Mapping Heat-Health Vulnerability Based on Remote Sensing: A Case Study in Karachi

Abstract

As a result of global climate change, the frequency and intensity of heat waves have increased significantly. According to the World Meteorological Organization (WMO), extreme temperatures in southwestern Pakistan have exceeded 54 °C in successive years. The identification and assessment of heat-health vulnerability (HHV) are important for controlling heat-related diseases and mortality. At present, heat waves have many definitions. To better describe the heat wave mortality risk, we redefine the heat wave by regarding the most frequent temperature (MFT) as the minimum temperature threshold for HHV for the first time. In addition, different indicators that serve as relevant evaluation factors of exposure, sensitivity and adaptability are selected to conduct a kilometre-level HHV assessment. The hesitant analytic hierarchy process (H-AHP) method is used to evaluate each index weight. Finally, we incorporate the weights into the data layers to establish the final HHV assessment model. The vulnerability in the study area is divided into five levels, high, middle-high, medium, middle-low and low, with proportions of 3.06%, 46.55%, 41.85%, 8.53% and 0%, respectively. Health facilities and urbanization were found to provide advantages for vulnerability reduction. Our study improved the resolution to describe the spatial heterogeneity of HHV, which provided a reference for more detailed model construction. It can help local government formulate more targeted control measures to reduce morbidity and mortality during heat waves.

1. Introduction

There is consensus among the global scientific community that climate change is increasing the frequency of extreme weather events [1]. Among the various extreme weather events, a heat wave may not be visually spectacular, but it will not only increase energy consumption but also (perhaps most concerning of all) exact direct effects on human health [2,3,4,5,6]. Generally, heat waves are described as a period of prolonged abnormally hot weather generally with or without high humidity. Due to several individual variations (e.g., age, socioeconomic status and education level) and thermal environment differences (e.g., urban heat island, vegetation and open space), the adaptation to heat waves varies markedly among distinct populations originating in various locations [7,8,9,10]. Thus, no unified standard has been established to define and grade heat waves.

While the definition of vulnerability has remained inconsistent, it cannot be separated from the demographic, environmental and social [7,11,12]. From the IPCC reports [13,14], the vulnerability was expressed as a function of three components, including exposure, sensitivity and adaptability, which has been widely accepted and applied [15,16]. Vulnerability measures the potential damage to a system when exposed to a hazard [17]. In epidemiological studies of heat mortality, some subgroups were defined as “vulnerable” for their sensitivity to external perturbation [18], for example, people older than 65, low-income earners, single person households, people below high school education, etc. [19,20,21]. Many HHV studies were developed given these subgroups data availability. Moreover, the necessity of the capacity to climate change emergencies was highlighted in the fourth and fifth IPCC meetings [1,14]. In addition to these, HHV cannot ignore the effects of the extreme climate events, which is named as exposure. Exposure can be written as a function of its intensity, frequency, and probability for any disasters [22]. While the current studies have identified heat waves as multi-featured events (e.g., the intensity, duration and frequency) [23], intensity often showed up as a single feature to represent the heat-wave hazard when land surface temperature (LST) intervene [24,25,26,27]. There is no doubt that a high correlation can be observed between the air temperature and LST [28,29,30,31]. However, few HHV studies have considered their gap in portraying human temperature perceptions in the past.

An absolute definition of a heat wave was the requirement to exceed a certain predetermined fixed temperature threshold for several continuous days [32]. Until now, various thresholds have been employed for heat-wave criterion, such as the 90th percent air temperature, the 95th percent air temperature, some fixed temperature (for example, 30 °C, 35 °C) [33,34,35,36]. Humans are born with the adaptation to temperature fluctuation, but this adaptation usually varies with geography and climate. To better understand the relationship between health and temperature, the minimum mortality temperature (MMT) was generally used to link temperature to death [37] or taken as a reference to evaluate the relative mortality risk during a heat wave [38]. The pity is that the statistics of heat-related mortality were not common for the backward countries. In other words, MMT was not available globally. Adjusting the heat-wave definition threshold to give an exact description of human body amenity is what we still need to explore.

Beyond the definition of heat wave, the selection of an appropriate quantitative evaluation method was also central to the assessment of HHV. There are various methods available at this stage. For example, the map overlay method [39], with the superiority in data processing and spatial analysis, has become the most common method. However, ignoring the variations in each layer has resulted in its loss of accuracy and reliability. In contrast, subjective weighting methods have more advantages in weight determination based on the decision makers. The analytic hierarchy process (AHP) [40], which combines qualitative and quantitative scoring by inviting experts to score, is the most popular subjective weighting method. Its drawback is the subjectivity of expert scoring and the error from hesitation. Out of subjective methodological shortcomings, scholars have proposed the objective weighting method, in which principal component analysis (PCA) [12,41] was often used for risk assessment. However, this method requires the input data follow the assumption of a normal distribution with a strong correlation. That is, although this method eliminated subjective errors and made a clear contribution of each indicator, its accuracy was overly dependent on index selection, making it unsuitable for our study. To solve the above issues, Zhu [42] developed the concept of the hesitant analytic hierarchy process (H-AHP) based on the traditional AHP. This indicator weighted method described the hesitation preferences with probabilities to erase the error caused by decision-makers and improve its performance.

South Asia, home to nearly one-fifth of the world’s population, has become one of the regions with a high risk of heat-related deaths due to the frequent occurrence of heat waves [10,43]. Actually, heat-related deaths are largely preventable as long as the spatial distribution of high-risk areas within the city is grasped in advance. The characterization of human health risks during extreme hot weather by measuring vulnerability can be helpful for formulating reasonable measures and taking immediate actions for high-risk areas, such as setting up public health interventions, monitoring and warning of heat-wave alerts, opening cooling centers, etc. and also for long-term urban planning purposes, such as modifying the urban built environment, greenfield development, etc., which can potentially remove heat-related mortality and morbidity [44,45]. Vulnerability assessment is the most widespread and popular form of the unitless measurement, describing the resilience of the population to natural disasters and hazards [46,47]. Currently, the research on heat-health vulnerability assessment (HHV) has been widely conducted in developed countries with constantly improving spatial accuracy [33,48,49,50,51,52]. However, it should be noted that the research on the spatial distribution of HHV in developing countries is still in its infancy. Existing studies have mainly been implemented at the administrative unit level, while few attempts focus on the specialized vulnerability assessment at the high-resolution raster level [53].

Therefore, this article aimed to take Karachi, Pakistan as an example to demonstrate a simple and flexible assessment framework for developing countries where demographic information and socioeconomic data are inconvenient to access. This framework relied on remote sensing data with 1 km × 1 km spatial resolution and some digital data to be easily replicated in other pivotal cities. Additionally, we introduced a concept from Yin et al. [54], named the most frequent temperature (MFT), to redefine a heat wave on accurate representation of the human body’s temperature perception, and employed the H-AHP method to the weight calculations. We hope that this research can inform a reference for a more precise HHV assessment model in the future.

2. Materials and Methods

2.1. Data Sources

To provide a visual representation of the data used in this study, we list all the relevant information including their name, source, spatial resolution, temporal resolution and description in

Table 1. Descriptions of the datasets.

Name	Spatial Resolution	Temporal Resolution	Source	Description
MOD11A1/MYD11A1	1 km × 1 km	Daily	https://ladsweb.modaps.eosdis.nasa.gov/search/, accessed on 20 June 2019	MODIS/Terra, Aqua Land Surface Temperature data. The basic data used to determine the intensity of heat waves (C1).
MOD13A3	1 km × 1 km	Monthly	https://ladsweb.modaps.eosdis.nasa.gov/search/, accessed on 20 June 2019	MODIS/Terra vegetation indices data, describing vegetation coverage (C6).
MOD02KM	1 km × 1 km	Daily	https://ladsweb.modaps.eosdis.nasa.gov/search/, accessed on 20 June 2019	Level 1B calibrated radiances, which are used to calculate the NDBI to describe the coverage of impermeable surfaces (C3).
DMSP/OLS	1 km × 1 km	Year	https://www.ngdc.noaa.gov/eog/dmsp/, accessed on 20 June 2019	DMSP-OLS night light data, which reflect the level of regional development and measure the urbanization level (C8).
GDP	1 km × 1 km	Year	[55]	GDP (C7) reflects the ability of a county to finance itself in a disaster-response process.
Age and sex Structure	100 m × 100 m	Year	https://www.worldpop.org/geodata/, accessed on 20 June 2019	These data describe the distribution of vulnerable people (C4) over 65 years old.
Poverty	1 km × 1 km	Year	https://www.worldpop.org/geodata/, accessed on 20 June 2019	Proportion of residents living in MPI-defined poverty (C2).
Pakistan POI	-	Year	https://www.openstreetmap.org/, accessed on 1 May 2019	We mainly use the data to confirm the location of hospitals and calculate the distance from medical resources (C5).
Meteorological Station Data	-	Daily	https://www.ncei.noaa.gov/maps/hourly/, accessed on 10 July 2021	The observation data of meteorological stations, which are used to count the occurrence of heat waves.

. The observation meteorological data here had two main uses: We used a total of 28 stations, located within Pakistan, to capture the relationship between LST and near surface air temperature (T_air). In addition, the only station in Karachi was used to monitor the annual variation of the T_air and record the heat wave duration. For Moderate Resolution Imaging Spectroradiometer (MODIS) LST, there were 120 (30 days × 4 images per day) LST images used for T_air estimation, in which four images per day were pooled into the daily LST via averaging. In addition, we selected the day with the maximum mean daily temperature during the longest heat-wave duration (26 June 2016 in this study) to represent the intensity of heat wave with the reference of observation data. The missing data resulting from cloud cover were filled by the mean value within three neighboring days. The age and sex structure data were collected with the spatial resolution of 100 m × 100 m and were resampled to 1 km × 1 km by count summation. The points of interest within Pakistan (Pakistan POIs) were employed for the calculation of the Euclidean distance from medical resources. More detailed of all data properties were available via the link given on the source.

2.2. Overview of the Study Area

Karachi, as the largest city in Pakistan, is located on the southern coast of Pakistan, northwest of the Indus Delta, south of the Arabian Sea, and on the plain between the Julie River and Mariel River (as shown in Figure 1). This city has a population of approximately 20 million people and covers an area of 3527 km², of which the urban area covers 1821 km². This area experiences a tropical climate encompassing warm winters and hot summers [56]. The average minimum temperature in winter is 13 °C, and the average maximum temperature in summer is 34 °C. Rainfall is scarce, with an average annual precipitation of only 200 mm.

Since the 1990s, Pakistan’s economy has been slow with a per capita income of approximately $600. In Sindh Province, where Karachi is located, over half of the population lives below the poverty line. Some areas have poverty rates over 80%. The metropolitan attraction and cultural diversity have led to an influx of migration into Karachi. In this case, a drastic population expansion has appeared in this region. Currently, the city is under tremendous pressure for jobs, housing, transportation and supplies of water and electricity, increasing the heat wave risk. Moreover, this city is crowded with a large number of residents of the Islamic faith. Ramadan customs also increase the mortality risk from heat waves. That is to say, assessing the heat wave risk level in Karachi and clarifying its spatial variations are quite paramount for rational planning of infrastructure construction and reduction in morbidity.

2.3. Methods and Procedure

We identified and assessed the HHV in the study area based on the following steps: first, specify the time of heat wave occurrence; then, assessment indicators selection and HHV assessment model construction; next, index weight calculation; and finally, results accuracy evaluation.

2.3.1. Heat Wave Definition

One common feature in the association between temperature and mortality is MMT, which is defined as the temperature where the minimum mortality rate is reached. It is a fixed temperature for variable geographic and subgroups with poor availability in undeveloped areas for its expensive cost at collection. Compared to MMT, MFT, the daily mean temperature occurs most frequently within a year, is a plain variable. Yin et al. [54] revealed a high consistency and stability between the MMT and the MFT in the same area during the same period by exploring the temperature-death relationship in 420 cities. In a word, using the MFT as a surrogate for the MMT, the mean error is only 0.9 °C (95% Confidence interval (CI): 0–3 °C). This finding provided a new idea for defining heat wave. Based on the existing criteria, we classified days with daily mean temperatures higher than the MFT of the region as hot days. When hot days lasted for more than 3 days, this period was called a heat wave. Under this concept, we use the daily mean temperature instead of the maximum temperature considering the mean temperature has been proven to be a better predictor of mortality than maximum and minimum temperatures as it is more likely to represent the temperature level across 24 h [57]. Heat-related mortality is widely known to be more severe when the temperature remains high within 24 h, causing inability of the body to cool down [58].

2.3.2. Determination of the Vulnerability Assessment Factors

Exposure

Temperature is traditionally captured from meteorological stations. The spatial interpolation method [59,60,61,62,63,64,65,66,67] can generate continuous surfaces from meteorological observation data with higher temporal resolution, but its accuracy is always affected by their sparse distribution and is sensitive to the season [60]. Compared with it, the moderate resolution imaging spectroradiometer land surface temperature (MODIS LST) can better describe the spatial heterogeneity of the temperature and has a good correlation with the air temperature (T_air) observation [61,62], even though there still have some gaps in the temporal resolution that need to be filled.

Here, we chose the mean MODIS LST (mean LST of four satellite transit times per day) as the basic data for exposure assessment because of the sparsity of meteorological stations in the study area (there are only two available stations). To describe the heat mortality exposure of heat waves as clearly as possible, we screened out the day with the maximum temperature during the longest heat wave. For this study, we chose 26 June 2016, when the mean temperature reached 34.6 °C and the maximum temperature reached 40 °C. We estimated the daily mean T_air from daily mean MODIS LST using linear regression. The selected meteorological stations (as shown in Figure 1) are all in Pakistan, for which the elevation is less than 500 m. Data from 1 April 2016 to 31 September 2016 were all used to estimate the coefficients for its seasonal similarity. Then, exposure results were used for the final assessment. Estimating the air temperature from the LST is a common and relatively simple algebraic method, and the relationship between the two was also affected by the variation of the land cover, weather and elevation [68,69], which we did not consider at this time. Since we have removed the impact of other variables as possible by selecting the similar stations.

$${\mathrm{T}}_{\mathrm{air}}=\mathrm{a}\times \mathrm{LST}+\mathrm{b}$$

(1)

where T_air(C1) is the estimated T_air and a and b are coefficients calculated from the selected stations.

Sensitivity

Several individual subgroups, such as elderly individuals over the age of 65 [70,71,72] and those living in the poverty [73] have been indicated to have greater sensitivity over the past decade. Apart from the above subgroups, urban areas may be more sensitive to heat than surrounding rural areas [74]. For city dwellers, the urban heat island (UHI) effect will cause additional risks because heat waves have shown more potential to amplify UHIs [75,76]. However, the UHI intensity is inequitably distributed in cities, where people of lower socioeconomic status typically live in areas with less vegetation and more heat-absorbing surfaces [7,8,9]. The main factor causing the UHI is the city’s underlying surface, which is often dominated by buildings [77]. Therefore, we used an impermeable surface ratio here to indicate the city dwellers who will be more troubled by the UHI. On this basis, the poverty rate (C2) and the vulnerable population (elderly individuals over 65 years old) (C4) were also selected as the main index factors in the sensitivity assessment layer. Here, we chose the normalized difference built-up index (NDBI) [78] (C3) to represent the distribution of impervious areas.

Adaptability

With the development of technology in recent years, the resolution of night-time light data has been continuously improved. Defense Meteorological Satellite Program Operational Line Scanner (DMSP/OLS) night-time light data (C8) have become an effective means for estimating the level of urbanization, population density, electric energy consumption and other factors [79,80]. A region’s adaptability to disaster mainly depends on the local medical excellence and financial status. Urban residents have access to more high-quality education, healthcare, housing, transportation and financial resources than people living in underdeveloped zones [81,82], meaning a stronger capacity to cope with the disasters. In this article, the GDP (C7) was selected to indicate the national economic development and government expenditure. The distance from a medical institution (C5) was selected to indicate the timeliness of obtaining professional medical rescue services. Furthermore, green coverage (C6) was selected to indicate the cooling effect for the surrounding area [83].

Above all, four indicators, namely, the urbanization level, green coverage, distance from a medical institution and GDP, were selected as the main index factors for adaptability assessment. Here, the euclidean distance was used to calculate the distance from a medical institution. The normalized difference vegetation index (NDVI) [84] is used to calculate the green coverage in a region of interest (ROI). As a note, all the above data used in vulnerability assessment were dimensionless with a resample value from 0 to 1 under maximum-minimum method.

2.3.3. Quantification of Evaluation Factors Based on H-AHP

Determining the weights of different evaluation indices is the key to model construction. The traditional AHP [85] can decompose complex analytical problems into different factors, but the greatest flaw of this method is that the hesitation process and uncertainty of the decision-makers during their judgment cannot be completely eliminated. To solve this problem, this paper choose the H-AHP method proposed by Zhu et al. [86] to calculate the weight in order to prevent this sort of problem. The specific steps are as follows:

• The decision-making problem is decomposed into several structural levels from top to bottom, which can be divided into target and rule layers and index levels. In this paper, it has been divided into exposure B1, sensitivity B2 and adaptability B3. Three experts in related fields (UHI remote sensing monitoring, geomorphology and natural disaster assessment, night light remote sensing and heat wave risk assessment) were invited to make important judgments this time. The specific hierarchical structure is shown in

  Table 2. Hierarchy of heat health vulnerability assessment and the weight of each indicator. The field, named Description, shows the impact of each index on HHV as positive (aggravate the vulnerability of heat-related morbidity/mortality) or negative (reduce the vulnerability of heat-related morbidity/mortality).

  Target Layer	Rule Layer	Index Layer	Weight W	Description
  Vulnreability A	Exposure B1	Intensity C1	1.00	Positive
  	Sensitivity B2	Poverty Rate C2	0.18	Positive
  		Impervious Surface C3	0.13	Positive
  		Vulnerable Population C4	0.68	Positive
  	Adaptability B3	Proximity to Medical Institutions C5	0.58	Negative
  		Green Coverage C6	0.15	Negative
  		GDP C7	0.17	Negative
  		Urbanization Level C8	0.10	Negative

  .
• The probabilistic hesitation product preference relation is then constructed. For set X = {X1, X2, ..., Xn}, it is assumed that the decision-maker (DM) can compare the elements in X in pairs, and then the probabilistic hesitation preference information according to the expert opinion is obtained, while the following probabilistic hesitation matrix preference relation (P-HMPR) is defined:

$$\mathrm{Y}={\left({\mathrm{y}}_{\mathrm{ij}}\right)}_{\mathrm{n}\times \mathrm{n}}$$

(2)

where ${\mathrm{y}}_{\mathrm{ij}}=\left(\mathrm{y}{\left(\mathrm{l}\right)}_{\mathrm{ij}}\left(\mathrm{p}{\left(\mathrm{l}\right)}_{\mathrm{ij}}\right){\displaystyle |}\mathrm{l}=1,\cdots \left|{\mathrm{y}}_{\mathrm{ij}}\right|{\displaystyle |}\right),\left|\mathrm{y}\right|$ is the number of possible values of y, and ${\mathrm{y}}_{\mathrm{ij}}$ is the preference of ${\mathrm{x}}_{\mathrm{i}}$ to ${\mathrm{x}}_{\mathrm{j}}$, which satisfies the following:

$${\mathrm{y}}_{\mathrm{ij}}^{\mathsf{\rho }\left(\mathrm{l}\right)}{\mathrm{y}}_{\mathrm{ji}}^{\mathsf{\rho }\left(\mathrm{l}\right)}{=1,\mathrm{y}}_{\mathrm{ij}}=1,\left|{\mathrm{y}}_{\mathrm{ij}}\right|=\left|{\mathrm{y}}_{\mathrm{ji}}\right|{,\mathrm{p}}_{\mathrm{ij}}^{\mathsf{\rho }\left(\mathrm{l}\right)}{=\mathrm{p}}_{\mathrm{ji}}^{\mathsf{\rho }\left(\mathrm{l}\right)},\mathrm{i},\mathrm{j}=1,2,\cdots ,\mathrm{n}$$

(3)

$${\mathrm{y}}_{\mathrm{ij}}^{\mathsf{\rho }\left(\mathrm{l}\right)}\le {\mathrm{y}}_{\mathrm{ij}}^{\mathsf{\rho }\left(\mathrm{l}+1\right)},\mathrm{i}<\mathrm{j}$$

(4)

where ${\mathrm{y}}_{\mathrm{ij}}^{\mathsf{\rho }\left(\mathrm{l}\right)}$ represents the $\mathsf{\rho }$ possible values of ${\mathrm{y}}_{\mathrm{ij}}$ and ${\mathrm{p}}_{\mathrm{ij}}^{\mathsf{\rho }\left(\mathrm{l}\right)}$ is the probability of ${\mathrm{y}}_{\mathrm{ij}}^{\mathsf{\rho }\left(\mathrm{l}\right)}$.

According to the HHV assessment index system constructed above, based on a 1–9 scale, relevant experts were invited to use each indicator in the index layer as the dominant element to conduct a pairwise comparison, which was subject to the given hesitation preference information. Then, a P-HMPR of each rule layer was constructed.

c.

Consistency testing ensures the validity of the preference information and the correctness of the results. In this paper, the row geometric mean method (RGMM) proposed by Crawford and Williams [87] was selected.

According to the RGMM, the priorities ${\mathrm{w}}_{\mathrm{i}}(\mathrm{i}=1,2,\dots ,\mathrm{n})$ can be simply found as the geometric means of the rows of A:

$${\mathrm{w}}_{\mathrm{i}}=\frac{{\left({\prod }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{y}}_{\mathrm{ij}}\right)}^{\frac{1}{\mathrm{n}}}}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\prod }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{y}}_{\mathrm{ij}}\right)}^{\frac{1}{\mathrm{n}}}}$$

(5)

Based on Equation (5), Aguarón and Moreno-Jiménez [88] proposed the geometric consistency index (GCI) for evaluating the consistency of ${\mathrm{MPR}\mathrm{Y}}^{\left(\mathrm{l}\right)}={\left({\mathrm{y}}_{\mathrm{ij}}^{\left(\mathrm{l}\right)}\right)}_{\mathrm{n}\times \mathrm{n}}$ as follows:

$${\mathrm{GCI}}_{\mathrm{Y}\left(\mathrm{l}\right)}=\frac{2}{\left(\mathrm{n}-1\right)\left(\mathrm{n}-2\right)}{\sum }_{\mathrm{i}<\mathrm{j}}{\log }^2{\mathrm{e}}_{\mathrm{ij}}{,\mathrm{e}}_{\mathrm{ij}}=\frac{{\mathrm{y}}_{\mathrm{ij}}^{\left(\mathrm{l}\right)}{\mathrm{w}}_{\mathrm{j}}}{{\mathrm{w}}_{\mathrm{i}}}$$

(6)

Let Y be a hesitant-judgment space; then, the consistency index of the expected set of Y can be defined as:

$${\mathrm{E}\left(\mathrm{GCI}\right)}_{\mathrm{Y}}=\left({\prod }_{\mathrm{i},\mathrm{j}=1}^{\mathrm{n}}\frac{1}{\left|{\mathrm{y}}_{\mathrm{ij}}\right|}\right){\sum }_{\mathrm{Y}}{\mathrm{GCI}}_{\mathrm{Y}\left(\mathrm{l}\right)}$$

(7)

Compared with the consistency ratio, Aguarón and Moreno-Jiménez [86] proposed the thresholds of GCI for different sizes of Y. Among these equations, the calculation of $\mathrm{E}{\left(\mathrm{GCI}\right)}_{\mathrm{Y}}$ is based on Monte Carlo simulations [89], a common random sampling method used to solve problems having a probabilistic interpretation, to obtain the GCI values of the preference relations of the various probabilistic hesitation product types. If $\mathrm{E}{\left(\mathrm{GCI}\right)}_{\mathrm{Y}}\le {\mathrm{GCI}}^{\mathrm{n}}$, then Y is with the acceptable consistency; otherwise, Y is inconsistent. For the unacceptable consistency, the iterative method given by Zeshui and Cuiping [90] were chosen as a basis to develop consistency improvement. All probabilistic hesitation product preferences established in this paper passed the consistency test via MATLAB experiments.

d.

Based on the RGMM, hesitant preference analysis (HPA) was applied to determine the ranking of the weights of the corresponding elements of the same layer corresponding to the relative importance of the elements of the upper layer. For P-HMPR, a probabilistic hesitation judgment space is composed of the hesitation judgment, and the H-AHP method [53] analyses this space to obtain the priorities of objectives with HPA.

For P-HMPR ${\mathrm{Y}=(\mathrm{y}}_{\mathrm{ij}}{)}_{\mathrm{n}\times \mathrm{n}}$, where ${\mathrm{y}}_{\mathrm{ij}=}{(\mathrm{y}}_{\mathrm{ij}}^{\left(\mathrm{l}\right)}\left({\mathrm{p}}_{\mathrm{ij}}^{\left(\mathrm{l}\right)}\right)|\mathrm{l}=1,\cdots ,\left|\mathrm{y}\right|)$, a comparison matrix ${\mathrm{Y}}^{\left(\mathrm{l}\right)}{=(\mathrm{y}}_{\mathrm{ij}}^{\left(\mathrm{l}\right)}{)}_{\mathrm{n}\times \mathrm{n}}$ can be obtained from Y following the probability distributions ${\mathrm{p}}_{\mathrm{ij}}{=\mathrm{p}}_{\mathrm{ij}}^{\left(\mathrm{l}\right)}(\mathrm{l}=1,\cdots ,\left|{\mathrm{y}}_{\mathrm{ij}}\right|)$. Let ${\mathrm{f}}_{\mathrm{ij}}{(\mathrm{y}}_{\mathrm{ij}}^{\left(\mathrm{l}\right)})$ be the density function of ${\mathrm{y}}_{\mathrm{ij}}$; then, the joint probability distribution of ${\mathrm{y}}_{\mathrm{ij}}^{\left(\mathrm{l}\right)}(\mathrm{i},\mathrm{j}=1,2,\cdots ,\mathrm{n})$ is specified by a density function $\mathrm{f}({\mathrm{y}}^{\left(\mathrm{l}\right)})$ as follows:

$$\mathrm{f}({\mathrm{y}}^{\left(\mathrm{l}\right)})={\displaystyle \prod }_{\mathrm{i},\mathrm{j}=1}^{\mathrm{n}}{\mathrm{f}}_{\mathrm{ij}}\left({\mathrm{y}}^{\left(\mathrm{l}\right)}\right)$$

(8)

According to ${\mathrm{Y}}^{\left(\mathrm{l}\right)}$ and Equation (5), we can obtain a priority vector denoted by ${\mathsf{\omega }}^{\left(\mathrm{l}\right)}{=(\mathsf{\omega }}_1^{\left(\mathrm{l}\right)}{,\mathsf{\omega }}_2^{\left(\mathrm{l}\right)},\cdots {,\mathsf{\omega }}_{\mathrm{n}}^{\left(\mathrm{l}\right)})$. Then, elements can be sorted from the best rank (r = 1) to the worst rank (r = n) by the following ranking function:

$${\mathrm{rank}}_{\mathrm{i}}\left({\mathsf{\omega }}^{\left(\mathrm{l}\right)}\right)=1+{\displaystyle \sum }_{\mathrm{k}=1}^{\mathrm{n}}{\mathsf{\rho }(\mathsf{\omega }}_{\mathrm{k}}^{\left(\mathrm{l}\right)}{>\mathsf{\omega }}_{\mathrm{i}}^{\left(\mathrm{l}\right)})=\mathrm{r}$$

(9)

where $\mathsf{\rho }\left(\mathrm{true}\right)=1,\mathsf{\rho }\left(\mathrm{false}\right)=0$. Let Y be a hesitant-judgment space, and based on the ranking function, the judgments that make the objective ${\mathrm{x}}_{\mathrm{i}}$ ranking $\mathrm{r}$ in the space can be analysed as follows:

$${\mathrm{Y}}_{\mathrm{i}}^{\mathrm{r}}\left({\mathrm{y}}^{\left(\mathrm{l}\right)}\right)=\left\{{\mathrm{y}}^{\left(\mathrm{l}\right)}\in {\mathrm{Y}:\mathrm{rank}}_{\mathrm{i}}\left({\mathsf{\omega }}^{\left(\mathrm{l}\right)}\right)=\mathrm{r}\right\}$$

(10)

Based on Equations (8) and (10), the acceptability rate of ${\mathrm{x}}_{\mathrm{i}}$ ranking $\mathrm{r}$ can be defined as a rank acceptability index ${\mathrm{b}}_{\mathrm{i}}^{\mathrm{r}}$. It is computed as the expected volume of ${\mathrm{Y}}_{\mathrm{i}}^{\mathrm{r}}{(\mathrm{y}}^{\left(\mathrm{l}\right)})$:

$${\mathrm{b}}_{\mathrm{i}}^{\mathrm{r}}={\int }_{{\mathrm{Y}}_{\mathrm{i}}^{\mathrm{r}}\left({\mathrm{y}}^{\left(\mathrm{l}\right)}\right)}\mathrm{f}\left({\mathrm{y}}^{\left(\mathrm{l}\right)}\right){\mathrm{dy}}^{\left(\mathrm{l}\right)}$$

(11)

where ${\mathrm{b}}_{\mathrm{i}}^{\mathrm{r}}ϵ\left[0,1\right],{\sum }_{\mathrm{r}=1}^{\mathrm{n}}{\mathrm{b}}_{\mathrm{i}}^{\mathrm{r}}=1$. The Monte Carlo simulation process can be used to compute ${\mathrm{b}}_{\mathrm{i}}^{\mathrm{r}}$.

With respect to the ranking acceptability indices, the acceptable probabilities of the objectives for each rank can be clearly identified. The acceptable probabilities for all ranks can be aggregated as a comprehensive ranking value, which can be implemented through aggregation operators, such as ordered weighted averaging (OWA) [91].

Letting ${\mathrm{h}}_{\mathrm{i}}$ be the holistic evaluation of ${\mathrm{x}}_{\mathrm{i}}$, then it is computed as:

$${\mathrm{h}}_{\mathrm{i}}={\displaystyle \sum }_{\mathrm{r}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{r}}{\mathrm{b}}_{\mathrm{i}}^{\mathrm{r}}$$

(12)

Starting from the bottom layer of the structure, the indicator weights (${\mathrm{w}}_{\mathrm{r}}$) in each layer were calculated. The results are summarized in Table 2, and the specific algorithm was established using MATLAB software.

2.3.4. Establishment of the Evaluation Model Based on the Map Overlay Method

First, to eliminate the mapping interval inconsistency problem of different data, we standardized each indicator layer. It should be noted that the normalization of the negative indicators is opposite to that of the positive ones, i.e., the larger the value is, the more it tends to 0 after normalization.

Finally, Equation (7) was used to calculate the rule layer index (RLI, e.g., B1, B2, B3) and Equation (8) was used to calculate the heat health vulnerability (HHV) for this region.

$$\mathrm{RLI}={\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i}}\times {\mathrm{x}}_{\mathrm{ij}}$$

(13)

$$\mathrm{HHV}=\left(\mathrm{B}1+\mathrm{B}2+\mathrm{B}3\right)/3$$

(14)

where ${\mathrm{W}}_{\mathrm{i}}$ is the index weight obtained based on the H-AHP and ${\mathrm{x}}_{\mathrm{ij}}$ is the standardized value of the index. Finally, we mapped the HHV for the study area and divided it into five grades of high, medium-high, medium, medium-low and low according to the equal interval method.

3. Results

3.1. Heat-Wave Statistics

With the cloud coverage remote sensing images usually have some missing data causing the heat wave process cannot be complete observed. However, the meteorological station can significantly remedy this defect. Here, we use observed data to clarify the frequency and intensity of heat waves in 2016 in Karachi based on our definition. The only meteorological station, named JINNAH INTERNATIONAL, is located in the northeast of Karachi (geographical coordinates: 24.907, 67.161) with an altitude of 30.5 m. As statistics, the MFT in this region was 30 °C in 2016 (all data were rounded up before the statistics on its frequency), which occurred 57 times throughout this year. The results indicated 91 hot days in Karachi during 2016, with 6 times heat waves. Among these, the longest duration was 59 days, lasting from 8 May to 6 July. The annual daily mean temperature variation in 2016 was shown in Figure 2.

3.2. Exposure

For estimating daily mean T_air from daily mean LST, a and b were calculated as 0.71 and 8.06, respectively. Figure 3a showed a high correlation between the daily mean LST and the observed daily mean T_air, whose R-square (R²) was 0.63. Based on the estimated T_air, the area where T_air was higher than the local MFT (30 °C) accounted for over 97% on 26 June 2016, and the maximum temperature exceeded 37 °C. Areas where T_air reached above 35 °C were mainly concentrated in Malir and Karachi west with scattered distribution in the other regions.

Figure 4a showed the exposure distribution of Karachi. The proportions of each grade (low, medium-low, medium, medium-high and high) were 2.38%, 20.92%, 41.94%, 27.46%, and 4.77%, respectively. The low-middle to middle-high grade exhibited the widest distribution, occupying almost all of Karachi except the northern barren zone. Among all the residential areas, the suburbs located Karachi west and Malir, which were obviously separated from the main urban areas, were all located in high-exposure areas and should be vigilant.

3.3. Sensitivity

Among sensitivity assessment, we found the suburbs and southeast of the main districts gathered many poor people, such as Karachi central, Karachi south, etc. These regions were severely aging but relatively wealthy. On the basis of the equal interval method, the area proportion of each grade from low to high was as follows: 23.52%, 71.07%, 3.36%, 1.64%, and 0.42%. Karachi central and Karachi south showed high-level sensitivity, while Karachi west, Karachi east, and Malir north showed medium-high sensitivity. Other areas showed medium-low grades and even below. That is to say, Karachi central was obviously more sensitive and may become the worst-hit area during heat waves, which needs to be focused on in the future.

3.4. Adaptability

According to Figure 4c, the adaptability in the southwestern parts of Malir, Karachi Central, Karachi South, Karachi East, and the eastern of Karachi West is the most superior. The coastland has rich medical resources and ishighly urbanized. Within these districts, the green space coverage is higher in the east. but the economy is more developed in the west, bringing together industry. In contrast, several suburbs and non-city regions have limited resilience in disaster response due to scarce resources. According to the classification, the area proportion of each grade from low to high is 11.21%, 38.50%, 29.29%, 12.88% and 8.13%. Judging from its distribution, northern Karachi central, Malir cantonment, Karachi east, Korangi, Karachi west and Malir are all key areas of concern. This result also proves the indispensablility of medical institutions during disasters, which serves as a reminder to improve the allocation of health care resources during urban development planning. At the same time, grassland and shrubs cannot play a shading role and thus they have a poor cooling effect and limited contribution to prevention.

3.5. Heat-Health Vulnerability

This assessment was conducted by stacking the above three criterion layers on the basis of Equation (10). Statistically, the areas with HHV level from low to high are 99 km², 1505 km², 1353 km², 276 km², and 0 km², accounting for 3.06%, 46.55%, 41.85%, 8.53% and 0% of the total area. We found that more than 50% of the areas had middle to high vulnerability. Only the northern part of Malir shows middle-high vulnerability. Karachi central, as the city with the highest concentration of aging population, was more vulnerable (middle-high risk) than other urban areas. For the full region, the west of Karachi West and the east of Karachi East had higher vulnerability levels. However, large residential areas were not located in these regions, the morbidity and death rates caused by heat waves will not be high. Despite this, we still suggested the local government paying more attention to these areas, particularly Karachi central, and focus on strengthening infrastructure construction, attaching importance to the risk prevention and raising residents’ awareness of heat waves.

3.6. Verification

The calculation of each indicator’s weight was the key to our model. There were many studies agree on making distinctions between the contributions of different indicators [34,53,92]. However, the selection of indicators in each study is certainly not the same, and thus, is inconvenient to copy from them directly. Comparing the rank of different indicators is one way to prove the credibility of our judgment. Therefore, we summarized the weight of indicators we choose this time from similar studies (

Table 3. The weight of indicators in similar studies.

	Tran et al., 2020 [92]	Estoque et al., 2020 [38]	Hulley et al., 2019 [98]	Oh et al., 2017 [99]	Phung et al., 2016 [100]
Sensitivity
Poverty rate	0.11	0.44	0.21	-	0.09
Impervious Surface	0.09	-	-	-	-
Vulnerable Population	0.18	0.57	0.62	0.2	0.12
Adaptability
Proximity to Medical Institutions	0.31	-	-	0.58	0.14
Green Coverage	0.27	0.46	-	-	-
GDP	-	0.32	-	0.21	-
Urbanization Level	-	0.22	-	-	-

). It can be seen that the rank of each indicator conforms to our conclusion. For example, the weight ranking was as Proverty rate > vulnerability population > impervious surface in the sensitivity layer from Tran et.al [92], which was consistent with our results.

Located in a climatically warm geographical region, Pakistan is vulnerable to extreme climate events such as heat waves, droughts, and floods [91]. In the literature, many heatwave related studies have been conducted in this region from different perspectives [10,15,93,94]. Through a comparison, we verified the veracity of this study. The results from ThinkHzard [95] show that Karachi, which is located in southern Pakistan, is a high heat hazard area. In their study, they used the wet bulb globe temperature (WBGT, in °C), which has a notable relevance to human health, to describe the heat-wave hazard. However, their conclusion is basically consistent with ours. Except this, the heat-related mortality risk prediction studies in Pakistan can also give some certain references. These studies, which rely on various models [94,96,97], all showed a similar conclusion with ours, i.e., the heat-related mortality risk (the same as our HHV) ranges from middle to high. As shown in Figure 4, the HHV area with a higher than middle risk level reached over 50%. In comparison, our mapping provides more details in spatial distribution, which provided a more powerful reference for the government to formulate effective preventive measures.

3.7. Sensitivity Analysis

We changed our settings of each rule layer weight in order to assess the robustness of our model with the designed following scenarios. Specifically, two scenarios of sensitivity analysis (S1 and S2) were set randomly without any support. In addition, we can find the unnoticed variations in the Figure 5, reminding us the potential impact of indicators weighted is not significant.

DS: the default model setting of our model with the average weighted among exposure, sensitivity and adaptability.

S1: the weight among exposure, sensitivity and adaptability are 0.5, 0.25, 0.25, respectively.

S2: the weight among exposure, sensitivity and adaptability are 0.2, 0.4, 0.4, respectively.

4. Discussion

Building a more reproducible HHV system will help understand high-vulnerability areas around the world. In this study, we established a kilometre-level HHV system with widely available data. Although the accuracy of this system can be generally verified, this model still has certain limitations.

Meteorological site and LST data [101,102,103] are the most common temperature data used in climate change research. For application, site data with poor spatial resolution often fails to meet expectations. LST data can effectively solve the problem of the uneven distribution of stations, but there are still deviations from the air temperature [104]. Here we estimated Tair from LST using a simple and common linear regressionmodel with limited precision which can be further improved. In addition, the data used to evaluate the exposure was the most severe single-day data of annual heat waves. It can describe the high-exposure distribution within the study area at the highest temperature. However, the continuous influence of heat waves was not considered, and thus, this model is more suitable for single-day assessment. How to eliminate the gaps in the satellite spatial-temporal data to achieve long-term continuous monitoring still requires more research.

Moreover, the mortality risk [105,106,107,108] has appeared in many studies. Since the heat-related mortality data was generally unavaiable for this study area, we redefine a heat wave by regarding the MFT as the minimum temperature threshold for HHV in order to illustrate the discomfort caused by extreme temperatures. This is the first known study performed in this manner, and we can do more to prove its universality through delving deeper.

Vulnerability analysis is usually divided into qualitative and quantitative procedures, of which the former will be described as high, medium or low level, while the latter will be described as a specific previously defined risk metric (e.g., the number of potential victims, economic losses, etc.) [109]. Especially when it is difficult to obtain quantitative data, qualitative analysis is more common. Earlier, the spatial vulnerability assessment models were developed based on the map overlay with equal weights, which depended on the basic multiplication, division or addition and subtraction [82,109,110]. As the complexity of the model increases, an ever-increasing number of scholars have realized that the contributions of different factors are not the same. The distinction of the index weights determines the specific performance. The combination of AHP and Geographic Information System (GIS) exists extensively within qualitative natural disaster risk assessment, such as floods, landslides and drought risks [111,112,113,114,115,116,117]. Considering that this method has a subjective influence that is difficult to eliminate, the fuzzy analytic hierarchy process (FAHP) and improved analytic hierarchy process (IAHP) methods [118,119,120] were used to reduce the subjective error. Here, we choose the H-AHP method. The main purpose is to provide a feasible HHV method reference for developing countries with limited spatial data availability. However, its applicability still requires complete and detailed demonstration. Moreover, an in-depth discussion is also needed to determine which approach is more scientific when considering the distinction between the subjective and objective weighted assignment.

The purpose of the constructed model is to determine the locations of regions with a high vulnerability and provide a reference for future proposals of rectification plans for specific defects. Considering the applicability of the model, all the data selected in this paper are publicly available, and this method is simple and easy to implement. At present, such an evaluation system cannot serve as an early warning system for heat-wave disasters. Under these circumstances, the manner in which spatial data are used to establish a heat-wave disaster early warning system to realize the implementation of disaster monitoring and vulnerability estimation is also the focus of future research in this field.

5. Conclusions

Heat waves are major climate disasters that occur throughout the world. At this stage, a unified HHV system for heat waves has not been established. The accuracies of the different evaluation methods are still being explored. Based on previous studies, this paper proposes a new method. We use the H-AHP method to calculate the weight of each evaluation index. Then, a comprehensive assessment model based on spatial data is constructed according to the weights of the different index layers, and the distribution and impact factor of the heat-wave vulnerability affecting Karachi, Pakistan, are calculated. This work has certain reference significance to better understand the vulnerability to heat waves and establish a heat-wave identification, monitoring and evaluation system.

Based on the assessment, the low-vulnerability area covered 99 km², and the middle-low vulnerability area covered 1505 km², while the total area with a middle vulnerability was 1353 km². The total area with a middle-high vulnerability was 276 km², and the high-vulnerability area totaled 0 km². The analysis revealed that a wide range of medical institutions and a high urbanization level can reduce the HHV to a certain extent, but the influence of green space coverage depends on the characteristics of the vegetation itself, such as the shading performance and the cooling effect. For Karachi, it is important to pay attention to the infrastructure in high-vulnerability areas and provide more protection for the elderly to reduce the incidence of disease and death caused by heat waves. In addition, the pervasion of indoor “cooling centres” is also a good way to avoid risks. This study was based on kilometre-level gridded spatial data. However, the limitation of the spatial data acquisition and cost, we did not consider the impacts of more sophisticated indicators such as air-conditioning ownership, which bring an inevitable error in our HHV results. It should be noticed that the HHV still have some limitation in its application. For example, it was not a universal spatial description for any years, only providing a reference for risk perception. In the future, these important indicators should be incorporated in to improve the comprehensiveness of the assessment. In addition, the spatial resolution should be further improved following the highest resolution satellite development.