1. Introduction
Northern Australia is an important region in terms of biodiversity, society, and economy. It has approximately 2 million hectares of rainforest, serving as the habitat for 60% of plant species and 40% of mammal species in Australia (Australian Bureau of Agricultural and Resource Economics and Sciences 2019). It is also home to a large proportion of Indigenous Australians and includes culturally important Indigenous art sites (Tourism Northern Territory Government 2023). In addition, it encompasses about 250 million hectares of agricultural land that comprises most of Australia’s tropical fruit production (ABS 2022). Notably, this region contributes to the production of 96% of sugarcane, more than 55% of beef, and 60% of avocados in Australia (ABS 2022) and has been projected to become one of the major Asian food production centers (Cranney 2021). However, northern Australia is susceptible to extreme weather events such as drought and flood, disrupting society, ecosystems, and agricultural production (Sangha et al. 2021; Wasko et al. 2021; Ridder et al. 2022).
Rainfall in northern Australia is highly variable across time scales with large diurnal cycles as well as high intraseasonal and interannual variability. Around 80% of the total yearly rainfall in northern Australia occurs from November to April, related to the Australian summer monsoon (ASM) (Sharmila and Hendon 2020). Longitudinal movement in the Walker circulation related to El Niño–Southern Oscillation (ENSO) and interdecadal Pacific oscillation also influences rainfall in northern Australia (Sharmila and Hendon 2020). Other studies have also examined the impacts of these modes of variability on northern Australian rainfall, with the most substantial impacts observed from September to November (McBride and Nicholls 1983; Cai and Cowan 2009; Forootan et al. 2016). Overall, the impacts of interannual variability on rainfall in Australia have been well studied. In contrast, the impacts due to intraseasonal variability, especially convectively coupled equatorial waves (CCEWs), are not well known.
Sources of variability on the intraseasonal time scale include the Madden–Julian oscillation (MJO) and the CCEWs (Dias et al. 2023; Schreck et al. 2020; Janiga et al. 2018). CCEWs are subseasonal waves in the tropics that can modulate convection and rainfall in the affected region (Wheeler and Kiladis 1999; Kiladis et al. 2009; Lubis and Jacobi 2015). They are equatorially trapped and are classified by frequency and direction of propagation. Some equatorial waves demonstrate features that are explained by the classical linear wave theory of Matsuno (1966), such as Kelvin waves, equatorial Rossby (ER) waves, mixed Rossby–gravity (MRG) waves, and inertio-gravity (IG) waves (Kiladis et al. 2009). These waves are primarily driven by intense tropical convection and are commonly referred to as CCEWs (Wheeler and Kiladis 1999; Kiladis et al. 2009). The equatorial waves are usually examined as the propagation of cloud clusters or geopotential height anomalies, with a unique horizontal structure for each class (Fig. 1). Moreover, previous studies have shown that ER, Kelvin, and MRG waves have influenced rainfall and extreme rain events in various tropical regions, such as Indonesia (Lubis and Jacobi 2015; Ferrett et al. 2020; Lubis and Respati 2021; Latos et al. 2021; Lopez-Bravo et al. 2023), Malaysia (Diong et al. 2023), the Philippines (Ferrett et al. 2020), southern Vietnam (van der Linden et al. 2016), and northern Africa (Schlueter et al. 2019a).
The theoretical horizontal structures for (a) Kelvin, (b) MRG, and (c) ER waves. Shaded region shows the convergence (blue) and divergence (red). Solid (dashed) contour shows the positive (negative) geopotential height. Contour and shading values are from −1 to 1 with an interval of 0.2.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
In addition to the wave types that the theory dictates, other wave types are observed. The easterly waves or tropical-depression-type (TD-type) waves and the MJO are among the modes the classical linear wave theory cannot describe (Takayabu 1994; Feng et al. 2020a). The TD-type waves form westward-propagating cyclonic (anticyclonic) vortices collocated with enhanced (suppressed) convection (Feng et al. 2020b). These vortices have been shown to influence tropical cyclogenesis in the North Pacific and Atlantic (Mao and Wu 2010; Schreck and Molinari 2011; Wu and Takahashi 2018; You et al. 2019). Also, the MJO is one of the dominant wavelike modes of rainfall variability in the tropics, characterized by eastward-propagating cloud clusters from the Indian Ocean to the western Pacific Ocean, with a period of around 40–50 days (Madden and Julian 1971; Wheeler and Hendon 2004). Previous studies have shown that the MJO influences the probability of precipitation over Australia during the Southern Hemisphere summer and autumn (Wheeler et al. 2009; Cowan et al. 2023; Dao et al. 2023). Phases 5–6 of the MJO increase the probability of above-median weekly rainfall by around 1.6–1.8 times over northern Australia, while phases 1–2 of the MJO decrease the above-median rainfall probability to approximately 0.4–0.6 times relative to average conditions (Cowan et al. 2023).
Theoretically, all CCEWs, except Kelvin waves, which are restricted to near the equator, are expected to have direct influences on off-equatorial convection (Fig. 1). Previous studies indicate apparent CCEW-associated convection over the Southern Hemisphere, especially during the austral summer and autumn (Huang and Huang 2011; Yang et al. 2007). However, no studies have been conducted to investigate the impacts of these waves on Australian rainfall. Understanding the impacts of CCEWs is crucial and has the potential to improve forecast skills in this region on subseasonal time scales. Any improvement in weather or subseasonal forecasting capability could help weather-sensitive industries, including the agricultural sector, and reduce the volatility of prices and yields during extreme weather (Adams et al. 2003; Letson et al. 2005; Asseng et al. 2012; Hoffmann et al. 2020; Ju et al. 2021; Potgieter et al. 2022). Thus, this study aims to quantify the impacts of CCEWs on daily rainfall and the probability of extreme rainfall during the austral summer (December–February) and autumn (March–May). We will focus on ER and MRG waves, as well as TD-type waves, and will address these main questions:
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To what extent do these waves influence daily rainfall anomalies across northern Australia?
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How much influence do these waves exert on rainfall extremes?
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What are the underlying large-scale dynamics influencing the wave–rainfall interaction?
The data and methods will be explained in section 2. Section 3 presents the impacts of CCEWs on rainfall in northern Australia and the impacts of concurrent CCEW activity. In section 4, we discuss the underlying dynamics behind the impacts. Last, the summary and conclusions will be presented in section 5.
2. Data and methods
a. Observation and reanalysis datasets
In this study, we use daily gridded rainfall from the Australian Gridded Climate Data (AGCD) version 1 (BoM 2019; Jones et al. 2009) from 1981 to 2018. The AGCD v1 is a daily gridded rainfall dataset with a spatial resolution of 0.05° or approximately 5 km per grid point. It is calculated from interpolation of the extensive rainfall station network in Australia and is the official gridded rainfall dataset from the Australian Bureau of Meteorology. In this project, the gridded rainfall was remapped to a 0.25° × 0.25° grid using conservative remapping. As the daily rainfall in these data is 24-h accumulated rainfall assigned to the date of the observation, a 1-day shift to the preceding day is conducted to make it consistent with other datasets (i.e., the rainfall on 2 January 1981 is shifted to 1 January 1981) as in van den Besselaar et al. (2017).
To understand the large-scale convective anomalies associated with the CCEWs, we use global daily interpolated outgoing longwave radiation (OLR) from NOAA/NESDIS from 1981 to 2018 with a spatial resolution of 2.5° × 2.5° (Liebmann and Smith 1996). Furthermore, we utilize the fifth major global reanalysis produced by ECMWF (ERA5) reanalysis (Hersbach et al. 2020) with a spatial resolution of 0.25° × 0.25° to explore the large-scale circulation linked with the rainfall. In particular, we use the daily average of wind and specific humidity at various levels and vertically integrated water vapor transport.
b. Wave filtering and local wave phases
This study investigated the impacts of three wave types, particularly the ER, MRG, and TD-type waves. To isolate the activity of these waves, we used a two-dimensional filtering technique as in Straub and Kiladis (2002), Lubis and Respati (2021), and Lubis and Jacobi (2015). The wavenumber, frequency, and equivalent depth used in this technique are given in Table 1. In addition, no symmetric/asymmetric wave decomposition is conducted in this method, owing to the latitudinally asymmetric convergence disturbance zone along the tropics (Lubis and Jacobi 2015). We only considered the austral summer and autumn seasons because those two are the only seasons with significant wave activities (Figs. S1 and S2 in the online supplemental material). This seasonality is attributed to the seasonal variation in insolation and the migration of ITCZ (Berry and Reeder 2014; Huang and Huang 2011; Roundy and Frank 2004; Fukutomi and Yasunari 2013; Žagar et al. 2011).
Details of the wavenumbers, periods, and equivalent depth of the CCEWs for the wave filter.
A local wave phase diagram was used to identify the convective or suppressive phase of the CCEWs. The method follows Riley et al. (2011), which used filtered OLR anomalies to construct a regional wave phase diagram analogous to the global real-time multivariate MJO (RMM) phase diagram (Wheeler and Hendon 2004). This method has been used extensively in other studies to elucidate the impact of CCEWs on rainfall over Indonesia (Lubis and Respati 2021; Respati et al. 2022), southern Vietnam (van der Linden et al. 2016), and North Africa (Schlueter et al. 2019a). Based on Riley et al. (2011), to make this index, we first isolate the wave activity from the OLR anomalies based on its wavenumber and frequencies (Table 1). Choosing the center longitude of 133°E, near the geographical center of Australia, we take the latitudinal average from 20° to 10°S to examine the time–longitude propagation of the waves. Next, we standardize the latitudinally averaged filtered OLR anomaly by its standard deviation for the whole longitude, with respect to the season (i.e.,
(a) Local ER wave index diagram and (b) ER wave propagation through northern Australia. Dashed lines indicate the reference point used to construct the diagram.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
There are a few limitations of using this method, as also pointed out by previous studies (Lubis and Respati 2021; Schlueter et al. 2019b; van der Linden et al. 2016): 1) The application of the index is limited to only the northern part of Australia and 2) the local phase diagram does not represent the spatial and temporal propagation of waves; instead, it quantifies the number of waves passing through at a given location. The benefit of this method is that we only consider waves that directly impact the OLR over northern Australia.
c. Composites
Before making the composites, we removed the tropical cyclone (TC) dates from the dataset. The TC days are obtained from the tropical cyclone databases of the Bureau of Meteorology (http://www.bom.gov.au/cyclone/tropical-cyclone-knowledge-centre/databases/). The day is removed if the TC is located within 104°–159°E and 25°–8°S. Previous studies have shown the importance of TC and wave interactions (Wu and Takahashi 2018; Schreck and Molinari 2011; Frank and Roundy 2006); however, this is beyond the scope of the current study. In general, this removes around 20%–30% of the data during December–February and March–May (see Tables S1 and S2 for details). In addition, some of the regions are masked due to low station density and the potential for erroneous trends in precipitation (King et al. 2013; King 2023) (see Fig. 3).
(a) Mean rainfall and (b) the 90th percentile of rainfall during the austral summer (DJF) and (c) mean rainfall and (d) the 90th percentile of rainfall during the austral autumn (MAM). Boxes indicate the regions of interest.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
For the statistical significance of each composite, a nonparametric bootstrap test was performed (Wilks 2006). Each of the composites was tested against 1000 synthetic composites from which a confidence interval was produced (i.e., 2.5th and 97.5th percentile for a two-sided test at the 95% confidence level) similar to Muhammad and Lubis (2023) and Muhammad et al. (2021).
d. Large-scale dynamics
3. Modulation of daily rainfall associated with CCEWs
a. Impact of CCEWs on rainfall
In this section, the rainfall anomalies and extreme rainfall probabilities during the eight defined phases of the ER, MRG, and TD-type waves are examined. We focus on the austral summer (DJF) and autumn (MAM) seasons. Each phase of these waves consists of approximately 9% of the days of a whole season. This is similar to the number of days in MJO phases. Figure 3a shows that the mean austral summer rainfall is between 5 and 12 mm day−1 in the Top End region, 4 and 10 mm day−1 in the Kimberley region, 7 and 12 mm day−1 in the Cape York region, 7 and 15 mm day−1 in the eastern coast of Queensland, and 1 and 4 mm day−1 in the inland Queensland. Furthermore, the 90th percentile during the austral summer varies between about 15 and 25 mm day−1 across the Kimberley, Top End, Cape York, and eastern coast of Queensland regions and between 2 and 10 mm day−1 across inland Queensland (Fig. 3b).
During the austral autumn (MAM), the mean rainfall and 90th percentile of rainfall are significantly lower than in the austral summer. Figure 3c shows that the mean rainfall during austral autumn varies between 0 and 6 mm day−1 in the Kimberley, Top End, and Cape York regions, 2 and 12 mm day−1 in the eastern coast of Queensland, and 0 and 2 mm day−1 in the inland Queensland. The 90th percentile of rainfall is also significantly lower in the austral autumn than in the austral summer. The 90th percentile of rainfall is between 0 and 10 mm day−1 in the Kimberley region, 2.5 and 15 mm day−1 in the Top End region, 5 and 22.5 mm day−1 in the Cape York region, 5 and 25 mm day−1 in the eastern coast of Queensland, and 0 and 2.5 mm day−1 in inland Queensland.
1) ER waves
Figure 4 shows the anomaly (contour) and P90 composites (shading) for each phase of ER waves during the austral summer. The shading in Fig. 4 indicates the anomalous likelihood of exceeding the 90th percentile of daily rainfall relative to the seasonal likelihood [defined as P90 in Eq. (1)]. For clarity, let a point have a 10% chance (by definition) of experiencing 90th percentile of rainfall in a season. Then, if the region has a P90 of 2, the chance of extreme rainfall becomes 20%, a twofold increase from 10%. A value of P90 equal to 1 means no changes in the probability relative to the whole study period, while a value larger (smaller) than 1 means an increase (a decrease).
Daily rainfall anomaly (contour; mm day−1) and extreme PR composites relative to the seasonal probability (shading) for ER waves during the summer. Contour is from −6 to 6 with an interval of 2, with dashed lines indicating negative anomalies and solid lines indicating positive anomalies. The number of days for each phase is given inside the parentheses at the top-left corner of the plot. Shading indicates a value that is significant at 95% confidence level. The median, maximum, and minimum values of RR anomaly and PR for the whole region are summarized at the top right corner of the plot.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
Generally, we can see the westward propagation of the rainfall anomaly and the P90 signature of the ER wave–associated convection. The result shows that, on average, ER waves increase the daily rainfall by around 1–3 mm day−1 and P90 by up to 1.9 times during phase 4 and between 3 and 6 mm day−1 and between 1.25 and 2.5 times during phases 5–6 (Figs. 4d–f). In phase 4, the increase in rainfall anomaly and P90 value of more than 1 can be mainly seen around the central and eastern parts of the Top End (Fig. 4d). Furthermore, during phase 5, a positive rainfall anomaly and P90 value of more than 1 are observed over the northern parts of Australia, with the largest increase seen to the west of the Top End (Fig. 4e). As the ER waves propagate further westward, they are associated with an increase in rainfall over the northwestern parts of Australia during phase 6 by up to 7.6 mm day−1 and P90 values between 1.25 and 1.8 (Fig. 4f). The increase in rainfall and P90 values can still be observed over the western part of Australia in phase 7, albeit with a smaller magnitude (Fig. 4g).
On the other hand, significant negative rainfall anomalies and P90 values of less than 1 are observed over eastern and northern Australia during phase 8 (Fig. 4h). Most of northern Australia also experiences a large decrease in mean rainfall and P90 values during phases 1 and 2 (Figs. 4a,b). The decrease in rainfall and P90 values is observed over large areas with a magnitude of around 1–5 mm day−1 and less than 0.8 times. These results suggest a robust influence of the ER waves on mean and extreme rainfall in northern Australia.
The influence of ER waves on daily rainfall and P90 during the austral autumn is shown in Fig. 5, with a significant impact observed at phase 3 over the east coast of Queensland, increasing the rainfall by up to 4 mm day−1 and P90 by up to 1.8 times compared to the season (Fig. 5c). The impact is comparably weaker than the summer season (Fig. 4c). Then, as the waves propagate westward, the area of impact becomes wider. In phase 4 of the ER waves, Cape York and the eastern part of the Top End experience an increase in daily rainfall and extremes (Fig. 5d). The strongest impact can be seen in phases 5 and 6 when the convective activity of the ER wave is right over the Top End (Figs. 5e,f). In phase 5, the ER waves increase the average daily rainfall and P90 by up to 3 mm day−1 and 1.7 times over the Top End. Moreover, ER waves increase the daily rainfall and P90 by around 1–1.5 mm day−1 and 1.4 times over the eastern Kimberley and western Cape York. Then, during phase 6, most of the Kimberley region and western Top End experienced an increase in rainfall and P90 between 1–2 mm day−1 and 1.25–2 times, respectively.
In contrast, phases 7, 8, 1, and 2 show a decrease in daily rainfall and P90 values in most regions in northern Australia. In phase 7, the decrease is mostly observed on the eastern coast, with a magnitude of around 1 mm day−1 for daily rainfall and 0.5 times for P90 (Fig. 5g). Similarly, a decrease is also observed during phase 8 over the Top End (Fig. 5h). The largest decrease is apparent throughout phases 1 and 2. During these phases, the decrease in daily rainfall is around 1–1.9 mm day−1 over the Kimberley and Top End and around 0.3–0.5 times for P90 (Fig. 5a).
In general, the impacts on rainfall during austral summer and autumn follow a similar pattern, despite a strong difference in mean rainfall between the two seasons. During both seasons, the daily rainfall and P90 increase when the convective center is over the Australian region (i.e., phases 4–6). However, the increase in daily rainfall and P90 during the autumn is lower than in the summer. Both rainfall anomalies and P90 are mostly collocated, indicating that part of the increase in mean rainfall anomalies comes from an increase in the likelihood of extreme rainfall in northern Australia.
2) MRG waves
We also observe pronounced rainfall anomalies and P90 for each of the active phases of MRG during the austral summer (Fig. 6). The rainfall signal propagates westward, although with a weaker amplitude than the ER waves. The daily rainfall increases during phase 5 by around 1–3 mm day−1 over the eastern and western parts of the Top End, while P90 values are between 1.1 and 1.8 times (Fig. 6e). In phase 6, an increase in both mean rainfall and P90 can also be seen over the northwestern part of Australia by around 1–3 mm day−1 and 1.4 times, respectively (Fig. 6f). On the other hand, the decrease in daily rainfall can be seen in nearly all northern Australia during phases 8–2 by approximately 1–3 mm day−1 and up to 0.3 times for P90 (Figs. 6h,a,b). The result shows that daily rainfall variability and P90 associated with the MRG waves are generally weaker and more scattered than the ER waves.
Daily rainfall anomaly (contour; mm day−1) and extreme PR composites relative to the seasonal probability (shading) for MRG waves during the summer. Contour is from −5 to 5 with an interval of 1. The number of days for each phase is given inside the parentheses at the top-left corner of the plot. Shading indicates a value that is significant at 95% confidence level. The median, maximum, and minimum values of RR anomaly and PR for the whole region are summarized at the top-right corner of the plot.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
On the other hand, Fig. 7 shows the influences of MRG waves on daily rainfall and P90 in northern Australia during the austral autumn. Here, we can see that the impact is weaker than during the summer (Fig. 7). The influence on daily rainfall is not apparent for MRG waves except at some regions in the western Top End during phase 5 and on the East Coast during phase 6. Overall, an increase of around 1 mm day−1 and a decrease of around 1–1.5 mm day−1 are observed during phases 5 and 6, respectively. In contrast to the mean rainfall, the P90 values show a more apparent westward propagation of the impacts, especially for the increase in P90. The suppressive phases also show a decrease in P90, albeit small and statistically insignificant (not shown). The increase to around 1.3–1.8 times relative to the climatology is observed during phase 5 over the eastern Top End, while a decrease to around 0.6–0.4 times climatology during phase 6 is observed over the East Coast (Figs. 7e,f). This result shows that there is almost no collocation of the rainfall anomalies and P90 values, contrasting that of the austral summer. This result indicates that the rainfall associated with MRG waves during the autumn is likely due to independent heavy rainfall events rather than a frequent increase in rainfall during the active wave phases.
3) TD-type waves
The contour in Fig. 8 shows the rainfall anomalies, and the shadings show P90 associated with the TD-type waves during the austral summer. The increase in rainfall and P90 is first observed during phase 2 of the TD-type waves, impacting the eastern coast of Queensland by the magnitude of 1–3 mm day−1 and up to 1.6 times, respectively (Fig. 8b). The westward propagation of the precipitation anomalies can be seen in the following phases as the waves propagate westward. Phase 3 shows a rainfall and P90 increase to the east of the Top End by around 1–2 mm day−1 and up to 1.7 times (Fig. 8c), while phases 4 and 5 increase rainfall over the Top End by around 1–3 mm day−1 (Figs. 8d,e). Interestingly, the P90 increase is mostly not observed in the northern part of the Top End, suggesting that the rainfall modulation comes from persistent nonextreme daily rainfall or extreme rainfall on subdaily scales. As the waves propagate westward, the mean rainfall anomalies and P90 are observed to increase by around 1–4 mm day−1 and by 1.25–1.9 times, respectively, over the western part of Top End and the eastern part of the Kimberley region during phases 6–7 (Figs. 8f,g). On the other hand, rainfall decreases are observed through phases 8, 1, and 2 over the Top End and Kimberley (Figs. 8h,a,b). In conclusion, TD-type waves also influence the daily rainfall in Australia during the austral summer, with a higher impact than the MRG waves but weaker than ER waves.
As in Fig. 6, but for TD-type waves.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
Figure 9 shows the rainfall anomalies (contour) and P90 (shadings) associated with TD-type waves during the austral autumn. Generally, the impact of TD-type waves is stronger than that of MRG waves during the austral autumn (Fig. 7). The increase in rainfall and P90 associated with the TD-type waves can be seen throughout phases 2–8 (Figs. 9b–h). During phase 2, the increase is observed over Cape York and along the East Coast, with a magnitude of around 1–3 mm day−1. An increase in 90th percentile of rainfall of around 1.4–2 times is also observed during this phase. Then, in phase 3, the increase in daily rainfall and P90 value is observed over the eastern Top End and northern Cape York, by approximately 1–2 mm day−1 for daily rainfall and around 1.25–1.7 times for P90. Similar to that of MRG waves, the increase in P90 (blue shading) is more apparent during autumn compared to the decrease (red shading). However, the suppressive impact of the waves is still present, albeit small and statistically insignificant.
Furthermore, during phase 4, an increase in daily rainfall by around 1–3 mm day−1 is observed over the eastern Top End and the northern tip of Cape York (Fig. 9d). This increase is also accompanied by the increase in P90 to around 1.25–1.7 times the climatological average. Next, in phase 5, as the convective activity of TD-type waves propagates westward, the increase in daily rainfall reaches the center of the Top End. During this phase, the decrease in daily rainfall is observed along the East Coast and Cape York, decreasing the rainfall by around 1–1.6 mm day−1. The decrease along the East Coast and Cape York is observed throughout phases 5–7 and 5–8, respectively.
Comparing the two seasons, we can see that the impact of TD-type waves is broadly similar. Most rainfall anomalies and P90 during the austral autumn and summer are collocated. Furthermore, the increase in daily rainfall over the coastal region during the austral autumn seems to be collocated with the increase in P90, especially in the Top End and East Coast. This result suggests that the activity of TD-type waves is associated with extreme daily rainfall near the coastal region during austral autumn. On the other hand, during the austral summer, the TD-type waves influence the daily rainfall but do not significantly impact P90 over the coastal region.
4) Concurrent wave activity and impacts on extreme rainfall
We have established the impact of each wave on rainfall in northern Australia. Next, we will analyze the impact of concurrent activity of tropical waves over the region in Fig. 10. Previous studies have shown that concurrent waves could either enhance or suppress the impacts on rainfall (Schlueter et al. 2019a; Lubis and Respati 2021; van der Linden et al. 2016). For clarity, the P90 values are calculated using the area-averaged rainfall over five regions of interest (Fig. 3): 1) Kimberley, 2) Top End, 3) Cape York, 4) Queensland East Coast, and 5) Inland Queensland. It has been found before that the MJO can influence the rainfall extremes over northern Australia (Cowan et al. 2023; Dao et al. 2023; Wheeler et al. 2009) and may also interact with the convective activity of CCEWs (Lubis and Respati 2021; van der Linden et al. 2016). Therefore, we will also include the impacts of the MJO in this section and its interactions with the CCEWs. For consistency, the phase of MJO is made with the local wave phases, like all the other waves (details of the wavenumber and period are given in Table 1). The convective phases of the MJO local indices over northern Australia (i.e., phases 4–6) are found to match with the Wheeler and Hendon (2004) real-time multivariate MJO indices (WH04)and OLR MJO indices (Kiladis et al. 2014) when the convective center is over northern Australia (i.e., phases 4–7) by around 70% and 76% of the time. Note that the local index used here only captures the MJO events that impacted northern Australia, indicating that some events may be too weak to be captured by the local index but strong enough globally.
Impacts on extreme rainfall probability when multiple waves are present over the regions of interest throughout DJF. Numbers are the ratio of extreme rainfall probability associated with the waves against the seasonal extreme rainfall probability [Eq. (1)]. The threshold is given on the top right of the plot (mm day−1). The number in the parentheses shows the percentage of events relative to total days (2551 days). The asterisk indicates the value is significant at the 95% confidence level.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
The wave activity is divided into the wet and dry phases. The wet phase is defined when the P90 value for each phase over each region is higher than 1.1 or 10/9, while the dry phase is defined when the value is lower than 0.9 or 9/10. As a result, the wet phase of each region may be comprised of different wave phases. For example, the wet phase in the Top End may include phases 4 and 5 of ER waves but only phase 5 of TD-type waves. The detail of which phases are included in each region is given in Table 2. The caveat in this selection is that the wave impact may be mixed with other types of waves. For example, we can choose the dates where ER and MJO happen concurrently, but some of those events can be mixed with several other wave activities. While this might be insignificant if the sample is large enough, this can cause a problem when the event samples are small. Moreover, we consider only a “wet” and “dry” phase of each wave and do not separate the influence into the individual phases.
The wet and dry wave phases included in the analysis for each region during the summer.
Figure 10 shows the relative likelihood of exceeding the 90th percentile of rainfall for concurrent wave activity over several regions during the austral summer. The diagonals of every quadrant indicate the average impact due to a single-wave type. The result shows that concurrent wave activities can enhance or suppress the impacts on P90, depending on the wave phases. A wet–wet or dry–dry combination will increase the average impact, while a wet–dry combination mostly decreases the average impact. For instance, in the Kimberley region (Fig. 10a), the impacts of MJO increase when they occur concurrently with ER waves, rising from 1.6 to 3.3 times, making the extreme rainfall more than three times as likely compared to the climatology. In comparison, a decrease in the impacts can be seen during wet ER waves and dry MJO (Figs. 10a–d). Generally, for a wet–wet wave pair, the impacts of the combination of either two of ER waves, MJO, or TD-type waves (i.e., wet ER waves and wet MJO, wet ER waves and wet MJO, and wet MJO and wet TD-type waves) are stronger than the other combinations. On the other hand, the dry phases of the MJO and ER waves appear to suppress P90 more than the other dry waves. Overall, the impact of concurrent wave activity can be seen throughout the selected regions.
Now, we will investigate the impact of concurrent wave activities on P90 during the austral autumn (MAM); like the austral summer (DJF), the effect of MJO is also included here, as previous studies have shown impacts of MJO during the austral autumn in northern Australia (Wheeler et al. 2009; Cowan et al. 2023; Dao et al. 2023). We follow the same method as during the austral summer (Fig. 7) but with different choices of the wet and dry phases of the waves. The details of which phases of each wave are included in wet/dry phases are given in Table 3. It should be noted that over inland Queensland (Fig. 11e), the 90th percentile of rainfall in this region is small, only around 1.6 mm day−1. Thus, the P90 value in this region should not be considered an extreme rainfall probability ratio. It is more accurate to see the P90 value in this region as the probability ratio of rainy days compared to the season.
As in Fig. 10, but for MAM. The number in the parentheses shows the percentage of events relative to total days (2898 days). The asterisk indicates the value is significant at the 95% confidence level.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
In general, it can be seen that the concurrent wave activity can enhance or suppress the impacts on rainfall during the austral autumn (Fig. 11) similar to that of austral summer (Fig. 10). Over all regions, the wet–wet combination between ER waves, MJO, and TD-type waves (e.g., ER waves and MJO, TD-type and ER waves, or TD-type waves and MJO) appears to have significant impacts, similar to the austral summer. For instance, the combination of wet ER and MJO over the Kimberley (Fig. 10a) can increase the P90 from 1.5 to 2.9. This means that the concurrent wave activity can nearly double the likelihood of P90 compared to the single-wave activity. On the other hand, the wet–dry combination can suppress the impact on P90. For example, the impact of TD-type waves in Cape York decreased when dry waves occurred (Fig. 10c). Similar to the austral summer, the dry phases of ER waves and MJO appear to significantly suppress the P90 value.
These results show that concurrent CCEW activity can either enhance or suppress the impact on rainfall in all regions in northern Australia. Generally, we can see that the influences of concurrent wave activity can be constructive (i.e., amplifying the impacts) or destructive (i.e., weakening the impact). Consequently, multiple wet or dry phases can enhance the impact on rainfall, whereas different wave phases (i.e., wet with dry) can suppress the impact on rainfall. In some cases, the change in P90 is reinforced when waves are active concurrently. For instance, the collocation of the wet ER wave and MJO pair in the Top End during the austral summer is 2.2 (i.e., 1.0 + 0.6 + 0.6), which is close to the concurrent P90 value during wet ER–MJO phases (i.e., 2.3 times) (Fig. 10b). Several other cases also show this interaction, such as wet MRG and TD-type wave pairs and wet MJO and MRG-type wave pairs (Fig. 10b). This interaction is similar to what happens in the deep tropics (Lubis and Respati 2021). On the other hand, some cases show negligible impact of concurrent wave activity, such as wet MRG and TD-type waves during the austral summer on the eastern coast of Queensland (Fig. 10d). These results suggest the complexity of the wave interactions and should be investigated in more detail in the future.
4. Large-scale dynamics of the wave–rainfall interaction
Previous studies have shown that most CCEWs can be considered as moisture modes due to their tight coupling with moisture (Mayta and Adames 2023; Mayta et al. 2022; Mayta and Adames Corraliza 2023; Adames and Maloney 2021), suggesting that their characteristics and impacts can be approximated using moisture budgets. This section examines the large-scale dynamics associated with the CCEWs. We investigate the moisture budget to help diagnose the processes related to the increase in rainfall [see Eq. (4)]. Previous studies suggested that the large-scale moisture convergence is mainly responsible for the increase in rainfall with CCEWs (Lubis et al. 2023, 2022; Respati et al. 2022; Muhammad et al. 2019; Adames and Wallace 2014; Adames et al. 2016; Kirshbaum et al. 2018). In this section, we only discuss the summer season (DJF), given the autumn season shows a similar pattern, albeit with a slight difference in magnitude (Figs. S6–S8).
Figures 12a–i show the composite of OLR, moisture advection, moisture convergence, and apparent moisture sink/source anomalies during phases 3–6 of the ER waves. A positive value in the apparent moisture sink/source indicates dominant moisture sources via evaporation (depicted in blue), while a negative value indicates a moisture sink via precipitation (depicted in red). In general, it can be seen that the positive (negative) anomalies of rainfall and the increase (decrease) in the P90 are collocated with the negative (positive) OLR anomalies (Figs. 4 and 12). The result further shows that the moisture advection provides a favorable environment for deep convection to the west of the negative OLR anomaly, while the moisture convergence contributes to the maintenance of the deep convection (Figs. 12a–h). This is consistent with preceding studies showing that moisture advection is responsible for ER wave propagation, while moisture convergence is responsible for their maintenance (Mayta et al. 2022; Nakamura and Takayabu 2022a). In addition, the cyclonic water vapor flux activity to the west of the convection enriches the troposphere with moisture via surface moisture convergence (Nakamura and Takayabu 2022b). Moisture sink anomalies are found to be collocated with moisture convergence and negative OLR anomalies (Figs. 12e–l), suggesting that the moisture sink via precipitation and/or condensational heating dampens the moisture convergence and convection (Figs. 12i–l), consistent with previous studies (Mayta et al. 2022; Nakamura and Takayabu 2022a,b).
Composite anomalies of (a)–(d) moisture advection −〈V ⋅ ∇q〉′ (kg m−2 s−1 × 10−6; color shading), (e)–(h) moisture convergence −〈q∇ ⋅ V〉′ (kg m−2 s−1 × 10−6; color shading), and (i)–(l) moisture sink/source −Q2/L (kg m−2 s−1 × 10−6; color shading) for phases 3–6 of ER waves during the austral summer. The contour line denotes the OLR (W m−2), and the vector denotes the vertically integrated water vapor flux (kg m−1 s−1). Solid (dashed) contour indicates negative (positive) OLR anomalies. Contour is from −9 to 9 with an interval of 3. Shading indicates a value that is significant at the 95% confidence level. The vector is drawn only if the value exceeds 7.5 kg m−1 s−1.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
In summary, the moistening troposphere via moisture advection and convergence provides a favorable environment for deep convection (indicated by negative OLR anomaly), hence increasing the daily rainfall and the probability of extreme rainfall. The collocation of the negative OLR anomaly with the moisture convergence also suggests that the moisture convergence enhances the upward air movement required for deep convection.
For MRG waves, the result shows that the moisture advection also leads to the negative OLR anomaly (Figs. 13a–d). The northerly water vapor flux transports the moisture from the ocean to the west of convection, enriching the region with moisture. The transport of water vapor indicated by the moisture advection suggests a gradual buildup of moisture to the west of the previous convection (Figs. 13a–d).
As in Fig. 12, but for MRG waves. The vector is drawn only if the value exceeds 1.5 kg m−1 s−1.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
It should be noted that MRG waves follow a different convective coupling mechanism from ER waves (Wang and Zhang 2015). MRG waves have been shown to have a tilted vertical structure of the specific humidity at the time of convergence (i.e., moist at the lower level but dry at the upper level) (Kiladis et al. 2009; Wang and Zhang 2015). Compared to the upright moisture structure of the ER waves (Nakamura and Takayabu 2022a; Kiladis et al. 2009), which can support rapid, deep convection given enough upward motion, the MRG wave convection is inhibited due to a dry midtroposphere associated with midtropospheric divergence and upper-tropospheric convergence (Wang and Zhang 2015). Therefore, preconditioning of the troposphere by shallow convection to moisten the troposphere and provide a favorable environment for deep convection is important (Wang and Zhang 2015).
Figures 13f–h show the moisture convergence during phases 4–6 of the MRG waves. The moisture convergence (divergence) is collocated with the negative (positive) OLR anomalies, indicating moisture convergence maintains the convection. However, the values of the anomalies (i.e., OLR and moisture convergence) are weaker compared to the ER waves (Figs. 12e–h and 13e–h). This indicates a weaker convective activity associated with the MRG waves, which is consistent with the smaller rainfall anomalies and P90 compared to ER waves (Figs. 6 and 4). Similar to ER waves, the moisture sink via precipitation is collocated with the negative OLR anomaly and moisture convergence, which indicates that condensational heating or precipitation during the time of convergence reduces available moisture content (Figs. 13i–l). The relatively fast movement of the MRG waves and the need for the deep convection to adjust might explain why the moisture convergence of the MRG waves is weaker than ER waves (Figs. 12 and 6), which suggests a weaker OLR and rainfall anomalies.
In the case of TD-type waves, the result shows that the moisture advection leads the convection, similar to the other waves (Fig. 14). This horizontal moisture advection directly moistens the lower- and midtroposphere, making it favorable for deep convection to occur (Feng et al. 2020b). Feng et al. (2020b) show that the moisture advection associated with TD-type waves is mainly controlled by the advection of the wave-scale moisture disturbances by the horizontal background flow. Similarly, Fukutomi (2019) demonstrates that the Australian monsoon is likely responsible for maintaining and growing the TD-type waves. Therefore, the enhanced moisture advection (Figs. 14a–d) could be strongly affected by the active Australian monsoon system during the DJF period. Furthermore, it can be seen that the enhanced moisture advection is roughly collocated with the convergence of easterly and westerly moisture transport (Figs. 14a–d). The enhanced moisture advection indicates a buildup of moisture by the moisture transport, which supports a favorable environment for convection.
As in Fig. 12, but for TD-type waves. The vector is drawn only if the value exceeds 1.5 kg m−1 s−1.
Citation: Journal of Climate 37, 22; 10.1175/JCLI-D-24-0042.1
In contrast to ER waves, the cyclonic activity throughout the atmosphere is relatively weaker in TD-type waves (Figs. 12a–d and 14a–d). Consequently, the moisture convergence leading to the development of deep convection is much weaker compared to the ER waves (Figs. 14e–h). Likewise, the contribution of the apparent moisture sink/loss is relatively weaker compared to the other two waves (Figs. 14i–l). This could be attributed either to the vertical structure of the baroclinic wave heating (with a dipole pattern in vertical) (Feng et al. 2020b,a; Kiladis et al. 2009) or to the waves being relatively faster. In addition, the unfiltered moisture advection anomalies indicate that deep convection related to TD-type waves may be influenced by other variability (not shown), presumably the Australian monsoon (Fukutomi 2019). This result is consistent with the previous studies, which show that the TD-type waves are mainly controlled by the horizontal background flow acting on the humidity associated with waves (Feng et al. 2020b). Further research is required to delve into such specific processes.
In summary, the moisture advection promotes a suitable environment for deep convection ahead of the preceding convection. The enhanced moist air ascent due to moisture convergence maintains and supports the deep convection. These two processes mainly contribute to increasing the daily rainfall and extreme rainfall probability during TD-type wave events.
5. Summary and conclusions
We have investigated the impacts of convectively coupled equatorial waves (CCEWs) on daily mean and extreme rainfall during the austral summer (DJF) and autumn (MAM) utilizing gridded rainfall from observation datasets operated by the Australian Bureau of Meteorology and reanalysis data. Our key results are summarized as follows:
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During the summer, the convectively active phases of ER waves increase the rainfall anomalies by up to 7 mm day−1. Similarly, the convectively active phases of MRG and TD-type waves increase the daily rainfall by around 1–4 mm day−1.
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The impact is weaker during the autumn than in the summer. The convectively active phases of ER waves increase the daily rainfall by up to 4 mm day−1. Likewise, the convectively active phases of MRG and TD-type waves increase the rainfall by around 1–1.5 mm day−1 and 1–3 mm day−1, respectively.
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A significant increase in the likelihood of exceeding the 90th percentile of probability (P90) is observed during the convectively active phase of these waves. In general, the convectively active phases of ER waves show the greatest impact on P90, increasing the probability to around 1.5–2.4 times (1.1–1.8 times) during the summer (autumn). The convectively active phases of TD-type waves followed after, increasing the P90 to around 1.25–1.9 times (1.27–1.7 times) during the summer (autumn). Last, the convectively active phases of MRG waves increase the P90 by around 1.4–1.6 times (1.3–1.8 times) during the austral summer (autumn).
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An analysis of concurrent wave activity indicates that wave activity that is collocated in space and time can lead to amplification or suppression of the impacts on rainfall. The wet–wet wave pair enhances the impact on P90, while the wet–dry wave pair suppresses the impact. However, some instances might show negligible impacts, suggesting the complexity of the impacts of wave-to-wave interactions on rainfall.
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In terms of large-scale dynamics associated with the wave–rainfall interaction, the results show that the changes in rainfall variability can be explained by the changes in terms of the vertically integrated moisture flux convergence (VIMFC) [see Eq. (4)]. The horizontal moisture advection is found to lead the precipitation and acts to moisten the troposphere to support the environment favorable for convection. This is then followed by moisture convergence, which induces deep convection.
It should be noted that this study does not consider other variability, such as El Niño–Southern Oscillation (ENSO), the Indian Ocean dipole (IOD), and monsoonal flow, which may also interact with the CCEW activity. Huang and Huang (2011) and Muhammad et al. (2019) show a high negative correlation between El Niño activity and the activity of MRG and TD-type waves over the northern part of Australia, meaning that El Niño (La Niña) weakens (strengthen) the CCEW activity. Moreover, Dao et al. (2023) and Cowan et al. (2023) found that in the summer during El Niño conditions, a greater reduction in daily rainfall is observed during the dry phases of MJO over Australia. Furthermore, analysis of wave activity shows a negative correlation with the IOD over the northern part of Australia (Huang and Huang 2011). On the other hand, the monsoonal flow may also influence the activity of TD-type waves in the Southern Hemisphere (Fukutomi 2019). Although the monsoonal flow may also impact other waves, it remains to be further studied. Likewise, the impacts of other variabilities on CCEW activity, such as cross-equatorial surges (Lubis et al. 2023; Hattori et al. 2011; Xavier et al. 2020; Lubis et al. 2022; Valentín et al. 2023), and their impacts on rainfall remain an open question and will be reserved for future studies.
The usage of daily data in this study means that we cannot investigate faster-moving waves, such as eastward inertia–gravity (EIG) and westward inertia–gravity (WIG) waves, the impacts on the diurnal cycle, and the information on the rainfall rate (RR) during the extreme rainfall. Sakaeda et al. (2020) show that the arrival of CCEWs can enhance or suppress the diurnal cycle of rainfall in the Maritime Continent. In particular, Kelvin waves have been shown to prolong the mesoscale convective systems over the west coast of Sumatra (Lopez-Bravo et al. 2023). Similarly, previous works have found an increase in the amplitude of the diurnal cycle prior to the MJO arrival (Vincent et al. 2016; Sakaeda et al. 2017; Peatman et al. 2014; Lestari et al. 2022). However, not much is known about the impact of CCEWs on the diurnal cycle, especially in northern Australia.
In addition, the concurrent wave activity analysis shows enhanced impacts on rainfall when the waves are both in convectively active phases. In contrast, concurrent convectively active and convectively suppressed phase activity will decrease the impacts on rainfall. As noted in the previous section (section 4), the mechanism of this wave-to-wave interaction is still unclear. Investigating the large-scale dynamics and mechanism during the multiple wave activity is worthy of future study.
Our results suggest that CCEWs significantly modulate rainfall and large-scale circulation over northern Australia. The importance of the impact of CCEWs on extreme rainfall highlights the potential for their explicit use in subseasonal to seasonal (S2S) prediction. Although previous work found inconclusive impacts of CCEWs on the S2S prediction skill in the model (Janiga et al. 2018), a better representation of CCEWs in the recent model can lead to greater prediction skill (Dias et al. 2023). Nonetheless, by including the MJO in the model, Schreck et al. (2020) have shown that the predictive skill doubles in the first two weeks. Furthermore, including ER waves in the model increases the predictive skill for the first week (Schreck et al. 2020). Thus, a thorough study looking into the predictive skill in the Australian region and attribution of the sources of predictability would be useful. Moreover, future climate projections also show potential intensification of CCEWs in CMIP6 models, suggesting more organized tropical convection and more significant impacts on extreme rainfall (Bartana et al. 2023). Ultimately, increasing the forecasting skill of rainfall variability can help farmers and other stakeholders prepare for droughts or floods (Adams et al. 2003; Letson et al. 2005; Hoffmann et al. 2020; Potgieter et al. 2022).
In conclusion, our results emphasize the influences of CCEWs on rainfall over the off-equatorial region and may provide sources of variability. This study also provides the importance of the lead–lag relationship between horizontal moisture advection, convection, and rainfall, which can be used as a precursor for wave–rainfall impacts. The understanding of the impact of CCEWs on extreme rainfall in Australia would not only improve the knowledge of the impact of various modes of intraseasonal variability but also serve as a basis for understanding the source of bias in extreme rainfall events in the S2S forecast models.
Acknowledgments.
This work was funded by the Melbourne Research Scholarship from the University of Melbourne and the Australian Research Council-Centre of Excellence for Climate Extremes (ARC-CLEX, CE170100023). This study was conducted with the assistance and resources from the National Computing Infrastructure (NCI), funded by the Australian Government. Special thanks to Todd Lane, Tim Cowan, and Robyn Schofield for the valuable comments and suggestions throughout the project. We also thank the Weather and Climate Interaction weather research program for their helpful suggestions during the project. Thanks to the CLEX CMS team for the computational support during the project. SL is supported by the Office of Science, U.S. Department of Energy-Biological and Environmental Research, as part of the Regional and Global Climate Model Analysis program area. CV and AK are supported by the ARC Centre of Excellence for the Weather of the 21st Century (CE230100012).
Data availability statement.
The daily precipitation dataset from Australian Gridded Climate Data (AGCD) is from the Australian Bureau of Climatology (https://doi.org/10.4227/166/5a8647d1c23e0). The ERA5 reanalysis data are available on the Copernicus Climate Data Store (https://doi.org/10.24381/cds.adbb2d47 for single-level and https://doi.org/10.24381/cds.bd0915c6 for pressure-levels). The real-time multivariate MJO (RMM) index and tropical cyclone dates are from the Bureau of Meteorology (https://www.bom.gov.au/climate/mjo/ and http://www.bom.gov.au/cyclone/tropical-cyclone-knowledge-centre/databases/). The OLR MJO index (OMI) is from the National Oceanic and Atmospheric Administration (https://psl.noaa.gov/mjo/mjoindex/). The codes are available by request and on the GitHub page (https://github.com/fadhlilmuhammad/CCEWS_analysis).
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