI and the strong heat area (HII > 5) of the 26 cities in the YRD. Generally, these cities can be grouped into four categories. The cities of the first group are located on the right in the scatterplot. The typical cities included Suzhou, Shanghai, and Nanjing. These cities were characterized with high HPI values and also large strong heat areas. They were all economically developed and densely populated cities situated in the central YRD. The cities in the second group exhibited large strong areas but relatively low HPI values. The most representative city is Hangzhou. Hangzhou had the largest strong heat area in the YRD, but its HPI value was just 0.54, lower than the average value of the YRD. As the capital of Zhejiang Province, Hangzhou has a large urban area with dense population, forming a large strong area. But the other areas in this city are mostly mountain areas covered with forest, which have obviously low HII value during the heat wave. The third category of cities had high HPI values but relatively small strong heat areas. The typical cities included Yangzhou, Zhenjiang, Ningbo, Jinhua, Hefei, Wuhu, and Maanshan. Most of these cities are located in plains, with relatively low urbanization levels. The small urban areas produced small strong heat areas. However, their suburbs also had relatively high HII values (levels 2~4) due to the low altitude and flat terrain. Therefore, their HPI values were high, indicating their overall high temperature intensities. The last group of cities was located in the lower left corner of the scatterplot, indicating low HPI values and also small strong heat areas. The most typical cities are Yancheng and Zhoushan. Zhoushan lies on the Zhoushan Archipelago, which contains a lot of islands. Influenced by the ocean and high forest coverage, it generally suffered relatively low heat during the heat wave. Zhoushan also has the smallest urban area of the YRD, resulting in the smallest strong heat area. Yancheng is the northernmost city of the YRD and also has a long coastline. The high latitude and the cooling effect of the ocean made it relatively cooler than most of the other cities in the YRD. Discussion above showed that different cities had different spatial patterns during a heat wave; therefore, different prevention and control measures should be considered.  Figure 8 shows the scatterplot between the HPI and the strong heat area (HII > 5) of the 26 cities in the YRD. Generally, these cities can be grouped into four categories. The cities of the first group are located on the right in the scatterplot. The typical cities included Suzhou, Shanghai, and Nanjing. These cities were characterized with high HPI values and also large strong heat areas. They were all economically developed and densely populated cities situated in the central YRD. The cities in the second group exhibited large strong areas but relatively low HPI values. The most representative city is Hangzhou. Hangzhou had the largest strong heat area in the YRD, but its HPI value was just 0.54, lower than the average value of the YRD. As the capital of Zhejiang Province, Hangzhou has a large urban area with dense population, forming a large strong area. But the other areas in this city are mostly mountain areas covered with forest, which have obviously low HII value during the heat wave. The third category of cities had high HPI values but relatively small strong heat areas. The typical cities included Yangzhou, Zhenjiang, Ningbo, Jinhua, Hefei, Wuhu, and Maanshan. Most of these cities are located in plains, with relatively low urbanization levels. The small urban areas coastline. The high latitude and the cooling effect of the ocean made it relatively cooler than most of the other cities in the YRD. Discussion above showed that different cities had different spatial patterns during a heat wave; therefore, different prevention and control measures should be considered.

Discussions
There are few studies focused on the heat spatial pattern of regions or urban agglomerations during extreme heat events, and most of them are based on meteorological observed Ta or remotely sensed Ts. This study estimated Ta from multi-source satellite data to discuss the characteristics of the spatial pattern during the 2013 extreme heat event in the YRD. Compared with the meteorological station data, remote sensing derived thermal information could better reveal the spatial characteristics of Ta. Remotely sensed Ta is more closely related to human comfort and public health than remotely sensed Ts. Hence, remotely sensed Ta is also more important for the monitoring of extreme heat events.
Previous study on urban or regional heat environments based on remote sensing mostly focused on the relative temperature difference between urban and rural areas. However, the urban-rural temperature difference cannot indicate the absolute severity of extreme heat events. Taking the definition of a hot day issued by China Meteorological Administration (35 °C) as the temperature threshold, the heat intensity index (HII) was proposed in this study. This index could directly reflect the risk of heat based on Ta derived by satellite data. In addition, considering the difference of heat spatial distribution, the heat proportion index (HPI) was calculated, which is an area weighted HII. It could comprehensively quantify the overall extreme heat intensity in each city or region.
There are also some limitations in this study. Due to the cloud cover, there were a lot of data gaps in the daily data. We used temporal averaging to produce a cloud-free temperature map to

Discussions
There are few studies focused on the heat spatial pattern of regions or urban agglomerations during extreme heat events, and most of them are based on meteorological observed Ta or remotely sensed Ts. This study estimated Ta from multi-source satellite data to discuss the characteristics of the spatial pattern during the 2013 extreme heat event in the YRD. Compared with the meteorological station data, remote sensing derived thermal information could better reveal the spatial characteristics of Ta. Remotely sensed Ta is more closely related to human comfort and public health than remotely sensed Ts. Hence, remotely sensed Ta is also more important for the monitoring of extreme heat events.
Previous study on urban or regional heat environments based on remote sensing mostly focused on the relative temperature difference between urban and rural areas. However, the urban-rural temperature difference cannot indicate the absolute severity of extreme heat events. Taking the definition of a hot day issued by China Meteorological Administration (35 • C) as the temperature threshold, the heat intensity index (HII) was proposed in this study. This index could directly reflect the risk of heat based on Ta derived by satellite data. In addition, considering the difference of heat spatial distribution, the heat proportion index (HPI) was calculated, which is an area weighted HII. It could comprehensively quantify the overall extreme heat intensity in each city or region.
There are also some limitations in this study. Due to the cloud cover, there were a lot of data gaps in the daily data. We used temporal averaging to produce a cloud-free temperature map to analyze the spatial pattern of Ta during this extreme heat event. However, the temporal variations of Ta cannot be studied. In the future, cloud-free reconstructions of remotely sensed Ta time series can be applied to develop a spatiotemporal continuous Ta dataset for better understanding the spatial and temporal variations of Ta during heat waves. Additionally, considering complicated relationship between near-surface air temperature and Ts, more spatial independent variables can be used for Ta estimation to improve the accuracy. The improved estimation of Ta will produce more accurate assessment on the spatial pattern of heat waves based on the HII and HPI indicators.

Conclusions
In this paper, we estimated daily Ta_max during the 2013 extreme heat event in the YRD, China, from multi-source remote sensing data by machine learning technology. Based on the remotely sensed Ta, the spatial thermal pattern during the heat event was analyzed by two proposed indicators (HII and HPI). The results show that the RF algorithm can be effectively applied to derive Ta by remote sensing, and AQUA daytime Ts is the most crucial independent variable during the estimation process of Ta. The temporally averaged temperature had a good accuracy (MAE = 0.94 • C and RMSE = 1.22 • C). According to the HII map, most of the YRD experienced extraordinary heat, and the spatial difference was very obvious. The HPI index qualified the overall heat intensity of each city in the YRD. Different cities had different characteristics. Some cities had both high HII values and large strong heat areas. Other cities showed high HII values and relatively small strong heat areas, or vice versa. The results in this study can be helpful for the understanding of the 2013 extreme heat event in the YRD. All the data used in this study can be easily collected, and the proposed method based on remote sensing data and machine learning technology can also be applied in other regions for extreme heat event study.