Climate science to inform adaptation policy: Heat waves over India in the 1.5°C and 2°C warmer worlds

Developing a better scientific understanding of anthropogenic climate change and climate variability, especially the prediction/projection of climate futures with useful temporal and geographical resolution and quantified uncertainties, and using that knowledge to inform adaptation planning and action will become crucially important in the coming years. Generating such policy-relevant knowledge may be particularly important for developing countries such as India. It is with this backdrop that, in this paper, we analyze future heat waves in India by using observations and a large number of model simulations of historical, + 1.5 °C, and + 2.0 °C warmer worlds. In both the future scenarios, there is an increased probability of heat waves during June and July when the Indian monsoon is in full swing and humidity is high, which makes the heat events even more of a health risk. While the highest temperatures in heat waves may not increase much in future climates, the duration and areal extent of the heat waves will most likely increase, leading to the emergence of new heat wave-prone zones in India. The results indicate that the joint frequencies of the longest duration and large area events could be nearly threefold greater in the + 1.5 °C and fivefold greater in the + 2.0 °C future scenarios compared to historical simulations. Thus, overall, the study indicates a substantial increase in the risk of heat events that typically elicit warnings from forecasters. The likely widespread and persistent nature of heat wave events in the future, as revealed by this study, will require planning and adaptation measures beyond the short-term disaster planning frameworks currently in place. Exploring what these measures might look like is beyond the scope of this study, but it underlines the importance of developing climate knowledge with high temporal and geographical resolution capable of informing adaptation policy and planning.


Introduction
The recently published Sixth Assessment Report (AR6; IPCC 2021) of the Intergovernmental Panel on Climate Change lays out an alarming future of climate and its impacts on the Indian subcontinent. Among the impacts already being felt are a more variable monsoon, heavy rainfall events and floods, severe droughts, unprecedented heat waves, and stronger tropical cyclones. Levels of global surface temperature change (global warming levels) are closely related to a range of hazards and regional climate impacts. As the AR6 notes, "projected changes in extremes are larger in frequency and intensity with every additional increment of global warming," which in turn will have substantial impacts on all sectors of Indian society and economy.
Thus, developing a better scientific understanding of anthropogenic climate change and climate variability and using that knowledge to inform adaptation planning and action will become crucially important in the coming years. The importance of such climate science to inform adaptation cannot be overemphasized since effective adaptation options can be developed only if climate futures can be predicted/projected at useful temporal and geographical resolution with quantified uncertainties. The importance of orienting and using climate science to inform adaptation has received attention in the literature (see, for example, Zhang et al. 2008, Harrington et al. 2022. In fact, it has been suggested that the most useful climate science at this point may well be science usable for informing adaptation (Sobel 2021). At the same time, there also is an increasing focus on the need to strengthen the interface between science and policy/practice (e.g., Mitchell and Laycock 2019;Rodrigues and Shepherd 2022). Usable science (Dilling and Lemos 2011) will also require strengthening of local efforts to develop policy-relevant knowledge. Generating such policy-relevant knowledge and connecting to policy and practice domains may be particularly important for developing countries (Conway 2011).
It is with this backdrop that in this paper we analyze the heat wave conditions in the past, present, and future, by using observations and a large number of simulations (100 ensemble members each from 5 models) for each experiment (historical, + 1.5 °C, and + 2.0 °C warmer worlds) using operational definitions of heat events (with modifications for gridded data as described in Joseph et al. 2018). We also discuss the implications of results for both the research community and policy makers. This is intended to provide an illustration of the kind of climate knowledge that could serve to inform policy in a warmer world.

Background
Heat waves are a common occurrence during the summer season in India. Recent decades have seen high mortality due to heat waves (16,000 deaths reported between 2000 and 2015; higher than three previous decades; NDMA 2019; MOES 2019). The heat wave of 2015 alone claimed 2040 lives in India (NDMA 2019) and 2016 saw the highest ever temperature recorded in India-51 °C in Phalodi, Rajasthan, beating the previous Indian record of 50.6 °C set in 1956. Heat waves have shown an increasing trend between 2010 and 2016 over the central and northwestern parts of India (MOES 2016). These events have occurred in the backdrop of increasing average temperatures over India (MOES 2019) which are in line with increases in global average temperature and have been attributed to anthropogenic emissions of greenhouse gases (Dileepkumar et al. 2018(Dileepkumar et al. , 2021. Numerous studies have identified heat wave-prone zones and documented the increasing trend in frequency and duration of heat waves (Pai et al. 2004(Pai et al. , 2013Bhadram et al. 2005;Jaswal et al. 2015; Ratnam et al. 2016;Rohini et al. 2016;Pattanaik et al. 2017;Sharma and Mujumdar 2017;Sandeep and Prasad 2018;Mandal et al. 2019;Singh et al. 2021). Rohini et al. (2016) found an increasing trend in the frequency, total duration, and maximum duration of heat waves over Central and Northwestern India. They use two definitions of heat waves, the first based on the 90th percentile threshold of maximum temperatures over a 5-day moving window (TMAX90) and the second based on excess heat and heat stress called excessive heat factor (EHF). Sharma and Mujumdar (2017) found substantial increases in the incidence of droughts and heat waves and significant changes in the spatial extent of heat waves. Singh et al. (2021) found a spatiotemporal shift in the occurrence of heat waves with a statistically significant increase in three regions, Northwestern, Central, and South-Central India, but a significant decreasing trend over the eastern region. Mazdiyasni et al. (2017) found significant increases in heat waves and a 146% increase in the probability of heat-related mortality events of more than 100 people. Heat waves accounted for about 20% of the mortality resulting from extreme weather events in India between 2001 and 2014 and increased over the period (Mahapatra et al. 2018). Chambers (2020) showed India has the second-largest total exposure of vulnerable people to heat wave days (227 million person-days in 2016), and the trend has been increasing since 2006.
The contribution of human-induced global warming to individual heat events has been studied using event attribution techniques. Wehner et al. (2016) used a "heat index" (which includes the role of humidity in addition to temperature) to show the role of anthropogenic climate change in exacerbating the heat wave of 2015 that led to over 2400 deaths in India and Pakistan. Using the highest daily maximum temperature of the year (TXx), Van Oldenborgh et al. (2018) showed that the 2016 extreme temperature event in Phalodi was rare (about once in 40 years) but that the 2015 event was relatively common at once in 15 years. They speculated that the increase in TXx was tempered possibly by cooling effects from anthropogenic aerosols and/or irrigation.
The AR6 concluded that "With every additional increment of global warming, changes in extremes continue to become larger. For example, every additional 0.5 °C of global warming causes clearly discernible increases in the intensity and frequency of hot extremes, including heatwaves (very likely) …" Im et al. (2017) analyzed future projections over the densely populated agricultural regions of South Asia using daily maximum wet bulb temperature (TWmax) thresholds of 31 °C (considered dangerous levels for most humans) and 35 °C (considered maximum for human survival). They estimate that "under RCP8.5, a small fraction of the South Asian population (~ 4%) projected to experience TWmax exceeding 35 °C by 2100. Approximately 75% of the population is projected to experience TWmax exceeding 31 °C, compared to 15% in the current climate and 55% under RCP4.5." They also point out that the deadly heat waves projected in the Indus and Ganges river valleys coincide largely with locations of highly vulnerable human populations. Rohini et al. (2019) studied the future projections of heat waves in India using models from the Coupled Model Intercomparison Project (CMIP5) and found an average duration increase of 12-18 days and concluded that heat waves are likely to affect the hitherto unaffected southern and coastal regions. Using CMIP5 models, Mishra et al. (2017) report that the frequency of severe heat waves would increase by 30 times and 75 times the current climate by the end-twenty-first century under a + 2 °C warming scenario and RCP8.5 respectively. They estimated that population exposure would increase 18-fold, 92-fold, and 200-fold respectively under a + 1.5 °C warming, a + 2 °C warming, and RCP8.5 scenarios by the end of this century. Saeed et al. (2021) conclude that some areas of South Asia have already started experiencing heat levels that affect productivity and survivability which is projected to become more common and widespread in the + 1.5 °C world and twice as likely in the + 2.0 °C future.
Most of the studies discussed so far use different criteria for defining heat waves over India, making it challenging to convey to decision-makers how the future risks relate to observations or lived experience. We believe that the use of criteria that has wide acceptance among forecasters and consumers of the forecasts will be a better way to communicate future changes in heat events. The India Meteorological Department (IMD) uses "hot day," "heat wave," and "severe heat wave" categorizations (IMD 2021) which are not restricted to the weather forecast community alone. The common occurrence of these events means these terms are familiar to the user community as well-such as the disaster management authorities as well as local and state governments in triggering their heat action plans through standard operating procedures in the areas of healthcare (MOHFW 2021), agriculture, power, and other sectors (Guleria and Gupta 2018). The definitions based on percentiles, EHF, etc. are common within the scientific community, but do not evoke the same understanding among consumers of the forecasts. We therefore deliberately choose to use the operational definitions (with modifications for gridded data as described in Joseph et al. 2018) in order to communicate to the larger community of stakeholders.
In India, the first systematic attempt at heat wave management planning was the Ahmedabad Heat Action Plan (Knowlton et al. 2014) launched in 2013. After the massive heat wave of 2015, the National Disaster Management Authority introduced a set of guidelines for the preparation of action plans across the country aimed at prevention and management of heat waves (NDMA 2019). A few other examples of heat action plans such as Jharkhand (2016) and the Gujarat State Disaster Management (2020) exist, but are principally local response plans. Guleria and Gupta (2018) highlighted the importance of humidity in the framework for heat wave risk management for the coastal states of Telangana and Odisha. Since 2015, location-specific heat index forecasts have been provided (MOES 2017) although development of a heat index for Indian conditions is a work in progress. However, these action plans and measures operate in the weather time horizon of up to a few weeks.
The studies highlighted above provide a coarse view of the significant increases in heat waves and the ensuing human (and other) costs that might result in India from climate change. But their ultimate policy relevance is limited in terms of supporting the development of appropriate adaptation plans. Such planning requires more detailed, nuanced, and systematic understanding of these impacts, which, in turn, can underpin the development of equally detailed and systematic long-range adaptation plans for various parts of the country.

Datasets used: observation and models
For observations, we use a gridded (1° × 1° resolution) dataset (Srivastava et al. 2009) of daily maximum (TMAX) and minimum (TMIN) temperatures available for the period 1951 to 2015 from IMD. This dataset for the Indian region was developed with observed temperature data from 395 stations using "a modified version of the Shapard's angular distance weighting algorithm for interpolating the station temperature data into 1° latitude × 1° longitude grids." Observed daily TMAX data for 3 stations for the period 1969-2015 was obtained from IMD Data Supply Portal (see Data availability statement).
To study the projected future changes in the various categories of heat events, we use data from HAPPI 1 (Half a degree Additional warming, Prognosis and Projected Impacts Page 5 of 19 64 (HAPPI)- Mitchell et al. 2017). The HAPPI project design includes large ensembles of simulations (> 100 ensemble members) of atmosphere-only models for three time slices-each a decade in length: the first being the recent observed 10-year period (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) named historical, the second two being estimates of a similar decade but under 1.5 and 2 °C conditions in the future (namely + 1.5 °C future and + 2 °C future). A weighted multi-model mean of the Coupled Model Intercomparison Project Phase-5 (CMIP5; Taylor Karl et al. 2012) from the representative concentration pathway 2.6 (RCP2.6) provided boundary conditions to all models for the 1.5 °C scenario, and a weighted combination of RCP2.6 and RCP4.5 provided boundary conditions for the 2 °C scenario of HAPPI project. These experiments aim to quantify the impacts on weather-related risks corresponding to + 1.5 °C and + 2 °C of warming relative to pre-industrial conditions as required by the Paris Agreement. The HAPPI database contains data from 5 global models (Table 1) that enables us to examine low probability events. We make use of the output from 5 models each with 100 members for each of the three experiments. The model outputs were regridded to 1° × 1° resolution (to match the IMD dataset resolution) using the "conserve" regrid method-a first-order conservative regridding as implemented in the Earth System Modeling Framework (ESMF 2 ). The regridded fields are then bias-corrected (details in the next section) before analysis is carried out. Although heat waves in India typically occur in the months of April, May, and June, we have used the March-August period in our analysis to capture any shifts in the heat wave occurrence in warmer climates.

Methods
Given the variety of definitions employed in the literature for heat waves and temperature extremes, it is quite a task to use the information for decision-making. Given that most existing protocols for action (e.g., heat action plans discussed in Section. 2) are triggered by operational warning levels, this study focuses on using the operational definitions.
The IMD has established station-based criteria (IMD 2021, Table 2) for classifying heat events in India. A few studies (Pai et al. 2004(Pai et al. , 2013Bhadram et al. 2005) used station observations and IMD's definitions to identify heat waves. Others (Ratnam et al. 2016;Pattanaik et al. 2017;Sharma and Mujumdar 2017;Sandeep and Prasad 2018;Singh et al. 2021) have applied the same criteria to identify heat waves in the IMD gridded (1° × 1°) daily temperature dataset (Srivastava et al. 2009). This may not be appropriate since the gridding procedure uses an anomaly correlation distance that ends up smoothing out peaks. Joseph et al. (2018) devised alternate criteria (Table 2) that use TMAX and TMIN for identifying the hot days, heat waves, and severe heat waves from gridded data (illustrated Table 1 List of participating institutions, models, resolution, and number of ensemble members for the historical (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015), + 1.5 °C (10 years), and + 2.0 °C (10 years in schematic Fig. S1(a)). A comparison of IMD's station-based definition and the Joseph et al. (2018) gridded definition for gridded datasets is shown in Supplementary Fig. S2, which shows clearly that the number of heat wave events identified in the gridded dataset by the Joseph et al. (2018) definition is closer to that of IMD's station-based definition on station data. We therefore adopt the Joseph et al. (2018) criteria for the gridded observations and modeled data. As per Joseph et al. (2018) criteria, if a particular day satisfies criteria A, it includes hot day, heat wave, and severe heat wave conditions; if it satisfies criteria B, it includes both heat wave and severe heat wave conditions; if it satisfies criteria C, it is a severe heat wave condition. In this study, we isolate the hot day (HD), heat wave (HW), and severe heat wave (SHW) days at each grid cell by masking out criteria C from B and B from A as illustrated in Figure S1.
We computed the daily climatological means and daily distribution (using a 31-day window centered on the day in question) of observed TMAX and TMIN over the 2006-2015 period. The TMAX and TMIN from individual models were processed the same way, except that all 100 ensemble members are used in calculating the climatological mean as well as distribution (see Supplementary Text S1). We use the empirical quantile mapping (EQM) method (Amengual et al 2012;Iturbide et al. 2019) to bias-correct the  Fig. 2, Fig. S6). While applying the criteria to isolate heat events in the + 1.5 °C and + 2.0 °C simulations, we use the respective model's bias-corrected historical daily mean climatology and distribution.

Observed heat events
We begin our analysis by looking at the annual mean duration of consecutive HD, HW, and SHW days (as defined in Section. 3.2) in the 1951-2015 period. An HD event is a set of consecutive days (of any duration) on which HD definition is satisfied. HW and SHW events are defined similarly. As shown in Fig. 1 (a-c), HD events are seen across India except over the Himalayas, northeast, and southwest regions with a mean duration of about 2 days. HW events have a similar spread (but less areal extent) across the country with a mean duration of 3 days. The SHW events are mostly seen over the northern plains, parts of the interior peninsula, and southeastern coast. The decadal trends in HD, HW, and SHW duration (Fig. 1, d-f) show decreasing HD duration over most of India, except the northwest (NW) and southeast (SE) regions. The decreasing trend in mean HD duration (number of events) is explained by an increase in the mean HW duration (number of events) over most of the same regions. This behavior is illustrated for specific grid cells in Fig. S4 (c, e, f) and Fig. S5 (c, e, f)). The NW and SE regions see increasing trends in HD both in terms of duration (Fig. 1) and number of events (Fig. S3). This behavior is also seen in the annual time series for specific locations shown in Fig. S4 (a, d) and Fig. S5 (a, d). The observations also indicate that in the NW and SE regions, HDs have occurred more (both in numbers and duration) in recent years resulting in a positive trend. In all three event categories, a consistent decreasing trend of duration and number of events ( Fig. 1 and Fig. S3 respectively) is seen over the eastern edge of the Gangetic plain (see also Fig. S4 (b) and Fig. S5 (b)). One possible explanation may be the increased loading of anthropogenic aerosols over the period (Li et al. 2017;Pandey et al. 2017).

Comparison of model simulations and observations
We compare the HAPPI model "historical" simulations against observations for the full period of 2006-2015 (10 years × 365 days). The bias-corrected mean error of the historical simulations (5 models with 100 ensemble members) varies between − 0.2 and 0.2 °C over most of India, with some regions (North East, Central India) having absolute mean error of > 0.5 °C as seen in Fig. 2. For comparison, the mean error before bias correction is an order of magnitude higher (see Fig. S6). Figure 3 shows the ensemble mean number of HD, HW, and SHW days over the historical period as simulated by each of the 5 HAPPI models and a Taylor diagram showing the model statistics (correlation, standard deviation, root mean square error) compared with observed data. The number of HD and HW events in the individual models matches the observation very well. The pattern correlations are fairly high and range from 0.95 to 0.99, while standard deviations range between 22 and 27, 24 and 28, and 2.5 and 3.6 days respectively for HD, HW, and SHW, which are very close to the observed standard deviations of 27, 28, and 3.5 days, respectively ( Fig. 3; g, n, u). The MIROC model has consistently lower standard deviation ( Fig. 3; d, k, r) than the other models and observation, resulting in a smaller RMSE. The number of HD and HW events in the individual models consistently matches the observation. However, the number of SHW events is slightly overestimated (by 1 day) in all the models over the eastern part of the Gangetic plain and along the east coast. The good agreement between bias-corrected historical simulations and observations gives us confidence in the use of bias-corrected + 1.5 °C and + 2.0 °C future simulations.

Probability of heat events in historical and future climates
To analyze future changes, we start by examining the probability of heat event days (that meet HW or SHW criteria) during April to July in each of the 3 experiments (Fig. 4). To compute the probability of heat event days for different months, we first calculate TE m , the total number of days that meet HW or SHW criteria in each month "m" over the 10-year simulations from all 500 ensemble members, and then divide by TD m -the total number   Fig. 1 The average annual mean duration (days) and its trend (days/decade) of HD events (a, d), HW events (b, e), and SHW events (c, f) are shown for the IMD gridded observation from 1951 to 2015. Trends significant at 95% level (using one-tailed t-test) are stippled. Gray shading represents grid cells that do not satisfy the criteria for HD, HW, or SHW conditions. The average count of annual events and its trend for HD, HW, and SHW categories are shown in Fig. S3 of days in month "m" over 10 years and 500 ensemble members. Where the probability of heat event days needs to be calculated for the whole year or a season, "m" includes all days of the year or season as required. The probability of HW or SHW days is highest in the months of May and June in the historical simulation with all 4 months showing progressively larger increases in the + 1.5 °C and + 2.0 °C futures. Although this study does not address the issue of humidity in heat events, the increased probabilities during June and July are of particular concern as these are monsoon months when the humidity is quite high. Next, we analyze the duration of heat waves in the historical and future climates. The probability of occurrence of heat events of different durations is computed at each grid point by first isolating heat events between March and August in the model simulations. Consecutive heat event days of "n" days are then counted up in the 500 ensemble members of each experiment and the probability is calculated by dividing that number by the number of possible non-overlapping samples of duration "n." We show probability ratios in Fig. 5 calculated by dividing the event probabilities for individual experiments (+ 1.5 °C and + 2.0 °C future) by the event probability of the historical experiments-all of which are shown in Fig. S7. Examining the probability ratios shows that shorter duration events (3-5 days long) are 2-10 times more probable in the + 1.5 °C and + 2 °C futures, whereas  longer events (7 and 9 days) increase by a factor of 10-30. The area likely to experience long duration events in future extends into regions previously not prone to such events with no regions likely to experience reduced probability of heat events.

Large heat wave events in the past and the future of such events
Having documented future changes in probability of occurrence and duration of heat events at the grid point level, we now look at observed "large" events, i.e., events with high mortality (greater than 1000; supplementary Table S1), and ask what might happen to intensity, duration, and geographical extent of such large events in the future. We identify the events of 2009, 2010, 2012, 2013, 2014, and 2015 for analysis and compute the start dates, duration, and spatial extent of each event by identifying grid cells that meet HW or SHW criteria on consecutive days (Fig. 6).
Most of these events begin in mid-May except the 2012 and 2014 events (Supplementary Fig. S8). Events last at least 2-3 days but all contain regions that last 8 or more days. We now examine the duration, intensity (daily maximum temperature), and areal extent of such events under present, + 1.5 °C, and + 2.0 °C climate scenarios. We consider the individual events shown in Fig. 6 and evaluate changes in duration, intensity, and spatial extent of such events in model simulations. Using only the grid cells that formed the extent of   Fig. 5 Probability ratios of heat events (HW or SHW category) of 3-, 5-, 7-, and 9-day duration (columns) are computed for + 1.5 °C and + 2.0 °C futures (rows) with respect to historical simulation (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015). The sky blue color indicates reduced probability of events in the future simulations, whereas the violet color indicates grid cells that do not experience such events in the historical period but do so in the future (i.e., probability ratio is infinity). The probabilities of historical, + 1.5 °C, and + 2.0 °C simulations from which the probability ratios are computed are shown in Fig. S7 each event, we look at durations, peak temperatures, and areal extent where HW or SHW criteria are met in the historical, + 1.5 °C, and + 2.0 °C simulations. First, we analyze the joint exceedance frequency for duration (consecutive days that meet the HW and SHW criteria) and daily TMAX (defined threshold range from 39 to 48 °C) in the grid cells that make up the selected events shown in Fig. 6. To compute the frequency, we count the grid cells (within the event area) in the IMD dataset during the 10-year historical period (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) that meet or exceed each threshold temperature and duration. In the model historical, + 1.5 °C, and + 2.0 °C future simulations, the counts from 500 realizations are calculated similarly and averaged. Figure 7 shows the exceedance frequencies for each of the selected events and experiments. The observed frequency is highest at durations not greater than 4 days and temperatures between 39 and 45 °C for all the events. The + 1.5 °C simulation frequencies are closer to observations rather than the historical experiments which tend to underestimate the frequency of lower duration events but spread across a larger range of durations compared to the IMD dataset. For example, durations in excess of 20 days are seen for 2013, 2014, and 2015 events in the historical simulation, while the IMD dataset does not show anything longer than 8 days (2013) or 15 days (2014). This can be expected when the model frequencies are an average across 500 realizations whereas there is only one realization of the observed. The frequencies progressively increase in the + 1.5 and + 2 °C simulations with longer durations becoming likely albeit with low frequencies in the 1-300 range (28-42 days in the + 2.0 °C future and  Table S1). The state boundaries within India are shown overlaid. The spatial extent of each event is represented by the number of grid cells shown in brackets in each panel 24-40 days in the + 1.5 °C future compared to a maximum of 12-20 days in the historical simulation). The highest frequencies (> 2100) can be seen exceeding 3 consecutive days and maximum temperature of 45 °C in the + 2 °C future.
In addition to the joint exceedance frequency of duration and intensity (TMAX), we analyzed the frequencies of duration and intensity separately in the grid cells that make up the large events (Supplementary Figs. S9 and S10). The modeled frequency in the historical simulation matches well with IMD observation in all large events except 2014 where historical simulations underestimate the observed duration which is closer to the + 1.5 °C simulations. Along lines of constant duration, the lowest frequency is from the historical simulations with progressively higher frequencies in the + 1.5 °C and + 2.0 °C simulations. Along lines of constant frequency, we can see progressively longer durations in the + 1.5 °C and + 2.0 °C simulations. Most events in the observations show the longest duration of about 10 days (15 days in the 2014) whereas the future simulations indicate a tenfold increase in the frequency of such events. More worrisome is that some grid cells show durations of 30-40 days in the + 2.0 °C future. In all large events considered, the duration of HW/SHW conditions increases dramatically between the historical and + 1.5 °C simulation with a lower increase between the + 1.5 °C and + 2.0 °C simulations. Similarly, the increase in frequencies of different TMAX values between historical and + 1.5 °C is larger than between + 1.5 °C and + 2.0 °C (Supplementary Fig. S9). It may also be noted that the highest temperatures in the + 1.5 °C and + 2.0 °C are not substantially larger and do not exceed 47 °C (in 1° × 1° gridded data). It is also interesting to note that the observed TMAX frequencies are consistent with historical simulation below 42 °C but more consistent with + 1.5 °C and + 2.0 °C above that. The differences between historical and the future scenarios are likely because of the HAPPI experimental design where the aerosols are kept unchanged between the + 1.5 °C and + 2.0 °C simulations, but aerosol loading in the + 1.5 °C simulations is considerably lower than during the historical (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) period (see Mitchell et al. (2017) for more details). The South Asian region being a region  Fig. 6 (columns). Duration is calculated as consecutive days meeting the HW or SHW criteria during March to August in observation (2006-2015, top row), from the HAPPI simulations of historical (second row), + 1.5 °C future (third row), and + 2.0 °C future (bottom row). Gray color represents zero frequency with large aerosol loading in the historical period, any reduction of aerosols would lead to increased local forcing and this can potentially inflate temperatures locally.
Finally, we analyze the changes in the areal extent of the selected events in the different experiments by examining the joint relative frequency for different fractions of area that experience events of different durations. Figure 8 shows the joint relative frequency from each of the historical, + 1.5 °C, and + 2.0 °C simulations, for area fractions and durations. By considering only grid cells within the area of each observed event (shown in Fig. 6), we calculate the area for each duration (consecutive days meeting the HW or SHW criteria during March to August) in each model simulation and convert it to an area fraction by dividing by observed event area. The joint frequency of event area and duration is calculated by pooling all 500 simulations from each experiment. Relative frequency is computed by normalizing the number of possible samples (overlapping by all but 1 day) for each duration across the whole ensemble. Note that there are a larger number of samples for shorter durations.
Higher values of relative frequency (> 0.2) are seen for smaller event area fraction (10-20%) in the historical simulations across all duration events. For larger fixed area fractions, the relative frequency tends to increase with longer durations implying that more widespread heat waves also tend to last longer. This feature is seen in both + 1.5 °C and + 2.0 °C simulations with higher relative frequencies compared to historical simulations. The clearly noticeable feature in the future simulations is the higher relative frequency (> 0.2) at longer durations and larger event area fraction (70-100%)-nearly threefold greater in the + 1.5 °C and fivefold greater in + 2.0 °C future, compared to historical simulations. The smaller relative frequencies (< 0.1) between 30 and 70% area fraction remain in both future simulations. Taken together, the clear message from Figs. 7 and 8 is that while the highest temperatures in heat waves may not increase much in the + 1.5 °C and + 2.0 °C future climates, the duration and area of the heat waves will most likely increase.

Discussion
In this study, we have explored the future changes in the occurrence of hot days, heat waves, and severe heat waves over India in the + 1.5 °C and + 2.0 °C future climates. We use these categories because they are more easily understood by both the forecasters and consumers of forecasts. We believe that this allows for a more useful comparison against the observed past and provides a better sense of the future changes to decision-makers. While the operational definitions (used by IMD) are for station level data, we use a modification of the same (as in Joseph et al. 2018) that is applicable to gridded datasets.
We have used a multi-model ensemble from the HAPPI project to investigate changes since the experiments were designed to generate large ensemble (~ 100 realizations) sizes to cover all the possible variations of the future climate. With 5 different models and a total of 500 realizations in each experiment, the sample size was large enough to capture low probability events.
We found that the models required bias correction in order to match the observed temperature distributions. After bias correction, the model-simulated distribution of HDs, HWs, and SHWs was reasonably close (pattern correlations are in the 0.95-0.98 range) to the observation.
As might be expected in a warmer climate, the frequency and duration of heat wave events increase in comparison to the historical (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) period. There are new regions that will be prone to heat waves in the future. The increased probability of HW or SHW events in the months of June and July is particularly worrisome because of the high humidity that these months experience due the prevailing summer monsoon season. Although we did not analyze the added impact of humidity, it is important to develop a heat index that is appropriate for the region and can be used operationally. This could help improve the preparedness of the healthcare sector's standard operating procedures for heat events (MOHFW 2021).
We analyzed 6 events from the 2006-2015 decade (each of which caused more than 1000 fatalities) to see what these events might look like in the + 1.5 °C and + 2.0 °C future climates. The differences (in probabilities of duration and intensity) between historical and + 1.5 °C (a difference of about 0.5 °C) are much larger than the differences between + 1.5 °C and + 2.0 °C. This is likely peculiar to the South Asian region-and other regions of high aerosol loading-and is a consequence of the experimental design which maintains the same aerosol loading between the + 1.5 °C and + 2.0 °C experiments, but has higher aerosol loadings in the historical period. In spite of this drawback in the experimental design, our results show a substantial increase in the risk of heat events that typically elicit warnings from forecasters. We looked at the joint exceedance frequency for intensity and duration as well as joint relative frequencies for duration and extent of events and found that the future scenarios consistently show higher probabilities of longer duration and more widespread (in terms of area extent).
The heat waves of the future are therefore likely to be more widespread in area and of longer durations. Such longer duration widespread heat waves might have already been observed in 2022 when large parts of Northwest India and Southeast Pakistan witnessed early (March-April) and prolonged heat wave conditions (Zachariah et al. 2022). The effects of prolonged heat waves could have far-reaching implications for managing the impacts on a wide range of sectors from health to agriculture, electricity, and industry. The responses to shorter duration, more localized events (that observations and historical simulations show) have been more of a disaster management approach (NDMA 2019) with some standard operating procedures covering healthcare (MOHFW 2021) which may be wholly inadequate for sustained and widespread events with a variety of impacts.

Conclusion
The likely increases in probability and extensification of heat wave events in the future in India, as revealed by this study, will require planning and adaptation measures beyond short-term disaster planning frameworks currently in place. Exploring what these measures might look like is beyond the scope of this study. But we believe that the study does illustrate and underline the importance of developing climate knowledge with high temporal and geographical resolution capable of informing adaptation policy and planning and the potential of doing so with climate science tools already available to us.
As a corollary, then, the study also highlights the need and relevance for strengthening such climate science efforts, particularly in developing countries that are likely to suffer significant climate impacts in a warming future. In fact, we suggest that the "climate science for adaptation" gap is no less important than the "adaptation finance" gap that dominates reflections on shortcomings in adaptation requirements in developing countries (see, for example, the UNEP Adaptation Gap reports). Hopefully, new initiatives such as the recently announced GCF-WMO effort Climate Science Information for Climate Action 3 will help to fill the gap. But as mentioned earlier, usable science will also require the local capacity and efforts to generate the relevant knowledge (Dilling and Lemos 2011). We hope that this study provides an illustration of the possibilities of doing so.
Author contribution All authors contributed to the study conception and design. Data collection and analysis were performed by Arulalan T. All authors contributed to writing the manuscript and approved the final manuscript.
Funding This research used science gateway resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. It also is supported by a grant from the Children's Investment Fund Foundation to the School of Public Policy at IIT Delhi.

Data availability
The IMD observed gridded (1° × 1°) daily TMAX and TMIN dataset is accessible  at web portals https:// cdsp. imdpu ne. gov. in/ home_ gridd ed_ data. php and https:// cdsp. imdpu ne. gov. in/ home_ dsp. php. The IMD observed daily TMAX data for individual stations can be obtained from IMD Data Supply Portal https:// dsp. imdpu ne. gov. in for a nominal charge. The HAPPI model dataset is available from C20C + Detection and Attribution Project at web portal https:// portal. nersc. gov/ c20c.

Competing interests
The authors declare no competing interests.