To investigate spatial patterns of summer EHDs over NA, daily maximum air temperature and mean temperature records with horizontal resolution of 0.5˚ × 0.5˚ were derived from National Oceanic and Atmospheric Administration – NOAA ( Kanamitsu et al., 2002 ). In this study, NA refers to the region of Africa located north of 10˚N latitude encompassing countries of Morocco, Algeria, Tunisia, Libya, Egypt, Mauritania, Mali, Niger, Burkina Faso, Eritrea, Western Sahara, Guinea, Senega, parts Sudan, Chad, Ethiopia and Nigeria. To diagnose the physical mechanism behind EHD patterns over this region, the following monthly mean datasets were employed; 1) Sea surface temperature (SST), surface air temperature at the height of 2 m, precipitation, mean sea level pressure (MSLP), geopotential heights and wind fields at multiple levels, all obtained ERA5 with horizontal resolution 0.25˚ × 0.25˚ ( Dee et al., 2011 ; Hersbach et al., 2020 ). The study focuses on summer months of May, June to July (MJJ) for the period covering 35 years (1979 to 2013). This time frame was selected as a baseline for comparison in our broad ongoing research work. Maintaining a consistent period promotes the overall robustness and rationality of the results across several related investigations and enables relevant cross-study comparisons.

To define the threshold of EHDs over Africa, percentile (relative) threshold approach was used ( Alexander et al., 2006 ; Fischer & Schär, 2010 ). Due to significantly large domain, this method is preferred than absolute threshold ( Hong et al., 2022 ) and accounts for regional differences ( Long et al., 2022 ) across the continent, therefore ensuring that, the defined EHDs reflects the regional climate variability. In this study, the percentile threshold of the 95% is used, this definition involves sorting of all daily records of maximum temperature for a specified period (1979-2013) and determine the 95th percentile as the threshold for EHDs at each grid. Days with temperatures exceeding this threshold were considered as EHDs.

The study utilizes Empirical Orthogonal Function (EOF) analysis, as given by Equation (1), to simplify the complexity and discover the most significant patterns that account for EHD variations ( Hannachi et al., 2007 ; Jolliffe & Cadima, 2016 ). EOF analysis is a common statistical tool used to identify dominant modes of spatial patterns in meteorological and oceanographic complex datasets. To ensure the leading modes are independent of other modes and capture significant variance in the datasets, we applied the North test ( North et al., 1982 ). The principal components (PCs) associated with EOFs provide clear interpretation on the variation of the dominant spatial patterns over time to deeper understand the underlying physical factors influencing the variability ( Lorenz, 1956 ). To link the EOF modes to physical mechanisms, correlation maps were generated between the PCs of the leading EOF modes and the climate variables.

${\Phi }_{ij}=\underset{k=1}{\overset{m}{{\displaystyle \sum }}}{\mu }_{ki}{T}_{kj}$(1)

where by: i = 1, …, m; j = 1, …, n; Φ_ij represent i^th components of the random vector (j^th) for the centralized data, µ_ki are the components of the eigenvectors of the correlation matrix; and T_kj are the dependent-time functions of the k^th component (principal components, PCs). m and n represent the number of grids and the length of time series respectively.

To explore the relationships between variables, we employed Pearson’s correlation coefficient (r) as given by Equation (2). This statistical measure quantifies the strength and direction of the linear association between two continuous variables, ranging from −1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 (zero) indicating no linear relationship. Correlation analysis was particularly useful in identifying the degree to which variability in one variable was associated with variability in another within our datasets. The significance of the correlation coefficients was tested at 95% confidence level to ensure that observed relationships were not due to random variation. We also utilized the student’s t-test (Equation (3)), which statistical test commonly used for evaluating whether the variables are significantly correlated.

$r_{xy}=\frac{{{\displaystyle \sum }}_{i=1}^N\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^N{\left(x_i-\bar{x}\right)}^2}\sqrt{{{\displaystyle \sum }}_{i=1}^N{\left(y_i-\bar{y}\right)}^2}}$(2)

$t=\frac{r_{xy}\times \sqrt{N-2}}{\sqrt{1-r_{xy}}}$(3)

where $r_{xy}$ stands for correlation between two variables x and y, N is the total number of observed events, t is the test statistic and $\bar{x}$ and $\bar{y}$ are mean values of x and y respectively.

It can be observed from Figure 1 that, 95^th percentile exhibit latitudinal gradient with highest threshold (exceeding 40˚C) in NA. This indicates that NA has more frequent and severely extremely high temperatures than other regions of Africa, reflecting the effects of semi-arid and arid regions surrounding it. Significantly, the 95^th percentile decreases southwards from latitude 10˚N towards the central and southern parts of Africa, reaching cooler temperatures below 25˚C.

Figure 2 shows seasonal distribution of climatological mean EHDs over Africa, indicating that the 95^th percentile threshold captures seasonal distribution of EHDs effectively from January to December. During January to March ( Figure 2(a) and Figure 2(c) ) significant number of EHDs (reaching 11 days per month) appear to be located over the equatorial region between latitude 10˚S to 10˚N. Meanwhile, between April and August ( Figure 2(d) and Figure 2(h) ), substantial number of EHDs (reaching above 13 days per month) were located between latitude 10˚N to 40˚N (Tropical to Subtropical Zone). In the rest of the months i.e., September to December ( Figure 2(i) and Figure 2(l) ), EHDs reaching about 10 days per month were concentrated south of latitude 10˚ (Subtropical Southern Hemisphere).

The spatial distribution of EHDs extracted at each grid over NA shows the highest number of EHDs in summer months of May, June and July (MJJ) with pick in June ( Figure 3(a) ). In this regard, MJJ was considered in this study as the main period of extremely high temperature days during summer months over NA (North of latitude 10˚N). Considering that, during MJJ, EHDs and mean temperature correlation over the large area of NA indicate substantial positive relationship at each grid, with domain average correlation coefficient (TCC) higher than 0.5 ( Figure 3(b) ). This relationship signifies that, evolution of both mean temperature and EHDs at each grid point are influenced by similar atmospheric circulation patterns.

In association with PCs time series, Figure 4 presents the EOF analysis intended for examining the drivers of summer EHD patterns over NA. The first three major EOF modes (EOF1, EOF2 and EOF3) of summer EHDs account for 43.0%, 11% and 8% of the total variance, respectively while the other modes account for the remaining small proportion of the total percentage variance ( Figures 4(d)-(f) , and Figure 5 ). The spatial loading (shaded regions), contours and wind vectors ( Figures 4(a)-(c) ) provides a clue to primary and secondary atmospheric circulation patterns influencing EHDs over NA. EOF1 mode ( Figure 4(a) ) captures strong influence over NA and demonstrates a homogeneous distribution of EHDs across the whole region. It corresponds to anomalous positive geopotential highs and anticyclonic flows at 850 hPa, which indicates intensifying extreme hot condition at the surface due to subsidence motion and advection of warm air from adjacent regions. The principal component (PC1) associated to this homogeneous mode ( Figure 4(d) ) shows inter-annual to decadal variation with a rising trend in the leading dominant mode, with negative values occurring before 1990 century and positive values after. This trend indicates that EHDs have become more common across NA in recent years as a result of climate change impacts, and that, there might be several underlying long term natural atmospheric processes influencing such extreme high temperatures ( Chen & Tung, 2018 ).

EOF2 shows two regions with opposite temperature anomaly patterns (meridional dipole structure) over NA ( Figure 4(b) ). The patterns this EOF orient North west to South east with negative loading to the closer to Mount Atlas and positive loading in the eastern part closer to River Nile basin. Such Meridional dipole spatial pattern suggests the presence of large-scale atmospheric circulation or surface conditions influencing extreme high temperatures over NA ( Chen & Tung, 2018 ). The principal component (PC2) associated with EOF2 mode ( Figure 4(e) ) exhibits significant interannual to decadal fluctuations signify the influence of natural climate variability in the region. EOF3 pattern ( Figure 4(c) ) demonstrates a mixed region of positive and negative anomalies across NA, with localized hotspots of EHDs over the region between latitude 10˚N and 20˚N. Atmospheric circulation features associated to this EOF may suggest complex drivers for EHD events, such as localized convective activity or regional wind patterns. The principal components (PC3) associated with EOF3 mode ( Figure 4(f) ) exhibits significant interannual which also signify the influence of local or transient atmospheric patterns on EHDs. Generally, the independence existing between the PCs of the first three EOF modes is verified by North test ( Figure 5 ) and suggests that the information captured by these initial EOF modes is distinct from that represented by other modes. Generally, it is evident that, EOF1, EOF2, EOF3 capture significant and unique sources of variation in the original data ( Pavithra et al., 2019 ; Wold et al., 1987 ), therefore they can represent spatial variation of EHDs over NA.

To examine the underlying physical mechanisms of these EOF modes, we analyze the correlation between the PCs (PC1, PC2 and PC3) and various monthly mean meteorological variables during MJJ season. The variables include SST and 2-meter temperature (2 mT) and 500 hPa geopotential height denoted by Z ( Figure 6 ), precipitation (PRE) and 850 hPa wind (UV) vectors, ( Figure 7 ) and 200-hPa geopotential height and mean wave activity flux (WAF) ( Figure 8 ). Figure 6 and Figure 7 which present the underlying patterns triggering the three modes of EHDs indicate that, EOF1 is characterized by extreme high-temperature days over NA. In this mode the positive anomalies of 2-meter air temperature coincide well with reduced rainfall across the entire region, this indicates that Precipitation and 2 m-temperature anomalies are well associated with intensification of EHDs ( Figure 6(a) & Figure 7(a) ).

Sea surface temperature anomaly (SSTA) on other hand reveal significant warming in the in the tropical and subtropical regions which includes the central Atlantic Ocean, Indian ocean and west pacific. Other SSTA warming is observed over Barents and Kara Sea ( Figure 6(a) ) which may result due to melting sea ice over this area. Significant cooling of SSTA is relatively experienced over North Pacific, western Europe experience relatively significant cooling ( Figure 6(a) ), This cooling is associated with low-pressure atmospheric pattern over these areas ( Figure 6(d) ). EOF2 is characterized by a weak dipole structure in the 2-meter temperature anomaly ( Figure 6(b) ) which corresponds with cooling of SSTA over western pacific, Indian ocean and Mediterranean region ( Figure 6(b) ). EOF3 is characterized by negative correlation scattered over North Atlantic and western pacific indicating the that, variability of this EOF may be influenced by localized SST anomalies. Moreover, the regions with negative (positive) summer mean 500-hPa geopotential heights anomalies ( Figures 6(d)-(f) ) match well with regions with low (higher) SSTAs and 2 m temperatures ( Figures 6(a)-(c) ) in both EOF modes.

In the correlation maps between PCs with precipitation and 850 hPa winds ( Figure 7 ), strong negative precipitation is indicated over NA signifying dry

condition over this region during MJJ season ( Figure 7(a) ), on other hand positive correlation appear over eastern Indian ocean, signifying increased convective activities over this region. Strengthening of easterly winds emanating from tropical Atlantic suggests weakening monsoon system into the NA ( Figure 8(a) ). Simultaneous correlation with PC2 ( Figure 8(b) ) indicates existence of dipole pattern with positive loading over western part of NA and negative loading over eastern part. This implies that EOF2 pattern over different parts of NA is associated with conflicting dry and wet conditions due transport of contrasting moisture properties.

The simultaneous correlation coefficients between PCs and meteorological fields at 200-hPa (i.e., geopotential height and mean wave activity flux (WAF)) shown in Figures 8(a)-(c) respectively revealed distinct pair of barotropic anticyclonic and cyclonic anomalies over north Atlantic, extending towards western Europe, Mediterranean and Eurasia. Specifically, the simultaneous correlation with PC1 ( Figure 8(a) ) features positive geopotential height anomaly appear over tropical to subtropical areas comprising NA, tropical North Atlantic and Eurasia, while negative geopotentials are featured over mid latitude Atlantic and to the east of Mediterranean region. The flow direction indicated by of wind vectors ( Figure 8(a) ) suggests significant fluxes of Rossby waves from North Atlantic towards NA.

Moreover, barotropic anticyclonic and cyclonic anomaly pairs portrayed in the simultaneous correlation with PC2 ( Figure 8(b) ) are dominated by positive geopotential height anomaly positioned between North eastern Atlantic and western Europe and stretches further to subtropics of North Atlantic. On other hand, the negative correlations persist over the central Eurasia signifying existence of Upper tropospheric meridional dipole patterns. The direction of Wave activity (WAF) vectors signify flow of Rossby waves from North Eastern Atlantic to NA via Europe ( Figure 8(b) ). Furthermore, these paired anomalies play a significant role in the energy dissipation and transfer ( Hurrell et al., 2003 ) and are well linked to their corresponding SST anomaly patterns displayed in Figures 6(a)-(c) . The direction flow from these barotropic systems is indicated by WAF vectors and suggests that their dynamics influence energy dissipation by westerly jets and Rossby waves towards NA. The simultaneous correlation of PC3 and 200 hPa geopotential height anomaly and WAF spread over mid latitude and tropical Atlantic, and central Pacific, while negative correlations appear over NA, Europe and Asia, indicating that, EOF3 ( Figure 8(c) ) is more influenced by localized atmospheric wave activity than EOF1 and EOF2.