Spatiotemporal trends of temperature extremes in Bangladesh under changing climate using multi-statistical techniques

The rise in the frequency and magnitude of extreme temperature phenomena across the globe has led to the recurrent incidence of global climate hazards, which have had severe effects on socioeconomic development. The daily maximum and minimum temperature datasets of 27 sites in Bangladesh were used to detect spatiotemporal trends of temperature extremes over Bangladesh during 1980–2017 based on ten temperature extreme indices using multi-statistical modeling namely linear regression, Pearson correlation coefficient, and factor analyses. Besides, mutation analyses based on the Mann-Kendall test, Sen’s slope estimator, and Pettit test were employed to show the changing trend in extreme temperature. Results show that except for warmest days, the warm indices showed an increasing trend, mainly since the 2000s, while the growth rate was faster, and the response to global climate warming was sensitive. The cold indices were demonstrated a reverse trend since the 2010s. Diurnal temperature range (DTR) and summer days (SU) increased faster, implying that the rising speed of daily max temperature was higher than of daily min-temperature in Bangladesh. The de-trended fluctuation analysis (DFA) revealed a continuous increase in temperature extreme in the future except for cold days. The probability distribution functions (PDF) analysis revealed an evident variation of the curves in recent decades compared to the past three decades. Besides the warm night, DTR and SU primarily control the general warming trend of temperature extremes over Bangladesh during the study period. The mutation of the warm indices occurred before the cold index, indicating that the warm indices were more sensitive to global climate warming. The temperature extremes recognized in our research suggest that elevated warm temperature extremes due to global climate warming may have huge implications on the sustainable development of Bangladesh in the forthcoming period.


Introduction
Temperature extremes have critical effects on ecosystem imbalance, agricultural productivity, water resources, and sustainable socioeconomic development (Allen et al. 2010;Benestad & Haugen 2007;Ciais et al. 2005;Easterling et al. 2000;Guo et al. 2019;Islam, Islam, Shahid, et al. 2021a;Rammig & Mahecha 2015;Schmidli & Frei 2005). Variations in temperature extremes in a warming climate have paid considerable attention in recent years due to the enormous impact of severe temperature occurrences on society and ecosystems (Bandyopadhyay et al. 2012;Sun et al. 2014). Furthermore, the scientific community has emphasized measure to tackle the climate change impact on ecosystems and human livelihoods for disaster prevention and mitigation (Smith 2011;Jiang et al. 2016;Endfield 2012;García-Cueto et al. 2014;Sharma et al. 2018). As climate extreme events increased in many parts of the world, including Bangladesh (Hasan & Rahman 2013;Shahid et al. 2016;Mahmud et al. 2018;Khan et al. 2019;Khan et al. 2020). Thus, it is crucial to investigate spatiotemporal changes in temperature extremes for sustainable development over Bangladesh.
Extreme temperature phenomena are changing across the globe due to global warming (Abiodun et al. 2013;Aguilar et al. 2005;Alexander et al. 2006;Coumou et al. 2013;Coumou & Rahmstorf 2012;Hidalgo-Muñoz et al. 2011;Omondi et al. 2014). The fact is that global and local average temperatures are increasing, which have no bearing on the occurrence of extreme events (Finkel & Katz 2018;Gleixner et al. 2020). However, severe temperatures may be more vital than mean temperatures for productivity and human survival, and local extreme temperature changes could significantly impact global mean temperature changes (Finkel & Katz 2018;Gao & Franzke 2017;Katz & Brown 1992). Several studies have reported that the frequency of warm temperature indices is increasing, while the frequency of cold temperature indices is decreasing (Alexander et al. 2006;Tank et al. 2006;Piccarreta et al. 2015;Sheikh et al. 2015;Guan et al. 2015;Sun et al. 2016;You et al. 2017;Ullah et al. 2019). All these studies looked at average temperature trends and temperature extremes, but the latter only looked at monthly and yearly maximum and minimum values as extremes. The Expert Team on Climate Change Detection and Indices (ETCCDI) has identified extreme temperature indices to illustrate better temperature extremes, commonly used in climate change-related studies in various parts of the world ). Therefore, a deep understanding of temperature extremes' trends and fluctuations is essential for developing accurate estimates of future climate change projections and answering scientific researchers, climate change analysts, and decision-makers unique concerns.
Bangladesh is one of the world's top ten countries that could be severely affected by climatic extreme (Das 2021;Eckstein et al. 2017). The most immediate impacts of climatic extreme in Bangladesh, as elsewhere globally, are mainly due to increased daily temperatures and temperaturerelated extreme phenomena (Shahid et al. 2016). Temperature extremes have been observed in the country's agriculture (Sikder & Xiaoying 2014) and other sectors (Shahid et al. 2016). Temperature variability is most likely to result in significant yield reductions in the agricultural industry in the future (Ghose et al. 2021). Plant development, pollination, and reproductive processes are all affected by higher temperatures (Sacks & Kucharik 2011;Tank et al. 2006). A short period of unusually high or low temperatures can significantly negatively impact crop growth and yield (Mearns et al. 1984). Due to temperature extremes, total rice production in Bangladesh is expected to decline by 7.4% per year from 2005 to 2050 (Sarker et al. 2012). Therefore, significant attempts should be made to estimate not only changes in mean temperature sequence but also changes in the frequency, magnitude, and duration of extreme temperature events (Alexander et al. 2006;Easterling et al. 2000;Jones et al. 2001;Moberg & Jones 2005). However, the characteristics of climate extremes are poorly understood at the regional level. So, it is urgently needed to keep track of spatiotemporal variations in temperature extremes regularly at the regional level, including Bangladesh.
In Bangladesh, many studies were performed to investigate the spatiotemporal variations of extreme climate indices (Hasan & Rahman 2013;Islam, Islam, et al. 2021b;Mahmud et al. 2018;Shahid et al. 2016). These studies reported that warm temperature events (cold temperature events) are rising (decreasing). However, the studies mentioned above are either concentrated on the two regions, and a limited number of meteorological stations (Mahmud et al. 2018), short-time scales and a limited number of temperature indices (Khan et al. 2019), and different data sources (Hasan & Rahman 2013). Besides, it is unclear whether and how those indices affect temperature extremes in Bangladesh both spatially and temporally. In addition to this, previous studies have not shown the long-term connection among extreme temperature indices using de-trended fluctuation analysis (DFA). To close the aforementioned research gaps, this study has four objectives: 1. To examine the spatiotemporal trends of temperature extremes from 1980 to 2017 in Bangladesh 2. To identify the association among extreme temperature indices 3. To predict long-term connection among ten temperature extremes indices 4. To analyze the factor affecting the extreme temperature variation over Bangladesh The novel aspect of this research is that the trends and the associated connection of extreme temperature were analyzed in Bangladesh to understand their spatial and temporal variability. The main contribution is that it is the preliminary thorough work assessing spatiotemporal trends and associations of extreme temperature events in the country by using the multi-statistical approaches, which have substantial implications on economy, agricultural sector, and ecology. The outcomes of this research can be used for adaption appropriate plans and the generation of an early warning method to lessen extreme temperature risks. The findings will serve as a scientific foundation for future severe event prediction and hazard mitigation and prevention.

Study area description
Bangladesh is a sub-tropical country of South Asia situated in between latitude 20° 34̍ ′ N to 26° 38′ N and longitude 88° 01̍ ′ E to 92° 41̍ ′ E ( Fig. 1) with complex hydrogeologic settings (Ghose et al. 2021;Jerin et al. 2021), excluding some hilly area of Bangladesh, maximum portions of the land area in the floodplain (80%) region (Islam, Islam, Shahid, et al. 2021a;Rahman & Islam 2019). In Bangladesh, the monthly average temperature ranges from 5.8 (January) and 35.7°C (August), whereas the monthly average precipitation varies between 1 (January) and 350mm (July). The annual average temperature is 26°C, and the average yearly rainfall is about 2400 mm Jerin et al. 2021). Seasonal variations in rainfall are indistinguishable characteristics of its climate. The country's climate is characterized by a hot and humid summer with heavy rain and a dry and mildly cold winter. Winter (December to February), pre-monsoon (March to May), monsoon (June to September), and post-monsoon (October to November) are the four predominant seasons of the country (Islam, Islam, Shahid, et al. 2021a;. Bangladesh has an average daily mean relative humidity of 80% and a 3.72 mm/day evapotranspiration rate, respectively . The coldest month is January and the hottest months in Bangladesh between April and October.

Data source and quality control of the dataset
Daily minimum and maximum temperature data are collected from Bangladesh Meteorological Department (BMD). Though BMD has 43 weather stations across the country, 27 sites were selected for this study because of the lack of availability of long-term temperature data. Thus, the daily T min and T max data of 38 years from 1980 to 2017 were used in this study with missing values of less than 4%. The selected stations are uniformly scattered all over the country, which is assumed to be a perfect representation for the whole country. Our study was reported the variations in extreme temperature indices based on daily minimum and maximum temperatures for 1980-2017. Many temperature series were omitted from our analysis due to inhomogeneity. Missing data at each site were filling-up from the records of nearby locations. In addition, the sites discarded due to the unavailability of data for a more extended period was also used to fill up the missing values . The BMD followed the World Meteorological Organization (WMO) guidelines for weather data record and collection. Nevertheless, the quality control of the dataset is still imperative before investigating climatic extremes because incorrect outliers influence the extremes significantly (Gao & Franzke 2017).
Quality control of site observation was initially done through systematic checking of data, namely, positive records of climate variables; T min is lower than T max , and temperature less than 45°C. The time series data were identified to be homogeneous and consistent at all locations (Hans 1986). The BMD staff also approved all data records through a data quality check. Serial autocorrelation is one of the critical problems in trend analysis (Praveen et al. 2020). Assessment of serial autocorrelation in time series for different lags showed correlation at p<0.05, except for a few cases. Data were quality-controlled by RClimDex1.1.
In this study, 10 extreme temperature indices were chosen from the indicators recommended by the Expert Team for Climate Change Detection Monitoring and Indices (ETC-CDMI). Recently, these 10 indices have been extensively adopted in extreme temperature study (Islam et al. 2021a, b;Zhou et al. 2020). The indices were computed by using the RClimDex software package developed by ETCCDI (http:// cccma. seos. uvic. ca/ ETCCDI). Table 1 presents a detailed description of these ten indices.

Pettitt's test
Pettitt's test is a non-parametric test introduced by Pettitt (1979) applied to detect a change point in any time series data with its significance test . In this study, Pettitt's test is used for detecting change points among different extreme temperature indices. This test employed Mann-Whitney statistic U t, that examines if the two sets of sample x 1 , x 2 , x 3 , …x t and x t+1 , x t+2 , x t+3 …x n are from the similar population or not (Mu et al. 2007). The U t can be expressed as follows: The K (test statistic) and ρ (confidence level) for the n (sample length) are defined by Eqs. (3-4): (1) The null hypothesis is rejected if ρ is lower than the specified significance level. The p (significance probability) can be expressed as follows: The main advantage of the Pettitt's test is that it does not need any prior assumptions about the distribution of the data excluding that they are continuous (Rybski & Neumann 2011). The extensive usage of this test may be due to its flexibility for the identification of a change point in the mean from an unknown point in time series data, as well as the providing of a p-value to evaluate its significance.

De-trended fluctuation analysis
DFA is a novel method for assessing the long-term relationship in the non-stationary time series data analysis, which is firstly presented by Peng et al. (1994) for the investigation of DNA. The DFA method can prevent the wrong identification of artificial relationships by eliminating local trends of the different time series (Rahman & Islam 2019;Islam et al. 2021a). Nowadays, this method has been employed mainly to identify long-range associations among natural systems following continuous improvement (Li & Zhang 2007). In this paper, DFA is used for predicting upcoming trends in extreme temperature indices. The following procedure can calculate it: For extreme climate series {x k , k = 1, 2, …N}, in which N represents the series length and x represents mean. The cumulative deviation of the original series can be computed as follows: Then the latest series y i is ordered into Ns different subintervals through s length by Eq. (7): For confirming the information as the series is not divisible, it is categorized again into inverse way. As a result, a total of 2Ns sub-intervals are created. Then, polynomial fitting is executed for each sub-interval v (v = 1, 2, ..2Ns) data to achieve the trend function y v(i) in that series. The original series trend in sub-function is filtered out by executing Eq. (8): wherein, y v(i) is second-order polynomial though it can be first or higher order polynomial. To eliminate the trend and computing of the each interval variance is calculated by Eqs. (9-10): The estimation of the second order wave function of the entire series by following Eq. (11): Power law relationship series of F(s) and s variations are computed by using Eq. (12): The datasets are close fitted using least square method in dual logarithmic where "a" (slope) of the trend is scaled DFA index. The whole procedure is randomly divided and independent if there is a=0 and 0 < a < 0.5 denotes the short-term relation with dependent process demonstrate that the time series data are inversed to the prevailing trend. On the other hand, 0.5 < a < 1 indicates the continuous series and approaching trend is same to the previous. When "a" is nearby to 1, the greater the change of similarity and a=1 denotes the procedure is 1/f sequence like a non-stationary casual cycle along with 1/f spectrum classified by scale invariance and a long-term relationship. Moreover, a ≥ 1.5 denotes the procedure is brown-noise sequence.
DFA has several benefits over traditional techniques like Hurst or spectral analysis, including the ability to detect inherent self-similarity embedded in an apparently non-stationary time series and the avoidance of artificial intrinsic self-similarity. Nowadays, this technique has been effectively employed to a variety of simulated and extreme hydro-climatological or hydro-meteorological time series (Rahman and Islam 2019;Islam et al. 2021a, b) prove its worthiness.

Trend analysis using multi-statistical techniques
The non-parametric Mann-Kendall (MK) test is employed to detect a trend in extreme temperature indices Islam, Islam, Shahid, et al. 2021a). It is renowned for its robustness in analyzing non-normally sequenced datasets and lower sensitivity to missing value (Islam et al. 2021a). A trend-free pre-whitening (TFPW) method was employed to remove serial autocorrelation (Jerin et al. 2021;Praveen et al. 2020). Correspondingly, Sen's slope (SS) estimator (Sen 1968) was employed to determine the frequency of change in extreme temperature indices. The elaborate Pearson's correlation coefficient was applied to reveal the relationship among extreme temperature indices. The factor analysis was employed to detect extreme temperature factors across Bangladesh (Rahman and Islam 2019). The univariate linear regression analysis was used to identify the trend rate of extreme temperatures indices in Bangladesh and each site (Donat et al. 2014). We Used the R studio software to perform the MK mutation test (Gallant & Karoly 2010;Panda et al. 2014) and use the student t-test to confirm the mutation change point and, increasing the credibility of the mutation outcome.

Linear regression trends analysis
The rate of the inter-decadal tendency of every single extreme temperatures index was quantified by employing the linear regression technique, and its significance was examined (Fig. 2). Based on the time scale, the warm indices of extreme temperature demonstrated an increasing trend except for TXX showed a decreasing trend during 1980-2015. The rate of the magnitude of DTR, SU, TXX, TNX, TX90p, and TN90p were 8.7e days/decades, 0.21 days/decades, 0.037 oC/decades, 0.01 oC/decades, 0.11 days/decades, and 0.12 days/decades, respectively (Fig. 2), denoting that the warm indices of extreme temperature are rising significantly in Bangladesh. Among them, the rising rate of DTR and TNX were relatively shorter during the study period 1980 to 2015. At the same time, the increasing rate of other indices was comparatively larger, mainly the rising rate of SU, which was the fastest, whose tendency of inter-decadal magnitude rate attained 0.21 days/decades (Fig. 2b). As shown in Fig. 2, except for TXX, the rest of the warm indices demonstrated an increasing trend from the 1990s to 2000, representing that there can be a warming occurrence in this period. DTR, SU, and TX90 were changed smoothly before 2010, while abrupt upward change started since 2010 (Fig. 2a, b, f). TN90 showed a comparatively short variation before the 1990s; after that, it had large fluctuations and showed an upward trend (Fig. 2e). TNX exhibited changes that started after 1995; before 1995, the fluctuation was short (Fig. 2h). The overall decreasing trend showed in TXX during the total study period, and two significant changes were in the 1990s and 2010s (Fig. 2j). Based on the discussion mentioned above, the warm indices of extreme temperature exhibited an overall upward trend in the study period except for TXX in this research. Since 1995, the warm indices showed a rapid upward trend in line with the global warming trend.
The cold indices of extreme temperatures TNN, TXN, TN10, and TX10 all exhibited decreasing trend, and the rate of magnitude were −0.019 °C/decades, −0.049 °C/decades, −0.15 days/decades and −0.078 days/decades, respectively. This demonstrates that these cold indices had a significant decreasing trend, of which the TN10 had the biggest decline and TNN had the most minor decrease that was also a certain tendency of global warming. Figure 2c shows that the TN10 significantly fluctuated before 2010, and from 2011 to 2015, the fluctuation was extremely short. TX10 demonstrated a decreasing trend where significant fluctuation had started since 1985 (Fig. 2d). In Fig. 2g, the TNN had the most noticeable change and fluctuation from the 2000s, while the most significant fluctuation was after 2010. The temporary fluctuation showed from 1980 to 1995 while the most considerable fluctuation and variation exhibited after 1995 with decreasing trend in TXN (Fig. 2f). By observing the above assessment, TX10, TN10, TXN, and TNN all exhibited a downward trend; notably, TX10 and TN10 showed a rapid decline speed.

Long-term connection analysis using DFA
To explore the trend behaviors of fluctuation in forthcoming temperature extremes, a long-term association Indeed, the warm temperature extremes will rise, and cold temperature extremes will decline in the forthcoming period. The rate of change in the warm temperature indices (SU, TNX, and TN90) will increase continuously than the other warm indices. The DFA values of these warm indices are not closer to 1. In cold temperature indices, TN10 will continue to decrease than the other cold temperature indices except for TX10 due to its DFA value being larger than the other cold indices. We explored that the sequence values of the DFA exponent of warm indices (SU, TNX, and TN90) are less than the cold temperature extreme (TN10). It demonstrates that the forthcoming trend pattern in temperature extreme has a strong long-term association with the current state and forthcoming trend pattern. By contrast, the DFA exponent value of the warm indices is higher than DTR, TXX, TX90, while in cold indices, the exponent value of DFA is lower than TNN, TXN, and TX10.
In Table 1, the correlation matrix of 10 temperature indices has been exhibited. We assessed the significant associations between the warm and cold indices (p<0.01) in this current study. There is a strong significant negative

Spatial patterns of extreme temperature indices
The spatial changes in temperature extremes are exhibited in Fig. 4. Nearly −081 to 1.12 days/decade was the change rate of DTR where southern and western parts had an increasing trend, and at the same time, another part faced the decreasing trend while 58% and 29% of areas under decreasing and increasing trends, respectively (Fig. 4a). In Fig. 4b, 65% of sites remain under the increasing trend of SU, and the change tendency rate was −0.93 to 1.44 days/decade; the southern part demonstrated decreasing tendency. TN10 had a decreasing trend in the south and south eastern regions, where 84% of areas occupied the decreasing trend (Fig. 4c). The trend change rate of TN10 was −0.5 to 1.22 days/decade in Fig. 4c. The trend rate of TX10 was −1.37 to 0.3 days/ decade, decreasing trend found in northern and southern parts, and 23% of areas remain under increasing direction (Fig. 4d). The change rate of TN90 was −0.25 to 1.63 days/ decade, and the northern and southern parts met the increasing trend where 50% of areas were under increasing trend (Fig. 4e). Figure 4f exhibits that TX90 had −1.6 to 1.45 days/ decade change rate and 67% area under increasing and 25% area under decreasing rate where western and southern part faced increasing trend and the other part met decreasing trend. The change rate of TNN was −1.50 to 1.51 days/decade, with 69% of station stayed under increasing tendency in the northern, western, and southern regions (Fig. 4g). TNX had a −1.14 to 1.50 rate of change; 80% of areas demonstrated a declining trend in the western and southern region (Fig. 4h). In Fig. 4i, the change rate was within −1.44 to 1.15 days/decade for TXN, and the higher decreasing rate was in the southern region; 73% station was under decreasing trend. The variation rate in TXX varied from −1.41 to 1.03 days/ decade, where 56% of areas show a declining pattern in the southern part of the study area (Fig. 4j). The trending behavior of extreme temperature indices varied spatially, further assured by temporal distribution in the earlier part (Table 2).

Factor analysis of temperature extreme indices
Factor analysis was carried out to detect the most influential factor affecting extreme temperature indices. F1, comprising TN90, SU, and TNX indices of temperature, the overall variance of temperature data is 40.76%, which denotes the warm night primarily controls the general warming trend of temperature extremes over Bangladesh from 1980 to 2015 (Table 3). Daily temperature range (DTR), SU, and TX90 control F2 calculated 22.40% of the whole variance, ensuring the rising of DTR is the principal factor that affects changes in yearly temperature. The DTR reflects the association between the minimum and maximum temperatures. About 11.83% of the total variance accounted for F3, where min T max (TXN) dominates the third factor. For F4, the coldest days (TNN) and warmest days (TXX) are the major dominant factors that represent the overall variance of 9.49% and 4.88%, indicating the warming climate has occurred daily minimum and maximum temperatures to rise significantly. In most cases, warm and cold extremes have a significant statistical association with the average annual temperature (You et al. 2011).

Variation of probability distribution functions of temperature extreme
Due to the variations in temperature extremes, the relative indices were chosen to explore the probability distribution function (PDF) of extreme temperature phenomena (Fig. 5) in the previous four decades. The frequency has declined in cold extremes while the frequency has increased in warm indices in a recent decade over Bangladesh, which also is consistent with temporal trend analysis. The cold extremes were moved negatively (Fig. 4c, e, g, i) while warm extremes (Fig. 4a, b, d, f, h, and j) positively shifted to their upper trails. The movement of negative and positive of the curve of PDF denotes that frequency is declined of cold extremes and increased in frequency of warm extremes. It is worth mentioning that the variations of the PDF curve are more evident in recent decades than in the past three decades. In warm indices, the highest peak was found in 1990 to 1999 and 2000 to 2009 for DTR, SU, and TXX. The recent two decades were for TNX, and 1980 to 1989 was for TN90, and 1990 to 1999 was for TX90. In cold indices, the maximum peak was found in the decades of 2000 to 2009 for TN10, TX10, and TXN and 1980 to 1989 was for TNN.

Rate of change analysis using Sen's slope estimation
The ordinary non-parametric system improved by (Zaiontz 2020) was employed to account for the slopes present in the rate of trend using the Sen's slope estimators (Fig. 6). The positive mark represents the increasing slope, and the declining slope denotes the negative impact. Figure 6a shows that the lowest negative Sen's slope value was −0.764, primarily found in the northeastern part, and the highest value was found in the southeastern region. The highest positive Sens value was 8.821 for SU (Fig. 6b), which generally exhibited in the northeastern part, while −3.019 was the lowest negative value for TN10 (Fig. 6c) which maximum distributed in the northern region of Bangladesh. In Fig. 6d Sen's slope value 3.649 for TN90 (Fig. 6e). The highest positive value was 5.312 for the TX90 (Fig. 6f), which mainly occupied southern and northern parts. The lowest value was −0.906 for the TNN (Fig. 6g), which was commonly found in the country's southern region. Figure 6h exhibits that the northeastern part met the lowest negative value of TNX, which was −0.089. For TXN (Fig. 6i), the lowest negative value was −1.4, mostly occupying the northern part of Bangladesh. The highest positive value was 0.406, which was distributed in the southern part of Bangladesh.

Mutation analysis of extreme temperatures indices
The MK change point detection analysis was performed for each extreme temperature index, and the change year was selected by combining the sliding t-test technique (Table 4). Table 4 shows that overall Bangladesh, the warm indices (DTR, SU, and TX90) and the cold indices (TNN and TX10) did not change, but the remaining warm (TN90, TNX, TXX) and cold indices (TN10 and TXN) were changed significantly (p<0.05). The station-wise warm and cold indices were muted. For warm index, in different stations, the points of change happened in the last twentieth and the beginning of the twenty-first century where stations like Patuakhali, Rangpur for SU; Mymensingh, Patuakhali, and Sitakundu for TXX; and Bhola, Jashore, Patuakhali, and Mymensingh for TX90 met the change point in the 1980s and later in 2008. In cold indices, their mutation point was also the beginning of the twenty-first and last of the twentieth, where Rangamati and Sitakundo for TNN, Chattogram and Teknaf for TN10 faced the mutation point after 1987 and 2005. The points of mutation of all indexes of temperature extremes passed 0.05 level of test of significance. It can be observed that the mutation point is varied from region to region. In those stations, warm indices such as TXX and TX90 were muted in 1986 and 1987, while cold indices including TNN and TN10 were muted in 1988 and 1989. Overall, the mutation points of warm indices were before cold indices and other indices. Similarly, it implied that the warm indices were more sensitive to global climate warming than cold indices.

Discussion
Extreme weather occurrences have drawn attention to the massive dominance of extreme climate changes on life, nature, and human production in recent years (Weaver et al. 2014;Li et al. 2013;Islam et al. 2021b). Due to getting how extreme climate influences the natural environment and society. It is significantly essential to assess climate extremes' spatial and temporal change trends. In this present study, we evaluated the temporal and spatial changes in temperature extremes in Bangladesh in the previous 36 years . The results exhibited that the trend of warm  Sun et al. (2015) investigated that cold extremes are significantly declining in China, similar to the current research. The warm occurrences are increased and decreased considerably the cold events stated by Ren et al. (2010), which is in line with the present study. The warm days are increased by 0-0.3 days/decade in China (Shi et al. 2018). Jiang et al. (2016) assessed that the cold indices TX10 and TN10 are declined whether the warm indices TX90 and TN90 increase in the Tibetan plateau. Cold extremes and warm extremes exhibited downward and upward trend, respectively, in the assessment of Yu and Li (2016), which is similar to the current research findings. We have explored the correlation between warm indices and cold indices. Warm and cold indices with each other were investigated. Those warm temperature indices (SU, TNX, and TN90) will be increasing in future than the other warm indices, while cold indices TN10 will decline in coming days than other cold indices by using the DFA exponent. The warm and cold extremes were significantly negatively correlated except for the relationship between SU and TNN, DTR and TXN, TXX and TN10. This outcome is consistent with Yu et al. (2015). A similar study has also done by You et al. (2013), You et al. (2011), andZhai andPan (2003). DTR is increasing in the southern and western part of Bangladesh for the SU, and southern part met the decreasing tendency, south and southeastern part demonstrating the decreasing trend for TN10, TX10 met the decreasing trend in the south and northern part. TN90 shows the increasing trend in the north and southern part of Bangladesh, south and western region met increasing trend for TX90. Approximately 69% of the northern, western, and southern parts of Bangladesh met increasing tendency of TNN, −.14 to 1.50 was the change rate of TNX and different parts of the country were faced decreasing. With a rising trend, southern part experiences the decreasing trend for TXN and TXX analyzed by spatial distribution in this current research work. Similar research work is also done by Zhou et al. (2020) where they found that the warm and cold indices are facing increasing and decreasing pattern in different parts of the study area. Li et al. (2020) found that TNN and TXX spatially varied, which agrees with the present study's outcomes. Some studies performed in North-Eastern regions of India are in good agreement with our finding (Jhajharia et al. 2014(Jhajharia et al. , 2021. Dabral et al. (2016) indicated that minimum temperature is rising in the northeastern part of India which is quite dissimilar to this finding. Results indicate that the frequency and intensity of warm night is enhancing in the North-Eastern region of India (Jhajharia and Singh (2011);and Dabral et al. (2016), similar to our study. Yu and Li (2014) investigated the spatial distribution of temperature indices in line with the current study's findings. The almost same study conducted by Zhao and Chen (2021), You et al. (2011), Nie et al. (2012, and Das (2021). The present study assessed the principal factor, which was DTR, and it also influences the variation of annual temperature, and its total variance was 22.40%. This outcome is consistent with Yu and Li (2014) where they found that SU25 is the principal factor of yearly temperature change. You et al. (2011) also explored similar findings. By using the probability distribution function, it discovered that warm indices are shifted positively. Cold indices are moved negatively, which further indicated that the warm indices are following an increasing trend while cold indices are decreasing trend and the density peak was different for each temperature extremes. The variations were most remarkable in the recent decades in this research study. This result is almost similar to Yu and Li (2014). Liu et al. (2021) found that the temperature extremes varied differently in different regions while the significant variations were in recent decades, consistent with the present study. The outcome of Fu and Ding (2021), Dey et al. (2021), and Khan et al. (2020) is in line with the current research.
In this study, we have analyzed the change point of temperature extremes where we found that the change point of warm and cold indices was last of the twentieth and beginning of the twenty-first century. Zhou et al. (2020) investigated that the mutation point for warm indices was beginning in the twenty-first century, which is in good agreement with the present research work. Liu et al. (2021) explored the change point of temperature extremes. By contrast, the daily maximum temperature altered quicker than the daily minimum temperature. The main reason is the probable urbanization impact on the extreme temperature indices (Zhou & Ren 2011). The urbanization impact may be aggravated by extreme temperature trends associated with daily maximum temperature in Bangladesh. However, the rapid urbanization impacts of extreme temperature indices related to daily minimum temperatures were generally trivial (Duan et al. 2012). Therefore, the increasing pattern of warm indices and decreasing cold indices have already influenced vegetation succession, soil and farm production over Bangladesh. There will be more intense consequences and uprising extreme weather occurrences and temperature forecasted in the coming days. The achieved outcomes have scientific and practical implications, which assist policy-makers in developing suitable measures to safeguard vegetation change and lessen the detrimental impacts triggered by extreme climatic phenomena. Our study aims to understand extreme climatic phenomena in Bangladesh.
Some drawbacks cannot be neglected in this work. Firstly, the change points of extreme temperatures were not secured, which might be an uncertainty due to limited metadata available. The addition of metadata can produce good results for homogeneous station. Secondly, greenhouse gas emissions and human-induced aerosols were not taken into consideration, influencing the probabilistic risk of extreme temperature. In spite of these drawbacks, our work gives in insight into the spatial and temporal variations in extreme temperature in Bangladesh. Environmental factors such as soil moisture content, potential evapotranspiration, pan evaporation, and land use/land cover changes should be considered in future studies. The extreme temperature influences vegetation dynamics based on CMIP6 datasets in Bangladesh deserves further investigation.

Conclusion
This paper aims to detect temporal and spatial trends of extreme temperature indices in Bangladesh in the past 37 years (1980-2017) using multi-statistical modeling approaches. The results show that warm temperature indices were increasing in the last four decades except for the warmest days (TXX), especially before the 2000s, while cold temperature indices showed a decreasing trend after 2000. DTR and SU showed an upward trend, indicating that the rising rate of daily maximum temperature was more than that of daily minimum temperature. This confirms that Bangladesh is uninterruptedly developing towards a warmer trend, which is a negative response to global climate warming.
Spatially, the change rate of warm indices was the largest in the northwest region and the smallest in the eastern part. Besides, the change rate of DTR at each station was less than that of other indices, whose changing tendency rate was the smallest in the central region and the decrease rate was more prominent in the northern part. The outcomes of DFA showed a long-range association among extreme temperature indices, implying that warm and cold indices will continue their present trend in the upcoming years, except for cold days. By using the PDF, the variations of the curves are more evident in recent decades than that in the past three decades. Based on factor analysis, the warm night primarily controls the general warming trend of temperature extremes over Bangladesh from 1980 to 2017. Mutation analysis revealed that the mutation points of the warm index were before the cold index and other indices, indicating that warm indices were more sensitive to global climate warming than cold indices. The increase in the warm indices and the decrease in the cold indices have eventually impacted agricultural  DTR  SU  TN10  TN90  TX10  TX90  TNN  TNX  TXN  TXX  Bangladesh stations crop production, soil fertility, and vegetation dynamics in northwest Bangladesh. Rising temperature and the increase in extreme climatic phenomena forecasted in the future will have detrimental impacts on the country's sustainable development. Studies deal with the reason of extreme temperatures is a prerequisite for sustainable development goals. Future works should examine this issue at a larger scale in detail. In fact, technological advances and effective policies may aid to address the climate change impact in Bangladesh as a whole and extreme temperatures may lead to the most noticeable. Thus, to achieve the country's sustainable development goals, governments and non-governments organizations at all levels should systematically take adequate countermeasures based on climate change characteristics and constantly develop their resilience to cope with extreme climatic phenomena.