A supply management of water resources management is a reservoir operation. A reservoir simulation model is a modeling technique that is used to analyze the behavior of a system on the computer for operating the reservoir. The rule curves of reservoir are basic monthly guides for long term operation. Normally, rule curves are searched by simulation model and optimization techniques. In the past decade, the rule curves are obtained by using several sets of trial rule curves to test in simulation model (Jain et al., 1998). This method is straightforward and applicable for both simple and complex systems. The monthly input data of reservoir simulation are inflows into reservoir, evaporation, rainfall, infiltration, physical characteristic of the reservoir and conditional rule curves etc (Xu and Ito, 1997; Tilmant et al., 2002). However, the simulation method does not guarantee to yield the optimal rule curves because of human adjustment.
A Dynamic Programming (DP) is another optimization technique applied to search the non-linear problems of water resource (Bellman, 1959; Yakowitz, 1982; Esogbue, 1989). Unfortunately, the application of DP to multi-reservoir system is limited due to a curse of dimensionality. To overcome this problem Chaleeraktrakoon and Kangrang (2007) applied the DP with a Principle Progressive Optimality (DP-PPO) to determine the optimal rule curves. The input data of this technique are similar to the data using in the simulation method. However, this method required the long period of dry inflow record for searching the optimal curves. Moreover, the starting condition of the search is set at the full capacity only.
Recently, Genetic Algorithms (GAs) embedded the simulation model have proposed to search the rule curves of the reservoir system (Chang et al., 2003, 2005; Chen, 2003) The best part of GAs is that they can handle any type of objective function. Furthermore, the model can handle several initial conditions of reservoir simulation such as initial reservoir capacity and the length of inflow record. The popular objective functions of the search are a shortage index, a frequency of water shortage, an average water shortage and a magnitude of water deficit. However, the proper objective function for searching the optimal curves is the minimum of average water shortage (Kangrang and Chaleeraktrakoon, 2007). Also, a smoothing function constraint is required to include into the model for fitting the obtained rule curves.
The simulation models which mentioned above require the same necessary input
data including inflows into reservoir, physical characteristic of the reservoir
(initial reservoir capacity) and conditional rule curves. Moreover, all models
require more long duration of dry historic inflows (Chaleeraktrakoon and Kangrang,
2007; Meigh and Reynard, 2005; Tospornsampan et al., 2005). Therefore,
this is the limitation search of some area lagging long inflow record. Further,
the starting conditions of the simulation models are assumed as the full reservoir
capacity only. This assumption is the barrier for some area having short period
record, because it will not meet the shortage situation that used to be the
objective function of the search for irrigated purpose reservoir. Hence, it
is difficult to obtain the optimal rule curves from the searches.
This study thus uses the GAs embedded the simulation model to search the optimal rule curves for finding the suitable length of historic inflow record. Furthermore, the effect of initial reservoir capacity is carried out in this study. The searching model is applied to the Bhumibol and Sirikit Reservoirs (the Chao Phraya River Basin, Thailand).
MATERIALS AND METHODS
Study area and data: The GAs embedded the simulation model was applied
to search the optimal rule curve of the Bhumibol and Sirikit Reservoirs locating
in the watershed area of the Chao Phraya River Basin (Thailand). Figure
1 shows the location of the Chao Phraya River Basin. Two sequences of 45
year (1956-2000) monthly-flow records of stations P.12 and SK covering several
dry and flooding years were commonly used for searching the optimal rule curves.
The others duration of monthly-inflow data are sub-period of this duration.
Figure 2 and 3 show the yearly inflow of
the two reservoirs from 1956 to 2000. The summation of yearly inflow was considered
to use in the rule curve search. The large duration of dry-year inflow is during
1970-1995 (26 years), the shortest length is 4 years (1985-1988). These duration
lengths were used to apply in the search. The other average hydrological data
for each month included series of evaporation losses and precipitation of the
reservoirs and those of side flows of stations W.4A (River Wang) and Y.5 (River
Yom) were used for the search.
Several conditions of the simulation model were set before starting to search
the optimal rule curves. This study considered the effect on duration length
of inflow records and the effect on the initial capacity of reservoir. The simulation
embedded GAs model was applied to search the optimal rule curve of the two reservoirs.
||Location of the Chao Phraya River
||Yearly inflow of the Bhumibol reservoir
||Yearly inflow of the Sirikit reservoir
The obtained rule curves were then assessed to examine the situations of water
shortage and excess release by comparing related characteristics (e.g., frequency,
magnitude and duration) of the referred circumstances with those of the optimal
curves. The Monte Carlo simulation study against 500 samples of generated monthly
flows of stations P.12 and SK (Chaleeraktrakoon, 1999) was used to compute the
interval (mean±standard deviation) of the referred statistics for the
assessment. There are two main conditions that were considered in this study.
Firstly, several durations of dry inflow were used to find the suitable length
of historicinflow data. Secondly, several initial reservoir capacities of starting
run were adjusted to find the minimum initial capacity of the reservoir. In
the following, the obtained assessment results of the considered water-deficit
and excess-release properties for all cases are presented.
Genetic algorithms embedded simulation model: The simulation model of
this study had been constructed based on the concept of HEC-3 (US, HEC-3, 1974)
and it can be used to simulate the reservoir operation. The reservoir operating
policies are based on the rule curves of individual reservoirs and the principles
of water balance concept. The reservoir system is operated along the standard
operating policy expressed in Eq. 1 as:
in which Rv,τ is the release discharges form the reservoir
during year v and period τ (τ = 1 to 12 representing month, January
to December). Dτ is the water requirement of month τ, xτ
is lower rule curve of month τ, Wv,τ is upper rule curve
of month τ and Wv,τ is the available water calculated using
simple water balance described in Eq. 2 as:
||Stored water at the end of month
||Monthly reservoir inflow
||Average value of evaporation loss
||Minimum reservoir storage capacity (the capacity of dead storage).
In the first equation, if available water is in a range of the upper and lover
rule level, then demands are satisfied in full. If available water over tops
the upper rule level, then the water is spilled from the reservoir in downstream
river in order to maintain water level at upper rule level and if available
water is below the lower rule level, reduce supply is made. The policy usually
reserves the available water Wv,τ for reducing the risk of water
shortage in future, when 0≤Wv,τ <xτ-D.
The results of simulation run are the situations of water shortage and excess release water (e.g., the number of failure year, the number of excess release water and the average annual shortage), they will be recorded for using in GAs technique.
The model of GAs technique was developed to connect with the simulation model. This GAs model requires encoding schemes that transform the decision variables (rule curves) into chromosome. Then, the genetic operations (reproduction, crossover and mutation) are performed. This study used population size = 80, crossover probability = 0.85, mutation probability = 0.01 (Jain et al., 1998).
The objective function of searching the optimal rule curve is the minimum of
average water shortage (Aver-MCM/year) (Kangrang and Chaleeraktrakoon, 2007)
obtaining from the simulation model which described as follows:
||Total number of considered year
||Water deficit during year υ
RESULTS AND DISCUSSION
Suitable duration length of inflow record: Table 1
and 2, respectively show the assessment intervals of water
shortage and excess release characteristics for all duration lengths of inflow
records (initial reservoir capacity is full). They indicate that the rule curves
of using long durations included 45, 26, 21, 17, 14 and 10 year give the magnitude
of water deficit are not different significantly and their situations less than
the situation using the 4 year duration.
||Frequency, magnitude and successive period of water shortage for all conditions
of dry-year inflow records
|μ = Mean, σ = Standard deviation
In addition, the rule curves of using 7 year inflow record are explicit higher
than the curves of using 10 year inflow records. Hence, it indicates that the
shortest duration length of dry inflow record is 10 year inflow. Moreover, the
magnitudes of excess release of using the 7 and 4 year inflow record are higher
than using the other periods. Therefore, the searching model using at least
10 year duration of inflow records can be used to run in the simulation model
embedded GAs technique.
From above tables, it can conclude that the shortest duration of dry-year inflow records is 10 years. However, the suggested duration of inflow records is smaller than 30 years using in the literature (Tatano et al., 1992; Tospornsampan et al., 2005).
Initial reservoir capacity effects: Figure 4 and
5 show the patterns of the rule curves between the two reservoirs generally
agree with each other due to the seasonal effects on reservoir inflows and considered
||Frequency, magnitude and successive period of excess release for all conditions
of dry-year inflow records
|μ = Mean, σ = Standard deviation
||Optimal rule curves of all initial capacities of the Bhumibol Reservoir
||Optimal rule curves of all initial capacities of the Sirikit Reservoir
||Frequency, magnitude and successive period of water shortage for all initial
|μ = Mean, σ = Standard deviation
Moreover, the optimal rule curves using the different initial capacity are
not different explicitly. These optimal rule curves were then evaluated to examine
the situations of water shortage and excess release by the Monte Carlo simulation
Table 3 and 4, respectively show the assessment
intervals of water shortage and excess release characteristics (e.g., frequency,
magnitude and duration) for all initial reservoir capacities. They indicate
that the situations of water shortage and excess release of all initial capacities
are not different significantly.
Generally, the initial reservoir capacity is set at full capacity in all runs
for simulating reservoir (Jain et al.,1998; Chaleeraktrakoon and Kangrang,
2007; Kangrang and Chaleeraktrakoon, 2007).
||Frequency, magnitude and successive period of excess release water for
all initial reservoir capacities
|μ = Mean, σ = Standard deviation
However, the results of this study indicate that at any reservoir capacity
the model can provide the outputs (rule curves) that are not different significantly.
Further, the situations of water deficit and excess release using the obtained
rule curves are not different significantly. Hence, it is concluded that the
least initial capacity of reservoir for simulation model is 10% of reservoir
Rule curves are basic guidelines for long term reservoir operation. Generally,
the optimal rule curves are searched by simulation model connected optimization
techniques. Reservoir inflow is one of required data for operating reservoir.
Often, some area lags long data record, it is the limitation of rule-curve search.
Hence, this paper thus used the GAs embedded the simulation model to search
the optimal rule curves for finding the suitable length of historic reservoir
inflow. The model had been applied to determine the optimal rule curves of the
Bhumibol and Sirikit Reservoirs (the Chao Phraya River Basin, Thailand). The
optimal rule curves of each condition were used to assess by the Monte Carlo
simulation. The results indicated that the shortest duration length of reservoir
inflow records is 10 year.
The second objective is to find the effect on initial reservoir capacity for searching rule curves using simulation model embedded GAs technique. The results found that the obtained rule curves using the initial capacity over 10% of full capacity are not different significantly. The obtained rule curves of each condition were used to evaluate by the Monte Carlo simulation. The results showed that the situations of water deficit and excess release using the obtained rule curves are not different significantly. Hence, it is concluded that the least initial capacity of reservoir for simulation model is 10% of reservoir capacity.
The authors would like to express their appreciation to the Faculty of Engineering, Mahasarakham University for financial support.