Southern Pakistan (Sindh) is one of the hottest regions in the world and is
highly vulnerable to temperature extremes. In order to improve rural and
urban planning, it is useful to gather information about the recurrence of
temperature extremes. In this work, return levels of the daily maximum
temperature

Extreme maximum temperature events have received much attention in recent
years because of the associated dangerous impact on the increased risk of
mortality (IPCC, 2012). Additionally, climate change scenarios suggest that
in most regions the probability of occurrence of extremely high temperature
is very likely to increase in the future (Sheridan and Allen, 2015). An
example of the potential impact of raising maximum temperatures is the recent
heat wave in southern Pakistan (Sindh), which occurred between 17 and
24 June 2015 and broke all the records with a death toll of 1400 people and
over 14 000 people hospitalized. The temperatures in different cities of the
Sindh region were in the range of 45.5–49

In summer, Sindh becomes very hot and with the arrival of a monsoon the
humidity increases in the region (Chaudhry and Rasul, 2004). The extremely
hot and humid conditions can have lethal effects and can impact the overall
human habitability of a region (Pal and Eltahir 2015). The human body
generally maintains a temperature of around 37

This study devotes special attention to Sindh (23.5–28.5

Extreme value theory (EVT) provides the statistical basis for increasingly widespread quantitative investigations of extremes in climate studies (Coles, 2001; Zhang et al., 2004; Brown et al., 2008; Faranda et al., 2011; Acero et al., 2014). The peaks over threshold (POT) approach aims to describe the distribution of the exceedances of the stochastic variable of interest above a threshold. Under very general conditions, the exceedances are asymptotically distributed according to the generalized Pareto distribution (GPD). The GPD has remarkable properties of universality when the asymptotic behavior is considered (Lucarini et al., 2016), while one can expect that the threshold level above which the asymptotic behavior is achieved depends on the characteristics of the analyzed time series. In particular, when looking at spatial fields, the threshold level depends on the geographical location.

In this study, we have chosen to analyze the temperature extremes in the Sindh region taking the point of view of threshold exceedances associated with the GPD family of distributions. We have done this because the statistical inference provided by the POT method provides a more efficient use of data and has better properties of convergence when finite datasets are considered with respect to alternative methods for the analysis of extremes, such as the block maxima method, which is used to fit the observed data to the generalized extreme value (GEV) distribution (Lucarini et al., 2016). Additionally, here we are interested in investigating the actual tails of the distributions and not the statistics of yearly maxima, for example. Thus, the POT approach is indeed more appropriate. While the POT method has been applied for studying temperature extremes in different regions of the world (Burgueño et al., 2002; Nogaj et al., 2006; Coelho et al., 2007; Ghil et al., 2011), to our knowledge, it has never been used to analyze the statistics of temperature extremes in Sindh. Thanks to the properties of universality of the GPD distribution (Lucarini et al., 2016), the POT approach can in principle provide reliable estimates of return periods and also the return levels (RLs) for time ranges longer than what is actually observed. This information and this predictive power can be beneficial for policy-makers and other stakeholders since it is exactly the kind of information planners need when designing infrastructures that must last a very long time. Note that commonly used, more empirical approaches to the study of extremes, such as those used more for assessing the “moderate extremes” (IPCC, 2012), do not have any property of universality and might have weak predictive power.

Code, name, geographic coordinates, and altitude of the stations.

It is useful to consider two indicators of extremely hot conditions:
(1) temperature extremes

The paper is organized as follows. In Sect. 2 we present the datasets we study and the statistical methods we use for assessing the properties of extremes. In Sect. 3 we show and discuss the main results. In Sect. 4 we make a summary of the main findings and present our conclusions and perspectives for future investigations.

The daily maximum temperature and relative humidity data recorded at nine meteorological stations in Sindh from 1980 to 2013 are provided by the PMD (see Table 1). We select nine stations, which contain a negligible amount of missing values after 1980 and are suitable for the POT analysis (Fig. 1). An additional criterion is that only those stations at which no changes occurred in measuring instruments during the last 33 years were chosen (Brunetti et al., 2006). None of the station data show gaps with a duration longer than 2 days, which are treated by replacing the missing value with the average of the two previous values.

Study domain (23.5–28.5

The temperature data are discretized unevenly with intervals up to
1

The gridded daily maximum temperature and relative humidity data of ERA-Interim reanalysis are obtained from the ECMWF Public Datasets web interface
(

The extreme temperature analysis is restricted to the summer season
(May–September) over a period of 33 years. We have tested the datasets by
applying the Mann–Kendall test; the results show that trends are not
significant in such a short time interval. One of the main requirements for
performing the POT analysis is assuming the stationarity of the time series.
Therefore, as in Bramati et al. (2014), the augmented Dickey–Fuller (ADF)
test of stationarity is performed on all time series (Dickey and Fuller,
1979). In all cases we find no sign of long-term correlations in the data.
Short-term correlations (daily timescale) typically lead to clusters of
extreme values and are studied by computing the extremal index

The wet-bulb temperature measures the heat stress better than other existing
heat indices because it establishes the clear thermodynamic limit on heat
transfer that cannot be overcome by adaptations like clothing, activity, and
acclimatization (Pal and Eltahir, 2015; Sherwood and Huber, 2010). Here, we
use an empirical equation developed by Stull (2011) to measure the wet-bulb
temperature.

In order to determine the return levels of extreme maximum temperatures and maximum wet-bulb temperatures, the POT approach is applied to the data obtained from the meteorological stations in Sindh and from the ERA-Interim archive.

Multiple occurrences are an important characteristic of extreme climatic events
and are referred to as clustering. Clusters are consecutive occurrences of
above-threshold events. It is important to post-process the clustered
extremes in order to take into account the assumption of a weak, short time
correlation between extreme events, which is crucial for our statistical
analysis. We have treated the clusters using the concept of the extremal index
(EI) (see Newell, 1964; Loynes, 1965; O'Brien, 1974; Leadbetter, 1983;
Smith, 1989; Davison and Smith, 1990). The EI

The EI

As mentioned before, for the exceedances over
threshold, we use the GPD, which is characterized
by two parameters, the shape

In particular, for a negative shape parameter

Additionally, we wish to investigate the

A simple bias correction is applied to each ERA-Interim time series through a
rescaling that adjusts the first two moments (mean and variance) to the
sample moments calculated for the corresponding observations (Acharya et al.,
2013). Therefore, the bias correction is applied to the entire time series
and it is not tailored to the extreme events only. The idea is to check
whether by adjusting the properties of the bulk of the statistics we improve
the skill of the ERA-Interim dataset considerably in describing extreme
events. The bias-corrected ERA-Interim time series

Modified scale (

The threshold selection is the first step in a POT analysis. One needs to
test whether the asymptotic regime is reached, i.e., whether one is choosing
true extremes. It must be noted that EVT does not predict where (in terms of
quantiles) one should expect the asymptotic regime to start. This can be
investigated by checking whether the best fits of the shape parameter

Results of the Kolmogorov–Smirnov goodness of fit test and Anderson–Darling test between empirical and GPD fits.

In addition to diagnostic plots of the modified scale parameter

Mean residual life plot of the station-observed

Estimated parameters shape

The goodness of fit is evaluated using quantile–quantile (

The

In order to assess the goodness of fit, we apply the Kolmogorov–Smirnov
test and Anderson–Darling test to the data of meteorological
stations, ERA-Interim, bias-corrected ERA-Interim

Spatial distribution of the shape parameters

Here, we analyze the shape parameter

Absolute
maxima A

The scale parameters

Once the shape parameters

Return level plots of the station-observed

The RLs are computed considering various return periods (2,
5, 10, 20, 50, 100 years). As stated above, using a statistical approach
based on the universality of EVT, we are able to extrapolate the results for
time horizons longer than the one for which observations are taken. Clearly,
uncertainties grow when longer time horizons are considered. The RL plots of the stations observed, the ERA-Interim, the bias-corrected
ERA-Interim daily maximum temperature

The 2-, 5-, 10-, 20-, 50-, and 100-year RLs estimated in Sindh for station
observed

Return level plots of the station-observed TW

The RLs of TW

The bias-corrected ERA-Interim

Spatial distribution of the station-observed

Spatial distribution of the station-observed TW

We also spatially plot the station and bias-corrected ERA-Interim

In summer, the temperature and humidity increase to an extent that there are high chances of pests rapidly spreading in the crops. Temperature extremes not just directly impact the quantity and quality of grains but can also be a reason for urban flooding affecting agricultural lands (Luo et al., 2015a). Sindh produces cotton, wheat, rice, mango, banana, and dates; thus, a correct estimate of temperature extremes is very important.

The spatial RLs of station and bias-corrected ERA-Interim
TW

The main objective of this study is the assessment of the return levels of
the extreme daily maximum temperatures

The POT method is applied to the daily maximum temperature (

Our results predict extremely high values of

We found that the RLs from the stations and ERA-Interim showed differences between
3 and 5

We applied a simple bias correction, i.e., adjusting the mean and standard
deviation for ERA-Interim

The results have practical implications for assessing the risk of extreme
temperature events in Sindh. All the results are placed in the web tool
SindheX (

The observation data are collected via email request to
the Climate Data Processing Center (CDPC), Pakistan Meteorological Department
(PMD) (

The authors declare that they have no conflict of interest.

We would like to thank Climate KIC, for funding this research. This publication is a part of a Climate KIC project “Extreme Events in Pakistan: Physical processes and impacts of changing climate”, which belongs to the adaptation services platform of the Climate KIC. Thanks to the Pakistan Meteorological Department (PMD) and the European Center for Medium-Range Weather Forecasts (ECMWF) for providing the datasets. The R development core team (2015) is acknowledged for providing statistics packages. We would like to thank the DFG Cluster of Excellence CliSAP for partially supporting this research activity. We would like to thank the reviewers, whose constructive criticisms have greatly helped to improve the quality of this paper. Edited by: Fubao Sun Reviewed by: five anonymous referees