2.1. Data sources

Near-surface air temperature data were derived from two primary sources. Observational data were obtained from the Climate Research Unit (CRU) monthly dataset, version 4.09 (Harris et al. 2023) at 0.5° × 0.5° resolution for 1995-2014, providing a robust baseline for model evaluation and bias correction. Historical and future projections for the mid-century (2041-2060) and late-century (2081-2100) periods were obtained from ten CMIP6 models under the SSP2-4.5 (moderate emissions) and SSP5-8.5 (high emissions) scenarios. CMIP6 datasets were accessed via https://data.ceda.ac.uk/badc/cmip6/data/CMIP6/.

All CMIP6 datasets were re-gridded to the CRU grid (0.5° × 0.5°) to ensure spatial consistency and were subsequently bias-corrected against the observational reference. Only models with complete monthly coverage over the historical period were included. A full list of models, along with their horizontal resolutions, variant labels, and key references, is provided in Table 1. These datasets were used to evaluate projected changes in near-surface air temperature over Sudan.

2.2. Study area

The study encompasses the entire territory of Sudan, which extends from approximately 8° N to 23.5° N in latitude and from 21° E to 39° E in longitude. Sudan spans a broad climatic gradient, ranging from hyper-arid deserts in the north to semi-arid plains and savannah landscapes in the central and southern regions. This gradient produces pronounced spatial differences in temperature, rainfall, and seasonal climate patterns, resulting in distinct hot-dry and cooler-wet periods across the country (Funk et al. 2011; WBG 2023).

Mean annual temperatures generally range from around 22°C in the southern savannahs to above 28°C in the northern deserts. Topography and elevation strongly influence local and regional temperature regimes and climate variability. Elevation ranges from roughly 200 m above sea level in the southern plains to approximately 1,800 m in the northern and eastern highlands, with the Jebel Marra volcanic massif in western Sudan rising above 3,000 m (Fig. 1). These topographic differences, along with land cover, soil properties, and proximity to rivers, shape local and topo-climatic conditions and modulate the distribution of heat across the country (WMO 2024).

Fig. 1.

Topographic map of Sudan illustrating elevation gradients from 200 m in the southern plains to 1,800 m in the northern and eastern highlands, with Jebel Marra exceeding 3,000 m.

Sudan’s sensitivity to climate variability, reliance on rain-fed agriculture, limited water resources, and exposure to extreme heat events make understanding seasonal temperature variability particularly important. Characterizing temperature changes across these diverse climatic zones provides essential information for agricultural planning, water-resource management, and public-health preparedness. A spatially explicit understanding of warming patterns is therefore critical for informing adaptation strategies and mitigating the impacts of projected mid-century temperature increases (NUPI, SIPRI 2022; WBG 2023).

3.1. Bias correction

CMIP6 model outputs were bias-corrected against CRU TS 4.09 observations to reduce systematic deviations in historical simulations and improve the reliability of future projections. Two complementary methods were employed: Empirical Quantile Mapping (EQM) for historical simulations and Delta Quantile Mapping (DQM) for future projections.

EQM is a non-parametric technique that adjusts the cumulative distribution of simulated values to match the observed distribution. For a raw model value X_raw, the bias-corrected value is defined as:

where F_mod represents the empirical cumulative distribution function (CDF) of the model data, and F_obs⁻¹ is the inverse CDF of the observational data (Gudmundsson et al. 2012). Applying EQM ensures that historical simulations accurately reflect observed climatology, providing a validated baseline for subsequent analyses.

Delta Quantile Mapping (DQM) was applied to future projections to adjust biases while preserving the projected climate signal. For a future model value X_fut, the corrected value is given by:

where p represents the percentile of the future value within the historical model distribution F_mod,mod,hist (Xavier et al. 2022). This method preserves anomalies relative to the historical period while adjusting for systematic biases. Comparative evaluations have shown that quantile-based methods such as DQM maintain the climate change signal more reliably than traditional quantile mapping techniques (Lehner et al. 2023).

Using both EQM and DQM provides a robust framework for assessing projected temperature changes. EQM ensures the historical baseline is accurate, while DQM allows future projections to retain their physical consistency, enabling reliable quantification of seasonal and annual temperature anomalies as well as inter-model uncertainty over Sudan.

3.2. Data processing, ensemble statistics, and model agreement

Monthly mean near-surface air temperature (TAS) from ten CMIP6 GCMs and CRU observational data (CRU TS 4.09; Harris et al. 2023) were aggregated into annual, summer, and winter climatologies for the 1995-2014 baseline period. To ensure spatial consistency with observations, all CMIP6 outputs were regridded to the CRU 0.5° × 0.5° latitude–longitude grid using conservative remapping in the Climate Data Operators (CDO) and masked to Sudan’s national boundary.

Future projections under SSP2-4.5 and SSP5-8.5 were evaluated for the mid-century (2041-2060) and late-century (2081-2100) periods. For each SSP and season, the multi-model ensemble mean was used to represent the central tendency of projected monthly mean TAS changes, while the ensemble standard deviation quantified inter-model spread. Grid cells where at least two-thirds of models projected warming of the same sign were classified as regions of likely change (≥66 % model agreement), following standard CMIP6 assessment protocols (Eyring et al. 2016; IPCC 2021).

Projected changes were tested for statistical significance at each grid cell using a two-sample Student’s t-test, comparing the historical baseline period (1995-2014) with the mid- and late-century periods. Grid cells with p < 0.05 were considered significant. Significance hatching in figures is applied only where both the t-test criterion and the ≥66 % model-agreement criterion are satisfied, ensuring that displayed changes reflect robust forced signals rather than natural variability (IPCC 2021; Harris et al. 2023).

3.3. Bias correction evaluation metrics

The fidelity of CMIP6 simulations over the 1995-2014 baseline was evaluated using the Pearson correlation coefficient, the modified Kling-Gupta Efficiency (KGE'), and Taylor diagrams (Taylor 2001; Kling et al. 2012; Enyew et al. 2024).

The modified Kling-Gupta Efficiency (KGE') combines correlation, variability ratio, and coefficient-of-variation ratio into a single metric, providing a robust assessment of model skill relative to CRU observations:

where r is the spatial correlation between model and observations, α=σmodσobs is the ratio of model to observed standard deviation (variability ratio), and

is the ratio of coefficients of variation (CV), with 𝜎 denoting the standard deviation and 𝜇 the mean. Specifically, CVmod=σmodμmod represents the relative variability of the model data, CVobs=σobsμobs represents the relative variability of the observational data. KGE' values closer to 1 indicate higher agreement with observations, whereas values closer to 0 indicate lower model skill.

Taylor diagrams were employed to visualize the spatial correlation, normalized standard deviation, and centered root-mean-square difference (CRMSD) for individual models and the ensemble mean. EQM bias-corrected outputs were included in this evaluation to illustrate improvements in model performance following systematic bias correction.

4.1. Temperature climatology and annual cycle (1995-2014)

The spatial distribution and temporal variability of mean annual temperature across Sudan during 1995-2014 are shown in Figure 2a. Observed mean annual temperatures exhibit substantial spatial variability, ranging from 17.9°C to 30.33°C. The coolest conditions (<20°C) occur in the northern desert regions, whereas the warmest conditions (>30°C) are observed in the central and southern parts of the country. The national mean temperature is 27.76°C, with a median of 28.31°C and a standard deviation of 1.80°C, reflecting moderate variability across Sudan.

Fig. 2.

Mean annual temperature over Sudan (1995-2014): (a) spatial distribution based on CRU observations; (b) annual cycle comparing CRU observations with the ensemble mean of 10 CMIP6 models.

The annual cycle of observed and simulated temperatures over Sudan is illustrated in Figure 2b. The CMIP6 ensemble successfully reproduces the characteristic seasonal evolution of temperatures across the country; however, noticeable departures from observations persist throughout the year. The ensemble shows a slight warm anomaly during the peak summer season (+0.55°C), marking the only period in which simulated temperatures exceed the CRU observations. During winter, the ensemble underestimates temperatures by −1.33°C (CRU: 22.21°C; Ensemble: 20.88°C), representing the most pronounced cold deviation of the year. For the other seasons, the simulated annual temperature cycle in the CMIP6 ensemble is within approximately 1°C of the observations. On the annual scale, the ensemble mean (26.65°C) remains close to the CRU estimate (27.03°C), resulting in a modest annual bias of −0.38°C.

Taken together, these results demonstrate that, while the ensemble captures the overarching structure and timing of Sudan’s annual temperature cycle, persistent but seasonally distinct deviations remain – most notably the summer warm excess contrasted with the larger winter cold bias. This integrated view of spatial climatology and seasonal evolution provides a robust baseline for evaluating climate model performance and bias-correction procedures.

4.2. Evaluation of temperature bias correction

The Empirical Quantile Mapping (EQM) method substantially improves the performance of CMIP6 temperature simulations over Sudan during 1995-2014 (Fig. 3). After correction, model standard deviations converge to a narrow range (3.32-3.37°C), nearly matching the CRU reference (3.34°C) and contrasting with the broader spread in the raw simulations (3.28-4.56°C). CRMSD values decrease markedly from 1.35-1.77°C in the raw data to 0.90-0.97°C after correction, indicating closer alignment with the observed spatio-temporal temperature structure. Correlation coefficients remain high (≈0.96), showing that EQM reduces systematic biases without altering the underlying temporal signal.

Fig. 3.

Evaluation of CMIP6 temperature simulations over Sudan (1995-2014). Left: heatmaps of raw and EQM-corrected model performance (Bias, CRMSD, correlation, KGE). Right: Taylor diagram showing improved agreement with CRU after bias correction.

The largest improvement is observed in the Kling-Gupta Efficiency (KGE) metric, where raw models range widely (0.37-0.88), but all EQM-corrected models achieve consistently high values (0.96). As illustrated in Figure 3, corrected models cluster tightly around the observational benchmark, emphasizing the strength and consistency of the improvement. Overall, EQM provides a robust enhancement of model skill, yielding corrected datasets that are more reliable for historical assessment and future projections.

Figure 4 illustrates the spatial patterns of temperature biases in raw and ΔBias-corrected CMIP6 simulations over Sudan. In the raw simulations, annual temperatures are modestly underestimated relative to CRU observations (mean −0.59°C; SD = 0.87°C). Summer biases are predominantly positive (mean +0.45°C; SD = 0.76°C), while winter exhibits the strongest cold bias (mean −1.52°C; SD = 1.31°C).

Fig. 4.

Spatial patterns of raw and ΔBias-corrected temperature biases in CMIP6 simulations over Sudan for annual, summer, and winter seasons. ΔBias correction substantially reduces biases across all seasons. Cross-hatched areas indicate regions of model agreement of 66% or greater.

Following ΔBias correction, median biases are substantially reduced across all seasons (annual: −0.65°C; summer: +0.48°C; winter: −1.51°C), accompanied by narrower interquartile ranges (annual: 1.88°C; summer: 1.46°C; winter: 2.73°C), indicating improved agreement with observations. The fraction of grid cells with positive biases (annual: 25%; summer: 73%; winter: 12%) highlights pronounced seasonal asymme-tries, likely linked to regional climate processes, particularly the influence of the West African monsoon during summer.

Hatched areas denote residual extremes outside the central 66% range, identifying localized regions where bias correction remains less effective. Overall, ΔBias correction markedly reduces both the magnitude and spatial extent of temperature biases, with the greatest improvements observed for annual and summer, while winter retains some localized cold bias.

Figure 5 presents the ensemble mean changes in annual near-surface air temperature relative to the 1995-2014 baseline for mid-century (2041-2060) and late-century (2081-2100) under the SSP2-4.5 (moderate emissions) and SSP5-8.5 (high emissions) scenarios. Panels show (a) mid-century SSP2-4.5, (b) mid-century SSP5-8.5, (c) late-century SSP2-4.5, and (d) late-century SSP5-8.5.

Fig. 5.

Ensemble mean annual temperature anomalies relative to the 1995-2014 baseline for the mid- and late-century periods under SSP2-4.5 and SSP5-8.5. Cross-hatched areas indicate regions of model agreement of 66% or greater.

By mid-century, ensemble mean warming over Sudan is projected to reach 1.65°C under SSP2-4.5 and 2.16°C under SSP5-8.5, with corresponding 66% likely ranges of 1.12-1.97°C and 1.55-2.48°C, respectively. Warming intensifies substantially by late-century, increasing to 2.67°C (66% range: 1.89-3.30°C) under SSP2-4.5 and 5.00°C (66% range: 3.92-6.01°C) under SSP5-8.5. These results underscore the strong scenario dependence of future warming in Sudan, with high-emission pathways leading to markedly greater temperature increases. Hatched regions denote areas of robust warming where both statistical significance (p < 0.05) and strong inter-model agreement (≥66%) are satisfied. The 66% likely ranges quantify inter-model uncertainty, and the corresponding numerical statistics are summarized in Table 2.

Figure 6 shows the ensemble time series of annual mean near-surface air temperature anomalies over Sudan for 2041-2100 under SSP2-4.5 and SSP5-8.5. Solid lines represent the ensemble mean, shaded envelopes indicate the 66% likely range, and dashed lines show the inter-model minimum and maximum. Under SSP2-4.5, anomalies increase gradually from 1.68°C in 2041-2060 to 2.68°C by 2081-2100, with the 66% likely range widening from 1.34-2.15°C to 2.02-3.52°C. The associated linear warming trend is 0.247°C decade^-1. In contrast, SSP5-8.5 exhibits much stronger warming, rising from 2.18°C in 2041-2060 to 4.87°C by late-century, with the 66% likely range expanding from 1.84-2.67°C to 4.11-6.17°C, corresponding to a linear trend of 0.703°C decade^-1.

Fig. 6.

Ensemble time series of annual mean near-surface air temperature anomalies over Sudan for 2041-2100 under SSP2-4.5 and SSP5-8.5. Solid lines represent the ensemble median, dashed lines indicate the ensemble mean, and shaded areas show the 66% likely range.

Overall, these projections are broadly consistent with IPCC AR6 Working Group I assessments, which report likely warming of approximately 1.5-2.5°C under SSP2-4.5 and 2.5-4.0°C under SSP5-8.5 for East Africa and the Sahel by mid-century (IPCC 2021). The slightly narrower uncertainty ranges in this study reflect the use of a bias-corrected subset of CMIP6 models focused specifically on Sudan. Nevertheless, the magnitude, spatial distribution, and temporal evolution of projected warming closely align with the broader multi-model patterns reported by the IPCC.

4.4. Future seasonal warming

Summer projections are shown in Figure 7, which presents the ensemble mean changes in near-surface air temperature relative to the 1995-2014 baseline for the mid-century (2041-2060) and late-century (2081-2100) periods under the SSP2-4.5 and SSP5-8.5 scenarios. Panels (a-d) correspond to mid- and late-century projections for both emissions pathways.

Fig. 7.

Ensemble mean summer near-surface air temperature anomalies relative to the 1995-2014 baseline for the mid-century and late-century periods under SSP2-4.5 and SSP5-8.5. Cross-hatched areas indicate regions of model agreement of 66% or greater.

During the mid-century period, ensemble mean summer warming is projected to reach 1.78°C under SSP2-4.5 and 2.30°C under SSP5-8.5, with 66% likely ranges of 1.49-2.18°C and 1.88-2.90°C, respectively. By late-century, warming intensifies further, increasing to 2.80°C (66% range: 2.53-3.21°C) under SSP2-4.5 and 4.79°C (66% range: 4.47-5.00°C) under SSP5-8.5.

Hatched regions indicate areas of robust warming where both statistical significance (p < 0.05) and strong inter-model agreement (≥66%) are satisfied. These results demonstrate that future summer warming in Sudan is strongly scenario dependent, with higher emissions leading to substantially greater temperature increases. The detailed numerical statistics for these projections are summarized in Table 2.

Winter projections are presented in Figure 8, with panels (a-d) corresponding to mid- and late-century projections under the SSP2-4.5 and SSP5-8.5 scenarios. During the mid-century period, ensemble mean winter warming is projected to reach 1.58°C under SSP2-4.5 and 1.98°C under SSP5-8.5, with 66% likely ranges of 1.51-1.64°C and 1.89-2.07°C, respectively. By late-century, winter warming intensifies to 2.57°C (66% range: 2.51-2.63°C) under SSP2-4.5 and 4.90°C (66% range: 4.75-5.00°C) under SSP5-8.5.

Fig. 8.

Ensemble mean winter near-surface air temperature anomalies relative to the 1995-2014 baseline for the mid-century and late-century periods under SSP2-4.5 and SSP5-8.5. Cross-hatched areas indicate regions of model agreement of 66% or greater.

Compared to summer, winter warming exhibits greater temporal stability and narrower uncertainty intervals, reflecting reduced inter-model spread. Hatched regions denote areas of robust warming, defined by both statistical significance (p < 0.05) and strong inter-model agreement (≥66%), consistent with the criteria applied to annual and summer projections.

Overall, these results indicate that while both seasons experience substantial warming, the magnitude and variability are consistently higher during the summer months. Corresponding winter statistics are summarized in Table 2.

Figure 9 illustrates the seasonal evolution of near-surface air temperature anomalies over Sudan from 2041 to 2100. Panel (a) presents summer anomalies, which display a pronounced upward trajectory. Under SSP5-8.5, the 66 % likely ranges progressively widen, indicating accelerated warming and increased inter-model divergence during the monsoon season. Panel (b) shows winter anomalies, which also increase over time but follow a more stable trend with narrower uncertainty intervals, consistent with the reduced model spread identified in the statistical analysis.

Fig. 9.

Ensemble time series of seasonal near-surface air temperature anomalies over Sudan for 2041-2100 under SSP2-4.5 and SSP5-8.5. (a) summer anomalies, (b) winter anomalies. Solid lines represent the ensemble median, dashed lines indicate the ensemble mean, and shaded areas show the 66% likely range.

Seasonal warming rates over 2041-2100 are estimated at approximately 0.265°C per decade (summer) and 0.243°C per decade (winter) under SSP2-4.5, and 0.742°C per decade (summer) and 0.718°C per decade (winter) under SSP5-8.5. These projections indicate that Sudan will continue to experience sustained warming throughout the 21st century in both seasons, with summer warming occurring at a faster rate and exhibiting greater variability than winter warming.

Overall, the results align closely with regional projections reported in the IPCC AR6, underscoring strong scenario-dependent warming across northern and north-eastern Africa.

4.5. Scenario divergence

The temperature differences between the moderate- and high-emission pathways exhibit a clear, increasingly pronounced divergence from mid-century to late-century (Fig. 10a-c). During the mid-century period (2041-2060), the separation between scenarios is already detectable, with consistently positive warming differences across all seasons. Annual differences remain modest yet robust, with a mean increase of 0.49°C and a narrow 66% likely range of 0.38-0.58°C, indicating strong inter-model agreement. Seasonal patterns follow a similar structure: winter differences average 0.41°C, while summer shows a larger response of 0.53°C, reflecting enhanced land-atmosphere coupling during hotter months. The tight uncertainty ranges across all mid-century estimates underscore the stability and consistency of the modeled scenario divergence.

Fig. 10.

Projected temperature differences (SSP5-8.5 minus SSP2-4.5) over Sudan. Panels a-c show mid-century (2041-2060) annual, winter, and summer differences; panels d-f show late-century (2081-2100) differences. Color shading indicates mean differences, and cross-hatched areas indicate regions of model agreement of 66% or greater.

By the late-century period (2081-2100), the contrast between emissions pathways intensifies substantially (Fig. 10d-f). Annual differences increase to a mean of 2.36°C, with a constrained 66% likely range of 2.13-2.63°C, highlighting the dominant influence of cumulative greenhouse-gas emissions on long-term warming. Seasonal differences reach comparable magnitudes, with winter and summer increases of 2.37°C and 2.39°C, respectively. Although inter-model spread widens slightly, particularly during summer due to amplified radiative forcing and surface feedbacks, warming remains consistently higher under the high-emission scenario across all models.

Overall, these results demonstrate that while mid-century scenario separation is moderate and tightly bounded, late-century divergence becomes pronounced and climatically significant. The persistence of

positive differences, combined with narrow mid-century uncertainty and coherent late-century ranges, provides high confidence that Sudan’s future thermal conditions, particularly summer heat stress, will be strongly governed by the global emissions trajectory.