Change in centre of timing of streamflow and its implications for environmental water allocation and river ecosystem management

Timing of delivery of environmental water is essential for restoring and conserving riverine ecosystems. However, change in the timing of occurrence of streamflow and its implications on environmental water allocation and river ecosystems are often ignored in current environmental water research and management. We adopted the centre of timing approach to analyse the change in the occurrence of streamflow due to climate change (through a change in rainfall) and river operations (flow regulation and diversion) in the Goulburn-Broken catchment, Victoria, Australia. It was found that annual streamflow in the catchment declined by an average of 47%, while centre of timing increased by an average of 36%. These changes were 52% attributable to rainfall decline and 48% to river regulation. A decline in annual streamflow (35%) and an increase in centre of timing (21%) across the Goulburn River would be observed by 2050 as an impact of climate change. Current management efforts should be directed at reversing the change in centre of timing to support the sustainable management of riverine systems. The Goulburn-Broken catchment is typical of managed catchments in many areas of the world with forecast rainfall reduction, and the findings are likely to be widely applicable.


Introduction
Environmental water plays a vital role in protecting and conserving riverine ecosystems. Environmental flows are widely practised but have failed to improve river ecosystem health in many regions of the world (Stewart et al., 2005;Dudley et al., 2017;Capon et al., 2018).
Both timing and magnitude of streamflow play a key role in connecting river channels with floodplains and wetlands, triggering the exchange of flux and material, maintaining water quality, facilitating species migration, supporting riverine biodiversity, and nourishing riparian vegetation (Poff et al., 1997;Patil et al., 2022a). Thus, environmental water requirements are not only volume dependent but also time dependent. For example, seasonal flood pulses trigger the exchange of flux and material essential for riverine food web (Harvey and Gooseff, 2015;Talbot et al., 2018) and reasonable autumn flows allow salmonid migration up-streams to spawning grounds (Fjeldstad et al., 2018). Additionally, native species of fish, frogs, riparian vegetation, and invertebrates, which are top-level prey for water birds and reptiles, need seasonal high flows to flourish (Kingsford, 2000;Kingsford et al., 2017). Similarly, shallow water species and aquatic vegetation are adapted to low flows during the dry period of the year (Pollino and Couch, 2014;Keller et al., 2019). However, river regulation and flow diversion have altered the magnitude and timing of streamflow which brought a significant shift in the floristic and faunistic structure of the riverine environments, resulting in varying water requirements for restoration of river ecosystems, such as in the Murray-Darling basin in Australia (Kingsford et al., 2017;Patil et al., 2018). Additionally, variation in streamflow due to seasonal climate change results in discrete environmental water requirements for wetlands and water quality which can bring complex effects on riverine environments, such as disruption to fish and frog breeding cycle (Reid et al., 2013;Hall et al., 2014;Leigh et al., 2015). In regulated rivers, such effects may also be associated with the delayed environmental water delivery. However, little is known about how the change in timing due to the combined effects of climate change and river regulation can affect the allocation and delivery of environmental water. An explicit assessment of the combined effects of climate change and river regulation on centre of timing is thus necessary to improve environmental water management for restoration and conservation of riverine ecosystem.
There is evidence of earlier trends in centre of timing in North America and Europe associated with earlier onset of winter and springtime snowmelt due to higher temperatures (Stewart et al., 2005;Dudley et al., 2017;Matti et al., 2017). Similar trends in early flood timing associated with increase in mean rainfall in north central Australia and reverse trends in south due to decrease in mean rainfall are reported by Wasko et al. (2020). These studies have very coarse spatial resolution which do not capture upstream to downstream variation in streamflow and centre of timing in regulated catchments, where timely delivery of environmental water (environmental flows) is inevitable to support degraded riverine ecosystems. Thus, recommendations from these studies for catchment-scale applications can diminish the benefits of adaptive environmental water allocation (and environmental flow delivery) in recovery and restoration of degraded riverine ecosystems. It can lead to issues such as insufficient allocation of environmental water and off-time delivery and riverine ecosystems may remain in degraded states (Pittock and Lankford, 2010;Vivian et al., 2014). This paper attempts to redress the lack of focus on the timing of environmental water delivery. It adopts the centre of timing approach to investigate the temporal and spatial change in centre of timing together with change in amount of streamflow for improving environmental water allocation and riverine ecosystems in the Goulburn-Broken Catchment, Victoria, Australia. Specifically, it includes the following objectives: 1) to analyse the long-term change in annual streamflow and centre of timing against river regulation and climate change (through rainfall variation); 2) to analyse the upstream to downstream change in annual streamflow and centre of timing against river regulation and climate change (through rainfall variation); 3) to predict the effects of climate change on annual streamflow and centre of timing. The findings from this study are expected to help water managers improve environmental water allocation and environmental flow practices for sustainable management of riverine ecosystems.

Study area
The study area is the Goulburn-Broken catchment in Victoria, Australia. The catchment is located about 100 km northeast of Melbourne and stretches as far north as where the Goulburn River meets the Murray River (see Fig. 1). It is one of the largest water catchments in the Murray-Darling River Basin (MDB) system (incorporating 2% of the total area of the basin), contributing 11% of the total annual inflow to the basin. It is also one of the most regulated catchments in the MDB system, with a long history of regulating and managing Goulburn River to secure water supply, motivated by post-war economic reconstruction (Bell, 1988). Goulburn Weir is the oldest diversion structure (existed since 1890) located upstream of Murchison station (see Fig. 1) that has a storage capacity of around 25.5 GL and diverts nearly 60% of the annual discharge of the Goulburn River (Nathan, 1992). The Lake Eildon, with an impoundment of 377.4 GL, was constructed in 1922 in the upper catchment (see Fig. 1) to regulate headwaters of the Goulburn River. Its storage capacity was increased nearly 10-times (3334 GL) in 1955 and its operations began in 1957. Currently, water from the upper catchment is stored in the largest regulation structure, Lake Eildon, and is released downstream according to consumptive (socio-economic) and environmental water requirements in the catchment and the wider MDB. Water is diverted off the Goulburn River via Stuart Murray canal and Cattanach canal for off-river storage, and via East Goulburn Main channel for irrigation (see Fig. 1).
The catchment supports cropping, dairy, fruit, and wine industries. It is a site of significant recreational activity including water sports and camping. The catchment is also home to diverse species of riparian trees (river red gum (Eucalyptus camaldulensis)), fish (Maccullochella peelii, Macquaria ambigua), burrowing frogs (Heleioporus australiacus, Litoria paraewingi), water birds, reptiles, lizards, micro-invertebrates, and mammals (Briggs, 1992;Kingsford, 2000;Victorian Environmental Water Holder (VEWH), 2016). This assemblage of taxa forms a significant component of Australia's biodiversity.
Following intensive river regulation and flow diversion, the catchment has experienced severe ecological and environmental degradation, evident from degraded water quality, fragmented habitats, and disturbed life cycles of many plants and animal species (Gippel and Finlayson, 1993;Patil et al., 2022b). The fragile ecosystem of the catchment is also under a constant threat of climate change (particularly declining rainfall and rising temperatures). The catchment receives an average annual rainfall ranging from 1600 mm in the southern headwater reaches to 500 mm on the northern plains. Over 70% of the total annual rainfall in the catchment is received during winter (Austral winter -June to August) and spring (September to November) under the influence of westerly fronts coming off the Great Australian Bight. Recent climate projections have indicated that Victoria faces a potentially hot and dry future, with an overall decrease in annual rainfall including a larger decrease in winter and spring rainfall and a comparatively smaller decrease in summer and autumn rainfall (Table 1) (Timbal et al., 2016). This is associated with a reduction of penetration of westerly fronts into this region. This will further worsen the environmental conditions causing habitat and water quality degradation, algae growth, floodplain and wetland degradation, and biodiversity loss (Patil et al., 2022a;Cottingham et al., 2014; GBCMA (Goulburn Broken Catchment Management Authority), 2021).
Environmental flows were recommended in 2011 and since then have been practised in the catchment to support the impacted river ecosystem; however, there is limited success in the recovery of riverine ecosystems (Victorian Environmental Water Holder (VEWH), 2015). Environmental flows are a measure of the quantity, timing, and quality of water flows required to sustain freshwater ecosystems (such as native fish, frogs, water birds and river-dependent plants and animals that rely on different flows to trigger migration and breeding) and the human livelihoods and well-being that depend on these ecosystems . Water for environmental flow delivery is allocated under the Commonwealth Environmental Water Holder (CEWH) and Victorian Environmental Water Holder (VEWH) through high reliability (HR) and low reliability (LR) entitlements. Under high-reliability entitlement, water for environmental purposes (also known as environmental water) is assured under most climatic conditions (under normal or average wet years), while environmental water under low-reliability entitlements is only available during climatic and hydrological extremes such as drought. Current environmental water allocation policies mainly depend on the high-reliability water entitlements (Victorian Environmental Water Holder (VEWH), 2016) while environmental flow delivery is still 'species centric' (Crossman et al., 2011;Cottingham et al., 2014).
We considered five major gauging stations Doherty, Eildon, Seymour, Murchison, and McCoy Bridge, and three tributaries (Delatite River, Big River, and Jamieson River) joining the Lake Eildon for analysis (Fig. 1). Murchison station has the longest streamflow record (1883-2020); thus, we analysed the long-term (historical) changes in centre of timing and streamflow at Murchison station to link them with the key historical stages of water resources development in the catchment. Other stations (located either across the Goulburn River or tributaries) have streamflow records starting after 1960 s. Therefore, we analysed upstream to downstream changes in streamflow and centre of timing from 1966 to 2020. For ease of comparative analysis and interpretation, we grouped the stations into upper catchment (Goulburn River at Doherty, Delatite River, Big River, and Jamieson River (flowing into the Lake Eildon)), middle catchment (Eildon and Seymour), and lower catchment (Murchison and McCoy Bridge) groups ( Fig. 1).

Methods
The concept of centre of timing was used in this study to track the changes in timing and magnitude of streamflow due to climate change (through a change in rainfall) and river regulation to inform environmental water allocation for restoring riverine ecosystems. Centre of timing is the time (usually in days) required to reach half of the total annual streamflow at any given point along a river in a year (Court, 1962). The half of annual streamflow in any given year is called the centre of mass (or volume) of streamflow in that year (McCabe and Clark, 2005). Mathematically, centre of timing (CT) can be expressed as (Stewart et al., 2005): where, t i is the time from the beginning of the year (water year) (in days) corresponding to q i , and q i is the streamflow value in the daily time series approaching to 0.5*Q, where Q is annual streamflow by volume. We determined the annual time series of centre of timing and streamflow based on the Australian Water Year starting from 1st of July and ending on 30th of June following year (BoM (Bureau of Meteorology), 2019). We wrote MATLAB and R codes to determine annual time series of streamflow and centre of timing from daily streamflow data at Doherty, Eildon, Seymour, Murchison, McCoy Bridge stations, and three tributaries (Delatite River, Big River, and Jamieson River) flowing into the Lake Eildon.

Analysing effect of rainfall variation and river regulation on longterm (historical) change in centre of timing and streamflow
Firstly, we analysed the long-term (1883 -2020) trends of annual time series of centre of timing, streamflow, and rainfall (annual and seasonal) at Murchison station using both the linear regression and the non-parametric Mann-Kendall trend test (Mann, 1945;Kendall, 1975) to understand the patterns of long-term change in centre of timing and streamflow.
Then, we used Pettit's test for single change-point analysis to detect long-term shift in centre of timing and streamflow time series. The change point analysis was carried out to detect long-term distributional shifts (e.g., existence of two different means) in a time series. Then we developed double mass curves of cumulative centre of timing and streamflow against cumulative rainfall based on the change point analysis. Alternatively, double mass curve also validated the abrupt change points detected in the change point analysis. The double mass Table 1 Details of climate projections (rainfall) (up to 2050) (CCIA (Climate Change in Australia), 2020) used for prediction purposes.

Variable
Climate change scenarios (up to 2050) curves were used to determine the actual relative change in magnitude of centre of timing and streamflow and to attribute the relative contribution of climate change (rainfall variation (C rain )) and river regulation (flow regulation and diversion) (C regulation ) in the change in centre of timing (CT) and annual streamflow (Q). To determine the contribution of rainfall variation, the total change in centre of timing (ΔCT total ) was determined as: where, CT postc is the centre of timing in post-change period and CT prec is the centre of timing during pre-change period. Then the change in centre of timing caused by variation in rainfall (ΔCT rain ) was determined as: where, CT predicted is the predicted centre of timing during post-change period. The CT predicted is determined from the regression relations fitted to the centre of timing during the post-change period using the double mass curve method (supplementary material). It means, if the river regulation had not implemented in the catchment, the change in the centre of timing would have been attributed to the rainfall variation alone. The contribution of rainfall variation (C rain ) in change in centre of timing was calculated as: Then the change in centre of timing caused by river regulation (ΔCT regulation ) was determined as: The contribution of river regulation (C regulation ) in the change in centre of timing was calculated as: Similarly, contributions of rainfall variation and river regulation in change in streamflow were determined by replacing CT (centre of timing) with Q (streamflow) in equations 2 -6.
The change in annual streamflow and centre of timing was analysed historically and spatially. We analysed the historical change at Murchison station (1883-2020) to attribute development of water resources infrastructure (river regulation) and climate change to the change in streamflow and centre of timing. We also analysed correlations of centre of timing and streamflow with rainfall (annual and seasonal) to detect relational change between these variables over pre-and post-change periods (i.e. pre-and post-regulation periods).

Analysing effect of rainfall variation and river regulation on upstream to downstream change in centre of timing and streamflow
Rainfall variation and river regulation not only affect the centre of timing and streamflow at longer temporal scales, but also tend to drive these changes at various spatial scales, such as, upstream to downstream of the catchment. To determine the spatio-temporal effects of rainfall variation and river regulation on centre of timing and streamflow, we analysed trends (1966-2020) of centre of timing, streamflow, and rainfall (annual and seasonal) from the upstream to the downstream of the catchment, and attributed changes (pre-and post-change between 1966 and 2020 after intensive river regulation was implemented in the catchment (during post-regulation period)) in river regulation and rainfall variation to the change in the centre of timing and streamflow. We adopted methods described in section 2.2.1 for analysing trends, detecting change points, and developing double mass curves, and analysing relational changes (using correlations) of streamflow and centre of timing with annual and seasonal rainfall.

Predicting effects of rainfall variation on centre of timing and streamflow
Variation in seasonal (winter and spring) rainfall dominates majority of streamflow (inflow) variation in the Goulburn-Broken catchment at the onset of the water year. This study focussed on centre of timing (commencing at the onset of the water year) and associated streamflow variation in the first half of the water year thus we predicted the impact of seasonal variation in rainfall (winter and spring rainfall) instead of annual rainfall.
We used linear regressions to predict the effects of the projected decline in winter and spring rainfall on streamflow and centre of timing under RCP (Representative Concentration Pathway) climate change scenarios (RCP4.5 -intermediate emission and RCP8.5 -high emission). Centre of timing and streamflow were fitted to winter and spring rainfall summed at annual basis. The regression relations were fitted at individual stations, but results are presented in summarized format at reach scale to avoid repetition. The performance of each of the regression equations was analysed based on R 2 , p-value, and Nash-Sutcliffe model efficiency (NSE) coefficient (supplementary material). The purpose was to understand how much variation in streamflow and centre of timing is explained by the seasonal rainfall events, which play key role in either earlier or delayed occurrence of the centre of timing, and increase or decrease in streamflow, and hence directly affects the water availability in the catchment and its relevance from the management perspective.

Data
The streamflow data of the stations mentioned in section 2.1 was sourced from the Victoria Government Department of Environment, Water, Land, and Planning (DELWP (Department of Environment, Land, Water, and Planning), 2019). For Murchison station, the streamflow time series was 138 years (1883-2020), and at other stations (Doherty, Eildon, Seymour, McCoy Bridge, Delatite River, Big River, and Jamieson River), the streamflow time-series was 55 years (1966 -2020). Rainfall data was sourced from the Bureau of Meteorology Australia (BoM (Bureau of Meteorology), 2019). Average monthly rainfall at the abovementioned stations were determined from the monthly rainfall of rain gauge stations located either on the hydrological gauges or the surrounding areas within 50 km radius of each hydrological gauging station. The rainfall projections data for the catchment was obtained from Victorian Climate Projections (VCP19) (CSIRO and Bureau of Meteorology, 2015; IPCC (Intergovernmental Panel on Climate Change), 2014; Timbal et al., 2016). The rainfall projections under climate change scenarios RCP 4.5 (intermediate emission) and RCP 8.5 (high emission) were used (Table 1).

Long-term changes in centre of timing and streamflow at Murchison station during 1883-2020
Historically, streamflow and centre of timing evolved significantly between 1883 and 2020 (Fig. 2). A significant shift in annual streamflow and centre of timing was observed at Murchison in 1957 following the full-scale operation of the Lake Eildon ( Fig. 2a and 2b). Annual and seasonal (winter and spring) rainfall at Murchison gradually declined from 1883 to 2020 (Fig. 2c). Peaks in streamflow time-series (Fig. 2a) reflect the flood events across the Goulburn River associated with extreme rainfall events (Fig. 2c) in the Goulburn-Broken catchment. On the other hand, peaks in centre of timing (Fig. 2b) reflect frequent dry periods across the Goulburn-Broken catchment since 1883 while prolong rise in centre of timing, such as between 1997 and 2009 (Fig. 2b) corresponds to the Millennium Drought. A strong long-term decreasing trend in streamflow (tau = -0.4) and increasing trend in centre of timing (tau = 0.127) were detected (Fig. 2d). The average annual streamflow at Murchison reduced from 2900 GL in 1883 to 500 GL in 2020 (Fig. 2a).
During this period, the centre of timing showed a steady increase (Fig. 2b). Based on the significant shifts in streamflow and centre of timing, the historical time-period was divided into pre-change (i.e. preregulation) (1883-1956) and post-change (i.e. post-regulation) periods . The average streamflow at Murchison reduced by 1327 GL during the post-change period  compared to the streamflow during the pre-change period   (Fig. 2e). The decline in rainfall contributed nearly 20% to this change, while river regulation contributed over 80% to the decline in streamflow. In the post-change period, the centre of timing increased by 54 days compared to the centre of timing during the pre-change period. This increase is contributed nearly 22% by rainfall changes and just under 79% by river regulation (Fig. 2f).
Streamflow and centre of timing were strongly correlated with seasonal rainfall (r = 0.82) than with the annual rainfall (r = 0.41) during pre-change period   (Fig. 2g). However, relationship between streamflow and seasonal rainfall weakened significantly (r = 0.61) during post-change period, while that with annual rainfall remained nearly unchanged (Fig. 2g). Contrarily, negative correlation between centre of timing and seasonal rainfall strengthened and its correlation with annual rainfall reversed during the post-change period (1957-2020) (Fig. 2h).  -1957). Strength of long-term trends is showed by d) Kendall's tau (values with asterisk (*) mark indicates significant trends (p < 0.05) and those without asterisk mark shows trends not significant (p > 0.05)). The percent contribution of climate change (through change in rainfall) and river regulation into a change in e) streamflow and f) centre of timing during the post-change period (1957-2020) as compared to the pre-change period if regulation had not implemented in the catchment. Correlations of g) streamflow, and h) centre of timing with annual and seasonal rainfall comparing relational changes over pre-and post-change periods at Murchison.

Upstream to downstream changes in centre of timing and streamflow across the Goulburn River during 1966-2020
Annual streamflow and rainfall (annual and seasonal) declined gradually across the Goulburn River after 1966 (Fig. 3). Significant declining trends of streamflow and rainfall were detected across the Goulburn River ( Fig. 3 and Table 2). The decline in streamflow is stronger than the decline in rainfall (Table 2). Across the Goulburn River, an average change year was observed in 1990. The rate of decline in streamflow is higher since 1990. The average annual streamflow after 1990 is significantly less compared to the average annual streamflow between 1966 and 1990. The minimum decrease in streamflow (29 GL) is observed in the upper catchment, while the lower catchment showed the largest decline (502 GL) (Fig. 4). In the upper catchment, climate change (through the change in rainfall) contributed most (93%) to this decline. In contrast, in middle and lower parts of the catchment, river regulation (average 70%) is a major contributor to streamflow decline (Fig. 4). The contribution of climate change (rainfall) (average 30%) in the middle and lower catchment is still important (Fig. 4).
The centre of timing increased steadily across the Goulburn River between 1966 and 2020 (Fig. 3). Increase in trends of centre of timing is significant at all the sites, except for Big River and Delatite River, where a weak insignificant decline in centre of timing was found ( Fig. 3 and   Fig. 3. Long-term trends (1966-2020) of annual streamflow, centre of timing, and annual and seasonal (winter and spring) rainfall in a) upper, b) middle, and c) lower catchments. Vertical dotted lines (in red) represent the average change year (here 1990).

Table 2
Trend estimates of streamflow, centre of timing, and annual and seasoanl rainfall from the upstream to the downstream of the catchment.

Streamflow
Centre of timing Note: Values with asterisk (*) mark indicates significant trends (p < 0.05) and those without asterisk mark shows trends not significant (p > 0.05). Table 2). The increase in the trends of centre of timing in the upper catchment is weaker compared to the increase in the middle and lower catchment, while the increase in centre of timing is strongest in the lower catchment (Table 2). After the 1990 s, the centre of timing increased significantly compared to before the 1990 s. In the upper catchment, the centre of timing increased by only 6 days mostly due to rainfall decline (94%) (Fig. 4). In the middle and lower catchment, the centre of timing increased by an average of 40 days and this increase was about 70% due to river regulation and 30% due to rainfall decline (Fig. 4). Peaks in streamflow (Fig. 3) show the flood events between 1966 and 2020 across the Goulburn River associated with extreme rainfall events (Fig. 3) in the Goulburn-Broken catchment. On the other hand, peaks in centre of timing (Fig. 3) correspond to dry periods across the Goulburn-Broken catchment since 1966 and a long-term rise in centre of timing, such as 1997-2009 corresponds to the Millennium Drought. A frequent prolong rise in centre of timing in the middle catchment is associated with less rainfall and regulation upstream which ultimately reduced streamflow across the Goulburn River.
Relationships of streamflow and centre of timing with annual and seasonal rainfall significantly changed after the 1990 ′ s (Fig. 5, Table 3). Between 1966 and 1989, streamflow across the Goulburn River was highly correlated to the seasonal rainfall (Table 3). After the 1990 ′ s correlation between streamflow and seasonal rainfall strengthened significantly in upper and lower catchment. Post the 1990 ′ s, correlation between streamflow and annual rainfall significantly increased while its correlation with seasonal rainfall declined substantially in the middle catchment (Fig. 5, Table 3).
Similarly, centre of timing was highly correlated to seasonal rainfall between 1966 and 1989 across the Goulburn River. Post the 1990 ′ s the correlations between centre of timing and seasonal and annual rainfall weakened significantly in upper and middle catchment. The middle catchment showed the most weakened relationship between centre of timing and rainfall. Contrarily, the correlation of centre of timing with annual and seasonal rainfall has substantially strengthened after 1990 ′ s in the lower catchment (Fig. 5, Table 3). Fig. 6 shows the predicted effects of seasonal (winter and spring) rainfall on annual average streamflow and centre of timing under RCP4.5 and RCP8.5 scenarios (see Table 1). A consistent decrease in annual streamflow and increase in centre of timing across the Goulburn River is predicted (Fig. 6). Average annual streamflow in the middle catchment will decline by 220 GL under RCP4.5, and 300 GL under RCP8.5 scenarios (Fig. 6a). The centre of timing in the lower catchment would increase by 25 days under RCP4.5 and 40 days under RCP8.5 scenarios, (Fig. 6b).

Discussion
This study aimed to analyse the combined impact of river regulation and climate change on centre of timing and streamflow for improving environmental water allocation and riverine ecosystem management. We analysed historical and upstream to downstream trends of centre of timing, streamflow, and rainfall, attributed contributions of river regulation and climate change into the change in streamflow and centre of timing, and predicted the impacts of seasonal rainfall variation on streamflow and centre of timing under RCP4.5 and RCP8.5 rainfall projections scenarios. Key findings from this study and their implications for the Goulburn River ecosystems are discussed below: Rainfall variation has been a long-term threat to the ecosystem and the water resources of the Goulburn-Broken catchment, which contributes over 11% annual inflow into the Murray-Darling River Basin. Although the long-term shift in the streamflow (Fig. 2a) and centre of timing (Fig. 2b) was mainly the result of intensive regulation of the Goulburn River (Fig. 2e, 2f), it may have persisted due to river regulation as well as climate change (Fig. 2). A large shift in streamflow and centre of timing, was clearly resulted from the impoundment of Lake Eildon (storage capacity 3334 GL). The average centre of timing increased by 54 days after 1957. Interestingly, operation of Goulburn Weir (began in 1896) had least or no effect on larger distributional shifts in streamflow or centre of timing. Although gradual decline in winter and spring rainfall in the Goulburn-Broken catchment was associated with a decline in streamflow and later centre of timing, the rate of increase (later) in centre of timing seemed to have been driven by longlasting dry periods (such as the millennium drought). More frequent dry periods could dominate later trends of centre of timing and decline in streamflow.
The upper catchment witnessed gradual decline in rainfall and streamflow volumes. The lack of regulation structure upstream of the Lake Eildon denoted the impact of winter and spring rainfall decline on streamflow and centre of timing. The peaks in streamflow were explicitly associated with wet years while peaks in centre of timing reflect dry years in the upper catchment. A more erratic pattern of streamflow and centre of timing showed less association with declining rainfall in the middle catchment. Overall, the change in streamflow and centre of timing are attributable to climate change in the upper catchment but they become progressively less attributable to climate change downstream of the Lake Eildon. Only tributaries inflow into the Goulburn River could reverse altered streamflow and centre of timing in the middle catchment. Urgent attention is needed for restoring streamflow and centre of timing in the middle catchment to support recovery of degraded river ecosystems. Weakened rainfall-streamflow or rainfallcentre of timing relationships imply that the regulated rivers with altered streamflow patterns can be more sensitive to the variation in rainfall (Patil et al., 2022a). Improved rainfall-streamflow or rainfallcentre of timing relationships in the lower catchment could be attributed primarily to tributaries inflow into the Goulburn River past Goulburn Weir (Murchison and McCoy Bridge stations). It implies that, any change in rainfall patterns, such as rainfall extremes or drought would result in additional shifts in streamflow and centre of timing in the lower catchment.
Massive shifts in the future patterns of streamflow and centre of timing depict that a uniform pattern of decline in streamflow and later (increased) centre of timing is highly likely. It implies that climate change alone through decline in winter and spring rainfall would result in as much as 20 GL less streamflow in the upper catchment, 250 GL in the middle catchment, and 300 GL in the lower catchment with likely delay of 20 days, 50 days, and 60 days in centre of timing (availability) in the upper, middle, and lower catchment respectively.
A decrease in streamflow and an increase in centre of timing would bring stark challenges in terms of environmental water availability and allocation. High reliability water entitlements are based on the Table 3 Coefficients of correlations (r) of streamflow and centre of timing with annual and seasonal rainfall before (1966-1989) and after (1990-2020) the change periods from the upstream to the downstream of the catchment.

Station/ tributary
Pre-change  Post-change (1990-2020)  precipitation received in winter and spring, which contributes over 70% of the Goulburn-Broken inflows. Declining streamflow would decrease the water availability in the storages (Lake Eildon), while the increase in centre of timing would delay the availability of expected volume of water in the storages, when demand for irrigation water begins to rise during late spring. This would compromise water allocation decisions and planning. The predicted change in streamflow and centre of timing under RCP4.5 and RCP8.5 climate change scenarios would result in unforeseen water demands for irrigation and environmental purposes (e. g. water quality requirements and habitat restoration requirements) which would challenge current management regime. The predicted pattern of change also suggests that future seasonal rainfall variation would have severe implications for high-reliability water entitlements currently practised in the Goulburn-Broken catchment (GBCMA (Goulburn Broken Catchment Management Authority), 2016a), indicating that it will decrease the availability of water for environmental purposes. It would reduce water quality (due to increased salinity), degrade aquatic habitats, and interrupt the breeding of native fish species due to insufficient environmental flows. The trends of decrease in streamflow and increase in centre of timing across the Goulburn River have severe implications for managing the riverine ecosystems. Decline in streamflow has disconnected floodplains and wetlands from the Goulburn River (Patil et al., 2020), affected native riverine species (Davies et al., 2012), caused poor water quality (Patil et al., 2022b); and reduced riverine biodiversity (MDBA (Murray-Darling Basin Authority), 2017) of the Goulburn-Broken catchment. Delay in the occurrence of timing of streamflow has altered the life cycle of invertebrates, fish (Murray Cod), and waterbirds (Blue-billed duck, Pelicans, Egrets) across the Goulburn River, which are adapted to seasonal winter and spring flows (Kingsford et al., 2000; GBCMA (Goulburn Broken Catchment Management Authority), 2013). It has brought a largescale shift in riverine food web by halting the exchange of flux and material due to reduced streamflow and delaying the cycle of mating and breeding of diverse riverine species due to an increase in the timing of occurrence of streamflow (centre of timing) (Cottingham et al., 2014). It resulted in a decline in the population of native species of fish, water birds, insects, micro-invertebrates, reptiles and mammals, which are heavily dependent on the riverine food web (Davies et al., 2012; GBCMA (Goulburn Broken Catchment Management Authority), 2021). For instance, the population of water birds and micro-invertebrates declined by over 60% during 1983 and 2016 due to inadequate flows resulting from drought (GBCMA (Goulburn Broken Catchment Management Authority), 2016b; Kingsford et al., 2017;Victorian Environmental Water Holder (VEWH), 2022). Reduction in winter and spring rainfall (-15%, see Table 1) as a result of predicted climate change would increase centre of timing by 32 days and decrease streamflow (by 260 GL). This would increase the water stress of irrigated crops, and of floodplains and wetlands, which can permanently dry out. For example, in the 2015-2016 agricultural season, due to delayed spring flow, crops (in the lower Goulburn catchment) failed due to an inadequate supply of irrigation water during late spring to early summer (GBCMA (Goulburn Broken Catchment Management Authority), 2017; BoM (Bureau of Meteorology), 2022, BoM (Bureau of Meteorology), 2023). In the same year (2015-2016), very poor water quality conditions occurred due to low levels of dissolved oxygen along with accelerated growth of algal blooms, and as a result there was a reduction in native fish population (GBCMA (Goulburn Broken Catchment Management Authority), 2016c; GBCMA (Goulburn Broken Catchment Management Authority), 2017; Webb et al., 2017). Delayed flow peaks are detrimental to breeding and spawning native fish species such as Murray Cod (Kingsford, 2000;Tonkin et al., 2022). An increase in the centre of timing would decrease crop production, further reduce water quality, and importantly, it would put the native species of water birds, micro-invertebrates, and fish at a greater risk of extirpation or extinction (Fig. 7).
The key findings from this study suggest that current water availability trends in the Goulburn-Broken catchment have failed to fulfil environmental water requirements (Chen et al., 2020;Patil et al., 2020). The change in seasonal flow patterns has led to an extended disconnection between floodplain and wetland ecosystems and Goulburn River (Patil et al., 2020). Similarly, a change in key streamflow metrics created poor water quality conditions and negatively impacted the health of the riverine ecosystem of the catchment (Patil et al., 2022b). Reassessment of the environmental water requirements from the perspective of change in centre of timing is necessary to inform the management regime to adapt to the changing water availability. Autumn releases from Lake Eildon could be delayed until peak flows in winter to release higher magnitude winter and spring flows which would help in reversing (reducing) centre of timing downstream. This would improve fish breeding and spawning, habitat connectivity, and cropping and grazing in the middle catchment, which is heavily impacted by the increased centre of timing and reduced seasonal flows due to regulation upstream (Lake Eildon) (Gippel and Finlayson, 1993;Cottingham et al., 2003; GBCMA (Goulburn Broken Catchment Management Authority), 2015). As Goulburn Weir is used less in the early part of the water year (winter and early spring), higher magnitude winter and spring releases from Lake Eildon would restore centre of timing in the Lower Goulburn which is essential to maintain water quality and for survival of water birds, reptiles, and micro-invertebrates (Scott, 1997; MDBA (Murray-Darling Basin Authority), 2017; Patil et al., 2022a;Patil et al., 2022b). This would minimize the impacts of inevitable reduction in streamflow due to climate change on the catchment ecosystems.
The increase in centre of timing and decrease in streamflow are common in the tropical, subtropical, and temperate regions (Wasko et al., 2020;Veldkamp et al., 2017). It is also observed in temperate rivers of water-stressed regions (Veldkamp et al., 2017). These are inevitable consequences of river regulation and flow diversion, exacerbated by reduced rainfall. Reduced rainfall and dam storages delay the availability of the expected amount of water leading to later centre of timing downstream while water diversion siphons off the flows, and as use increases, available water in rivers declines. Findings from this study can be extended to most river systems to inform the management regime. The management regimes should include reversing the change in centre of timing as a primary objective that would support natural systems to thrive and enhance water storage in lower parts of the river systems which are prone to drought.

Conclusions
This study adopted a centre of timing approach to determine the direct impacts of river regulation and climate change on timing and amount of streamflow in the Goulburn-Broken catchment. It was found that, historically, the average annual streamflow of the Goulburn River declined by 58%, while the centre of timing increased by 45%, the contribution from rainfall reduction and river regulation was 20% and 80% respectively. From upstream to downstream, the average annual streamflow of the Goulburn River declined by an average of 47%, while centre of timing increased by an average of 36%, the contribution from rainfall reduction and river regulation was 52% and 48% respectively. A consistent pattern of decline in annual streamflow (35%) and increase in centre of timing (21%) across the Goulburn River would be witnessed in the near future (by 2050) due to a decline in winter and spring rainfall as an impact of climate change. The current water management regime should focus on restoring the patterns of centre of timing as a priority to support the sustainable management of riverine systems and enhance water storage in lower parts of the river systems prone to drought.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.