When based on the zones of available water in storage, hedging has
traditionally used a single hedged zone and a constant rationing ratio for
constraining supply during droughts. Given the usual seasonality of
reservoir inflows, it is also possible that hedging could feature multiple
hedged zones and temporally varying rationing ratios but very few studies
addressing this have been reported especially in relation to adaptation to
projected climate change. This study developed and tested Genetic Algorithms
(GA) optimised zone-based operating policies of various configurations using
data for the Pong reservoir, Himachal Pradesh, India. The results show that
hedging does lessen vulnerability, which dropped from
The realization that projected climate change will affect reservoir future inflow series and hence performance has led to the intensification of research efforts to assess these impacts as a precursor to the development of effective mitigation and adaptation strategies (see e.g. Nawaz and Adeloye, 2006; Fowler et al., 2003; Li et al., 2009). Most of these studies have reported deteriorating performance notably with regard to vulnerability unless improved operational practices are developed.
The use of rule curves for guiding reservoir operation (Yin et al., 2015) is
schematically illustrated in Fig. 1a. Full satisfaction of demand is
attempted whenever the water available (WA) is in the interval [LRC
Although they are easy to use, rule curves often produce large water shortages or vulnerability (see e.g. Chiamsathit et al., 2014). Hedging, which is the deliberate cutting back of supplied water even when there is sufficient water, has been shown to moderate the vulnerability associated with rule curve operation (Eum et al., 2011).
Figure 1b illustrates a critical rule curve (CRC) delineated hedging zone
integrated with the rule curve of Fig. 1a. Below the CRC, a maximum fraction
“
Schematic illustration of zone-based operating rules for
The aim of this work is to evaluate the effectiveness of GA-optimised hedging policies in moderating reservoir vulnerability during projected climate change perturbations. The work used the Pong reservoir located on the Beas River in Himachal Pradesh, India and serves irrigation and hydropower purposes. In the following section, further details of the adopted methodology are given. This is then followed by the description of the case study, following which the results are presented and discussed. The final section contains the main conclusions and recommendations of the study.
The methodological approach is illustrated in Fig. 2; brief details of the different aspects are provided in the sub-sections below. Additional information is available elsewhere (see Adeloye et al., 2016).
Genetic Algorithms (GA) (see Michalewicz, 1992; Wardlaw and Sharif, 1999)
were used for optimising the hedging policies because of its various
advantages, including their potential to search the solution from population
of points (not a single point), its use of objective function information
itself (not any derivatives), and its use of probabilistic transition rules.
For these reasons, GA have been widely used for solving complex optimisation
problems in various branches of science including water resources. The
objective function for the optimisation was:
Let total available water, WA
Methodology flow chart for optimising and performance evaluation of the hedging policy.
For the single stage hedging, the decision variables for the optimisation
are the CRC
Map of India and the Beas river catchment.
Average monthly inflow and irrigation demands from the Pong reservoir (data: 2000–2008).
The assessment of the effects of projected climate change on reservoir
inflows employed the delta perturbation approach (see Anandhi et al., 2011;
Vicuna et al., 2012) in order to avoid the notorious uncertainties
associated with GCM projections and their downscaling. The delta
perturbations in temperature
Reservoir simulation used the reservoir mass balance equation and associated constraints shown in Eqs. (1a–e). At the end of the simulation, reservoir key performance indicators were evaluated as follows (McMahon and Adeloye, 2005; Sandoval-Solis et al., 2011):
GA optimised rule curves
The Pong dam (and its reservoir, see Fig. 3) is located at longitude
76
Monthly reservoir inflow and irrigation demands from January 2000 to
December 2008 (9 years) were available for the study. The historic mean
annual runoff (MAR) at dam site is 8485 Mm
The genetic algorithm (GA) optimised basic (i.e. without water hedging) rule curves were developed by Adeloye et al. (2016) for the reservoir as part of the wider study and are shown in Fig. 5a. These rule curves formed the bases for the development of the hedging-integrated rule curves as outlined in Sect. 2.1.
Table 1 summarises the effects of the projected climate change perturbations on the reservoir inflow. As expected, more inflows are recorded as the catchment precipitation increases. Table 1 also shows that the runoff increased for all the temperature increases even when the precipitation had remained unchanged. As noted earlier, there are significant glaciers and seasonal snow in the upper part of the Beas catchment. The simulated increase in the runoff at high temperatures is due to the additional runoff generated from the melting of the snow/glaciers at elevated temperatures, which appeared to have more than compensated for any evapotranspiration increases.
The optimised hedging integrated rule curves are shown in Fig. 5b and c; as noted previously, Fig. 5a is the basic, no-hedging set of rule curves. While Fig. 5b is single stage, Fig. 5c has two stages; both policies, however, used constant hedging (or rationing ratios).
The CRC that triggers the water rationing in Fig. 5b lies everywhere between the URC and LRC as expected and allows attempting to supply the full demand over a very wide range of water availability in the system during the high flow monsoon (May–September) season. The range of water availability in which the full supply can be attempted is much narrower for the drier, post-monsoon periods. Water rationing will occur whenever the available water falls below the CRC. However, as shown in Fig. 5b when water rationing takes place, only 17 % of the full demand is cut back, leaving 83 % of the full demand being attempted. This deliberate cut-back is moderate and is thus not expected to cause undue hardship for water users.
Change (%) in mean annual and seasonal runoff under climate change.
In Fig. 5c with two hedging stages, the upper critical curve is everywhere lower than the single critical curve of Fig. 5a, implying that more water will be available for release in the upper hedging zone of the two stage hedging policy than from the single hedging zone of Fig. 5a. This has been confirmed by the value of the optimised rationing ratio for the upper hedging zone of Fig. 5c, which at 85 % is higher than the 83 % optimised for the single stage hedging policy of Fig. 5a. As expected, the lower critical curve (and hedging zone) has intensified the rationing in response to the dwindling water stock by allowing only 76 % of the full demand to be attempted whenever the available water falls into the lower hedging zone. As noted previously, hedging is expected to temper reservoir vulnerability and any evidence of this will be reported in the next section when the reservoir performance is discussed. However, a re-assuring aspect of the hedging policies is that the amounts of water cut back represented by the optimised rationing ratios as obtained herein are modest and lesser than the 25 % tolerable shortage suggested by Fiering (1982).
The hedging policies in Fig. 5 relate to static, i.e. constant rationing ratios situation; however, a further aim of the work had been to investigate dynamically varying rationing ratios. Although both the monthly and seasonally varying options were investigated, only the results of the monthly are presented to save space. The CRC for the dynamically varying hedging policies are shown in Fig. 6a (single stage) and 6b (two-stage), respectively; their associated optimised supply limits (or rationing ratios) are shown in Table 2. Unlike the static situation for which the rationing ratio was constant, dynamic rationing has varied monthly, reflecting the relative water abundance in the various months.
Rationing ratios for monthly varying hedging policies.
Thus, as seen in Fig. 6a for example, the proportion of the demand supplied in the monsoon months was highest, almost approaching 100 %. As the available water reduces, e.g. during the winter and pre-monsoon seasons, the proportion of the demand supplied attained its least value of < 80 %. Another feature of the dynamic scheme is that the optimised critical storage curves that trigger hedging have also responded to the reservoir inflow situation in that during the low inflow winter season, the curves are below those for the static case ensuring that the water available for meeting the full demand is more and hence occasions when reductions will be needed will be few. On the other hand during the high inflow, monsoon seasons, the critical curves for the dynamic policies are higher than those of constant hedging, meaning that rationing will occur more frequently albeit the cut back amounts would be very small since the associated rationing ratios are close to unity. For the 2-stage policy in Fig. 6b, the monthly rationing ratios presented in Table 2 behave as expected, with those for the lower zone being less than those for the upper zone.
The implication of this is that the dynamic policies will offer improvement in performance over the static policy but the question remains by how much? The attractiveness of the dynamic policies therefore would stem from their effect on the system performance: a very significant improvement in performance over the static policy case would be required to justify the preference for the former.
To save space, discussion on the performance evaluation will be limited to the reliability (time- and volume-based) and the vulnerability. Figures 7–9 show the results of the performance evaluation using: time-based reliability (Fig. 7); volume-based reliability (Fig. 8) and the vulnerability (Fig. 9).
With no hedging, the time-based reliability is high under existing
conditions but decreases when less water is projected by climate change, and
increases when more inflow is projected. The effect of temperature rise on
the inflow contributions from melting ice and snow has manifested in the
time reliability, with the projected 2
GA optimised rule curves
Hedging effect on reservoir performance (time-reliability).
Hedging effect on reservoir performance (volume-reliability).
Hedging effect on reservoir performance (vulnerability).
The volume reliability shown in Fig. 8 has confirmed that
The vulnerability (or maximum single-period water shortage) is shown in Fig. 9. Also shown on the plots is the horizontal line for a vulnerability of 25 % which, as remarked previously, represents the suggested tolerable shortage limit for most water users. With no hedging, the vulnerability is high (approximately 60 %) under existing conditions and intensifies to about 65 % when the catchment becomes drier due to projected reduction in precipitation by climate change. The vulnerability is tempered for wetter conditions but even for the most benign of these, i.e. projected 10 % rise in precipitation, the recorded vulnerability was still above 47 %, much higher than the 25 % tolerable vulnerability threshold suggested by Fiering (1982).
The dramatic effect of hedging on the vulnerability can be seen in the evaluations for both the static and the dynamic policies. For example for the static policy, hedging reduced the vulnerability to below the 25 % from the high of 65 %. It should be noted that only 17 % of the demand was hedged back when necessary by the single-stage, constant rationing ratio policy; yet what these results show is that such modest reductions that can be easily tolerated by most water users have almost eliminated the calamitous 65 % water shortage that could occur without hedging on some occasions. As was the case with the other performance indices, the vulnerability was slightly less relative to the single stage, constant rationing policy when the dynamic (monthly) and 2-stage policies were deployed. This reduction in vulnerability does not justify the extra efforts in developing and deploying the more complicated policies.
This study has developed optimised static and dynamic zone-based hedging policies for the Pong reservoir in India and compared its performance with that of a basic, zone-based policy that incorporates no hedging as a way of testing the usefulness of hedging in moderating the vulnerability of climate-change induced water shortages. GA was used to optimise the decision variables for the policies, including the rationing ratios and the target storage values that trigger hedging in each month of the year. The optimisation carried out considered 1-stage and 2-stage hedging policies and rationing ratios that were either static (constant all year round) or dynamic (i.e. varying monthly or seasonally). A delta perturbation approach was used to develop alternative reservoir inflow responses to plausible changes in temperature and precipitation. Subsequent reservoir simulations to test the effectiveness of the various operating policies showed that without hedging, performance of the reservoir (reliability- time- and volume-based and vulnerability) deteriorated significantly when the reservoir inflow is projected to reduce due to climate change; the opposite occurred when the future is wetter.
The vulnerability was particularly high, reaching over 60 %. However, as hedging was introduced, the vulnerability reduced significantly because the modest, deliberate cut-backs during hedging prevented the occurrence of large, single-period water shortages. Indeed, for both the static and dynamic hedging policies, the vulnerability was reduced to below 25 % even for the worst (direst) climate change projections. However, because hedging deliberately fails to meet full demand on occasions, the occurrences of failures increased, which led to significant deterioration in the evaluated time-based reliability. However, since the amount of water shortages for most of these additional shortage periods was low-to-moderate, the overall volumetric reliability of the reservoir was practically unaffected. This is re-assuring since what should matter most in reservoir operation is not the number of failure occasions but the deficit sustained during such failures. All this confirms that water resources systems have inherent buffering capacity that if well-harnessed through improved operating practices such as the hedging policies developed in this work will offer effective and low-cost mitigation for climate change induced water shortages.
In terms of the overall system's performance, the dynamic hedging policies outperformed the constant hedging policy but only marginally. The same marginal improvement was recorded for the 2-stage policy when its performance was juxtaposed with that of the 1-stage policy. Given the complexity associated with the development and deployment of the dynamic and multi-stage policies, the marginal improvement recorded here is not sufficient reason for preferring the dynamic policy for reservoir operation.
The data used in developing the results presented in this paper are openly
available at
The authors declare that they have no conflict of interest.
This article is part of the special issue “Innovative water resources management – understanding and balancing interactions between humankind and nature”. It is a result of the 8th International Water Resour. Manage. Conference of ICWRS, Beijing, China, 13–15 June 2018.
The work reported here was funded by the UK-NERC (Project NE/N016394/1) – “Sustaining Himalaya Water Resources in a Changing Climate (SusHi-Wat)” – as part of the UK-India Newton-Bhabha Sustainable Water Resources (SWR) thematic Programme. Edited by: Wenchao Sun Reviewed by: two anonymous referees