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Development of probabilistic operating rules for Hluhluwe Dam, South Africa
Physics and Chemistry of the Earth xxx (2016) 1e10
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Development of probabilistic operating rules for Hluhluwe Dam, South Africa J. Ndiritu a, *, J. Odiyo b, R. Makungo b, B. Mwaka b, c, N. Mthethwa c, C. Ntuli c, A. Andanje d a
School of Civil and Environmental Engineering, University of the Witwatersrand, South Africa Department of Hydrology and Water Resources, University of Venda, South Africa c Department of Water Affairs and Sanitation, South Africa d Rashima Consultants, South Africa b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 May 2016 Received in revised form 5 October 2016 Accepted 28 October 2016 Available online xxx
Hluhluwe Dam, with a 30 million m3 reservoir that supplies water for irrigation and Hluhluwe municipality in Kwa-Zulu Natal Province, South Africa, was consistently experiencing low storage levels over several non-drought years since 2001. The dam was operated by rules of thumb and there were no records of water releases for irrigation - the main user of the dam. This paper describes an assessment of the historic behaviour of the reservoir since its completion in 1964 and the development of operating rules that accounted for: i) the multiple and different levels of reliability at which municipal and irrigation demands need to be supplied, and ii) inter-annual and inter-decadal variability of climate and inflows into the dam. The assessment of the behaviour of the reservoir was done by simulation assuming trigonometric rule curves that were optimized to maximize both yield and storage state using the SCEUA method. The resulting reservoir behaviour matched the observed historic trajectory reasonably well and indicated that the dam has mainly been operated at a demand of 10 million m3/year until 2000 when the demand suddenly rose to 25 million m3/year. Operating rules were developed from a statistical analysis of the base yields from 500 simulations of the reservoir each using 5 year-long stochastically generated sequences of inflows, rainfall and evaporation. After the implementation of the operating rules in 2009, the storage state of the dam improved and matched those of other reservoirs in the region that had established operating rules. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Historic reservoir performance Multiple reliabilities of supply Probabilistic reservoir operating rules Trigonometric operating rule curves
1. Introduction Hluhluwe dam is one of the major dams in the Northern KwaZulu Natal drainage region of South Africa. The dam started operating in 1966 with a net storage capacity of 29.66 Mm3 which had reduced to 25.9 Mm3 in 1999 as revealed by a basin survey by the South African Department of Water Affairs (DWAF). The dam supplies water for an annual irrigation demand of 11.8 Mm3/year and municipal demand to Hluhluwe town which had been steadily increasing since 1999 to 1 Mm3/year in 2007. Since 2002, the Hluhluwe dam storage levels were often considerably lower than those of the other dams in the drainage region as seen in Fig. 1. Controlled releases from Hluhluwe dam were based on the operator's judgement and experience and not on comprehensive quantitatively-derived operating rules. This was considered as a
* Corresponding author. E-mail address: [email protected] (J. Ndiritu).
major reason for the observed low storage states and DWAF thus instituted a study to develop comprehensive operating rules for the dam. A field visit to the site did not avail records of the actual releases for irrigation from the dam. There are many methods of developing and optimizing reservoir operating rules and these were comprehensively reviewed by Yeh (1985) and later by Labadie (2004). Most of these are based on linear and dynamic programming although evolutionary techniques have been applied to reservoir operation more recently (Chaves and Kojiri, 2007; Chiu et al., 2007; Janga and Nagesh, 2007). In South Africa, an approach that combines simulation with network flow programming and a detailed evaluation of supply reliabilities to multiple users (McKenzie and Allen, 1990; Basson et al., 1994) has been applied since the late 1980s. This approach helped make important operational decisions during a drought period in the early 1990s in South Africa (Basson and Van Rooyen, 2001) and is currently still widely applied. It was therefore decided that the development of the reservoir operating rules for Hluhluwe follow this basic approach whilst allowing for realistic
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Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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Fig. 1. Storage trajectories of the 3 major dams in Northern Kwa Zulu Natal from 2000 to 2008.
innovations. An appropriate innovation was to use an optimizer that allows for optimization of non-linear functions in place of the network flow programming that requires objective functions to be linear. The Shuffled Complex Evolution (SCE-UA) method (Duan et al., 1992), a population-based method that combines deterministic and probabilistic search approaches was selected for optimization. The SCE-UA method is widely applied in catchment model calibration but has only found few applications in reservoir operation (Cui and Kuczera, 2003; Ngo et al., 2007). Kuczera (1997) and Franchini et al. (1998) found the SCE-UA to perform better than the Genetic Algorithm (GA) though the GA has been applied much more widely for reservoir operation (Wardlaw and Sharif, 1999; Chen, 2003; Ndiritu, 2003; Akter and Simonovic, 2004; Nagesh et al., 2006; Chen and Chang, 2007; Cheng et al., 2008). Ndiritu (2005) found the GA to take long computation times to optimize the operation of a system of 2 reservoirs and later found the SCE-UA (Ndiritu and Sinha, 2009) to obtain better defined operation rules in considerably lower computation times for the same problem. For this problem, operating rule curves were modelled using simple trigonometric functions to improve parsimony. Prior to developing the operating rules, an assessment of the yield potential and an analysis of the historic behaviour of Hluhluwe dam were done. These are described in Sections 3 and 4 respectively after a description of the study area and acquisition of data in Section 2. Section 5 informs how the stochastic operating rules were developed. The operating rules have been in use since 2009 and an assessment of the impact of applying the rules on Hluhluwe dam performance is presented in Section 6. Discussion and conclusions finalise the paper. 2. Location and data acquisition Hluhluwe dam (Fig. 2) is located in the Usutu to Mhlatuze water management area of South Africa and has a drainage basin of 734 km2 consisting of quaternary catchments W32D and W32E. Time series data of the daily and monthly storage levels of Hluhluwe dam (station W3R001), the monthly releases from the dam at gauging station W3H022, the monthly rainfall and Symon's pan evaporation from a nearby meteorological station (W3E003) located 8 km from the dam were available for the 40-year long period from 1966 to 2005. Station W3E003 was the closest station to the reservoir and was in the same rainfall and evaporation zone as delineated in the WR2005 study (Middleton and Bailey, 2009). The only river gauging station within the basin was W3H021 on
Hluhluwe River with a catchment area of 507 km2. This station had 10 years of stage measurements but no rating curve to determine the flow rates. Downstream of the dam, the next gauging is W3H015 with a catchment area of 925 km2. The monthly supplies to Hluhluwe municipality from the dam from 1983 to 2005 were also available and the DWAF provided the annual target supply to irrigation and its monthly distribution. There was however no data on the historic supplies to irrigation although gauging station W3H022 included the water released to irrigation in addition to the uncontrolled spillway flows. The height-surface areaevolume relationship of the dam was also available as well as net storage of the dam from three basin surveys of the dam conducted in October 1977, February 1987 and October 1999. The inflow time series into the reservoir is essential for reservoir yield and operation analysis and was obtained from a monthly water balance of Hluhluwe dam assuming that the rainfall and pan evaporation data from W3E003 were representative of the respective monthly rainfall and evaporation of the reservoir. Alvarez et al. (2007) obtained coefficients ranging from 0.72 to 0.86 in an experimental study in Spain and an uncertainty study of evaporation (Lowe et al., 2009) obtained pan coefficients averaging about 0.8 for 6 reservoirs in Australia. No experimental study of pan evaporation in South Africa was found and it was decided to adopt a pan factor of 0.85 as applied by Ndiritu (2005) for a reservoir operation study in South Africa. 3. Assessment of the historic yield potential of the dam The potential yield of a reservoir can be assessed using two approaches (McMahon and Adeyole, 2005; Ndiritu, 2003, 2005); i) assuming that the reservoir can supply a set maximum yield constantly throughout the analysis period (firm yield) and ii) considering the reservoir to supply various levels of set demands (target drafts) that can only be met for certain proportions of time and not for the entire period of analysis. The assessment of the historic yield potential therefore involved the determination of historic firm yield and the determination of the levels of supply that can be achieved for a range of target drafts. The net storages from the 3 basin surveys of the dam conducted by the DWAF in October 1977, February 1987 and October 1999 were 29.66, 28.77 and 25.89 Mm3, respectively, indicating a low but increasing reduction in net storage capacity. It was considered realistic to assume that catchment sedimentation rate during the time that the developed rules will be used will follow the trend observed historically by the basin surveys. Any closely-fitting model can therefore be used to extrapolate the reservoir capacity. The capacity reduction rate fitted
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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Fig. 2. Location of Hluhluwe dam.
well into a second-order polynomial and this fit was extrapolated to estimate the net storage in 2007 (Fig. 3). The estimated net storage of 23.10 Mm3 was then assumed in the assessment of the historic yield potential of the dam. 3.1. Historic yield analysis The aim here was to determine the historic firm yield defined as the maximum unrestricted annual supply that can be obtained from the reservoir assuming no restrictions to supply. This was done using a simulation-optimization set up where yield was
maximized using the SCE-UA method with any individual solution (out of the population of solutions of the SCE-UA search) that violated the set minimum storage state being heavily penalized and therefore rendered unfit. The SCE-UA optimization parameters recommended by Duan et al. (1994) were used here and in the subsequent optimizations. Typical firm yield determination allows unrestricted supply to emptiness (dead storage) (McMahon and Adeyole, 2005) but this is unrealistic in practice. Firm yield was therefore obtained for minimum storage states of 0, 20 and 40%. Considering the possibility that the water users could alter their monthly demands if this would increase the overall yield, a scenario in which the distribution of monthly water demand was itself optimized was analysed in while the other scenario used the monthly distribution provided by DWAF. Table 1 presents a summary of the results obtained from the firm yield analysis. The increases in historic yield as a result of optimizing demand distribution are not considered insignificant but the demand distributions for these scenarios had unrealistic high variability. The firm yield was found to be 10.80 Mm3/year by the usual definition of firm yield in which the reservoir is allowed to reach dead storage just once. If higher minimum storages are specified, the firm yield reduces reduced considerably as shown on Table 1. 3.2. Assessment of levels of supply for specified target drafts
Fig. 3. Reduction of Hluhluwe Dam net storage capacity with time.
This analysis was considered more realistic than the historic firm yield analysis (Section 3.1) and determined the maximum proportion of time that specified target drafts could be met and the respective proportion of the water demanded that was actually supplied (volumetric reliability) while ensuring that the storage levels do not fall to unacceptable levels by applying restrictions to demand. After some trial runs, reduction of supply to 80%, 50% and 30% of the demand depending on the storage state of the reservoir and the month of the year were found to provide trajectories that
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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Table 1 Firm yields for various minimum storage states. Monthly demand distribution scenario
Minimum storage state (%)
Yield (Mm3/year)
Yield/MAR
Average % FSL
Actual demand (from DWAF)
0 20 40 0 20 40
10.8 8.1 5.4 11.5 8.8 6.2
0.2157 0.161 0.1073 0.2296 0.1749 0.1243
81 89 93 78 87 92
Optimized
FSL: Full supply level; MAR: Mean Annual Runoff; FSL: Full supply level.
match the historic one closely and were adopted. The rule curves were modelled as simple trigonometric functions as described by Ndiritu and Sinha (2009) and an objective function that seeks to maximize yield and storage state and defined by equation (1) (in Section 4) was applied. The ratios of the volume supplied to that demanded and the proportion of times that the demands would be met are shown on Fig. 4. For the annual demand of 12.8 Mm3/year in 2007, Fig. 4 shows that it was possible to supply 90% of the demand with unrestricted supply occurring 75% of the time. In Fig. 5, the proportions of time that restrictions of varying severity would be met for specific target drafts are shown. It is seen that a target draft of 12.5 Mm3/year obtains a considerably lower proportion of restrictions than a draft of 15 Mm3/year but the proportion for 50% restriction for 15 Mm3/year is slightly lower than for 12.5 Mm3/ year. Fig. 6 presents the optimized operation rule curves obtained for two target drafts.
80
proportion of time res tric tion is made (% )
a
a
Target draft (Mm3/year) 7.5
70
10 12.5
60
15 50
17.5 20
40
25
30 20 10 0 0
10
20
30
There were no records of the actual releases made to irrigation since the reservoir started operating in 1966 and there were also no records of how water allocation decisions had been made. It was however expected that the operator/s of the dam made releases depending on the variation of demand within the year and the volume of storage in the reservoir with the aim to i) meet the demand whenever possible and ii) to ensure that the storage volume
1.00
ratio
0.70
0.60
0.50 volume supplied / volume demanded
0.40
time that supply is unrestricted / total period of analysis
0.30 5
10
15
20
Target Draft (Mm3/year) Fig. 4. Volumetric reliability and proportion of time that demand is met.
25
60
70
80
in the reservoir was maintained at a reasonably high level whenever possible. An operating rule that aimed to maximize these 2 objectives was therefore adopted as a surrogate of the historic operation. Equation (1) defines the function based on these two objectives that was optimized by the SCE-UA method. The trigonometric rule curves (Ndiritu and Sinha, 2009) were also applied here.
Maximize wd
0.80
50
Fig. 5. Proportions of restrictions of varying severity.
"
0.90
40
Percent restriction
4. Analysis of the historic storage behaviour of Hluhluwe dam
PN P12 i¼1
j
N TD
ai;j
!
PN P12 þ ws
i¼1
j¼1 si;j
12 N Ci;j
!# (1)
where wd and ws are weights to indicate the relative value assigned to maximizing yield and storage state, respectively, N is the number of years of analysis, ai,j is the actual supply from the reservoir in month j of year i, TD is the annual target draft (assumed constant for each simulation-optimization run), si,j is the simulated storage level in month j or year i and Ci,j is the net storage capacity of the reservoir in month j of year i. The reservoir was then simulated at a monthly time step for the 40-year period for which the historic reservoir storage trajectory was available. The simulation assumed a reducing net storage capacity (Ci,j) due to sedimentation using the relationship shown in Fig. 3 and equal weights wd and ws of 0.5 were found to obtain realistic simulations. The simulation was carried out for various target drafts (annual water demands) assuming the monthly demand distribution provided by the DWAF. The resulting simulated storage trajectories were compared with the recorded historic one in order to inform the likely target drafts that the dam has been supplying over the 40 year period of operation. Fig. 7 compares the
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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Fig. 6. Historic operating rule curves for two annual target drafts.
historic trajectories with trajectories for target drafts of 10 and 25 Mm3/year as these were found to closely match the historic trajectory for various periods. The historic trajectory (Fig. 7) revealed that the reservoir operation was not prioritizing water storage in the first 5 years (1967e71) as large releases (greater than 25 Mm3/year) were made over this period while storage state averaged less than 20%. Large storage drawdowns in the early years of 1980s, 1990s and 2000s which are likely to be the result of the droughts that occurred in Southern Africa over those periods (Masih et al., 2014; Vogel et al., 2010; Rouault and Richard, 2005) are also evident in Fig. 7. The simulated storage trajectories generally matched the changes in historic trajectory but varied in the amplitude of changes. More specifically, the following was inferred from Fig. 7 for various periods: Jan 1967 - Dec 1971: Storing water in the reservoir was not prioritized as the annual release exceeded 25 Mm3/year over this period while storage state remained very low.
Jan 1972 - Dec 1978: The target draft was about 10 Mm3/year. It is expected that most of the demand was met. Jan 1979 e Dec 1983: Two dry periods occurred corresponding to a target draft of about 25 Mm3/year. It is expected that restrictions were implemented and the actual supply was considerably less than 25 Mm3/year as Figs. 4 and 5 indicate. Jan 1984 e Dec 2000: The target draft was about 10 Mm3/year except for the dry periods in 1986e87 and 1992e93 where a draft higher than 10 Mm3/year but lower than 25 Mm3/year occurred. Most of the demand was most likely met except for the two dry periods. Jan 2001 e Dec 2005: The historic trajectory was below that for 25 Mm3/year for most of the period suggesting a demand exceeding 25 Mm3/year. This high target draft was most likely not met and the actual supply was likely considerably less as Figs. 4 and 5 suggest. Jan 2006 e June 2006: The historic trajectory dropped steadily while the simulated ones for both target drafts of 10 and
Fig. 7. Historic and simulated trajectories for target drafts of 10 and 25 Mm3/year.
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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25 Mm3/year rose steadily. This implies massive water releases from the dam were being made.
January. 5.1. Stochastic streamflow generation
5. Development of operating rules As stated in Section 1, the development of the operating rules followed the basic method that has been used in South Africa since the late 1980s (McKenzie and Allen, 1990; Basson et al., 1994). Following are the main features of this method. The operating rule is used to decide how much water is available to allocate the various demands for a period of one year starting from a decision date which is often the end of the rainy season. The rule also allows for additional decisions to be made within the year if the observed changes in storage warrant this. The ability of the reservoir to meet the annual demands is assessed via simulation of the reservoir over a short period of time (typically 5 years) assuming a range of possible storage states at the start (the decision date). Since the inflows into the reservoir over the operating period (in the future) are not known and climate is known to exhibit large inter-annual and inter-decadal variability, an appropriate probabilistic approach is applied in order to obtain operating rules that adequately specify the reliabilities associated with water allocation decisions. This is done by carrying out reservoir simulation using a large number of artificial (stochastically generated) sequences of plausible inflows whose central statistical attributes are similar to those of the historic inflows. Since reservoir water balance also includes rainfall gains and evaporation losses, stochastic sequences of rainfall and evaporation that are statistically similar to the historic ones whilst maintaining historic inter-dependence with the inflows are also generated and applied. The reliabilities at which supply to the various demands need to be supplied usually varies and set proportions of each demand are usually assigned specified levels of reliability. The water allocation decisions prioritize supply based on the specified reliabilities of the multiple demands. For Hluhluwe dam, the irrigation demand was taken as constant 11.8 Mm3/year with a specified monthly variation. The municipal demand was observed to be increasing steadily at a linear rate and it was decided to develop operating rules using the municipal supply expected in 21/2 years from mid-2007 considering that DWAF routinely updates reservoir operating rules after about 5 years. The projected municipal demand at this time (end of year 2010) was estimated as 1.57 Mm3/year. For water supply in South Africa, DWAF specifies the reliabilities at which set proportions of irrigation and municipal supply need to be supplied. For Hluhluwe dam, the proportions and actual annual demands are presented in Table 2. Hluhluwe dam is located in the summer rainfall region of South Africa and April (the usual end of the rainy season) was therefore set as the main water allocation decision date. Other decision dates were set at 3 month intervals as July, October and
Table 2 Reliability levels required for set proportions of irrigation and municipal demand. Percentage of demand supplied at reliability (target allocation Mm3) Reliability (RI)a Municipal Irrigation a
90% (1:10) 10 (0.157) 70 (8.26)
98% (1:50) 20 (0.314) 20 (2.36)
RI ¼ Expected recurrence interval of shortage.
99% (1:100) 70 (1.099) 10 (1.18)
The Auto Regressive Moving Average (ARMA) multisite monthly stochastic generator used widely in South Africa (DWAF, 1986; Pegram and McKenzie, 1991; Basson et al., 1994) and currently packaged as STOMSA (Van Rooyen and McKenzie, 2004) was used to generate 100 stochastically generated streamflow sequences, each 1000 years long using the 40 year long historic inflow time series obtained via mass balance (Section 1). STOMSA includes several tests to assess how well the statistics of the generated sequences match the historic ones and 4 of the graphical comparisons are presented in Fig. 8. The historic statistics are all within the range of the stochastic values and more than half lie within the interquartile ranges of the box plots and this was observed for most of the other statistics. The generated sequences were therefore considered to be adequately plausible during the operation period of the dam. STOMSA generates only 100 stochastic sequences and this was considered low for a precise computation of reliabilities. For each decision month five hundred (500) 5 year-long stochastic sequences were obtained from the 100 one thousand year-long sequences with a gap of at least 10 years in between so that they were independent. 5.2. Development of operating rule curves The minimum annual yield (base yield) for each 5 year sequence was obtained by monthly simulation of the reservoir for eight starting storage states (%FSL ¼ 100, 80, 60, 50, 40, 30, 20 and 10) and annual target drafts (demands) ranging from 0 to 10 Mm3/year for 10 and 20%FSL and 0e20 Mm3/year for the other starting storage states. For all the starting storage states except the lowest (% FSL ¼ 10), the minimum %FSL in any of the 60 months (5 years) of analysis was set to 10%. For a starting storage of 10%FSL the constraint on minimum storage was set to 5%. The monthly distribution of the actual water demands from the dam (obtained from DWAF) was used to obtain the monthly target drafts. The rainfall gains into and evaporation losses from the reservoir to use in the simulation were obtained in two steps: i) finding the historic annual streamflow closest in magnitude to the annual stochastic rainfall and ii) selecting the historic rainfalls and evaporation rates that fell in the same year as this streamflow for the simulation during that year. The 500 base yields obtained at each starting storage state and target draft were then ranked and the probability that any specified base yield is not exceeded in the 5 year period computed using the Weibull plotting position formula (Equation (2)).
pn;5 ¼
m nþ1
(2)
where m is the rank of the base yield with the lowest out of all the base yields ranked as 1, n is the number of base yields (¼500) and pn;5 is the probability that the base yield has not been exceeded in 5 years. The probability of the base yield being exceeded in any year and the corresponding return period were then computed as follows. If the probability of a given base yield being exceeded in any year is pe;1 then the probability of this base yield not being exceeded in any year is 1 pe;1 : Assuming these non-exceedance probabilities to be independent, then their product for a period of 5 years equals the probability that the base yield is not exceeded over the continuous 5 year period (Equation (3)).
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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Fig. 8. Representative statistical tests of generated streamflow sequences.
1 pe;1
5
¼ pn;5
(3)
The yearly recurrence interval (ri Þ of exceedance of the base yield is therefore obtained as
ri ¼
1 ¼ pe;1
1
1 pn;5
ð1=5Þ
(4)
Fig. 9 shows the relationship between base yield and recurrence
Fig. 9. Base yield e recurrence interval e initial storage state relationships.
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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interval obtained for the April decision month (meaning the simulations started in April) for initial storage states of 20 and 80%. Each curve represents the base yields obtained for a set target draft and the straight portions indicate that for some of the simulations, the base yields equalled the target drafts. For those cases, the reservoir was able to meet the target draft without any shortfall over the 5 year period and the recurrence interval of not meeting a given target draft can therefore be obtained from these base yieldrecurrence interval relationships. For example for the initial storage of 80% in Fig. 9, the recurrence interval of not meeting a target draft of 10 and 18 Mm3/year is 60 and 8 years, respectively. Relationships between recurrence interval and target draft for different initial storage states (e.g. Fig. 10) were then obtained from the base yield e recurrence interval e initial storage state relationships. These were then used to obtain curves that inform the maximum annual demand that can be supplied when the reservoir is at a set storage state in the decision month for the recurrence intervals of interest which are 1 in 100, 1 in 50 and 1 in 10 years as specified in Table 2. Since a higher assurance demand needs to be prioritized over a lower assurance demand, the supplies were obtained in a cumulatively progressive manner (1 in 100, 1 in 100 þ 1 in 50 and 1 in 100 þ 1 in 50 þ 1 in 10). For the April decision month, these curves together with the corresponding total annual demands are shown in Fig. 11. It is found that the 1 in 100, 1 in 50 and 1 in 10 demands could be met for initial storage states equal to or higher than 15%, 27% and 45%, respectively. At lower storage states, the demands could not be met and the available water was apportioned in direct proportion to the demands (Table 2) for each recurrence interval. This lead to the rule curves for allocations to the municipality and irrigation as shown on Fig. 12 for the decision month of April. Similar analyses were carried out for the other 3 decision months (July, October and January) and rule curves similar to Fig. 12 were obtained. It was thus possible to review the April allocation decisions at these other months if the change in storage state called for this. This could be due to an unexpectedly large reduction in storage or a replenishment of the reservoir when restrictions are in place.
Fig. 11. Storage state e Draft curves for specified recurrence intervals.
6. Has implementing the operating rules improved Hluhluwe dam performance? The operating rules have been used to guide the water allocation decisions since April 2009 and are into the 7th year of use. New operating rules for Hluhluwe dam are currently being developed as a longer hydrological dataset is available and the Hluhluwe municipal demand has increased substantially (from 1.57 in 2010 to 2.9 Mm3/year in 2015). The net storage capacity of the dam is also expected to have reduced due to sedimentation in accordance with the trend presented in Fig. 3. Fig. 13 shows the trajectory of the 3 major dams in Northern Kwa Zulu Natal since 2009 when the operating rules for Hluhluwe came into use. Significant restrictions to supply happened in 2009 and less severe restrictions needed to be implemented in 2010. No restrictions were implemented from 2010 to 2014 and the dam experienced storage states that were as high as those of the other dams in the region. Southern Africa has been experiencing drought since mid-2014 and this is evident in the observed drop in storage in the last two years. Restrictions to irrigation and municipal supply were implemented to Hluhluwe water supply in April 2015 but the storage level has still been reducing as for the other two reservoirs. The current state of Hluhluwe is unlike the earlier period in the last decade (Fig. 1) when it exhibited considerably lower storage states than the other dams in the region. This indicates that the operating rules helped to improve the annual water allocation decisions of the dam. 7. Discussion and conclusions
Fig. 10. Recurrence interval-target draft Curves.
This study aimed to assess the historic yield potential of Hluhluwe dam, analyse its historic performance and finally to develop comprehensive operating rules for the dam. The historic firm yield of the dam was found to be 10.8 Mm3/year. A more detailed analysis of the historic yield potential found that 90% of the annual demand (in year 2007) of 12.8 Mm3/year could be supplied and that restrictions would not be needed 75% of time. For the projected demand of 13.37 Mm3/year in 2010, the respective proportions were 88% and 68%, respectively, while for the year 2015 demand of
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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Fig. 12. Rule curves for municipal and irrigation supply for April decision month.
Fig. 13. Storage trajectories of the 3 major dams since implementing operating rules for Hluhluwe dam.
14.7 Mm3/year, the proportions reduced to 84% of supply with unrestricted supply 54% of the time. The assessment of the historic yield potential reveals that Hluhluwe dam could not adequately meet the irrigation demand of 11.8 Mm3/year without restrictions. As municipal demand increases into the future, more frequent restrictions are to be expected unless Hluhluwe dam supply is augmented by an alternative water source. Improved water demand management could also help reduce the severity and frequency of restrictions. Although there were no quantitative records of the historic operation of the dam, simulated storage trajectories that matched the historic trajectory reasonably well were obtained (Fig. 6). This was achieved by formulating realistic operating rules and optimizing them using an objective function based on the expected aims of water supply dam operation; maximizing supply and maintaining a high storage state. The analysis revealed that historically, the dam was operated at an annual demand of about 10 Mm3/year during most non-drought years till year 2000. During the drought years, the demands were found to be about 25 Mm3/ year although these were unlikely to be met as substantial restrictions were most likely implemented as Figs. 4 and 5 reveal. The analysis of the historic performance of the dam also revealed massive water releases in the first 5 months of year 2006 that were considered highly imprudent since the reservoir was at a low storage state of 40% in January 2006. Comprehensive but easy-to-use operating rules were developed via statistical analysis of the minimum annual (base) yields obtained from 500 5-year long simulations of the system using a range of possible starting storages at the beginning of the
simulation. The 500 5 year-long stochastic monthly inflows stochastics were obtained from 100 one thousand years long stochastic sequences generated using STOMSA, an ARMA model that is widely used in South Africa. The use of stochastic streamflows helped to incorporate the expected inter-annual and inter-decadal variability of climate in developing the rules. The rule curves inform what annual allocations of water supply need to be made to the municipality and to irrigation as a function of the storage state of the reservoir at the decision date. Fig. 12 shows the rule curves for the main decision month of April and similar curves were developed for July, October and January enabling water allocation decisions based on the analysis to be made every 3 months if required. The rule curves for the 4 months took similar forms (shapes) and can be interpolated to make acceptable operational decisions at any time of the year. The operating rules have been in use since April 2009 and Hluhluwe dam storage variation has since matched those of the other large dams in the region more closely. The operating rules have therefore improved the operation of the dam. References Akter, T., Simonovic, S., 2004. Modelling uncertainties in short-term reservoir operation using fuzzy sets and a genetic algorithm. Hydrol. Sci. J. 49 (6), 1081e1098. Alvarez, V.M., Gonzalez-Real, M.M., Baille, A., Martınez, J.M.M., 2007. A novel approach for estimating the pan coefficient of irrigation water reservoirs Application to South Eastern Spain. Agric. Water Man. 92, 29e40. Basson, M.S., Allen, R.B., Pegram, G.G.S., Van Rooyen, J.A., 1994. Probabilistic Management of Water Resource and Hydropower Systems. Water Resources Publications, p. 424. Basson, M.S., Van Rooyen, J.A., 2001. Practical application of probabilistic
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approaches to the management of water resource systems. J. Hydrol. 241, 53e61. Chaves, P., Kojiri, T., 2007. Stochastic fuzzy neural network: case study of optimal reservoir operation. J. Water Resour. Plann. Man. 133 (6), 509e518. Chen, L., 2003. Real coded genetic algorithm optimization of long term reservoir operation. J. Am. Water Resour. Assoc. 39 (5), 1157e1165. Chen, L., Chang, F., 2007. Applying a real-coded multi-population genetic algorithm to multi-reservoir operation. Hydrol. Process. 21 (5), 688e698. Cheng, C., Wang, W., Xu, D., Chau, K., 2008. Optimizing hydropower reservoir operation using hybrid genetic algorithm and chaos. Water Resour. Man. 22 (7), 895e909. Chiu, Y., Chang, L., Chang, F., 2007. Using a hybrid genetic algorithm-simulated annealing algorithm for fuzzy programming of reservoir operation. Hydrol. Process. 21 (23), 3162e3172. Cui, L., Kuczera, G., 2003. Optimizing urban water supply headworks using probabilistic search methods. J. Water Resour. Plann. Man. 129 (5), 380e387. Duan, Q.Y., Sorooshian, S., Gupta, V., 1992. Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour. Res. 28 (4), 1015e1031. Duan, Q.Y., Sorooshian, S., Gupta, V., 1994. Optimal use of the SCE-UA global optimization method for calibrating watershed models. J. Hydrol. 158, 265e284. DWAF., 1986. Stochastic Modelling of Streamflow. Report No. PC000/00/5186 by BKS (Pty) Ltd for the Department of Water Affairs and Forestry as Part of the Vaal River System Analysis Study. South Africa, Pretoria. Franchini, M., Galeati, G., Berra, S., 1998. Global optimization techniques for the calibration of conceptual rainfall-runoff models. Hydrol. Sci. J. 43 (3), 443e458. Janga, R.M., Nagesh, K.D., 2007. Multi-objective particle swarm optimization for generating optimal trade-offs in reservoir operation. Hydrol. Process. 21 (21), 2897e2909. Kuczera, G., 1997. Efficient subspace probabilistic parameter optimization for catchment models. Water Resour. Res. 33 (1), 177e185. http://dx.doi.org/ 10.1029/96WR02671. Labadie, J., 2004. Optimal operation of multireservoir systems: state-of-the-art review. J. Water Resour. Plann. Manag. ASCE 130 (2), 93e111. Lowe, L.D., Webb, J.A., Nathan, R.J., Etchells, T., Malano, H.M., 2009. Evaporation from water supply reservoirs: an assessment of uncertainty. J. Hydrol. 376, 261e274.
, F.E.F., Trambauer, P., 2014. A review of droughts on the Masih, I., Maskey, S., Mussa African continent: a geospatial and long-term perspective. Hydrol. Earth Syst. Sci. 18, 3635e3649. http://dx.doi.org/10.5194/hess-18-3635-2014. McKenzie, R., Allen, R.B., 1990. Modern water resource assessment techniques for the Vaal System. Proc. Instn Civ. Engrs, Part 1 (88), 995e1014. McMahon, T.A., Adeloye, A.J., 2005. Water Resources Yield. Water Resources Publications, LLC, Colorado, USA. Middleton, B.J., Bailey, A.K., 2009. Water Resources of South Africa, 2005 Study (WR2005), WRC Report No. TT 382/08. Nagesh, K., Raju, K., Srinivasa, A., 2006. Optimal reservoir operation for irrigation of multiple crops using genetic algorithms. J. Irrig. Drain. Eng. (ASCE) 132 (2), 123e129. Ndiritu, J.G., 2003. Reservoir system optimisation using a penalty approach and a multi-population genetic algorithm. Water SA 29 (3), 273e280. Ndiritu, J.G., 2005. Maximising water supply system yield subject to multiple reliability constraints via simulation-optimisation. Water SA. 31 (4), 423e434. Ndiritu, J.G., Sinha, P., 2009. A parsimonious trigonometric model of reservoir operating rules. In: Proc., Int. Conf. Water, Environment, Energy, and Society (WEES), New Delhi, India, II, pp. 1025e1033. Ngo, L., Madsen, H., Rosbjerg, D., 2007. Simulation and optimisation modelling approach for operation of the Hoa Binh reservoir. Vietnam J. Hydrol. 336 (3e4), 269e281. Pegram, G.G.S., McKenzie, R.S., 1991. Synthetic Streamflow Generation in the Vaal River System Study. The Civil Engineer in South Africa, pp. 15e24. Rouault, M., Richard, Y., 2005. Intensity and spatial extent of droughts in southern Africa. Geophys. Res. Lett. 32, L15702. http://dx.doi.org/10.1029/2005GL022436. Van Rooyen, P., McKenzie, R., 2004. Monthly Multi-site Stochastic Streamflow Model, STOMSA User Guide, South African Water Research Commission Report No. 909/1/04. Vogel, C., Koch, I., Zyl, K.V., 2010. “A persistent truth” e reflections on drought risk management in Southern Africa, Weather. Clim. Soc. 2, 9e22. http://dx.doi.org/ 10.1175/2009 WCAS1017.1. Wardlaw, R., Sharif, M., 1999. Evaluation of genetic algorithms for optimal reservoir system operation. J. Water Resour. Plann. Man. 125 (1), 25e33. Yeh, W.W.G., 1985. Reservoir management and operation models: a state-of-the-art review. Water Resour. Res. 21 (12), 1797e1818.
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Development of probabilistic operating rules for Hluhluwe Dam, South Africa J. Ndiritu a, *, J. Odiyo b, R. Makungo b, B. Mwaka b, c, N. Mthethwa c, C. Ntuli c, A. Andanje d a
School of Civil and Environmental Engineering, University of the Witwatersrand, South Africa Department of Hydrology and Water Resources, University of Venda, South Africa c Department of Water Affairs and Sanitation, South Africa d Rashima Consultants, South Africa b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 May 2016 Received in revised form 5 October 2016 Accepted 28 October 2016 Available online xxx
Hluhluwe Dam, with a 30 million m3 reservoir that supplies water for irrigation and Hluhluwe municipality in Kwa-Zulu Natal Province, South Africa, was consistently experiencing low storage levels over several non-drought years since 2001. The dam was operated by rules of thumb and there were no records of water releases for irrigation - the main user of the dam. This paper describes an assessment of the historic behaviour of the reservoir since its completion in 1964 and the development of operating rules that accounted for: i) the multiple and different levels of reliability at which municipal and irrigation demands need to be supplied, and ii) inter-annual and inter-decadal variability of climate and inflows into the dam. The assessment of the behaviour of the reservoir was done by simulation assuming trigonometric rule curves that were optimized to maximize both yield and storage state using the SCEUA method. The resulting reservoir behaviour matched the observed historic trajectory reasonably well and indicated that the dam has mainly been operated at a demand of 10 million m3/year until 2000 when the demand suddenly rose to 25 million m3/year. Operating rules were developed from a statistical analysis of the base yields from 500 simulations of the reservoir each using 5 year-long stochastically generated sequences of inflows, rainfall and evaporation. After the implementation of the operating rules in 2009, the storage state of the dam improved and matched those of other reservoirs in the region that had established operating rules. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Historic reservoir performance Multiple reliabilities of supply Probabilistic reservoir operating rules Trigonometric operating rule curves
1. Introduction Hluhluwe dam is one of the major dams in the Northern KwaZulu Natal drainage region of South Africa. The dam started operating in 1966 with a net storage capacity of 29.66 Mm3 which had reduced to 25.9 Mm3 in 1999 as revealed by a basin survey by the South African Department of Water Affairs (DWAF). The dam supplies water for an annual irrigation demand of 11.8 Mm3/year and municipal demand to Hluhluwe town which had been steadily increasing since 1999 to 1 Mm3/year in 2007. Since 2002, the Hluhluwe dam storage levels were often considerably lower than those of the other dams in the drainage region as seen in Fig. 1. Controlled releases from Hluhluwe dam were based on the operator's judgement and experience and not on comprehensive quantitatively-derived operating rules. This was considered as a
* Corresponding author. E-mail address: [email protected] (J. Ndiritu).
major reason for the observed low storage states and DWAF thus instituted a study to develop comprehensive operating rules for the dam. A field visit to the site did not avail records of the actual releases for irrigation from the dam. There are many methods of developing and optimizing reservoir operating rules and these were comprehensively reviewed by Yeh (1985) and later by Labadie (2004). Most of these are based on linear and dynamic programming although evolutionary techniques have been applied to reservoir operation more recently (Chaves and Kojiri, 2007; Chiu et al., 2007; Janga and Nagesh, 2007). In South Africa, an approach that combines simulation with network flow programming and a detailed evaluation of supply reliabilities to multiple users (McKenzie and Allen, 1990; Basson et al., 1994) has been applied since the late 1980s. This approach helped make important operational decisions during a drought period in the early 1990s in South Africa (Basson and Van Rooyen, 2001) and is currently still widely applied. It was therefore decided that the development of the reservoir operating rules for Hluhluwe follow this basic approach whilst allowing for realistic
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Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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Fig. 1. Storage trajectories of the 3 major dams in Northern Kwa Zulu Natal from 2000 to 2008.
innovations. An appropriate innovation was to use an optimizer that allows for optimization of non-linear functions in place of the network flow programming that requires objective functions to be linear. The Shuffled Complex Evolution (SCE-UA) method (Duan et al., 1992), a population-based method that combines deterministic and probabilistic search approaches was selected for optimization. The SCE-UA method is widely applied in catchment model calibration but has only found few applications in reservoir operation (Cui and Kuczera, 2003; Ngo et al., 2007). Kuczera (1997) and Franchini et al. (1998) found the SCE-UA to perform better than the Genetic Algorithm (GA) though the GA has been applied much more widely for reservoir operation (Wardlaw and Sharif, 1999; Chen, 2003; Ndiritu, 2003; Akter and Simonovic, 2004; Nagesh et al., 2006; Chen and Chang, 2007; Cheng et al., 2008). Ndiritu (2005) found the GA to take long computation times to optimize the operation of a system of 2 reservoirs and later found the SCE-UA (Ndiritu and Sinha, 2009) to obtain better defined operation rules in considerably lower computation times for the same problem. For this problem, operating rule curves were modelled using simple trigonometric functions to improve parsimony. Prior to developing the operating rules, an assessment of the yield potential and an analysis of the historic behaviour of Hluhluwe dam were done. These are described in Sections 3 and 4 respectively after a description of the study area and acquisition of data in Section 2. Section 5 informs how the stochastic operating rules were developed. The operating rules have been in use since 2009 and an assessment of the impact of applying the rules on Hluhluwe dam performance is presented in Section 6. Discussion and conclusions finalise the paper. 2. Location and data acquisition Hluhluwe dam (Fig. 2) is located in the Usutu to Mhlatuze water management area of South Africa and has a drainage basin of 734 km2 consisting of quaternary catchments W32D and W32E. Time series data of the daily and monthly storage levels of Hluhluwe dam (station W3R001), the monthly releases from the dam at gauging station W3H022, the monthly rainfall and Symon's pan evaporation from a nearby meteorological station (W3E003) located 8 km from the dam were available for the 40-year long period from 1966 to 2005. Station W3E003 was the closest station to the reservoir and was in the same rainfall and evaporation zone as delineated in the WR2005 study (Middleton and Bailey, 2009). The only river gauging station within the basin was W3H021 on
Hluhluwe River with a catchment area of 507 km2. This station had 10 years of stage measurements but no rating curve to determine the flow rates. Downstream of the dam, the next gauging is W3H015 with a catchment area of 925 km2. The monthly supplies to Hluhluwe municipality from the dam from 1983 to 2005 were also available and the DWAF provided the annual target supply to irrigation and its monthly distribution. There was however no data on the historic supplies to irrigation although gauging station W3H022 included the water released to irrigation in addition to the uncontrolled spillway flows. The height-surface areaevolume relationship of the dam was also available as well as net storage of the dam from three basin surveys of the dam conducted in October 1977, February 1987 and October 1999. The inflow time series into the reservoir is essential for reservoir yield and operation analysis and was obtained from a monthly water balance of Hluhluwe dam assuming that the rainfall and pan evaporation data from W3E003 were representative of the respective monthly rainfall and evaporation of the reservoir. Alvarez et al. (2007) obtained coefficients ranging from 0.72 to 0.86 in an experimental study in Spain and an uncertainty study of evaporation (Lowe et al., 2009) obtained pan coefficients averaging about 0.8 for 6 reservoirs in Australia. No experimental study of pan evaporation in South Africa was found and it was decided to adopt a pan factor of 0.85 as applied by Ndiritu (2005) for a reservoir operation study in South Africa. 3. Assessment of the historic yield potential of the dam The potential yield of a reservoir can be assessed using two approaches (McMahon and Adeyole, 2005; Ndiritu, 2003, 2005); i) assuming that the reservoir can supply a set maximum yield constantly throughout the analysis period (firm yield) and ii) considering the reservoir to supply various levels of set demands (target drafts) that can only be met for certain proportions of time and not for the entire period of analysis. The assessment of the historic yield potential therefore involved the determination of historic firm yield and the determination of the levels of supply that can be achieved for a range of target drafts. The net storages from the 3 basin surveys of the dam conducted by the DWAF in October 1977, February 1987 and October 1999 were 29.66, 28.77 and 25.89 Mm3, respectively, indicating a low but increasing reduction in net storage capacity. It was considered realistic to assume that catchment sedimentation rate during the time that the developed rules will be used will follow the trend observed historically by the basin surveys. Any closely-fitting model can therefore be used to extrapolate the reservoir capacity. The capacity reduction rate fitted
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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3
Fig. 2. Location of Hluhluwe dam.
well into a second-order polynomial and this fit was extrapolated to estimate the net storage in 2007 (Fig. 3). The estimated net storage of 23.10 Mm3 was then assumed in the assessment of the historic yield potential of the dam. 3.1. Historic yield analysis The aim here was to determine the historic firm yield defined as the maximum unrestricted annual supply that can be obtained from the reservoir assuming no restrictions to supply. This was done using a simulation-optimization set up where yield was
maximized using the SCE-UA method with any individual solution (out of the population of solutions of the SCE-UA search) that violated the set minimum storage state being heavily penalized and therefore rendered unfit. The SCE-UA optimization parameters recommended by Duan et al. (1994) were used here and in the subsequent optimizations. Typical firm yield determination allows unrestricted supply to emptiness (dead storage) (McMahon and Adeyole, 2005) but this is unrealistic in practice. Firm yield was therefore obtained for minimum storage states of 0, 20 and 40%. Considering the possibility that the water users could alter their monthly demands if this would increase the overall yield, a scenario in which the distribution of monthly water demand was itself optimized was analysed in while the other scenario used the monthly distribution provided by DWAF. Table 1 presents a summary of the results obtained from the firm yield analysis. The increases in historic yield as a result of optimizing demand distribution are not considered insignificant but the demand distributions for these scenarios had unrealistic high variability. The firm yield was found to be 10.80 Mm3/year by the usual definition of firm yield in which the reservoir is allowed to reach dead storage just once. If higher minimum storages are specified, the firm yield reduces reduced considerably as shown on Table 1. 3.2. Assessment of levels of supply for specified target drafts
Fig. 3. Reduction of Hluhluwe Dam net storage capacity with time.
This analysis was considered more realistic than the historic firm yield analysis (Section 3.1) and determined the maximum proportion of time that specified target drafts could be met and the respective proportion of the water demanded that was actually supplied (volumetric reliability) while ensuring that the storage levels do not fall to unacceptable levels by applying restrictions to demand. After some trial runs, reduction of supply to 80%, 50% and 30% of the demand depending on the storage state of the reservoir and the month of the year were found to provide trajectories that
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Table 1 Firm yields for various minimum storage states. Monthly demand distribution scenario
Minimum storage state (%)
Yield (Mm3/year)
Yield/MAR
Average % FSL
Actual demand (from DWAF)
0 20 40 0 20 40
10.8 8.1 5.4 11.5 8.8 6.2
0.2157 0.161 0.1073 0.2296 0.1749 0.1243
81 89 93 78 87 92
Optimized
FSL: Full supply level; MAR: Mean Annual Runoff; FSL: Full supply level.
match the historic one closely and were adopted. The rule curves were modelled as simple trigonometric functions as described by Ndiritu and Sinha (2009) and an objective function that seeks to maximize yield and storage state and defined by equation (1) (in Section 4) was applied. The ratios of the volume supplied to that demanded and the proportion of times that the demands would be met are shown on Fig. 4. For the annual demand of 12.8 Mm3/year in 2007, Fig. 4 shows that it was possible to supply 90% of the demand with unrestricted supply occurring 75% of the time. In Fig. 5, the proportions of time that restrictions of varying severity would be met for specific target drafts are shown. It is seen that a target draft of 12.5 Mm3/year obtains a considerably lower proportion of restrictions than a draft of 15 Mm3/year but the proportion for 50% restriction for 15 Mm3/year is slightly lower than for 12.5 Mm3/ year. Fig. 6 presents the optimized operation rule curves obtained for two target drafts.
80
proportion of time res tric tion is made (% )
a
a
Target draft (Mm3/year) 7.5
70
10 12.5
60
15 50
17.5 20
40
25
30 20 10 0 0
10
20
30
There were no records of the actual releases made to irrigation since the reservoir started operating in 1966 and there were also no records of how water allocation decisions had been made. It was however expected that the operator/s of the dam made releases depending on the variation of demand within the year and the volume of storage in the reservoir with the aim to i) meet the demand whenever possible and ii) to ensure that the storage volume
1.00
ratio
0.70
0.60
0.50 volume supplied / volume demanded
0.40
time that supply is unrestricted / total period of analysis
0.30 5
10
15
20
Target Draft (Mm3/year) Fig. 4. Volumetric reliability and proportion of time that demand is met.
25
60
70
80
in the reservoir was maintained at a reasonably high level whenever possible. An operating rule that aimed to maximize these 2 objectives was therefore adopted as a surrogate of the historic operation. Equation (1) defines the function based on these two objectives that was optimized by the SCE-UA method. The trigonometric rule curves (Ndiritu and Sinha, 2009) were also applied here.
Maximize wd
0.80
50
Fig. 5. Proportions of restrictions of varying severity.
"
0.90
40
Percent restriction
4. Analysis of the historic storage behaviour of Hluhluwe dam
PN P12 i¼1
j
N TD
ai;j
!
PN P12 þ ws
i¼1
j¼1 si;j
12 N Ci;j
!# (1)
where wd and ws are weights to indicate the relative value assigned to maximizing yield and storage state, respectively, N is the number of years of analysis, ai,j is the actual supply from the reservoir in month j of year i, TD is the annual target draft (assumed constant for each simulation-optimization run), si,j is the simulated storage level in month j or year i and Ci,j is the net storage capacity of the reservoir in month j of year i. The reservoir was then simulated at a monthly time step for the 40-year period for which the historic reservoir storage trajectory was available. The simulation assumed a reducing net storage capacity (Ci,j) due to sedimentation using the relationship shown in Fig. 3 and equal weights wd and ws of 0.5 were found to obtain realistic simulations. The simulation was carried out for various target drafts (annual water demands) assuming the monthly demand distribution provided by the DWAF. The resulting simulated storage trajectories were compared with the recorded historic one in order to inform the likely target drafts that the dam has been supplying over the 40 year period of operation. Fig. 7 compares the
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5
Fig. 6. Historic operating rule curves for two annual target drafts.
historic trajectories with trajectories for target drafts of 10 and 25 Mm3/year as these were found to closely match the historic trajectory for various periods. The historic trajectory (Fig. 7) revealed that the reservoir operation was not prioritizing water storage in the first 5 years (1967e71) as large releases (greater than 25 Mm3/year) were made over this period while storage state averaged less than 20%. Large storage drawdowns in the early years of 1980s, 1990s and 2000s which are likely to be the result of the droughts that occurred in Southern Africa over those periods (Masih et al., 2014; Vogel et al., 2010; Rouault and Richard, 2005) are also evident in Fig. 7. The simulated storage trajectories generally matched the changes in historic trajectory but varied in the amplitude of changes. More specifically, the following was inferred from Fig. 7 for various periods: Jan 1967 - Dec 1971: Storing water in the reservoir was not prioritized as the annual release exceeded 25 Mm3/year over this period while storage state remained very low.
Jan 1972 - Dec 1978: The target draft was about 10 Mm3/year. It is expected that most of the demand was met. Jan 1979 e Dec 1983: Two dry periods occurred corresponding to a target draft of about 25 Mm3/year. It is expected that restrictions were implemented and the actual supply was considerably less than 25 Mm3/year as Figs. 4 and 5 indicate. Jan 1984 e Dec 2000: The target draft was about 10 Mm3/year except for the dry periods in 1986e87 and 1992e93 where a draft higher than 10 Mm3/year but lower than 25 Mm3/year occurred. Most of the demand was most likely met except for the two dry periods. Jan 2001 e Dec 2005: The historic trajectory was below that for 25 Mm3/year for most of the period suggesting a demand exceeding 25 Mm3/year. This high target draft was most likely not met and the actual supply was likely considerably less as Figs. 4 and 5 suggest. Jan 2006 e June 2006: The historic trajectory dropped steadily while the simulated ones for both target drafts of 10 and
Fig. 7. Historic and simulated trajectories for target drafts of 10 and 25 Mm3/year.
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25 Mm3/year rose steadily. This implies massive water releases from the dam were being made.
January. 5.1. Stochastic streamflow generation
5. Development of operating rules As stated in Section 1, the development of the operating rules followed the basic method that has been used in South Africa since the late 1980s (McKenzie and Allen, 1990; Basson et al., 1994). Following are the main features of this method. The operating rule is used to decide how much water is available to allocate the various demands for a period of one year starting from a decision date which is often the end of the rainy season. The rule also allows for additional decisions to be made within the year if the observed changes in storage warrant this. The ability of the reservoir to meet the annual demands is assessed via simulation of the reservoir over a short period of time (typically 5 years) assuming a range of possible storage states at the start (the decision date). Since the inflows into the reservoir over the operating period (in the future) are not known and climate is known to exhibit large inter-annual and inter-decadal variability, an appropriate probabilistic approach is applied in order to obtain operating rules that adequately specify the reliabilities associated with water allocation decisions. This is done by carrying out reservoir simulation using a large number of artificial (stochastically generated) sequences of plausible inflows whose central statistical attributes are similar to those of the historic inflows. Since reservoir water balance also includes rainfall gains and evaporation losses, stochastic sequences of rainfall and evaporation that are statistically similar to the historic ones whilst maintaining historic inter-dependence with the inflows are also generated and applied. The reliabilities at which supply to the various demands need to be supplied usually varies and set proportions of each demand are usually assigned specified levels of reliability. The water allocation decisions prioritize supply based on the specified reliabilities of the multiple demands. For Hluhluwe dam, the irrigation demand was taken as constant 11.8 Mm3/year with a specified monthly variation. The municipal demand was observed to be increasing steadily at a linear rate and it was decided to develop operating rules using the municipal supply expected in 21/2 years from mid-2007 considering that DWAF routinely updates reservoir operating rules after about 5 years. The projected municipal demand at this time (end of year 2010) was estimated as 1.57 Mm3/year. For water supply in South Africa, DWAF specifies the reliabilities at which set proportions of irrigation and municipal supply need to be supplied. For Hluhluwe dam, the proportions and actual annual demands are presented in Table 2. Hluhluwe dam is located in the summer rainfall region of South Africa and April (the usual end of the rainy season) was therefore set as the main water allocation decision date. Other decision dates were set at 3 month intervals as July, October and
Table 2 Reliability levels required for set proportions of irrigation and municipal demand. Percentage of demand supplied at reliability (target allocation Mm3) Reliability (RI)a Municipal Irrigation a
90% (1:10) 10 (0.157) 70 (8.26)
98% (1:50) 20 (0.314) 20 (2.36)
RI ¼ Expected recurrence interval of shortage.
99% (1:100) 70 (1.099) 10 (1.18)
The Auto Regressive Moving Average (ARMA) multisite monthly stochastic generator used widely in South Africa (DWAF, 1986; Pegram and McKenzie, 1991; Basson et al., 1994) and currently packaged as STOMSA (Van Rooyen and McKenzie, 2004) was used to generate 100 stochastically generated streamflow sequences, each 1000 years long using the 40 year long historic inflow time series obtained via mass balance (Section 1). STOMSA includes several tests to assess how well the statistics of the generated sequences match the historic ones and 4 of the graphical comparisons are presented in Fig. 8. The historic statistics are all within the range of the stochastic values and more than half lie within the interquartile ranges of the box plots and this was observed for most of the other statistics. The generated sequences were therefore considered to be adequately plausible during the operation period of the dam. STOMSA generates only 100 stochastic sequences and this was considered low for a precise computation of reliabilities. For each decision month five hundred (500) 5 year-long stochastic sequences were obtained from the 100 one thousand year-long sequences with a gap of at least 10 years in between so that they were independent. 5.2. Development of operating rule curves The minimum annual yield (base yield) for each 5 year sequence was obtained by monthly simulation of the reservoir for eight starting storage states (%FSL ¼ 100, 80, 60, 50, 40, 30, 20 and 10) and annual target drafts (demands) ranging from 0 to 10 Mm3/year for 10 and 20%FSL and 0e20 Mm3/year for the other starting storage states. For all the starting storage states except the lowest (% FSL ¼ 10), the minimum %FSL in any of the 60 months (5 years) of analysis was set to 10%. For a starting storage of 10%FSL the constraint on minimum storage was set to 5%. The monthly distribution of the actual water demands from the dam (obtained from DWAF) was used to obtain the monthly target drafts. The rainfall gains into and evaporation losses from the reservoir to use in the simulation were obtained in two steps: i) finding the historic annual streamflow closest in magnitude to the annual stochastic rainfall and ii) selecting the historic rainfalls and evaporation rates that fell in the same year as this streamflow for the simulation during that year. The 500 base yields obtained at each starting storage state and target draft were then ranked and the probability that any specified base yield is not exceeded in the 5 year period computed using the Weibull plotting position formula (Equation (2)).
pn;5 ¼
m nþ1
(2)
where m is the rank of the base yield with the lowest out of all the base yields ranked as 1, n is the number of base yields (¼500) and pn;5 is the probability that the base yield has not been exceeded in 5 years. The probability of the base yield being exceeded in any year and the corresponding return period were then computed as follows. If the probability of a given base yield being exceeded in any year is pe;1 then the probability of this base yield not being exceeded in any year is 1 pe;1 : Assuming these non-exceedance probabilities to be independent, then their product for a period of 5 years equals the probability that the base yield is not exceeded over the continuous 5 year period (Equation (3)).
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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Fig. 8. Representative statistical tests of generated streamflow sequences.
1 pe;1
5
¼ pn;5
(3)
The yearly recurrence interval (ri Þ of exceedance of the base yield is therefore obtained as
ri ¼
1 ¼ pe;1
1
1 pn;5
ð1=5Þ
(4)
Fig. 9 shows the relationship between base yield and recurrence
Fig. 9. Base yield e recurrence interval e initial storage state relationships.
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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interval obtained for the April decision month (meaning the simulations started in April) for initial storage states of 20 and 80%. Each curve represents the base yields obtained for a set target draft and the straight portions indicate that for some of the simulations, the base yields equalled the target drafts. For those cases, the reservoir was able to meet the target draft without any shortfall over the 5 year period and the recurrence interval of not meeting a given target draft can therefore be obtained from these base yieldrecurrence interval relationships. For example for the initial storage of 80% in Fig. 9, the recurrence interval of not meeting a target draft of 10 and 18 Mm3/year is 60 and 8 years, respectively. Relationships between recurrence interval and target draft for different initial storage states (e.g. Fig. 10) were then obtained from the base yield e recurrence interval e initial storage state relationships. These were then used to obtain curves that inform the maximum annual demand that can be supplied when the reservoir is at a set storage state in the decision month for the recurrence intervals of interest which are 1 in 100, 1 in 50 and 1 in 10 years as specified in Table 2. Since a higher assurance demand needs to be prioritized over a lower assurance demand, the supplies were obtained in a cumulatively progressive manner (1 in 100, 1 in 100 þ 1 in 50 and 1 in 100 þ 1 in 50 þ 1 in 10). For the April decision month, these curves together with the corresponding total annual demands are shown in Fig. 11. It is found that the 1 in 100, 1 in 50 and 1 in 10 demands could be met for initial storage states equal to or higher than 15%, 27% and 45%, respectively. At lower storage states, the demands could not be met and the available water was apportioned in direct proportion to the demands (Table 2) for each recurrence interval. This lead to the rule curves for allocations to the municipality and irrigation as shown on Fig. 12 for the decision month of April. Similar analyses were carried out for the other 3 decision months (July, October and January) and rule curves similar to Fig. 12 were obtained. It was thus possible to review the April allocation decisions at these other months if the change in storage state called for this. This could be due to an unexpectedly large reduction in storage or a replenishment of the reservoir when restrictions are in place.
Fig. 11. Storage state e Draft curves for specified recurrence intervals.
6. Has implementing the operating rules improved Hluhluwe dam performance? The operating rules have been used to guide the water allocation decisions since April 2009 and are into the 7th year of use. New operating rules for Hluhluwe dam are currently being developed as a longer hydrological dataset is available and the Hluhluwe municipal demand has increased substantially (from 1.57 in 2010 to 2.9 Mm3/year in 2015). The net storage capacity of the dam is also expected to have reduced due to sedimentation in accordance with the trend presented in Fig. 3. Fig. 13 shows the trajectory of the 3 major dams in Northern Kwa Zulu Natal since 2009 when the operating rules for Hluhluwe came into use. Significant restrictions to supply happened in 2009 and less severe restrictions needed to be implemented in 2010. No restrictions were implemented from 2010 to 2014 and the dam experienced storage states that were as high as those of the other dams in the region. Southern Africa has been experiencing drought since mid-2014 and this is evident in the observed drop in storage in the last two years. Restrictions to irrigation and municipal supply were implemented to Hluhluwe water supply in April 2015 but the storage level has still been reducing as for the other two reservoirs. The current state of Hluhluwe is unlike the earlier period in the last decade (Fig. 1) when it exhibited considerably lower storage states than the other dams in the region. This indicates that the operating rules helped to improve the annual water allocation decisions of the dam. 7. Discussion and conclusions
Fig. 10. Recurrence interval-target draft Curves.
This study aimed to assess the historic yield potential of Hluhluwe dam, analyse its historic performance and finally to develop comprehensive operating rules for the dam. The historic firm yield of the dam was found to be 10.8 Mm3/year. A more detailed analysis of the historic yield potential found that 90% of the annual demand (in year 2007) of 12.8 Mm3/year could be supplied and that restrictions would not be needed 75% of time. For the projected demand of 13.37 Mm3/year in 2010, the respective proportions were 88% and 68%, respectively, while for the year 2015 demand of
Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017
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Fig. 12. Rule curves for municipal and irrigation supply for April decision month.
Fig. 13. Storage trajectories of the 3 major dams since implementing operating rules for Hluhluwe dam.
14.7 Mm3/year, the proportions reduced to 84% of supply with unrestricted supply 54% of the time. The assessment of the historic yield potential reveals that Hluhluwe dam could not adequately meet the irrigation demand of 11.8 Mm3/year without restrictions. As municipal demand increases into the future, more frequent restrictions are to be expected unless Hluhluwe dam supply is augmented by an alternative water source. Improved water demand management could also help reduce the severity and frequency of restrictions. Although there were no quantitative records of the historic operation of the dam, simulated storage trajectories that matched the historic trajectory reasonably well were obtained (Fig. 6). This was achieved by formulating realistic operating rules and optimizing them using an objective function based on the expected aims of water supply dam operation; maximizing supply and maintaining a high storage state. The analysis revealed that historically, the dam was operated at an annual demand of about 10 Mm3/year during most non-drought years till year 2000. During the drought years, the demands were found to be about 25 Mm3/ year although these were unlikely to be met as substantial restrictions were most likely implemented as Figs. 4 and 5 reveal. The analysis of the historic performance of the dam also revealed massive water releases in the first 5 months of year 2006 that were considered highly imprudent since the reservoir was at a low storage state of 40% in January 2006. Comprehensive but easy-to-use operating rules were developed via statistical analysis of the minimum annual (base) yields obtained from 500 5-year long simulations of the system using a range of possible starting storages at the beginning of the
simulation. The 500 5 year-long stochastic monthly inflows stochastics were obtained from 100 one thousand years long stochastic sequences generated using STOMSA, an ARMA model that is widely used in South Africa. The use of stochastic streamflows helped to incorporate the expected inter-annual and inter-decadal variability of climate in developing the rules. The rule curves inform what annual allocations of water supply need to be made to the municipality and to irrigation as a function of the storage state of the reservoir at the decision date. Fig. 12 shows the rule curves for the main decision month of April and similar curves were developed for July, October and January enabling water allocation decisions based on the analysis to be made every 3 months if required. The rule curves for the 4 months took similar forms (shapes) and can be interpolated to make acceptable operational decisions at any time of the year. The operating rules have been in use since April 2009 and Hluhluwe dam storage variation has since matched those of the other large dams in the region more closely. The operating rules have therefore improved the operation of the dam. References Akter, T., Simonovic, S., 2004. Modelling uncertainties in short-term reservoir operation using fuzzy sets and a genetic algorithm. Hydrol. Sci. J. 49 (6), 1081e1098. Alvarez, V.M., Gonzalez-Real, M.M., Baille, A., Martınez, J.M.M., 2007. A novel approach for estimating the pan coefficient of irrigation water reservoirs Application to South Eastern Spain. Agric. Water Man. 92, 29e40. Basson, M.S., Allen, R.B., Pegram, G.G.S., Van Rooyen, J.A., 1994. Probabilistic Management of Water Resource and Hydropower Systems. Water Resources Publications, p. 424. Basson, M.S., Van Rooyen, J.A., 2001. Practical application of probabilistic
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Please cite this article in press as: Ndiritu, J., et al., Development of probabilistic operating rules for Hluhluwe Dam, South Africa, Physics and Chemistry of the Earth (2016), http://dx.doi.org/10.1016/j.pce.2016.10.017