2.1 Data
SST data used in this study were from the National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation Sea Surface Temperature V2.1 (OISSTv2.1) dataset. These 0.25° gridded global SST data are from high-resolution infrared and microwave satellites blended with in-situ observational data from ships and buoys and comprise daily SSTs from 1982 to the present day (Reynolds et al., 2007; Banzon et al., 2016; Huang et al., 2021).
The atmospheric data were taken from the National Centre for Environmental Prediction/National Centre for Atmospheric Research (NCEP/NCAR) Reanalysis 2 product. These data were generated using a forecast model that assimilates observational data (Kanamitsu et al., 2002) and, with a relatively coarse spatial grid of 2.5 degrees, is well suited for analysis of large scale processes (Dufek et al., 2008). Variables from the NCEP/NCAR reanalysis used in this study include mean sea level pressure (MSLP) to calculate the SAM and STRH indices, zonal wind data to calculate the MJO index, and the meridional wind fields to show anomalous wind patterns. Outgoing longwave radiation (OLR) data used to calculate the MJO index were taken from NOAA’s OLR dataset estimated from polar-orbiting satellites and interpolated to include global spatial coverage on a daily timescale (Liebmann and Smith, 1996).
For our heat budget and Ekman transport analysis, we used model output from Bluelink ReANalysis (BRAN) 2020 (Chamberlain et al., 2021) which incorporates observations into an eddy-resolving, near-global ocean circulation model, the Ocean Forecasting Australia Model (OFAM) v3 (Oke et al., 2013). This model is forced by atmospheric fluxes from the Japanese Meteorological Agency 55-year reanalysis (JRA-55) (Kobayashi et al., 2015). Ocean variables are available on a daily timescale at 0.1° resolution.
2.2 Calculation of climate indices
2.2.1 El Niño Southern-Oscillation (ENSO) index
The phase of ENSO was determined using the Oceanic Niño Index (ONI). Using a three month running mean of SST anomalies derived from the OISSTv2.1 dataset in the Niño 3.4 region (5°S - 5°N, 170°W-120°W), an El Niño state is detected with a period of at least five consecutive months with SST anomalies >+0.5°C, and a La Niña state detected when SST anomalies <-0.5°C for a period of at least five consecutive months, and all other periods are considered neutral (Barnston, 1997).
The daily ENSO index was calculated as the daily SST anomalies (temperature deviations from the mean, calculated using the full daily climatology from 1982-2022), averaged over the Niño 3.4 region (Philander, 1983).
2.2.2 Indian Ocean Dipole (IOD) index
The phases of the IOD were determined from the differences between SST values, from OISSTv2.1 dataset, in the western Indian Ocean (between 10°S-10°N and 50°E-70°E) and the tropical south-eastern Indian Ocean (between 10°S-0° and 90°E-110°E). The positive phase shows higher temperatures in the western Indian Ocean and cooler temperatures around Indonesia in the east (Saji et al., 1999). The IOD is considered to be in the positive phase when this difference is >+0.4°C, and in the negative phase when this difference is <-0.4°C for at least eight consecutive weeks, with all other times considered as neutral (Saji et al., 1999).
2.2.3 Southern Annular Mode (SAM) index
The daily SAM index was calculated by projecting daily MSLP anomalies, from NCEP/NCAR Reanalysis 2, onto the principal component (PC) time series of the leading empirical orthogonal function (EOF) of observed monthly MSLP anomalies between 25°S and 75°S (see Marshall et al., 2014). SAM positive events are identified when the index is one standard deviation, or greater, above the mean and SAM negative events when the index is at least one standard deviation below the mean. Anything in between is characterised as SAM neutral. While there is more variability in the SAM index using daily data, the general spatial structure of the mode does not differ from one generated using monthly values.
2.2.4 Subtropical Ridge High (STRH) index
The STRH index was devised by Marshall et al. (2014) to describe the persistent high pressure blocking systems over the Tasman Sea located within the region of the subtropical ridge. The index is calculated using area averaged MSLP data, from NCEP/NCAR Reanalysis 2, in the region of 150°E-165°E, y°S ± 7.5° (where y is the latitudinal centre of the subtropical ridge, which varies monthly from the northernmost extent of 27.5°S in August to southernmost of 40°S in February). The positive phase is determined when the index is greater than one standard deviation above the mean, and the negative phase when the index is less than one standard deviation below the mean.
2.2.5 Madden Julian Oscillation (MJO) index
The phase and amplitude of the MJO is determined by the leading pair of EOFs from equatorially-averaged (15°S-15°N) fields of 200 hPa and 850 hPa zonal winds and OLR, which are used to compute the Real-time Multivariate MJO (RMM) index (Wheeler and Hendon, 2004). The pair of PCs that go with the leading EOFs are referred to as RMM1 and RMM2, and effectively describe the evolution of the MJO along the equator. To determine the relationship between the phases of the MJO with other drivers, we calculated each of the phases of the MJO as its own index, following the same method used by Virts and Wallace (2014) and Wang and Hendon (2020).
Figure 1 shows a 3D schematic summary of these drivers, based on the figure by McKay et al. (2023), with the addition of the EAC and the Leeuwin Current, two poleward flowing warm-water boundary currents that can also contribute to MHWs.
2.3 Calculation of MHW metrics
To calculate MHW metrics we followed the methodology of Hobday et al. (2016), who defined a MHW occurrence when ocean temperature exceeds the 90th percentile relative to daily climatological values for at least five consecutive days. We calculated MHW statistics in the Australian region (0° - 50°S, 100°E - 180°) from NOAA OISSTv2.1 data from 1982-2022. Where a MHW occurs, the intensity (i.e., the difference between the observed temperature and the climatological mean), was recorded at each grid point. (note: the absence of a MHW event has an intensity of 0).
2.4 MHW hazard index
Here, we created a simple MHW hazard index by considering the increased weekly heat stress that a region is exposed to during each of the driver phases during each season. First, we summed the daily MHW intensity at each grid point for each week. We then composited these weekly intensities based on the phases of the weekly climate mode indices and separated by season. Finally, we removed the average seasonal MHW signal (far right column Fig.2), which is dominated by the west Australian and Tasman Sea regions in all seasons.
The MHW hazard index developed here was created using the average temperature (oC) per week excess or deficit for the driver phase and season of interest. When the value is <-1.5°C, we say the MHW hazard level is very low. When the value is between -0.5°C and -1.5°C, it is seen as lower than average. When it is between -0.5°C and 0.5°C, we consider there is no effect. When it is between +0.5°C and +1.5°C, it is seen as higher than average. When between +1.5°C and +2.5°C, it is seen as very high. And finally, when it is >+2.5°C, we classify it as extreme.
2.5 Average oceanic and atmospheric states during phases of climate modes
Our study area encompasses the broader Australian region bounded by latitudes 0° - 50°S and longitudes 100°E - 180°. Figure 2 provides an overview of the study region, with the top map outlining the key regions mentioned throughout. These include the northwest shelf (NWS), Western Australia (WA), the Great Australian Bight (GAB), Tasman Sea west (TAS-W), Tasman Sea east (TAS-E), the East Australian Current region (EAC) and northeast Queensland (NE QLD). The columns below show a visual representation of average and anomalous temperatures categorized by season. Given our focus on the southern hemisphere (SH), we employ austral seasons: summer (DJF), autumn (MAM), winter (JJA), and spring (SON). The first column shows the average SST for each season highlighting a consistent trend of higher temperatures in the northern Australian tropical waters, gradually transitioning to cooler temperatures in the southern temperate zones. The second column illustrates the maximum SST anomalies, emphasizing regions that frequently experience recurring MHW incidents. Positive ocean temperature anomalies are particularly evident along the Western Australian coast during summer and autumn, aligning with 'Ningaloo Niño' occurrences (Marshall et al., 2015). The Tasman Sea's eastern and western edges experience substantial SST anomalies during spring and summer. Additionally, the EAC and its extension show strong positive SST anomalies throughout all seasons. The third column shows the standard deviation (std) of SST anomalies, closely matching the patterns exhibited in the final column depicting average MHW intensities per season. On the western coast, elevated std and MHW average intensity are concentrated near the northwest shelf in summer, shifting slightly southward in autumn, and enveloping the southwest coast in winter. The EAC region demonstrates elevated variance and MHW intensities across all seasons, prominently spanning the Tasman Sea, particularly in summer. Notably, during spring, an exceptional maximum SST anomaly is evident in the eastern Tasman Sea. However, the slight divergence between the std and average MHW intensity maps in this instance implies the possibility of a single, disproportionately intense, event compared to the typical spring pattern extreme event.
Understanding the individual influence of any single driver is complicated by the fact that they rarely exist in isolation. Figure 3 shows the time series of the ONI, IOD, SAM and STRH from 1982 to 2022, highlighting the difference in the variability of the modes, with the resident times of the ONI phases being the longest and those of the STRH the shortest. In Figure 3 we can also identify periods in which various modes are in phase. For example, in 1997/98 (during the period of extreme El Niño) we can see alignment of the positive ONI, positive IOD, negative SAM and positive STRH. Statistically significant correlation coefficients between these various modes are shown in Table 1, including phases 1-4 of the MJO (phases 5-8 are the inverse of these first four phases). To account for the serial correlation in the time series, we considered the autocorrelation (ρ) to calculate the effective sample size (neff = n (see Marshall et al. 2014). This effective sample size was used to assess statistical significance using a two-tailed t-test (Student, 1908). To eliminate signals from other drivers that showed strong correlations in the same seasons, we followed Werner et al.'s (2012) approach and used a regression analysis to remove the signals associated with any other driver with a significant correlation during corresponding seasons. The significant influence of each of the drivers is identified through composite maps of daily SST anomalies during the relevant positive and negative phases. To each of these maps, we also include MSLP and wind speed anomalies to assess the mechanisms that could lead to the accumulation of heat in any region.
Table 1 Correlation coefficients between daily climate driver indices. Those with p-values <0.05 are shown in bold, those with p-values>0.1 are not shown
Summer (DJF)
|
Niño34
|
IOD
|
SAM
|
STRH
|
Phase1
|
Phase2
|
Phase3
|
Phase4
|
Niño34
|
1
|
|
|
|
|
0.061
|
0.061
|
0.032
|
IOD
|
|
1
|
|
|
-0.12
|
-0.11
|
-0.049
|
0.038
|
SAM
|
-0.19
|
-0.083
|
1
|
|
-0.077
|
-0.14
|
-0.12
|
-0.043
|
STRH
|
0.078
|
-0.033
|
0.069
|
1
|
|
0.11
|
0.13
|
0.097
|
Autumn (MAM)
|
Niño34
|
IOD
|
SAM
|
STRH
|
Phase1
|
Phase2
|
Phase3
|
Phase4
|
Niño34
|
1
|
|
|
|
0.073
|
0.12
|
0.096
|
|
IOD
|
-0.04
|
1
|
|
|
0.044
|
|
-0.04
|
-0.057
|
SAM
|
|
|
1
|
|
-0.05
|
|
|
0.045
|
STRH
|
|
0.054
|
0.042
|
1
|
|
0.15
|
0.19
|
0.11
|
Winter (JJA)
|
Niño34
|
IOD
|
SAM
|
STRH
|
Phase1
|
Phase2
|
Phase3
|
Phase4
|
Niño34
|
1
|
|
|
|
|
|
|
|
IOD
|
0.3
|
1
|
|
|
|
0.078
|
0.1
|
0.05
|
SAM
|
|
0.066
|
1
|
|
|
0.057
|
0.1
|
0.074
|
STRH
|
0.074
|
0.15
|
0.12
|
1
|
0.3
|
0.32
|
0.18
|
-0.12
|
Spring (SON)
|
Niño34
|
IOD
|
SAM
|
STRH
|
Phase1
|
Phase2
|
Phase3
|
Phase4
|
Niño34
|
1
|
|
|
|
0.18
|
0.28
|
0.22
|
|
IOD
|
0.45
|
1
|
|
|
0.18
|
0.14
|
|
-0.13
|
SAM
|
-0.13
|
-0.12
|
1
|
|
-0.083
|
-0.066
|
|
0.059
|
STRH
|
0.07
|
-0.11
|
0.077
|
1
|
0.15
|
0.25
|
0.22
|
0.033
|
2.6 Understanding the mechanisms driving extreme regional ocean warming.
Lastly, our analysis looks at understanding the compounding influences of ENSO and the MJO. The sources of excess heat in the Ocean’s upper layer can be evaluated using the heat budget equation (Eq. 1). We use this heat budget equation to better understand the mechanisms that drive ocean warming in the WA region (see Fig. 2) during La Niña states with the various phases of the MJO, following the methodology of Marshall and Hendon (2014).
\(\frac{\partial T}{\partial t}=\frac{{Q}_{net}}{\rho {C}_{p}H}-\left[u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}\right]-w\frac{\partial T}{\partial z}+res\) (Eq. 1)
where the temperature tendency (\(\frac{\partial T}{\partial t})\) is due to contributions from the total heat flux (Qnet) (scaled by the density of seawater (ρ = 1025kg/m3), the heat capacity of water (Cp=3850J/kgC) and the mixed layer depth (H)), the horizontal advection \(\left(u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}\right),\) and the vertical advection (\(w\frac{\partial T}{\partial z}),\) plus smaller contributions from entrainment and diffusion and second order terms – here captured as the residual.
We also consider the combined influence of La Niña with the MJO in the NE QLD region (see Fig. 2). As this region is directly impacted by changes to tropical wind patterns, we investigate the role of Ekman transport by considering the proportion of total horizontal convergence (\(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y})\) (calculated from the anomalous geostrophic meridional and zonal currents) that is due to Ekman convergence (\(\frac{\partial {u}_{E}}{\partial x}+\frac{\partial {v}_{E}}{\partial y})\). Here, the Ekman convergence is directly related to the Ekman currents arising from anomalous meridional (τy) and zonal (τx) wind stress using equations 2 &3.
\({v}_{E}=- \frac{1}{f\rho }\frac{\partial {\tau }_{x}}{\partial z}\) (Eq. 2)
\({u}_{E}=\frac{1}{f\rho }\frac{\partial {\tau }_{y}}{\partial z}\) (Eq. 3)