The regulated Murrumbidgee River basin (84 000 km2) was selected to evaluate the benefit of using forecasted reservoir inflow (Fig. ). In this basin, two major water storage reservoirs, the Burrinjuck and Blowering reservoirs, provide the required resource for the water allocation process. The New South Wales Office of Water announces the water allocation for different users in the basin starting on 1 July of each year based on the available water in storage, the expected reservoir inflows for the next 12 months, and water requirements downstream. The inflow to the Blowering reservoir depends on both the discharge release from an upstream hydropower system (Snowy Hydro Scheme) and the natural runoff, while the inflow to the Burrinjuck reservoir depends mainly on natural runoff. Currently, a conservative estimate of the total inflow to the storages of 2.33×108 m3 yr-1 (based on climatology) is used to determine the expected reservoir inflow for the next 12 months. In the Murrumbidgee basin, the water year runs from 1 July through to 30 June of the next calendar year, while the cropping season for annual (irrigated) crops is between 1 November and the end of February. Each water user (e.g. irrigation, urban, and environment) holds a water entitlement (water share), which is a license to extract water from the basin. Depending on the available water, the basin authority announces a fraction of the total volume of that entitlement that will be met in a year, which is defined as the water allocation . Water is allocated to different water users according to established priorities. In water-abundant conditions each user gets their agreed full entitlement. When water shortage occurs, the highest priority is to satisfy human water consumption and the lowest priority is to satisfy the irrigation demand of annual crops. This is reflected in the type of license users pay for, with irrigators holding a High Security license having a higher priority to water than irrigators holding a General Security license. Normally, irrigators growing annual crops hold a General Security license, though it is the annual crops that require the highest volume of water. Once the water has been allocated, users can decide how they would like to employ the resources available to them. A maximum of 30 % of the volume entitlement can be carried over from one year to another. This provides flexibility to the water users as they can hold a certain volume of their allocation in the storage reservoirs and make it available for the next year. During the water year the basin authority may revise the initial water allocation and announce a new allocation for each user depending on the then available water storage volume and the estimate of the remaining inflow to the end of the water year. In the currently established regulations the water allocation cannot be decreased but only maintained or increased, unless exceptional circumstances dictate. This process generates expectations among the irrigators about the amount of water volume they are going to get, especially for the General Security (GS) license holders. To illustrate the process, Fig.  shows the recorded water allocation decisions made in the 2016–2017 water year. On 1 July 2016, the initial water allocation for GS license holders was established at 40 %. Two weeks later, the water allocation was increased from 40 % to 52 %. Successive revisions over the next 4 months resulted in a final water allocation of 100 % at the start of the cropping season (November), which was subsequently maintained until the end of the season. Certainly, irrigators are aware that the allocated water can be higher in the announcements made closer to the start of the cropping season. This means that farmers may well act on the expectation that the allocation is typically revised upwards, taking the risk of a certain water volume finally being allocated. We argue that this risk affects decision making among the farmers and their ability to correctly plan the area to be cropped. Farmers more averse to risk may tend towards cropping according to the conservative water allocation, leading to potential losses (opportunity cost), while less risk-averse farmers may face losses in yield if the final allocation they expect is not met. Ideally, water users would like to be informed about the true water allocation as early as possible to better plan their activities. This means that the ideal allocation scenario is when the water allocation is set at the start and then remains constant during the water year.

A preliminary calibration of the allocation framework was developed for the 2011–2016 water years using the conservative inflow estimate (2.33×108 m3 yr-1) and the recorded allocation decisions. The main calibration parameter is the allocation use reduction factor, which determines the percentage of the water allocated to them that users decide to use, with the remainder being reserved for carry-over to the next year. In reality, this factor varies between users as well as between years and may be influenced by a variety of factors, including many that do not depend on water availability. We simplify this by considering a bulk allocation use reduction factor across all General Security users and also consider this to be equal across years. The allocation use reduction factor derived for the 2011–2016 period is then assumed to also hold for evaluating the FoGSS datasets for the 1982–2009 water years, for which recorded allocation decisions are not available as a different policy for the allocation of water to the different users was then in place. The allocation use reduction factor was established as 78 %, for which similar simulated and actual carry-over volumes are obtained, as well as the simulated storage in the reservoirs at the end of each water year (itself a function of the carry-over volume which remains in the reservoir). Figure  shows the simulated water storage in the reservoirs, as well as the observed and simulated carry-over volumes. For the years 2011 to 2016, the emulated water allocation decisions for GS are shown in Fig.  and compared to the actual allocation decisions recorded in those years. Two simulations are shown. In the first, the initial storage condition of the reservoirs (day 1 of the 2011 water year) was set equal to the actual water storage, followed by an open-loop simulation as in Eq. () for the full 6-year period. In the second, the water level in the reservoirs is reset to be equal to the observed reservoir level at the start of each year (simulated nudged). These simulations show that across the 6 years volume differences range from 1 % to 30 % of the actual water storage at the start of each of the water years. Derived emulated water allocation decisions for GS show an underestimation of the allocation compared to the actual volume for most years, especially for the 2014 water year. These differences occur because a constant factor is used (78 %) to simulate the carry-over between water years. Results from simulated nudged show how the daily water storage simulations and the water allocation for GS would behave using the actual water storage information (including the actual carry-over volume), by nudging the simulated storage levels to the observed ones at the start of each water year (Fig. ). The daily water storage simulations and water allocation to GS are now closer to the actual values, especially for the 2014 water year. However, for both simulations, the emulated decisions show a similar trend when compared to the actual decisions. Upward revisions as well as where the water allocation remains constant (no revisions) occur at the corresponding announcement dates, and although results are slightly biased in volume, the emulation of allocated water decisions does follow the pattern of the actual decisions. We apply the water allocation framework to simulate the water storage continuously over the 1982–2009 water years, assuming a constant allocation use reduction factor of 0.78 for all water years. The framework is applied to compare water allocation decisions using different estimates of available water for allocation informed by seasonal forecasts of reservoir inflow, including the seasonal forecast datasets (FoGSS).

Prior to applying the FoGSS forecasts to emulate the water allocation decisions, the reliability of the seasonal predictions of available water is evaluated. In Figs.  and rank histograms are shown for both the POAMA and ESP+ datasets for the forecast ensemble of 1000 members (FoGSS) of the expected inflows into the Burrinjuck reservoir. The expected inflow shown is the total inflow from the forecast month through to the end of the water year, which is the information on the available water that is required to inform the water allocation decision. Rank histograms for expected flows for the Goobarragandra River at Lacmalac show a similar pattern and are available in the Supplement (Figs. S12 and S13). The rank histogram shows the frequency of the rank of the observed inflows in the ensemble, with a well-calibrated ensemble exhibiting a uniform distribution . For easier interpretation, the ensemble is pooled into five classes. The light grey bar shows the frequency of the observed rank being higher (or lower) than the highest (lowest) forecast value in the ensemble.

The rank histograms of the expected inflows to end of season for forecasts made in the months from July until January show that the ensemble is under-dispersed as the distribution is increasingly U-shaped, with the POAMA dataset exhibiting better performance than the ESP+ dataset. The first three of these months (July to September) are the wetter season. As this recedes, the under-dispersion increases until December, after which the performance again improves, with the expected inflows in February showing a near-uniform distribution, though reliability of the forecast again decreases as the accumulation period becomes shorter.

We additionally measure the accuracy of water year forecasts at each issue time with the continuous ranked probability skill score (CRPSS, ), with a climatology reference forecast generated by drawing random samples from a log-sinh transformed normal distribution fitted to observations using the Bayesian Joint Probability model . Positive CRPSS values indicate that FoGSS is more accurate, on average, than the climatology forecasts. Results show that skill is quite consistent for the forecasts flows of the Goobarragandra River, while the inflows of the Burrinjuck reservoir are only skilful for forecasts issued for July–September. In general, POAMA does have slightly better skill for forecasts issued earlier in the water year (see Fig. S11). In summary, the reliability of the forecast ensembles is better between February and June compared to July and January, while forecast skill is better for the beginning of the water year (considering that the inflows to Burrinjuck are larger than the Goobarragandra River flows). In our study we are primarily interested in the predictions of the expected inflows from July to February to support water allocation decisions for the cropping season, which are made from November to February. For this period, the forecast ensemble is shown to be somewhat overconfident, especially for forecasts issued for December. In addition, the ESP forecasts are slightly negatively biased for August–October (i.e. they tend to underestimate inflow). How this affects the water allocation decisions, and if using the forecast ensemble leads to better estimates of available water compared to the currently used conservative estimate based on climatology, is evaluated using both the ESP+ and the POAMA forecasts to inform the water allocation decisions.

Water allocation decisions for GS were emulated for the 1982–2009 period using four datasets of expected inflows to the reservoir to determine water availability: (i) observed inflow (considered perfect information); (ii) the conservative inflow (or reference information as currently used by the decision maker); (iii) the FoGSS seasonal forecast based on POAMA; and (iv) the FoGSS seasonal forecast based on ESP+. Water allocations using the perfect information and the reference information provide the benchmark against which the decisions informed by the ensemble forecasts are compared. For each of the two ensemble forecasts, two set-ups were tested. In the first, the inflow prediction at the beginning of the water year is obtained from the ensemble forecast made on 1 July, and this is then maintained for the next 12 months (non-updating FoGSS set-up). This means that the forecast of the available water that is established on 1 July is not updated by newer forecasts as the water year progresses. This was done to mimic the current procedure used by the basin authority when using the conservative inflow estimate based on climatology, where the expected inflow is established at the beginning of the water year and then maintained to the end of the water year. In the second set-up that was tested, the full potential of the ensemble forecast is explored. The water availability estimate to the end of season is now updated each month using the FoGSS forecasted inflows determined from the seasonal forecast made at the start of that month. In determining the expected water availability from the FoGSS forecasted inflows for both set-ups, different non-exceedance percentiles of the forecast ensemble are selected to provide the expected availability of water for allocation, starting with the 1st non-exceedance percentile (commensurate with a very conservative estimate of water availability) and increasing this to the 50th non-exceedance percentile (commensurate with the ensemble median).

FoGSS is an experimental seasonal ensemble streamflow forecast for a 12-month horizon developed for the Australian continent . FoGSS post-processes climate forecasts, either derived from ESP+ or POAMA to force a monthly hydrological model. ESP+ is an ensemble of seasonal precipitation forecasts based on climatology, while POAMA is an ensemble coupled ocean–atmosphere general circulation model (CGCM). A long time series (28 years) of climate predictions was used assuming a full representation of climate variability. The time period includes extremely dry years between 2001 and 2009 referred to as the Millennium Drought and very wet years, such as 1988 and 1989 .

The derived inflow predictions were transformed into accumulated inflow volume from each prediction month until the end of the water year (June). This set-up was used to mimic the current water allocation process in which the basin authority uses a conservative inflow prediction at the beginning of the water year for the next 12 months. In our approach a prediction of the inflow to the end of the season is updated each month using the forecast ensemble as a new forecast becomes available. Our approach to verifying the FoGSS seasonal forecasts is a novel extension of the traditional forecast skill assessment in that inflow predictions are evaluated for the next n months until the end of the water year, representing the decision variable used in the water allocation framework. In addition, key decision dates for water allocation are evaluated to provide insight into the reliability of those forecasts that have an impact on farmers' planning and operational decisions, especially for months before and during the cropping season.

As the seasonal forecast is updated each month, with a progressively shorter lead time to the end of the season, we would expect progressively more accurate forecasts of the water year. This is, however, only partly reflected in the inflow forecast skill results. Inflow forecasts to Goobarragandra are skilful year-round, with a slight dip for forecasts issued around December and a rise at the end of the water year (May–June) as the accumulation period shortens. FoGSS forecasts for Burrinjuck tend to be less accurate, and skill varies greatly through the year: skill is high for forecasts issued at the beginning of July and August but decreases every month from July until December, after which it again improves. The accuracy of Burrinjuck forecasts is thus clearly a function of season. For predicted forecasts issued in July–September (towards the end of the wetter winter season) the accuracy of accumulated volume forecasts is dominated by initial hydrological conditions and information from recent (high-flow) months. Flows are much lower by December, meaning that flow volumes in accumulated inflow forecasts are dominated by higher flows late in the water year (April–June). Predicting the rise of the annual hydrograph accurately relies on rainfall forecasts, which are usually not skilful at longer lead times. Thus water year forecasts issued for Burrinjuck in the driest months (December–February) tend to have the poorest skill. Inflow predictions to Burrinjuck after February do progressively improve due to the shorter lead time of the prediction, as the updated climate forecasts compensate for the model uncertainty.

In both catchments, the use of calibrated POAMA climate forecasts to force FoGSS adds skill to inflow forecasts issued in July–September. reported positive skill for calibrated POAMA forecasts from July to October, broadly coinciding with this period. While overall seasonal climate forecasts may not always add skill to inflow forecasts , we show that for these catchments seasonal climate predictions offer a small but marked improvement in forecast accuracy. The use of calibration to ensure coherent climate predictions –- i.e. as skill declines with lead time climate forecasts revert to climatology – ensures these gains in skill are not lost through poor climate forecasts at longer lead times.

Currently, only upward water allocation revisions are made during the water year in river basins in Australia. This is because in the current allocation a conservative inflow for the next 12 months based on climatology is used to determine the water allocation. Essentially this results in an estimate of available water that is always on the safe side from the point of view of the allocation decision. We estimate that the conservative estimate used in the current policy equates to the inflow that is exceeded 97 % of years, which would imply that in virtually all years the actual inflow is higher than the initial estimate. Depending on the initially available water in the storage reservoirs, this results in upward revisions of water allocations as the season progresses for most years, with the exception of the most extreme dry years (such as 2006). To the farmer, advance knowledge of the ultimate allocation is beneficial as it allows for better planning. We show that using information from a seasonal forecast ensemble to predict the inflows to the reservoirs and inform the water allocation decision can reduce the upward revisions. Although using the seasonal forecast ensemble does not reduce the frequency of upward revisions (or positive inconsistency) in all years, it does improve the accuracy in estimating water available for allocation. This implies there is benefit to using the seasonal forecast ensemble to inform the decision process. However, this comes at a cost. There is a trade-off between obtaining better predictions of water available for allocation than the conservative low estimate as it comes at the cost of more downward decisions during the water year. This is evident in dry years, particularly where the positive bias in the forecast at the start of the season results in downward revisions of the water allocation as the year progresses. In wet years upward revisions are reduced (compared to the reference water allocation) and only very minor downward revisions occur. Despite this, for both dry and wet years the accuracy of the available water for allocation using the forecast ensemble improves during the water year. This is most evident on the decision date around 14 September, where the accuracy of the water allocation decision informed by the forecast improves significantly and maintains this accuracy until the end of the water year. This is evident from the results of the RMSD, which shows the magnitude of the difference in the allocation decision through the season when compared to that made with the perfect knowledge of the amount of water available. The root mean square difference with the forecast ensemble attains a value more or less equal to the root mean square difference obtained with the conservative inflow, but 2 months before the original decision date (moving forward from about 13 November to 14 September). This means that for the same accuracy of predicted water allocation, decision makers can rely on the forecast ensemble information 2 months earlier when compared to the conservative inflow information. This may be of significant benefit to the farmers as they can then better plan their irrigation season based on the amount of water they would expect to be allocated.

Whether the basin authority in charge of water allocation announcements would choose to adopt a seasonal forecast system such as FoGSS and change the water allocation policy will depend very much on how acceptable downward revisions of allocated water are. The current policy has been designed to avoid such downward revisions unless exceptional circumstances dictate. Using the full potential of the seasonal forecast (including a monthly update of the expected inflow as new forecasts become available) provides more accuracy in water allocation estimates at the cost of downward revisions. Following maximum utility theory, the acceptability of downward revisions will depend on the impact these have compared to the benefit of the improved and earlier information on the water allocation. The ratio of downward and upward revisions is also influenced by the selection of the non-exceedance percentile. For dry years, selecting a lower, more conservative, percentage would appear to be the best strategy, while for the wet years a higher percentage should be selected. A non-exceedance percentile of 10 % appears to provide the best performance on average for both dry and wet years evaluated in this study, but a more dynamic approach could also be taken depending on the forecast as well as the available storage at the beginning of the water year. It would appear that the downward revisions (that occur mainly in the dry years) are primarily due to biases in the inflow forecast. Comparing the results of allocation decisions informed by the FoGSS forecasts based on the POAMA dataset to those based on the ESP dataset, the number of revisions (both upward and downward) in Figs.  and S10 indicate that these are marginally less for the POAMA-based dataset. This would suggest that further improving the seasonal forecast can contribute to reducing undesirable downward revisions. Additional improvements to the inflow predictions by reducing the uncertainty in the hydrological model of the basin will also contribute to reducing the bias of the inflow predictions and improving allocation results.

Allocation decisions made depend not only on the available water in reservoirs and the expected inflows, but also on the actual demand from the crops planted by farmers. In our study demand is taken as the sum of the entitlements of farmers, reduced by the use reduction factor we introduce. Given the water allocated to meet their entitlement, farmers will make their decisions on the crops they plant for the season. In the Murrumbidgee basin, farmers may, however, also trade the water they are entitled to or store part of their allocation for use in the next season by deciding to leave it in the upstream reservoirs as carry-over . As a result, there are quite complex feedbacks as the decision to carry water allocated over to the next season will influence the allocation decisions at the basin level in that next season. Decisions made by the farmers on what and how much to crop are complex and depend on a range of factors that include the available water through allocation but also economic factors and personal preferences. The allocation use reduction factor we introduce to consider these decisions made by farmers, and we find a value of an average use of 78 % of water entitled to best emulate actual decisions made, on average. While this factor could be optimised mathematically, a detailed understanding of how farmers make decisions is then required. develop a decision model based on interviews of farmers in the Ebro basin in Spain, showing that decisions on what to crop depend on their perception of water availability and will differ between seasons considered wet and seasons considered dry as well as their aversion to risk and technological capacities. They find that the availability of information on available water as the season develops, such as provided through a seasonal forecast, will influence perceptions of water availability and consequently cropping decisions. Further research into how farmers in the Murrumbidgee basin make decisions using for example agent-based models could shed more light on the influence on water allocation decisions made at the basin levels.

The impact in irrigated agriculture of uncertainty in the available water resources has been widely assessed in Australia considering climate variability and climate change scenarios . Adaptation measures, reallocation strategies, and policy reform are currently in discussion to prevent future impacts due to extreme events . In this study we explore the possibility of using a seasonal forecast ensemble to secure the right amount of allocated water at the right time during the water year. In the Murrumbidgee basin, farmers decide on the area to be cropped for annual crops based on the water allocation announcement for General Security. The water year starts on 1 July, but the summer cropping season starts on 1 November and ends on 1 March. In that sense, the period to decide on the area to be cropped is between 1 July and 1 November, and the period for operational decisions (e.g. irrigation schedule, weed management) is from 1 November to 1 March. While it would seem logical that farmers wait until the last allocation announcement before 1 November to decide on the area to be cropped, due to pre-cropping planning activities and investments (e.g. buying seeds, maintenance of irrigation assets, or investing in agricultural equipment and machinery) they prefer to take decisions earlier, therefore relying on water allocation announcements made at an earlier date. By using the seasonal forecast to inform water allocation decisions we show that farmers could rely on the water allocation announcement made on 14 September, some 1.5 months earlier. This would allow them to plan their activities better, thus reducing potential negative impacts of having to take decisions on the area to be cropped before the actual water allocation on 1 November is established.