It is well understood that Australian climate is affected by natural climate variability such as El Niño–Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD), and the Southern Annular Mode (SAM), depending on seasons and regions. However, studies on Australian climate extremes associated with natural climate variability remain limited. This study examines the observed impact of natural climate variability on inter-annual changes in seasonal extremes of rainfall and temperature over Australia during 1957–2010. We use non-stationary Generalized Extreme Value (GEV) analysis, where GEV parameters are specified as a linear function of modes of climate variability, and compare results with the case when climate variability is not considered. Results from two station-based observational data sets consistently suggest that extreme responses overall resemble mean responses to climate variability. Anomalously drier and hotter conditions occur over northeastern Australia and the southern coast during El Niño and a positive phase of the IOD in the cold seasons, while wetter and cooler conditions are observed during La Niña and a negative phase of IOD. A positive (negative) phase of the SAM brings wetter and cooler (drier and warmer) conditions over much of the eastern continent in summer. Covariation and relative importance of ENSO and the IOD as well as an inverse relationship between rainfall and daily maximum temperature are also found to hold for extremes. This suggests that teleconnection mechanisms responsible for seasonal mean variations may be at work for inter-annual changes in extremes, providing important implications for climate model evaluations and regional climate change projections.
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 Australian climate is significantly influenced by natural climate variability such as the El Niño–Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD), and the Southern Annular Mode (SAM) with different seasonal and regional features. ENSO and IOD are principal modes of climate variability over the tropical Pacific and Indian Ocean, respectively, arising from air-sea interaction [Neelin et al., 1998; Saji et al., 1999]. It is well known that ENSO tends to induce drier and warmer conditions over much of eastern Australia in austral winter and spring during El Niño and wetter and cooler conditions during La Niña [McBride and Nicholls, 1983; Ropelewski and Halpert, 1987; Halpert and Ropelewski, 1992; Power et al., 1998; Watterson, 2009]. On the other hand, the IOD impact is felt mainly by southern Australia with anomalously dry conditions during positive phases and wet conditions during negative phases [Nicholls, 1989; Ashok et al., 2003; Cai et al., 2009]. Recent studies [Meyers et al., 2007; Risbey et al., 2009] suggested that while the direct impact of the Southern Oscillation (SO) is primarily responsible for the northeastern rainfall response, Rossby wave train mechanisms [Hoskins and Karoly, 1981] emanating from the eastern Indian Ocean largely explain the southeast rainfall response [Saji and Yamagata, 2003; Cai et al., 2009, 2011a]. Further, Cai et al. [2011a] showed that ENSO's impact on southeast Australia is conducted through the Indian Ocean by forcing convective anomalies in the tropical Indian Ocean. The SAM is a dominant mode of climate variability over the Southern Hemisphere extra-tropics [Thompson and Wallace, 2000], reflecting the wave-driven zonal flow vacillation [Hartmann and Lo, 1998]. The positive phase of SAM is typically associated with wetter and cooler conditions over much of Australia during spring and summer but with drier and cooler conditions over the southwest and southeast coasts of the continent during winter [Gillett et al., 2006; Cai and Cowan, 2006; Hendon et al., 2007; Meneghini et al., 2007; Watterson, 2009; Cai et al., 2011b].
 While seasonal mean responses are well understood, studies on responses of Australian climate extremes to climate variability remain very limited. From global scale analyses using station or station-based data sets, Kenyon and Hegerl [2008, 2010], Alexander et al. , and Arblaster and Alexander  identified a significant influence of ENSO on extreme temperature and precipitation over Australia, bringing warmer and drier extremes during El Niño and cooler and wetter extremes during La Niña, in accord with mean responses. Examining the SAM influence on rainfall and temperature extremes, Hendon et al.  showed that patterns of extreme responses resemble those of the seasonal mean response. Cai et al. [2011b] showed that during the positive phase of the SAM, synoptic extreme weather systems shift poleward.
 Extreme events are characterized by heavy tails of the probabilistic distribution. In order to better diagnose this nature, extreme value theory [Coles, 2001] has been extensively applied in an increasing number of climate studies [Kharin et al., 2005, 2007; Zhang et al., 2010; Katz, 2010; Sillmann et al., 2011]. However, there have been few studies for Australian climate extremes using the extreme value theory, with existing studies rather focusing on statistical modeling and climate model evaluation [Li et al., 2005; Perkins et al., 2009]. Recently, Zhang et al.  applied non-stationary Generalized Extreme Value (GEV) analysis in order to assess the impact of climate variability modes on wintertime precipitation extremes over North America. In this method, climate variability modes are incorporated into GEV modeling as covariates of GEV parameters (see below for details). In order to assess the statistical significance of the influence of climate variability on extremes, one can compare GEV models with and without covariates using an appropriate statistical hypothesis test [Coles, 2001]. Sillmann et al.  applied the same approach to examine the influence of atmospheric blocking on extreme minimum temperatures in Europe. Aryal et al.  used similar methods to examine trends in rainfall extremes over southwest Western Australia.
 In this study, we employ the same non-stationary GEV approach as used in Zhang et al.  and investigate the possible impact of ENSO, the IOD, and the SAM on seasonal extremes of rainfall and temperature over Australia. Daily maximum temperature is analyzed, as it is known to have a closer relationship with rainfall [Power et al., 1998; Jones, 1999] and is also relevant to extreme heat waves that affect Australia more strongly than cold events do. In addition, by comparing with the seasonal mean responses that are based on a simple linear regression and also with patterns reported from previous studies, we attempt to identify responsible physical mechanisms for relationships between climate variability and extremes.
Section 2 describes the indices of climate variability and observational data sets used as well as methods for GEV analysis. Results of response patterns of rainfall and temperature extremes are examined in section 3 for each individual mode of climate variability with comparison to patterns of seasonal mean responses. Covariation and the relative importance of modes of climate variability are also discussed together with sensitivity tests in the same section. Conclusions are provided in section 4.
2 Data and Methods
2.1 Climate Variability
 We consider four Australian seasons as March–May (MAM, autumn), June–August (JJA, winter), September–November (SON, spring), and December–February (DJF, summer). The analysis period covers 54 years from March 1957 to February 2011. For consistency between seasons, we refer to 1957–2010 below as the analysis period such that 1957 DJF indicates December 1957 to February 1958. In order to analyze ENSO, we use the Niño3.4 SST index (referred to as N34), which is defined by area-mean SST anomalies over 5°S-5°N, 170°W-120°W. The IOD is quantified using the dipole mode index (DMI) which describes the difference in SST anomalies between the tropical western Indian Ocean (10°S-10°N, 50°E-70°E) and the tropical southeastern Indian Ocean (10°S-0°, 90°E-110°E) [Saji et al., 1999]. Monthly SST fields are obtained from the Hadley Center Sea Ice and Sea Surface Temperature data set (HadISST) [Rayner et al., 2003]. To analyze the SAM, we use the observation-based index of Marshall , which is defined as the difference in normalized zonal mean sea level pressures between 40°S and 65°S. Seasonal indices of N34, DMI, and SAM are obtained from monthly anomalies relative to 1971–2000 means. Table 1 shows inter-annual standard deviations of these seasonal indices. ENSO shows larger variability in DJF and SON, and the IOD becomes stronger in JJA and SON. In contrast, there is a lack of seasonality in SAM variability. Linear trends during 1957–2010 are also compared in Table 1. Statistically significant trends toward the positive phase are found for the DMI in all seasons except DJF and for the SAM in MAM and DJF. Note that the DMI in MAM and DJF does not describe a dipole, as the IOD normally commences development in June and does not persist into DJF. Thus, the DMI in these two seasons may in part reflect the coherence of the Indian Ocean with ENSO. No significant trends are found for ENSO. Main findings are not affected by the exclusion of linear trends, and results shown below are based on detrended data.
Table 1. Inter-annual Standard Deviations and Linear Trend Slopes of N34, DMI, and SAM Indices During 1957–2010a
Linear Trend Slope
aEstimates of slopes are computed by least squares, and detrended indices are used to calculate standard deviations. Statistically significant trends at 5% and 1% level (from Mann-Kendall test) are marked with * and **, respectively. Units are given in square brackets.
 Modes of climate variability can interact with each other [e.g., Cai et al., 2011c], which needs to be taken into account when interpreting the impacts of climate variability. Table 2 lists correlation coefficients between detrended N34, IOD, and SAM indices for different seasons during 1957–2010. ENSO and the IOD show a positive relationship in JJA and more strongly in SON. During DJF, the SAM has a negative correlation with ENSO, and it has been suggested that the inter-annual variations of the SAM are forced by ENSO [L'Heureux and Thompson, 2006]. Mechanisms for interrelations between climate variability modes are still a point of contention, including which modes lead the others, and requires further investigation. Nevertheless, in order to isolate the impact of each climate variability mode, we remove dependency of one index on another using a simple linear regression. For instance, to remove the DMI influence from N34, N34 is regressed onto the DMI and then the regressed component is removed from the original N34. This gives a residual N34 index which is linearly independent of the DMI, expressed as N34|DMI. The sensitivity of our results is tested to the use of independent indices for the ENSO-IOD relationship during SON and the SAM-ENSO relationship during DJF.
Table 2. Correlation Coefficients Between Detrended N34, DMI, and SAM Indices During 1957–2010a
aStatistically significance at 5% and 1% level is marked with * and ** respectively. Note that a strong DMI-SAM correlation in DJF (in italic font) may partly reflect the N34-SAM relationship, since the IOD does not usually persist into DJF.
2.2 Rainfall and Temperature Observations
 We use seasonal maximum daily precipitation (RX1d) and seasonal maximum daily maximum temperature (TXx) over Australia from two observational gridded data sets. One is the Australian Water Availability Project (AWAP) data set [Jones et al., 2009] which provides daily gridded rainfall and maximum temperature. Original resolution is 0.05° × 0.05°, but we use 0.25° × 0.25° resolution data prepared by the Bureau of Meteorology. Seasonal RX1d and TXx are calculated from daily rainfall and maximum temperature data for the period of 1957–2010. Rainfall extremes from AWAP data are assessed to be suitable for studying inter-annual variability and trends when compared to high-quality station observations, but results might be spurious in data sparse regions [King et al., 2013]. In case of maximum temperature, AWAP daily data (and extremes) may have larger errors near the coast around northwest Australia and about the Nullarbor Plain, where very strong gradients exist between the coast and inland deserts and are difficult to capture with relatively poor data coverage [Jones et al., 2009].
 The other data set is extreme indices based on the Global Historical Climatology Network (GHCNDEX) [Donat et al., 2013]. The gridded extreme indices including RX1d and TXx (2.5° × 2.5° grid) are constructed using all operational stations available through the GHCN, for which only stations with at least 40 years of data are included during 1951–2010. The global spatial coverage of GHCNDEX is poor over some regions, e.g., Africa and South America, due to the limited availability of operational stations. However, Australia has better coverage because of the inclusion of daily weather records obtained from the Australian Bureau of Meteorology. For RX1d, we exclude very dry areas from our GEV analysis, where GEV distribution is likely to be inappropriate (see below), by requiring RX1d climatology to be higher than 10 mm for each season. This partly removes areas of very low station density with less reliability in rainfall extremes [King et al., 2013]. We do not apply any mask for maximum temperature, but note that there are small regions with less reliability as described above.
2.3 Extreme Value Analysis
 We fit the generalized extreme value (GEV) distribution to 54 year samples (x) of extremes (RX1d and TXx) at each grid point. In order to examine the possible influence of climate variability on extremes, we use non-stationary GEV models and compare results with the stationary GEV model following previous studies [Katz et al., 2002; Kharin and Zwiers, 2005; Zhang et al., 2010; Sillmann et al., 2011]. In both cases, the method of maximum likelihood is used to estimate GEV parameters following Kharin and Zwiers . The cumulative density function of GEV distribution is expressed as follows:
where μ, σ, and ξ are location, scale, and shape parameters, respectively. In the stationary GEV analysis, it is assumed that GEV parameters are fixed with time, which we refer to as model M0. In the non-stationary GEV setting, we use climate variability vt (here N34, DMI, or SAM index) which varies with time t as a covariate of the location parameter like
which is referred to as model M1. Here μ0 is the location parameter at time t0, and μ1 is the slope coefficient representing the relationship between climate variability and location parameter. Thus, the location parameter varies with time experiencing the influence of climate variability, which represents shifts of the GEV distribution up and down with time, while its width and shape (scale and shape parameters) remain unchanged.
 In addition to the location parameter, one could set the scale parameter as a function of climate variability, for which log linear regression is usually employed so as to keep the scale parameter always positive, i.e. ln σt = ln σ0 + σ1(vt − v0) where σ0 is the value at time t0 and σ1 is slope coefficient. We find the additional use of a varying scaling parameter has a negligible influence (not shown) when comparing two GEV models using a likelihood ratio test (see below). Similarly, we have found negligible influence of varying shape parameter, which is consistent with previous studies [Kharin and Zwiers, 2005; Zhang et al., 2010; Sillmann et al., 2011]. This indicates that the influence of climate variability on extremes occurs through shifting GEV distributions. All results shown below are from the model M1, with the location parameter varying linearly with covariates.
 To assess the impact of climate variability on extremes, we conduct a likelihood ratio test between M0 and M1 following Kharin and Zwiers . We let the log likelihood of the model M0 and M1 be l0 and l1, respectively. The log likelihood ratio statistic is then D = 2 (l1 − l0), which follows asymptotically a χ2 distribution with q degrees of freedom, where q is given by the difference in the number of free parameters (q = 1 in our case). A significant impact of climate variability is then found at the 5% level if D is larger than the 95% percentile of the χ2 distribution. This is equivalent to rejecting the null hypothesis of a stationary GEV distribution (M0) against a GEV distribution with a varying location parameter (M1).
 In order to evaluate whether the GEV distribution provides a reasonable description of the observed samples of seasonal extremes, we conduct a parametric bootstrap Kolmogorov-Smirnov (K-S) test at each grid point, following Zhang et al. . The null hypothesis that the observed extremes originate from a GEV distribution is rejected at the 10% significance level when the observed K-S statistic (maximum absolute difference between empirical and fitted cumulative distribution functions) exceeds a critical value. The critical value here is determined using 1000 randomly generated samples (90th percentile of K-S statistics). The 10% significance level is used here in order to consider that the power of goodness-of-fit tests is typically low for small sample sizes. At this significance level, we expect the fraction of grids where the null hypothesis is rejected to be about 10% if GEV distribution fits extremes satisfactorily. For the case of the non-stationary GEV distribution, the observed extremes are transformed into standardized variables and the goodness of fit is assessed for a standard Gumbel distribution [Coles, 2001]. Results show that in general, the GEV distribution provides an appropriate fit to seasonal extremes of temperature and precipitation over Australia in either case of a stationary or non-stationary GEV distribution (not shown). This is consistent with previous observational studies [Zhang et al., 2010; Zwiers et al., 2011]. Exceptions occur over very dry areas, particularly over northern Australia in JJA, which is excluded from our analysis below.
3.1 Climatology and Variability Patterns
 Before examining influence of ENSO, IOD, and SAM on Australian extremes, we briefly describe the climatology and variability of rainfall and daily maximum temperature and their extremes. Figure 1 shows spatial patterns of the climatology and inter-annual standard deviation of seasonal mean rainfall (Rmean) and RX1d during 1957–2010. Rmean shows a strong seasonality, with northern Australia and the east coast experiencing most rainfall during summer, while southeastern and southwestern regions receive more rain in winter. A dry climate with Rmean<25 mm is seen over Western-central deserts all year round. The seasonal climate pattern of RX1d(μ0) largely resembles that of Rmean, with μ0>40 mm being evident over northern and east coast during summer and autumn. There are limited areas with μ0>25 mm over the southwest and southeast in winter, suggesting a weak contribution of heavy rainfall to the seasonal mean over these regions. Very dry (white) areas with seasonal mean RX1d < 10 mm are in accord with dry climate areas with Rmean<25mm. Spatial patterns of inter-annual standard deviations of Rmean and RX1d are similar to the climatology patterns, representing larger year-to-year variability over wet regions and less variability over dry regions. Tasmania possesses an east-west dipole pattern for both Rmean and RX1d in terms of climatology and variability.
 Climatology and year-to-year variability of daily maximum temperature are displayed in Figure 2. Seasonal mean maximum temperature (TXmean) shows a typical north warm-south cool pattern over the year except for summer when a large hot area (>36°C) extends over central and northwestern regions inland. Relatively cooler TXmean is apparent over wet areas along the northern and eastern coasts. TXx climatology presents a pattern distinct from TXmean. A north-south gradient is essentially absent except in winter, and rather, hot areas (>36°C) dominate over large parts of the continent, accompanied by relatively cool areas along the northern and eastern coasts. Inter-annual variability of TXmean shows mixed patterns among seasons with standard deviations ranging from 0.4 to 1.6K, with a slight tendency to be higher inland, in part reflecting seasonal differences in the influence of various climate variability modes [Jones, 1999]. Unlike TXmean, TXx is characterized by stronger variability over southern Australia with a peak along the southern coast, which seems most evident during the transition seasons (MAM and SON). This might be related to the variability of wind direction in these seasons [Watterson et al., 2008].
3.2 ENSO Influence
 ENSO has a significant impact on Australian rainfall, increasing the risk of dry conditions during El Niño and wet conditions during La Niña over large parts of Australia during winter and spring [e.g., McBride and Nicholls, 1983; Ropelewski and Halpert, 1987]. Figure 3 shows the spatial pattern of regression coefficients of Rmean and RX1d onto the N34 index using AWAP data. Note that the Rmean response is based on a simple linear regression, while RX1d results are obtained from GEV analysis using N34 as a covariate. RX1d results obtained from using GHCNDEX are displayed together for comparison. Only areas with a statistically significant response at the 5% level are shaded in color. Gray shading represents non-missing data coverage, and dry areas are also illustrated in white (see above). Rmean response patterns show that an inverse N34-rainfall relationship tends to be confined to the northeast portions of Australia in winter, while it is felt by a larger region including southeastern Australia in spring, in good agreement with previous studies [Meyers et al., 2007; Risbey et al., 2009; Cai et al., 2011a].
 The RX1d response to ENSO matches up with the Rmean response, implying weakened (strengthened) extreme precipitation during El Niño (La Niña) over near-tropical eastern Australia in winter and over northeastern and southern Australia in spring. A very similar response of RX1d to ENSO is found when using GHCNDEX data (Figure 3, bottom) as well as when using different analysis periods of 1957–1983 and 1984–2010 (not shown). This suggests that the extreme rainfall response to ENSO is generally consistent with the seasonal mean response [Kenyon and Hegerl, 2010] and that the same teleconnection mechanisms associated with the SO and Rossby wave trains [Cai et al., 2011a] can be used to interpret the extreme rainfall response to ENSO during the cold seasons. Excluding the IOD influence from ENSO removes much of the influence over southern Australia, confirming the finding of Cai et al. [2011a] that much of ENSO's influence is conducted through the IOD (see below for covariation of ENSO and IOD in spring).
 The ENSO influence on temperature is characterized by warmer conditions during El Niño and cooler conditions during La Niña over northern and eastern Australia [Halpert and Ropelewski, 1992], and maximum temperature responses tend to be in a good agreement (negative correlations) with rainfall responses, due to the impact of cloud cover on daily maximum temperature [Power et al., 1998; Jones, 1999; Jones and Trewin, 2000; Gallant and Karoly, 2010]. Figure 4 shows responses of TXmean and TXx to ENSO. The regression pattern of TXmean reveals increased warming (cooling) over a large part of Australia, with a peak slightly inland of the eastern coast in spring during El Niño (La Niña). This pattern corresponds to the mean rainfall reduction during El Niño, which would increase surface shortwave radiation with reduced cloudiness [Power et al., 1998]. Lower latitude regions where latent heating is more important in determining maximum temperature do not show a significant response of TXmean, possibly due to reduced convection during El Niño [Power et al., 1998]. The TXx response to ENSO exhibits a similar pattern to the TXmean pattern, with a dominant warming (cooling) over the eastern continent in spring during El Niño (La Niña). It is notable that TXx shows a stronger response than TXmean. GHCNDEX results for TXx are in good agreement, showing robustness as in RX1d and thus indicating different gridding methods and horizontal scales of interpolation have a negligible influence on results. In short, cold-season TXx response to ENSO is in concert with TXmean response and is highly associated with rainfall responses, confirming previous findings [Kenyon and Hegerl, 2008; Alexander et al., 2009; Arblaster and Alexander, 2012].
3.3 IOD Influence
 Many previous studies have found that the IOD makes a significant contribution to Australian rainfall variation during winter and spring [Ashok et al., 2003; Ummenhofer et al., 2008; Risbey et al., 2009; Cai et al., 2009, 2011a], mainly affecting southern Australia with rainfall reduction (increase) during the positive (negative) phase of IOD, and that equivalent-barotropic Rossby wave trains emanating from the Indian Ocean has been suggested as a teleconnection mechanism [Cai et al., 2011a]. Patterns of seasonal mean rainfall responses to the IOD (Figure 5) display a rainfall reduction (increase) over southern Australia during the positive (negative) phase of the IOD in both winter and spring. The winter drying pattern is similar to that of spring, although of weaker amplitude, which suggests the same teleconnection mechanism is at work during both seasons [Cai et al., 2011a]. RX1d response patterns to the IOD are very similar to those of Rmean, representing a weakening (intensification) of heavy rainfall during the positive (negative) phase of the IOD over southern Australia. TXmean and TXx response patterns to the IOD are illustrated in Figure 6. The maximum temperature response is established only in spring, with an extensive warming of TXmean over southern Australia during the positive phase of the IOD and with TXx warming being confined to the southern coast of the continent where a significant RX1d reduction is experienced. This corresponds with the close interrelationship between rainfall and maximum temperature as seen in the ENSO influence above. It is interesting to note that over southern Australia the IOD influence on spring TXmean is stronger than that of ENSO (Figure 4).
 Rainfall responses to ENSO and the IOD overlap greatly in SON, as indicated by a high-correlation coefficient between N34 and DMI (0.62, Table 2). In order to isolate their influence from each other, we repeat our analysis using independent indices, i.e., N34|DMI and DMI|N34 for SON (Figures 3-6, right panels). Response patterns of Rmean and RX1d onto independent indices (Figures 3 and 5) show that the ENSO-only influence occurs mainly over northeastern Australia and the IOD-only influence dominates over southern Australia, confirming previous studies [Meyers et al., 2007; Risbey et al., 2009; Cai et al., 2011a]. The TXmean and TXx results also show consistent patterns (Figures 4 and 6) although the IOD-only influence on spring TXx is hardly observed when using GHCNDEX. This also provides support that the individual and combined teleconnection mechanisms responsible for the influences of ENSO and the IOD on Australian mean rainfall and temperature may also be responsible for some of the variations of rainfall extremes and associated temperature extremes.
3.4 SAM Influence
 The positive phase of the SAM accompanies a southward shift of storm tracks and associated synoptic behavior [Thompson and Wallace, 2000], which usually brings anomalously wet and cooler conditions to much of Australia in spring and summer, and drier and cooler conditions over the southwest and the southeast of the continent in winter [Gillett et al., 2006; Hendon et al., 2007; Meneghini et al., 2007]. Here we examine the SAM influence on Australian mean climate and extremes, focussing on spring and summer when the rainfall response is strongest. Figure 7 shows regression patterns of Rmean and RX1d onto the SAM index during 1957–2010. A positive SAM index is associated with an Rmean increase over the eastern half of Australia, peaking along the southeastern coast, previously shown to be related to increased eastern upslope flow [Hendon et al., 2007]. Conversely, decreased rainfall is observed on the west coast of Tasmania, due to reduced westerlies during the positive phase of the SAM [Hendon et al., 2007]. An Rmean increase observed in summer over northwestern Australia seems to be due to the ENSO influence (see below). The SAM impact on RX1d is similar to its impact on Rmean: during the positive phase of the SAM, heavy rainfall is intensified over much of eastern and southeastern Australia, which is observed using both AWAP and GHCNDEX data. Compared to Rmean, the RX1d response to the SAM extends further into southeastern Australia during summer. These results are generally consistent with those of Hendon et al.  based on a composite method for a shorter period.
 Maximum temperature responses to SAM (Figure 8) are consistent with rainfall responses for both seasonal mean and extremes. A significant cooling occurs in the central east coast of the continent during the positive phase of SAM where rainfall increases (i.e., enhanced cloudiness) [Watterson, 2000; Hendon et al., 2007]. This means that as for ENSO and IOD, the relationship between rainfall and daily maximum temperature [Power et al., 1998; Jones, 1999] also holds for the SAM influence. A stronger TXx response is seen in spring than in summer over the southeast. This seems to contribute to larger variability of TXx in spring (Figure 2).
 The SAM has a statistically significant correlation with ENSO in summer (Table 2). We have repeated our analysis using independent SAM indices, SAM|N34. Exclusion of the ENSO influence removes rainfall and temperature responses located over Western Australia (Figures 7 and 8, right panels) but does not affect responses over eastern Australia, although TXx in the east seems to be affected. This is consistent with Hendon et al.  who found that the rainfall response to the SAM is insensitive to the removal of ENSO influence.
 The SAM is also known to influence Australian winter rainfall and temperatures, inducing a rainfall decrease and cooling in the southwest and southeast of the continent during its positive phase [Cai and Cowan, 2006; Hendon et al., 2007; Nicholls, 2010; Cai et al., 2011b]. Cooling is apparent from daily minimum temperature (TN), not from daily maximum temperature, which is assumed to be due to enhanced clear-sky nighttime cooling associated with the reduced rainfall and cloud cover [Hendon et al., 2007]. From our regression analysis, we found a similar pattern of Rmean reduction in winter over the southwest and southeast (Figure 9). However, RX1d reveals little response to the SAM, which is presumably due to a lack of heavy rainfall events over the region in winter (Figure 1). In contrast, an anomalous cooling is seen from both seasonal mean and minimum of TN (TNmean and TNn, respectively, Figure 9), supporting previous findings.
4 Conclusions and Discussion
 We examine the observed impact of ENSO, the IOD, and the SAM on Australian seasonal extremes of rainfall and temperature using an extreme value analysis. A non-stationary GEV analysis is employed by incorporating modes of climate variability into GEV modeling as a covariate of location parameter. Significance of the influence of climate variability is assessed through comparison with stationary GEV distribution analyses without a covariate. It is demonstrated that as a whole, spatial patterns of rainfall and temperature extreme responses to ENSO, IOD, and SAM are very similar to those of seasonal mean responses.
 The strongest influence of ENSO on extremes is associated with weakened heavy rainfall during El Niño and intensified heavy rainfall during La Niña over near-tropical eastern Australia in winter. Anomalously drier and hotter extremes are observed over northeastern and southern Australia in spring during El Niño and wetter and cooler extremes during La Niña. The positive (negative) phase of the IOD tends to induce weakened (strengthened) heavy rainfall over southern Australia during winter and spring and also increase (decrease) the risk of hotter extremes in spring over the southeast. Covariation and relative importance of ENSO and IOD impacts on extremes in SON are found to hold as for the mean response, such that IOD plays a more important role over southern Australia while the ENSO impact is stronger over the northeastern portion of the continent. The SAM influence on extremes is more pronounced in spring and summer with the positive (negative) phase of SAM bringing an intensification (weakening) of heavy rainfall and associated cooling (warming) over large parts of southeastern Australia.
 It is found that the inverse relationship between rainfall and daily maximum temperature holds reasonably well for both the mean and extreme responses and over all climate variability modes analyzed, confirming the dominant role of cloud cover changes associated with rainfall in determining daytime temperatures. As a whole, these results suggest that teleconnection mechanisms responsible for seasonal mean rainfall and temperature can be reasonably used to interpret inter-annual variations of extreme rainfall and daily maximum temperature extremes. Two station-based gridded data sets which have different gridding methods and spatial scales provide very similar results, representing robustness of our findings. It should be, however, noted that there is some dependence between two data sets because they use largely the same input station data to create grids.
 We use detrended indices of the climate variability modes for our analysis. Our results are not affected by the use of raw indices with trends retained, indicating a negligible impact of trends for the analysis period. Comparing results from 1957 to1983 and 1984 to 2010 suggests that results are largely insensitive to the selection of different analysis periods. Furthermore, we find little impact of climate variability on the GEV scale and shape parameter (i.e., width and tail behavior of the extreme probability distribution respectively, not shown), implying that climate variability affects Australian extremes mainly through shifting the whole distribution.
 It should be noted that asymmetry in climate response and decadal variability such as the Pacific Decadal Oscillation can affect regional patterns of extreme rainfall and heat waves [Power et al., 2006; Cai et al., 2010; Cai and van Rensch, 2012] and are not considered here. Also, the impact of long-term trends of climate variability, in particular for the IOD and the SAM, which might be in part associated with anthropogenic influence such as greenhouse gases and aerosols [Cai et al., 2003; Murphy and Timbal, 2008; Cai et al., 2009; Nicholls, 2010; Gallant and Karoly, 2010], is not explicitly taken into account here. These issues are beyond the scope of this study and require further investigation. Nevertheless, our results can be utilized to evaluate climate models in terms of extreme responses to climate variability and may have important implications for future projections of regional climate change [Perkins et al., 2009; Cai et al., 2011d].
 We thank Yun Li for his help in obtaining AWAP data, Markus Donat and Lisa Alexander for providing GHCNDEX data. We are grateful to Ian Watterson, Ariaan Purich, and three anonymous reviewers for their thoughtful and constructive comments. This study is supported by the Goyder Institute for Water Research.