The analysis presented here uses several weather metrics that are often considered for climate risk and adaptation purposes in Australia, including near-surface daily maximum temperature (tasmax; with units of °C) and minimum temperature (tasmin; with units of °C), as well as daily precipitation (pr; with units of mm). The Forest Fire Danger Index (FFDI: unitless; McArthur, 1967) is also used, interpreted here as a useful way to combine several weather conditions known to influence fire behavior, noting various similar fire weather indices are also available and used in other regions of the world. The FFDI is calculated as shown in Equation 1 using inputs of daily maximum temperature, mid-afternoon (i.e., 0600 Universal Time from the 6-hourly model data used here corresponds to mid-afternoon local time for Australia) values of relative humidity and wind speed, as well as a Drought Factor based here on the Keetch Byram Drought Index (KBDI) (Keetch and Byram, 1968) that estimates accumulated moisture deficit based on rainfall and temperature. Further details on FFDI are also available in previous studies including for FFDI data sets based on observations and model projections (Dowdy, 2020).

where T = Temperature (°C), RH = relative humidity (%), V = horizontal wind speed averaged over a 10-min period at a height of 10 m above the surface (km.hr.⁻¹) and DF = Drought Factor (unitless).

The results presented in this study include analysis of mean values as well as of extremes based on exceeding various thresholds. There are many ways to analyze extremes, such as defining individual thresholds for each location defined by a particular occurrence frequency. For example, metrics of the order of 90th to 99th percentile for the magnitude of a value are used for representing extremes in some studies (Dowdy, 2020; Peter et al., 2024), representing extremes that occur several times a year on average based on daily values. However, what is considered extreme is somewhat arbitrary and could depend on the intended application, noting that for design standards extremes are typically defined using multi-year return periods, e.g., very rare events that may be expected to occur on average only once in several years (Gumbel, 1958; Wasko et al., 2024). Extremes can also be defined based on fixed magnitude thresholds applied through a broad region. For example, the number of days with maximum temperature above 45°C (or similarly for 46°C, or 47°C, etc.) could be examined at all locations throughout Australia. This means that some places will exceed a given threshold more frequently than other places, such that results should be interpreted accordingly. This study includes analysis for extremes defined using percentile-based thresholds, showing results based on exceeding a threshold corresponding to the value that is exceeded once a year on average (equal to the 99.7^th percentile) during a historical period from 1980 to 2005. Some results are also shown using a fixed magnitude threshold, based on daily minimum temperature being lower than 0°C, noting relevance for freezing of water at that temperature.

Many different sources of climate projections data are available for Australia. Some examples include State and Territory activities for individual regions within Australia (e.g., Corney et al. (2010); Evans et al. (2014); Fita et al. (2016); Clarke et al. (2019)) as well as other examples with national coverage such as collated by previous projects including Climate Change in Australia (CSIRO and Bureau of Meteorology, 2015), the ESCI project (Dowdy et al., 2021; Thatcher, 2021) and the National Hydrological Projections (NHP) project (Srikanthan et al., 2022; Vogel et al., 2023; Peter et al., 2024).

The projection data selected for use here were based on an ensemble collated by the ESCI project that included outputs from the CMIP5 set of GCM projections (Taylor et al., 2012) with three different RCM approaches applied: NARCliM (New South Wales and Australian Regional Climate Modelling: Evans et al., 2014; Nishant et al., 2021), CCAM (Conformal Cubic Atmospheric Model) (McGregor, 2005; Thatcher, 2021) and BARPA (Bureau of Meteorology Atmospheric Regional Projections for Australia) (Su et al., 2021; Thatcher, 2021). These data have been used in various previous applications and studies have documented aspects such as model assessment, representativeness and projected future changes for many different quantities relating to those data (CSIRO and Bureau of Meteorology, 2015; Dowdy et al., 2021; Thatcher, 2021). The ensemble consists of 16 members from a range of model approaches as follows:

The 16-member model ensemble covers a historical baseline period from 1980 to 2005 as well as the period from 2006 to 2099 using two different emissions pathways: a low-moderate emissions pathway (RCP4.5) and a high emissions pathway (RCP8.5) (Taylor et al., 2012). Global average temperature data for each GCM (obtained from https://github.com/traupach/warming_levels) were used for the analysis of projected changes per degree of global warming, with a boxcar moving average of ±10 years applied to those temperature data to help represent the average climate around a given time period.

The ESCI project also applied bias correction to the projections data using the QME (Quantile Matching for Extremes) (Dowdy et al., 2021; Dowdy, 2023; Peter et al., 2024). The QME bias correction in the ESCI project was applied to the projections data at 0.05×0.05-degree grid cells in latitude and longitude through Australia, with quantile-quantile matching to the observations-based dataset known as AWAP (Jones et al., 2009). Previous studies have found the AWAP data to be suitable for use in climate analysis (King et al., 2013) while noting limitations such as the observations network being relatively sparse in parts of the central and western desert regions where additional care should be taken when interpreting results.

The climate analysis presented here using the ESCI projections dataset as described above is intended to provide examples of plausible climate change, including based on ensemble-based metrics, while noting that values above or below those given could also be possible and acknowledging a broad range of factors that contribute to confidence and uncertainties. The range of model spread is also considered here, providing additional estimates of plausible changes above and below the ensemble mean. Additionally, a smoothing of 0.25-degrees is applied to figures in this study, as a moving average in latitude and longitude, to help the interpretation of regional features. For results throughout this study, projected changes are shown only if they are statistically significant at the 90% confidence level (using bootstrapping with 500 iterations).

An expanded ensemble of model data is used in this study with an aim of increasing sample size for enhanced confidence in results. This is based on calculating the projected change per degree of global warming for several combinations of different emission pathways with different time periods, then using all of those projected changes together to increase the number of members in the ensemble. The available emission pathways in the dataset used here included relatively low (RCP4.5) and high (RCP8.5) pathways. Emissions in recent decades have been following the high emissions pathway RCP8.5 more closely than other emissions pathways (Schwalm et al., 2020), while noting that reductions in global emissions in coming decades are likely such that RCP8.5 could be considered a high pathway when considering this likelihood for later this century (Taylor et al., 2012; IPCC, 2021). The steps used are as follows:

The above steps are one example of how this could be done, noting a range of other variations based on this that might be considered in future potential research and applications. For example, instead of 1°C and 1.5°C global warming, it could similarly be done for other warming levels (e.g., 2°C or more perhaps), such as depending on the emissions pathway or time periods considered for a given application.

An important point to note is that the changes calculated here per degree of global warming are intended to be interpreted considering that about 1.1°C of global warming has already occurred due to anthropogenic causes since industrialization (IPCC, 2021). As such, the change per degree of global warming can be interpreted as an estimate of the change that has already occurred due to human-caused climate change (or a slight underestimation given global warming in now slightly higher than 1°C). Additionally, further anthropogenic global warming is expected in coming decades added on top of these changes that have already occurred, with potential to soon exceed global warming above the 1.5°C level recommended to try to limit the worst impacts of climate change (King et al., 2017; IPCC, 2021).

Rainfall is highly variable in Australia, including on seasonal to interannual time scales, due to the influence of modes of natural climate variability such as ENSO (Nicholls et al., 1997; King et al., 2015a; McKay et al., 2023). As such, it can be beneficial to have large sample sizes when examining the climatology of Australian rainfall. Methods are tested here for expanding the sample size based on combining model data from different time periods and emissions pathways.

Figure 1A shows the mean annual rainfall based on the 16-member model ensemble for a historical period from 1980 to 2005 based on the available data from the ESCI projections dataset. There are higher totals in northern and eastern Australia and lower values in inland regions consistent with observations noting uncertainties for rain data in regions of sparse observations such as some of those shown here with low values of mean rainfall (e.g., King (2023)). Projected changes in annual rainfall are also shown in Figure 1, calculated using a range of different methods that are described here as follows. Figure 1B shows the projected change for a low emission pathway (RCP4.5) corresponding to a climate period of ±10 years centered on when each model reaches 1 degree of global warming above the mean for the historical period (as listed in Table 1), following the method detailed in Section 2.3. Those projections indicate decreased mean rainfall through many regions of Australia, with the main exceptions of northwest and adjacent inland regions, along the east coast in a narrow region, as well as for the island of Tasmania to the south of the Australian continent for which increased rainfall is shown.

A similar method is used for the results shown in Figure 1C, but using a later time period for each model, based on when they reach 1.5 degrees of global warming for the low emissions pathway (as listed in Table 1). The projected changes are then divided by 1.5, so that they represent the change per degree of global warming. This results in similar magnitudes for the projected changes in Figure 1C to what was seen previously in Figure 1B, as they both now represent the change per degree of global warming, even though Figure 1C is based on data from later time periods than used for Figure 1B. The methods used for Figures 1D,E are the same as used for Figures 1B,C, respectively, apart from being based on a high emission pathway for the projections and their corresponding time periods (as listed in Table 1).

The four different versions of the projected changes per degree of global warming (Figures 1B–E) show some similar spatial features such as reduced rainfall projected in many locations with increases around the northwest. Some small-scale localized variations are also indicated, such as narrow region of increased rainfall not apparent along the east coast in Figure 1D to the extent seen in Figure 1B. However, some of these fine-scale details might relate to natural variability, including from weather processes and randomness noting the inherent chaotic nature of the atmosphere (Lorenz, 1965), and potentially could look somewhat different if a larger sample size was available.

The general similarities between the changes calculated per degree warming in those four different ways (as shown in Figures 1B–E) suggests potential for considering those data all together in combination with each other. This expanded ensemble, based on using 2 emissions pathways and 2 different time periods for each model in the 16-member ensemble, effectively provides 64 estimates of the projected change per degree of warming (i.e., 2 × 2 × 16 = 64 members). The mean change based on that 64-member expanded ensemble is shown in Figure 1H. Additionally, to provide an indication of the variation between models, the 10^th and 90^th percentiles of the projected change is shown in Figures 1F,G, respectively. Those percentiles are calculated individually for each grid cell location. For example, the 10th percentile value at a given location is the projected change for the model ensemble member that has the 6th smallest projected change from the 64-member ensemble. Similarly, the 90th percentile value at a given location is the projected change for the model ensemble member that has the 6th largest projected change from the 64-member ensemble.

The variation between models in the ensemble is considerable, as demonstrated by the 10th and 90th percentile changes being opposite in sign at all locations throughout Australia (Figures 1F,G). This variation is much larger than the degree of variation between the four methods shown in Figures 1B–E. Another notable feature of these results is that significant changes (at a 90% statistical confidence level) are identified for a much larger area for the expanded ensemble (Figure 1H) than for its constituents (Figures 1B–E).

Annual rainfall projections are considered further in Figure 2, presenting results based on the 250 mm contour line for a region of southern Australia. Metrics such as this can be associated with drought and vegetation–weather relationships relevant for ecology, fire management or agricultural sectors. One example is Goyder’s Line, such as approximated by 250 mm annual rainfall, noting a range of other measures can also be used for that agricultural indicator (Meinig, 1961; Nidumolu et al., 2012; Tozer et al., 2014). This 250 mm contour line is shown for the historical period 1980 to 2005, as well as changes in that line corresponding to different global warming levels (using the results shown in Figure 1H), such as +1°C and + 2°C above that historical period. The results shown in Figure 2 are an example of considering how the future climate in a particular location might become similar to the climate from other locations based on what they had in the past (e.g., based on their historical climate). This relates to the concept of a ‘climate analogue’ between different locations and time periods, such as examined in King (2023) for some Australian locations.

The results show that the 250 mm contour line moves further south for higher global warming amounts (Figure 2). The historical period used here already has some global warming above the preindustrial period, noting that about 1°C global warming has already occurred (IPCC, 2021), such that a contour line is also shown in Figure 1 corresponding to −1°C below that historical period of 1980 to 2005, which results in the 250 mm contour line shifting further to the north. A satellite image is also shown in Figure 2 for qualitative illustrative purposes, with somewhat similar spatial patterns (i.e., variations between vegetation and desert regions) to what is indicated based on the 250 mm rainfall contour. For example, this provides some indication of where ecosystems currently change from the light brown desert regions in northern regions to the darker brown and green vegetated regions towards the more southern regions in general, while noting potential for many other metrics and climate analogue approaches that could also potentially be considered.

Results such as presented in Figure 2, or similar analyses for other metrics, might be useful for different types of climate adaptation. For example, one kind of adaptation (‘Type 1’) might involve moving away from a current location, to be a location that has a similar future projected climate to what the current location had in the past. A second type of adaptation (‘Type 2’) might involve not moving away from a current location, but instead changing the situation at that location such as to be more similar to other locations with similar past climates to what is projected in the future for the current location (to the extent that may be possible). Maps similar to Figure 2 that show a range of suitable locations for these different types of climate analogues might be useful for various ecological decision making, including in relation to threatened species management in our changing climate.

Results are presented for daily maximum temperature (tasmax) in Figure 3, using the same set of methods as used for rainfall in Figure 1. Mean values are shown for the historical period, similar to observations-based data such as King (2023), with projected changes also shown based on multiple methods that are detailed here as follows. The temperature projections show little variation depending on the emissions pathway and degree of global warming (i.e., comparing the panels for Figures 3B–E).

It is useful to confirm this strong consistency in projections calculated per degree of warming using these four different methods, given that there is some potential for variations in this. For example, the global mean surface temperature is largely associated with ocean regions, with ocean temperatures warming more slowly than land regions (IPCC, 2021). If the land-ocean temperature difference changes over time, then land regions potentially could have different changes per degree global warming for different time periods. However, the land-sea temperature difference scales approximately linearly with global warming for different emission pathways such as RCP4.5 and RCP8.5 (IPCC, 2021). The linearity in the relationship can be accounted for, such as demonstrated here by dividing the projected changes for 1.5°C global warming by 1.5 to convert to changes per degree global warming. Consequently, the results presented in Figures 3B–E are useful in showing similar magnitude changes per degree of global warming when calculated using these four different approaches representing different time periods and different emissions pathways.

Figure 3 also shows results based on combining the projected changes per degree of warming from those 4 different methods for use as an expanded ensemble. The mean change based on that expanded ensemble is shown (Figure 3H), together with the 10th percentiles (Figure 3F) and 90th percentiles (Figure 3G) of the model values from the ensemble. Those metrics are calculated individually for each grid cell location. A feature of these projections is somewhat larger increases for inland regions, particularly towards the west of the continent, as compared to near-coastal regions in general. As seen for the rainfall projections (Figure 1), the ensemble range as represented by the 10^th and 90^th percentiles (Figures 3F,G) is broader than the differences in results between the four methods used to calculate the per degree warming projected changes (i.e., differences between results shown in Figures 3B–E). However, the values are all positive in sign throughout Australia, including for both the 10th and 90th percentiles of the ensemble range, in contrast to the larger degree of variation seen for the rainfall range (Figures 1F,G) which had opposite signs of change between the 10th and 90th percentiles at all locations.

Results are presented for daily values of the Forest Fire Danger Index (FFDI) in Figure 4. This uses the same methods as used for rainfall and temperature in Figures 1, 2, respectively. The average daily FFDI values are shown in Figure 4A, showing higher values for inland regions than for regions closer to the coast in general, consistent with previous studies such as Dowdy (2020). The four methods used for the projected changes, based on the two different emission pathways and two different magnitudes of global warming (i.e., Figures 4B–E), all show increases throughout Australia. This is broadly similar to previous studies that have also shown future increases in FFDI based on gridded model projections throughout Australia (Dowdy et al., 2019).

Relatively little variation in results between these four methods is apparent (Figures 4B–E). It is useful to have confirmed this is the case, given potential for some variations as discussed above in relation to the temperature results.

Figure 4 also shows results based on combining the projected changes per degree of warming from those 4 different methods (as shown in Figures 4B–E) for use as an expanded ensemble. The mean change based on that expanded ensemble is shown (Figure 4H), together with the 10th percentiles (Figure 4F) and 90th percentiles (Figure 4G) of that ensemble. The mean values of the expanded ensemble show increases projected through all regions of Australia (Figure 4H). There are some locations where reductions are indicated based on the 10th percentile of the ensemble range (Figure 4F), including for regions in the northwest and nearby inland locations, noting that those locations also showed potential for increased rainfall (e.g., from Figure 1H). However, the magnitudes of those FFDI reductions for the 10th percentile range projections are relatively small, including as compared to the ensemble mean increases (Figure 4H) and the much larger magnitude increases for the 90th percentile of the model ensemble (Figure 4G).

Extremes are examined in this section based on the value that is exceeded on average once per year during the historical period 1980 to 2005 (referred to here as the 1-year return period). These historical threshold values are shown for precipitation (Figure 5A), daily maximum temperature (Figure 6A) and FFDI (Figure 7A). Projected changes are also shown in Figures 5–7, based on how the occurrence frequency of exceeding the 1-yr return period changes per degree of global warming. Similar to the figures in the previous sections, the projected changes are presented individually for the four different methods of calculating the changes per degree of global warming: i.e., two different emission pathways for each of the two different magnitudes of global warming. Expanded ensemble results are also shown similar to the approach used in previous sections, based on combining the ensemble results from those four different methods, including for the expanded ensemble average values, as well as the 10^th and 90^th percentiles of the expanded ensemble.

The projections for rainfall extremes clearly show increases in general throughout Australia (Figures 5B–E). This is very different to the projections for mean rainfall that showed decreases through most of Australia (e.g., from Figure 1H), noting some similarities to previous future projections that have also indicated extreme rain increases in Australia in general including in some locations where mean rainfall decreases (CSIRO and Bureau of Meteorology, 2015). The projected changes are positive in most locations, but with some small-scale variations. Those variations include some projected decreases shown interspersed closely with regions of projected increase, while noting that the locations of projected decreases are not very consistent between the different methods shown (Figures 5B–E), suggesting relatively low confidence in those regions due to potential influences of natural variability to some degree (e.g., from weather and chaotic processes (Lorenz, 1965)). The expanded ensemble results have less of that small-scale spatial variation, as well as with a larger area shown statistically significant results. This highlights the point that climate analysis of rainfall extremes could benefit from using sample sizes as large as possible, given large variability in rainfall (as was also discussed in Section 3.1).

The projected increases in occurrence frequency for these classes of extremes such as shown in Figure 5 is a commonly reported finding of many other climate change studies. This includes many examples of studies that provide physical process understanding behind what is causing the changes in extremes for Australia (CSIRO and Bureau of Meteorology, 2015; Perkins-Kirkpatrick et al., 2016, 2022; Dowdy, 2018; Guerreiro et al., 2018; Clarke and Evans, 2019; Dowdy et al., 2019; Dey et al., 2019; Gross et al., 2019; Harris and Lucas, 2019; Rauniyar and Power, 2020; NESP, 2020; van Oldenborgh et al., 2021). A recent example of this is Wasko et al. (2024), presenting a systematic review of studies examining the influence of climate change on extreme rainfall and flooding in Australia, finding a central estimate of 8% increase per degree global warming in the intensity of extreme daily rainfall in general throughout Australia.

The projected changes in extremes of daily maximum temperature (Figure 6) and FFDI (Figure 7) are positive in sign throughout Australia. This is the case for each of the four different approaches used to calculate the change per degree of global warming (i.e., two different emission pathways for each of the two different magnitudes of global warming) as well as for the expanded ensemble results. The 10th percentiles of the expanded ensemble are also positive in sign for daily maximum temperature (Figure 6F), whereas some locations are negative in sign for FFDI (Figure 7F) indicating a somewhat larger degree of uncertainty.

In addition to the methods described above for analysis of extremes, there are also many other useful ways for climate analysis to be presented and communicated, such as when considering the detection and attribution of changes. Examples include examining time series, such as annual values of a metric representing extremes, for analysis of the timing of emergence for human-caused climate change influences on extremes (e.g., King et al. (2015b)). Other methods can consider the differences between two time periods or changes per degree warming such as shown in Figure 5, including based on metrics such as the fraction of attributable risk (FAR: e.g., Allen (2003) and Perkins-Kirkpatrick et al. (2022)). FAR is equal to 1 – the inverse of the Probability Ratio (PR, also sometimes known as the Risk Ratio), where PR may be calculated as P_fact/P_cfact with P_fact the probability of an event occurring in a state with more global warming than an earlier reference state and P_cfact the probability of an event occurring in that reference state (Lewis and Karoly, 2013; Perkins-Kirkpatrick et al., 2022). For example, P_fact could represent a current climate period or a future projected climate period and P_cfact could represent a historical climate period.

As an example of time series analysis for extremes, Figure 8 presents annual values of FFDI averaged throughout Australia for December. This is shown individually for each of the 16 members of the model ensemble from 2006 to 2,100, for the low emissions path (RCP4.5) and the high emissions path (RCP8.5), as well as for the observations-based FFDI data that covers the period back to 1950 (Dowdy, 2020). The Black Summer of 2019/2020 had the most severe fire weather on record for Australia, including particularly high values (daily FFDI >40) on average for Australia in December 2019 as shown in Figure 8. The ESCI projections dataset is used here to examine how the occurrence of conditions similar to those observed in December 2019 is influence by climate change. The results show that values of around that magnitude rarely occur in the model-based FFDI data for the current climate period, with a much greater occurrence frequency for higher amounts of global warming that occur towards the later part of the century for these emissions pathways. This is particularly apparent for the high emissions path, but also seen to some degree for the low emissions path.

In contrast to average values for the whole of Australia as discussed above, Figure 8 also considers more localized extreme fire weather events. Analysis is presented based on Black Saturday 7 February 2009 where the observations-based FFDI value was 136 for Melbourne (corresponding to the grid location for 144.9°E and 37.8°S: Dowdy (2020) and Pepler et al. (2018)), noting that 173 people tragically lost their lives from the fires on that day (BS Royal Commission report to be referenced). The results show how often the model data have FFDI ≥136 calculated individually for each of the 16 members of the model ensemble from 2006 to 2,100. This is presented individually for the low and the high emissions paths available for the ESCI projections dataset. The model data show that values exceeding this threshold are relatively rare around the time of Black Saturday but become more frequent in time through this century. A faster rate of increase is apparent for the high emissions path, with a more moderate rate of increase for the low emissions pathway, further demonstrating the influence of greenhouse gas emissions on causing more dangerous weather conditions for fires.

This analysis also helps indicate the value of increased sample size for enhanced confidence in projections. For example, if considering the model data used here from when the period of projections starts until now (i.e., the 19-yr period from 2006 to 2024), rare events such as those fire weather extremes examined in Figure 6 do not occur in several of the individual model ensemble members. However, when using the 16-member ensemble as shown in each panel of Figure 8, the sample size is now effectively 16 times larger for that 19-yr period. These results also show that consideration of model data based on both emission pathways here can increase the sample size further (i.e., doubling the sample size) to help represent rare extremes such as Black Saturday and the Black Summer. This is similar in concept to the UNprecedented Simulated Extreme Ensemble (UNSEEN) approach, using larger sample sizes from models to consider potential for rare events that might have been unlikely to have occurred within a limited period of available observations (Thompson et al., 2019; Kelder et al., 2020).

A final example of analysis for extremes is presented here in Figure 9. This uses the same methods used for Figures 1, 3, 4, but presented for the occurrence frequency of days per year with temperature less than 0°C (based on daily minimum temperature: tasmin). The results show that this occurs very rarely through many midlatitude parts of Australia, including not at all in some locations particularly for northern Australia. The projected changes based on the 16-member ensemble average are broadly similar between the four different methods shown in Figures 9B–E: i.e., for the low or high emissions pathways based on the timing of 1°C or 1.5°C warming above the historical period 1980 to 2005.

Combining the projected changes per degree of global warming from those four methods into an expanded ensemble of 64 members is used to show the ensemble mean and the ensemble range. The changes are all negative in sign for the mean, with larger magnitude negative changes for the 90^th percentiles. There are some positive values for the 10th percentiles in central and western regions, with negative values in the east. The potential for global warming to cause an increased frequency of extremely cold days in parts of Australia could potentially relate to decreased cloudiness leading to colder nights in some cases. For example, a strengthening of the subtropical ridge over southern and central parts of Australia due to climate change (Dittus et al., 2014; CSIRO and Bureau of Meteorology, 2015; Pepler et al., 2018) could potentially lead to decreased cloudiness. However, further research might be beneficial to explore reasons for the differences between eastern Australia with negative values compared to central and western regions with positive values in Figure 9H, such as potential orographic influences on nocturnal cloudiness in the more mountainous region of the Great Dividing Range along eastern Australia.