Identifying historical climate changes in Australia through spatial analogs

Spatial analogs have previously been used to communicate climate projections by comparing the future climate of a location with an analogous recent climate at a different location which is typically hotter. In this study, spatial climate analogs were computed using observational data to identify and quantify past changes. A sigma dissimilarity metric was computed to compare the recent climates of nine major Australian cities and early 20th century climate across Australia. Evidence is found for climate shifts, particularly in Darwin where temperature variability is lower than in extratropical cities. Analogs designed to capture extremes, including a human health-relevant climate analog, were constructed and these also highlight significant climate shifts. The analogs may also be used to examine extreme events in the context of a reference city climate and identify unusual events. This work demonstrates the utility of climate analogs for monitoring past climate changes and extreme events as well as examining and communicating future change. Care should be taken in interpretation of the movement of analogous climates and the design of analyses, but climate analogs have many potential applications beyond previous uses. Tailored analogs could be studied to communicate climate changes relevant to specific stakeholders.


Introduction
The world is warming due to anthropogenic greenhouse gas emissions. To date, the planet has warmed by around 1.1 • C relative to pre-industrial levels (IPCC 2021). Global warming has been accompanied by local warming across almost all of the world and significant precipitation changes in some locations as well as other earth system changes. Scientists have used observational datasets to quantify changes in the climate to date and compute other relevant metrics beyond trends, such as climate emergence statistics (Mahlstein et al 2012, Hawkins et al 2020. As greenhouse gas emissions remain very high (Davis et al 2022, Friedlingstein et al 2022 and global warming will continue as long as emissions remain significantly net-positive (MacDougall et al 2020, King et al 2022), further warming and other climate changes are expected. Climate projections are made based on model simulations to provide estimates of future local changes. Projections are communicated in different ways, but one popular method is spatial climate analogs. Analogs have been used to illustrate changes by projecting that a location's climate may become more like another location's, typically hotter, current climate, if greenhouse gas emissions continue. The use of analogs has been popular for examining different climate impacts including in climate-sensitive industries such as health (Kalkstein and Greene 1997) and agriculture (Bergthórsson et al 1988, Webb et al 2013. Climate analogs have previously been computed from global and regionaldownscaled model simulations and are used by organizations including Copernicus (https://climateanalogues.climate.copernicus.eu/) and the Commonwealth Scientific and Industrial Research Organisation in Australia (www.climatechangeinaustralia.gov. au/en/projections-tools/climate-analogues/) to display analogous climates for locations under different greenhouse gas emissions scenarios for the 21st Figure 1. Maps of (a) average temperatures and (b) average precipitation across Australia for 1991-2020. Cities for which analogs are computed are marked in (a) in alphabetical order: 'a' for Adelaide, 'b' for Alice Springs, 'c' for Brisbane, 'd' for Canberra, 'e' for Darwin, 'f ' for Hobart, 'g' for Melbourne, 'h' for Perth, and 'i' for Sydney. (c)-(f) Changes in seasonal-average temperatures between 1910-1937/38 and 1994-2021/22 for March-May, June-August, September-November, and December-February respectively. (g)-(j) Changes in seasonal-average precipitation rates between 1910-1937/38 and 1994-2021/22 for March-May, June-August, September-November, and December-February respectively. White areas within Australia are masked due to poor observational coverage. century. Spatial climate analogs are relatively straightforward to communicate and understand and may be computed based on multiple variables.
In this study, I investigated whether analogs may be used to identify past climate changes in observational datasets, rather than their common use for projections. Prior analyses of historical climate analogs using instrumental data have been extremely limited (MacKenzie and Mahony 2021), but there is potential for use in communicating past changes as well as possible futures. In this instance, the recent climate of a location was compared with the climate at all locations in the past to identify the best historical analog. Analysis of historical climate analogs supports previous work to understand the extent of climate changes to date, such as emergence metrics, and provides a framework for their use for climate monitoring efforts. Here, I computed climate analogs for nine major cities in Australia ( figure 1(a)).
Australia is a continent with diverse local climates, including tropical, arid and temperate climate types (Peel et al 2007), and population centers spread across these climates. Annual-average temperatures vary from below 10 • C in mountainous parts of the southeast of the continent to above 28 • C in the tropical north ( figure 1(a)). Precipitation varies with the arid interior receiving less than 1 mm d −1 whereas some coastal and high-altitude areas experience more than 6 mm d −1 on average ( figure 1(b)). Australia has also warmed (figures 1(c)-(f); Grose et al 2023), especially the southern half of the continent in spring and summer, with temperatures rising an average of about 1.4 • C since 1910 (Australian Bureau of Meteorology 2020b). Precipitation change has been more spatially variable with increases in the north and interior and drying in the coastal south (figures 1(g)-(j)). Australia's diverse climate and significant climate changes in the observed record make it a suitable study region for examining past spatial climate analogs to the recent climate.

Observational data
Observational data from the Australian Gridded Climate Dataset (AGCD; Jones et al 2009, Evans et al 2020 were used in this study. Gridded observational data for daily precipitation totals, maximum temperature and minimum temperature from January 1910 to August 2022 were interpolated from a native regular grid of 0.01 • to 0.25 • using a conservative regridding method. Areas of central Australia with sparse coverage of long-running weather stations were masked. These areas are known to exhibit erroneous trends in precipitation variables (King et al 2013). The data were separated into the four meteorological seasons: March-May (MAM), June-August (JJA), September-November (SON) and December-February (DJF). Five sets of climate analogs were computed for which results are shown here: 1. Seasonal mean maximum and mean minimum temperatures and total precipitation values were calculated and these 12 variables formed the basis of the mean climate analogs analysis. 2. To better understand the mean climate analog results, analogs computed from only the eight seasonal temperature variables were also computed. 3. Similarly, analogs were computed for only the four precipitation variables too. 4. The first climate extremes analog used eight variables based on two indices recommended by the Expert Team on Climate Change Detection and Indices: seasonal values of the highest maximum temperature (TXx) and seasonal values of the highest daily precipitation totals (Rx1day). 5. The second climate extremes analog was an attempt to develop a health-relevant metric and this uses four variables: seasonal 90th percentile values of daily maximum temperature in austral spring (SON) and summer (DJF) and seasonal 10th percentile values of daily minimum temperature in austral autumn (MAM) and winter (JJA).
Climate analogs for nine major cities were examined and their locations are shown in figure 1(a). This includes the eight state and territory capitals of Australia and Alice Springs is included as it is characterized by a different climate to all other cities studied here. In total, over 17 million people live in these nine cities.
The observations were divided into four periods of equal length: MAM 1910-DJF 1937/38, MAM 1938-DJF 1965/66, MAM 1966-DJF 1993/94, and MAM 1994-DJF 2021. The climate analogs were computed for each of the first three periods relative to the climate of the city of interest in the 1994-2021/22 period. The results shown here are comparing the 1910-1937/38 period with the climate of the city of interest in 1994-2021/22, but selected results for other periods are shown in supplementary information. For analysis of individual years JJA 1910-MAM 1938 was compared with each year (June-May) throughout the entire 1910-2022 period, so recent extreme events could be examined and the effect of natural variability related to the El Niño-Southern Oscillation (ENSO) could be examined (see supplementary text for discussion of ENSO analysis).

Climate analog identification
The objective of climate analogs previously has been to identify locations with similar climates in a future climate scenario to a present-day climate at a specific location. This has been done by comparing means and variability in temperature and precipitation (e.g. Bergthórsson 1988). Gavin et al (2003) compared methods for analog identification leading to subsequent studies using standardized Euclidean distance (SED) for the purpose of analog analysis (e.g. Williams et al 2007, Veloz et al 2012. SED is defined as: where N is the number of variables analyzed, a is the mean of variable k at the location of interest, j, in the recent climate, b is the mean climate at a different time (usually a future scenario) at location, i, and s kj is the standard deviation of climate variable k at location j. The SED is straightforward to compute and interpret which has made it a popular choice for use in analog studies.
While the SED has been well used, it does not account for covariance between variables that are used as inputs, and comparison between SED statistics based on different numbers of input variables (N in the equation for SED) is challenging (Mahony et al 2017). Mahony et al (2017) developed an alternative method based on standardizing the data and extracting principal components (PCs) before computing similarity in this transformed data space. This approach has been used in some subsequent analyses (Fitzpatrick andDunn 2019, Lotterhos et al 2021).
Covariance between variables is an issue in the Australian region as seasonal-average temperature and precipitation variability is associated with climate modes, such as ENSO, which may persist for multiple seasons. Also, seasonal and annual temperature and precipitation are inversely correlated in some areas of Australia (e.g. Nicholls 2004). Thus, the SED approach is sub-optimal for examining Australian climate analogs. In this study, an adaptation of the method developed by Mahony et al (2017) was used instead. For a given location and set of variables the following steps were taken: 1. A cube root transformation was applied to all precipitation indices. The data for each temperature and precipitation variable at the city of interest for 1994-2021/22 were standardized based on the mean and standard deviation over the 28 values for each season in the period. 1910-1937/38 and 1938-1965/66 and 1966-1993

Mean values of all variables for
where k is the number of degrees of freedom. The conversion of Mahalanobis distance to sigma dissimilarity allows comparability of results between analog analyses where k is different.
For fuller discussion of this methodology I refer the reader to Mahony et al (2017). However, there are a few key differences between this study and Mahony et al (2017) that must be highlighted. The most obvious difference is that here analogs with the recent climate were identified for past climates rather than future climates. Gridded observational data were used to represent the recent climate and the standard deviation in step 1 is computed from the location gridcell, whereas in Mahony et al (2017) a collection of local station data were used. The construction of AGCD, based on interpolation of station data (Jones et al 2009, Evans et al 2020, means that the gridcell standard deviation is derived from multiple stations, although their relative influence depends on station density and the variable in question. Part of the motivation for computing analogs for major cities was that these are locations where station density is high and the climate variability in the gridded dataset should be more accurate. Another difference is that Mahony et al (2017) applied a log-transformation to precipitation variables whereas I used a cube-root transformation. The purpose of these transformations is to make the distributions of precipitation variables nearer normal. A log-transformation fails where precipitation totals are zero for a season which is sometimes the case in parts of Australia.
The sigma dissimilarity metric is useful for monitoring climate changes and has been used to examine climate emergence (Mahony and Cannon 2018). The change in sigma dissimilarity between periods of time may be used to show how the climate has changed relative to a reference city climate. Results from this analysis are shown in figures S1-S3 and discussed in supplementary text.

Climate means analysis
Sigma dissimilarity values show the level of agreement between the recent climate (1994-2021/22) of a given location and the climate at all locations further in the past (1910-1937/38). For the cities analyzed here, Darwin shows the biggest difference between recent and past climates at its location at 3.3σ (figure 2). As Mahony et al (2017)   While other cities do not show strong dissimilarity between their recent and past climates, the best analogs to recent city climates tend to be further north for the cities in southern Australia with the exception of Adelaide. In general, the best historical analogs to present day city climates may be found in warmer locations. If an approach was taken where analogs were only identified if the city's climate had substantially changed (Hamann et al 2015) then in most cases, including where analogs are far from city locations like Adelaide and Melbourne, the city's climate of the past would be considered an acceptable analog.
Sigma dissimilarity values at city locations computed only from temperature and only from precipitation variables are also shown (figure 2). No substantial dissimilarity in precipitation at city locations is identified, but there are large dissimilarities in temperature, particularly in Darwin and Brisbane.
When the analysis was repeated comparing the recent period with later historical periods the sigma dissimilarity for Darwin decreases and the best analogs tend to move nearer to the city locations (figures S4 and S5). There is little evidence of interannual or decadal variability affecting the sigma dissimilarity patterns in these results, despite the strong climate variability on these timescales that Australia experiences. Sensitivity tests using shorter windows found greater variability in dissimilarity patterns.

Climate extremes analysis
Analysis on extreme climate indices (seasonal TXx and Rx1day) was also performed but showed little dissimilarity between the recent climate and historical climate of 1910-1937/38 at the city locations ( figure S6). This is due to much higher interannual climate variability in these indices compared with the climate means. This effect is also illustrated by the broad swaths of Australia with low sigma dissimilarity values for past relative to recent city climates. The best analogs still show movement towards warmer climates.
Climate analogs may take different input variables to be useful to specific stakeholders. An example for temperature extremes specifically is provided here. Hot and cold extremes cause health problems and increased mortality rates including in Australia (Gasparrini et al 2017, Cheng et al 2019, Coates et al 2022, although the relative importance of heat and cold for excess fatality is debated (Longden 2019). Acclimatization is relevant to heat extremes with people more vulnerable to heat that comes after cold periods (Nairn and Fawcett 2014). Thus, the 90th percentile of seasonal maximum temperatures in spring and summer, and the 10th percentile of seasonal minimum temperatures in autumn and winter were used as input variables for a health-relevant climate analog.
The input variables in this case have lower interannual variability than TXx and Rx1day, so the sigma dissimilarity is broadly higher (figure 3). Darwin is still the only city to have transitioned to experiencing a truly novel climate with respect to this health-relevant analog with local dissimilarity of 3.2σ between the recent period and 1910-1937/38 window. However, as with the climate means analog, the best health-relevant analogs are in warmer locations than the city of interest. For example, Sydney's healthrelevant climate analog for the 1994-2021/22 period is a location near Brisbane in the 1910-1937/38 period. There is potential for stakeholders to use climate analogs information to understand the challenges their sector may face in the current climate.
Climate analogs for individual extreme years may be identified by computing sigma dissimilarity for each year relative to a reference period (in this instance JJA 1910-MAM 1938. Unlike the previous analysis where a recent reference period was used, here an early period is chosen so recent extremes may be analyzed. The sigma dissimilarity at Sydney (figure 4(a)) and Canberra (figure 4(b)) relative to their respective past climates is greater after the reference period, as expected by construction, and there is high interannual variability in dissimilarity. The locations of the best analog in each year to Sydney's and Canberra's recent climates are shown in figures 4(c) and (d). While there is high interannual variability, there is a general pattern whereby the most similar recent climates to each city's historical climate are in climatologically cooler locations. This is another indicator of the warming trend observed over the last century.
The year 2018/19 exhibits low similarity to the recent climate in both Sydney and Canberra. This period included the hottest summer on record in Sydney and, indeed in the Australian-average. As the recent climate is so much warmer the nearest analog to Sydney's 1910Sydney's -1938 climate in 2018/19 is south

Discussion and conclusions
This analysis is the first to apply climate analog techniques to comprehensively study past climate changes in the instrumental period rather than future climate scenarios. Through using an adapted version of the Mahony et al (2017) methodology, analogs were computed and significant changes in climate were identified, particularly in Darwin, while other major Australian cities experienced more subtle changes between the early 20th century and recent period. Darwin was the only tropical location studied here and showed the strongest climate shift in the observational record. In general, climate changes in the tropics are clearer than in high-latitude regions due to lower interannual variability (Diffenbaugh and Scherer 2011, Mahlstein et al 2011, Hawkins et al 2020. As the climate continues to change, analogs could be updated. Seamless analysis of past and future analogs could be conducted by blending information from suitable observations and historical and future high-resolution projections, but such data are available in few areas of the world.
The focus on Australia and analogs to major Australian cities was due to the need for extended highquality observational data and a large enough domain so suitable analogs may be identified. Studies may be possible in other continental-scale areas where such data exist, including North America, Europe and East Asia. Global-scale analyses could also be conducted but calculations on coarser grids are inherently less useful to stakeholders. In principle, analogs that incorporate other variables beyond temperature and precipitation indices could be examined but the requirement of high-quality data is likely a limiting factor.
The approach of Mahony et al (2017) formed the basis of the methodology, but sensitivity tests were performed. This included computation of an 8-variable analog with seasonal mean temperatures instead of seasonal-average maximum and minimum temperatures which shows slightly weaker changes between past and recent climates (figure S7) than the 12-variable analogs used here. Analogs computed from shorter baselines are more sensitive to natural variability and tend to result in larger dissimilarities. Analogs computed without the prior cube-root transformation of the precipitation variables exhibit stronger influences of precipitation change and the change in local climate at Perth becomes clearer. Perth experienced significant rainfall decline (Hope et al 2006, Delworth andZeng 2014) over the 20th century.
While the sigma dissimilarity method has been demonstrated to be useful for analog and emergence analyses (Mahony et al 2017, Mahony andCannon 2018), defining the best analog as the location with the minimum sigma dissimilarity can lead to major shifts in the analog with minor methodological changes. An approach where the nearest acceptable analog below a given threshold (e.g. 1σ) may be suitable in some circumstances. Studies on 'climate velocity' which typically consider species impacts of climate changes and possible habitat movements (Dobrowski et al 2013, Ordonez et al 2016 do not adopt uniform approaches to analog identification (Brito-Morales et al 2018) but thresholds for movements have been applied (Hamann et al 2015). The illustration of sigma dissimilarity negates the need for such an approach here but a threshold for analog identification should be considered especially if this is the only information displayed.
Climate analogs for extremes indices were explored in this study. In general, high interannual variability in climate extremes reduces sigma dissimilarity values between present and past climates but shifts in best analogs to warmer locations are still identified. Australia has experienced significant increases in the frequency and intensity of heat extremes over the past century (Perkins and Alexander 2013, Lewis and King 2015, Alexander and Arblaster 2017, while changes in rainfall extremes have been less clear and are more complex (Alexander and Arblaster 2017, Dey et al 2019, Dey et al 2020).
Analogs for individual years may be computed if a long enough reference period is used as a baseline. The analysis here uses an early-20th century baseline to study recent extremes, but this can also be reversed so a recent baseline is applied for the study of historical extremes. The approach is flexible and may also be used for annual analyses with extreme indices.
This study uses only observational data to explore historical climate analogs. Thus, the changes identified here cannot be directly attributed to anthropogenic influences. However, the underlying warming of Australia (Eyring et al 2021) and increased frequency and intensity of hot extremes (Seneviratne et al 2021) have been attributed to anthropogenic forcings previously. This study adds a new way of framing historical climate changes in Australia.
This study focused on only major Australian cities where there is a reasonable density of weather stations (Jones et al 2009). Extending analyses to rural locations could be useful, particularly if analogs are designed with stakeholders such as local agriculture or water management, but results may be harmed by poor data quality. The application of climate analogs to specific stakeholders requires careful thought and co-design between scientists and sectoral experts.
This work has shown that analogs may be used to identify past climate changes as well as for communicating projections as has been done previously. Further work to make historical analogs relevant to different stakeholders could be beneficial.