Performance evaluation of CMIP6 GCMs for the projections of precipitation extremes in Pakistan

Extreme weather events are more detrimental to human culture and ecosystems than typical weather patterns. A multimodel ensemble (MME) of the top-performing global climate models (GCMs) to simulate 11 precipitation extremes was selected using a hybrid method to project their changes in Pakistan. It also compared the benefits of using all GCMs compared to using only selected GCMs when projecting precipitation extremes for two future periods (2020–2059) and (2060–2099) for four shared socioeconomic pathways (SSPs), SSP1-2.6, SSP2-4.5, SSP3-7.0 and SSP5-8.5. Results showed that EC-Earth3-Veg, MRI-ESM2-0 and NorESM2-MM performed best among GCMs in simulating historical and projecting future precipitation extremes. Compared to the MME of all GCMs, the uncertainty in future projections of all precipitation indices of the selected GCMs were significantly smaller. The MME median of the selected GCMs showed increased precipitation extremes over most of Pakistan. The greater increases were in RX1day by 6–12 mm, RX5day by 12–20 mm, Prcptot by 40–50 mm, R95ptot by greater than 30 mm, R99ptot by more than 9 mm, R4mm ≥ 4 mm by 0–4 days, R10mm by 2–6 days, R20mm by 1–3 days, and SDII by 1 mm/day, CWD by one day, CDD by 0–4 days in the northern high elevated areas for SSP5-8.5 in the late future. These results emphasize the greater influence of climate change on precipitation extremes in the northern, high-elevation areas, which provide the majority of the country’s water. This emphasizes the necessity to adopt suitable climate change mitigation strategies for sustainable development, particularly in the country's northern regions.


Introduction
Extreme weather events severely damage agriculture, livelihoods and properties (Agyekum et al. 2022).However, it is challenging to define extreme weather event as it varies with regional factors (Stephenson et al. 2008).The most recent research uses extreme indices based on the recurrence of a specified amount of precipitation or exceedance of specific thresholds to assess extremes.However, the duration and intensity thresholds used to define extremes are regionspecific (Data 2009).For example, the threshold defining heat waves in the middle latitude cannot represent heatwave over the tropics (Perkins et al. 2012).Thus, the Expert Team on Climate Change Detection and Indices planned twenty-seven extreme indicators for the analysis of climatic extremes globally and over specific regions (Sillmann et al. 2013;Klutse et al. 2021).These indices show how the climate would be more variable by detailing the magnitude and frequency of daily temperature and precipitation extremes (Tank et al. 2009).
The sector having the highest risk of climate extremes is agriculture and water resources (Ahmed and Schmitz 2011;Ali et al. 2022;Di Santo et al. 2022).Climate extremes resulted in crop and cattle losses (Goodland and Anhang 2009), low production of crops (Lal 2004;Hatfield and Prueger 2015), disease eruption and pest infestations (Rosenzweig et al. 2001).Numerous studies attempted to solve the challenges posed by contemporary and future climate extremes (Stocker et al. 2014;Sillmann et al. 2017).The frequency and severity of worldwide and regional climatic extremes have risen in recent years (Stocker et al. 2014;Wang et al. 2022a).Particularly, extreme event analysis has indicated increased heavy precipitation events (Edenhofer et al. 2014;Dibaba et al. 2020).Numerous studies reported changes in annual and seasonal precipitation patterns globally and locally (Iqbal et al. 2020;Praveen Extended author information available on the last page of the article et al. 2020; Šraj and Bezak 2020;McHale et al. 2021;Heureux et al. 2022;Sobh et al. 2022a).Areas with a variety of topography, such as dry and semi-arid regions, are more vulnerable to extreme precipitation events (Qin et al. 2018;Sharafati et al. 2020;Qiu et al. 2022).Pakistan, dominated by a semi-arid to an arid climate, is experiencing extreme precipitation increase with a further expected rise in the future (Zahid and Rasul 2011;Samo et al. 2017;Bhatti et al. 2020).Recently, some studies also indicated the dynamic changes in extreme precipitation across the country (Abbas et al. 2018(Abbas et al. , 2022;;Bhatti et al. 2020;Xu et al. 2022a).Increased precipitation extremes have resulted in meteorological hazards like floods, landslides, and economic damages (Hassan and Ansari 2015;Mahmood and Jia 2016;Salehie et al. 2022a).
The global circulations models (GCMs) remained a primary tool for investigating climate change and its dynamic mechanism (Flato et al. 2014;Agyekum et al. 2018).The Coupled Model Intercomparison Project (CMIP) was set up to assess the effectiveness of GCMs in simulating past, present, and future climate variables under various conditions.Recently, the CMIP6 has been released, which integrated the representative concentration pathways (RCP) and shared socioeconomic pathways (SSP) and made future projections more authentic (Eyring et al. 2016).CMIP6 GCMs also improve spatial resolution and increase parametrization schemes for climate systems (Tian-Jun et al. 2019).Evaluating historical and future climate extremes and understanding the physical processes are the primary focus of the scientific work done for CMIP6 GCMs (Eyring et al. 2016;Marotzke et al. 2017).Nonetheless, before using GCMs, evaluating their capabilities in reproducing the observed climate conditions is essential.This evaluation reduces errors and provides reliable future projections using the appropriate GCMs (Flato et al. 2014;Agyekum et al. 2018).
The accuracy of CMIP6 models in reproducing global and regional climate extremes has been evaluated in several studies.For example, Kim et al. (2020) identified CMIP6 GCMs performed well in replicating the extreme temperature and precipitation indices.Furthermore, studies revealed that the ensemble mean of GCMs performed robustly in reproducing extreme events during rainy months in East Africa (Akinsanola and Zhou 2019;Shiru et al. 2019Shiru et al. , 2020)).The two approaches have been widely used for selecting GCMs; past performance and envelope-based approach.In the first approach, the selection is made based on the past performance of GCMs in simulating the historical climate (Raju and Kumar 2014;Salman et al. 2018).In the second approach, GCMs provide future projections within a confidence interval is selected (Warszawski et al. 2014).Since the envelope approach does not choose GCMs that can reliably model historical climate, and the past performance method cannot guarantee GCM selection that can consistently simulate future climate, neither method is ideal.Therefore, combining both approaches can solve the problem where initial screening is done based on future projections of GCMs between the upper and lower band of the projection variety, and then the final selection of GCMs is established on historical climate (Lutz et al. 2016).
Many scientists have previously assessed the capability of CMIP6 GCMs to reproduce the weather conditions in Pakistan and its neighbours (Ali et al. 2015;Ahmed et al. 2020;Almazroui et al. 2020;Karim et al. 2020;Hamed et al. 2022c;Abbas et al. 2022).However, the characteristics of precipitation extremes differ in different regions (Easterling et al. 2017;Kulkarni et al. 2020;Shiru and Chung 2021).Some regions may experience increased precipitation but not precipitation extremes (Agyekum et al. 2022).From the available literature review, studies related to the performance evaluation of CMIP6 GCMs in reproducing the climate extremes in the study area are lacking.It motivated this study to investigate CMIP6 GCMs and select topperforming GCMs that can simulate the climate extremes in the study area for reliable projections of climatic extremes.The intention is to provide reliable future projections with reduced uncertainties.
This study was designed to select CMIP6 models that best simulate historical distribution and future projections of precipitation extremes indices in Pakistan.Future alteration of precipitation extremes and associated uncertainty was estimated using the best-performing models.This study would help in understanding the capability of CMIP6 models in replicating precipitation indices over Pakistan's diversified and complex regions.This can serve as a starting point for future research on weather extremes in the area.The extreme precipitation estimates can be used to refine the projections for CMIP5 scenarios.

Pakistan's topography
Pakistan is located in South Asia between 23.5° North and 37.0° North, and 60.5° East and 78° East.It has a diverse topography, as shown in Fig. 1.The arid to semi-arid climate is observed in the southern and central plains, whereas humid weather is in the northern mountains (Abbas et al. 2014).Pakistan is classified as an arid to semi-arid region with significant variations in temperature and precipitation.It mostly experiences two precipitation patterns: monsoons and westerlies.Monsoon and westerly systems contributed nearly 95% to the region's annual precipitation (Khan et al. 2014;Ullah et al. 2018).The yearly average temperature changes from 0 ℃ in the far north to 32 ℃ in the south.The maximum temperature varies between 15 and 35 ℃, and the minimum temperature ranges between 0 and 20 ℃ (Chaudhry et al. 2009;Hamed et al. 2022a).

CMIP6 GCMs
The daily precipitation simulations of CMIP6 GCMs for 1975 − 2014 were used to measure their relative performance in the study area.Twenty CMIP6 GCMs were chosen because of their ability to provide precipitation information for past and projected SSPs.The study used the GCMs available at https:// esgf-node.llnl.gov/ search/ cmip6/.The models' initial variant (r1i1p1f1) was chosen for an unbiased assessment.Variant index (r1) indicates the ensemble members, (i1) indicates initialization states, (p1) describes physical parametrization, and (f1) shows the forcing index.The GCMs are summarised in Table S1.Shared Socioeconomic Pathways are a new type of scenario introduced in CMPI6.SSPs consider global financial and demographic shifts and greenhouse gas emissions for their climate simulations.SSP1 and SSP5 indicate more contributions to the health sector, education sector, higherlevel institutions and fast economic growth.The critical difference between SSP1 and SSP5 is that earlier implies a speedy move to a sustainable society, and the latter implies fossil-fuelled-based economic growth.SSP3 and SSP4 describe a low-developed economy with a high growth in population, resulting in the unequal allocation of resources (Hausfather 2018).SSP2 represents the position between SSP1 and SSP3.

ERA5 dataset
European Centre for Medium − Range Weather Forecasts (ECMWF) developed the ERA − 5 dataset, the fifth edition of the Copernicus Climate Change Service (C3S).The ERA5 reanalysis, with a geographic resolution of 0.1° × 0.1°, was mined for hourly precipitation data from 1975 to 2014.Previous studies have also used it for higher resolution and reliable estimates of the observed precipitation (Lee et al. 2022;Liu and Yang 2022;Wang et al. 2022b).Hourly ERA5 was converted to a daily precipitation timeframe.The daily GCMs' skills in modelling precipitation indices were evaluated using a reference dataset (daily ERA5).Observation data remained challenging due to the shortage of long − term records in developing countries like Pakistan.Therefore, the ERA5 dataset has been used widely in the area (Zittis et al. 2016;Mistry et al. 2022;Syed et al. 2022b;Waseem et al. 2022).The data was downloaded from https:// cds.clima te.coper nicus.eu/# !/ home.

Methodology
This study used 11 ETCCDI extreme precipitation indices as described in Supplementary Table S2.These indices are useful for studying global and regional climate extremes (Heureux et al. 2022;Salehie et al. 2022b;Xu et al. 2022b;Khan et al. 2022).Since the available GCMs and ERA5 data had different spatial resolutions, this study employed bilinear interpolation to bring them to a uniform resolution of 1° × 1°.This technique applies a distance-weighted average of four surrounding points around the targeted point to provide smooth interpolation (Hamed et al. 2022b).Therefore, the bilinear interpolation for performance evaluation of CMIP6 GCMs has been used worldwide (Chen et al. 2021;Iqbal et al. 2021;Hamed et al. 2022b;Salehie et al. 2022b).The models' calculated precipitation extremes varied between the base period and the four SSPs.Similarly, ERA5 precipitation data for the reference period was used to determine all precipitation indices.The steps to achieve the objectives are shown in the flowchart of Fig. 2.

Ranking of GCMs based on hybrid envelope approach
The fluctuation in GCM accuracy over time makes it difficult to rank GCMs based on their capacity to simulate over different periods.It is possible that GCMs that do a good job of replicating the climate of the past will fail to do so in the future.Therefore, a hybrid approach was used in this study to select GCMs that can perform well in simulating the past and projecting the future climate.The researchers recommend a hybrid approach for selecting GCMs due to its efficiency in minimizing historical, future and spatiotemporal uncertainties (Lutz et al. 2016;Salman et al. 2018).In this study, GCMs were screened out by calculating the future projections of 11 precipitation indices by all GCMs for all four SSP scenarios.The 97.5th percentile, median and 2.5th percentile of all GCMs for all indices for all SSPs were calculated till the end of the twentyfirst century.The GCMs showing values between the 95th percentile confidence interval (CI) band for all indices for all scenarios were initially selected.A 95% confidence interval is most commonly used for assessing GCM's uncertainty (Lutz et al. 2016).Therefore, this study also used a 95% confidence interval for future projections to select GCMs.
In the second step, GCMs' skill in replicating the precipitation extremes indices for the historical period was evaluated using Kling − Gupta Efficiency (KGE) metrics.KGE evaluates three statistical metrics as a single measure, i.e., spatial variability ratio, Pearson's correlation and normalized variance, as represented below: (1) where r denotes the Pearson's correlation between GCMs simulations (s) and ERA5 data (o), denotes the bias stabilized by the standard deviation of observed data, is defined as a fraction of variation indicating spatial variability, and u and show the mean and standard deviation of GCM simulation and observed data, respectively.
Considering the capabilities and sensitivity to extremes, the KGE metric is preferred to quantify GCM's skills (Radcliffe and Mukundan 2017).The KGE is considered a robust spatial assessment metric (Nashwan et al. 2019;Salehie et al. 2022b;Sobh et al. 2022b).The range of KGE values lies between 1 and ∞.A value of 1 represents the best match.The GCMs performed better than the median for all indexes finally chosen.

Uncertainties in projected changes
The simulations of the indices using all GCMs and selected GCMs for all SSPs were prepared to compare the uncertainty ranges.However, the multimodel ensemble technique reduced projection uncertainty (Karmalkar et al. 2019;Yue et al. 2021).Therefore, spatial maps of the multimodel ensemble (MME) median, 97.5th percentile and 2.5th percentile of all indices based on all GCMs and selected GCMs were prepared to show the difference in the spatial variability in projections by all GCMs and the selected GCMs.In addition, maps showing the median MME of the selected GCMs for all precipitation extreme indices for SSP1-2.6,SSP2-4.5, and SSP5-8.5 in the near future (2020-2059) and far future (2060-2099) were created to illustrate the spatial distribution of absolute changes in precipitation extreme indicators over Pakistan.Water Meteorological Organization suggested 30 years or more to define climate.Several recent studies used 40 years spans (i.e., 2020-2059 and 2060-2099) to project future climate change (Homsi et al. 2020;Iqbal et al. 2020;Abbas et al. 2023).Therefore, the present study also adopted this span to project rainfall extremes.The precipitation in Pakistan varies widely over Pakistan from nearly zero in the western desert to more than 1000 mm in the far north.When presented as a percentage, this causes high values in future precipitation changes in the low precipitation region.Therefore, the study used absolute changes in precipitation and precipitation extremes to project future changes in Pakistan.

= s∕us o∕uo
Fig. 3 Future projections of a one-day maximum precipitation (RX1day) and b Simple daily intensity index (SDII) by all GCMs for all SSPs.The black line indicates the median, and the upper and lower red lines indicate 97.5th and 2.5th percentiles ◂

GCM ranking
The future projections of all indices using all GCMs for all SSPs were used to assess the consistency in projections.
For example, the future projections of four extreme indices (RX1day, SDII, R10mm and R20mm) using all GCMs for all SSPs for 2020-2099 are shown in Fig. 3.The projections' 2.5th and 97.5th percentile (i.e., 95% CI band) values are presented in Supplementary Table S3.The table also contains the 95% CI band of the projections of all indices.It shows that the projections of two GCMs, i.e., ACCESS − ESM1 − 5 and FGOALS − g3, were out of the 95% CI band for many indices.Few GCMs also showed projections out of the 95% CI band for one to four indices, but their projections were within the 95% CI band for most indices.Therefore, only two GCMs, ACCESS − ESM1 − 5 and FGOALS − g3, were discarded in the initial screening of GCM selection, considering their unrealistic projections of extreme precipitation.The initially selected GCMs were further evaluated against the ERA5 precipitation for the historical period (1975 − 2014) using KGE to select the best-performing GCMs.The obtained data is displayed in Table S4 of the Supplementary files.The KGE values were then used to rank the GCMs for each index separately.The rankings of the GCMs in simulating various precipitation indicators are shown in Table 1.The GCMs were finally selected by applying the criteria that it was not ranked below the median rank (below 9th position) in simulating any of the precipitation indices.The process selected EC − Earth3 − Veg, MRI − ESM2 − 0 and NorESM2 − MM.These three GCMs showed consistent projections and also performed best in simulating past climate.

Uncertainties using all and selected GCMs
The MME mean, and uncertainty in future projections of the indices using all GCMs and selected GCMs were evaluated to show how selected GCMs reduced projection uncertainty.The MME and 95% CI band of the projections of RX1day and RX5day using all GCMs and selected GCMs for different SSPs for 2020-2099 are presented in Figs. 4 and 5 as examples.It indicated that the CI band of selected GCMs was much thinner (with less uncertainty) than all GCMs in all cases.Consistent findings across multiple indices point to sizable reductions in uncertainties when employing only some GCMs rather than all of them.

Projected changes using all and selected GCMs
The spatial changes in precipitation indices using all GCMs and selected GCMs' MME with their 95% CI band values were estimated to compare the relative discrepancy.
Figures 6 and 7 show the outcomes for RX1day and RX5day, respectively.The results for other indices are presented in supplementary materials (from Figs.S1-S9).Figure 6 shows the historical and projected changes in RX1day based on the MME median, 2.5th and 97.5th percentiles of all GCMs and selected GCMs for two future periods and two SSPs, 1-2.6 and 5-8.5.The MME median of all GCMs and selected GCMs for the historical periods ranged between 5 and 44 mm.Furthermore, the MME median of all GCMs for SSP1-2.6 and SSP5-8.5 remained almost identical in both futures, except for the far future in SSP5-8.5.The median MME of the chosen GCMs projected an increase in RX1day across the board, with a few isolated exceptions in the country's central and southern regions.Contrarily, all GCMs indicated a rise of up to 15 mm in median MME.SSP5-8.5 showed the best prospective increase.The 2.5th and 97.5th percentile changes of RX1day using all GCMs were much lower and higher, respectively, than those estimated using the selected GCMs.The average change for all GCMs in the 2.5th and 97.5th percentile were 2.79 and 11.29, respectively, while it was 0.80 and 6.16 mm for the selected GCMs, respectively.The projected changes in RX5day based on the MME median, 2.5th and 97.5th percentiles of all GCMs and selected GCMs are presented in Fig. 7.The pattern of MME of all GCMs and selected GCMs for the future periods were like RX1day.The results indicate less uncertainty range in Fig. 4 Temporal evaluation of annual mean RX1day (mm) for all GCMs (yellow) and selected GCMs (blue) for different SSPs: (first row) SSP1-2.6 and SSP2-4.5 and (second row) SSP3-7.0 and SSP5-8.5.The shaded portion indicates a 95% CI band the MME median of the selected GCMs than all GCMs.The average change (median) for all GCMs was 6.58, while it was 5.77 for the selected GCMs.The above two figures and the supplementary figures (S1 to S9) revealed the superiority of the chosen GCMs in this study for projecting precipitation extremes over Pakistan.

Projection of precipitation extremes using selected GCMs
The geographical changes in precipitation indices using selected GCMs for three SSPs were estimated to show their future projection changes.The MME median change of  S14).The anticipated shifts in RX1day across Pakistan are depicted spatially in Fig. 9. RX1day will range from − 9 mm to 13 mm for various SSPs, depending on where in the country you are.For all SSPs and future periods, the spatial pattern showed that RX1day decreased or remained constant in the western arid region while increasing in the northeast high elevated areas.However, there was a large variability in projections for different SSPs in the far future.SSP2-4.5 showed decreased RX1day over most of the study area, while SSP5-8.5 indicated an increase of 1 to 13 mm over most of the country.However, the discrepancy in the spatial distribution was relatively less for the near future.For SSP1-2.6, the gap between these two periods was also narrower.This indicates a large uncertainty in future projections of RX1day in the far future for higher SSPs. Figure 9 indicates the geographical distribution of projected changes in CDD over the study region.The results exposed a change in CDD over Pakistan by − 15 to 15 days.A decrease in CDD dominated most regions for all SSPs and future periods.Similarly, a relatively more discrepancy was observed among SSP projections in the far future than in the near future.The change was negative for SSP1-2.6 in the near future (− 2.54 days), while it was 1.31 days in the far future.The opposite pattern was observed in SSP2-4.5 and 5-8.5, with the highest decrease in the future with − 15 and − 13 days, respectively.However, there was an increase of up to 8 days in the northern high elevated areas in the far future for different SSPs.
Projected changes in yearly total precipitation (Prcptot) of more than 1 mm for all SSPs and both future periods are illustrated in Fig. 10.The results revealed an overall increase in the study area up to 57 mm, especially in the north region.However, a decrease of 11 mm was observed in the south and east in the near future for SSP2-4.5.The most increase was in the northern regions in the far future for SSP5-8.5.While the Prcptot decline was more pronounced in the near future, a rise was more pronounced in the far future across the entire study area.Figure 11 shows the projected changes in R95ptot under three SSPs and future periods.The results illustrate an overall precipitation rise of up to 38 mm in both future periods for all SSPs, except a decrease of 8 mm in the south and east in the near future for SSP2-4.5.However, the highest increase was observed in the north in the far future for SSP5-8.5.Both indices were similar in their pattern of increase and decrease.
Figure 12 presents projected changes in R10mm for three SSPs and two future periods.R10mm increased by two days in both the future and present periods across most of the research area.However, a small decrease of 2 days in the southern and eastern regions along the Indian border was observed in the near future for SSP2-4.5.In the far future, SSP5-8.5 showed the largest 7-day increase in the north.Figure 13 shows projected changes in SDII.It would slightly change (± 1 mm/day) in the near future for all SSPs, except for a decrease in the central and southern regions for SSP2-4.5.In contrast, precipitation will be more intense (an increase of SDII by more than 1 mm/day) in the far future, especially for SSP5-8.5.

Discussion
The present study evaluated CMIP6 GCMs in reproducing the precipitation indices proposed by ETCCDI using a hybrid approach.Past research has mostly focused on evaluating CMIP5 and CMIP6 GCMs and their abilities to stimulate the country's average precipitation and temperature (Ullah et al. 2018;Almazroui et al. 2020;Iqbal et al. 2020;Waseem et al. 2022).No study assessed CMIP6 GCMs' skill in replicating precipitation extremes indices in the study region.In this study, 20 CMIP6 models were used to evaluate their skill in simulating precipitation indices through a hybrid-envelope approach.The envelope approach suggested discarding the Fgoals − g3 and ACCESS − ESM1 − 5 in the initial screening as their projections were out of the 95% CI band for most indices.After comparing ERA5 data (1975-2014) with the GCM simulations of precipitation indices, the KGE was used to determine a final ranking for the GCMs.This study used ERA5 data as the previous studies widely employed it to explore precipitation extremes in nearby regions (Ullah et al. 2021;Shen et al. 2022).Three models, EC-Earth3-Veg, MRI-ESM2-0 and Nor-ESM2-MM, were most successful in consistently simulating the precipitation indices in the future and duplicating extremes of the reference period.The temporal analysis of extreme indices projections using the selected GCMs indicated a more significant improvement in uncertainty reduction than all GCMs.The 95% CI band of selected GCMs was much narrower than all GCMs for all SSPs.Furthermore, the projected spatial changes in indices based on the MME median, 2.5th and 97.5th percentile of selected GCMs showed much less uncertainty than those using all GCMs.
Generally, future projected changes in the median MME of selected GCMs revealed an increase in RX1day, Prcptot, R95ptot, R10mm and SDII indices in the most study area in the far future for all SSPs.However, the greatest changes were observed in northern high-elevated areas, followed by southern parts for SSP5-8.5 in the far future.The findings are in line with those of other research efforts (Ali et al. 2015(Ali et al. , 2019;;Wu et al. 2017;Iqbal et al. 2020;Saddique et al. 2020), which revealed more wet climate in future and a further increase in precipitation in northern high elevated areas.Particularly, increases in precipitation extreme indices under SSP585 in the far future have been reported in recent studies (Ullah et al. 2020;Syed et al. 2022a;Abbas et al. 2023).Furthermore, projected changes in CDD indicated a decrease in most areas, except in the north for different SSPs in both future periods.The outcome are aligned with previous studies (Ali et al. 2019;Sajjad and Ghaffar 2019;Reddy and Saravanan 2023).For accurate predictions of future climate extremes in the region, this study recommended the chosen GCMs.
The northern and southern parts of the country showed high spatial variability in precipitation indices.This is mainly due to high topographic variability, which causes a heterogeneous climate in Pakistan (Bhatti et al. 2020;Iqbal et al. 2020).This increase in the precipitation amount may be beneficial for crop agriculture in the region.However, increased precipitation extremes may cause flooding to become more common in the future.Furthermore, it may result in loss of agriculture and damage to infrastructures.The nation's water supply is vulnerable to changes in the severity of precipitation in the northern source region.This study provided adequate information for investigating

Conclusion
This research aimed to identify the best CMIP6 GCMs for forecasting precipitation indicators in Pakistan.The CMIP6 GCMs were ranked corresponding to their ability to project the heaviest precipitation events.The study revealed EC-Earth3-Veg, MRI-ESM2-0 and Nor-ESM2-MM as the best model for simulating future precipitation extremes consistently and replicating historical precipitation extremes reliably.The results revealed a considerable decline in uncertainties in the projections of all precipitation indices using MME of selected GCMs compared to all GCMs.Most types of extreme precipitation were projected to alter significantly throughout the study's period using the chosen projection method.It was predicted that the northern areas with the highest elevation would experience the greatest increase in extremes, followed by the southern regions.Future periods would have larger rises for SSP5-8.5.
The study revealed that the northern sub-Himalayan regions, which are the major source of all major rivers, would experience an increase in precipitation amount and intensity, indicating a higher impact of climate change.This might increase the frequency and intensity of floods, which could negatively affect the economy and human lives.The maps of extreme precipitation projections generated in this study can aid policymakers in developing water resources and disaster risk management strategies to address climate change.
The present study employed 20 GCMs as they were only available during the study period for the SSPs considered.Future studies could explore incorporating more GCMs to determine the best possible subset for climate projections.Furthermore, selecting GCMs based on precipitation and temperature extremes may enhance their relevance for various climate change impact assessments.

Fig. 1
Fig. 1 Topography map of the study area Fig. 2 Procedures used in the research the selected GCMs for two future periods, compared with the historical period 1975 − 2014, were estimated for this purpose.Results for RX1day, CDD, R95ptot, R10mm and SDII are presented inFigs.8, 9, 10, 11, 12, 13. Results for other indexes are included in the appendices (Figures S10 to

Fig. 6
Fig. 6 Spatial changes in RX1day (mm) in the study area indicating 97.5th percentile, median and 2.5th percentile of all GCMs and selected GCMs for the historical period and in the near (2020 − 2059) and far (2060 − 2099) futures for SSP1-2.6 and SSP5-8.5

Fig. 8
Fig. 8 Spatial distribution of changes in RX1day (mm) in study area indicating Median MME of selected GCMs in the period of (2020 − 2059) and (2060 − 2099) for different SSPs

Table 1
Ranking of GCMs for their capability to replicate the studied region's precipitation indices Numbers in bold are the top 50th percentile, while the final selection GCMs are highlighted in bold