Extreme compound events in the Agulhas Leakage

Marine heatwaves (MHWs) and ocean acidity extremes (OAXs) are intensifying under anthropogenic climate change, and their compound co-occurrence can amplify ecological impacts. Yet the Agulhas Leakage, a key gateway transferring warm, saline Indian Ocean water into the Atlantic, remains understudied. Here we characterise MHWs over 1982–2024 and OAXs, and their compound events in this region over 1982–2021, comparing analyses of original and linearly detrended data. Under a fixed baseline, MHW cumulative intensity rose from approximately 29.95 to 109.51 °C-year in the original data and 49.4 to 66.7 °C-year after detrending between the first and fourth decades. OAX intensity increased from approximately 0.24 to 4.10 nmol kg - ¹-year in the original data and from 0.35 to 0.46 nmol kg - ¹-year after detrending. Compound events emerge only after the 2000s. Detrending reveals that most of this increase reflects the long-term warming and acidification trends, while residual variability remains in the dynamically active Agulhas Retroflexion, where anticyclonic eddies trap warm, high [H + ] Indian Ocean waters. A likelihood multiplication factor confirms statistically significant positive MHW–OAX dependence that persists after detrending, indicating statistically significant positive co-occurrence between MHW and OAX on interannual timescales, consistent with physical coupling through carbonate chemistry. Baseline choice critically shapes compound-extreme risk assessment.

Over the past few decades, intensifying anthropogenic emissions of CO 2 and other greenhouse gases have driven profound changes in the climate system (IPCC, 2023), leading to increases in both the frequency and intensity of extreme events worldwide, such as marine heatwaves (MHWs) and ocean acidity extremes (OAXs) (Oliver et al., 2018; Laufkötter et al., 2020; Burger et al., 2020). These changes have resulted in widespread impacts on marine ecosystems (Rodrigues et al., 2025a), as well as on fisheries (Cheung et al., 2021), and both local and global economies (Smith et al., 2021). When extremes occur simultaneously in space and time, they are referred to as compound extreme events and can produce amplified impacts through the interaction and reinforcement of their individual effects (Zscheischler et al., 2018; Gruber et al., 2021; Burger et al., 2022).

The Agulhas Leakage is a key oceanic region in the southeastern Atlantic Ocean (Figure 1a), located off the southwestern coast of Africa, where water is transferred from the Indian Ocean into the Atlantic Ocean (Beal et al., 2011). This exchange is driven by the retroflexion of the Agulhas Current, which, upon encountering the westerly winds and the continental geometry, turns back toward the Indian Ocean, shedding large warm and saline eddies, known as Agulhas rings, into the Atlantic (Lutjeharms, 2006; Biastoch et al., 2009). The region lies north of the Antarctic Circumpolar Current (ACC), the world’s largest current system, whose strong eastward flow around Antarctica influences the regional circulation and water mass exchanges of the Southern Ocean (Rintoul and Sokolov, 2001; Wan et al., 2025). The transfer of Indian Ocean waters through the Agulhas Leakage plays a crucial role in feeding the upper limb of the Atlantic Meridional Overturning Circulation (AMOC) (Gordon et al., 1992), a system that is fundamental to global climate regulation (Nian et al., 2026). In this context, variability in Agulhas Leakage is thought to affect the AMOC through the transport of warm saline Indian Ocean waters into the Atlantic, potentially influencing North Atlantic heat and salt budgets, although the extent and mechanisms of this influence remain debated (Großelindemann et al., 2025). Additionally, adjacent to this region lies the Benguela Upwelling System (BUS), where coastal upwelling associated with the Benguela Current sustains one of the most productive marine ecosystems in the global ocean (Puccinelli et al., 2023; Ryther, 1969), supporting the base of the food web and promoting the development of diverse marine life (Puccinelli et al., 2016). In this context, the Agulhas Leakage is particularly suitable for studying thermal–acidification compound extremes because: (i) anticyclonic Agulhas eddies carry warm, high-[H + ] Indian Ocean waters into the Atlantic, creating co-located thermal and acidification anomalies; (ii) these eddies dominate the regional heat and carbon budgets at interannual timescales; and (iii) the region sits at the intersection of two major ocean systems (Indian Ocean and ACC), producing strong gradients in both SST and carbonate chemistry that amplify the co-occurrence of thermal and acidification extremes.

Despite this, no study has systematically quantified compound MHW–OAX extremes in the Agulhas.

Leakage over a multi-decadal record, nor compared the relative contributions of the long-term forced trend and interannual internal variability to their occurrence. Marine heatwaves have been previously identified in this region by Schlegel et al. (2017). The authors showed that these events are related to long-term ocean warming and driven by changes in atmospheric and oceanic conditions, including anomalous circulation patterns and wind forcing. More recently, Rodrigues et al. (2025b) identified the occurrence of triple compound events of marine heatwaves, high acidity, and low chlorophyll across the Atlantic Ocean using a fixed baseline and a 20-year record (1999-2018). They show that the frequency and intensity of compound events have increased over the past two decades. In the Agulhas Leakage region specifically, these compound extremes were linked to eddy trapping and a southward shift of the South Atlantic subtropical high. However, a detailed characterisation of compound extremes (MHWs and OAXs) in the Agulhas Leakage remains poorly constrained, particularly given its intense mesoscale activity and its role as a gateway between ocean basins, highlighting the need for further investigation in this region.

Here, we extend the analysis of MHWs and OAX extremes in the Agulhas Leakage region to the period 1982–2021, focusing specifically on the compound co-occurrence of MHW and OAX. We perform a systematic comparison between analyses computed with the original (non-detrended) and linearly detrended data. This approach allows us to address the following questions: (i) How have MHW, OAX, and compound MHW–OAX events evolved in the Agulhas Leakage over 1982–2021? (ii) How much of this evolution reflects the long-term forced trend versus internal variability? (iii) Is there statistically significant co-occurrence between MHW and OAX after trend removal, and if so, which physical mechanisms can explain it? Understanding the role of internal variability is important for assessing the predictability of compound extremes and the vulnerability of marine ecosystems to events that occur even in cooler-than-average periods within the long-term warming trajectory. The novelty of this study lies in (i) the systematic comparison of original and detrended MHW and OAX metrics over a 40-year record, (ii) the quantification of the long-term trend’s contribution to compound extreme intensification, and (iii) the demonstration that statistically significant MHW–OAX co-occurrence persists on interannual timescales after trend removal, pointing to dynamically driven compound risk in the Agulhas Leakage.

Defining the extremes and data sets

Daily sea surface temperature (SST) data with a spatial resolution of 0.25° × 0.25° were obtained from the NOAA Optimum Interpolation Sea Surface Temperature (OISST) dataset (Reynolds et al., 2007), which integrates satellite and in situ observations, covering the period from 1982 to 2024. Marine heatwaves (MHWs) were identified following the methodology of Hobday et al. (2016). Within this framework, an MHW is defined as a prolonged event lasting at least five consecutive days with SST exceeding the 90 th percentile threshold relative to a climatology based on at least 30 years of data. The climatological baseline was computed over the full 1982–2024 OISST record, following the recommendation of Hobday et al. (2016) for records of at least 30 years. Seasonal climatology was derived using an 11-day centred window for each calendar day, and the 90 th percentile threshold was computed from this smoothed seasonal cycle. No additional smoothing was applied to the percentile. In addition, we compute MHW cumulative intensity, which is the total heat stress accumulated during a marine heatwave. It integrates both the daily temperature anomaly (degrees above the historical baseline) and the total duration of the event, measured in units of °C-days. Long-term trends were estimated using a linear least-squares fit over the 1982–2024 period, and their statistical significance was assessed using the nonparametric Mann–Kendall test at the 95% confidence level.

Monthly surface hydrogen ion concentration ([H + ]) data at 1° × 1° resolution for the period 1982–2021 were used to identify ocean acidification extremes (OAXs). The [H + ] dataset, generated by Burger and Frölicher (2023) from the output of the Geophysical Fluid Dynamics Laboratory Earth System Model version 2M (GFDL ESM2M) model, is derived from monthly fields of temperature and salinity from the Hadley Centre Evaluation Number (EN) 4.2.2 objective analyses, fugacity of CO 2 (f CO 2) from Max Planck Institute – Self-Organizing Map Feed-Forward Neural Network (MPI-SOMFNN) v2022, and total alkalinity estimated using the Locally Interpolated Alkalinity Regression version 2 (LIARv2) algorithm (Carter et al., 2018). These variables were combined within the CO 2 System (CO2SYS) framework to compute [H + ]. Ocean acidification extremes were defined following Burger et al. (2022) and Rodrigues et al. (2025b) as months in which [H + ] exceeds the 90 th percentile of the monthly climatology. The 90 th percentile for OAX detection is calculated separately for each calendar month (i.e., a seasonally varying threshold). This prevents seasonal bias in detecting OAX events. Here, long-term trends were also estimated using a linear least-squares fit, and the Mann–Kendall test at the 95% confidence level was used to assess statistical significance.

We use linear detrending because, over the 40-year period, the anthropogenic forced response in both SST and [H + ] is well approximated by a linear function of time. Although higher-order nonlinear acceleration appears in multi-century model projections, polynomial detrending of a ~40-year record carries a significant risk of overfitting, thereby eliminating low-frequency internal variability associated with modes of climate variability, such as ENSO. Furthermore, consistency with the compound extremes literature supports our choice. Burger et al. (2022) linearly detrended all SST and [H + ] data before computing MHW-OAX LMF, and Burger and Frölicher (2023) applied linear detrending to [H + ] time series to define the OAX percentile threshold. Linear detrending is also widely used in the observational MHW literature to assess whether anthropogenic trends have influenced MHW occurrence (Capotondi et al., 2024).

Defining compound extremes

Compound extreme events were calculated by combining marine heatwave and ocean acidification extreme metrics in a common temporal and spatial framework. As the [H + ] dataset is available at monthly resolution, SST-derived daily MHW intensity fields, originally calculated at 0.25° × 0.25° resolution, were first interpolated onto a 1° × 1° grid to match the [H + ] data using linear spatial interpolation. The interpolated daily MHW intensities were then aggregated into monthly cumulative values, defined as the sum of daily intensities for each month. We used a linear spatial interpolation method. When we compute the MHW and OAX events independently, we use the same 90 th percentile threshold, according to the methodology of Hobday et al. (2016). However, when we obtain the monthly cumulative intensity of the MHWs to compute compound occurrence with OAXs, we need to apply an additional threshold to determine which MHW months are considered extreme. Since the MHW cumulative intensity is already obtained by applying the 90 th percentile to the original SST data, we apply a less stringent threshold to the monthly MHW cumulative intensity (the 50 th percentile). Following Rodrigues et al. (2025b), we tested the 50 th, 60 th, and 70 th percentiles for the latter and found similar spatial patterns, including in the Agulhas Leakage region, thereby confirming the robustness of the methodology (Supplementary Figure S1 in the Supplementary Material). Note that the individual analysis of MHWs covers the period from 1982 to 2024. However, the [H+] data are available up to 2021. Therefore, the OAX and MHW-OAX analyses are conducted over the period 1982–2021, when the two datasets overlap. Compound events are thus defined as the co-occurrence of MHW (monthly cumulative intensity exceeding the 50 th percentile) and OAX extremes (monthly [H + ] exceeding the 90 th percentile) in the same grid cell. The intensity of compound events was calculated from the normalised monthly intensities of both variables, and, for each month, the spatial extent of compound events was quantified as the percentage of area experiencing simultaneous extremes.

Defining the likelihood multiplication factor

LMF is defined as the ratio between the observed joint probability of two events and the joint probability expected under the assumption of independence (Ridder et al., 2020), as shown in Equation 1. It was used to quantify the dependence between two extreme events based on their co-occurrence. Under independent conditions, the joint probability of two events A and B is given by the product of their individual probabilities.

Values of LMF greater than one indicate that the events co-occur more frequently than expected by chance, suggesting a positive dependence, whereas values lower than one indicate a reduced likelihood of co-occurrence, consistent with negative dependence. An LMF equal to one implies independence between events. In this study, the LMF was calculated for MHW–OAX using observed frequencies of individual and joint occurrences over the period 1982–2021. The range of LMF values is constrained by the percentile thresholds used to define extremes, with the upper bound determined by the threshold (here, the 90 th percentile).

Confidence intervals for the LMF were estimated by treating compound MHW–OAX occurrences as a binomial process, with joint events as “successes”. For each grid cell, exact 95% Clopper–Pearson intervals (Clopper and Pearson, 1934) were computed for the joint probability and propagated to the LMF using L M F = p j o i n t (p M H W · p O A X), based on observed marginal probabilities. Statistical significance was determined by whether the confidence intervals include unity (LMF = 1).

Statistical dependence between MHW and OAX occurrences was further assessed using a two-sided Fisher’s exact test applied to binary monthly time series at each grid cell. Contingency tables were constructed from joint and individual occurrences Because Fisher’s exact test assumes independent observations, temporal autocorrelation in the monthly occurrence series may reduce the effective number of independent observations and lead to anti-conservative p-values. Therefore, Fisher-test significance should be interpreted with this limitation in mind. To account for multiple spatial testing across grid cells, the resulting Fisher-test p-values were corrected using the Benjamini–Hochberg false discovery rate (FDR) procedure (Benjamini and Hochberg, 1995), with statistical significance assessed at an FDR-adjusted level of 0.05.

Marine heatwaves in the Agulhas Leakage region

The Agulhas Leakage region exhibits a pronounced warming signal over the period 1982-2024 (Figure 1a) with mean values ranging from 14 °C to 21 °C between 25°S and 42°S, where the warmest temperatures form a corridor extending from south of the African continent toward the central South Atlantic. In contrast, the region around 45°S, closer to the Antarctic Circumpolar Current, exhibits lower temperatures ranging from 7 °C to 14 °C. The linear SST trend (Figure 1d) revealed a widespread, significant warming pattern across nearly the entire region, with maximum trends of 0.05 °C per year, particularly in the southern part of the African continent, where interocean water transfer occurs. Negative trends were observed at a few locations along the southwestern African coast, with minimum values of −0.04 °C per year. However, satellite data are not reliable near the coast.

When MHWs are defined relative to a fixed (non-detrended) climatological baseline, both the mean annual frequency and cumulative intensity of MHWs are high across the region (Figures 1b, c). The highest MHW frequencies are observed in the southwestern portion of the study area, reaching up to 66 days per year, whereas the lowest values, 21 days per year, are concentrated in the middle of the region and near the coast (Figure 1b). Trends in frequency are also strongest in the southwestern region (Figure 1e), extending eastward and northward throughout the domain. In contrast, cumulative intensity and related trends reach their highest values along the Agulhas Leakage region (Figures 1c, f). In this area, cumulative intensities reached up to 166.6 °C-year. Their spatial pattern is similar to the SST trends (Figure 1d).

The time series of spatially averaged MHW cumulative intensity (Figure 1g) shows a clear acceleration in MHW activity after 2000, with the most intense events occurring after 2015. Note that MHW cumulative intensity measures both frequency and intensity; higher cumulative intensity values indicate higher frequency and intensity. Notable peaks are evident around 2016, 2018–2019, and 2024, consistent with the remote influence of the 2015/16 El Niño and subsequent years of record ocean warming. Oliver et al. (2018) have shown that during El Niño years, MHW events increase globally. In addition, Rodrigues et al. (2025b) have found that El Niño events shift the South Atlantic subtropical high poleward, enhancing the leakage of warmer waters from the Indian Ocean into the eastern South Atlantic via the shedding of anticyclonic eddies and weakening of Benguela upwelling, thereby warming the Agulhas Leakage region. The decadal comparison (Table 1) confirms that MHW cumulative intensity increased by a factor of 3.66 (from 29.95 to 109.51 °C-year) between the first and fourth decades under the non-detrended analysis, corresponding to an increase of 265.7%.

After linearly detrending the SST data, the spatial pattern of MHW trends is substantially altered (Figure 2). The large-scale positive trend that dominated the non-detrended analysis is removed, revealing a more heterogeneous spatial structure. Positive trends in MHW frequency and cumulative intensity remain statistically significant in isolated patches, particularly in the southeastern corner of the domain along the Agulhas Leakage region (around 39–42°S, 12–18°E), suggesting that internal variability contributes to MHW intensification in these areas beyond the mean trend. In contrast, some areas show weakly negative or near-zero trends after detrending. Further details on MHW metrics are available in Supplementary Figure S2 of the Supplementary Material. The time series of detrended MHW cumulative intensity (Figure 2c) shows a more stationary character with no obvious long-term increase, confirming that the upward trajectory in the non-detrended case is primarily driven by the long-term SST trend. Nonetheless, the fourth decade still exhibits a slightly higher MHW cumulative intensity than the first, 49.38 vs. 66.73 °C-year, an increase of 35.1% (Table 1).

Ocean acidity extremes in the Agulhas Leakage region

The mean concentration of surface hydrogen ions ([H + ]) over the Agulhas Leakage region ranges from approximately 7.5 to 8.4 nmol kg - ¹, with higher concentrations in the northern part of the domain (Figure 3a). In contrast, the lowest concentrations were primarily concentrated within the Agulhas Leakage region (Figure 3a). This spatial distribution is opposite to that observed for SST, which exhibits its highest values within the leakage region (Figure 1a). The linear trend indicates a widespread increase in [H + ] across the entire domain, with the strongest trends in the southern sector, reaching up to 0.04 nmol kg - ¹ per year (Figure 3d). This reflects the ongoing oceanic uptake of anthropogenic CO 2 and the consequent acidification of surface waters (Woosley et al., 2016), consistent with published estimates of ocean acidification rates for this region (Rodrigues et al., 2025b; Ma et al., 2023).

The OAX frequency is particularly large in the southern portion of the study region, where values reached up to 12 months per year. The lowest frequencies, 3 months per year, were mainly observed close to coastal areas (Figure 3b). Frequency trends were relatively homogeneous across the entire domain (Figure 3e). Annual cumulative intensity exhibited higher values in nearly all regions where the highest frequencies occurred, with maxima reaching 8.53 nmol kg - ¹-year in the south and minima of 1.20 nmol kg - ¹-year along the coast (Figure 3c). The trend in cumulative intensity showed a widespread increase throughout the region, with stronger intensification along the southern and northwestern boundaries of the domain (Figure 3f). The time series of OAX intensity (Figure 3g) shows a dramatic increase after approximately 2006, with very few OAX events detectable before that time. This is entirely consistent with the findings of Rodrigues et al. (2025b) for the Agulhas Leakage subregion.

The most striking result is the 17-fold increase in OAX cumulative intensity between the first and fourth decades under the non-detrended analysis, from 0.24 to 4.10 nmol kg - ¹-year (Table 1). OAX frequency increased by a factor of 5 from 1.33 to 6.74 months per year (Table 1). These increases far exceed those seen for MHWs, reflecting the greater contribution of the long-term acidification trend to OAX exceedances relative to the warming trend for MHWs.

After removing the long-term trend from the [H + ] data, trends in both the frequency (Figure 4a) and cumulative intensity (Figure 4b) are negative but non-significant across most of the domain. The only statistically significant trends in both metrics are concentrated along the southwestern boundary of the study region and are linked to cooler subantarctic waters. The monthly cumulative intensity time series further highlights the influence of the long-term trend. The time series of detrended OAX intensity (Figure 4c) no longer shows the dramatic late-period increase seen in the non-detrended case. OAX cumulative intensity increases by only 32.4% and frequency by 12.7% (Table 1), a far more modest increase consistent with the removal of the dominant acidification trend. Additional analyses of OAX metrics are shown in Supplementary Figure S3 of the Supplementary Material.

Compound extremes in the Agulhas Leakage region

Compound MHW–OAX events have become increasingly frequent over time, displaying clear spatial patterns and a marked rise in occurrence during recent decades (Figure 5). The mean compound frequency across the domain reaches up to 26 months per decade in the southern Agulhas Leakage corridor (region defined by Garzoli and Gordon, 1996), extending northwest, with the highest values concentrated in the northern sector where both SST and [H + ] trends are strong (Figure 5a). The spatial pattern of compound frequency trend is positive and statistically significant over the entire domain (Figure 5b), with values reaching 0.09 months per year per year.

The time series of normalised compound intensity of MHWs and OAX (red and blue histograms in Figures 5d, respectively) shows that compound events were essentially absent (0 compound months were detected) in the first half of the record (1982–2005), with MHW intensities dominating the early period. A rapid transition occurs after approximately 2006–2008, coinciding with the emergence of OAX events driven by accelerating acidification. After 2010, compound events occurred nearly every year, with particularly intense and widespread events in 2008–2010, 2014–2016, and 2018–2021. The spatial coverage of compound events has increased substantially over the last decade, exceeding 50% of the area in recent years (asterisks in Figure 5d).

Under the detrended analysis, the frequency of compound events is highest in the Agulhas Leakage corridor, reaching up to 10 months per decade, which is considerably lower than that observed in the original dataset. The southern part of the domain shows reduced values. The trend in compound frequency shows a dipole pattern (Figure 6b), with positive and statistically significant trends concentrated in the northern Agulhas corridor (27–33°S) with magnitudes substantially lower than those shown in Figure 5b. The trends are slightly negative and non-statistically significant in the south. The time series shows that detrended compound events are more evenly distributed throughout the record (Figure 6d), with no sharp onset in the mid-2000s, confirming that the dramatic increase in the non-detrended case is largely linked to the OAX trend. Still, the spatial extent of compound extremes reached a maximum of approximately 30% of the study area, mainly during the last decades, which is around 20% lower than that observed in the original dataset with the long-term trend included (Figure 5d).

The decadal comparison (Table 1) shows that compound event frequency increased from 0 months per year in the first decade to 3.04 months per year in the fourth decade under the non-detrended analysis, while compound intensity rose from 0 to 0.95 (normalised units). Under the detrended analysis, both the first and fourth decades recorded compound events, with frequency increasing from 1.47 to 1.55 months per year (+5.0%) and intensity from 0.68 to 0.90 (+31.9%). The smaller relative increases in the detrended case reflect the removal of the long-term trend, mainly in OAX, which was the primary driver of the dramatic non-detrended increase.

Statistical dependence between MHW and OAX events

To quantify the dependence between MHW and OAX events when they occur together, we calculate the likelihood multiplication factor (LMF), which measures how many times more/less frequent compound events are compared to their expected frequency under the assumption of independence (see Methods for more details). Regions where LMF is different from one indicate that MHWs and OAXs events co-occur more often (LMF > 1, red shades in Figure 5c) or less often (LMF < 1, blue shades in Figure 5c) than if variations in SST and [H + ] anomalies were independent (LMF = 1). Under the non-detrended analysis (Figure 5c), the LMF exceeds 1, indicating positive dependence over most of the northern and central Agulhas Leakage domain, with values reaching up to 4.5 in the northern sector. In other words, compound events occur 4.5 times as often as expected if they were independent. Statistical significance using Fisher’s exact test (dots in Figure 5c) is widespread, confirming that the co-occurrence of MHW and OAX events is significantly more frequent than expected by chance. This is consistent with the physical expectation that SST warming drives both MHW occurrence and an increase in [H + ] via carbonate chemistry (Burger et al., 2022). Note that we also used confidence interval (CI) analysis to assess statistical significance, and the areas where the LFM is statistically significant are very similar using both methods (Supplementary Figure S4a).

After detrending (Figure 6c), the LMF values are reduced but remain above 1 over the northern half of the domain (27–36°S), with values reaching up to 3.1. Statistically significant positive dependence (dots in Figure 6c) is retained in the northern Agulhas region. The fraction of LMF > 1, corresponding to positive dependence, is 93.4% in the original dataset (Figure 5c) and 62.8% in the detrended dataset (Figure 6c), a difference of 30.6%. Along the Benguela upwelling coastal region and the southern part of the domain (36–42°S), LMF values are near or below 1, suggesting independence or weak negative dependence between detrended MHW and OAX events in the southernmost sector (Figure 6c). In the southern region, LFM is statistically significant only with Fisher’s exact test (see Supplementary Figure S4b for the CI method). This spatial gradient is consistent with the contrasting dynamics of the northern Agulhas Leakage (dominated by warm Indian Ocean inflow) versus the coastal region influenced by Benguela upwelling and the southern region by cooler subantarctic waters.

The persistence of statistically significant positive LMF values after detrending indicates statistically significant positive dependence between MHW and OAX events, consistent with physical coupling through carbonate chemistry, but does not by itself demonstrate the underlying mechanism. It also confirms that this dependence is not solely an artefact of their shared long-term trends. Rather, on interannual timescales, warm SST anomalies in the Agulhas Leakage region co-occur with elevated [H + ] anomalies, generating genuine compound extremes that are independent of the forced warming and acidification trends. This could be associated with enhanced Agulhas ring shedding, anticyclonic eddy trapping, or southward shifts of the South Atlantic subtropical high during El Niño events (Rodrigues et al., 2025b).

Our results demonstrate that both MHWs and OAX extremes have intensified dramatically in the Agulhas Leakage region over the 1982–2024 period, with the most pronounced increases driven by the long-term trends in SST and [H + ]. The 17-fold increase in OAX cumulative intensity between the first and fourth decades of the record under the non-detrended analysis largely reflects the emergence of widespread OAX events only after approximately 2006, consistent with the findings of Rodrigues et al. (2025b) for this region. This pattern underscores the critical importance of the baseline choice in compound extreme event analyses: a fixed climatological baseline will yield rapidly increasing event frequencies as the forced trend pushes the mean state away from the reference period, even before changes in variability are considered (Le Grix et al., 2025).

The detrended analysis provides a complementary perspective by isolating the contribution of interannual variability to the occurrence of compound events. In other words, linear detrending of SST or [H + ] removes the spatially coherent, radiatively forced warming signal, which is primarily driven by anthropogenic greenhouse gas accumulation acting through air-sea heat fluxes. What remains after detrending are the interannual-to-decadal anomalies likely dominated by, internal climate variability and ocean dynamic processes such as advection, eddy heat flux convergence, and frontal migrations, whose interannual variability is not well captured by a linear trend. After detrending, the residual trends concentrate in specific dynamically active regions near the Agulhas system. Linear detrending removes the low-frequency component of the time series that is well approximated by a linear function of time, retaining interannual and shorter-period variability. It suppresses the spatially uniform, air-sea flux-driven warming that is dominant in subtropical and tropical regions while preserving the dynamically driven variability that is dominant in the Agulhas system and the ACC boundary. The Agulhas Retroflexion is special because anticyclonic eddies trap warm, high [H + ], nutrient-poor Indian Ocean waters independently of the mean warming trend (Orselli et al., 2019a), the retroflexion position itself fluctuates on interannual timescales, and the ACC/Agulhas front modulates cross-frontal heat and carbonate exchanges in ways that are largely decoupled from the linear trend. Together, these processes sustain residual MHW and OAX trends even after removal of the linear trend, which is consistent with, and likely dominated by, anthropogenic forcing. Moreover, Agulhas Leakage variability can modulate the occurrence of compound MHW-OAX extremes via either the direct inflow of warmer waters from the Indian Ocean into the South Atlantic or the shedding of anticyclonic eddies. El Niño events generally shift the South Atlantic subtropical high poleward, enhancing the leakage and weakening of Benguela upwelling, thereby warming the Agulhas Leakage region (Rodrigues et al., 2025b).

In addition, the persistence of compound events and statistically significant LMF values after detrending in the northern Agulhas region suggests that the relationship between SST and [H + ] anomalies persists on interannual timescales. An increase in temperature during an MHW can cause a direct rise in [H+] via changes in the carbonate chemistry equilibrium, while concurrent decreases in dissolved inorganic carbon (DIC) can act in the opposite direction, reducing [H + ]. The former often outweighs the latter mainly in the subtropics and within anticyclonic eddies (Burger et al., 2022). Ocean warming during an MHW in these regions may therefore contribute to increases in [H + ] and ocean acidification. In the Agulhas Leakage region, possible mechanisms include the enhanced inflow of warm, high [H + ] Indian Ocean waters during periods of intensified Agulhas ring shedding and anticyclonic eddy trapping (Orselli et al., 2019b; Rodrigues et al., 2025b). The influence of mesoscale activity on CO 2 fluxes may result from the interplay between temperature and DIC anomalies. While the elevated SST within anticyclonic eddies tends to reduce CO 2 solubility and increase pCO 2, the concurrent decrease in DIC acts in the opposite direction. In subtropical regions, however, the positive temperature effect on [H + ] generally outweighs the opposing DIC effect, increasing the likelihood of compound MHW–OAX conditions (Burger et al., 2022). These competing effects could therefore contribute to compound extremes, although their relative contributions are not directly assessed in the present study. This is consistent with the contrast between the northern and southern sectors of our study domain in the detrended LMF analysis. In the northern sector, positive LMF values persist after detrending, consistent with the dominance of warm Indian Ocean waters and anticyclonic eddies that carry both elevated SST and elevated [H + ] (Ford et al., 2023). In the southern sector and coastal region, the detrended LMF approaches or falls below 1, possibly reflecting the competing influences of cooler subantarctic waters and upwelled Benguela waters, which can decouple SST and [H + ] anomalies.

This study investigates the evolution of MHWs, OAX, and their compound co-occurrence in the Agulhas Leakage region of the southeast Atlantic over the period 1982–2024, using both original and linearly detrended data. MHW cumulative intensity and frequency increased substantially between the first (1982–1991) and fourth (2012–2021) decades of the record. Under the non-detrended analysis, MHW intensity increased by a factor of 3.66 (+265.7%) and frequency by a factor of 3.39 (+239.4%). After detrending, the increases are more modest (+35.1% and +27.1%, respectively), indicating that both the long-term SST trend and internal variability contribute to MHW intensification. OAX events show the strongest increase. Non-detrended OAX cumulative intensity increased 17-fold between the first and fourth decades (+1611%), driven primarily by the long-term ocean acidification trend. OAX events were essentially absent (0 months) in the first decade and became ubiquitous after approximately 2006. After detrending, OAX intensity increased by only 32.4% and frequency by 12.7%. The dominance of the non-detrended OAX increase over the detrended increase is consistent with the long-term ocean acidification trend being the primary driver, though formal attribution analysis would be required to confirm this.

In addition, compound MHW–OAX events were absent (0 months) in the first decade under the non-detrended analysis but reached a mean frequency of 3.04 months per year in the fourth decade. After detrending, compound frequency increased more modestly from 1.47 to 1.55 months per year (+5.0%), while intensity increased by 31.9%. The LMF analysis confirms statistically significant positive dependence between MHW and OAX events over most of the northern Agulhas Leakage domain, both before and after detrending. The persistence of significant LMF values after removing the long-term trends demonstrates that physical coupling between SST and [H + ] anomalies on interannual timescales generates compound extremes independent of the forced trend.

The comparison between detrended and non-detrended analyses highlights the critical importance of the baseline choice in compound extreme event assessment. A fixed baseline captures the full biological impact of the forced trend, while the detrended analysis isolates the contribution of interannual variability. Both perspectives are necessary for a complete understanding of compound extreme event risk. Nevertheless, we acknowledge that linear detrending is an imperfect proxy for the true anthropogenic forced response, and that a shifting baseline or ensemble-based signal removal would be more rigorous in principle. However, the detrended baseline approach requires removing the low-frequency warming signal, and in a climate modelling framework this is typically achieved by averaging over large numbers of single-model ensemble simulations. This approach cannot be applied to real-world observational data. Given the constraints of our observational datasets, and consistent with established compound extremes literature, we consider linear detrending the most robust and reproducible approach available, and one that does not qualitatively affect the spatial patterns or physical interpretation of our results.

The biological implications of our findings are significant. The Agulhas Leakage region supports diverse marine ecosystems and is connected to the broader South Atlantic circulation. Compound MHW–OAX extremes in this region can affect calcifying organisms, fish larvae, and primary producers that depend on stable thermal and chemical conditions. The fact that statistically significant compound events occur even after removing the long-term trends implies that marine ecosystems are exposed to acute physiological stress from interannual variability, not only from the gradual forced trend. As the mean state continues to warm and acidify, these interannual extremes will be superimposed on an increasingly stressful baseline, compounding the ecological risks.

Our study has some limitations. The [H + ] product relies on a neural network-interpolated p CO 2 field that is comparatively uncertain in the South Atlantic due to sparse in situ measurements (Burger et al., 2022). Future work should incorporate additional higher-temporal-resolution f CO 2 observations to constrain the acidification signal in this region and assess the sensitivity of compound-event patterns to alternative temporal co-occurrence windows. Moreover, the [H+] dataset has coarser temporal and spatial resolutions than the SST datasets, limiting our ability to understand the physical mechanisms underlying submesoscale and mesoscale dynamics, particularly in the Agulhas Leakage region. Therefore, the spatial patterns of compound events should be interpreted with caution given the 1° resolution of the [H + ] field, which may not capture mesoscale structures associated with individual Agulhas eddies. Additionally, we focus only on compound MHW–OAX events here. The next step is to extend the analysis to other extreme events, including low-chlorophyll extremes and low-oxygen extremes (Le Grix et al., 2023). Finally, our spatial domain encompasses the broader Agulhas Leakage region; future work should examine whether the results differ within more precisely defined dynamical sub-regions, such as the Agulhas Ring Corridor.