Retrospection of Heatwave and Heat Index: A Case Study using ERA5 Dataset

The frequency and intensity of extreme events especially Heat Waves (HW) are growing all around the world which ultimately poses a serious threat to the health of individuals. To quantify the effects of extreme temperature, appropriate information, and the importance of HW and Heat Index (HI) are carefully discussed for different parts of the world. Varied denitions of the HW and HI formula proposed and used by different countries are carried out systematically continent-wise. Different studies highlighted the number of denitions of HW, however mostly used Steadman’s formulae for the calculation of HI that uses surface air temperature and relative humidity as climatic elds which was developed in the late 1970s. Since then, dramatic changes in climatic conditions have been observed as evident from the ERA5 datasets which need to be addressed. Likewise, the denition of HW, which is modied by the researchers as per the geographic conditions, necessary modication in Steadman’s equation also needs to be done. This study will help the researcher community to understand the importance of HW and HI and think about its modication which further helps in better adaptation and application. Furthermore, it opens the scope to develop an equation based on the present scenario keeping in mind the basics of an index as considered by Steadman.


Introduction
The occurrence and strength of extreme heat events are increasing all around the world which has direct and indirect impacts on the health of living beings and the ecological system. Extreme heat events are physical hazards that cause health issues in eerie (Kent et al. 2014). These events also affect the earth's warming process. One of the main reasons for the warming of the earth is due to the increase in concentrations of greenhouse gases received from different anthropogenic sources that produce a higher level of pollutions (Fischer, Brunekreef, and Lebret 2004). Researchers believe that this scenario of increase in temperature (Pattnayak et al. 2017), will continue aggressively in the future as well if no necessary steps are taken to control the pollution level. Modernization and industrialization provide new technologies that improve the lives of human beings but along with this, severe impacts are observed on the environment. Because these new technologies consume a lot of energy that later on leads to produce air pollution and a lot of heat in the atmosphere which triggers many respiratory diseases (Fischer et  The impact of the heatwave (HW), is not limited to the health of human beings (Nitschke et al. 2011;Zhang et al. 2017)but agriculture, ecosystems, and the national economy too are also signi cantly affected by it (Luan et al. 2019). Extreme events like HW, cold waves, drought, oods, cyclones, tornadoes, hurricanes, etc. initially gained attention in the developed countries but, soon due to its global impacts it is discussed and of keen interest worldwide. However, it must be noticed that the events such as oods, tornadoes are a matter of concern if their occurrence leads to loss of human life but events such as heatwaves and cold waves have both direct and indirect long-and short-term impacts on the environment and human life.
Amongst all the months, these extreme heat events normally occur in mid-summer and less intense heat waves also occur in early autumn and during spring. In summers, the value of feel like the temperature is much higher than that of the actual temperature. The feel-like temperature is scienti cally termed as the Heat Index (HI) which accounts for humidity along with the actual temperature (Montero et al. 2013).
Humidity is the amount of moisture or water vapors present in the atmosphere which is expressed in the terms of Relative Humidity. It makes the hot temperature even more unbearable as the presence of humidity in the environment reduces the ability of the body to cool itself. Due to this, in most HI formulas, the contribution of both, air temperature and relative humidity is visible.
There is no globally accepted standard HW de nition (discuss in detail in coming section), although it is commonly de ned as limited successive days with high temperatures above a certain threshold based on community and physiology (Montero et al. 2013). To study and manage heat-related risks imposed on health, HW and HI are needed to be considered wisely. The extent of adverse effects of HW can be carefully studied if HI is known for a particular region that has a direct relation with HW. Hence, in the coming sections, the de nition of HW and the concept of HI are studied to understand their basics. The aim of the assessment done in the present paper is to clarify the de nition of HW and HI so that their understanding shall help to reproduce the same. The key purpose is to understand the methods used by different countries to develop the relation of HI for their country as characterized by the data accumulated from different sources. In this paper, efforts are made to systemize maximum information about the basics of HW and HI to build a foundation for its understanding and to open new perspectives for young researchers, environmentalists, and policymakers, etc. for further modi cation and its application to minimize the hazardous effects of HW. The following section deals with the descriptions of HW and HI. Section 3 deals with the datasets used and the methodology adopted for this study. The classi cation of HW and HI across the different regions of the world has been discussed in Sect. 4, while the discussion has been made in Sect. 5. Summary and concluding remarks are provided in Sect. 6.

Heat Wave (HW)
Extreme heat events are named like HW, heat advisory, excessive heat event, and hot spell, etc. are commonly referred to as temperatures that are either unusually high compared to characteristic local environments or extend to the level which may harm human health and infrastructure. HW is one of the slightest considered terms which have systematic signi cant risks to the world. HW is tough to characterize, and there is no speci c meaning of an HW because similar meteorological situations can establish an HW in one place but not in another. De nition of HW is based on the three categories i.e., media, area-wise, and an all-inclusive one (Perkins and Alexander 2013). Due to the absence of a generic de nition of HW, different countries are using different criteria for HW, which are observed from Table 1 (Tong, Wang, and Barnett 2010). It demonstrates the diverse de nitions used to characterize HW and distinctive criteria were taken to characterize its meaning in the diverse era. To characterize the heat waves from various nations, distinctive sources are taken. It is clearly understood from Table 1 that different nations used their de nition in which reference temperature and duration varied as per the variation in their meteorological parameters. Table 1 highlighted that there are several diverse de nitions of HW which are adapted by the researchers based on their local climatic zones. These HW de nitions are based on the duration of HW, a threshold of temperature (e.g., a relative threshold or an absolute threshold), and temperature indicator e.g., daily average, minimum, and maximum temperature, etc. To support the above statement, a review done by the various authors on different continents will be highlighted in the later section with the only aim is to understand the logic behind the adoption of a different de nition of HW. Before that rst of all understand the brief about the HI.

Heat Index (HI)
Along with temperature, Relative Humidity (RH) plays a vital role to calculate the effects of extreme heat events, because it is not only the heat that poses an effect. It is also the RH that is used to determine how hot and humid it feels based on the combined effect of temperature and humidity. This combined effect is represented by the mathematical term called HI. Basically, HI measure how hot it feels actually when RH is considered with air temperature. HI is one of the methods which can be used to access the potential risk of an extreme event like HW. As the environmental conditions of all the countries in the world are not the same, different countries use different de nitions to de ne the HW based on different metrological parameters range. Additionally, they calculated HI for their area using the Steadman Scheme. This is developed by using multiple regressions such as the Poisson Regression analysis technique on the meteorological data (Steadman 1979). This formula which is called HI is applicable over a certain threshold value of temperature depending on the maximum temperature and relative humidity and shown in the equation below.
Where HI: Heat Index in ºF; RH: Relative Humidity in %, T: Ambient Dry Bulb Temperature in ºF. This formula is used by different researchers around different parts of the world to access the effects of HW on human beings. Based on HI, the heat index calculator or heat index chart provide different zones like caution, extreme caution, danger, and the extreme danger zone. By understanding these zones, necessary steps will be taken to minimize the effects of HW. It is interesting to nd in the coming section that most countries use Eq. 1 for the measurement of HI with their own modi ed HW de nitions. HW studies and reviews done by authors in most of the continents of the world like the United States, Africa, Europe, Australia, and Asian countries like India, Taiwan, and Bangladesh, are discussed in the coming section of this paper. Studies are selected in such a way that it gives the basic idea of HW and HI and covers almost all the continents. De nitions used to characterize the HW of these countries are summarized in Table 2 which are elaborated in the next sections, along with several other countries to understand the reason behind the difference in the de nitions.  . The rate of increase in temperature is more in the polar region than in the tropical and subtropical regions. In the northern pole, the temperature has increased by more than 3°C, while the temperature change is about 1-2°C over the tropical region. The change in RH (Fig. 2c) is a more or less similar pattern to the temperature (Fig. 1c). In most of the regions, where the temperature has increased the RH has also increased and vice versa. In the Antarctica region, the RH decreased and over the Arctic region, it is increased. Furthermore, the change in the climatic elds over the continents has been discussed in the following subsections. Few regions have been selected in each of the continents just to show how the climatic elds have changed and how it may affect HI.

Asia
Asia is one of the largest and populated continents of the world and is supposed that 60% of the total population of Earth is living here. Asia has extremely diverse climates range from arctic and subarctic in Two de nitions are quoted in this paper, one de nition is based on absolute criteria when the daily maximum temperature greater than 35°C. Another de nition is relative i.e. if the daily maximum temperature is greater than the 90th percentile threshold of the local daily temperature distribution of the data. The analysis shows that HW events sharply increased in northwestern China and eastern China.
The frequency and intensity of HW both increase signi cantly in China. ERA5 temperature suggests that the average temperature has increased by about 2°C in the last 40 years (Fig. 3a).

India
India has a wide range of temperatures. States lying in Eastern part of India has comparatively high temperature than western states but lower than that of northern states. annual temperature is about 1°C over India and there is no signi cant trend in relative humidity pattern (Fig. 3b).

Bangladesh
Bangladesh faced one of the major heat waves between January 1994 and December 2002, as a total 13,720 lives were lost due to Heat Wave excluding external causes. In Bangladesh absence of normal premonsoonal rainfall which is brought by aberrant strong low-level westerly winds and weak southerlies for consecutive 10 days is de ned as Heatwaves (Nissan et al. 2017). During the HW in 2008 for consecutive  Table 3 below. This study by division of the country into various parts will help in understanding the procedure or methodology to develop HI for India. Using the real-time data of 20 stations out of 35 stations from Bangladesh Meteorological Department which included monthly dry bulb temperature and relative humidity for a period 1961-1990, HI was calculated. Such a formula in Eq. (1) is appropriate only when air temperature and humidity are higher than 26ºC and 39% respectively. The HI value has an error of ± 1.3°F, as it has been obtained by multiple regression analysis (Steadman 1979). It can be observed from Fig. 3c that there is no signi cant change in both the climatic elds observed over Bangladesh.

Taiwan
HW study conducted in Taiwan, where extended mortality during warm waves has been attributed generally to cardiovascular conditions and cerebrovascular issues   (Fig. 3d).

Africa
One of the hottest continents of the World i.e., Africa in which the maximum average temperature of Earth is quoted at Dallol, Ethiopia. Many severe HW events were observed in different parts of Africa. One of the studies done by Lyon 2009 in Southern Africa, de nes HW as a daily maximum temperature greater than 95 percentiles for at least 3 consecutive days. Ceccherini et al. (2017), reviewed the HW in Africa for a period from 1981 to 2015, consider the HW as a "period ≥ 3 consecutive days with maximum temperature above the 90th percentile of daily maxima temperature, centered on a 31-day window" (Ceccherini et al. 2017). De nition of HW is designed or modi ed after considering the metrological conditions of African countries. Figure 4 shows the interannual variation of temperature and relative humidity for the last 40 years. It suggests that the temperature has increased by 1°Cand the relative humidity has decreased by about 3%. After 2000, both the climatic elds have been changed signi cantly.

North America
The United States has been chosen to represent North America for this study, Smith et al. (2013), reviewed the HW in the United States for 40 years(Smith, Zaitchik, and Gohlke 2013). In this paper, the authors' summarize data from the North American HW indices from 1979 to 2011. Sixteen de nitions of HW indices were quoted, which differ in terms of temperature type i.e., minimum, maximum or average, threshold, durations, and type i.e. relative and absolute. etc. It is observed from this paper that HW is not unique meaning, but it is changed as per the geographical conditions, but focus and basic objective are the same in all the studies. There is a signi cant increasing trend in temperature has been observed in the last 40 years (Fig. 5).

Europe
Europe was affected by two of the worst heat waves in summer 2003, the extreme maximum temperature of 35˚C to 40°C was frequently recorded in July, which extended in August in most of the southern, and central countries from Germany to Turkey. It led to the hottest summer ever recorded in Europe since 1540, with estimated excess mortality varying between 25,000 and 70,000 death in Western Europe (D'Ippoliti et al. 2010). A de nition was given to HW according to which HW for Europe is de ned as "A time interval of at least 2 days with maximum apparent temperature exceeding the 90th percentile of the monthly distribution or a time interval of at least 2 days in which minimum temperature exceeds the 90th percentile and maximum apparent temperature exceeds median monthly value". Concerned with this treacherous HW, an attempt was made to develop the HI equation which could be used for further analysis in two regions of Europe i.e. Marmara and Naple region.

Marmara Region
In Turkey, Marmara Region is the highest populated area. The HI here was distributed according to months accounted by the average values and not the extreme ones. For a period of 2007 and 2016, meteorological data like RH, wind speed, and temperature data were taken from 14 weather observation stations in Marmara Region, which were later utilized to calculate the HI (BURSALI and ŞEN 2017). For warm weather conditions (temperature greater than 21ºC), HI is calculated by the same formula given in Eq. 1. Based on these index formulas, humans live comfortably below 21ºC, semi-comfortable up till 24ºC, and very uncomfortably above the temperature of 27ºC. There is a steady increase in the temperature is noticed in the ERA5 data (Fig. 1a). The temperature is increased by 1.5°C as compared to the 1980s. Conversely, the relative humidity has been decreased by about 4%.

Naples Region
Major two severe heat waves in 2003 of Europe which was taken into consideration while calculating HI of Naples. The temperature is affected by the hotter African anticyclone and milder Azores anticyclone during meridional circulation(Di Cristo, Mazzarella, and Viola 2007). Again Eq. 1 is used to calculate HI when the value of air temperature and humidity are higher than 26°C and 39%, respectively along with the wind speed to be 2.6 m/s. The rate of the change of temperature is moreover Marmara region (Fig. 6b). It may be noticed the 2°C warmings have already occurred as compared to the 1980s.  (Tong et al. 2010). In this, the authors summarize the different de nitions of HW used in between 1996 to 2005 for Brisbane, Australia. Total ten de nitions of HW used in this study but HI used is based on Steadman Eq. 1. Ten de nitions of HW include the daily maximum temperature greater than or equal to 1 to 5 % for consecutively more than 2 to 5 days. This paper indicates that it is di cult to rely upon or use one de nition of HW for different regions but rely on the Steadman Eq. 1. No signi cant change is observed in any of the climatic elds (Fig. 7).

Discussion
There are several diverse de nitions of HW which are adapted by the researchers on the basis of their local climatic zones. These HW de nitions are based on the duration of HW, exposure threshold of temperature (e.g., a relative threshold or an absolute threshold), and temperature indicator (e.g., daily average, minimum and maximum temperature), etc as shown in Fig. 8. Figure 8 shows that HW is the consequence of climate change, air pollution, or/and Global Warming which is quanti ed mathematically by using HI. De nition of HW depends upon different parameters and HI depends upon the relative humidity and temperature, which is used by Steadman in his equation by using the regression technique ( Fig. 8). This Steadman equation (Eq. 1) was derived in 1980's and still, researchers used this equation to quantify the effect of HW.
The main purpose of this study focused on the de nition of HW and HI for different countries which is characterized by the data accumulated from different sources. It is surmised from the survey that all the countries do not follow the same de nition of HW as given by World Meteorological Organization (WMO) i.e., "A period during which the daily maximum temperature exceeds for more than ve consecutive days by the maximum normal temperature of 9°F (5°C)" but most of the countries have modi ed the de nition as per their regional metrological data. Quantitatively, HI con rmed that the temperature experienced during the summer months with high humidity values is more in comparison to the other months. Generally, the different researchers used the Steadman equation for the calculation of HI. Accordingly, different countries developed or suggested their own precautionary steps to minimize the effects of HW caused by heatstroke and heat exhaustion like living in airconditioned homes etc. A warning system based on HI can be designed to study the effect of extreme events based on combined observation of high daytime temperatures, warm nighttime temperature, high humidity, and light winds for several successive days.

Conclusion
It is inferred from different studies that there is no exact de nition of HW, as these vary with respective regions. Different studies implied that it is di cult to develop a generic formula for HW for all the countries worldwide. It is observed from HI calculation that both relative humidity and temperature are the main components for the equation and in most cases; Steadman's equation is used to quantify the effect of an extreme event like HW. Hence, to develop/modify an equation of HI depends upon a diverse range of meteorological parameters like temperature, RH, etc. Therefore, an enormous study of such parameters is required.
The development of a generic index for HW requires special correction parameters (or factors) or a value or a relation with respect to region. For this purpose, study on a mass level is required and countries need to be selected region-wise and based on meteorological variations so that every perspective of diverse variation in weather can be included. This study summarizes the basic ideas about the HW and HI so that this knowledge can provide a platform to develop or modify the existing de nitions and formulas so that necessary steps can be taken to minimize the hazardous effect of extreme events like HW. As there are several de nitions for HW, but for HI, Steadman's equation is still used as a generic equation. There is a need to develop separate HI equations as per different geographical and climatic conditions. Therefore, the development/modi cation of the appropriate HI equation is need for an hour and acts as future scope for this paper. The mathematical aspect of the HI equation can be handled by the mathematical expert with the joint effort with environmentalists for the development of HI.

Declarations
The authors declare no competing interest.

Data and Code Availability Statement
All data used in this study are freely available and can obtained directly from the source: ERA5 data (https://cds.climate.copernicus.eu/live/queue). Alternatively, the data and codes can be made available on request to the authors.
Author's Contribution A.A. and K.C.P. conceived the study. A.A., K.V. and K.C.P. performed the analyses and wrote the initial draft of the manuscript. All authors contributed to the interpretation of the results, discussion of the associated mechanisms, and re nement of the paper.