Can climate knowledge enable Warragamba Dam, Sydney, Australia to be used to manage flood risk?

Dams that serve a dual purpose of water supply and flood mitigation operate to maintain a defined full supply level of water that balances the two conflicting requirements. To optimize the use of available storage space, the full supply level may be adjusted to reflect changing risks of future water shortages and future flood inflows based on known seasonal variations and current observations. The Warragamba Dam in eastern Australia is located upstream of the populated Hawkesbury-Nepean valley which has one of the largest flood exposures in the country. However, the operating protocol of the reservoir does not include provisions to reduce the full supply level of the dam for flood mitigation. Large scale climate indicators that are known to influence the hydroclimate of this region may potentially contain useful information to inform the dual use of this reservoir, but their utility for this purpose has not been studied. Here we explore whether current observations of large-scale climate along with antecedent catchment conditions can be used to estimate the probability of large inflows into the reservoir in the next 3- and 6 months, to aid flood management. We find that the predictors have a substantial influence on the probability of large inflows. The probability differences during opposite predictor phases vary by season and range from 30% to 70%. Our results indicate that considering current climate information to inform dual use of the Warragamba dam has merit.


Introduction
Large on-river dams have been constructed on waterways upstream of populated areas to serve multiple purposes.Water storage is commonly the primary purpose, to balance water availability between periods of high and low rainfall.In some regions, the principal need is to balance annual supplies between often reliably wet and reliably dry seasons.Other areas may be prone to less regular variability involving multiyear wet periods and prolonged multi-year periods of drought.
Some large on-river dams have been constructed for the purpose of mitigating what would otherwise be large and damaging flood events (Mei et al 2018).This is achieved by providing temporary storage for large inflows and subsequently releasing some or all of those inflows in a manner that reduces downstream flooding impacts.Flood mitigation may be achieved by enabling more gradual release of water compared to inflow rates and by delaying releases to avoid peak flows coinciding with high flows into the same river basin from other sources.
Many dams serve both purposes of water storage and flood mitigation to a greater or lesser extent (Jain et al 2023).Some multipurpose dams have formal operating protocols designed to achieve a balance between the dam's effectiveness for each of these two roles.Such protocols inevitably involve compromise since operation to maximise water storage conflicts with optimum operation to maximise flood mitigation capacity (Jain et al 2023).Maximum storage capacity is achieved by maximising the available reservoir volume for seasonal or longer water storage.Conversely, maximum flood mitigation capacity is achieved by maintaining storage well below maximum capacity to enable temporary use of available storage capacity to capture flood inflows.
Operating protocols aimed at achieving a balance between water storage capacity and flood mitigation capacity typically define a 'full supply level' (FSL) as the height of water to be maintained for water storage, which is less than the maximum height of water that could be held in the reservoir.In some cases, the terminology adopted is the 'full supply volume' (FSV), referring to the volume to be maintained for water storage, less than the maximum volume available.The remaining storage capacity is then the flood mitigation capacity.A target FSL or FSV can be adjusted at various times, reflecting variation in the anticipated likelihood of large inflow events and/or the consequences of them occurring.That is, an FSL or FSV may be adjusted in response to a changing balance between risks associated with future supply shortage and future inflows requiring flood mitigation.
For multipurpose water storages, a flood control rule curve may be established to describe how the available storage capacity might be distributed between serving water storage objectives and flood mitigation objectives across a seasonally variable year.However, reservoir management based on strict adherence to a set flood control rule curve may fail to effectively account for current observations that deviate from assumed or averaged conditions that underpin the rule curve.To overcome this, some researchers have proposed the adoption of dynamic flood control rule curves (Chaleeraktrakoon and Chinsomboon 2015).A dynamic flood control rule curve is one for which the reservoir operational rules are modified in response to current observations.In this paper, we examine the potential of using climate data to inform dynamic adjustments of the FSL of the Warragamba Dam in eastern Australia.
Warragamba Dam is a water storage upstream of the Hawkesbury-Nepean Valley in western Sydney, New South Wales.Lake Burragorang is the reservoir created behind Warragamba Dam and is the largest supply of water to more than four million people in the Sydney Basin.The Burragorang Valley, which is impounded by Warragamba Dam is also a major source of flood water, with a history of severe flooding of the populated Hawkesbury-Nepean Valley, which is one of the largest flood exposures in Australia (Infrastructure NSW 2017).However, the current operating protocol for Warragamba dam includes no provision for the dam operators to intentionally reduce water storages for the sake of maintaining a significant flood mitigation capacity.Enhancing flood mitigation capacity in this region is of immediate relevance in the light of recent severe flooding events (Turner et al 2016, Kelly andKuleshov 2022), and proposed urban developments which would result in more people with low perceptions of flood risks living in this region (Neale 2015, Masud et al 2019).
On the east coast of Australia, severe droughts and floods are often associated with observable climatic indicators in the surrounding oceans (Ummenhofer et al 2009, Van Dijk et al 2013, Sewell et al 2016).Variability in the Pacific (El Niño Southern Oscillation; ENSO) and Indian (Indian Ocean Dipole; IOD) Oceans are the dominant largescale modes that influence interannual variations in rainfall, streamflow, and soil moisture (SM) in this region (Chiew and McMahon 2003, Risbey et al 2009, Ummenhofer et al 2011).These large-scale patterns affect the hydroclimate of eastern Australia by inducing changes in synoptic patterns and weather systems (Cai et al 2011, Holgate et al 2022, Gillett et al 2023) and changing the occurrences of rainfall events (Pui et al 2012).Information from these teleconnections have been used to understand and predict various regional patterns, including that of continuing drought (King et al 2020, Devanand et al 2023), heatwaves (Reddy et al 2021), crop yields (Yuan and Yamagata 2015), flood magnitude and frequency (Liu et al 2018).To enable dynamic adjustment of the FSL of the Warragamba Dam, here we examine whether the information of large-scale variability combined with antecedent catchment conditions can be used to forecast the probability of large inflows into the reservoir.
Statistical approaches for rainfall and streamflow forecasting using climate and hydrologic indicators as predictors have been explored in prior research in Australia (Sharma 2000, Wang et al 2009, Westra and Sharma 2009, Wang and Robertson 2011, Zhao et al 2016, Troin et al 2021).These forecasting methods have evolved to use increasingly complex multisite predictive models to maintain spatial covariances at multiple gauges.Judicious use of such forecasts can aid reservoir managers to optimise the use of available storage space to avoid sharp fluctuations in outflows and reduce downstream flood risks (Jain et al 2023).Prior research in the Warragamba region indicates that climate and antecedent covariates capture the direction of inflow changes but underestimate the magnitude of extremes (Westra and Sharma 2009).A more recent analyses of other catchments in southeast Australia reports that streamflow forecasts using antecedent and climate predictors are more skilful than climatology (Zhao et al 2016), indicating the potential utility of these predictors within this region.
In contrast to the existing work on streamflow forecasting, here we focus on a potentially simpler question about the probability of exceedance of inflows above a threshold at a single location (the Warragamba Dam) without forecasting the inflow volumes, for a tailored application.We investigate whether the Warragamba FSL could be temporarily reduced, below the full storage capacity, to provide some flood mitigation capacity without severely compromising the drought resilience role of the dam.This temporary reduction in FSL would be informed by the observation of climate data, indicating variable and changing risks of forthcoming periods of drought or flood-inducing heavy rainfall.

Data and method
The location of the Warragamba dam and the catchment of the reservoir is shown in figure 1(a).We use the historical monthly inflows into Lake Burragorang from January 1970 to July 2022 to model the probability of large inflows based on climate and antecedent indicators.Monthly inflow data to the reservoir were estimated by summing daily flows from the four major stream sources to the reservoir.Daily inflows data were retrieved from stream flow data maintained and archived by WaterNSW for Coxs River at Kelpie Point (Gauge 212250), Kowmung River at Cedar Ford (Gauge 212260), Nattai River at The Causeway (Gauge 212280), and Wollondilly River at Jooriland (Gauge 212270).The archived data for these daily stream flows were largely complete between January 1970-July 2022, but included some data gaps from periods in which gauges failed to record data.Since these four streams are geographically close (within 60 km of each other) and experience similar climate conditions, data gaps for each of the four streams were filled by extrapolating flows recorded from 2 or 3 other nearby stream gauges.Details of the procedure used for data extrapolation are provided in supplementary text 1.
We use indices of the ENSO and IOD, which are the dominant large climate modes that affect the interannual variability in the regional hydroclimate of the study region as the climate predictors.We use the Southern Oscillation Index (SOI) timeseries calculated from sea level pressure in Tahiti and Darwin provided by the Bureau of Meteorology (BoM) (www.bom.gov.au/climate/enso/soi/) that represents the state of ENSO, and the Dipole Mode Index (DMI) timeseries provided by NOAA (Saji et al 1999) (https://psl.noaa.gov/gcos_wgsp/Timeseries/DMI/) that represents the state IOD, as the climate indicators.SOI and DMI are commonly used indices that represent the state of variability in the Pacific and Indian oceans and are available from climate centres in near real-time for operational applications.We also use sea surface temperature anomalies in the Niño3.4region (Niño3.4)provided by NOAA (https://psl.noaa.gov/gcos_wgsp/Timeseries/) to assess the sensitivity of our results to a different ENSO index.Antecedent catchment SM which is a dominant factor that affects streamflow peaks (Wasko and Nathan 2019) is used as the antecedent indicator.
Here we use the catchment average SM in the top 1 m depth of the soil column from the Australian Water Resources Assessment Landscape (AWRA-L) historical dataset (Frost et al 2018) which is available in near real time through the Australian Water Outlook provided by BoM.Lake Burragorang inflows are affected by the lagged states of these indicators.Figures 1(b)-(d) shows the variation in 3-month reservoir inflows (in gigalitres, GL) with climate indicators of the previous month and initial SM at the start of the accumulation period.The distribution of inflows during wet and dry phases of the indicators are markedly different.The median 3-month inflows during wet phases of SOI, DMI, and SM are 138 GL, 143 GL, and 375 GL respectively.During dry phases the median inflows are much lower and amount to 70 GL, 24 GL, and 33 GL during dry phases of SOI, DMI, and SM respectively.When SOI and DMI are in their wet phases, the 3-month inflows exceed 200 GL about 40% of the time, whereas during the dry phases of the climate modes the 3-month inflows are above this threshold only 8% to 18% of the time, indicating the potential to use these climate indicators as predictors for this application.

Estimation of exceedance probabilities
We use logistic regression which is a form of generalized linear model (GLM) to estimate exceedance probabilities.The predictand of logistic regression is bounded by zero and one, and the model is well suited to model probabilities as a function of one or more predictors (Lo et al 2007, Prasad et al 2010).Here we use the logistic regression formulation to estimate the probability of large inflows into the Warragamba reservoir at seasonal to interannual timescales of 3and 6 months using the selected lagged indicators, SOI and DMI of the previous month (SOI previous-mon , DMI previous-mon ) and SM at the start of the accumulation period (SM initial ), as predictors.We also use an oceanic index of ENSO, Niño3.4,instead of the SOI and present the results in the supplementary.We select two inflow thresholds for analysis, and estimate the probability of 3-month inflows exceeding 200 GL and 6-month inflows exceeding 400 GL.Other inflow thresholds relevant for operational application may be used in practice.The models are of the form shown below, where p is the probability of exceedance log We estimate the model parameters separately for each season as there are seasonal variations in the influence of large-scale climate modes on rainfall in eastern Australia (Risbey et al 2009).We employ a moving 'fair-all' calibration window (Risbey et al 2021) which uses all available data prior to the predicted year to estimate model parameters and probabilities, for a validation period from 2005 to 2022.We validate the model probability estimates using reliability diagrams that compare the modelled probabilities with observed proportions calculated using inflow observations in each model probability bin.The reliability diagrams of GLMs that model probabilities of exceedance of 3-month and 6-month inflows above the selected thresholds are shown in supplementary figure 7.There is a close match between the observed proportions and model estimates indicating good model performance.

Influence of the predictors
We analyse the influences of the predictors on the modelled probabilities and quantify the added value of model estimates that utilize climate and antecedent predictor information over exceedance proportions estimated from the inflow data alone.Figure 2 shows the differences in model estimated probabilities from the seasonal exceedance proportions and the variation with predictors during different seasons based on data for the validation period 2005-2022.The overall pattern combining the data from all seasons is shown in supplementary figure 8.The model estimated probabilities are substantially different from the seasonal/overall exceedance proportions, and the magnitude of differences increase if one or more predictors are further away from their neutral state.This is evident in the increasing intensity of colour shading, away from the centre of the panels in figure 2. Consider conditions when two of the predictors, SOI and SM, are in phases conducive for higher (SOI ⩾ 8, SM ⩾ 90th percentile) and lower inflows (SOI ⩽ −8, The magnitude of variation in modelled probabilities due to changes in SOI and SM are quantified as the mean difference in probability (Prob.diff) and indicated in the bottom right corner of each panel.These are calculated for predictor states conducive for higher inflow (SOI ⩾ 8 and SM in the top decile), and for predictor states conducive for lower inflow (SOI ⩽ −8 and SM in the bottom decile).The probability differences are not estimated if there are fewer than two instances of predictor states conducive for higher or lower inflows in that season.SM ⩽ 10th percentile).The mean differences in probabilities during these opposite phases range from 0.3 to 0.7, depending on the season and timescale.
There are seasonal differences in the influences of the predictors on estimated probabilities (figure 2).The mean differences in probabilities during contrasting phases of each predictor is listed in supplementary table 1, and we discuss the major seasonal patterns here.In winter (JJA, June to August), all predictors have a strong influence on probabilities.The differences between the combined extreme opposite phases of the SOI and SM predictors are around 0.7 (figures 2(c) and (g)).When the SOI and SM states are conducive (unconducive) for higher inflows, the model estimated probability of exceedance is about 0.3 higher (lower) than the seasonal exceedance proportion (figures 2(c) and (g)).In seasons MAM (March to May) and SON (September to November), the differences in modelled probabilities with changes in predictors are lower than in JJA (figures 2(b), (f), (d) and (h)).The influence of SM is weaker in SON for the higher inflow threshold, possibly because the SM at the beginning of the accumulation period exerts a lower influence as it typically depletes during the transition into the summer season.In contrast, during MAM, the antecedent predictor, SM, has the strongest influence on probabilities with opposite phases resulting in probability differences of 0.5-0.56.This indicates that the state of SM at the end summer is a strong determinant of the likelihood of large inflows in the following season.In MAM, the opposite phase of the SOI is associated with negligible modelled probability differences of 0.05 or lower while opposite phases of the DMI are associated with probability differences higher than 0.3.IOD events typically develop in winter, so the non-negligible influence of this mode in autumn is perhaps surprising.Such an influence is also reported in a prior assessment of flood magnitude and frequency in eastern Australia (Liu et al 2018) and they hypothesise that this is driven by the occurrence of cold southerlies in eastern Australia associated with positive DMI values in autumn (Liu et al 2018).In December to February (DJF), the combined influence of the predictors is weaker than that during the other seasons.The is because the influences of both SOI and DMI are weaker in DJF compared to JJA and SON, and the influence of SM is weaker in DJF compared to MAM and JJA (supplementary table 1).
The seasonal differences in the influences of the predictors estimated using Niño3.4instead of the SOI as the ENSO predictor are similar (supplementary table 2).A minor difference is that the ENSO influences are slightly stronger (+0.01 to +0.05), and the IOD influences are slightly weaker (−0.03 to −0.1) in JJA and SON, when Niño3.4 is used as the ENSO predictor instead of the SOI.

Probabilities during the historical period
We use the modelled probabilities of exceedance during the historical period to demonstrate how this approach may be used to manage flood risk.For operational applications, the estimated probabilities can be used to decide if the FSL of the reservoir should be reduced to reserve storage for expected inflows when there are high probabilities of large inflows in the next few months.Lowering the FSL would result in release of water from the reservoir in cases where the dam water levels are near capacity.Based on the probability levels used for decision making, there would be instances when the subsequent inflows do not exceed the relevant thresholds, rendering the decision to reduce the FSL non-optimal.In hindsight, this is inevitable when using a probabilistic approach to manage the risk that low-probability events (such as inflows not exceeding the relevant thresholds) will occur, albeit infrequently.
Figure 3(a) shows the historical monthly inflow timeseries for the validation period 2005-2022.Figures 3(b) and (c) shows the 3-month and 6month exceedance probabilities estimated using our method for the same period, with markers showing instances when the estimated probabilities are higher than a probability threshold of 0.6.The precision, recall and false positive rates of several probability thresholds (0.5, 0.6, 0.7, 0.8) are calculated (supplementary text 2) and the threshold of 0.6 is selected to maintain a high precision (0.64-0.67) and low false positive rate (0.02-0.03) required to meet the primary water supply objective of the Warragamba reservoir.However, this threshold has low recall rates of 0.12 and 0.11 for 3-month and 6-month inflows, respectively (supplementary text 2).These low recall rates may be partly related to the occurrence of east coast lows (ECLs) (Dowdy et al 2019, Pepler et al 2021) during dry phases of one or more strong predictors within the season (supplementary text 3).
Figures 3(b) and (c) highlights whether the cumulative inflows exceeded the relevant thresholds in the subsequent 3-and 6 months when high probabilities are predicted.These dates and inflows corresponding to the high probabilities are also listed in supplementary tables 5 and 6.In the historical period from January 2005 to July 2022, there are 9 time instances where modelled probability that the inflows in the next 3 months will be higher 200 GL and 11 instances where the modelled probability of inflows in the next 6 months will be higher than 400 GL, is higher than 0.6.The reservoir operator may decide to reduce the FSL at these times.The subsequent inflows were higher than the relevant thresholds in 6 of these instances in the case of 3month and 7 of these instances in the case of 6-month inflows.This indicates that the decision to reduce the FSL would have been optimal in 67% of cases over subsequent 3 months, and 64% of cases over subsequent 6 months.The risk of decisions that lead to non-optimal outcomes would vary with the flow thresholds and probability levels used for decision making, which could be selected based on the risk appetite of the reservoir management.

Discussion
The Hawkesbury-Nepean floodplain is considered by the Insurance Council of Australia to be the region of highest single flood exposure in New South Wales, and potentially Australia (Infrastructure 2017).At the same time, multiple additional urban developments are under consideration for the flood plain.We explored to what degree the Warragamba reservoir could be used to manage flood risk.
Our results indicate the potential of utilising climate and antecedent information to manage part of the flood risk in the Hawkesbury-Nepean floodplain.Specifically, we examined the degree to which knowledge of the state of the SOI and DMI provided information to aid a correct decision on reducing the volume of water in the Warragamba reservoir to accommodate inflows that would otherwise contribute to downstream flood.If a decision maker used knowledge of the state of the SOI, IOD and antecedent SM and decided to lower water volumes, an optimal decision would have been made 67% of the time over the following 3 months and 64% of the time over the following 6 months, using a probability threshold of 0.6.
We note three limitations of this result.First, Sydney experiences water shortages driven largely by limited supply and climate change, which in combination with population grown, is exacerbating limitations (Barker et al 2021).A decision to lower the water volume in the reservoir to accommodate anticipated inflows of 200 GL or 400 GL that proves incorrect 33% of the time over the following 3 months might not be acceptable.Second, using a probability threshold of 0.6 results in high precision results with low recall rates.The low recall rates do not pose an additional risk to use of this method to mitigate flooding, as there are no dynamic FSL adjustments in response to low probabilities.However, it does mean that there are instances, partly related to the occurrence or temporal clustering of intense ECLs during dry predictors phases, which cannot be mitigated based on the probabilities from the current model formulation.It may be possible to improve the recall rates by including additional predictors that provide skill for multi-week ECL predictions, as research in this area evolves.Overall however, this approach offers an avenue for flood mitigation during wet phases of climate and antecedent indicators which are associated with increase in flood disasters on the east coast (Sewell et al 2016).Third, inflows of 400 GL are large, but not at a level that if they occurred coincident with a full reservoir would lead to catastrophic downstream flooding.We could not examine the degree of predictability of events close to 1000 GL due to their rarity in the historical record.Thus, realistically, using the Warragamba reservoir to manage flood risk may need to be restricted to conditions where the climate drivers and SM are most strongly indicative of likely very high inflows, and used to ameliorate (but not fully negate) downstream flooding.This implies that using the Warragamba reservoir to manage flood risk needs to be part of an integrated flood risk management system that includes strong planning controls on future flood plain development, engineering solutions in some locations, careful consideration of evacuation strategies and a systematic examination of risks associated with recent and future climate change.
We note that there are other methods and predictors for predicting inflow probabilities.Other approaches include non-parametric techniques (Sharma 2000), Bayesian methods (Wang et al 2009), or machine learning (Zarei et al 2021).It is of particular interest to assess if the operational method used by the BoM to predict 1-3 month streamflow/reservoir inflows (Feikema et al 2017) can be used to estimate exceedance probabilities of Warragamba inflows and how the results compare with estimates from our GLM approach.Alternate climate and antecedent indicators may also be used as predictors.We use SM from AWRA-L as the antecedent indicator and our results show that it is the strongest predictor in three seasons.An alternate antecedent indicator may be lagged inflow, as used in operational streamflow prediction in Australia.We use readily available indices of the ENSO and IOD as the climate indicators which are available in near real time for operational applications.Alternate climate indicators may include other climate indices, sea surface temperature anomalies, or sub-seasonal forecasts of climate states, potentially leveraging predictor selection methods such as partial mutual information (Sharma et al 2000) or pseudo-Bayes Factors (Robertson and Wang 2012).The climate indicators used in this study are selected based on prior knowledge that ENSO and IOD are dominant large scale climate modes that influence eastern Australia.The literature indicates that ENSO may potentially be used as a predictor in several other regions, as it exerts a dominant influence on the water availability and flooding in many regions of the world (Ward et al 2014, Kundzewicz et al 2019).Other large-scale modes in the Atlantic and northern Oceans that affect the interannual variability of floods in areas of Europe, North and Central America may be used for applications in those regions (Kundzewicz et al 2019, Zanardo et al 2019, Moulds et al 2023).Lastly, our method estimates the probability of exceedance, which is in essence a binary forecast of large reservoir inflows in the context of decision making for reservoir operation.Forecasts of flood peak magnitudes would be even more useful.Future work may examine the skill of such forecasts using climate and antecedent covariates (Kundzewicz et al 2019, Zanardo et al 2019, Steirou et al 2022).

Summary
We use a GLM formulation to estimate the probability of large inflows into the Warragamba reservoir to inform dual use of reservoir storage.The method uses information from lagged climate and antecedent indicators, and our results show that the predictors have substantial influence on the probability of large inflows.The probability differences during opposite predictor phases vary by season and range from 30% to 70%.
Overall, our analysis points to the potential of dynamic adjustment of the Warragamba Dam FSL to effectively adjust the balance of water shortage risks and flood risks in the Hawkesbury-Nepean basin.Our results suggest that the Warragamba Dam FSL can be one of several tools to help manage risk given the risk of non-optimum decisions and the magnitude of contribution a managed flood mitigation capacity can have on peak flows in an extreme event.However, given the vulnerability of existing and planned developments on the Hawkesbury-Nepean floodplain, adjusting the Warragamba Dam FSL may reduce risks to life and property and that likely brings net benefits accounting for the relatively rare wrong decision.
Globally, the risk of flood is increasing (McDermott 2022) due to a range of factors including catchment modification, increasing population pressure and climate change.Many reservoirs are already multi-purpose, and our results may provide an avenue to improve the management of these.Some reservoirs are only used for water supply and our methods provide a way that might allow some of these to become dual purpose.In each case, an examination of the roles of climate drivers will be needed and the relevant drivers will vary by location, but we suggest our methodology (Devanand et al 2023b) is likely broadly transferable to catchments in other parts of the world.

Figure 1 .
Figure 1.(a) The location of Warragamba dam and catchment of the reservoir.Scatter plots of the variation in cumulative 3-month reservoir inflow (in GL) with changes in climate and antecedent indicators (b) SOI of the previous month, (c) DMI of the previous month, and (d) initial catchment SM (in fraction of fullness).The box plots summarise the inflow data during wet and dry phases of the indicators, marked by the vertical dashed lines in the panels.The (wet, dry) phases shown in this figure are based on thresholds (8, −8) for SOI, (−0.4,0.4) for DMI, and (90th percentile, 10th percentile) for SM.

Figure 2 .
Figure 2. The differences in the model estimated probabilities from seasonal exceedance proportions (colour shading) with variation in the predictors, SOI (y-axes), soil moisture SM (x-axes), and states of the IOD (markers) for (a)-(d) probability of 3-month inflow ⩾ 200 GL, and (e)-(h) probability of 6-month inflow ⩾ 400 GL by season, based on data from 2005-01-2022-07.The magnitude of variation in modelled probabilities due to changes in SOI and SM are quantified as the mean difference in probability (Prob.diff) and indicated in the bottom right corner of each panel.These are calculated for predictor states conducive for higher inflow (SOI ⩾ 8 and SM in the top decile), and for predictor states conducive for lower inflow (SOI ⩽ −8 and SM in the bottom decile).The probability differences are not estimated if there are fewer than two instances of predictor states conducive for higher or lower inflows in that season.

Figure 3 .
Figure 3. (a) Observed monthly inflows into Lake Burragorang during the period 2005-01-2022-07.Model estimated probabilities of large inflows during the same period for (b) probability of large inflows (3-month inflow ⩾ 200 GL), and (c) probability of large inflows (6-month inflow ⩾ 400 GL).Probabilities higher than 0.6 are highlighted in panels (b) and (c), and the different colors indicate whether the subsequent inflows exceeded the thresholds.