Assessing Climate Change Impacts on Yield of “Dual‐Priority” Water Rights in Carryover Systems at Catchment Scale

Future water availability is threatened by changes in both climate and water demand. Water rights with differing priorities are an important foundation of demand‐side tools (e.g., buyback, water pricing, and water market) to improve water use efficiency and reduce water scarcity, especially in highly regulated river systems. This paper assesses the impact of climate change on water yields from carryover storage with dual‐priority (high/low) water rights allocation systems using a simple and rapid analytical method. The method characterizes reservoir inflows using readily available flow characteristics (annual mean and Cv). We evaluate this method against a water resource simulation model in the Goulburn River basin, Australia. In general, our analytical “dual‐priority” Gould‐Dincer model reproduces water allocation estimates from the simulation model. We further demonstrate this method across 12 Australian catchments to investigate the climate change impact on “dual‐priority” water rights yield at the catchment scale. The hydrological projections show decreasing mean annual runoff and increasing annual runoff variability, except for some catchments in northern Australia. Water yield for high‐priority water rights (HPWRs) and low‐priority water rights (LPWRs) decreases for most catchments except for some catchments in northern Australia. South Dandalup in the 2070s (RCP8.5) shows the largest percentage decrease in HPWR and LPWR yield (about −53.53% and −56.81%, respectively). Our results show that changes in mean annual inflow have a more significant influence on water yield of HPWR and LPWR than Cv. Overall, the simple method provides a rapid assessment of water yields with “dual‐priority” water rights which is applicable across multiple sites at regional or even global scale.

manage water scarcity problems.In particular, water rights are legal entitlements that grant individuals, organizations, or governments the exclusive or shared authority to use, access, or manage water resources within a defined area and for specific purposes.These water rights are essential foundations for the functioning of demand-side measures in water resource management (Gómez Gómez et al., 2018;Hughes, 2015;Lago et al., 2015).
Water rights regimes specify the water users (water rights holders) and the rules for allocating water between those users, with several regimes already implemented in countries such as Australia, Spain, and the western United States (Gómez-Limón et al., 2020).Allocation rules vary by country and region, with examples including proportional sharing or sequences of priority uses.For example, in the Australian states of Victoria and New South Wales (NSW), water allocation follows a two-step procedure, under the principle of security-differentiated priority (e.g., high and low security; Freebairn & Quiggin, 2006).First, water rights holders (i.e., entitlements) are sorted according to their priority level.Second, the amount of water for each priority class is proportionally allocated.There are two common types of water rights based on this allocation mechanism: high-priority water rights (HPWRs) and low-priority water rights (LPWRs; Moore et al., 2020).HPWRs are allocated first, and LPWRs are allocated after HPWRs are fully allocated (Quiggin, 2001).Thus, HPWR has a higher probability of obtaining full allocation than LPWR.There are lots of benefits for dual-priority water systems.First, implementing dual-priority water systems can enhance the allocation of water resources.For example, dual-priority water rights grant specific water users with different priority use (e.g., urban users and profitable crops may hold HPWRs, while annual crop irrigators may hold LPWRs).Then, these water rights can help allocate limited water resources to achieve the highest market value in periods of shortage.Second, dual-priority water systems provide a simple and quick way to achieve efficient water resource allocation in areas where there is no water market (trade or carryover, Hughes, 2015;Hughes et al., 2023) or water markets are at an early stage of development (Brennan, 2006;Freebairn & Quiggin, 2006;Young & McColl, 2002).For example, implementing dual-priority water systems can mitigate the necessity for extensive water trading between users, especially when trade is constrained or costly.It should be noted that the responses of HPWR and LPWR in the dual-priority water systems to changes in water availability caused by climate change may vary in terms of yield, reliability, and economic value, which may result in more social or political concerns, such as climate change impacts on water allocation efficiency and/or water supply equity among different water user groups.Thus, it is necessary to explore climate change impacts on dual-priority water systems.
Current research for analyzing climate change impacts on water availability mostly focuses on yield for single water right systems (Elliott et al., 2014;McFarlane et al., 2012;Mengistu et al., 2021), which may not be applicable to more complicated systems with "dual-priority" water rights (Ren et al., 2022).Furthermore, studies investigating climate change impacts on water availability (yield) mostly rely on a hydrological model to simulate runoff (or streamflow) under specific global climate model (GCM) scenarios (Arnell & Gosling, 2013;Haddeland et al., 2014;McFarlane et al., 2012;Mengistu et al., 2021;Schewe et al., 2014;Wasko et al., 2021) and reservoir operation models to simulate reservoir behavior.Such models can be demanding in terms of data and computations (John, Fowler, et al., 2021;Ren et al., 2018) and thus may constrain the assessment of climate change uncertainty (John, Horne, et al., 2021).The complexity of these commonly used methods means that they are usually applied in a single river or catchment.Larger-scale applications (e.g., in a large river basin with multiple reservoirs) are very demanding in terms of data requirements and cost (e.g., CSIRO, 2008).Here, we provide a simpler and much less data-demanding approach, the "dual-priority" Gould-Dincer method (Ren et al., 2022) to assess the impact of climate change on "dual-priority" water rights from a carryover reservoir.
The benefits and novelties of the "dual-priority" Gould-Dincer are as follows.First, this method is simple and has fewer data requirements, which provides a rapid way for the analysis of water yield, especially at a large scale (e.g., catchment scale, global scale).Our catchment-scale study implements the same analysis over 12 catchments across Australia as a test case of the method to evaluate its potential for application at larger scales.Second, contrary to previous studies (which consider a single yield with constant single reliability), this method takes "dual-priority" water rights into account, representing a major advance in achieving more efficient water use and maximizing economic efficiency of water resources management when combined with monetary value for each water right (Ren et al., 2022).While this method is not intended to replace existing detailed methods based on simulation modeling, it can effectively and usefully complement them, providing an initial assessment for a given system (with known inflow characteristics) or where streamflow time-series data are not available, which includes alternate climate scenarios.

10.1029/2023WR035376
3 of 19 In the next section, we introduce the simple analytical method that is applied to assess climate change impacts on dual-priority water rights.In Section 3, we introduce the case studies for model evaluation and application.Sections 4 and 5 demonstrate the results and discussion, respectively.The conclusion part is illustrated in Section 6.

Method: "Dual-Priority" Gould-Dincer Method
The Gould-Dincer method was developed to estimate the storage-reliability-yield relationship for a single carryover reservoir for preliminary design purposes (Gould, 1964;McMahon, 1976;McMahon et al., 2007).The equation is as follows: where S is the storage capacity, α is a constant annual yield (as a ratio of mean annual inflow), Z p is the standardized normal variate at 100 (1 − p)% reliability.C v and μ are the coefficient of variation and mean of annual inflows, respectively.For a regulated river with a known (or assumed) storage capacity, yield (α) can be estimated from the given storage capacity, the coefficient of variation of annual inflows (C v ), and desired reliability (Z p ) of supply using Equation 1.Note that "yield" and "reliability" alone are not sufficient to fully describe the characteristics (and economic value) of water rights.For more details on the application of the Gould-Dincer method, please refer to McMahon et al. (2007).Ren et al. (2022) further developed the "dual-priority" Gould-Dincer method based on the Gould-Dincer method to consider two types of water rights (HPWR and LPWR).The equation is as follows: where α l and α h are water yields of LPWR and HPWR, respectively.The reliability of HPWR and LPWR is characterized, respectively, by Z ph and Z pl .
Similar to the original Gould-Dincer method, the yield of LPWR (α l ) can be estimated by the given storage capacity (S), the coefficient of variation of annual inflows (C v ), the yield of HPWR (α h ), and desired high and low reliability (Z ph and Z pl ) of supply using Equation 3 (a rearrangement of Equation 2).For more details of the "dual-priority" Gould-Dincer method, please refer to Ren et al. (2022).
Whatever   or   or   , they are all based on the assumption that annual streamflow is normally distributed.A further variation of the Gould-Dincer method allows for annual inflows that are gamma (Gould, 1964;McMahon & Adeloye, 2005) and lognormal distributed (McMahon et al., 2007) (5)

Study Area: Goulburn River, Victoria, Australia
Our case study area is the Goulburn River in the state of Victoria, Australia (Figure 1).The Goulburn River is a tributary of the Murray River, providing 11% of mean annual streamflow to the larger Murray Darling Basin, despite only occupying 2% of the total Murray Darling Basin area.The Goulburn River basin is a large and highly regulated system managed for multiple objectives, including supplying water for irrigation, drinking for small regional towns, and sustaining a river-related ecosystem.There are two main reservoirs in the Goulburn River basin: Lake Eildon (3,390 GL storage capacity, 89% of the whole storage capacity), a carryover storage in the headwaters of the Goulburn River, and Waranga (430 GL storage capacity, 11% of the whole storage capacity) an off-stream distribution storage lower in the catchment.Lake Eildon harvests about 48% of the inflows of the whole Goulburn basin.Waranga is an offline storage, which has little natural inflows of its own and harvests a portion of streamflow provided by unregulated tributaries downstream of Lake Eildon.Water in these two storages is allocated to water users proportionately based on two categories of water entitlements: HPWR, ∼1,130 GL, and LPWR, ∼461 GL.HPWRs are first allocated once provision is made for losses, trade volumes owed to other systems, carryover of allocation from previous seasons and some other minor considerations.
LPWRs are only allocated once full allocation of HPWR is achieved and there is enough water in storage to guarantee full HPWR in the following year (John et al., 2022).

Water Resource Model
An existing water resource model (documented in John et al. (2022), and the supplementary materials therein) is used to simulate monthly water inflows, storage, allocations, releases, streamflows, and withdrawals.This model simulates monthly water allocations to HPWR and LPWR, which can be summed to annual scale (for consistency with the "dual-priority" Gould-Dincer method) and further analyzed to assess reliability of HPWR and LPWR.
Reliability in this situation is the proportion of years that water rights are fully met.The model has been calibrated and tested against observations to ensure it produces realistic streamflows and water allocations (see Supporting Information of John et al. (2022)).

Scenarios for Evaluation
We test our "dual-priority" Gould-Dincer method by comparison with results from the simulation-based water resource model for a range of inflow conditions (mean and C v of annual inflow).For a given inflow and reservoir capacity, our method relates four variables: the yield and reliability of LPWR and HPWR.We choose to test LPWR yield estimates for given HPWR yield scenarios (where reliability of the two entitlements are simulated) because LPWR yields are heavily dependent on HPWR yields and hence the most rigorous test of our method.
The Goulburn can be considered as two nested water supply systems: Lake Eildon is a headwater supply system but this is managed within the broader water supply system that includes the off-stream storage Waranga Basin, which is supplied from Lake Eildon and tributaries entering the Goulburn River between Eildon and the Waranga offtake (Figure 1).While the simulation model can represent the water balance of the two storages explicitly including tributary inflows downstream of the larger Lake Eildon Reservoir, our Gould-Dincer model represents the system using a single storage volume.
We test whether our method can adequately reproduce the LPWR estimates from the water resource model for both of these nested systems using two scenarios.
Scenario I considers the Goulburn River basin as the whole system (Goulburn scenario) for the evaluation.The total storage capacity and water entitlements of the Goulburn scenario are listed in Table 1.While the simulation model can represent the water balance of the two storages explicitly including inflows from four tributaries downstream of the larger Lake Eildon Reservoir, our Gould-Dincer model represents the system using a single storage.
For the Gould-Dincer model, we need to estimate the mean and C v of annual inflow of the whole Goulburn system.Only a portion of tributary inflows below Eildon are harvested by Waranga Basin depending on storage levels and downstream demands during the irrigation season (∼August-May).We estimate the average proportion of tributary inflows transferred to Waranga Basin and combine this with Eildon inflows in the calculation of "system-wide" mean annual inflow and C v .In this study, we assume 10% of inflows from the four tributaries are transferred in a given year to estimate the system-wide mean and C v of annual inflow (1,627 GL and 0.41, respectively).
Scenario II just considers the carryover storage of Lake Eildon for the evaluation (Eildon scenario).The storage capacity, mean, and C v of annual inflow of Lake Eildon are 3,390 GL, 1,472 GL, and 0.40, respectively (Table 1).However, it is difficult to estimate water entitlements supplied from the Eildon reservoir specifically because water entitlements for the whole Goulburn basin are allocated based on both Eildon releases and tributaries inflows downstream of Eildon.Given that the storage capacity of Eildon is 89% of all storage volume of the Goulburn River basin, we consider 89% of entitlements of HPWR and LPWR are supplied from Eildon, which are 1,006 and 410 GL (Table 1).

Evaluation Process
We assess the performance of the "dual-priority" Gould-Dincer method by comparing the yield of LPWR estimated by the simulation-based water resource model (   ′ ) against the "dual-priority" Gould-Dincer method LPWR estimate (α l ).First, we simulate seasonal allocations using the water resource model to determine the yield and reliability of HPWR and LPWR.Second, we input storage capacity, mean, and C v of annual inflow (Table 1), along with the simulated HPWR and reliability of HPWR and LPWR into the "dual-priority" Gould-Dincer method (Equation 3) to estimate LPWR yield.We set the threshold of low reliability as 5%, because there is large uncertainty in water resources model when low reliability is less than 5% (John et al., 2022).In other words, if the reliability of LPWR is lower than 5%, the model simulations are not considered further.Annual inflows approximately follow a gamma distribution (Ren et al., 2022), so Z p is substituted by G p using Equation 4. Finally, we compared the estimated LPWR from the "dual-priority" Gould-Dincer method (α l ) with simulated LPWR from the water resource model (   ′ ).
We modeled a range of inflow scenarios to extend the evaluation.For this, we scaled the Eildon inflow by the desired factors (i.e., for a perturbation of +10%, the entire inflow time series is multiplied by 1.1).We chose five factors for scaling mean and C v of annual inflow: −20%, −10%, 0%, 10%, and 20%.We used the coefficient of determination (R 2 ) to evaluate the goodness of fit between LPWR  ( ′ ) from the water resource model and LPWR (α l ) from the "dual-priority" Gould-Dincer method for all modeled inflow scenarios.

Study Area: Australian 12 Catchments
We also applied our method to 12 catchments across Australia (Figure 2).These catchments are all regulated with carryover storage (Table 2), have a broad range of mean and C v (as shown in Figure 4), and a range of catchment

National Hydrologic Projections Product of Australia
A National Hydrologic Projections product is published by the Bureau of Meteorology (BoM) to support decision-making processes in Australian future water resource management, adaptation, and water policy developments (Bureau of Meteorology [BoM], 2022).This product is derived from GCM projections from the Coupled Model Intercomparison Project Phase 5 (CMIP5) data set (Taylor et al., 2012) based on certain emission scenarios, which are bias corrected and downscaled using a regional climate model (RCM) and bias correction method.The bias-corrected data are input into a hydrological model (Australian Water Resources Assessment Landscape model) to generate the National Hydrologic Projections product.To achieve that, two emission scenarios (RCP4.5 and RCP8.5), four GCMs (ACCESS1-0, CNRM-CM5, GFDL-ESM2M, and MIROC5), and four bias correction methods (i.e., downscale methods; CCAM-ISIMIP2b, ISIMIP2b, MRNBC, and QME) were chosen (Table 3).
For more details on hydrologic projection processing, please refer to BoM (2022).
We collated projections of bias-corrected annual runoff series for the 12 catchments for the period 1975-2099.Then, we defined the period from 1976 to 2005 as the baseline period (the 1990s).The midcentury period was defined as 2016-2045 (the 2030s), and the late-century period was defined as 2056-2085 (the 2070s).

Application Process
We applied the "dual-priority" Gould-Dincer method to assess the impact of climate change on "dual-priority" water rights.First, we estimated mean and C v of annual projected runoff for three time periods (baseline, the 2030s, and the 2070s) at 12 catchments across Australia, under two RCP scenarios (RCP4.5 and 8.5) and 16 annual projected runoff ensembles (four GCMs × four downscaling methods) for each RCP.Then, we demonstrated the impact of climate change on flow characteristics by comparing the mean and C v of the future periods against that of the baseline period.
Second, we investigated the impacts of climate change on HPWR by assuming the yield and reliability of LPWR of the "dual-priority" Gould-Dincer method was 0. It should be noted that this leaves two unknown parameters in our Gould-Dincer model (Equation 2): yield and reliability of HPWR.
Here, we apply two strategies to evaluate the climate change impacts: (a) we set the reliability of HPWR to be 95% for all catchments to illustrate how the yield of HPWR changes in the future; (b) we set the yield of HPWR to be 0.8 times the mean annual inflow of the baseline period for all catchments to illustrate how the reliability of HPWR changes in the future.
Finally, we demonstrated the impact of climate change on the relationship between the yield of HPWR and LPWR by using the "dual-priority" Gould-Dincer method (Equation 3) by holding the reliability of HPWR and LPWR fixed at reasonable values (95% and 60%, respectively, similar to Ren et al. (2022)

ISIMIP2b
The quantile-based approach preserves trends in data (Hempel et al., 2013)

MRNBC
The quantile-based approach models the extremes well (Dowdy, 2020) QME An approach that preserves the interdependence among the variables and the low-frequency characteristics (Mehrotra & Sharma, 2016)

Model Evaluation
We assess the performance of the "dual-priority" Gould-Dincer method over the Goulburn River basin for the two scenarios shown in Table 1 (Figures 3a and 3b).In general, the scatter plots show that there is a strong relationship between the Gould-Dincer estimated LPWR (α l ) and simulation model LPWR estimates (   ′ ) under both Goulburn and Eildon scenarios (Figure 3, R 2 = 0.94 and 0.85, respectively).The linear regression line of Goulburn scenario (with a slope of 1.05) is closer to the 1:1 line compared with that of Eildon scenario (with a slope of 0.91), which indicates that the "dual-priority" Gould-Dincer method matches very well for the Goulburn scenario, but less well for the Eildon scenario.Overall, the "dual-priority" Gould-Dincer method could reproduce the results of the water resources model under these two scenarios.

Flow Characteristics (Mean and C v )
Most projected annual runoff scenarios suggest that C v increases for almost all catchments except Argyle under RCP8.5, which exhibits a slight decrease during the 2030s (Figure 4).The changes in C v of Lake Mackintosh and Lake Burbury are small.The highest magnitude increases in C v are evident at Wuruma under RCP4.5, of which the median increases from a baseline of 1.04-1.32by the 2030s, and further to 1.36 by the 2070s.
In contrast to the increase in C v , there is a clear decrease in mean inflow for all catchments under both RCP4.5 and 8.5, except Somerset under RCP4.5 during the 2030s, Fairbairn under RCP4.5 and 8.5, and Argyle under RCP8.5 which exhibits a slight increase (Figure 4).Changes in the mean of Wuruma under RCP4.5 and 8.5, and Argyle under RCP4.5 are not significant.During the 2030s, the mean of almost all catchments exhibits a decrease, and this decrease persists during the 2070s.The highest magnitude decreases in mean are observed at Lake Burbury under RCP8.5, of which the median decreases from a baseline of 1,762 to 1,710 mm/year by the 2030s, and further to 1,586 mm/year by the 2070s.

High-Priority Water Right
In general, a large source of uncertainty in the HPWR yield estimates is due to different GCMs, especially in northern Australia (Figure 5).GDFL-ESM2M (squares in Figure 5) projects the greatest reduction in HPWR yield compared with the other three GCMs, whether in the 2030s or 2070s, because this GCM exhibits the driest climate projection.Similarly, the projected runoffs using CCAM-ISIMIP2b downscaling methods (blue shapes The dots represent the comparisons of different inflow scenarios (mean and C v of a perturbed inflow is −20%, −10%, 0%, 10%, and 20%, respectively).Note that because we set the threshold of low reliability as 5%, the dots which represent the model simulations with the reliability of LPWR lower than 5% are removed (as a result, there are six dots removed under Goulburn scenarios).
in Figure 5) also suggest lower future yield of HPWR compared with the other three downscaling methods, especially for the catchments of western Australia (e.g., Serpentine, and South Dandalup).
In terms of median projected change of HPWR yield under both RCP4.5 and 8.5 scenarios (Figure 5 and Table 4), catchments of northern Australia (e.g., Argyle, Fairbairn, and Wuruma) and Pindari generally show an increase, but that of all other catchments of Australia decreases in the future.In general, the magnitude of decreases under RCP8.5 is larger than that under RCP4.5.The 2070s period shows larger decreases than the 2030s.Changes in the HPWR yield of Argyle and Somerset under RCP4.5, and Wuruma under RCP8.5 are small.Similar to the change in mean, the highest absolute decreases in HPWR yield are observed at Lake Burbury under RCP8.5 in the 2070s, which is about 180.25 mm/year.Meanwhile, South Dandalup shows the highest percentage decrease (−53.53%).In terms of the difference between RCP4.5 and 8.5 results, Fairbairn and Wuruma exhibit distinct differences, while there is less difference for other catchments.
If yield is to be maintained in the future, the HPWR reliability will decrease in most catchments (Figure 6 and Table 4), except for some scenarios (CNRM-CM5 and MIROC5 with different downscaling methods) in northern Australia (e.g., Argyle, Fairbairn, and Wuruma; Figure 6).The HPWR reliability of most catchments decreases, whether in the 2030s or 2070s.For instance, the high reliability in Serpentine and South Dandalup will decrease by 100% under RCP4.5 in the 2030 and 2070s, and under RCP8.5 in the 2070s.Similar to the percentage change, absolute change in HPWR reliability in Serpentine and South Dandalup is also higher than that of other catchments.Specifically, the highest absolute decreases could be observed at South Dandalup under RCP8.5 in the 2070s, which is up to −99.97%.Meanwhile, Serpentine, South Dandalup, Pindari, and Wyangala exhibit relatively distinct differences in HPWR reliability results between RCP4.5 and 8.5.

"Dual-Priority" Water Rights
In general, the yield of LPWR will increase with a decrease in the yield of HPWR.In rivers with low-flow variability (C v = 0.1), there is a generally linear relationship between the yield of HPWR and LPWR except for higher HPWR yields in some cases (Figure 7).With higher C v , the upper limit of HPWR decreases, and the volume of LPWR becomes more sensitive to small changes in the volume of HPWR near this upper limit.(1976-2005, the 1990s).The lower and upper boundaries of the boxplot indicate the 25th and 75th percentiles, respectively.The lines inside the box mark the median.Note that because mean of annual runoff for Lake Burbury and Lake Mackintosh is significantly larger than other catchments, we separate the plots for these catchments for visualization purposes.When demonstrating the relationship between LPWR and HPWR by using 16 projected runoff ensembles, similar to the climate uncertainties of HPWR yield estimates, there is also a larger uncertainty, especially in Pindari, and Wuruma catchments (Figure 7).In general, the magnitude of water yield (whether for HPWR or LPWR) for the 2030s decreases at catchments in western (South Dandalup and Serpentine) and southeast mainland Australia (Lake Eildon, Wyangala, and Googong), which persists during the 2070s (green dash-dotted line > blue dotted line > red solid line).For example, under RCP8.5 scenarios, water availability at South Dandalup decreases from 150 to 110 mm (in the 2030s), and further to about 50 mm (in the 2070s).On the contrary, Argyle and Fairbairn of northern Australia clearly show a gradual increase in water yield from the baseline period to the 2030s, and further to the 2070s under RCP8.5.Whereas, other catchments, such as Lake Burbury and Lake Mackintosh, Somerset, and Argyle do not show a major change between periods under RCP4.5.
If assuming all water resources are classified as LPWR, in other words, there is no HPWR (Table 5), catchments of northern Australia (e.g., Argyle, Fairbairn, and Wuruma) and Pindari generally show an increase, but that of all other catchments of Australia decreases in the future.Similar to the change in HPWR, the magnitude of decreases under RCP8.5 scenarios shows a larger decrease than that under RCP4.5, and the 2070s period also exhibit a larger decrease than 2030s.The highest absolute decreases in LPWR yield could be observed at Lake   Burbury under RCP8.5 in the 2070s, which is about 176.51 mm/year.Meanwhile, South Dandalup shows the highest percentage decrease (−56.81%).

Could the "Dual-Priority" Gould-Dincer Method Represent a Real Dual-Priority Allocation System?
In this paper, we evaluate the "dual-priority" Gould-Dincer method against a water resource simulation model of the Goulburn River basin, known to reproduce observed streamflow and water allocations.The "dual-priority" Gould-Dincer method replicated the simulation model estimates.Moreover, we ran this model to output multiple estimates based on two scenarios (Goulburn and Eildon scenarios) and adjusted the inflow series to represent multiple flow characteristic conditions.Given these results, we suggest that in the Goulburn River basin the method is applicable to represent the dual-priority allocation system and the response of allocations to changing streamflow inputs.

Climate Change Impact on Water Rights Across 12 Australian Catchments
There is a drying trend of annual runoff (i.e., decreasing mean annual runoff) in most of our study catchments except for the catchments of northern Australia (e.g., Argyle) which show an increase in annual runoff, similar to other researches (Chiew et al., 2017;Kiem et al., 2016;Kirono et al., 2020;Wasko et al., 2021).Also, variability of annual runoff (C v ) generally increases under future climate in these catchments, which means that climate change causes relatively more contrast between high-flow years and low-flow years.For example, the mean projected runoff of Wuruma decreases while the variability of annual runoff increases, which indicates that mean annual runoffs might be lower, but the variability of the runoffs relative to the mean might be larger.Changes in the yield of different water rights are to be expected to accompany these changes in streamflow.
When illustrating climate change impact on the yield of HPWR for a fixed reliability, we found that the yield of almost all catchments decreases in the future except for the catchments of northern Australia (e.g., Fairbairn, Wuruma, and Argyle), which is consistent with the projected changes in future mean runoff.Furthermore, we demonstrate how the change in HPWR yield is impacted by the change in mean and C v of annual inflow, respectively (Figure 8).There is a strong correlation between the percentage change in HPWR yield and that in mean (R 2 = 0.99), rather than C v (R 2 close to 0), which means that the projected changes in mean annual inflow have a larger impact on the yield of water rights compared with the changes in C v , which is in line with the parameter sensitivity analysis of McMahon et al. (2007).We further explored climate change impact on the dual-priority water rights, similar to the change in future mean and yield of HPWR, the yields of HPWR and LPWR for almost all catchments decrease in the future except for the catchments of northern Australia.For those catchments with a projected increased mean annual runoff (e.g., Fairbairn and Argyle of northern Australia), both HPWR and LPWR have a potential increasing trend in water yield, while for those catchments with a projected decreased mean annual runoff (e.g., Lake Eildon of southeast Australia) both HPWR and LPWR have a potential decreasing trend in water yield.

Possible Economic and Policy Implications
The importance of climate-induced changes in relative HPWR and LPWR (both water yield and reliability) highly depends on the maturity of water markets, including both water trading and carryover mechanisms (Brennan, 2006;Freebairn & Quiggin, 2006;Hughes, 2015;Hughes et al., 2023;Young & McColl, 2002).
In mature water markets, water rights holders are more likely to have established well-designed policies and mechanisms for trading and transferring water allocations.Thus, water markets allow users to respond to changes in water availability caused by climate variability or long-term climate change.First, water markets can act as risk mitigation tools for water users.For example, in mature markets, users may have access to a range of risk management strategies, including the ability to purchase additional water during dry periods (e.g., HPWR) or sell excess water during wet periods (e.g., LPWR).This risk-sharing can help users better manage the impacts of climate variability.Second, mature water markets are often better at allocating water to its highest value uses.When climate-induced changes in water availability occur, mature markets can respond by reallocating water more efficiently.For example, during a drought, HPWR may be traded to sectors with higher economic value,   while LPWR can be used for less critical purposes.Therefore, mature water markets offer greater flexibility, risk management options, and incentives for efficient water allocation to adapt to climate change.
However, in regions without mature water markets, due to lacking risk management strategies and policies, change in climate poses a larger threat to both HPWR and LPWR of dual-right systems.In particular, in cases where LPWR is highly sensitive to changes in climate, this can undermine the initial purpose of dual right systems (to create rights that match the needs of specific types of water users).For example, in the extreme case where declines in inflow lead to a zero yield/reliability outcome for LPWR, these rights may no longer match the needs of their holders.If these users cannot buy water on a market, valuable water use opportunities (to plant crops, etc.) may go unmet (even in years when HPWR holders have more than they need).
It should be noted that even in regions where water markets are well-developed, the implementation of dual-priority rights will cause distinctive impacts on different water user groups in the context of climate change.These impacts may include changes in the economic value and water supply reliability of water rights.For example, although mature water markets may decrease the loss of LPWR holders (i.e., declines in water rights/ entitlement prices), LPWR holders may be more exposed to the downside risks of climate change irrespective of the presence of markets.It may be undesirable from a social equity perspective.

Possibilities for Global Implementation
Compared with alternatives, our method provides a simpler, quicker, and less data-demanding way to estimate yield for dual-priority water right systems, especially under changing climate.The method provides opportunities for global implementation that would not have been possible before, paired with its reliance on flow characteristics (mean and C v ) that can be inferred from spatially continuous climate data (McMahon et al., 2011).For example, we could use concepts of climate elasticities of runoff to estimate global hydrological statistics (mean and C v ) by using global historical and future precipitation, and potential evapotranspiration data sets.Combining these global hydrological statistics with our methods, it is easier and more rapid to evaluate climate change impacts on dual-priority water rights systems.In our study, catchment-scale applications over 12 catchments of Australia illustrate that this method has the potential to be applied at a larger scale (even global scale by using global data sets, such as G-RUN ENSEMBLE (Ghiggi et al., 2021)).We clarify that this method is not intended to replace, but to complement existing simulation-based water resource models by providing a rapid initial assessment or an assessment at large spatial scales that would be impractical otherwise.

Uncertainties and Limitations
Undoubtedly, there is larger uncertainty in future water availability (yield) estimates due to differences in GCM models (Teng et al., 2012), bias correction methods (Chen et al., 2011), and RCP assumptions (Wilby & Harris, 2006).In this study, from mean and C v estimates of annual runoff (Figure 4) to water yield estimates (Figures 5-7), there is great uncertainty concerning future climate change.Thus, errors in water yield estimates are inevitable, which exacerbates the uncertainty of results.It is necessary and important for water managers and decision-makers to apply powerful frameworks and theories (e.g., Decision Making under Deep Uncertainty [DMDU] framework, Lempert et al., 2003;Marchau et al., 2019) in making informed and robust choices when faced with complex and potential uncertainties in the context of climate change.After effectively controlling uncertainties, it is possible to evaluate and identify future change trends in water availability caused by global warming, especially at a larger scale to understand and ameliorate future water scarcity.
Due to a lack of published water resource models for other river basins that simulate the operation of two priority water rights, we only evaluate the "dual-priority" Gould-Dincer method over the Goulburn River basin.However, to demonstrate our model is reliable, we performed tests at two spatial scales with different storage and inflow conditions.We acknowledge that this is a limitation and hope that future studies will take advantage of other regions to allow the assumptions to be tested further.Meanwhile, the water allocation behavior of the Goulburn River basin may have some unique aspects compared to that of other regions (e.g., USA), we acknowledge that the water allocation behavior of the Goulburn River basin may be not generalized.
Second, our paper does not use the actual water allocation data for model evaluation.However, we acknowledge that it is an interesting direction for future research by using actual water allocation data for model evaluation, which may further progress this simple analytical method for real-world application.Meanwhile, it is an interesting point to explore climate change impacts on actual yield targets and related water policies in different regions.It is clear that when inflows are variable, and HPWRs are high, the yield and reliability of LPWR shares become very sensitive to changes in inflow (Figure 7).By combining the relationship between HPWR and LPWR (Figure 7) and actual yield targets, it is interesting and possible to further extend research among multiple disciplines, including climate, water resources, and social policies.
Furthermore, we acknowledge that the Gould-Dincer method may not account for full probability distributions over water right allocations.We also acknowledge that the simple analytical method cannot account for impacts from spill issues and the related actual carryover decisions.Thus, our analysis does not account for user carryover (where some portion of the allocated water right is held in storage).In this case, water users may alter their carryover behavior and control the effective yield and reliability of water rights to mediate the effects of climate change (Brennan, 2010;Hughes et al., 2023).For more general limitations of the Gould-Dincer method, please refer to McMahon et al. (2007), and Ren et al. (2022Ren et al. ( , 2023)).

Conclusion
This paper applies a simple and rapid model, the "dual-priority" Gould-Dincer method, to assess the impact of climate change on the yield of two constant water rights at the catchment scale.First, we evaluate this method by using a more detailed water resource model that operates on a monthly step, the results show that there is a strong relationship between the estimated LPWR from the "dual-priority" Gould-Dincer and the simulated LPWR from the hydrological model based on two scenarios.The "dual-priority" Gould-Dincer method can reproduce the results of the detailed water resource model that operates on a monthly step.
Second, climate change impacts on dual-priority water rights were demonstrated based on future scenarios (32 ensembles) at 12 catchments by using the Australian National Hydrologic Projection runoff data set.Most projections show decreases in mean annual runoff but increases in the variation of annual runoff with the exception of a few catchments in northern Australia (e.g., Fairbairn and Argyle).Lake Burbury under RCP8.5 shows the highest magnitude decreases (from 1,762 mm/year by the baseline to 1,710 mm/year by the 2030s, and further to 1,586 mm/year by the 2070s), while Wuruma under RCP4.5 exhibits the highest magnitude increases in C v (from 1.04 by the baseline to 1.32 by the 2030s, and further to 1.36 by the 2070s).
Similar to the change in the mean, most projections show that HPWR yield generally decreases for all catchments with the exception of Argyle, Wuruma (under RCP4.5), and Fairbairn of northern Australia and Pindari of Eastern Australia in both the 2030s and 2070s.South Dandalup in the 2070s (under RCP8.5) shows the highest percentage decrease (−53.53%) in HPWR yield, and Lake Burbury illustrates the highest absolute decrease (−180.25 mm/year) in HPWR yield.Particularly, GDFL-ESM2M and ISIMIP2b generally project less future yield of HPWR compared with the other GCMs and downscaling methods.If keeping the yield unchanged in the future, the HPWR reliability of all catchments decreases except for Lake Burbury and Lake Mackintosh.
When evaluating the impact of climate change on the relationship between HPWR and LPWR, it is clear that the magnitude of water yields of both HPWR and LPWR decreases for almost all catchments with the exception of Fairbairn and Argyle of northern Australia.The highest absolute decreases in LPWR yield could be observed at Lake Burbury in the 2070s (under RCP8.5; about 176.51 mm/year), and South Dandalup in the 2070s (under RCP8.5) shows the highest percentage decreases (−56.81%).Meanwhile, the results show that mean annual inflow has a more significant influence on the water yield of HPWRs or LPWRs compared with the C v .In general, the method potentially provides a rapid and simple way to be applied at the global scale to assess the impact of climate change on the global water yield of two constant priority water rights.

Figure 2 .
Figure 2. The location of 12 study catchments across Australia for application, and spatial distribution of eight natural resource management (NRM) clusters (adapted from CSIRO and BoM (2015)).

Figure 3 .
Figure 3. Evaluation of estimated low-priority water right (LPWR; α l ) from the "dual-priority" Gould-Dincer method versus simulated LPWR (   ′ ) from the water resource model under Goulburn (a) and Eildon (b) scenarios.The dots represent the comparisons of different inflow scenarios (mean and C v of a perturbed inflow is −20%, −10%, 0%, 10%, and 20%,respectively).Note that because we set the threshold of low reliability as 5%, the dots which represent the model simulations with the reliability of LPWR lower than 5% are removed (as a result, there are six dots removed under Goulburn scenarios).

Figure 4 .
Figure 4. Projected changes in flow characteristics (C v and mean of annual runoff) in the medium century (2016-2045, the 2030s), the late century (2056-2085, the 2070s) at 12 catchments across Australia, under RCP4.5 and RCP8.5 scenarios based on 16 projected runoff ensembles compared with baseline(1976-2005, the  1990s).The lower and upper boundaries of the boxplot indicate the 25th and 75th percentiles, respectively.The lines inside the box mark the median.Note that because mean of annual runoff for Lake Burbury and Lake Mackintosh is significantly larger than other catchments, we separate the plots for these catchments for visualization purposes.

Figure 5 .
Figure 5.Comparison of percentage changes in the yield of high-priority water right (HPWR) in the 2030s, and the 2070s at 12 catchments across Australia.These percentage changes of the maximum HPWR yield are estimated based on 16 projected runoff ensembles (four global climate models [GCMs] × four downscaling methods) under RCP4.5 and RCP8.5 scenarios by assuming the reliability is constant (95%).The four different colors represent four types of downscaling methods, and four different shapes represent four different GCMs.The black and green stars mark the median percentage change of HPWR yield under RCP4.5 and RCP8.5 scenarios, respectively.

Figure 6 .
Figure 6.Comparison of percentage changes in the reliability of high-priority water right (HPWR) in the 2030s, and the 2070s at 12 catchments across Australia.These percentage changes in the reliability are estimated based on 16 projected runoff ensembles (four global climate models [GCMs] × four downscaling methods) under RCP4.5 and RCP8.5 scenarios by assuming the HPWR yield is constant (0.8 times mean annual inflow).The four different colors represent four types of downscaling methods, and four different shapes represent four different GCMs.The black and green stars mark the median percentage change of reliability under RCP4.5 and RCP8.5 scenarios, respectively.

Figure 7 .
Figure7.The relationship between the yield of high-priority water right (HPWR) and low-priority water right (LPWR) at 12 catchments across Australia in the baseline, the 2030s, and the 2070s, under RCP4.5 and RCP8.5 scenarios based on 16 projected runoff ensembles.The curves are estimated based on the "dual-priority" Gould-Dincer method.For each period (i.e., baseline, the 2030s, the 2070s), the bottom and top of the band are the minima and maximum estimated curves, and the green, blue, and red curves are the median conditions of each period.

Figure 8 .
Figure 8.The relationship between percentage change in high-priority water right (HPWR) yield and percentage change in mean and C v of annual inflow of 12 catchments across Australia in the 2030s, and the 2070s, under RCP4.5 and RCP8.5 scenarios based on 16 projected runoff ensembles.Note that "Δ" represents the percentage change in each variable.

Table 1 The
Storage Capacity, Water Entitlements, and Flow Characteristics of Two Scenarios Over the Goulburn River Basin for Evaluationareas from 311 to 45,152 km 2 .These catchments are located within different natural resource management (NRM) clusters (which are defined and grouped by broad-scale climate and biophysical regions of Australia, and each has a unique and special set of priorities for responding to climate change;CSIRO & BoM, 2015), to ensure a variety of different climate regimes were considered in the application.

Table 2
).The Reservoir Name, Location, Reservoir Storage Capacity, and Catchment Area of the 12 Catchments for Application

Table 3
Descriptions for Different Components (RCPs, GCMs, RCM, and Bias Correction Methods) of the National Hydrologic Projections Product(BoM, 2022)

Table 4
The Median Projected Change (Both Absolute and Percentage Change) in the Yield of HPWR Under RCP4.5 and 8.5 in the 2030s and 2070s

Table 5
The Median Projected Change (Both Absolute and Percentage Change) in the Yield of LPWR UnderRCP4.5 and 8.5 in the 2030s and 2070s (i.e., There Is No  HPWR)