The Link Between the Madden‐Julian Oscillation and Rainfall Trends in Northwest Australia

Rainfall during the monsoon in northwest Australia has increased since the 1950s. Previous studies have explored possible causes of the rainfall increase; however, the trend has not been fully explained. Understanding the cause of this trend is important for interpreting climate projections and local water‐sensitive services. We explore the role of the Madden‐Julian Oscillation (MJO) in explaining the rainfall increase. The MJO, since 1974, has had a longer duration in phases associated with enhanced rainfall in northwest Australia (Phases 5 and 6) during the monsoon. We show that the rainfall trend in northwest Australia is identified only during MJO phases associated with enhanced rainfall, with a large change in daily rainfall distribution in these phases. The increasing occurrence of these MJO phases explains most of the rainfall increase, as opposed to an increase in daily rainfall independent of MJO phase, albeit with some sensitivity to MJO definition.

models have found simulations with all atmospheric forcing present, including aerosols, better capture the observed rainfall trend in northwest Australia . These findings suggest that the cause of the north-west rainfall trend may be related to increasing atmospheric aerosols. However, not all of the increasing rainfall trend was able to be explained by atmospheric aerosols -suggesting there may be other factors that may have caused the increasing rainfall trend .
Rainfall trends elsewhere in Australia have been proposed to be caused by changes in climate modes of variability, so such an effect should be considered as a possible mechanism behind the rainfall increase in northwest Australia. Cai et al. (2010) suggested a breakdown in the relationship of ENSO with Australian rainfall may be causing a decrease in rainfall in eastern Australia. However, large decadal-scale variability and model deficiencies in the simulation of ENSO and its relationship to Australian rainfall suggest difficulty in extracting a clear anthropogenic signal (King et al., 2015;Taschetto et al., 2014). Additionally, the effect of ENSO on rainfall in northwest Australia is relatively minor compared to eastern Australia (Risbey et al., 2009;Sharmila & Hendon, 2020) and thus, is not likely to have caused the northwest Australia rainfall trend . In the southwest of Australia, the decrease in rainfall that has been observed here may be due to changes in Southern Annular Mode (SAM). In recent decades SAM has been occurring more frequently in its positive phase (Arblaster & Meehl, 2006;Fogt & Marshall, 2020) which is associated with drier conditions during June, July and August in southwest Australia (Cai & Cowan, 2006;Cai et al., 2003). This is believed to be due to human-caused climate change (Delworth & Zeng, 2014). SAM has teleconnections in tropical Australia, however, they are minor compared to those of other climate drivers (Risbey et al., 2009), and are unlikely to have played a major role in the increasing rainfall trend in the northwest. Other sources of variability that influence northwest Australia are the Indian Ocean Dipole (IOD) and the MJO (Madden-Julian Oscillation). The IOD has strong teleconnections to northwest Australia, but the teleconnections are strongest in June to October-out of phase with northwest Australian monsoon season (Risbey et al., 2009), and thus also unlikely to explain the rainfall trend.
In contrast to other modes of variability, the MJO has a significant impact in northwest Australia. During the monsoon period the MJO is a key source of thermodynamic-dynamic variability in the tropics, influencing both the large-scale circulation and rainfall (Madden & Julian, 1971, 1972. The MJO manifests as a couplet of anomalously dry and rainy conditions that travels eastward across the tropical Indo-Pacific region. Around 55% of the weather variability in the tropics can be explained by the MJO (Kessler, 2001). A typical cycle of the MJO starts in the warm waters of the Indian Ocean and propagates eastward in the tropics, bringing rainfall and moist westerly winds to northern Australia. Upon reaching the cooler waters of the eastern Pacific, the convective signature of the MJO decays. This journey lasts about 30-90 days (∼5 m/s phase speed) and covers a zonal distance of approximately 12,000 to 20,000 km. During that journey, the MJO has important impacts on northern Australia (Risbey et al., 2009;Wheeler & Hendon, 2004;Wheeler et al., 2009). The MJO influence is so large in northern Australia, that the probability of heavy weekly rainfall (greater than the 80th percentile) is three times greater when the MJO enhances convection compared to when it suppresses convection (Wheeler & Hendon, 2004).
The cycle of the MJO has been found to be modified by the expansion of the Indo-Pacific warm pool -the largest body of permanently warm sea surface temperatures (SST > 28˚C). This expansion of the warm pool is likely due to climate change (Fan et al., 2016;Weller et al., 2016). Due to the warm pool expansions, from 1981 to 2018, the MJO active phases were discovered to be occurring less over the Indian Ocean by three to four days, and more over the Maritime Continent by five to six days each cycle. The overall length of a full cycle is found to stay approximately constant. This modified cycle has resulted in increased rainfall anomalies in many regions including northern Australia (Roxy et al., 2019). This paper aims to expand on these results by exploring the relationship between the MJO and the increasing rainfall in northwest Australia. To do this, we use gridded rainfall observational datasets and apply several statistical methods to explore the possibility of the MJO being related to the increasing rainfall trend in northwest Australia. Due to data limitations, as the MJO is typically studied using data derived from satellites, the timeframe of this study is restricted to 1974 onwards.

Rainfall Observations
The Australian Water Availability Project (AWAP) data set has been used in this study for rainfall observations. AWAP uses splining to interpolate in situ Bureau of Meteorology rainfall observations from weather stations on . Stippling shows trends significant at the 5% level using the Mann-Kendall test, hatched region denotes poor data quality. The boxed region is the northwest Australia region (10°S to 25°S latitude and 110°E to 135°E longitude) where the rainfall trend is primarily occurring. The trend in the number of days each monsoon the MJO is in the enhanced phases (RMM Phases 5 and 6 and RMM amplitude greater than 1) (c). The trend is significant at the 5% level using the Mann-Kendall test. Data is for 46 monsoons for the years 1974/75 to 2019/2020. to a grid (Jones et al., 2009). AWAP is available from 1900 to the present, on a 0.05° × 0.05° latitude × longitude grid across Australia. We have re-gridded AWAP to 0.25° × 0.25° resolution using a conservative re-gridding method. This was done as there are few stations in northwest Australia and the original resolution would have had too many grid cells without a station.

MJO Index
In this study, the real-time MJO Multi-variate Index (RMM) has been used (Wheeler & Hendon, 2004) to classify the MJO phase. The RMM index is calculated by applying Empirical Orthogonal Functions (EOFs) to outgoing longwave radiation (OLR) and wind fields in the lower and upper troposphere (850 and 200 hPa heights) from the NCEP-NCAR reanalysis (Kalnay et al., 1996). The EOF analysis of the fields returns two principal components, RMM1 and RMM2. The amplitude of an MJO event is defined as √ RMM1 2 + RMM2 2 . Amplitudes less than one represent inactive MJO events, and when the amplitude is greater than one, the MJO is active. Active MJO events are further divided into eight phases depending on the location of the enhanced tropical convection between the Western Indian Ocean (Phase 1) and the Eastern Pacific (Phase 8).
To increase sample sizes, the eight active phases of the MJO have been combined into phases that have similar rainfall responses in northwest Australia. Phases 5 and 6, which are associated with increased rainfall probabilities in northern Australia during the monsoon, have been combined into one enhanced rainfall phase (Figures S2e,S2f,and S3 in Supporting Information S1). Similarly, phases 1, 2 and 3 are combined into one suppressed rainfall phase, as these phases cause reduced rainfall anomalies (Figures S2a-S2c in Supporting Information S1). The remaining phases, 4, 7 and 8, have no clear rainfall response in the north and are called the transition phases ( Figures S2d, S2g, and S2h in Supporting Information S1). Thus, we have four combined MJO phases: enhanced, suppressed, transition and inactive phase. The names of each of these phases represent the impact of the grouped RMM phases on rainfall in northern Australia, and not the change in the behavior of the MJO itself. The rainfall anomalies for each of the four phases can be seen in Figure S4 in Supporting Information S1, and the correlation of the number of days in each phase with the rainfall in northern Australia in Figure S5 in Supporting Information S1. Henceforth, the phases will be known as the combined phases, and the original phases from Wheeler and Hendon (2004) will be referred to as the RMM phases.
RMM Phases 5 and 6, which together represent the combined enhanced phase, have been found to be occurring for longer durations during the Australian monsoon ( Figure 1c) (Roxy et al., 2019;Yoo et al., 2011). Between the years of 2000-2018, the duration of the MJO during RMM Phases 5, 6, and 7 was found to increase by 5-6 days per cycle compared to the 1981 to 1999 period. This has been suggested to be due to a doubling of the size of the Indo-Pacific warm pool (Roxy et al., 2019), due to climate change (Fan et al., 2016;Weller et al., 2016). However, it has also been suggested by Lyu et al. (2019) that this trend may be due to blended low-frequency variability signals. Lyu et al. (2019) have proposed several other MJO indices as alternatives to the RMM that contain trends of varying significance. However, the RMM is still by far the most widely used and well-understood index for measuring the development and propagation of the MJO, so will be used in this study.
Calculations of the RMM index are restricted to 1974 onwards-the OLR is only estimated to reasonable accuracy using satellite-era data, which began in 1974. To extend the RMM further back in time, Oliver and Thompson (2012) have created a reconstruction of the RMM using data from twelve weather stations. While the RMM components have been found to correlate strongly, the increasing trends found in several MJO phases are not found to exist in the corresponding Oliver and Thompson (2012) phases (Figures S6 and S7 in Supporting Information S1). Thus, as the trends are not present in this version of the index, it is likely there will be no relationship with the increasing rainfall trend in northwest Australia.

Methods
A total of 46 monsoons (1974/75 to 2019/2020) were used due to the availability of the RMM index. We have defined the monsoon as December to March (Wheeler & McBride, 2012). The study area for the northwest rainfall trend comprises a region of 10°S to 25°S latitude and 110°E to 135°E longitude (Dey, Lewis, Arblaster, & Abram, 2019;Shi et al., 2008). For the analysis, we initially explored the trend in two different rainfall indices: the total amount of rainfall and the number of rain days. Only days where the rainfall is greater than 1 mm are used, due to the under-reporting of small rainfall events (see Haylock & Nicholls, 2000). We then applied several different statistical methods to relate the MJO to the increasing rainfall trend.
First, we calculated the linear trend for the two rainfall indices each monsoon and each MJO combined phase. We then converted the gradient of the trend to percent per decade, by dividing by the mean of all values for a grid cell. Trends were represented as percent per decade to show the trend in relation to the climatological rainfall of the location. This was done so that trends are irrespective of the climatological rainfall. Next, to examine if these trends were related to a change in the number of days in a combined phase or a change in the intensity of rainfall, the trends were recalculated for indices divided by the number of days in the respective combined phase. Thus, these indices are the fraction of days that have rainfall and the rainfall per day. It is important to consider if these trends are significant compared to natural variability especially in northern Australia, where there is high inter-annual variability in rainfall (Nicholls et al., 1997). To assess if these trends are significant compared to natural variability, the nonparametric Mann-Kendall test was used, where significance is assessed at the 5% significance level. For more details on the Mann-Kendall test see Appendix A.
Another useful tool for analysis was to create probability density functions (PDFs) of the rainfall indices calculated for each monsoon. A distribution was created for the first and second half of the data (01-December-1974 to 31-March-1997 and 01-December-1997 to 31-March-2020 respectively) and for all grid points in the northwest region. The two PDFs, which each encompassed 23 monsoons, were used to analyse how the distribution of monsoon rainfall has changed over time in each combined phase of the MJO.

Results
In the enhanced phases, the number of rain days and the total amount of rainfall (Figure 2a and 2c), show large statistically significant increases. In many locations, the number of rain days has increased by 5%-20% per decade, and the total amount of rainfall has increased by 15%-25% per decade. The raw value of this trend is greatest around coastal regions (where the climatological rainfall is greatest), not just in the northwest, but right across all of northern Australia (Figures S8a and S8b in Supporting Information S1). The significance of the increase in rainfall in the enhanced phases is also supported by a bootstrapping method that shows over 99% of the trends in the total number of rain days and rainfall are positive when picking random data (with replacement) (Text S2 and Figure S3 in Supporting Information S1). The trend in the total rainfall in the enhanced phases ( Figure S8a in Supporting Information S1) is also of similar magnitude and spatial pattern compared to the overall trend (Figure S1c in Supporting Information S1)-suggesting the rainfall increase during the enhanced phases is linked to the overall rainfall increases in northwest Australia.
The change in enhanced phase rainfall can also be seen when comparing distributions of the two rainfall indices in the enhanced phase of each monsoon between the two periods 1997/1998 to 2019/2020 and 1974/1975 to 1996/1997 (Figures 2b and 2d). The distributions show a shift to more grid cells having more rainfall and more rain days. This change is particularly evident for the number of rain days, where the distribution has shifted to substantially more rain days at grid cells each monsoon. For example, the number of grid cells having 15 rain days in the enhanced phases each monsoon has doubled in the later period. This change is not as substantial for the total rainfall each monsoon, with increases in the later period mostly seen in the extremes of the distribution. For example, the number of grid boxes having 300 mm of rainfall in a monsoon has almost doubled in occurrence (500 in the first period and 1000 in the second period).
In the transition and suppressed phases, there are also statistically significant increases in the number of rain days and the amount of rainfall (Figures S8 and S10 in Supporting Information S1). However, the rainfall increases are not as large and widespread compared to those in the enhanced phases. Additionally, when looking at this trend in millimeters per decade ( Figure S8 in Supporting Information S1), the magnitude is very small compared to the trends in the enhanced phases and the overall trend ( Figure S1 in Supporting Information S1) (the overall trend in rainfall is between 15 and 60 mm per decade, whilst in the suppressed phases it is only at mostly less than 10 mm per decade), and thus the relative contribution of the increased rainfall during the suppressed phases to the overall increasing rainfall trend in minimal. This is also demonstrated by the almost identical distributions of the rainfall indices for the two periods 1974/1975to 1996/1997and 1997/1998 in Supporting Information S1). Rainfall trends during suppressed and transition MJO combined phases may be related to changes in rain due to other weather systems, such as TCs (Lavender & Abbs, 2013), as the transition phases are the RMM phases that are associated with the MJO having little impact on northwest Australian rainfall. The trend in the monsoon number of rain days (a) and monsoon rainfall (mm) (c) in percent per decade for the MJO enhanced phases. Stippling shows trends significant at the 5% level using the Mann-Kendall test. The boxed region is the northwest Australia region (10°S to 25°S latitude and 110°E to 135°E longitude) where the rainfall trend is primarily occurring, and the hatched region denotes poor data quality. The figure also shows distributions of monsoon rain days (b) and monsoon rainfall (mm) (d) for 1974/1975 to 1996/1997 (brown) and 1997/1998 to 2019/2020 (green) for all grid cells in the northwest Australia region.
In the inactive phase there is a decrease in the number of rain days and the total amount of rainfall each monsoon ( Figures S8, S10, and S11 in Supporting Information S1). The decreasing trend is only statistically significant for the number of rain days each monsoon. This suggests that there is a decrease in non-MJO related rainfall. Less rainfall in the inactive phase may also explain why the rainfall trends are stronger and more statistically significant in the enhanced phases than the overall rainfall trend (Figure 1).
The above results demonstrate the northwest Australian increasing rainfall trend is related to the MJO, as the trend only occurs when the convective center of the MJO is over or near northwest Australia (RMM Phases 5 and 6). However, the trend could arise due to the increasing number of days in the enhanced phases or an increase in the intensity of daily rainfall associated with the MJO, or both. To explore this, the rainfall and number of rain days occurring during the enhanced phases were normalized by the number of days in the enhanced phases for each monsoon (now rainfall per day and the number of rain days per monsoon). Trends were then calculated for these two new indices (see Figures S12 and S13 in Supporting Information S1 for all MJO combined phases). For the enhanced phases (Figures 3a and 3c) there are no strong or statistically significant increases for both the frac tion of days as rain days and the rainfall per day in each monsoon. The distributions of both of these indices are also approximately the same ( Figure S14 in Supporting Information S1). Thus, the northwest Australia rainfall trend appears to be mostly due to an increase in the number of days in the enhanced phases rather than an increase in the intensity of daily rainfall in the enhanced phases. This is also supported by examining trends in the mean intensity of rainfall events at each grid location, where the trends vary between increasing and decreasing, with few statistically significant points ( Figure S15 in Supporting Information S1).
Trends in the suppressed phases for the fraction of days that are rain days, rainfall per day (Figures S12 and S13 in Supporting Information S1), and rainfall per rain day ( Figure S15 in Supporting Information S1) indices are statistically significant across a wide area-particularly for the rainfall per day index. Thus, it appears there has been a small increase in the number of rain days and the intensity of rainfall in the suppressed phases. However, the raw values for the trend in the suppressed phases are small compared to the overall inter-monsoon trend for these indices ( Figure S1 in Supporting Information S1).

Discussion and Conclusion
This study has found that the increased duration of the MJO in RMM phases 5 and 6 appears to have made a large contribution to the increasing rainfall trend in northwest Australia. The increasing rainfall trend was found to only occur in the enhanced phases (RMM phases 5 and 6) suggesting that there has been an increase in the amount of MJO-associated monsoon rainfall. There was a large increase in grid cells experiencing more monsoon rain days and monsoon rainfall in the enhanced phases (see Figure S16 in Supporting Information S1 for enhanced phase definition sensitivity test). The increase in the intensity of rainfall events associated with the MJO was found to contribute little to the increasing rainfall trend. This suggests that the changing MJO may be the main driver of the increasing rainfall trend in northwest Australia. Additionally, there was a small increase in the number of rain days and the total rainfall in the suppressed phases, but the values of these trends are small compared to the trends in the enhanced phases, so this does not explain as much of the increasing rainfall trend. We note here that we find small increases in the number of rain days and the total rainfall during the suppressed phases, but the absolute values of these increases are small and, hence, cannot explain the observed rainfall trend in NW Australia. Finally, we find a decreasing rainfall trend during an inactive MJO.
The rainfall trends in northwest Australia used in this study (Figures 1a and 1b, and Figure S1 in Supporting Information S1) are not as statistically significant as those found in other studies (Alexander et al., 2007;Shi et al., 2008). Other studies have been able to extend the rainfall records back to the 1950s, but, in this study, as the RMM requires satellite data to be calculated, rainfall records have only been used since 1974.
The changes in the occurrence of MJO in different phases has been found to be linked to an increase in the size of the Indo-Pacific warm pool, which in turn is associated with climate change. To directly link human-caused climate change to the increasing rainfall trend in northwest Australia would require a comprehensive modeling study to assess how anthropogenic climate change has affected the MJO, and teleconnections to northwest Australia rainfall. However, current climate models typically do not simulate the MJO well (Ahn et al., 2017;Chen et al., 2022), with even the latest generation of models (CMIP6) significantly underestimating the intra-seasonal Figure 3. The trend in the number of rain days (a) and rainfall amount (b) normalized by the number of MJO enhanced-phase days during each monsoon season. The monsoon is defined as December to March. Stippling shows trends significant at the 5% level using the Mann-Kendall test. The boxed region is the northwest Australia region (25°S to 10°S latitude and 110°E to 135°E longitude). variability caused by the MJO (Le et al., 2021) and MJO events weakening too much over the maritime continent (Hsu & Lee, 2005;Zhang & Ling, 2017). Low-fidelity MJO simulations may help to explain why climate models forced only with greenhouse gases don't simulate strong increasing rainfall in northwest Australia . Model deficiencies in MJO simulation and teleconnections are also likely related to the uncertainty in model projections of rainfall trends in this region Weller et al., 2016).  found the increase in rainfall was only present in climate model simulations where all forcings are present-and not just greenhouse gases-suggesting that the rainfall trend in northwest Australia is related to changes in atmospheric aerosols. However, there is uncertainty in these results, in part due to the large diversity of aerosol effects in climate models (Grose et al., 2020). Additionally,  found that the aerosols do not entirely explain the increasing rainfall trend, and perhaps could be explained by the increased occurrence of the MJO in phases associated with enhanced phases.
There is uncertainty in MJO changes as there appears to be some dependence on index selection. Lyu et al. (2019) suggest the trends in RMM Phases 4, 5, and 6 may be exaggerated due to blended low-frequency variability signals that exist within the RMM. Lyu et al. (2019) propose several new indices that can be used to measure the RMM, that do not suffer from this issue. Each of these new indices has a different trend associated with it (RMM Phases 4, 5 and 6 when combined using the different methods have trends of 0.16, 0.24, and 0.41 days per year), and could potentially have different relationships with the rainfall trend in northwest Australia. Another MJO index that could have been used for this study is the Oliver and Thompson (2012) reconstruction of the RMM. This version of the RMM was found to not include trends in the RMM phases and would have likely also given different results. This suggests a need for a comprehensive exploration of how the different RMM constructions (Oliver & Thompson, 2012;Wheeler & Hendon, 2004) and indices from Lyu et al. (2019), are capturing the propagation and development of the MJO. By using the Wheeler and Hendon (2004) index, we have focused on the most widely used and understood MJO index, but acknowledge that a comprehensive analysis in future may be helpful.

Appendix A: Mann-Kendall Test
The Mann-Kendall test is a widely used test to determine if there is a significant trend in a time series x1, x2, …, xn (Gilbert, 1987, p. 208). The benefits of this test are that it is non-parametric -it requires no assumption about the shape of the trend. For this test, an S-value is first calculated by summing the sign of the difference between every point in a time series with every future in a time series: This method allows for a trend to be detected, without defining the characteristics of the trend. From the S-value, the variance statistic is then computed. The Mann-Kendall-statistic (Z MK ) can now be calculated with the formula: The Z MK value can then be used to calculate the p-value, and thus the statistical significance of the trend can be determined.