Modeling seasonal trends in optimum temperatures over India

Global warming is being quantified as the change in global mean temperature due to natural and anthropogenic activities. It has triggered natural disasters and threatened human life in various ways. Its manifestations include rising sea levels, decreasing air quality, extinction of species, outbreak of infectious diseases, shifting of seasons and changes in rainfall patterns. The occurrence of weather extremes in the form of heat waves, flood and drought are also causing an imbalance to the hydrological cycle and affecting production of crops. India is an agriculture based country where more than 60% of the population, living in rural areas, subsists on agricultural produce. Agriculture in India is largely dependent on precipitation and availability of ground water. During the 20th century India emerged as a major emitter of carbon, contributing to an increase in the level of greenhouse gas (GHG) emissions on a local and global level. The rising sea levels and warming oceans have also made Indian coasts vulnerable to weather extremes.

Research concerning climate change and temperature trends has gained immense popularity in India during recent decades. Different studies have shown significantly increasing surface temperature trends corresponding to different parts of India (Dhorde et al. 2009; Pal & Al-Tabbaa 2010; Jaswal et al. 2013; Jayasooryan et al. 2015; Lunagaria et al. 2015). Some of them have calculated the number of cold and warm days to demonstrate the extent of warming in different regions of India (Dash & Mamgain 2011; Manikandan et al. 2019). Other studies have emphasized the increased number of weather extremes due to the change in surface temperatures (Panda et al. 2014; Radhakrishnan et al. 2017). The changes in surface temperature have also been correlated with air pollution due to climate change (Ross et al. 2018).

Apart from surface temperature, the importance of the upper atmosphere has also been highlighted in certain studies. A number of studies have shown that natural resources and GHGs have acted differently on the near surface and upper troposphere temperature (TT) distribution (Vinnikov et al. 2006; Randel et al. 2017). The presence of more carbon molecules is expected to influence cloud nucleation which will significantly alter the vertical profile of static stability, latent heat, surface-radiation processes and rainfall patterns associated with it. Thus, the trend analysis of vertical temperature distribution is necessary to make inferences about changes in cloud types, precipitation processes and their impacts on the ambient atmosphere. There have been few satellite-based studies on global temperature trend analysis reporting an increase in middle and upper tropospheric warming during the last few decades (Thorne et al. 2011). For the Indian subcontinent, Kumar et al. (1987) used ten radiosonde stations to analyze seasonal and annual TT during 1944–1985, but found no significant trends in the upper atmosphere up to 200 hPa. They observed slight warming up to 200 hPa before 1958, and cooling thereafter. Similarly, Mallik & Lal (2011) analyzed the TT trend for Delhi and Kolkata during 1973–2008 and found significant warming at 700 hPa.

In order to understand the role of anthropogenic activities in climate change the scientific community is trying to understand the causes of non-homogeneity in global temperature anomalies through a number of state-of-the-art models. These models are expected to provide reliable estimates of inclining temperature as the response of GHGs. Therefore, modeling studies concerning global and regional warming trends are also growing rapidly (Maryanaji et al. 2017; Beyaztas et al. 2019; Samadianfard et al. 2019; Homsi et al. 2020). One such study by Po-Chedley & Fu (2012) raised the issue of inconsistency between a model and observational Upper Tropospheric Warming (UTW). They showed that exaggeration in calculating the lapse rate in some of the general circulation models (GCM) overestimated UTW. On the contrary, Gillett et al. (2016) found agreement between middle to upper TT warming in observations and an average of 37 model outputs from the Coupled Model Intercomparison Project Phase 5 (CMIP5). In a recent study by Li et al. (2019), the UTW over the west Pacific is shown from model and satellite datasets. These studies also reveal significant warming in the upper troposphere in comparison to the surface over the Pacific and Atlantic Oceans.

The advent of state-of-the-art regional models has gained major attention from the scientific community for the study of regional climate. RCMs have simulated weather and its statistics more realistically in comparison to GCMs (Semmler & Jacob 2004; Früh et al. 2010; Kunz et al. 2010). They added value in describing mesoscale variability compared to the driving global reanalysis for variables such as near-surface temperature (Feser et al. 2011). Among the various RCMs, the RegCM community model provided by the International Centre for Theoretical Physics (ICTP) has created tremendous growth in the simulation and projection of climate change. The model has undergone a substantial evolution both in terms of software code and physics representations in its revised versions. The major deficiency of RegCM is found to be its inability to provide two-way nesting and a few systematic errors (Giorgi 2014). It has been revised with the latest version (RegCM v4.6) which was released in 2017 and has been used in the present study.

The existing body of literature indicates that most of the climate studies based on surface temperature are comprised of daily and monthly predictions. Such studies have analyzed the extreme temperature trends without pondering their significant monotonicity. Studies concerning climate change and changes in upper air temperature over India are very few in number and are mostly based upon station and satellite data. Further, such studies include several regions and the modeling studies analyzing regional TT are still difficult to find. Consequently, we tried to perform our analysis on the basis of previous studies on surface temperature to explore the possible mechanisms by analyzing multiple level data obtained from the model. With this background, the present study intends to make inferences about the monotonic trends in TT on the seasonal basis using the regional climate model (RegCM v4.6). We aim to quantify the extent of temperature extremes corresponding to winters, summers, monsoon, and post-monsoon seasons in India using different statistical measures.

The present study utilizes a monthly mean dataset from RegCM v4.6 outputs. The model was run at 25 km horizontal resolution spanning the horizontal domain in a 60°E–110°E longitude and 0°N to 35°N latitude range. The model time step was taken to be 60 seconds in order to maintain stability and the solutions were obtained for 25 years (1982–2006) of study. For the model run the input initial and lateral boundary conditions were given from a 6-hourly Era-Interim reanalysis dataset. The sea surface temperature (SST) data used was optimum interpolation (OI) from the National Oceanic and Atmospheric Administration (NOAA) website (Reynolds et al. 2002). The condition of surface elevation and land vegetation were obtained from the USGS Global Land Cover Characterization (GLCC) dataset. The model run also required the utilization of different parameterization schemes. The NCAR CCM3 package was used for radiation. For triggering convection and maintenance of cloud processes a convective parameterization scheme by Emanuel & Živković-Rothman (1999) was implemented. Similarly, the boundary layer fluxes and friction were evaluated using a planetary boundary layer scheme by Holtslag et al. (1990). The response of soil moisture, vegetation cover and evapotranspiration was handled by a biosphere-atmosphere transfer scheme (BATS) sub-model. The details of model validation can be found in Kumar et al. (2019).

Previous studies have investigated the daily trends in extreme temperature indices. Very few studies have focused on seasonal temperature trends. A recent study by Roy (2019) reported the seasonal temperature tendency based on daily data. The present study is focused on analyzing the seasonal temperature extremes based on the gridded monthly data output of the RegCM model. We converted monthly mean data into seasonal mean corresponding to four different seasons, namely January-February-March (JFM), April-May-June (AMJ), July-August-September (JAS) and October-November-December (OND). For processing of results the non-parametric statistical methods and temperature indices were calculated for each season. Since we are not assuming the data to follow any specific distribution curve, the non-parametric statistical techniques became most suitable for this purpose. Among the existing statistical tools, the Mann–Kendall non parametric test (Basarir et al. 2018) is the most popular for obtaining strict monotonicity in the given dataset. We used it along with Sen's slope parameter and analysis of density function. These techniques are expected to provide useful information about vertical temperature trends over the Indian landmass region.

This is now a standard normal variate. The positive and negative values of Z_c indicate the increasing and decreasing trends of a time series. To test the monotonicity in upward and downward trend patterns a two-tailed test is applied at 5% level of significance. Before proceeding to our analysis we need to ensure the dataset is ready to be used for the tests since raw datasets often suffer from redundancies, which can often lead to misleading inferences. Therefore, it becomes necessary to pre-process them so that the required method can be applied. The Mann–Kendall test assumes that the input data is independent, i.e. the absence of auto-correlation is required. Thus, we applied pre-whitening to our dataset in order to minimize the effect of lag 1 autocorrelation, i.e. the correlation between values that are one time period apart. Pre-whitening is a method that can be used to make the time series serially independent (Yue et al. 2002). We applied this test on our spatio-temporal data and obtained the results in the form of 0 and 1 for each region. These numbers correspond to the acceptance and rejection of H_0, respectively. To further quantify the intensity of trends present in our time series we rely on Sen's slope parameter as it is considered to be a robust tool to quantify the slope of trend present in the dataset (Salmi et al. 2002; Jain & Kumar 2012).

To quantify the changes in extreme temperature trends, we needed to determine how the seasonal maximum, minimum, and mean temperatures are evolving with time. We also aimed to understand the widening and narrowing of two temperature extremes. To accomplish these objectives we calculated the seasonal extremes from the monthly data. Thus the nature of trends can be estimated by stratifying the data into indices corresponding to different characteristic extremes. Here, we calculated maximum, minimum, mean and range of our seasonal data. Their detailed description is provided in Table 1.

The seasonal temperature time series were used to identify significant trends in data values corresponding to each season. The Mann–Kendall non-parametric test was assumed to be most suitable for this purpose as it is used to determine the monotonic upward or downward trend of a time series. Here it was applied to the spatio-temporal data in order to identify the areas having a significant trend. We wanted to make inferences about the trend patterns in the near surface, boundary layer, middle and upper troposphere and we expected that these levels were sufficient to make inferences about the vertical extent of thermal energy balance in the atmosphere. Corresponding to these, we considered standard pressure layers of 1,000, 850, 500 and 200 hPa for our analysis. We also calculated the estimate of Sen's slope in these regions. Figures 1 and 2 show the values of Sen's slope parameter in the lower, middle and upper TT, respectively. The values correspond to the regions having a significant (p < 0.05) trend. The non-significant regions have been filtered out and their values are not shown here.

In Figure 1 the estimate of Sen's slope is shown for the lower TT. The parameter values reveal a significant declining trend in the near surface and boundary layer during winters (JFM) in west and west-central India. This shows the likelihood of cooler winters and springs in these areas. During the boreal summer (AMJ) the values show a sharp decline in east and eastern India. This region is prone to tropical storm related threats from the Bay of Bengal due to coastal vulnerability in pre-monsoon and the decline in temperature trends over this region indicates a higher amount of cloudiness and precipitation in later years. Thus there are higher chances of increased storm threats in this area. These storms are also likely to be of higher intensity which further increases the risk of storm surges, lightening and devastation of crops. These changes are consistent with a recent finding which shows increased rainfall due to pre-monsoonal activity (Vinay Kumar & Venkateswara Naidu 2020). During monsoon there is a slight increasing tendency near north-central India and a decreasing tendency further west. This can be associated with the number of dry spells or drought in central Indian regions near Delhi, southern India, although it does not show any significant trend in this season. The post-monsoon season, however, showed significant warming in major parts of India. The season is the transition period from wet to dry; it often brings cool and dry airs in major parts of the country from the northeast. This is the period of winter onset as well, which shows significant warming in later years. The annual temperature has shown warming in almost the whole of India, except in northern parts of central-east India

Similarly, in the middle and upper troposphere (500 and 200 hPa), the temperature trends were observed to be not statistically significant in major parts of the country. For the middle troposphere temperature trends were found to be significantly negative, i.e. central India showed cooling during the summer season. The trend became negative near the eastern Indian Ocean during the post-monsoon season. The annual temperature trend showed negative values in major parts of the country. In the middle troposphere near the eastern Indian Ocean and Bay of Bengal, it showed slightly increasing tendencies. In the upper troposphere the situation became slightly different where the annual, JFM and OND temperature values showed increasing trends over the northern Indian Ocean. No significant trends were observed during the summers and monsoon seasons at this level. The trends are quite surprising although the reasons are not certain. Instead of having strict monotonicity it may also exhibit increasing/decreasing patterns for some years. This can be attributed to the time span of the study, model's efficiency, upper level convergence/divergence, and precipitation changes in this domain. The regions above the ocean were not considered as they may provide unrealistic trends due to the lack of updated SST. The annual temperature trends showed slight cooling in most regions of the country.

Figures 3 and 4 represent mean temperature anomalies, i.e. mean deviation from their long-term climatological value corresponding to significant regions in the lower and upper troposphere. The red line shows the trend of the mean anomaly. The mean anomaly is shown to have a decreasing tendency during all the seasons in the lower troposphere. In Figure 3, we observe a decreasing trend in mean temperature anomalies corresponding to the lower troposphere. The slope of the anomaly is steepest during the pre- and post-monsoonal season (AMJ and OND) in the lower troposphere, showing a rapid decline in mean temperature in significant regions. During monsoon (JJA) and JFM we observed a slightly decreasing pattern. The mean temperature anomalies are also shown in Figure 4 for the middle and upper troposphere. The anomalies are negative during the first decade (1982–1992) and become positive in the latter decade (1992–2006). Moreover, in the upper troposphere the slope is relatively steeper only during the spring and summers. The annual mean temperature is seen to incline in the upper atmosphere and decline in the lower atmosphere. One possible reason for this tendency could be the enhanced convection rate in the upper troposphere as the amount of solar insolation would be constant every year in the model. The changes can arise due to the increased amount of cloud mass as it absorbs a higher amount of radiation therein. If the amount of cloud formation were increased, there would also be an increase in the latent heat of condensation (or cloud nucleation), leading to a positive temperature trend in the region. The lower level, on the other hand, would tend to cool down because of the decreased amount of incoming shortwave radiation or the sunlight on the surface as there is increased cloud cover at upper levels. This will also result in higher chances of precipitative cooling on the surface.

Figure 5 shows the density function (CDF) of temperature anomalies corresponding to multiple levels for all seasons. We observed a bimodal structure of anomaly distribution for all the seasons except for monsoons (JAS). The averaged anomalies lie between 0 and 0.1 with maximum probability for almost all the seasons. This shows the highest chances of warming by 0–0.1 °C during all the seasons, except the monsoon. The second peak is observed over negative anomalies exhibiting relatively smaller chances of cooling at all the levels. During monsoons, the unimodal anomaly distribution is moderately skewed negatively, showing the higher percentage of values residing in this range. Thus, the mean monsoon curve does not reveal any significant peak but from visual inspection it seems that the chance of cooling is greater than warming at all the levels.

Figures 6 and 7 depict the temperature maxima of the significant trend region at the lower, middle and upper troposphere. The lower TT maxima are shown to have a declining trend on a seasonal and annual basis. This shows that the warmest areas have the chance of facing below normal temperatures during all the seasons. The downward trend in maximum warming at these levels can only be related to cloudiness and air pollution. The other factors include heat trapped by multistorey buildings and monuments, warming due to air conditioners and other industrial systems. Similarly, the maximum temperature in the middle and upper troposphere has a slightly increasing tendency. This can be due to increased production of daytime clouds in the model that upper levels are able to absorb, reflect and scatter incoming shortwave radiation at a higher rate. In such a case there would also be an increase in the released amount of latent heat. It is worth noting that the increase in maximum temperature is arising in the middle and upper levels but not in the lower levels in the model in spite of air pollution. There exist few aerosol categories that absorb more radiation than scattering it, hence acting like a shade and cooling down the surface. Black carbon is one of them and therefore it can also contribute to the distinct pattern of upper and lower level warming.

Figure 8 shows the density function of maximum temperature anomaly for all the seasons. The maximum temperature index exhibits the sharpest peak during the winter and spring seasons between 2 and 3 °C. This trend shows the warmest temperature has the maximum possibility to increase during the JFM season. The shape of the pre- and post-monsoonal curve shows a similar bimodal structure with the highest chances of 1.5–2 °C of warming. The maxima curve during the monsoon season is flatter when compared to the other curves. The maximum temperature is likely to increase around 1–2 °C. Annually, the maximum temperature increases between 0.5 and 1.8 °C over all the levels.

The tendency of temperature minima for four vertical layers of the study is shown in Figures 9 and 10. The slope of the coolest temperature over the regions of significant trend shows further cooling in the lower atmosphere for all the seasons. During winters and spring the 850 hPa layer shows an increase in the minimum temperature. Similarly, the middle and upper levels show an increase in minimum temperature during all the seasons. Hence, the minimum temperature at these levels is increasing in the later decade due to various reasons such as latent heat at these levels and absorption of solar radiation which can contribute to an increased minimum temperature therein.

The density function of temperature minima is also shown in Figure 11 for describing the shape of minima curves during different seasons of the study. The curves show a bimodal structure during all the seasons, except in winters and spring which exhibits several low intensity peaks. The minimum temperature during this period shows cooling of 1.5–3 °C. The primary peak of pre- and post-monsoon minima lies between 1 and 3 °C, which shows possible cooling within this range during these seasons. The monsoon curve exhibits a shorter peak with a maximum spread between 0.5 and 2.5 °C of the lowest temperature values. Similarly, the primary peak of annual temperature curve ranges between 0.4 and 1.8 °C.

TT range is defined as the difference between maximum and minimum temperature values and thus demonstrates the gap between the warmest and coolest temperature trends. The trend of temperature range for the lower, middle and upper level is shown in Figures 12 and 13. The trend in temperature range is declining for almost all the levels and during all the seasons. It is inclining at the middle and upper troposphere during pre-monsoonal and monsoonal season which shows a widening in extreme temperature values at this level. All the other levels show that the gap between temperature warming and cooling has been narrowing in recent years. The sharpest decline in temperature range is observed in the monsoon and post-monsoon seasons. If the temperature maxima are observed during daytime and minima due to nocturnal cooling at night, the reduced values of range can be interpreted as the homogeneity in temperature over a day. This is happening due to the cooling of warmer temperature and warming of cooler temperature. Thus, we observed homogeneity in regional temperature patterns over the given time period during all the seasons. This shows inconsistencies in regional temperature trends for the given time period which can give rise to abrupt climate conditions in later years.

The CDF of temperature range is shown in Figure 14 for all the seasons. The shape of these curves follows the shape and density of temperature maxima. That means variability in maximum temperature is affecting the temperature range more as compared to the temperature minima. This may happen if the variability in maximum temperature is sharp and intense in comparison with the minimum. The values of winter and spring maximum temperature anomalies lie between 3.8 and 5.8 °C. The pre- and post-monsoon indices are again depicting a similar bimodal structure and have a wider spread in their distribution of between 2 and 6 °C. These values occupy maximum density of the distribution over this range and, therefore, it has the highest chances of attaining these values. The distribution of monsoon curve is again lean with a maximum peak between 2 and 4 °C. Annually, the temperature range lies between 1 and 3.8 °C.

Global warming and climate change are the most important factors for the ecosystem and socio-economic growth of a country. Rising temperature trends all across the globe have resulted in abrupt climate conditions and vulnerability to weather extremes. In the present study we have tried to analyze the monotonic trends in TT over India. The multilevel temperature data was obtained from the historical run of the RegCM v4.6 model output for the statistical analysis of temperature extremes. The spatial distribution of Sen's slope shows cooler winter and spring in western India and warming in the eastern part at the lower troposphere. During the pre-monsoonal season the presence of negative slope near eastern and central India can be inferred as the increased precipitation accumulation and cloud cover in this area due to higher pre-monsoonal activity and storm related threats. There is warming in north-central India during monsoon that can be due to the higher number of drought related cases and cooling is seen in the western part. This can be associated with the higher precipitation in western India. Similarly, the post-monsoon or autumn season is showing warming in major parts of India during recent years. The trend analysis of the middle and upper troposphere does not reveal a significant trend in most parts of the country. There is a slight warming tendency in southern India during JFM which becomes cooler during the post-monsoon season. Annually, India is seeing a declining trend in the upper TT in large parts of the country. The trend analysis of mean TT time series reveals a declining temperature tendency near the surface during most seasons. On the other hand, the upper TT shows an increasing trend during the later years of the study. The tendency of minimum and maximum temperature is also changing with this pattern. The magnitude of temperature range is also declining, which shows homogeneity between minimum and maximum temperature values. The kernel density of mean and extreme temperature indices is also extracted for every season. Most of the seasons exhibit a bimodal temperature tendency for all the levels. The pre- and post-monsoon seasons follow a similar structure for temperature extremes. The CDF of temperature extreme is sharpest during the winter and spring seasons with the highest chances of attaining 0–0.1 °C mean, 2–3 °C of warming in maxima and 1.5^–3 °C of cooling in minima. These changes in lower, middle and upper atmospheric temperature are associated with the release of latent heat, cloud cover and atmospheric pollutants. We still need to investigate the cause and effect relationship of temperature tendencies that can provide useful information behind other dynamical processes using other parameters. We also faced scarcity of observational studies on this subject, therefore the impact of weather extremes in India needs to be investigated. We hope that this analysis can be useful in examining the perturbed state of the atmosphere, shift in weather patterns and its impact on mean seasonal circulation in the near future.

We are thankful to the Department of Science and Technology for financial assistance for this research work through a research project under Climate Change Program. We also thank all the anonymous reviewers who helped improve the quality of this manuscript.

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