Indian heatwaves in a future climate with varying hazard thresholds

India has experienced remarkable changes in temperature extremes in recent decades due to rapid global warming leading to extreme heat events with disastrous societal impacts. In response to continuing global warming, this study investigates summertime (March–June) heatwave characteristics over India in the present and future climate. During 1951–2020, India Meteorological Department observational data show rising trends in heatwave characteristics such as frequency, intensity, duration, and season length, mainly over India’s northwest, central, and south peninsular regions. Further, the present study explores the changes in future heatwave characteristics using the state-of-the-art statistically downscaled bias-corrected climate models data from Coupled Model Intercomparison Project Phase 6 (CMIP6) of the Shared Socioeconomic Pathway scenario. This study uses varying hazard thresholds, namely fixed (time-invariant historical climatological threshold) and decadal moving thresholds (time-varying future climatological threshold), to define heatwaves and examine the future changes in heatwave characteristics over India. Results show a significant increase in mean summertime heatwaves defined using fixed thresholds in terms of their frequency, duration, number, amplitude, cumulative magnitude, and season length in the near future (NF) (2025–2054) and the far future (FF) (2065–2094) compared to the baseline period (1985–2014) over much of India, with the most substantial increases seen in the FF. However, heatwaves defined using the decadal moving thresholds show no significant changes in their characteristics during the NF but a substantial change in the FF over many parts of India. This work is the first attempt to use bias-corrected CMIP6 models data to project heatwave characteristics utilising the concept of the varying hazard thresholds across India. Overall, this study provides a comprehensive assessment of climate change’s impact on Indian heatwaves, which can help in planning better adaptation and mitigation strategies.


Introduction
The average surface temperature and recurrent heatwaves have steadily increased since mid of the 20th century across the globe, affecting many sectors, especially in developing countries (Piticar et al 2019). These extreme heat events can be directly or indirectly accountable for increased human morbidity and mortality, increased energy demand (e.g. greater demand for air conditioning), stress on energy supply infrastructure, increased demand for water, and increased risks for sporting and outdoor recreation activities (Coumou andRahmstorf 2012, Añel et al 2017). A heatwave is a period of scorching weather accompanied by humid conditions, leading to a risk of life. Based on geographic or climatic relativism, a wide range of heatwave definitions and indices have been developed scientifically throughout the globe. In recent times, heatwaves have been defined from absolute or relative thresholds or both. The heatwave definitions vary by region, and there is no universally accepted definition, method, or index of heatwave as it is relative to a specific area and a particular time of the year (Smith et al 2013, Kent et al 2014.
Record-breaking brutally hot weather is a significant health threat in India and other parts of the world. In India, heatwaves typically occur between March-June, causing severe human health impacts (Pai et al 2013, Im et al 2017, Pattanaik et al 2017. These severe heatwaves resulted in thousands of deaths of humans and livestock in eastern Odisha in 1998, Andhra Pradesh in 2003, and Ahmedabad and other parts of the western Indian state of Gujarat in 2010 (Pattanaik et al 2017). In 2015, a significant heatwave affected large parts of India and Pakistan, claiming around 3500 lives. The heatwaves of 2015 and 2016 have been lethal across the Indian subcontinent because of a simultaneous spike in temperature and humidity (van Oldenborgh et al 2018). Episodic occurrences of extremely high surface air temperatures spanning multiple days across the Indian subcontinent have risen during the last five decades, particularly across the north, northwest, central, and east coast regions (Ratnam et al 2016, Rohini et al 2016, Panda et al 2017. With the sole exception of the Indo-Gangetic plains, India has seen a marked increase in heatwaves in the last five decades (Joshi et al 2020).
India's comprehensive climate change assessment report mentioned that India's average temperature has risen by around 0.7 • C during 1901-2018. The warming is more pronounced, and warming trends are significant over the Indian region (Krishnan et al 2020). This report also highlights that heat extremes are already occurring across the Indian sub-continent and are projected to increase in the future. In response to the combined rise in surface temperature and humidity, amplification of heat stress is expected across India, particularly over the Indo-Gangetic and Indus River basins. Global and regional climate model projections suggest that heat stress intensification will continue throughout the 21st century across India (Rao et al 2020). Therefore, improving understanding of future climate is necessary, particularly for increasing extreme temperature events over India.
Deadly heatwaves frequently occur in India and can significantly affect human health, as witnessed in the spring months of 2003of , 2010of , and 2015of (Rao et al 2021. Human beings are closely linked to the atmospheric environment via heat budget. Koppe et al (2004) highlighted that several concomitant factors might contribute to the high excess mortality, in terms of length and intensity of heat events, the lack of healthcare preparedness, intervention plans, and social systems. The health effects of individual heatwaves were associated with heatwave intensity, duration, and timing, with large heterogeneity across communities (Medina-Ramon and Schwartz 2007). Extreme heat conditions occurring early in the season can severely harm people's health because of the lack of acclimatisation. Excessive heat can affect the body's physiological responses and functions, such as mild skin irritation (heat rash), cramps, swelling, and fatigue towards heat exhaustion and heat stroke, mainly occurring when body temperature climbs above 40 • C. Several factors can amplify the health risks of excessive heat, including air pollution and wildfires (Lee et al 2019). The prolonged heat events can affect outdoor labour working hours and agricultural and cattle productivity (Kjellstrom et al 2009, Asseng et al 2011. Hence, it is important to focus on various characteristics of Indian heatwaves, which have a wide variety of societal and ecological impacts. The present study explores the changes in future heatwave projections using different hazard thresholds such as fixed thresholds (i.e. heatwaves relative to a historical baseline) and decadal moving thresholds (i.e. heatwaves relative to a future decadal climatology) by following Vogel et al (2020) approach. Vogel et al (2020) found a substantial increase in heatwave characteristics in the future with fixed thresholds. In contrast, only a few significant changes in heatwave characteristics are projected with increasing warming levels based on the moving thresholds. They have considered these moving threshold projections as proxies for hypothetical adaptation levels to climate change and these moving threshold are based on the hypothesis that we adapted to the mean temperature. These future projections of heatwaves using varying hazard thresholds are useful for planning long-term adaptation strategies for future heatwave hazards. Beniston et al (2007) stated that adopting absolute parametric thresholds agrees with the rigorous analysis of heat extremes for a fixed intensity instead of relative thresholds that measure extreme episodes of a fixed rarity. Therefore, it is necessary to investigate possible changes in heatwaves characteristics over India in response to global warming levels with varying thresholds.
Only a few studies have analysed the historical trends in heatwave metrics across India. Rohini et al (2016) examined the variability and trends in heatwaves over India from 1961 to 2013. Their study analysed the limited heatwave metrics (frequency, duration, and number); here, the present study complements the previous study with a more detailed analysis of multiple heatwave characteristics, which have varying significance across different sectors. A recent study by Das and Umamahesh (2021) showed the expected changes in heatwave properties (intensity, frequency, and duration) using the Coupled Model Intercomparison Project Phase 6 (CMIP6) models data under different climate scenarios over India. The present study builds on the previous studies by calculating the characteristic changes in heatwaves with more metrics and varying hazard thresholds in response to global warming. This work is the first attempt to use bias-corrected CMIP6 models data to project heatwave characteristics using the concept of the moving threshold across India. The outcomes from this work will help to strengthen and improve the current climate change mitigation and adaptation strategies by providing more credible evidence for decision-makers to cope with the heatwave hazards caused by global warming in the future. The rest of the paper is organised as follows: the datasets and methodology employed in this study are presented in section 2, followed by the results in section 3. A summary of the main findings and general conclusions are discussed in section 4.

Data
The observed daily mean temperature data from India Meteorological Department (IMD) at 1 • × 1 • spatial resolution for the period 1951-2020 is used to calculate Indian heatwave trends. This observational gridded dataset is generated using quality-controlled station data (Srivastava et al 2009). The IMD dataset has been widely used for heatwave-related studies over the Indian region (Ratnam et al 2016, Rohini et al 2016. The new generation of the state-of-the-art Global Climate Models (GCM) simulations produced by Coupled Model Intercomparison Project Phase 6 (CMIP6) (https://esgf-node.llnl.gov/search/cmip6/) is the most advanced dataset currently available for climate studies (Eyring et al 2016). The present study analysis is carried out with the statistically downscaled, bias-corrected, and high resolution (0.25 • × 0.25 • ) daily maximum and minimum temperatures developed by Mishra et al (2020a and2020b) over the Indian sub-continent for assessing the future heatwave characteristics. High-resolution data is essential in getting reliable climate projections at a local or regional scale, which is necessary for formulating adaptation strategies (Haarsma et al 2016). Downscaling and bias correction techniques are the two methods that are usually used to get relatively accurate climate change projections at a regional scale (Wilby et al 2004, Fowler et al 2007, Christensen et al 2008, Maraun et al 2017. The details of the model data used in the present study are given in table 1. The historical simulations of CMIP6 models during 1985-2014 and their projections during 2015-2100 under the Shared Socioeconomic Pathways (SSP5-8.5) are used in this study. The future climate projections were driven by considering SSPs (Eyring et al 2016). SSPs consider varying greenhouse gas and aerosol emissions and also include specific changes in societal development indicators, such as the population, economy, and urbanisation. SSPs are designed to work in combination with the Representative Concentration Pathways (RCPs). The SSP5-8.5 is a high emission fossil-fuelled developments scenario driven by high economic growth and strong reliance on fossil fuels socioeconomic pathway and in combination with the target radiative forcing level of 8.5 W m −2 towards the end of the 21st century. The SSP5-8.5 scenario is a possible trajectory if no measures are taken to reduce GHGs emissions. To assess the future projections of heatwave characteristics with consistency among the CMIP6 models, the 21st century is split into three different periods-the historical period , the near future (NF;2025-2054, and the far future period (FF; 2065-2094).

Heatwave definition
According to IMD, a heatwave is confirmed if the maximum temperature reaches at least 40 • C or more for plains and at least 30 • C or more for hilly regions, and the maximum temperature departure is at least 4 • C-6 • C notches above normal. At the same time, a severe heatwave is declared if the departure from the maximum temperature is more than 6 • C or the actual maximum temperature is ⩾47 • C (Ratnam et al 2016, Rohini et al 2016, Pai et al 2017. This definition does not accurately accommodate the climatological temperature variations between various geographical regions and seasons as well. A heatwave definition using the time-varying percentile-based threshold approach can overcome this limitation and thus can be applied across different climatic regions (Perkins et al 2012, Perkins andAlexander 2013). Hence, this study identifies and measures heatwaves using the excess heat factor (EHF) index (Nairn and Fawcett 2013) based on the relative/percentile threshold. The EHF index is widely used all over the globe for measuring heatwave metrics. EHF is calculated according to Reddy et al (2021a) and is expressed as follows  where T is the daily mean air temperature, T i represents the daily mean temperature on ith day, and T 90 represents the climatological 90th percentile of the baseline period. The T 90 values are calculated using the 15 d centred window for each day of the year for the selected period. According to the EHF definition, a period of three or more consecutive days with a positive EHF value (>0) is considered a heatwave. However, Baldwin et al (2019) showed that heatwaves could continue after minor interruptions of cold days with similar features to those that persist through consecutive days. To overcome this, according to Baldwin et al (2019) and Rastogi et al (2020) the present study defined the heatwave at a given grid cell as a period of at least three consecutive days with an EHF value greater than zero and considered to continue until at least two consecutive days with an EHF value less than or equal to zero are recorded. The heatwave metrics are calculated according to Reddy et al (2021b). They are heatwave frequency (HWF), heatwave duration (HWD), heatwave number (HWN), heatwave amplitude (HWA), heatwave cumulative magnitude (HWC), heatwave season length (HWS), and first heatwave timing (HWT) and the details are presented in table 2. In this study, heatwave metrics are computed during summertime (March-June), when heatwaves have adverse socioeconomic and ecological impacts.
This study calculates the heatwave metrics trend using the Sen slope (Sen 1968). The (Mann 1945, Kendall 1957 test is a non-parametric statistical test widely used in climatology and hydrology to detect trends. This study uses the MK test with trend-free pre-whitening (Yue et al ) to assess the significance of statistically significant trends (Keellings et al 2018, Reddy et al 2021b. Further, the present study assesses the statistical significance of future changes in heatwave characteristics using the Mann-Whitney U test (α = 0.05). Following Tebaldi et al (2011) approach to assessing the ensemble mean significance, this study considers the difference in a grid cell is statistically significant when at least 50% of the models show significant differences and at least 80% of those models agree on the sign or direction of the change. If at least 80% of models do not agree on sign change, then the difference values are not shown (masked) irrespective of model agreement on significant change. However, the multimodel mean difference values are shown without indicating significance if at least 50% of models do not agree on a significant difference, and at least 80% agree on sign change (Nishant et al 2021). Vidal et al (2012) proposed the moving threshold concept to account for different adaptation scenarios for characterising future changes in spatiotemporal droughts. For a detailed discussion on the use of moving thresholds for defining hot days and its potential links with adaptation policy refer to Vogel et al (2020). This study applies fixed and moving thresholds to determine heatwaves before computing the heatwave metrics following Vogel et al (2020). Fixed thresholds are the heatwaves relative to a historical period, and the decadal moving thresholds are heatwaves relative to future decadal climatology. In the case of the fixed thresholds, T 90 in the EHF is calculated for a time-invariant selected reference period 1981-2010. For decadal moving thresholds, T 90 is computed based on a time-varying decadal moving base period, i.e. for the current decade, the previous 30 yr are considered as a base period (for the 2050s it is 2021-2050, 2060s it is 2031-2060, 2070s it is 2041-2070, 2080s it is 2051-2080, 2090s it is 2061-2090). Due to the availability of SSP5-8.5 scenario data from 2015 to 2100, the T 90 of the period 2016-2045 is considered the decadal moving threshold for the 2020s, 2030s, and 2040s.

Observed trends in the heatwave metrics
This section presents the observed spatial patterns of long-term trends in heatwave metrics over the Indian sub-continent during 1951-2020. Figure 1 shows statistically significant positive trends in HWF, HWD, and HWS over most parts of North West (NW) India, Central India (CI), and South Peninsular India (SPI). An apparent elongated area/regional spread of the heat advection diagonally from the NW to the SPI region can be seen in figures 1(a), (b) and (f). The HWF is larger in NW India (desert region) than in other parts of India. Since most of the areas in and around NW are dry and semi-dry regions and it clearly shows that heatwaves are more frequently occurred in these regions than in the wet areas (figure 1(a)), which is consistent with the notion of extreme heat rooted in dry soils (Alexander 2010).
The spatial trend pattern is similar between HWA and HWC, which are statistically significant over many areas. The HWC provides a basis for understanding the study region's extra heat felt during heatwaves. The areas with more robust trends in HWA and HWC experienced an increase in extra heat during the heatwaves period. These heatwave magnitudes show an increasing trend, mainly in NW and parts of SPI. It is noticed that most of the SPI exhibited negative trends in HWT. In contrast, parts of NE India show an increasing trend in HWT, but this is not statistically significant. The negative trend values of HWT represent an earlier onset of heatwaves in a season. The regions which show negative HWT trends also experienced positive HWS trends. This means that the extended HWS length is mainly due to the early onset of heatwaves in those regions. The observed patterns show that heatwave spells are occurring early in summer in recent periods and have extended through southern parts of the country. Heatwaves that occur earlier in the spring can catch people off-guard and increase exposure to the health risks associated with heatwaves.
Results indicate that heatwave trends are significantly increasing in terms of frequency, duration, amplitude, magnitude, and season length in recent periods compared to the past, particularly across the NW, CI, and SPI regions (figure 1). These results are consistent with previous studies (e.g. Ratnam et al 2016, Rohini et al 2016. Singh et al (2021) mentioned that heatwave characteristics have significantly increased in recent years and are becoming more frequent and expanding in areas where previously no or very few heatwave events occurred. Rohini et al (2016) found that, over CI and NW parts, a significant increasing trend in the frequency, duration, and maximum duration of heatwaves are observed during April-June based on the 90th percentile of maximum temperature over a five-day window and EHF. Panda et al (2017) confirmed that the warm spell and heatwaves increased significantly during 1981-2013, which are mainly an undenied influence of post-1980s global warming. Recent studies by Mukherjee and Mishra (2018) reported an increasing trend in intensity, frequency, and duration of heatwave events since the post-1950s in India. In addition to the studies mentioned above, this work showed that the Indian landmass exhibited a continuous increase in heatwave events during 1951-2020 and displayed dramatic trends in the spatial extent in response to ongoing global warming.

Historical climate simulations and future projections of mean temperature
The spatial distributions of the seasonal (March-June) mean temperature climatology for the Indian subcontinent derived from 13 CMIP6 simulations along with their multi-model mean (MMM) and IMD observational data sets from 1985 to 2014 are presented in figure 2. The climatological seasonal mean temperature over a large part of India is noticed to be higher than 33 • C in all CMIP6 individual simulations (figures 2(a)-(m)), MMM (figure 2(n)), as well as in IMD observational data ( figure 2(o)). Results show that most models and their MMM displayed the higher temperatures over SPI, CI, and NW India adjoining areas, where the summer temperatures are more elevated than other regions. Overall, a slightly warm/cold bias has been noticed in the mean temperatures during summertime (March-June) in some regions ( figure 2(p)). The biases are reduced in these statistically downscaled, bias-corrected datasets. Most CMIP6 individual models and their MMM show better capability in reproducing the seasonal mean temperature patterns and show a good agreement with each model and their MMM compared to the observed data over the Indian landmass in the baseline period. Also, the results show that the MMM is desirable for providing a more reliable estimation of mean temperatures compared with observations. Figure 3 shows future warming over many parts of the Indian landmass. The MMM simulations show warming exceeding 1.0 • C over many regions in the NF under the SSP5-8.5 scenario. Note that in the FF, substantial warming of more than 3.0 • C is apparent in the SSP5-8.5. Under the SSP5-8.5, it is observed that central and northern India gets warmer than southern India by about 2 • C in the FF. Mahlstein et al (2012) reported that lower latitudes display considerably smaller natural climate variability than high latitudes, which impedes identifying apparent changes in warming signals. A similar feature was observed by Purnadurga et al (2017) that the north Indian region would warm more than the southern Indian region during the period 2001-2014 when compared to 1979-2000. This warming over northern India was attributed to the black carbon aerosols (mainly from fossil fuel and incomplete combustion, absorption of the solar radiation), which primarily produce the heating effect and positive radiative forcing effects (Jacobson 2010, Ban-Weiss et al 2012). The most robust temperature increase is seen in the FF over entire India under the SSP5-8.5 scenario. Figure 3 clearly shows the gradual increase in the temperature spatially across the country in the NF and FF. This is highly significant given that India might experience severe hot weather during the summer months in the near and FF. The projected changes are significant at a 0.05 level and robust over entire India in both NF and FF under the SSP-5-8.5 scenario.
The area-averaged mean temperature during summertime over the Indian land points in the historical period  and for the future (from 2015 to 2100) under SSP5-8.5 scenarios is shown in figure 4 as plumes. The temperature values are expressed as anomalies from the baseline period of 1985-2014. The time series of normalised mean temperatures and the shading indicates a MMM of ±1 SD, respectively, are shown here. Figure 4 compares the summertime temperature anomalies derived from the IMD and MMM in the historical period and future projections beyond 2014. The IMD data broadly compares with the MMM in the historical period. Therefore, the temperature anomaly (in o C) time series compared with the IMD data supports the evaluation with the CMIP6 models. Both the CMIP6 MMM and IMD show a warming trend. Overall, the SSP5-8.5 scenarios exhibit a gradual increase in the mean temperature until the end of the 21st century. Bathiany et al (2018) reported that the climate models show increasing temperature variability over India, evidenced by the increase in the standard deviations of temperature, which is because of the domination of radiation on the latent heat fluxes over the northern hemispheric regions. The temperature anomalies continue the warming trend until the 2040s but diverge toward the end of the century. However, there is a spread among the models, and the MMM shows that temperature will increase by around 4.5 • C by the end of the century, higher than what has been pledged by the 2015 Conference of Parties of the United Nations Framework Convention on Climate Change (Im et al 2017). The rate of temperature change is more significant for SSP5-8.5 after 2040. This suggests that the temperature increase would be more dramatic by the end of the 21st century, particularly in the higher emission scenario. Therefore, characterising and analysing future HWs over the Indian subcontinent is a noticeable issue during boreal spring and early summer. This shows the effectiveness of expected climate mitigation strategies while primarily reflecting the design of the SSP scenarios in terms of the radiative forcing.

Historical and future changes in heatwave metrics
In this section, the characteristic changes in seven key heatwave metrics with fixed and moving thresholds for the near (2025-2054) and FF (2065-2094) relative to the historical period  are investigated. The period 1985-2014 is selected for the reference climatology to obtain future changes in simulated climate from the CMIP6 models.

Heatwave frequency (HWF)
The spatial distribution of summertime (March-June) climatology of HWF (total number of heatwave days per season) for the baseline period is illustrated in figure 5(a). Based on MMM, and the regions experience an average of 7 (in CI) and 11 (in SPI) heatwave days per season. Notably, parts of SPI and south-CI, NW witnessed sustained HWF, and these are the hottest regions compared to the rest of the country. Figures 5(b) and (d) show the changes in HWF in the NF and FF relative to the historical period (fixed thresholds). A statistically significant positive change in the mean proportion of HWF is seen over the entire Indian landmass in the NF ( figure 5(b)). Specifically, the SPI and parts of CI regions exhibit positive change with an increase of 30-60 d per season, and it is projected to rise more in the future. The FF projections show the rise in HWF is even more substantial over the whole of India, with an increase of 80 d per season ( figure 5(d)). This increase in HWF might be attributed to the significant increase in the temperatures in the future ( figure 3(b)). The changes in HWF in the NF and FF could manifest as more or less spatially extensive across India.
In the NF, no significant changes are noticed with decadal moving thresholds (figure 5(c)), whereas an increase in the FF was projected (figure 5(e)) with more number of days compared to the NF ( figure 5(c)). Parts of SPI, NW, central North India, and the eastern coastal regions are likely to witness an increment HWF of about 20 d per season in the FF. A remarkable feature noted here is that the change in HWF with fixed thresholds has amplified to a greater extent (figures 5(b) and (d)). According to Das and Umamahesh (2021), the heatwaves frequency is likely to increase in India with an increase in temperature towards the end of the century under the SSP5-8.5 scenario. The longer-lasting and more frequent heatwaves lead to an increased count of heatwave days per season, with the greatest changes being projected for most of the Indian subcontinent. This finding shows that much more drastic changes are discernible in the frequency of the heatwaves, and it majorly shows the great impact of higher greenhouse emissions. Figure 6(a) displays the MMM of HWD climatology in the baseline period. The spatial pattern shows a diverse range of HWD across India, ranging from 4 to 6 d per event. Particularly parts of NW, Southcentral, and SPI have witnessed more HWD than other regions. These projected changes in HWD are consistent with changes in HWF. Figures 6(b) and (d) illustrate the changes in the HWD (in days) in the NF and FF with fixed thresholds. This HWD index is paramount because heat-related mortality due to heatwaves mainly depends on the duration of the heatwaves (Li and Bou-Zeid 2013). In the NF, the heatwaves consistently show a significant positive change with a duration of around 6-25 d per event. These changes showed in the SPI, and some parts of CI would experience a longer duration than the other areas ( figure 6(b)). It is also projected with a substantial increase in heatwaves with prolonged durations in the FF ( figure 6(d)). These most significant changes in the HWD are associated with increasing temperatures over the subcontinent in response to global warming. Overall, the HWD is projected to increase by more than 45 d per season in the FF over many parts of India with fixed thresholds. This shows that most of the days in the season are considered heatwave days. This result implies that the increment of HWD over the Indian sub-continent is more significant; thus, the heatwaves will be more extreme with a higher duration.

Heatwave duration (HWD)
The moving thresholds are projected to experience a significant increase over NW, SPI, CI, and adjoining areas with a positive change in the FF (figure 6(e)) compared with the NF (figure 6(c)). No significant changes are detected in the NF with the moving thresholds. Further, the FF projected an increase in long durations with the rate of 10-15 d through moving thresholds. In addition, the Indian sub-continent is more sensitive to climate warming in the NF and FF; the changes in HWD with moving thresholds are much less than the fixed ones (figures 6(b) and (d)). Figure 7(a) summarizes the climatology of HWN for the baseline period. The spatial pattern shows an occurrence of two heatwaves (on average) per season-it is evident that southern India is experiencing a more significant number of heatwaves than the north Indian region.

Heatwave number (HWN)
The spatial distribution of HWN changes in the NF and FF is shown in figures 7(b) and (d) with fixed thresholds. The HWN shows a positive shift in India, with the most significant increase over three events per season in the NF ( figure 7(b)), though the changes are stronger over many parts of NW and CI. Notably, more statistically significant areas are found over the northern Indian latitudes with high spatial variability, increasing more than five events per season in the FF at higher global warming levels ( figure 7(d)). This apparent positive change in HWN in NF and FF shows that the country has experienced frequent heatwave events with an increased number of hot days. Decadal moving thresholds detected the change in HWN of around two events per season in the NF, which are not significant (figure 7(c)). Interestingly, the HWN increment in FF was spatially more uniform than in NF. Entire India was detected with a positive difference in the FF; mainly, a significant positive change was observed from SPI through CI and adjoining areas (figure 7(e)). Overall, these moving thresholds also show a statistically significant difference, but with a smaller in magnitude. However, the regional climate sensitivity responses at higher global warming levels are stronger across India.

Heatwave amplitude (HWA)
The MMM simulates the spatial pattern of mean amplitude ranging from 1 to 8 • C 2 season −1 during the historical period ( figure 8(a)). The MMM suggests that, on average, the HWA is more prominent in the northern latitudes of India, particularly in NW regions. HWA show higher values like HWF (figure 5(a)) over NW and parts of CI in the present-day climate compared to SPI.
The NF projections ( figure 8(b)) suggest an increase in HWA across the northern latitudes of India. The MMM indicates a rise of 2-12 • C 2 season −1 over the region. A substantial increase (with values of 5 to more than 25 • C 2 season −1 ) in HWA was projected in the FF over the whole Indian sub-continent ( figure 8(d)). In the FF, intense heatwave events are likely to affect the central and northern Indian states. The most robust warming is projected in the north Indian regions compared to the other areas. Thus, the spatial coverage of HWA also likely increase and spread over large areas in future climate scenarios with fixed thresholds. An increase in HWA will have severe adverse health impacts.
In the NF, the moving thresholds show a slight increase in amplitude over north Indian states with statistically insignificant values. In contrast, the east coast belt shows a slight significant positive change ( figure 8(c)). An upsurge in HWA in most regions is noticed in the FF with a statistically significant positive change (figure 8(e)), particularly parts of NW, CI, and SPI are more prominent with increasing amplitude of around 10 • C 2 season −1 . Most regions could experience the highest rise in HWA under high emission scenario. The HWA values are much lesser with moving thresholds when compared with the fixed ones (figures 8(b) and (d)). Figure 9(a) represents the spatial pattern of HWC (which measures extra heat felt during heatwaves) during the baseline period. The MMM shows significant heating with an average of more than 18 • C 2 season −1 in CI and more than 30 • C 2 in parts of NW India, and the magnitude is low in the parts of SPI.

Heatwave cumulative magnitude (HWC)
In the NF, fixed thresholds showed an increase of ∼70-120 • C 2 season −1 in HWC over many parts of India, especially the heating is more in CI and NW India ( figure 9(b)). The FF projections suggest a substantial increase in HWC across the country, which shows an increase of more than 240 • C 2 season −1 ( figure 9(d)). An increase in HWC will have severe adverse health impacts in the future period (Panda et al 2017). The spatial pattern of HWC illustrates the regions where the HWA is more robust, so the regions are experiencing maximum heatwave intensity and excess heat during the heatwaves. Moving thresholds noticed detectable changes in the NF along the eastern coastal regions (less than 20 • C 2 ), and some areas in the northern Indian states would probably be affected by HWC. Still, the changes are statistically insignificant (figure 9(c)). However, a considerable increase is noticed in the FF over northern Indian states and parts of SPI (around 100 • C 2 ) with statistically significant positive change (figure 9(e)). Thus, the spatial coverage of HWC is likely to increase and spread in the future, and similar patterns are also apparent in HWA.

Heatwave season duration (HWS)
The spatial distribution of HWS (a difference between the last and first heatwave day in a season) in the baseline period is shown in figure 10(a). The results show that the MMM of HWS was around 20-32 d per season in the baseline period. For the NF ( figure 10(b)), the HWS shows a significant positive increase by around 31-65 d per season over entire India ( figure 10(b)). Similarly, the HWS is projected to rise significantly across India, with an increase of around 80 d per season in the FF ( figure 10(d)). Noticeable differences are observed between the NF and FF with widespread higher HWS, with increases of around 45 d over most areas with fixed thresholds. When moving thresholds are used, HWS in the NF shows a slight positive change. However, these changes are statistically insignificant ( figure 10(c)). The tremendous increase of HWS around 50 d per season is projected across India in the FF. Therefore, the results in figure 10(e) indicate a significant shift in the HWS change from the NF to FF. Figure 11(a) depicts the climatology of the occurrence of HWT in the baseline period. Climatologically, the first heatwave occurs mainly between the second half of April, starting in SPI, and by the second half of May, it spreads over parts of NW and CI. The first heatwave day in a season is characterized as the day in the season when the first heatwave hits a particular location. With fixed thresholds, the changes in HWT in the NF relative to the baseline period show a statistically significant negative change over many parts of India, which means that the heatwaves may start by the end of March or early April ( figure 11(b)). While towards the FF, substantial negative changes are observed with statistically significant differences ( figure 11(d)). The early onset of heatwaves might likely occur in the FF from early March. The moving thresholds also show chances of early onset in some places in the NF (figure 11(c)), and most regions are statistically insignificant. In the FF (figure 11(e)), a statistically significant negative change was observed over the entire of India (which means heatwaves are expected to Figure 11. Climatology of first heatwave timing (HWT) in the baseline period (a). Future changes in HWT in the near (b) and far future (d) relative to the baseline period with fixed thresholds. Future changes in HWT in the near (c) and far future (e) with moving thresholds. The stippled regions represent the statistically significant changes at a 0.05 level. start in early March). Variability is high in the FF changes in HWT from the regional point of view. The negative change values of HWT represent an earlier onset of heatwaves in a season, which indicates a high chance of an extended HWS duration. The early onset of heatwaves could severely influence the population and agriculture. These results suggest that the intensification and early occurrence of heatwaves in SPI, North and CI, and are severe in response to global warming.

Summary and conclusions
The present study aims to understand the heatwave characteristics during summertime (March-June) over India in response to ongoing global warming based on the observations and using the state-of-the-art statistically downscaled bias-corrected CMIP6 models. Heatwaves occur more often in significant areas across the Indian subcontinent with increased intensity, frequency, and duration (Ratnam et al 2016, Rohini et al 2016, Rao et al 2020. Detailed analysis of the present study emphasises the trends in summertime heatwave metrics (such as heatwave frequency, amplitude, cumulative magnitude, season duration, and the timing of the first heatwave) over most regions of Indian landmass are significantly increasing during the period 1951-2020. This increasing instances of heatwaves can have a devastating impact on human health and even lead to an increase in the number of heatwave casualties.
Most of the CMIP6 individual models and their MMM show better capability in reproducing the patterns of the seasonal mean temperature in the baseline period. The mean temperature is projected to increase by more than 3.5 • C by the 21st century under in SSP5-8.5 scenario. These future temperature projections show that there will be continued warming until the end of the century over the Indian landmass. This study showed the projections of heatwave metrics with fixed thresholds under the SSP5-8.5 scenario for two different time slices (NF and FF) of future changes compared to the baseline period. With fixed thresholds, the heatwaves would last longer, be more intense, occur more often, and begin early in the NF (2025-2054) and in the FF (2065-2094) relative to the baseline period .
The moving thresholds can help us understand climate conditions suitable for normal climate system response, and if the conditions exceed those thresholds, impacts may occur. However, the moving thresholds can better scrutinise the events expected to impact things we care about (IPCC 2021). Developing tailored climatic impact-driver indices representing these thresholds helps to provide action-relevant climate information for adaptation and risk management. Adaptation efforts can change these thresholds, altering the profile of climate conditions that would be problematic and increasing overall climate-resilience (IPCC 2022). In this study, we adopted the decadal moving thresholds criteria, which are considered a proxy for adaptation to the respective prevailing future climate for understating the heatwave characteristics (e.g. Vogel et al 2020). These moving thresholds are based on the hypothesis that we adapted to the mean temperature. The varying hazard thresholds can be seen as proxies for hypothetical adaptation levels to climate change. Given the strong sensitivity of projected heatwaves to these thresholds, this analogy underlines the active role of adaptation for projected changes in impacts from heatwaves in the future. Adaptation to extreme heat is happening globally in response to the different effects and varying implementation scales. However, to estimate expected changes in future HW impacts, one must consider changes in exposure and vulnerability and their link with adaptation levels. This study identified that decadal moving thresholds detected moderate changes in heatwave characteristics in the near and FF over the Indian region. For future heatwaves, this study finds a strong sensitivity in heatwave characteristics to the choice of threshold.
Specifically, in India, the seasonal mean warming in the future is larger than the present climate; as a result, the decadal moving thresholds implying for adaptation to the respective prevailing future environment, and these thresholds should be considered in the projections of potential future heat-related impact studies in the present warming world. The present study results lend additional credibility to the projected increase in heatwave characteristics due to anthropogenic GHGs, which will likely impose significant human health risks with large heterogeneity across communities.
Therefore, this study's findings can help us understand the current and possible future conditions of changes in the occurrence of heatwave events across India. Under a warming climate, such knowledge could be applied to develop effective climate risk management to reduce future heatwave impacts on society, the economy, and the environment.
The early and prolonged heatwaves in India during March and April of 2022 have severely affected the crops' life cycle, thus leading to reduced productivity, particularly in the northwest and central Indian regions (Bal et al 2022). The extra heat and intensity characteristics of Indian heatwaves can have severe effects on human health, poultry, and fisheries (Bal et al 2022). This highlights the importance of considering various heatwave characteristics in the Indian region. Hence, this study's multi-characteristic analysis of Indian heatwaves could help in preparing advanced heatwave plans for the human health, industrial and agriculture-related sectors according to their needs.