Examining past and projecting future: an 800-year streamflow reconstruction of the Australian Murray river

Managing water security and sustaining ecosystem functions under future warming poses substantial challenges for semi-arid regions. The Murray–Darling Basin (MDB) is particularly vulnerable given the considerable demand for water that underpins Australia’s agricultural production and contribution to the national economy. Understanding future drought risk requires a robust assessment of natural variability in drought length, frequency, and magnitude. In the absence of long instrumental records, past drought characteristics can be inferred from paleo-records. We reconstruct over 800 years of Murray River streamflow using a suite of tree-ring chronologies from regions with strong climate teleconnections to the MDB. The reconstruction (1190–2000 CE) captures a broad spectrum of natural climate variability, not fully represented in instrumental records, contributing to an improved understanding of the occurrence rate of multi-year droughts. We found that the Millennium Drought, which occurred in the 2000s, was the most severe (joint duration, magnitude, and peak) during the 800-year reconstruction. The return period of this event is estimated to be ∼2500 years. However, droughts in the early-1200s were of a longer duration and similar magnitude to the Millennium Drought. We used climate models to assess how the occurrence probability of severe droughts might change in the future. Compared to the 800-year baseline, climate models project an increase in future drought severity. While the increase in drought occurrence is within the uncertainty range for most future projections, the driest forecast shows a significant increase in the likelihood of severe droughts compared to natural variability. Our results highlight the need for water management strategies not to rely solely on instrumental data as it may not fully represent current and future risks. Ensuring a resilient MDB under future warming will require a robust water security policy that captures a broader range of natural and anthropogenic variability than currently recognised.


Introduction
The Murray-Darling Basin (MDB) produces twothirds of Australia's irrigated agriculture and is often termed Australia's 'food bowl' (Hart et al 2021).This region is characterized by extreme interannual rainfall variability, and both droughts and floods are naturally recurring features.Since reliable instrumental rainfall records began around the start of the 20th Century, three protracted (multi-year) droughts, and several droughts of shorter duration, have occurred (Verdon-Kidd et al 2017).Such events have severe consequences for the Basin's population and environment, decreasing water security, causing crop and livestock loss, increasing food and cotton prices, and causing environmental and social harm.For instance, record low streamflow during the 'Millennium drought' (∼2001-2009) devastated agricultural communities, industries, and the environment in southeast Australia (Van Dijk et al 2013).While of shorter duration, the most recent 'Tinderbox drought ' (2017-2020) was the worst on record for the upper Basin, with very low streamflow and extreme heat leading to catastrophic environmental consequences in the lower Darling River (Vertessy et al 2019).The fact that this region has experienced two major droughts within the last 20 years has raised questions about the causes and implications for the future of the MDB and its vitally important 'food bowl' .
Climate modes play an important role in interannual precipitation variability across the Basin, most notably the El Niño-Southern Oscillation (ENSO), Indian Ocean Dipole (IOD) and Southern Annular Mode (SAM) (Gallant et al 2012, King et al 2020, Holgate et al 2022).Prolonged droughts in the MDB are influenced by interactions between these drivers (Ummenhofer et al 2009, Verdon-Kidd and Kiem 2009, King et al 2020), and by multi-decadal climate variability (Verdon-Kidd et al 2014), influenced by the phases of the Inter-decadal Pacific Oscillation (Power et al 1999).
However, the short length of instrumental records in Australia (maximum of around 130 years) limits our understanding of how decadal to multi-decadal climate variability influences the likelihood of severe droughts in the MBD.Insights from paleoclimate records show that the instrumental period does not account for the full range of natural climate variability in Australia (Verdon and Franks 2007, Gallant and Gergis 2011, Ho et al 2015, Palmer et al 2015, Flack et al 2020, Kiem et al 2020).Thus, observed climate alone is insufficient to characterise baseline climate risks, particularly for extreme events like droughts, which are by nature infrequent and poorly sampled in relatively short historical records.
Anthropogenic climate change poses substantial further risks to the region, with evidence that the Basin is already being impacted.For example, winter/spring streamflow has been declining across the MDB over the last 50 years (BOM 2020, Speer et al 2021), consistent with expected changes in the anthropogenic forcing of precipitation (Mckay and Dowdy 2023).Rising temperatures, which have increased by 1.5 • C since records began, contribute to more severe streamflow deficits in droughtaffected catchments than predicted by precipitation deficits alone (Cai and Cowan 2008, Ummenhofer et al 2009, Nguyen et al 2021).While there is uncertainty in future streamflow projections, most models agree that climate change will further decrease surface water availability over the MDB region, particularly the southern MBD (Timbal et al 2015, Srikanthan et al 2022).
Managing future water security and ecosystem functions poses substantial challenges for the MDB, particularly as greater demand is placed on water availability.At the core of this issue is the need for a robust assessment of how long, how frequent, and how severe future droughts could be.To achieve this, a thorough understanding of natural climate variability is required to better quantify future drought risk (Kiem et al 2020).Due to the limitations of the instrumental record, paleoclimate data can be used to provide a much longer time series to evaluate recent droughts.A previously published multi-proxy reconstruction of Murray River streamflow suggested the Millennium Drought was highly unusual compared to the last ∼200 years (Gallant and Gergis 2011).Since this reconstruction was developed, the proxy network has increased, offering an opportunity to improve and extend the analysis back further in time to capture a greater range of natural variability.
Here we present a new paleo-streamflow reconstruction of austral spring and summer (September-February) Murray River discharge based on climatesensitive tree rings that capture over 800 years of variability in the MDB.We use this extended record to benchmark the severity of past drought events, including the Millennium and Tinderbox droughts.Using a suite of downscaled and bias-corrected climate model outputs, we then contextualise how future drought risk may change compared to the past eight centuries.

Streamflow data
Along with their tributaries, the Darling and Murray Rivers form Australia's largest river system.The MDB covers one million square kilometres in southeast Australia (figure 1).The diversion, storage, and extraction of water from the MDB system have resulted in large reductions in Murray River streamflow and the reversal of the natural flow seasonality in some reaches (Thoms andSheldon 2000, Leblanc et al 2012).Tree-ring streamflow reconstructions build on the correlation between tree growth and discharge, and cannot be directly developed for heavily managed catchments that exhibit non-stationarity in these relationships (Galelli et al 2021).Thus, we use modelled discharge from the MDB Authority's EWater Source Murray Model 'Without Development' scenario, which estimates naturalised discharge in the absence of water management measures (Jakeman et al 2019).Discharge is modelled at the Murray River  S4).
upstream of lock number 7 (Lock-7), predominantly representing flow in the lower MDB.
Daily naturalized discharge was available from July 1895 to June 2009.Source model inflows are a combination of long streamflow gauge records in the largely unmanaged upper catchment and modelled flow for the rest of the basin.Lumped conceptual rainfall-runoff models were calibrated against unregulated streamflow; however, the calibration periods typically reflect post-catchment clearing for agriculture.To extend the naturalised records beyond 2009 to cover the periods of the Millennium and Tinderbox droughts, we scaled monthly instrumental streamflow records from 2010 to 2020 by basin-wide runoff estimated using the Australian Water Resource Assessment Landscape model v6 (AWRA-L; Frost and Wright 2018) using a linear relationship calculated over the 1911-2009 period.See supplementary information for details.

Reconstruction methods
Murray River streamflow at Lock-7 was reconstructed using a nested, principal components linear regression method (Cook et al 1999(Cook et al , 2007(Cook et al , 2010)).As there are no high-resolution paleoclimate proxies from the MDB, and very few from mainland Australia (Haines et al 2016), we leveraged climate teleconnections to incorporate remote tree-ring chronologies to reconstruct MDB streamflow.The predictors were selected from a suite of publicly available tree-ring chronologies from regions with strong teleconnections to the same large-scale climate drivers influencing MBD streamflow (e.g.ENSO, IOD, SAM, see supplementary for details).Chronologies were standardised using several methods, predominantly using an agedependent spline with the 'signal-free' (Melvin and Briffa 2008) method (see table S4 for details of standardisation methods applied).
The seasonal relationships between the major climate drivers affecting MDB precipitation and streamflow at Lock-7 are shown in figures S1, S3 and S4.ENSO and the IOD have the strongest influence on rainfall during the austral winter and spring, corresponding to the high flow period in the lower MBD which occurs approximately between July to January (figure S2), lagging rainfall by around two months (figure S5).We tested streamflow reconstructions for all six-month spans within the high streamflow period when precipitation is most strongly affected by the climate drivers and for the water year (from June to May).The September-February period, which corresponds to July-December rainfall, covering the peak growing season of the Northern Hemisphere and the Southern Hemisphere spring, accounts for more than 60% of water-year streamflow, and produced the strongest and most stable reconstruction model.
The final year of reconstruction is 2000 (September 1999-February 2000), which represents the end date of many tree-ring chronologies.While naturalized discharge is available from mid-1895, the number and spatial coverage of streamflow gauges is low prior to 1922 (DPE 2011).The availability of precipitation stations declines sharply before 1926 as well.Thus, due to low data availability, the earliest portion of the modelled streamflow time series is considered less reliable.We selected the 1921-2000 CE portion of the time series for calibration and retained the 1897-1920 CE period for independent validation.
Predictors were pre-selected only to include proxies with a significant relationship (p ⩽ 0.1) to powertransformed naturalised streamflow over the 1921-2000 CE calibration period with both concurrent and lagged connections considered.Both the powertransformed streamflow data and the paleoclimate proxies were autoregressively pre-whitened before modelling.Predictor selection, calibration and verification of the model were undertaken on the transformed, autoregressively modelled data, with the final reconstruction reddened and transformed back into data units.The verification tests included the reduction of error (RE) and coefficient of efficiency (CE) (Cook and Kairiukstis 1990).
Reconstruction uncertainty in the form of 'prediction intervals' (Olive 2007) was estimated using 300 maximum entropy bootstrap replicates of streamflow (Vinod andLópez-de-Lacalle 2009, Cook et al 2013).The reconstruction and bootstrap replicates were bias-corrected using quantile mapping to adjust for biases in the tails of the streamflow distribution resulting from the linear reconstruction methods (Robeson et al 2020).

Historical drought analysis
To compare instrumental droughts to the streamflow reconstructions, droughts were ranked by separately assigning a rank score to each event by duration, magnitude (cumulative streamflow anomaly), and peak value (maximum streamflow anomaly), with increasing ranks for increasing parameter values.Each of the three rank scores was then summed to obtain the final score, where a higher score represents a stronger drought episode (Biondi et al 2005).Drought events were defined as one or more consecutive years with streamflow below the long-term median (Peel et al 2005).The analysis of all three drought variables is sensitive to the definition of a drought, which is determined by the reference level (Hessl et al 2018).Therefore, the start and end of drought episodes identified in this analysis do not necessarily correspond to the accepted beginning and end of historical drought periods, which were defined based on other metrics.
The various drought elements (duration, magnitude, and peak) have different distributions and are typically correlated, necessitating a joint probability approach (Hessl et al 2018).The joint distribution of drought duration and magnitude was estimated using a bivariate distribution with geometric marginals for the duration and exponential marginals for drought magnitude (Biondi et al 2005, Kozubowski andPanorska 2005).Similarly, the joint distribution of drought duration and peak was estimated by a bivariate distribution with geometric marginals for the duration and truncated logistic marginals for the event peak (Biondi et al 2008, Kozubowski andPanorska 2008).The bivariate models were used to calculate the chance of occurrence of a drought of both longer duration and higher magnitude or peak than a given drought, with the return period of that drought approximated as the inverse of its exceedance probability (Kim et al 2003).Uncertainty in the bivariate distribution parameters was calculated using the reconstruction bootstrap replicates and thus the 90% uncertainty bands consider both reconstruction and probability model uncertainty.

Future drought occurrence
Climate projections were sourced from the Australian Bureau of Meteorology's Australian Water Outlook (AWO) dataset.Future projections in the AWO are derived from four CMIP5 climate models, chosen from amongst the subset of models which best represent Australian climate conditions, with minimal bias in the representation of ENSO and IOD (Srikanthan et al 2022): ACCESS1-0, CNRM-CM5, GFDL-ESM2M, and MIROC5.The selected subset is broadly representative of the full suite of CMIP5 models, although precipitation scenarios are more moderate, without either dry or wet extremes, and there is less warming than the full suite (Srikanthan et al 2022).The GCMs have been downscaled to 0.05 degrees using three bias correction methods and one dynamical downscaling model.Here, only model simulations based on the Multivariate Recursive Nested Bias Correction method (Johnson and Sharma 2012, Mehrotra and Sharma 2016) were used as this bias correction led to the best simulations of historical streamflow for the AWO dataset (Vogel et al 2023).
Projections of the landscape water balance components were generated from the bias-corrected CMIP5 model outputs using the AWRA-L model.Runoff projections, generated at 5 km resolution, were downloaded from the AWO website (https:// awo.bom.gov.au/).Streamflow was estimated as the basin-average runoff lagged by two months scaled to the instrumental mean, i.e., July-December runoff was used to predict September-February streamflow at Lock-7 (see supplementary).

Past and future Murray River streamflow
We used 114 tree-ring chronologies to reconstruct naturalised streamflow for the Murray River upstream of Lock-7 for the September-February season (figure 2).The streamflow reconstruction covers the period 1190-2020 CE, with instrumental data appended to the reconstruction from 2001-2020.Prior to 1190, the validation statistics (especially VCE) indicated that the reconstruction was too weak to be used.The bias-corrected reconstruction accounts for ∼67% of the variance in naturalised streamflow over the 1897-2000 calibration period and ∼86% of decadal-scale variability over the same period (see figure S7 for full nested calibration and validation statistics).Average monthly streamflow over the entire reconstruction interval is not statistically different from the average streamflow during the instrumental period (38 000 vs 38 700 GL, Student's t-test p > 0.1).The reconstruction reproduces the strong drying trend observed in the instrumental data, beginning around 1970 (Mann-Kendall trend test p < 0.001).Protracted dry epochs can be observed throughout the reconstruction interval, with the early 1200s emerging as a period of unusually persistent low flows, consistent with independent paleoclimate data representing the broader eastern Australian region (Vance et al 2013, Cook et al 2022).
Future Murray River streamflow projections were derived from an ensemble of four CMIP5 climate models that represent the range of potential future conditions over Australia.The models indicate a drier future for the MDB, with average streamflow over the 2021-2100 period projected to be between 2 and 26% lower than average streamflow over the last 800 years.All models predict a decrease in streamflow compared to the long-term average despite differences in the timing and direction of precipitation changes (table S3).The multi-model median shows a significant decreasing trend (p < 0.001) in streamflow from 2021 to the end of the century.These projections suggest that declines in mean Murray streamflow observed over the last 50 years of instrumental data are likely to continue, consistent with projected decreases in winter rainfall in southeast Australia (Moise et al 2015, Timbal et al 2015).

Contextualising instrumental droughts
We fitted joint probability models to characteristics of drought events identified in the reconstruction (table S2) to assess whether the recent drying trend was unusual compared to long-term climate variability.Two of the five most severe droughts in the last 800 years occurred during the instrumental period, the Millennium Drought (rank 1) and the World War II Drought (∼1940-1947, rank 3).The remaining three events all occurred during the early 1200s.Based on the combined drought characteristics, the Millennium Drought is shown to be exceptional compared to the 800 year paleorecord.The probability that a drought would have lasted for more than nine years and had a larger cumulative streamflow deficit than the Millennium drought is very small at 0.045%, estimated as a 2500 year return period.
Figure 3 shows the 40 most severe drought events identified in the full reconstruction period .Events are plotted against selected quantiles derived from the fitted conditional probabilities of drought magnitude and peak given droughts of durations between 2 and 14 years.Fourteen years is the longest event duration observed during the reconstructed period (figure 3).The droughts of the early-1200s were of longer duration and similar magnitude (cumulative streamflow deficit) to the Millennium drought, however the peak streamflow deficit during the Millennium drought event was unmatched at any point during the reconstruction period.There is a ∼3% probability that a nine-year drought would have exceeded the magnitude of the Millennium Drought and a ∼6% probability of a year with lower streamflow than 2007 (the lowest flow year).
The Millennium Drought was broken by widespread heavy rains in 2010/11, which caused flooding in parts of eastern Australia (King et al 2020).Since this event, streamflow at Lock-7 has been below the long-term median in every year except 2016 (2012-2016 rank 24), when another heavy rainfall event temporarily increased streamflow at Lock-7 just prior to the start of the Tinderbox Drought (rank 42).These events demonstrate that recent dry conditions are highly unusual, but not unprecedented, compared to the past 800 years of reconstructed Murray River streamflow.

Longer, more severe future droughts
To investigate how drought risk might change in the future, the joint probability analysis was repeated four times, with each time series comprised of the reconstruction (1190-2020) and one climate model projection (i.e., all future projections are considered equally likely).Historical and future droughts are plotted against the median modelled quantiles calculated from the time series considering natural variability and climate change (figure 4).To account for the difference in length between the historical and future periods, the top 80 droughts from the historical period (blue) are compared to the top 20 future drought across all projections (red).
Under the median future projection, there is only a small increase in the likelihood of severe droughts.The chance of a nine-year drought exceeding the magnitude of the Millennium drought increases from 3% to 3.4%, the probability of a larger peak deficit increases from 5.8% to 6.3%.Moreover, the probability of a drought of more than nine years with a larger cumulative streamflow deficit than the Millennium Drought increases from 0.045% to 0.074%.All these values are well within the 90% uncertainty interval considering both reconstruction and joint probability modelling uncertainty.
However, the driest climate model projects a significant increase in future drought severity, with droughts of much greater duration and higher magnitude than any previous drought, including those of the early 1200s.Under the driest projection, the probability of a drought of more than nine years with a larger cumulative streamflow deficit than the Millennium drought falls outside the calculated uncertainty bands at 0.111%.While the probability remains small, this represents a decrease in the return period from approximately 2500 years under natural variability to 900 years considering climate change.

Discussion
Several characteristics contribute to the 'severity' or the impact droughts have on people and environments.For water supply planning, drought duration and magnitude (cumulative streamflow deficit) are the most important features (Van Loon and Laaha 2015, Biondi and Meko 2019).Water management in Australia is more resilient to short droughts with smaller cumulative deficits, even if there is an extreme peak deficit in a single year (due to water storage carryovers).However, short sharp droughts can still have far-reaching environmental impacts through declines in soil moisture, vegetation health and adverse effects on aquatic ecosystems (Vertessy et al 2019).
Multi-year droughts affecting the MDB are rare in the instrumental record, and each event has had different spatial and temporal characteristics (Verdon-Kidd and Kiem 2009), making them difficult to predict and manage.This constrains the development of robust water security policy and infrastructure to mitigate the impacts of future droughts, as the instrumental record may not contain the longest or most severe drought caused by natural climate variability (Flack et al 2020, Kiem et al 2020).The tendency to view each new extreme event as the 'worst on record' also hinders risk management strategies for future unprecedented events (Van Dijk et al 2013, Kreibich et al 2022).To help overcome this limitation, paleostreamflow reconstructions can provide more accurate estimates of the baseline likelihood of drought occurrence.Science-based management and policy decisions can then be informed by numerical probability statements about drought occurrence (Biondi et al 2005).
We reconstructed 800 years of Murray River streamflow variability at Lock-7 to help contextualise instrumental period droughts.Notably, the reconstruction aligns with previously documented decadal fluctuations in streamflow over the past two centuries (Gallant and Gergis 2011; see supplementary S4 and figure S11), improving confidence in the results.
Considering all drought characteristics together, the Millennium Drought was the most severe over the reconstructed period, consistent with previous estimates (Gallant and Gergis 2011).That streamflow has been below the long-term median in all except two years since the end of Millennium Drought supports previous studies suggesting that increasing temperatures are amplifying the impact of precipitation deficits in eastern Australia (Cai and Cowan 2008, Cai et al 2009, Cook et al 2016).Nevertheless, the most recent period of persistent low flows is not unprecedented in the paleo-record; three of the top five ranked droughts occurred within the first half of the 13th century.Droughts of longer duration and similar magnitude as the Millennium Drought have occurred without anthropogenic influence.
With this context, we also considered the influence of climate change on future drought likelihoods.All four climate model projections suggest a small increase in the possibility of severe, multi-year droughts compared to the long-term record.Evapotranspiration-driven catchment drying and continued high inter-annual precipitation variability result in an increased likelihood of drought events in the MBD, even for models where basinaverage water year precipitation is projected to increase by the end of the century.While the increase in drought occurrence is within the uncertainty range for most future projections, the driest forecast shows a significant increase in the likelihood of severe droughts compared to natural variability.
Streamflow reconstructions in eastern Australia are limited by the paucity of high-resolution paleoclimate proxies collected in-situ from the Australian mainland.The reconstruction in this study was based on remote tree-ring proxies only, a limitation consistent with all previous reconstructions for this region.Thus, the reconstruction only captures variability due to large-scale climate processes and is unlikely to account for interim drought relief from local synoptic-scale events, for instance, East Coast Lows, ex-tropical cyclones and monsoon troughs that can drive extreme short-term flooding (Pittock et al 2006, Verdon-Kidd et al 2017).The importance of heavy rains for breaking drought events in the MDB highlights the need to better capture high flow extremes in the reconstruction (see supplementary) as information on the maximum interval between drought-relieving rain events could be critical in refining the risk of future, multi-year droughts.The development of new tree-ring chronologies or other high-resolution proxies from eastern Australia would help verify the findings presented here and improve the interpretation of recent drought events.

Conclusions
With the increasing risk of high-impact climate extremes in the MDB (and Australia more broadly), there is an urgent need for more resilient drought management practices informed by an improved understanding of natural conditions.Our results demonstrate that paleo-streamflow reconstructions can be used to better estimate instrumental drought return periods and thus contextualise recent extremes.From this baseline, we calculated how climate change could shift the occurrence probability of severe droughts.While the likelihood of a drought exceeding the Millennium Drought in both length and magnitude is small, droughts of 20 years' duration and double the magnitude of the Millennium Drought are plausible in future under climate change and should be considered in longterm water management planning, given the potential socio-economic and environmental consequences.

Figure 1 .
Figure 1.Location of lock number 7 (black dot) within the Murray-Darling Basin (MDB; dark blue).Red circles indicate the locations of the 114 tree-ring predictors used in the streamflow reconstruction.The radii of the circles are scaled to their weighting in the regression equation.Darker red circles indicate overlapping chronologies (e.g.Tasmania, see tableS4).

Figure 2 .
Figure 2. (a) Reconstructed (blue) versus naturalised instrumental (black) Murray River September-February streamflow over the calibration (1921-2000) and verification (1897-1920) periods.The 90% confidence interval is based on 300 maximum entropy bootstrap replications; (b) Reconstructed Murray River September-February streamflow as departures from the 'historical' period mean (1190-2020 CE; blue and brown bars, with 90% confidence interval as lightly shaded bars), along with the 20-year low-pass filtered reconstruction (black) highlighting multi-decadal variability.The instrumental naturalised Murray streamflow between 1897 and 2020 CE is shown as black bars.The range of the four CMIP5 RCP8.5 models over the 'future' simulation period (2006-2099 CE) is shown as grey bars.The median 20-year low-pass filtered projected streamflow is shown as a bold red line, with the dashed red lines indicating the range of the low-pass filtered streamflow projections.

Figure 3 .
Figure 3.The top ranked droughts during the historical period (1190-2020 CE) at Murray River Lock-7 compared to selected quantiles of the conditional distribution for (a) drought duration and magnitude and (b) drought duration and peak in median distribution units (MDU).For clarity, only the 40 most severe events are displayed.Grey bands represent the 90% uncertainty interval for the selected quantiles.The colours indicate the time window when the drought began, and points with similar rank are jittered for display purposes.

Figure 4 .
Figure 4.The top 80 ranked droughts during the historical period (1190-2020 CE; blue) compared to the 20 highest ranked droughts in the streamflow projections (2021-2099 CE; red) for the Murray River at Lock-7 for (a) drought duration and magnitude and (b) drought duration and peak.The black dot indicates the Millennium drought.The dashed black lines represent selected quantiles of the conditional distribution based on historical data, and the dashed brown lines represent the median quantiles for the conditional distribution of historical and projected streamflow.Grey bands represent the 90% uncertainty interval for the selected quantiles.