Comparative study on the reservoir operation planning with the climate change adaptation

As the earth warms, storage water in the reservoir is expected to change due to the availability, timing and water quality effects by the global warming or climate variability. The heat rising day by day encourages evaporation to occur faster than in the normal condition contributing to the drought and flood events in critical areas. Additional natural activities such as increasing losses due to high evaporation rate on the water surface, wastage due to the water transfer activity, seepage and infiltration into the underground may reduce the capability of the reservoir. The profitability of the reservoir is also more difficult to achieve if real-time operation is still implemented on the field. The weakness of this operation is that the water release decision was based on the previous experience of water manager and it was not applicable in the critical condition of climate. The situation worsens if they have poor data and there is a lack of information regarding to the reservoir operation, maintenance and capacity. The difficulty often enlarges owing to multi-use reservoir that attempts to achieve optimal water allocation for various uses. Therefore, the risk analysis must be done to solve all uncertainties problems in the real-time operation system [15].

The connection scenarios between climate and water resources were evaluated and proved by many researchers at different study areas. Duran-Encalada et al. [4] revealed that the 5% change in temperature and 20% of rainfall deduction will cause the water deficit in the year 2038. Meanwhile, [1] state that the uncertainty of climate brought large impact to the downstream runoff at Nierji Reservoir, Northeast China. The increment of 1 °C temperature causes the deduction of < 1% of mean monthly runoff during reservoir operation. Shaaban et al. [12] projected the changing future of annual precipitation and temperature pattern in Malaysia and estimated an increase in the frequency and severity of droughts and floods at specific locations. The modification of the reservoir operation including the size and number of dams can be a significant solution in facing the vulnerability of water resources system [5].

Changes in the hydrological regimes will have positive and negative impacts on the reservoir systems depending on how it is used and managed. The reservoir optimization methods are using widely the water resources planning for sufficient capacity and capability of storage. Therefore, a multi-objective evolutionary algorithm (MOEA) has been proposed by various authors as an aid to the decision makers in managing the reservoir system efficiently, especially in multi-objective demands [6, 14]. Moreover, MOEAs have the ability to find multiple Pareto optimal solutions in one single simulation run compare to the classical optimization methods that do not consider all objectives simultaneously by using weighted approach or constrained approach.

Thus, the study aims to evaluate the impact of local climate change on the reservoir operating management system using one of the famous MOEAs, NSGA-II. The case study was evaluated based on two different analyses: Analysis 1 (including climate assessment) and Analysis 2 (excluding climate assessment).

1.1 Reservoir optimization

1.1.1 Non-dominated sorting genetic algorithm (NSGA-II)

NSGA-II is a modification of genetic algorithm (GA)-based concept in producing better approximation of Pareto optimal front in a single run. It was proposed by [3] to overcome several problems from other evolutionary algorithm (EA) model, which have high computational complexity of non-dominated sorting, have lack of elitism and need to specify the share parameter. It also can assess optimal quantities and reduce the time needed to reach the optimal quantity of decision variables [14]. The upgraded version of these GAs, NSGA-II, becomes the most popular method among multi-objective optimization by EAs, and the potential has been proved by ([10]; [7]; [2]) in their study.

Generating set of Pareto optimal solutions, NSGA-II uses five major steps—initialization, generation of initial population, non-domination sorting, criterion to prepare population for next generation and selection of best compromise solution [3]. The steps are discussed below:

1. 1.

   Initialization Parent population (P_t) is initialized based on two different parents’ chromosome to create a new offspring (Q_t). Here, the parent is referred to as the water demand of Pedu–Muda reservoir.

    
2. 2.

   Generation of initial population P_t and Q_t are randomly combined by using tournament selection to form a new population, known as R_t.

    
3. 3.

   Non-domination sorting R_t undergoes non-dominated sorting to classify the entire population. The solution that is not dominated by others is classified as non-dominated fronts.

    
4. 4.

   Criterion to prepare population for next generation Crowding distance is calculated and ranked according to the boundaries of objectives values. A lower rank and higher crowding distance is the selection criteria. The crossover process is carried out to create new solutions which have some of the attributes of their parents.

    
5. 5.

   Selection of best compromise solution Mutation process is conducted to provide new genetic material in finding better global optimization solution and produce new population Q_t+1.

    

The steps are repeated until the termination criteria are satisfied. The optimization operation is handled by GANetXL to solve complex optimization and search problems.

1.1.1.1 Analysis 1

The SDSM was used to downscale the global circulation model (GCM) output to project future climate change in the study area. It calculates the statistical relationships between large-scale and local climate variables based on multiple linear regression techniques. The downscaling using SDSM requires two types of data, viz. predictand and predictor. In the present study, historical rainfall (1961–1990) recorded at twenty locations and temperature (1972–2008) recorded at one station of Kedah (Fig. 2) were used as predictand, and the National Center for Environmental Prediction (NCEP) reanalysis data of the study area for the time period of 1961–2008 were used as the predictor. For downscaling of rainfall, the model was calibrated for the time period of 1961–1975 and validated for the period of 1976–1990. For downscaling of temperature, the model was calibrated for the time period of 1972–1999 and validated for the period of 2000–2008. GCM outputs of the Hadley Center General Circulation Model (HadCM3) under A2 scenario for the period of 2010–2100 were used for projecting future rainfall and temperature. The A2 scenario chosen for this study provides an upper bound on future emissions, and it is selected from an impacts-and-adaptation point of view; if it is adaptable to large climate change, it will have no problem with smaller climate change and lower end scenario, although low emission scenario gives less information from this point of view (NARCCAP 2007).

Next, a hydrological model was used to simulate the water streamflow under projected change in climate known as the Identification of unit Hydrographs and Component flows from Rainfall, Evaporation and Streamflow (IHACRES). It characterizes the dynamical relationship between rainfall and streamflow by using rainfall and temperature (potential evaporation) data to predict time series of streamflow. IHACRES is preferred because it has a simple structure and parsimonious parameterization. Thus, it provides parametric efficiency and statistical rigor in presenting the dynamic response characteristics of the catchment area [9]. The model consists of a nonlinear loss module and a linear unit hydrograph module. The nonlinear loss module calculates the effective rainfall (\(u_{k}\)) from observed rainfall (\(r_{k}\)) for every time step k. The linear unit hydrograph module estimates streamflow (\(x_{k}\)) from effective rainfall by using the equations given below:

$$x_{k} = ax_{(k - 1)} + bu_{k}$$

(1)

$$u_{k} = r_{k} s_{k}$$

(2)

$$s_{k} = Cr_{k} + (1 - \frac{1}{{\tau_{w} (t_{k} )}})s_{(k - 1)}$$

(3)

$$\tau_{w} (t_{k} ) = \tau_{w} e^{{0.062f(R - t_{k} )}}$$

(4)

where a and b are the parameters of unit effective rainfall in a linear unit hydrograph module with b > 0 and − 1 < a<0; \(u_{k}\) is refer to the effective rainfall; \(s_{k}\) is known as catchment wetness index which value ranges between 0 < \(s_{k}\) < 1; \(\tau_{w}\) is a catchment drying time constant; R is a reference temperature; \(t_{k}\) is a monthly temperature; C is a proportion of the rainfall; and f is a temperature modulation factor [11]. The runoff at Pedu–Muda reservoir was calibrated for the time period of 1988–1993 and validated for the time period of 1995–2000. Its performance was then evaluated using the determination coefficient (D) and percentage of average relative parameter error (% ARPE). These two values are calculated using the following equations:

$$D = 1 - \frac{{\sum {(x - \hat{x})^{2} } }}{{\sum {(x - \overline{x} )^{2} } }}$$

(5)

$$\% {\text{ARPE}} = \frac{1}{n}\sum\limits_{i = 1}^{n} {\frac{{(x_{{{\text{estimated}}(i)}} - x_{{{\text{observed}}(i)}} )}}{{x_{{{\text{observed}}(i)}} }}} *100$$

(6)

where \(x\) refers to the streamflow, \(\bar{x}\) is the mean of streamflow, \(\hat{x}\) is error in the predicted streamflow, and n is the size of streamflow. A high D and low % ARPE indicates that the model has been well calibrated and validated. The projected rainfall and temperature data were used to simulate the streamflow from year 2010 to 2100.

Next, a crop water model was used in this study to estimate future change in crop water demand at the region. The paddy fields at the Muda Irrigation Scheme are cultivated twice a year; the first season starts in March and ends in August, while the second starts in September and ends in January the following year. Water is supplied three times in three different phases (Phase I, II and III) every season. CROPWAT 8.0 was applied to calculate the total irrigation water requirement using the following equation:

$$W_{\text{irr}} = {\text{ET}}_{\text{crop}} + W_{\text{lp}} + W_{\text{ps}} + W_{\text{l}} - P_{\text{e}}$$

(7)

where \(W_{\text{irr}}\) is the irrigation water requirement; \({\text{ET}}_{\text{crop}}\) is the crop evapotranspiration; \(W_{\text{lp}}\) is the water required for land preparation; \(W_{\text{ps}}\) is the percolation and seepage losses of water from paddy field; \(W_{\text{l}}\) is the water required to establish standing water layer; and \(P_{\text{e}}\) is the effective precipitation. Crop evapotranspiration is calculated as:

$${\text{ET}}_{\text{crop}} = {\text{EC}} \times {\text{ET}}_{\text{ref}}$$

(8)

where EC is the crop coefficient and \({\text{ET}}_{\text{ref}}\) is the reference evapotranspiration. The Penman method is used to calculate the reference evapotranspiration from climate data. The effective rainfall is considered as a dependable rainfall event, as suggested by FAO, using the following equation:

$$P_{\text{eff}} = 0.6*P - 10/3\quad {\text{for}}\;P({\text{month}}) \le 70/3\,{\text{mm}}$$

(9)

$$P_{\text{eff}} = 0.8*P - 24/3\quad {\text{for}}\;P({\text{month}}) > 70/3\,{\text{mm}}$$

(10)

Other parameters such as water required for land preparation and losses from paddy field are calculated from soil information. The irrigation demand in this study, is taken as 80% supplied by the Pedu-Muda reservoirs and the remaining 20% was contributed by uncontrolled river flow. The prediction of monthly water demand for paddy field is used in this analysis for optimization purpose. The results produced by these steps are remarked as Analysis 1 that practically concern the climate impact assessment.

1.1.1.2 Analysis 2

A sequence flow of Pedu–Muda reservoir was generated using spatial disaggregation technique—Valencia–Schaake (V&S) method. This method was selected due to its ability in dividing annual flow into finer-scale time series (in month) within each year based on cross-correlation concept. The undemanding data series, easier understanding and simple application have made V&S a well-liked method in recent years. Besides, the method can generate unlimited stochastic flow by the use of limited historical flow time series. The potential of V&S among other available disaggregation techniques was proved by Ismail et al. [8]. The basic form of V&S is:

$$Y_{t} = AQ_{t} + B\varepsilon_{t}$$

(11)

where \(Y_{t}\) is a seasonal flow value of \(Q_{t}\); \(Q_{t}\) is annual flow value of year t; \(\varepsilon_{t}\) refers to the m × 1 matrix of independent standard normal deviates; A and B refer to the parameter matrices with dimensions of m × 1 and m × m, respectively, by methods of moment (MOM) with m is the 12 months in a year. The parameter matrices of A and B were estimated by equation below:

$$A = M_{0} (YQ)M_{0}^{ - 1} (Q)$$

(12)

$$BB^{T} = M_{0} (Y) - M_{0} (YQ)M_{0}^{ - 1} (Q)M_{0} (QY)$$

(13)

In Analysis 2, Stochastic Analysis Modeling and Simulations (SAMS) developed by [13] was applied to simulate the stochastic time series of flow for the Pedu–Muda reservoir during year 1972–2099. However, the analysis was exclude the climate assessment and loss factors on the site study. This outcome was used as data input in the NSGA-II optimization.

The generated inflows produced by Analysis 1 and Analysis 2 were compared, and the accuracy was measured by using various statistical parameters below:

$${\text{Mean}} = \frac{{\sum {X_{{{\text{est}},i}} } }}{n}$$

(14)

$${\text{MAE}} = \frac{1}{n}\sum {(X_{\text{est}} - X_{\text{obs}} )}$$

(15)

$${\text{MSE}} = \frac{1}{n}\sum {(X_{\text{est}} - X_{\text{obs}} )}^{2}$$

(16)

$${\text{SD}} = \sqrt {\frac{1}{n}\sum ( X_{\text{est}} - \overline{{X_{\text{est}} }} )^{2} }$$

(17)

$${\text{Skew}} = \frac{{\frac{1}{n}\sum {(X_{\text{est}} - \overline{{X_{\text{est}} }} )^{3} } }}{{{\text{SD}}^{3} }}$$

(18)

$${\text{CV}} = \frac{\text{SD}}{{\overline{X} }}$$

(19)

$${\text{CC}} = \frac{{n\sum {(X_{\text{est}} } X_{\text{obs}} ) - (\sum {X_{\text{est}} )(\sum {X_{\text{obs}} )} } }}{{\sqrt {n(\sum {X_{\text{est}}^{2} ) - (\sum {X_{\text{est}} )^{2} } } } \sqrt {n(\sum {X_{\text{obs}}^{2} ) - (\sum {X_{\text{obs}} )^{2} } } } }}$$

(20)

where \(X_{\text{est}}\) and \(X_{\text{obs}}\) refer to the monthly flow estimated and observed, respectively; \(\bar{X}\) refers to the mean of flow; SD, CV and CC indicate the standard deviation, co-variance and correlation coefficient, respectively.

1.1.1.3 Reservoir optimization

The NSGA-II was applied by using Analysis 1 and Analysis 2 fit to the multi-objectives purposes; (1) first is to optimize the reservoir operation so that the monthly supply can be maximized to meet the irrigation demand of the paddy fields. The amount of water supplied depends on the availability of monthly Pedu reservoir storage. (2) Second is to minimize water shortage, which is equivalent to the sum of monthly water shortage within a year. (3) Third is to maximize monthly reservoir storage after considering the release and other loses from the reservoir storage. In the NSGA-II model, the optimal Pareto front was obtained from a Pareto set of 150 populations (the maximum population of chromosomes available in GANetXL) after running 1000 generations. The crossover and mutation rate were set as 0.95 and 0.06, respectively. Five constraints were set for 12 months to get the optimal Pareto front. The objective functions, formulated for 12 months, are mentioned as:

$${\text{Maximize}}\;\sum\limits_{t = 1}^{12} {R_{t} }$$

(21)

$${\text{Minimize}}\;\sum\limits_{t = 1}^{12} {(D_{t} - R_{t} } )$$

(22)

$${\text{Maximize}}\;\sum\limits_{t = 1}^{12} {S_{t} }$$

(23)

The constraints can be equated by using the following mass balance equation:

$$S_{(t + 1)} = S_{t} + P_{t} + I_{t} - Eva_{t} - R_{t} - See_{t} - Sp_{t} + S_{\text{muda}}$$

(24)

$$S_{\hbox{min} } \le S_{t} \le S_{\hbox{max} }$$

$$R_{\hbox{min} } \le R_{t} \le R_{\hbox{max} }$$

$$D_{t} \le R_{t}$$

where \(R_{t}\) is the water released by reservoir in period \(t\); \(D_{t}\) is the irrigation demand in period \(t\); \(S_{t}\) refers to the Pedu reservoir storage at end of the \(t\)th month; \(S\) refers to water storage at Pedu reservoir; \(P_{t}\) is the rainfall amount in period \(t\); \(I_{t}\) is the inflow into the reservoir in period \(t\); \(Sp_{t}\) is the water spill for the period \(t\) when the reservoir storage exceeds the limit; and \(Eva_{t}\) and \(See_{t}\) are the evaporation and seepage losses from reservoir in period \(t\).

Additional constraints had also been set to minimize water transfer from the Muda reservoir when the Pedu reservoir has insufficient water storage and to minimize water spill from the Pedu reservoir when the stored water exceeds monthly reservoir capacity.

$${\text{Water}}\;{\text{transfer}}\;{\text{from}}\;{\text{Muda}}\;{\text{reservoir}} = {\text{If}}\left\{ {\begin{array}{*{20}l} {S_{t} < S_{\hbox{min} } ,\quad 0} \hfill \\ {S_{t} > S_{\hbox{min} } ,\quad S_{t} - S_{\hbox{min} } } \hfill \\ \end{array} } \right.$$

(25)

$${\text{Water}}\;{\text{spill}},\;SP_{t} = If\left\{ {\begin{array}{*{20}l} {S_{t} < S_{\text{capacity}} ,\quad 0} \hfill \\ {S_{t} > S_{\text{capacity}} ,\quad S_{t} - S_{\text{capacity}} } \hfill \\ \end{array} } \right.$$

(26)

The detailed procedure is illustrated in Fig. 1.

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Pedu–Muda reservoirs were located in Kedah state, Northern of peninsular Malaysia. These reservoirs mainly supply water to the Muda Irrigation Scheme which the largest paddy cultivation area in Malaysia. Practically, Pedu reservoir acts as the main water storage to supply the required water of paddy field meanwhile Muda reservoir acts as the backup water storage of Pedu reservoir. It connected to the farmer through a 6.8 km of Saiong tunnel.

Figure 2 shows the detail location of the study. The area of Muda Irrigation Scheme was 97,000 hectares. Geographically, the area lies between 5°45′–6°30′N latitude and 100°10′–100°30′E longitude. The area was almost flat with a slope ranging from 1 in 5000 to 1 in 10,000. The soil was heavily clayey in nature. The area’s climate can be classified into four seasons, viz. southwest monsoon (May–September), northeast monsoon (November–March) and two intermonsoon seasons. December–February and June–July were considered as warm seasons, while April–May and September–November are humid seasons. The mean temperature in the area varies between 27 and 32 °C. The relative humidity fluctuates between 54 to 94%.

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Analysis 1 (operating rule curve with consider all the climate factors) and Analysis 2 (operating rule curve without consider climate factors) have been developed to determine the impacts of climate change on water balance of the reservoir and to optimize the reservoirs’ operation accordingly by using NSGA-II model. These analyses were simulated, and the performance results were compared based on statistical tests and the formation of Pareto optimal solution. The results were siding to Analysis 1 because it produced a consistence monthly flow reading, lesser monthly error in MAE test and higher association with the historical records. In the formation of Pareto solutions, Analysis 1 generated better solution considering all the objectives demands than Analysis 2. Considering of climate factors in the analysis may change the water inlet pattern of reservoir storage. Applying NSGA-II in Analysis 1 also can improvised and re-managed the reservoir storage efficiently. As proven, it can reduce the dependability of Pedu reservoir than the Muda reservoir with full use of storage (no spill water) compared to the historical records.

A simple analysis like V&S (Analysis 2) was very friendly modeling but producing bigger error than Analysis 1. Besides, Analysis 2 was also produced insufficient optimal solution and only successfully to achieve one optimization's objective without concerned another objectives in the study.

Thus, the climate aspects could be considered in preparing reservoir management. The implication may affect the reliability of the reservoir water supply due to the global climate changes. Practicing NSGA-II amplifies this analysis simulation in producing many optimal solution choices for the decision makers to improve the quality of reservoir system.