DSS annual snow accumulation is calculated by dating the ice cores drilled at DSS , East Antarctica. The length of this DSS snow accumulation record has been extended to 2035 years, from 2012 CE back to 22 BCE .

In addition, the latest DSS snow accumulation data have been extended to 2015 CE using a recent new ice core (DSS1617). We use the annual layer thickness data from this new core for the period from 1990 to 2015 CE to extend and replace the DSS1213 annual layer thickness data for the period from 1990 to 2012 used in and then calculate the corresponding snow accumulation record using their power law vertical strain rate model. Therefore, the DSS snow accumulation record that we use in this study will be a 2038-year long-term record from 22 BCE to 2015 CE.

The SWWA rainfall station records are monthly records which are obtained from BoM. We initially selected 16 stations, which are as the same as van Ommen and Morgan (). As the instrumental rainfall records for station Avondale Farm (ID 10795; 32.12∘ S, 116.87∘ E) are only available for 51 years (1965–2015), which is substantially shorter than the average record length of the remaining 15 stations (around 118 years), we will not discuss the rainfall records of this station any further. The other 15 stations cover the period from the 1900s to 2019 CE.

To investigate the spatial variability more completely and reconstruct SWWA rainfall, we use AWAP Australian Gridded Climate Data (AGCD) . These AWAP data are gridded data that have a 0.05∘ longitude × 0.05∘ latitude geospatial resolution and an 119-year availability from 1900 to 2018 CE.

The model simulations used for palaeoclimate data–model comparison are from the CSIRO Mk3L climate model. CSIRO Mk3L is a reduced-resolution coupled general circulation model, comprising components that describe the atmosphere, ocean, sea ice and land surface . The model is explicitly designed for studying climate variability and change on millennial timescales. The atmospheric component of CSIRO Mk3L is taken from the CSIRO Mk3 climate model , although with reduced horizontal resolution. Both CSIRO Mk3 and CSIRO Mk3L produce credible simulations of large-scale precipitation, including over Australia . The model is also skilful at capturing the dominant modes of large-scale variability in the Southern Hemisphere – ENSO and SAM – including the teleconnections between these modes and precipitation over Australia .

In this study, we use four ensembles of simulations based on a combination of orbital forcing (O), greenhouse gases (G), solar irradiance (S) and volcanic aerosols (V) . The four ensembles (O, OG, OGS and OGSV) are generated by combining each of these forcings (Table ). Each ensemble contains three members, which differ only in that they are initialised from different years of a pre-industrial control simulation. As the initial states therefore differ, the internal variability will be different between each member, but the responses to external forcings will be consistent.

To compare the CSIRO Mk3L simulations with the SWWA rainfall reconstruction, we use all 12 simulations, 3 for each of the 4 ensembles. The simulations have a geospatial resolution of 5.625∘ longitude × 3.1857∘ latitude. The model has been run globally for 2000 years from 1 to 2000 CE, and the simulations have been published . For nine simulations (three members for each of the O, OG and OGS ensembles), 2000 years of simulation is available covering the period from 1 to 2000 CE. For the three members of ensemble OGSV, 1500 years of data are available covering the period from 501 to 2000 CE. The model simulations consist of monthly mean data.

All of the data that we use in this study, including the stations rainfall, gridded rainfall, DSS record and model simulations, are for the growing season from May to October.

We use one-sample Kolmogorov–Smirnov tests (hereafter KS tests) to assess the normality of the observational data. There is statistically significant evidence that the 15 BoM stations' data (interpreted periods up to 2015 CE), the AWAP gridded data and the DSS snow accumulation data (interpreted the period 1900 to 2015 CE) all fit the normal distribution corresponding to their mean and standard deviation respectively. A visual validation, which consists of comparing the differences between the empirical and normal cumulative distribution functions (CDFs), is presented in Fig. S1 in the Supplement. The 15 BoM stations' data, the AWAP gridded rainfall and the DSS snow accumulation data empirical CDFs approximately fit their corresponded normal CDFs with minimal biases (Fig. S1). With no irregularity between the empirical and normal CDFs, the visual validation for the observational data is consistent with the results of a one-sample KS test. Therefore, we are confident that the data are described by a normal distribution.

Low-pass filtering (or smoothing) the data increases the correlation of the precipitation time series between SWWA and Law Dome . Annual-scale noise arises from site surface processes including local snow deposition variability which is ameliorated by the smoothing. In order to determine the optimal window size for running average smoothing, we test smoothing using windows sizes of 1–10 years on SWWA and DSS data and then calculate the Pearson correlation coefficients. As smoothing reduces the temporal degrees of freedom, we estimate the effective sample sizes (ESS) or temporal degrees of freedom by first calculating the lag-1 autocorrelation for each sample and then applying the following formula: 1ESS=N1-r1r21+r1r2, where N is the sample size, and r1 and r2 are the lag-1 autocorrelation coefficients that correspond to the two samples . Next, we calculate the Student's t statistic using 2tS=rESS-21-r2, where r is the Pearson correlation coefficient, and then compute the corresponding p value. We repeat the above calculations for both the gridded and the station rainfall data matching DSS snow accumulation data. A 6-year window (Fig. S2 in the Supplement) maximises the area of the correlation between AWAP gridded rainfall and DSS snow accumulation data with statistical significance. For the 15 BoM stations' data, the number of the stations to show a statistically significant correlation is maximised by a window size of 5 years (Fig. S2). However, the rainfall changes and the drivers of rainfall attenuation that we are interested in in this study are for the SWWA region, rather than for separate stations. Therefore, for consistency with the AWAP gridded data, we also use a 6-year window for the BoM stations' data

To define a region with a statistically significant correlation between observed (AWAP) and reconstructed (DSS) rainfall over SWWA, we independently calculate the correlation coefficient and test its significance for 110 local government areas (Australian Government, ) in WA (Table S1 in the Supplement). There are nine local government areas smaller than the 0.05∘ longitude × 0.05∘ latitude geospatial resolution of the AWAP data grid. Therefore, we actually calculate and test 101 areas. There are 52 areas that are statistically significant (6-year window, p < 0.05). We combine these 52 areas to define the significant region (Fig. ) over SWWA. For convenience, we name this significant region “MASK”.

The correlation map (Fig. ) shows the correlation coefficients for 6-year smoothed AWAP rainfall and DSS snow accumulation. The map shows that the strongly negatively correlated (r ≤ -0.5) areas are mainly concentrated in the southwestern corner. Areas in the top right show positive correlations with no statistical significance (p > 0.05). MASK covers almost the whole SWWA region apart from some coastal areas in the south. Southern coastal areas show no statistical significance (p > 0.05), which is consistent with the findings of who reported local rainfall on the south coast related to onshore northward flow that weakens the anticorrelation with DSS that prevails across the rest of the region.

In order to quantify the MASK correlation coefficient and evaluate the statistical significance, we multiply the MASK matrix (areas inside the region have a value of one, and areas outside of the region have a value of zero) of the MASK by the AWAP gridded data to generate the MASK rainfall. Hereafter, the SWWA rainfall that we describe is the MASK rainfall for the MASK region, as delineated in Fig. . We then calculate the SWWA rainfall correlation coefficient with DSS and test its statistical significance.

Table  integrates the results of the significance testing and correlations. The SWWA rainfall and DSS snow accumulation show a strong negative significant correlation (p < 0.05). The BoM stations' rainfall data also show consistent results. From the 15 stations tested, there are statistically significant (p < 0.05) correlations with DSS for 4 stations. These four stations are all geographically located in the MASK region (Fig. ), showing the consistent significance of MASK. Five other stations within the region have correlations of a similar magnitude, but these correlations are not significant at the 5 % probability level (Fig. S4 in the Supplement). The squares of the correlation coefficients show that the explained variance is around 30 %–40 %. We note that the tropics and subtropics can also play an important role in driving rainfall changes in SWWA . Nevertheless, using Law Dome accumulation to reconstruct SWWA rainfall focuses on the SAM-related component of the rain-bearing systems, not the tropical or subtropical components. However, our analysis shows that it makes a valuable contribution to our ability to reconstruct past climate and so we construct a linear model for SWWA rainfall and DSS snow accumulation.

The time series and the scatter plot for SWWA rainfall and DSS snow accumulation are shown in Fig. a and b respectively. The data show a generally linear distribution with a negative slope (Fig. b). We use ordinary least squares linear regression to construct a linear model for SWWA rainfall and DSS snow accumulation (for the four BoM stations, see Fig. S3 in the Supplement), and we estimate the 95 % confidence interval (CI) in the gradient and the intercept as 1.96 multiplied by the standard error of the model.

The model is rain = snow ⋅ (-0.389 ± 0.114) + 672 ± 82 mmyr-1 in the growing season for the period from 1900 to 2015 CE. The gradient interval [-0.503, -0.274] is always negative, which is consistent with the result from the Pearson correlation test: the coefficient is negative and statistically significant (p < 0.05).

Figure c is a histogram of the raw residuals using probability density function scaling. Residuals broadly follow a normal distribution. Figure d is a scatter plot of fitted rainfall data and residuals. The distribution of residuals has no obvious regularity or trend and is generally symmetric along y=0. Furthermore, we assess the robustness of the model in Sect. S5 in the Supplement. We calculate the autocorrelation length (where the autocorrelation coefficient is equal to or below zero) of the SWWA rainfall for the period from 1900 to 2015 CE and perform a jackknife (modified) analysis. The correlation coefficients of each individual jackknife ensemble member are all consistent with the period from 1900 to 2015 CE (Table S4 in the Supplement), and the 95 % confidence intervals for the gradient and intercept overlap (Table S4), showing the statistical indistinguishability between each individual jackknife ensemble member. Taken together, there is no obvious evidence to reject the linear model. Thus, we use this linear model and the time series of DSS snow accumulation to reconstruct SWWA rainfall from 2015 CE back to 22 BCE.

The cumulative summation (CUSUM) technique has been used to investigate rainfall data . CUSUM is a method to sum the data anomalies using 3yp=∑k=1pxk′, where x′ is the anomaly relative to the mean of the whole series . The aim of CUSUM is to identify the step change in a time series by continuously accumulating anomalies. A step in the original data would be identified by the change in the gradient of the CUSUM data.

Numerical integration enhances the signal-to-noise ratio. Using the CUSUM data to both pick the break point (and evaluate its significance) and estimate the timing uncertainty potentially offers advantages compared with using the original data, especially at lower signal-to-noise ratios.

To specifically determine the break point and evaluate its significance, we use the BREAKFIT analysis software on the CUSUM data.

In light of the different spatial resolutions of the model simulations and AWAP gridded rainfall, we perform an interpolation so that model simulations are the same geospatial resolution as the AWAP gridded rainfall; we then multiply the MASK matrix by the interpolated model simulations to consistently capture the same region.

The rainfall reconstruction of SWWA back to 22 BCE is carried out using the linear model over MASK region, where the AWAP gridded rainfall and the DSS snow accumulation data are statistically significantly correlated. The rainfall simulation is the precipitation simulation of the CSIRO Mk3L model, run as four ensembles combining four climate forcings (Table ). We use the CUSUM analysis to compare the simulation of each ensemble and three members of CONTROL (a pre-industrial control simulation; ) to the rainfall reconstruction. Also, as each ensemble member represents the different randomly initialised weather states, we compare the mean of each ensemble member to the rainfall reconstruction to estimate the uncertainties in the simulated rainfall.

To statistically compare the rainfall reconstruction with the model simulations and test the differences, we use Welch's t test to calculate the adapted t statistics using 4tW=x1¯-x2¯s12n1+s22n2, where x1¯ and x2¯, s12 and s22, and n1 and n2 are sample mean values, standard deviations and sample sizes for two samples respectively. We also estimate the adapted degrees of freedom (DFs) using the Welch–Satterthwaite equation: 5DFs=s12n1+s22n22s14n12(n1-1)+s24n22(n2-1).

Taken together, we calculate the p value using t statistics and DFs.

To evaluate the specific time period that we are interested in, for example, the rainfall before and after 1850 CE, we calculate the root-mean-square error (RMSE) between reconstructions and model simulations, and also calculate the Pearson correlation coefficients, ESS (Eq. ), and the Student's t statistic (Eq. ) and its adjusted p value.

Figure a shows the reconstructed SWWA rainfall time series for the growing season (May to October) from 22 BCE to 2015 CE. We further validate the rainfall reconstruction in Sect. S5 in the Supplement. We have found that the temporal stability of large-scale circulation over the mid-latitude Australasian and higher-latitude Law Dome regions is consistent, which is indicated by the correlation fields between Law Dome precipitation and mean sea level pressure in each member of the CSIRO Mk3L OGSV ensemble (Fig. S5 in the Supplement). This rainfall reconstruction has shown that it is possible to use ice cores to investigate the longer-term context of rainfall variability over SWWA prior to the instrumental era. We should also be aware that the Law Dome–SWWA precipitation correlation is stronger during periods of enhanced (stronger/more frequent) meridional circulation, whereas it is weaker during periods of weaker meridional circulation . Thus, the robustness of the reconstruction may be reduced during periods of reduced meridional flow between southern Australia and Law Dome (Sect. S5 in the Supplement). Furthermore, the CSIRO Mk3L simulations exhibit variability in the correlation between Law Dome accumulation and SWWA precipitation on decadal to centennial timescales (Fig. S6 in the Supplement). Therefore, some caution is needed when interpreting the reconstruction. We choose 1850 CE to be the year that separates before and after the Industrial Revolution, consistent with other studies e.g..

Next, we assess whether the growing season rainfall in SWWA before and after 1850 CE belongs to the same distribution. We divide the rainfall reconstruction into two periods: 22 BCE to 1849 CE and 1851 to 2015 CE. We plot the empirical distribution function (Fig. a) and probability density function scaling histogram (Fig. b) for each sample as well as its corresponding normal distribution (black dashed line) with the same mean and standard deviation.

The distribution functions (Fig. ) for the period from 1851 to 2015 CE are shifted left relative to the period from 22 BCE to 1849 CE, indicating that rainfall has decreased after 1850 CE. To quantify the rainfall reduction and test its statistical significance, we perform a two-sample KS test on the two samples and independently conduct a Welch's t test to validate the two-sample KS non-parametric test results.

Results from the two-sample KS test reject (p < 0.01) the null hypothesis that the samples are from same continuous distribution. Independently, the Welch's t test also allows us to reject (p < 0.01) the null hypothesis that the means are equal.

The mean of the growing season rainfall reconstruction for 1851 to 2015 CE is 398 mmyr-1, which is around 98 % of the rainfall mean from 22 BCE to 1849 CE (405 mmyr-1). The attenuation of the rainfall before and after 1850 CE is statistically significant, but the degree is around 2 %. The 1851–2015 CE sample is missing the higher end of the distribution (i.e. there are no years with rainfall greater than 440 mmyr-1), and this lack of recharging events might have more of an impact than the shift in the mean e.g.. Moreover, the 1851–2015 CE sample has a lower low end of the distribution than the 22 BCE–1849 CE sample, indicating more prevalent dry years. This suggests the possibility of an anthropogenic influence on the hydroclimate of this region.

The time series of the rainfall reconstruction indicates that another rainfall attenuation event may have occurred after 1850 CE, around the late 20th century (Fig. a, b). In order to accurately determine the changes in rainfall after 1850 CE, we calculate the CUSUM time series (Eq. ) for the rainfall time series (Fig. a) and use BREAKFIT analysis to identify any significant changes in the gradient. As CUSUM continuously accumulates anomalies in the rainfall reconstruction along the timeline, the variability in the rainfall becomes clearly visually observable (Fig. b). The sign and magnitude of the gradient of the CUSUM plot indicate rainfall anomalies: a positive (negative) gradient indicates a positive (negative) anomaly corresponding to a rainfall increase (decrease) event. The larger the magnitude, the higher the degree of the event. For consistency with the duration of the simulated rainfall, which is available from 501 to 2000 CE, we take the rainfall reconstruction for the same period to calculate the CUSUM time series and conduct BREAKFIT analysis.

Figure  shows the rainfall reconstruction CUSUM time series from 1850 to 2000 CE. Results from BREAKFIT show that the break point is at 1971 CE ± 7 years (95 % CI). The gradients for the intervals [1850, 1971] CE and [1971, 2000] CE are -1.4 mmyr-1 [-3.2, -0.4] and -37.16 mmyr-1 [-45.9, -28.8] respectively. Thus, the break in the gradient at 1971 is statistically significant.

We test the findings of break-point analysis on the CUSUM time series by analysis of the original data. Breaking the rainfall into two samples, we found a shift of the distribution to lower rainfall after 1971 CE in both the empirical distribution function (Fig. a) and the probability density function scaling histogram (Fig. b). The shift is around 30 mmyr-1, showing a nearly 8 % attenuation after 1971 CE, more than 4 times the reduction from 1850 CE. Two further statistical tests were preformed to verify this finding.

Results from the two-sample KS test allow us to reject the null hypothesis (p < 0.01) that the samples are from the same continuous distribution. Independently, it is statistically significant (p < 0.01) that the result from the Welch's t test can also allow us to reject the null hypothesis that the two samples have equal means. The mean rainfall during the period from 1972 to 2000 CE is 373 mmyr-1, which is 92 % of the mean rainfall during the period from 1850 to 1970 CE (406 mmyr-1). This change is more than 4 times bigger than the change around 1850 CE. Not only is there a large reduction in the mean rainfall, but the 1972 to 2000 CE sample's distribution has also largely shifted to lower values compared with 1850 to 1970 CE. There are no years with rainfall over 410 mmyr-1, and nearly half of the years have rainfall of less than 375 mmyr-1 in the 1972 to 2000 CE sample (Fig. b). This likely has a larger impact on agriculture than the rainfall shift before and after 1850 CE.

Results from the two individual statistical tests are very consistent with the BREAKFIT analysis results on the CUSUM time series which indicate that 1971 CE marks the change in gradients from 1850 to 2000 CE. Comparison of Fig.  with Fig.  reveals that the shift in the rainfall distribution at around 1971 CE was much more pronounced than the shift at around 1850 CE. The reduction in the mean rainfall at around 1971 CE resulted in a prolonged drought in SWWA. This drought continued during the 2015–2020 CE period (Fig. S7 in the Supplement). To highlight dry epochs of an equivalent duration to the observed drought to date, we calculate the 45-year running change in the CUSUM time series (Fig. c). Over the 45 years from 1971 to 2015 CE, this prolonged drought is expressed by an integrated rainfall reduction of more than 1000 mm (Fig. c). We note there are two comparable prior epochs during the past two millennia: from around 385 to 429 CE and from around 732 to 776 CE (Fig. c).

Consistent with the analysis applied to the rainfall reconstruction, we analyse the simulated rainfall from CONTROL and the four forced ensembles. We divide the simulated time series for each simulation into two samples: 501–1849 CE and 1851–2000 CE. We further divide the industrial period into samples before and after the observed shift in 1971 CE. We then independently perform the two-sample KS test and the Welch's t test. We also use two different metrics to assess the degree of agreement between the CUSUM time series for the various model simulations and the reconstruction: the differences in the slope and the root-mean-square error (RMSE).

Summary statistics for the model simulations are shown in Table S5 in the Supplement. The model can be seen to have a dry bias, but the simulated internal variability is of a similar magnitude (∼ 80 %) to the reconstruction. The simulated rainfall for each individual ensemble member is shown in Fig. S8 in the Supplement, with the corresponding CUSUM time series shown in Fig. S9 in the Supplement. Within each forced ensemble, there are considerable differences between the CUSUM time series for individual ensemble members. This highlights the role of unforced internal variability in driving SWWA rainfall, consistent with the findings of .

A number of prolonged droughts that approach the magnitude of the current integrated rainfall deficit are apparent in the reconstruction (Fig. c), as discussed in Sect. . These prior drought epochs occurred during the pre-industrial era, suggesting that they may have arisen through natural climate variability or natural forcings such as volcanoes. To explore this within the model simulations, the 45-year changes in the CUSUM time series for the pre-industrial control simulation are shown in Fig. S10 in the Supplement. A number of prolonged droughts are also apparent in all three ensemble members, for example, from 589 to 633 CE in Control1 (Fig. S10b). This supports the hypothesis that prolonged droughts of a similar magnitude to the currently observed drought can arise through natural climate variability or natural forcings.