How Do CMIP6 HighResMIP Models Perform in Simulating Precipitation Extremes over East Africa?

: This work assesses the ability of nine Coupled Model Intercomparison Project phase 6 (CMIP6) High-Resolution Model Intercomparison Project (HighResMIP) models and their ensemble mean to reproduce precipitation extremes over East Africa for the period 1995–2014. The model datasets are assessed against two observation datasets: CHIRPS and GPCC. The precipitation indices considered are CDD, CWD, R1mm, R10mm, R20mm, SDII, R95p, PRCPTOT, and Rx1day. The overall results show that HighResMIP models reproduce annual variability fairly well; however, certain consistent biases are found across HighResMIP models, which tend to overestimate CWD and R1mm and underestimate CDD and SDII. The HighResMIP models are ranked using the Taylor diagram and Taylor Skill Score. The results show that the models reasonably simulate indices, such as PRCPTOT, R1mm, R10mm, R95p, and CDD; however, the simulation of SDII CWD, SDII, and R20mm is generally poor. They are CMCC-CM2-VHR4, HadGEM31-MM, HadGEM3-GC31-HM, and GFDL-CM4. Conversely, MPI-ESM1-2-XR and MPI-ESM1-2-HR show remarkable performance in simulating the OND season while underestimating the MAM season. A comparative analysis demonstrates that the MME has better accuracy than the individual models in the simulation of the various indices. The findings of the present study are important to establish the ability of HighResMIP data to reproduce extreme precipitation events over East Africa and, thus, help in decision making. However, caution should be exercised in the interpretation of the findings based on individual CMIP6 models over East Africa given the overall weakness observed in reproducing mean precipitation.


Introduction
Climate change is evident globally, mainly characterised by an increase in temperature and an increase in the intensity and frequency of extreme events (IPCC 2021, [1]).East Africa remains vulnerable to the effects of climate change due to recurrent extreme precipitation events (mainly droughts and floods) and over-reliance on rainfed agriculture for sustainability.For instance, recurrent droughts from 2021 to 2022 due to precipitation failure caused food insecurity in the entire Greater Horn of Africa (WMO 2022, [2]).The associated impacts caused the loss of lives and destroyed the environment, derailing socioeconomic growth and the overall realisation of climate-dependent Sustainable Development Goals (SDGs) in the region [3,4].This calls for understanding not only the present climate extremes but also the future for planning purposes.
Global climate models (GCMs) are important in understanding the climate system and investigating its changes both in the past and future.The Coupled Model Intercomparison Project (CMIP) provides a collection of different climate model outputs in a standardised format for ease of intercomparison [5].
The climate situation in East Africa is likely to get worse under global warming, where an increase in the frequency and/or intensity of heavy precipitation and pluvial flooding is projected [1].The recently released sixth assessment report (AR6) of the Intergovernmental Panel on Climate Change [1] projects a reduction in meteorological drought at 4 • C due to global warming.However, the models used in the Coupled Model Intercomparison Project Phase 6 (CMIP6) [6] exhibit inconsistencies, just like the earlier versions (phases 3 and 5), in reproducing mean precipitation over East Africa [7,8].Despite the limitations, [9] used CMIP6 models to investigate future changes in precipitation extremes over East Africa.The authors of [10] found several consistent biases across 25 CMIP6 models in reproducing extreme precipitation over Eastern Africa.The models tend to overestimate the total wet day precipitation and consecutive wet days, while most models underestimate very wet days and maximum 5-day precipitation in the two precipitation seasons.
Improvements in computing power have led to high-resolution runs of the CMIP6 models under the High-Resolution Model Intercomparison Project (HighResMIP) [11].The outputs are meant to promote the analysis and understanding of the impact of model resolution on climate simulations.Past studies have shown that globally increasing the horizontal resolution of climate models improves their ability to simulate thermodynamic and dynamic processes [12,13].Thus, the runs are more reliable in assessing climate risks, especially those associated with small-scale weather phenomena.However, in a study over West Africa, ref. [14] observed that improving the horizontal resolution may not necessarily reduce biases from the CMIP6 models.The biases were persistent in simulating drought over the region as well [15].Similarly, ref. [16] observed that no one model best agrees with Climate Hazards Group Infrared Precipitation with Stations (CHIRPS) in reproducing the onset and cessation dates during the bimodal season in southern West Africa.The results also noted that IPSLCM6A-ATM-HR, a model among the five HighResMIPs considered, best agrees with CHIRPS in representing onset and cessation dates during the unimodal precipitation season.
So far, the ability of HighResMIP for CMIP6 to reproduce mean and extreme precipitation over East Africa has not been evaluated.This work aims to evaluate the ability of HighResMIP for CMIP6 to reproduce precipitation extremes over East Africa.The study employs extreme climate indices distinct by the Expert Team on Climate Change Detection Indices (ETCCDI; [17]).The listed indices mainly considered aspects of extreme intensity, frequency, and duration of precipitation events over the study area [17].These indices have been widely used for extreme-rainfall-related studies [18,19].Further, this study employs robust statistical approaches, such as correlation coefficient (CC), root mean square error (RSME), normalized root mean square error (NRMSE), and mean bias (MB), to evaluate the performance of the models and ranks them based on the Taylor diagram and Taylor Skill Score (TSS) technique.The output will help users gauge the confidence of HighResMIP projections of extreme precipitation events in decision making.

Study Area
East Africa is defined by geographical coordinates of longitude 28 • E-42 • E and latitude 12 • S-5 • N (Figure 1).Physical and geomorphological features, such as the large expanse of arid and semi-arid lands (ASAL), high-elevation points reaching ~5800 m, and freshwater lakes and rivers, among others, encompass the study locale.These features regulate the local climate from one region to another.Overall, the climate of the region is classified according to Koppen-Geiger as tropical climate (Af) and arid, desert hot (BWh), despite being situated in the equatorial region [17].Seasonal precipitation over East Africa is controlled by the movement of the tropical rain belt [20].This is due to its location along Hydrology 2024, 11, 106 3 of 26 the equator, which implies that the movement of seasonal changes in climate is affected by the Hardley circulation, which migrates twice a year across the region from south to north and backwards from north to south [20].This migration is accompanied by change in the wind direction, from a northerly direction in the boreal winter to southerly direction in boreal summer, characteristics of monsoons.Thus, the region receives more than 1000 mm annually, especially along the regions of western Kenya and Lake Victoria, Uganda, and parts of southern Tanzania.Rainfall declines eastward in the Western Rift (below 1000 mm) along the regions of eastern Kenya and northern Kenya.Consequently, the rainfall received supports agricultural activities from March to May (MAM) and October to December (OND), locally known as 'long rains' and 'short rains', respectively [21][22][23].Similarly, the maximum solar heating regulated by the oscillation of the inter-tropical convergence zone (ITCZ) results in annual mean temperatures ranging between 5 and 35 • C [9].More detailed information regarding the region's climatology can be obtained from previous literature such as [20,24].
Hydrology 2024, 11, 106 3 of 27 regulate the local climate from one region to another.Overall, the climate of the region is classified according to Koppen-Geiger as tropical climate (Af) and arid, desert hot (BWh), despite being situated in the equatorial region [17].Seasonal precipitation over East Africa is controlled by the movement of the tropical rain belt [20].This is due to its location along the equator, which implies that the movement of seasonal changes in climate is affected by the Hardley circulation, which migrates twice a year across the region from south to north and backwards from north to south [20].This migration is accompanied by change in the wind direction, from a northerly direction in the boreal winter to southerly direction in boreal summer, characteristics of monsoons.Thus, the region receives more than 1000 mm annually, especially along the regions of western Kenya and Lake Victoria, Uganda, and parts of southern Tanzania.Rainfall declines eastward in the Western Rift (below 1000 mm) along the regions of eastern Kenya and northern Kenya.Consequently, the rainfall received supports agricultural activities from March to May (MAM) and October to December (OND), locally known as 'long rains' and 'short rains', respectively [21][22][23].Similarly, the maximum solar heating regulated by the oscillation of the inter-tropical convergence zone (ITCZ) results in annual mean temperatures ranging between 5 and 35 °C [9].More detailed information regarding the region's climatology can be obtained from previous literature such as [20,24].

Observations and Model Outputs
This study uses daily high-resolution satellite observation datasets sourced from the Climate Hazards Group Infrared Precipitation with Stations version 2 (CHIRPS.v2).In order to account for uncertainty, this study used the Global Precipitation Climatology Centre version 2020 (GPC) to evaluate the models.The CHIRPS data span from 1981 to now with horizontal resolutions of 0.05° × 0.05°.On the other hand, GPCCv2020 spans from 1982 to 2019 with a horizontal grid resolution of 1° × 1°.Comparable to other existing sources of proxy observational datasets, CHIRPS and GPCC have been found to robustly

Observations and Model Outputs
This study uses daily high-resolution satellite observation datasets sourced from the Climate Hazards Group Infrared Precipitation with Stations version 2 (CHIRPS.v2).In order to account for uncertainty, this study used the Global Precipitation Climatology Centre version 2020 (GPC) to evaluate the models.The CHIRPS data span from 1981 to now with horizontal resolutions of 0.05 • × 0.05 • .On the other hand, GPCCv2020 spans from 1982 to 2019 with a horizontal grid resolution of 1 • × 1 • .Comparable to other existing sources of proxy observational datasets, CHIRPS and GPCC have been found to robustly represent the local climate of East Africa [25][26][27][28].The two observation datasets employed in the current study have distinct differences, with CHIRPS being satellite product developed from combination of interpolation technique and high-resolution precipitation estimates from infrared Cold Cloud Duration (CCD) observations.The data also incorporate fine grid satellite imagery, in addition to daily, pentadal, and monthly CCD-based precipitation products.On the other hand, GPCC has been developed from rain-gauge measurements and comprehensive quality control.It should be noted that despite the robust performance of the two gridded datasets used as proxy of observed products, they are still marred with uncertainties that result from low density of observational networks that are used to build them and the interpolation techniques [29,30].Details regarding the datasets' algorithms, including the background information and techniques used to build them, can be obtained from [26] for CHIRPS and [27] for GPCC.High-Resolution Model Intercomparison Project version 1.0 (HighResMIP v1.0) for CMIP6 (hereafter, simply HighResMIP) is used in the present study.The daily data span from 1950 to 2050, with horizontal grid resolutions ranging between 0.28 and 1 • .The overarching objective of HighResMIP is to ascertain the capabilities of enhanced horizontal model resolution in simulating the atmosphere and ocean.Due to the high computational cost and processes involved, only a few models are presently available on the Earth Systems Grid Federation (ESGF).This study employs the listed models in Table 1.Previous studies based on CMIP6 models have equally demonstrated better performance of the listed models utilized in the current study [9,10,31].Thus, this was the motivation to employ the downscaled and high-resolution versions of the models to affirm how they perform over the region.Many studies [32][33][34] have reported that the coarser resolution is one fundamental reason as to why most models show poor performance due to their inability to capture convective processes and other internal variability.Thus, we selected some suitable models with relatively higher resolution.For example, [11] provides more information on the model datasets.This study uses a historical period of 1995-2014 in line with the baseline period of the Sixth Assessment Report (AR6; IPCC, 2021 [1]).The models used in this study are interpolated to a common 1.0 • × 1.0 • latitude- longitude grid using the Kriging interpolation method.It is a widely used technique for spatial interpolation that calculates the undefined values at a known geographical location; moreover, this method reduces the error of the estimated values.Numerous studies have indicated that using the Kriging method results in lower interpolation errors [35][36][37][38].The multi-model mean (MME), which represents the mean of the 9 HighResMIP GCMs, is calculated over East Africa, covering the period of 1995-2014.
Table 1.HighResMIP GCMs and their reporting institutions and countries, and horizontal resolutions.The variant label r1i1p1f1 is used in this study.

Name
Modelling Centre/Country Horizontal Resolution (lat × lon)

Methods
This study considers East Africa's annual precipitation and examines how High-ResMIP models simulate observed precipitation extremes, as defined by the Expert Team on Climate Change Detection and Indices (ETCCDI) [17].They include the simple daily intensity index (SDII), wet days (R1mm), heavy precipitation days (R10mm), and very heavy precipitation days (R20mm).Other indices used to denote frequency and duration are consecutive dry (wet) days (CDD/CWD) and the annual maximum amount of precipitation accumulated over 1 day (Rx1day).The indices are employed to demonstrate the capability of HighResMIP global circulation models (GCMs) to simulate extreme events that are detrimental to natural and societal ecosystems.More information about the indices used is highlighted in Table 2.Many studies have employed these indices in different East African regions and other sub-regions of Africa to assess the impact of extreme precipitation events [9,10,18,19,39].These indices were also used in other regions, such as Southeast Asia [40,41].Statistical metrics, such as root mean square error (RMSE), normalized root mean square error (NRMSE), percentage bias (Bias), and correlation coefficient (CC), are used to quantify the models' performance over the region.The mathematical formulas of the metrics are shown in Equations ( 1)-( 4): where M is the model and O is observation.The Taylor diagram and Taylor Skill Score (TSS) are used to rank the models [42].This approach has been employed in many studies in the region [27,43,44].A Taylor diagram is a graphical illustration showing the similarity of two patterns in terms of their CC, centred RMSD, and the amplitude of their variations (represented by the standard deviation) [42].All three metrics are presented in one plot, as illustrated mathematically in Equation ( 5).The plot is useful in evaluating multiple aspects of complex models or gauging the relative skill of different models [45].
where E is the centred RMSE and C is the correlation coefficient.
σ m and σ o are the standard deviations of the model and reference or observed datasets, respectively.
The TSS (Equation ( 6)) is a numerical summary of the Taylor diagram to express a synthetic measure.
where R m is the pattern correlation coefficient of the climatological mean between simulation and observation, R o is the maximum attainable correlation coefficient (set to 0.999), while σ m and σ o are the climatological means and standard deviations for the simulated and observed spatial patterns, respectively.The closer the value of TSS is to 1, the better the agreement between simulation and observation.A similar approach has been successfully employed in previous studies [46][47][48].

Annual Climatology of Mean Precipitation
First, this study examines the characteristics of monthly averaged precipitation over East Africa as simulated by HighResMIP models against the observed data.The annual cycle of precipitation from models and observations (CHIRPS and GPCC) is presented in Figure 2a.Meanwhile, the mean difference between the HighResMIP models and the mean of the observations are presented in Table A1.The two observations demonstrate a bimodal pattern, with peaks during MAM and OND [25,27,49].June-September (JJAS) is the dry season, with July being the driest month (<1.2 mm/day).The two peaks shown in the observed data are associated with the tropical rain belt that oscillates between 15 • S and 15 • N throughout the year [50].Most HighResMIP models reproduce the observed annual precipitation cycle over East Africa.This shows better reproducibility of annual precipitation over this study region by new generation models.However, most models underestimated the MAM peak, while overestimation is noted during OND (Figure 2a).To illustrate, HadGEM3-GC31-MM and HadGEM3-GC31-HM overestimate the MAM (OND) season by up to 3.30 mm/day (3.84 mm/day).Conversely, MPI-ESM1-2-XR and MPI-ESM1-2-HR show remarkable performance in simulating OND peaks, despite underestimations of the MAM season.Interestingly, MME captures the annual cycle pattern with minimum biases for MAM and OND seasons.For instance, MME underestimates the MAM season by −0.27 mm/day while overestimating OND by 1.27 mm/day over this study region.However, considering the mean bias of all models, including the MME, the results shows that MME demonstrated the least bias during all seasons as compared to individual models (Table A1).The results agree with previous studies [51][52][53].Further analysis to demonstrate the monthly performance of models in simulating anomalies is shown in Figure 2b.Generally, stronger wet (dry) biases occur during November (April), while excellent performance by most models is noted during the simulations of the dry season (i.e., June and July).It is also noted that the models present a larger range during the short rains (OND) than the long rains (MAM).This could be attributed to the large-scale teleconnection that controls the short rains, resulting in more rainfall events during the short rains compared to the long rains [54][55][56].
Figure 3 presents a comparison of the annual precipitation spatial distribution over East Africa during 1995-2014 based on the HighResMIP MME and observations.The simulated annual precipitation shows the largest wet biases (>6.5 mm/day) around the Lake Victoria region and most parts of Uganda (Figure 3a).The difference between the HighResMIP MME and the observation indicates good model performance in representing local annual precipitation spatial distribution.Typically, the results show agreeable model performance in simulating the local annual mean cycle.However, persistent wet biases have been equally reported in previous studies that utilised coarser CMIP5 and 6 GCMs and higher-resolution CORDEX regional climate models over the region [52,57,58].Several comparative studies across other regions globally equally show varying performances, with some studies illustrating improved performance by HighResMIP models and their ensemble means [15,59].Figure 3 presents a comparison of the annual precipitation spatial distribution over East Africa during 1995-2014 based on the HighResMIP MME and observations.The simulated annual precipitation shows the largest wet biases (>6.5 mm/day) around the Lake Victoria region and most parts of Uganda (Figure 3a).The difference between the HighResMIP MME and the observation indicates good model performance in representing local annual precipitation spatial distribution.Typically, the results show agreeable model performance in simulating the local annual mean cycle.However, persistent wet biases have been equally reported in previous studies that utilised coarser CMIP5 and 6 GCMs and higher-resolution CORDEX regional climate models over the region [52,57,58].Several comparative studies across other regions globally equally show varying performances, with some studies illustrating improved performance by HighResMIP models and their ensemble means [15,59].Figure 3 presents a comparison of the annual precipitation spatial distribution over East Africa during 1995-2014 based on the HighResMIP MME and observations.The simulated annual precipitation shows the largest wet biases (>6.5 mm/day) around the Lake Victoria region and most parts of Uganda (Figure 3a).The difference between the HighResMIP MME and the observation indicates good model performance in representing local annual precipitation spatial distribution.Typically, the results show agreeable model performance in simulating the local annual mean cycle.However, persistent wet biases have been equally reported in previous studies that utilised coarser CMIP5 and 6 GCMs and higher-resolution CORDEX regional climate models over the region [52,57,58].Several comparative studies across other regions globally equally show varying performances, with some studies illustrating improved performance by HighResMIP models and their ensemble means [15,59].

Mean Annual Maximum Dry/Wet Spell Length
An analysis of the annual variability in observations, MME, and HighResMIP models during 1995-2014 is shown in Figure 4.The overall results indicate that HighResMIP reproduces the annual variability of R10mm, R20mm, R95p, precipitation, and Rx1day fairly well.However, consistent biases are evident across HighResMIP models; for instance, all models tend to underestimate CDD and SDII.Similarly, this underestimation was also reported by [10].Conversely, HighResMIP models overestimated CWD and R1mm during the entire study period.
IFS-LR are able to capture the mean annual distribution of CDDs.On the other hand, MPI-ESM1-2-HR and MPI-ESM1-2-XR exhibit notable drying patterns over the entire domain of up to >100 days.Conversely, CMCC-CM2-VHR4 captures low CDDs (<20 days) over most of the domain except for some parts of Tanzania.Previous studies [9,10,28] evaluated the performance of CMIP6 models over the region and also reported considerable differences between the models and observations.The spatial distribution of annual consecutive dry days (CDDs) is presented in Figure 5. CHIRPS and GPCC exhibit fewer CDDs (<30 days) over the western side of the region, covering western Kenya, the entirety of Uganda, and parts of Rwanda.Most parts of Kenya, Burundi, and Tanzania have large CDDs (>60 days).The GFDL-CM4 and ECMF-IFS-LR are able to capture the mean annual distribution of CDDs.On the other hand, MPI-ESM1-2-HR and MPI-ESM1-2-XR exhibit notable drying patterns over the entire domain of up to >100 days.Conversely, CMCC-CM2-VHR4 captures low CDDs (<20 days) over most of the domain except for some parts of Tanzania.Previous studies [9,10,28] evaluated the performance of CMIP6 models over the region and also reported considerable differences between the models and observations.The spatial mean annual distribution of CWD is presented in Figure 6.The observation datasets depict CWD over the region of ~25 days.Most models reasonably capture the overall CWD distribution, although considerable biases still exist.For instance, HadGEM3-GC31-MM, MPI-ESM1-2-HR, and MPI-ESM1-2-XR overestimate the magnitude of CWD by ~60 to 80 days, especially around the Lake Victoria region and parts of Uganda, as compared to the observed datasets.The large overestimations of extreme events in the models could be attributed to the model parameterization scheme, such as failure to adjust cloud physical parameterization and aerosol emission factors of the model.This resulted in their inability to describe meso-and micro-scale complex topography and the considerable role of orography in water vapor transport and condensation [60,61].Such weakness in the GCMs have been resolved with the development of the convective-permitting models (CPMs) and regional climate model (RCM) dynamical downscaling, showing evidence of improved performance [59].Similar observations of model performance in representing CWD over this study region were reported in a recent study that utilised CMIP6 GCMs models over the region [10].However, they reported larger CWD values, with attribution to a common challenge in most GCMs that tends to reflect more precipitation occurrences in Eastern Africa.  1) over East Africa.
The spatial mean annual distribution of CWD is presented in Figure 6.The observation datasets depict CWD over the region of ~25 days.Most models reasonably capture the overall CWD distribution, although considerable biases still exist.For instance, HadGEM3-GC31-MM, MPI-ESM1-2-HR, and MPI-ESM1-2-XR overestimate the magnitude of CWD by ~60 to 80 days, especially around the Lake Victoria region and parts of Uganda, as compared to the observed datasets.The large overestimations of extreme  vective-permitting models (CPMs) and regional climate model (RCM) dynamical downscaling, showing evidence of improved performance [59].Similar observations of model performance in representing CWD over this study region were reported in a recent study that utilised CMIP6 GCMs models over the region [10].However, they reported larger CWD values, with attribution to a common challenge in most GCMs that tends to reflect more precipitation occurrences in Eastern Africa.

Frequency of Wet, Heavy, and Very Heavy Precipitation Days
The mean distribution of wet days (R1mm), heavy precipitation days (R10mm), and very heavy precipitation days (R20mm) is displayed in Figures 7-9, respectively.Comparing the two observation datasets, CHIRPS shows a lower R1mm over eastern Kenya (<30 days), while GPCC shows more wet days (~50 days) over most parts of the region (Figure 7).Meanwhile, most models depict higher R1mm over the study region, covering the entire domain, especially for models such as HadGEM3-GC31-MM, HadGEM3-GC31-HM, and CMCC-CM20VHR4.

Frequency of Wet, Heavy, and Very Heavy Precipitation Days
The mean distribution of wet days (R1mm), heavy precipitation days (R10mm), and very heavy precipitation days (R20mm) is displayed in Figures 7-9, respectively.Comparing the two observation datasets, CHIRPS shows a lower R1mm over eastern Kenya (<30 days), while GPCC shows more wet days (~50 days) over most parts of the region (Figure 7).Meanwhile, most models depict higher R1mm over the study region, covering the entire domain, especially for models such as HadGEM3-GC31-MM, HadGEM3-GC31-HM, and CMCC-CM20VHR4.Remarkably, MPI-ESM1-2-XR simulates the observed R1mm over the region relatively well.Generally, most models capture the few incidences of R1mm noted over eastern Kenya and the coastal areas, with CNRM-CM6-HR depicting low R1mm (<5 mm) over the tip of the northwest region of Kenya and Uganda.This shows that most models can reasonably capture the observed patterns of wet days over the region.the study period.This shows that the region experienced relatively few heavy precipitation days during the study period.On the other hand, CMCC-CM2-VHR4, HadGEM3-GC31-MM, and HadGEM3-GC31-HM substantially overestimated R10mm over the Lake Victoria region, as compared to the other models.In addition, CNRM-CM6-HR notably underestimated R10mm over the northern part of EA.Remarkably, MPI-ESM1-2-XR simulates the observed R1mm over the region relatively well.Generally, most models capture the few incidences of R1mm noted over eastern Kenya and the coastal areas, with CNRM-CM6-HR depicting low R1mm (<5 mm) over the tip of the northwest region of Kenya and Uganda.This shows that most models can reasonably capture the observed patterns of wet days over the region.
Figure 8 shows the spatial patterns of heavy precipitation days (R10mm) over the study area.The results show that the region experienced R10mm for up to 145 days during the study period.This shows that the region experienced relatively few heavy precipitation days during the study period.On the other hand, CMCC-CM2-VHR4, HadGEM3-GC31-MM, and HadGEM3-GC31-HM substantially overestimated R10mm over the Lake Victoria region, as compared to the other models.In addition, CNRM-CM6-HR notably underestimated R10mm over the northern part of EA.
Models such as ECMWF-IFS-LR, ECMWF-IFS-HR, and GFDL-CM4 accurately simulated the observed spatial variance in R10mm over the study area (Figure 8).
The spatial patterns of very heavy precipitation days (R20mm) are displayed in Figure 9. Observed R20mm based on CHIRPS and GPCC shows up to 20 days of R20mm over the study area.MPI-ESM1-2-HR and MPI-ESM1-2-XR show lower R20mm over the study area, with approximate values between 0 and 0.8 days.In contrast, HadGEM3-GC31-HM and GFDL-CM4 show R20mm around Lake Victoria and a section of Uganda with values around 20 to 40 days.
The occurrence of heavy precipitation events noted around the lake region could be attributed to the mesospheric influence of convectional activities around the lake region, which results in more frequent heavy downpours, as simulated in the models [54].In a recent study, ref. [62] noted an increase in heavy precipitation events, with a total of 822 cases, mostly concentrated in the northern section of Tanzania.This study further attributed the upsurge in heavy precipitation events to several factors, such as low-level westerly convergence, intensified advection of moisture from both the Indian Ocean (IO) and Congo Basin, and distinct tropospheric warm temperature anomalies [62,63].

Intensity of Precipitation Occurrence
The mean intensity of daily precipitation events (SDII) is presented in Figure 10 for the two observation datasets and the HighResMIP GCMs.CHIRPS shows a higher SDII in central Kenya and coastal parts of Tanzania compared to the GPCC.However, the SDII declines towards the western parts of the EA.In contrast, GPCC showed a lower SDII over the entire region during the study period.Most models satisfactorily simulate the observed SDII over the region.Particularly, GFDL-CM4 and HadGEM3-GC31-HM demonstrate robust performance, while MPI-ESM1-2-HR and MPI-ESM1-2-XR show lower SDII of approximately 2-4 mm/day.

Daily Extreme Precipitation Events (95th Percentile)
Extreme precipitation events greater than the 95th percentile (R95p) are presented in Figure 11.Ref. [64] noted that R95p are rare events that often cause serious impact on natural and societal systems.The spatial distributions of CHIRPS and GPCC are quite different.Moreover, the models show wide variability in the simulation of R95p.Relative to CHIRPS, CNRM-CM6-HR, ECMWF-IFS-HR, and ECMWF-IFS-LR display a good simulation of R95p, while CMCC-CM2-VHR4, GFDL-CM4, and HadGEM3-GC31-HM depict an overestimation of R95p over the region, with values ranging from 300 to 900 mm/day.It is important to note that CNRM-CM6-HR, ECMWF-IFS-HR, and ECMWF-IFS-LR models that mimic similar patterns as observations show lower R95p over eastern Kenya, which is characterised by an ASAL climate and, hence, fewer precipitation events.This shows that most HighResMIPs can robustly mimic the local climate of the region.Interestingly, previous studies based on CMIP6 GCMs across many domains reported unsatisfactory simulations of R95p [10,18,19,62].The poor R95p simulations by some models could be linked to the model's ocean biogeochemical component, which has been primarily updated to simulate the biogeochemical cycles of carbon, nitrogen, phosphorus, iron, and oxygen [65].It is important to note that R95p impacts the local population and infrastructure heavily since it results in extreme events such as floods, leading to the destruction of properties and livelihoods [66].Hence, accurate simulation of this index is paramount for planning, mitigation measure formulation and implementation.

Daily Extreme Precipitation Events (95th Percentile)
Extreme precipitation events greater than the 95th percentile (R95p) are presented in Figure 11.[64] noted that R95p are rare events that often cause serious impact on natural and societal systems.The spatial distributions of CHIRPS and GPCC are quite different.Moreover, the models show wide variability in the simulation of R95p.Relative to CHIRPS, CNRM-CM6-HR, ECMWF-IFS-HR, and ECMWF-IFS-LR display a good simula- linked to the model's ocean biogeochemical component, which has been primarily updated to simulate the biogeochemical cycles of carbon, nitrogen, phosphorus, iron, and oxygen [65].It is important to note that R95p impacts the local population and infrastructure heavily since it results in extreme events such as floods, leading to the destruction of properties and livelihoods [66].Hence, accurate simulation of this index is paramount for planning, mitigation measure formulation and implementation.

Mean Total Precipitation and Maximum Daily Precipitation
The mean total precipitation (PRCPTOT) and maximum daily precipitation (Rx1day) over East Africa during 1995-2014 are presented in Figures 12 and 13

Statistical Metrics and Ranking of HighResMIP Models
In this study, we employ portrait diagrams to display the performance of the nine extreme precipitation indices in the evaluation for mean bias (MB), correlation coefficient (CC), and root mean square error (RMSE) for the HighResMIP models with CHIRPS and GPCC as reference values (Figure 14).Further, a summary of the model performance in simulating extreme precipitation events over the region is presented by the Taylor diagram (TD) and Taylor Skill Score (TSS) (Figure 15).The HighResMIP model performances in the representation of biases relative to CHIRPS and GPCC are presented (Figure 14a).In this study, indices such as R1mm and CWD are satisfactorily simulated by most Rx1day is an important index, since it represents extreme precipitation of a moderate duration or more persistent events that often cause severe impacts on society.Long-term changes in these indices have been evaluated in numerous studies and various assessments of the IPCC [1,67,68].These annual extremes have also been used to estimate the probability of rare events, such as 100-year return values, which are used in infrastructure design.Several studies have examined the trends in these annual precipitation events globally and at the regional level [9,69,70].Similarly, PRCPTOT plays a significant role in quantifying the annual total precipitation accumulation critical for agricultural activities and water harvesting for domestic or industrial usage.

Statistical Metrics and Ranking of HighResMIP Models
In this study, we employ portrait diagrams to display the performance of the nine extreme precipitation indices in the evaluation for mean bias (MB), correlation coefficient (CC), and root mean square error (RMSE) for the HighResMIP models with CHIRPS and GPCC as reference values (Figure 14).Further, a summary of the model performance in simulating extreme precipitation events over the region is presented by the Taylor diagram (TD) and Taylor Skill Score (TSS) (Figure 15).The HighResMIP model performances in the representation of biases relative to CHIRPS and GPCC are presented (Figure 14a).In this study, indices such as R1mm and CWD are satisfactorily simulated by most models.On the contrary, SDII and PRCPTOT show an overestimation and underestimation with large biases.1.
Similarly, the evaluation of the models in terms of CC shows varying performances depending on the observational datasets employed (Figure 14b).For instance, positive CC is demonstrated by most HighResMIP models against GPCC compared to CHIRPS.To illustrate, indices such as R1mm, R95p, PRCPTOT, and Rx1day are satisfactorily simulated by the models against GPCC, with a CC of about ~0.5.Conversely, CDD and SDII continue to show low performances, with most models depicting negative CC (−0.1 to −0.4), except for CNRM-CM6-HR and ECMWF-IFS-LR(HR), which exhibit positive CC for the two indices.Interestingly, previous studies that evaluated the performance of most precipitation extreme indices using CMIP6 GCMs over East Africa reported large uncertainty in the simulation of CDD and SDII [9,10].This calls for further investigations to understand the sources of persistent uncertainties in the simulation of CDD and SDII.Previous studies have reported that model uncertainty results from either internal variability, scenario, or inter-model dependency [71].
Furthermore, Figure 14c shows that most indices have an acceptable level of RMSE over the study area.This is well demonstrated for PRCPTOT, R10mm, R1mm, and Rx1day by most models.In contrast, R20mm and R95p are poorly simulated by MPI-ESM1-2-XR and MPI-ESM1-2-HR in both GPCC and CHIRPS.Similar to MB and CC, CWD shows large RMSEs.Overall, the performance of HighResMIP in the simulation of precipitation extremes for most indices based on the three statistical metrics shows acceptable performance for most indices.Equally, the models vary in performance from one index to another.However, some indices have persistently poor simulation across the region in almost all models (e.g., CWD and SDII).Comparative analysis shows the better performance of MME compared to individual models in the simulation of various indices.
Finally, Figure 15 summarises the model performance for extreme precipitation indices, as represented in the TSS for all indices simulated in the present study.The CC of MME shows a robust simulation of PRCPTOT (0.90), R1mm (0.91), R10mm (0.87), R95p (0.72), and CDD (0.70).On the other hand, CWD, Rx1day, and SDII display poor overall performance based on TD.The SDII and CWD show the lowest CC/SD for most models, indicating higher inter-model uncertainty.
Additional examination of the HighResMIP models based on TSS shows a good representation of most indices in the latest model outputs.The results show higher TSS for CMCC-CM2-VHR4, HadGEM31-MM, HadGEM3-GC31-HM, and GFDL-CM4.The results show the capability of the HighResMIP to robustly simulate the spatio-temporal pattern of most precipitation indices over the study area.HighResMIP models demonstrate better simulation of PRCPTOT, R1mm, R10mm, R95p (0.72), and CDD (Figure 15).CWD, SDII, and R20mm are poorly simulated by most models over East Africa.
Overall, most models tend to overestimate heavy precipitation events.This has been observed in the CMIP3, 5, and 6 models [10,52,72].The poor performance of CMIP models to reproduce East African precipitation has been attributed to course resolution that does not capture local features such as topography well [73].As a result, the rainfall bias can be explained by the bias in the convective instability.This emphasises the need for further studies that consider resolution more explicitly by assessing models in varying grid configurations.In a downscaling effort over East Africa [74], it was observed that the top-ranked general circulation model (GCM) for the boundary conditions leads to a better dynamical downscaling simulation than a low-ranked GCM.Thus, top-performing models can be selected and downscaled to provide relatively better results in the simulation of precipitation extremes.In agreement with [75], they proved that downscaling of the second-generation Canadian Earth System Model (CanESM2, 1961-2100) over East Africa produced promising results that could be used to drive impact assessment and adaptation studies in this region.

Summary and Conclusions
This study evaluates the ability of nine HighResMIP GCMs and their MME to reproduce extreme precipitation over East Africa.The models and MME are compared against the CHIRPS and GPCC datasets as a proxy for observation during 1995-2014.Statistical metrics such as MB, RMSE/NRSME, and CC are employed for evaluation, with the final ranking of models being based on TD and TSS metrics.The models are evaluated for their ability to simulate ETCCDI indices that represent mean annual maximum dry/wet spell length (CDD/CWD), frequency of wet (R1mm), heavy (R10mm), and very heavy precipitation (R20mm), intensity of precipitation occurrence (SDII), daily extreme precipitation events at the 95th percentile (R95p), mean total precipitation (PRCPTOT), and mean maximum daily precipitation in 24 h (Rx1day).The key conclusions are presented as follows: The models well reproduce the bimodal precipitation pattern over the region.The results show that some models slightly overestimate while others slightly underestimate the MAM season.In addition, most models highly overestimate the short rains.HadGEM3-GC31-MM and HadGEM3-GC31-HM overestimate both MAM (OND).Conversely, MPI-ESM1-2-XR and MPI-ESM1-2-HR show remarkable performance in simulating the OND season despite underestimating the MAM season.The MME captures the annual cycle with minimal biases for both the MAM and OND seasons.Generally, stronger wet (dry) biases occur during November (April), while excellent performance by most models is noted during simulations of the dry season (i.e., June and July).The best-performing HighResMIP models that satisfactorily simulate the spatial climatology of extreme precipitation indices over East Africa include CMCC-CM2-VHR4, HadGEM31-MM, HadGEM3-GC31-HM, and GFDL-CM4.Moreover, indices such as PRCPTOT, R1mm, R10mm, R95p, and CDD are reasonably simulated by most models.In contrast, SDII CWD, SDII, and R20mm are poorly simulated by most models over East Africa.Comparative analysis shows better performance of the MME compared to individual models in the simulation of the various indices.
The persistent underestimation of long rains and overestimation of the short rains by HighResMIP models were equally noted in the performance of native CMIP6 models over East Africa [9,10].This shows that the improvement in the horizontal resolution is not necessarily the major factor in the model improved performance, as previously reported in other studies [76][77][78].Thus, in order to obtain more realistic simulation results, it is important to further improve model parameterization schemes such as cloud physics and aerosol emission factors [79].Additionally, reducing the uncertainty in precipitation simulation can be attained by further employing approaches such as model downscaling, in addition to the improvement in horizontal grid resolution.A case example is the improvement in native CMIP6 models to NASA Earth Exchange Global Downscaled Projections (NEX-GDDP-CMIP6; [80]).These models have demonstrated robust simulation of mean and extreme precipitation over Africa [81].
Considering the proneness of precipitation extremes over East Africa, it is important to understand the observed and projected changes in the extremes for informed decision making when devising adaptation measures.Although the findings herein provide an indication of how HighResMIP performs in reproducing extremes over East Africa, caution should be exercised in the uptake of the findings.This is due to the observed weakness in CMIP6 models that tend to overestimate short rains and underestimate long rains over East Africa.This weakness was also observed in previous versions of CMIP models, calling for investigations that explicitly factor resolution by assessing models in varying grid configurations.

Figure 1 .
Figure 1.Elevation (m) and physical features of East Africa.The inset shows the location of East Africa within Africa.The terrain elevation data is obtained from the Digital Elevation Model (DEM) derived from the Shuttle Radar Topography Mission (SRTM) 90 m spatial resolution.

Figure 1 .
Figure 1.Elevation (m) and physical features of East Africa.The inset shows the location of East Africa within Africa.The terrain elevation data is obtained from the Digital Elevation Model (DEM) derived from the Shuttle Radar Topography Mission (SRTM) 90 m spatial resolution.

Figure 2 .
Figure 2. (a) Annual cycle of monthly averaged daily precipitation (mm/day) over East Africa based on two observational datasets, HighResMIP models and MME.(b) Box-and-whisker plots of the mean difference between the HighResMIP models and the mean of the observational datasets (mm/day).The boxes indicate the interquartile range.

Figure 2 .
Figure 2. (a) Annual cycle of monthly averaged daily precipitation (mm/day) over East Africa based on two observational datasets, HighResMIP models and MME.(b) Box-and-whisker plots of the mean difference between the HighResMIP models and the mean of the observational datasets (mm/day).The boxes indicate the interquartile range.

Figure 2 .
Figure 2. (a) Annual cycle of monthly averaged daily precipitation (mm/day) over East Africa based on two observational datasets, HighResMIP models and MME.(b) Box-and-whisker plots of the mean difference between the HighResMIP models and the mean of the observational datasets (mm/day).The boxes indicate the interquartile range.

Figure 4 .
Figure 4. Inter-annual variability in precipitation indices from CHIRPS, GPCC, multi-model mean (MME), and 9 HighResMIP models over East Africa for 1995-2014.The reddish shading represent the standard deviation of the 9 HighResMIP model.

Figure 4 .
Figure 4. Inter-annual variability in precipitation indices from CHIRPS, GPCC, multi-model mean (MME), and 9 HighResMIP models over East Africa for 1995-2014.The reddish shading represent the standard deviation of the 9 HighResMIP model.

Figure 7 .
Figure 7. Same as Figure 5 but for the number of wet days (R1mm).

Figure 7 .
Figure 7. Same as Figure 5 but for the number of wet days (R1mm).

Figure 8 .
Figure 8. Same as Figure 5 but for the number of heavy precipitation days (R10mm).

Figure 8 .
Figure 8. Same as Figure 5 but for the number of heavy precipitation days (R10mm).

Figure 9 .
Figure 9. Same as Figure 5 but for the number of very heavy precipitation days (R20mm).

Figure 9 .
Figure 9. Same as Figure 5 but for the number of very heavy precipitation days (R20mm).
, respectively.CHIRPS and GPCC perform similarly in capturing the spatial patterns of PRCPTOT and Rx1day.For instance, PRCPTOT shows large values over most of East Africa except for the eastern and northeastern parts of Kenya (600-1500 mm).Likewise, Rx1day shows uniform spatial variation over the region, with an approximate value of 40 to 70 mm/day.For PRCPTOT, ECMWF-IFS-HR and ECMF-IFS-LR depict similar patterns, as observed, while MPI-ESM1-2-XR exhibits a strong underestimation (10-250 mm) over eastern Kenya.Conversely, in the case of Rx1day, ECMWF-IFS-HR, ECMF-IFS-LR, MPI-ESM1-2-HR, and MPI-ESM1-2-XR, which show a satisfactory simulation of PRCPTOT, demonstrate strong underestimation of Rx1day over East Africa.Meanwhile, GFDL-CM4, HadGEM3-GC31-HM, and CMCC-CM2-VHR4 skilfully simulate Rx1day over the region.This shows that the models' performance varies from one model to another and from one extreme index to another, especially in the presentation of spatial variance over the study domain.

Figure 13 .
Figure 13.Same as Figure 5 but for maximum precipitation received in 24 h (Rx1day).

Figure 13 .
Figure 13.Same as Figure 5 but for maximum precipitation received in 24 h (Rx1day).

Hydrology 2024 ,
11, 106 20 of 27 models.On the contrary, SDII and PRCPTOT show an overestimation and underestimation with large biases.

Figure 14 .
Figure 14.Portrait diagram depicting (a) the mean bias, (b) pattern correlation coefficient, and (c) normalized pattern root mean square error (mm) for the HighResMIP datasets calculated relative to CHIRPS (red), and GPCC (blue) over East Africa during 1995-2014.

Figure 14 .
Figure 14.Portrait diagram depicting (a) the mean bias, (b) pattern correlation coefficient, and (c) normalized pattern root mean square error (mm) for the HighResMIP datasets calculated relative to CHIRPS (red), and GPCC (blue) over East Africa during 1995-2014.

Figure 15 .Figure 15 .
Figure 15.Taylor diagrams (a-i) and (j) Taylor Skill Score show the performance of the HighResMIP models in simulating annual precipitation extremes against CHIRPS over East Africa for nine precipitation indices.The dashed blue solid line in (j) represent the MME of the models used for this study.Angular axes for Taylor diagram (a-i) show correlation coefficients between simulated andFigure 15.Taylor diagrams (a-i) and (j) Taylor Skill Score show the performance of the HighResMIP models in simulating annual precipitation extremes against CHIRPS over East Africa for nine precipitation indices.The dashed blue solid line in (j) represent the MME of the models used for this study.Angular axes for Taylor diagram (a-i) show correlation coefficients between simulated and observed fields; radial axes show the spatially centred RMSE (normalized against the observed).The blue numbers indicate the HighResMIP models listed in Table1.

Table 2 .
List of precipitation (Pr) indices, with their IDs, names, and definitions.

Table 1 )
over East Africa.