Genetic Algorithm Optimization Model for Central Marches Restoration Flows with Different Water Quality Scenarios

: A Genetic Algorithm optimization model is used in this study to find the optimum flow values of the Tigris river branches near Ammara city, which their water is to be used for central marshes restoration after mixing in Maissan River. These tributaries are Al-Areed, Al-Bittera and Al-Majar Al-Kabeer Rivers. The aim of this model is to enhance the water quality in Maissan River, hence provide acceptable water quality for marsh restoration. The model is applied for different water quality change scenarios ,i.e. , 10%,20% increase in EC,TDS and BOD. The model output are the optimum flow values for the three rivers while, the input data are monthly flows(1994-2011),monthly water requirements and water quality parameters (EC, TDS, BOD, DO and pH).The objective function adopted in the optimization model is in a form the sum of difference in each of the 5 water quality parameters, resulting from the mixing equation of the waters of the rivers, from the accepted limits of these parameters , weighted by a penalty factor assigned for each water quality parameter according to its importance. The adopted acceptable limits are 1500,1000, 6,4 and 7, while the penalty factors are 1,0.8,0.8,0.8,and 0.2 for EC,TDS,BOD,DO,and pH respectively. The constraints adopted on the decision variables which the monthly flows of the three rivers are those that provide the monthly demands downstream each river, and not exceed a maximum monthly flow limits. The maximum flow limits adopted are for three flow cases, wet, average and dry years. For each flow case three scenarios for the monthly water quality parameters were adopted , the average values(scenario 1),the 10% increase in EC,TDS, and BOD (Scenario 2),and the 20% increase in these three water quality parameters (Scenario 3). Hence nine cases are adopted and for each an optimum monthly flows are found for each river. The genetic optimization model adopt a variable number of population of 100 to 1000 in a step of 100,0.8 and 0.2 cross over and mutation rates, and three iterations to reach the stable optimum solutions. The results indicates that the flow analysis shows a significant decrease in the flow values of the three rives after year 2000,hence, the flow values for the period of (1994-1999), are excluded and the only used values are those for (2000-2011). The estimated monthly demands exhibits low variation. The observed optimum monthly flow values decrease in general as the case flow changed from wet to normal and dry cases. The change in Scenarios from S1 to S2 and S3 , do not necessarily increase all the required optimum monthly flow values. The obtained minimum objective functions do not exhibits a certain trend with the change in the flow cases and/or the change in the scenarios.


INTRODUCTION:
The past activities in the Iraqi Marshes region had destroyed the environment and the nature of these marshes.These activities are either, establishing agriculture projects, holding ground roads , redistributing the rural settlement, and diverting water from those marshes by constructing dykes and canals.The central marsh is one of the largest marshes of the Mesopotamian.
It Al-Badri and Artin (1972) had studied the salinity problem in Tigris and Euphrates rivers and Thurthar lake.They concluded that at future an expected increase in the salinity levels due to upstream increasing water use and disposal and due to the Turkish activites proposed a case which observed later.Buras (1972) had proposed an optimum management of water resources for Iraqi marshes for a better water quality..  Nicholson et. al,(2002), andClarck et. al,(2001) had conducted an environmental study of Iraqi marshes and pointed out the negative effect of the drying process.Iraq Foundation (2003) had studied the scientific bases for marshes restoration in Iraq.Richardson and Hussain (2005) had conducted an ecological study for the Iraqi marshes and pointed out the importance of water quality to the eco-system of these marshes.Farhan (2005) had reported the importance of water quality for marshes restoration.
The construction of Maissan River with dykes along its sides was the main action performed by the past regime for conducting a drying process for the central marshes..The alignment of this river prevents water of the Tigris three tributaries Al-Areed, Al-Bittera and Al-Majar Al-Kabeer from entering the central marshes.The proposed restoration process is to remove or break these dykes to allow the water to enter the marshes.Therefore the control of this river water quality is important for this restoration process.The problem of the high salinity level of the dried soil of the marshes left after the drying process is an important issue; hence, the proper control of the salinity and other environmental parameters will improve the water quality in Maissan river and will have an important role on the quality of the water used for the restoration process.Since at the upstream side of each of the three rivers Al-Areed, Al-Bittera and Al-Majar Al-Kabeer there exists a regulator , which can control the released flow.An optimization model could be adopted to find these optimum releases to get the best water quality in Maissan river, and then the best water quality of the water entering the marshes for restoration.In this research , a proposed optimization model was used for this purpose.This model is a modified one of that proposed optimization model used by Al-Suhaili and Hraze (2006).The modifications made herein from this model are the use of additional flow and water quality measured data of these rivers (2006)(2007)(2008)(2009)(2010)(2011), in addition to the original set used in the former model (1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005).This modification impose changes in the constraints used for the optimization process.Moreover the proposed solution of the new model is the use of Genetic Algorithm instead of the general search method.Furthermore the estimation of monthly demands along the mentioned three rivers was also extended to the new period added.Moreover the model analysis was extended for three scenarios (S1: using obtained average monthly water quality parameters as Electrical Conductivity EC, Total Dissolved Solids TDS,Biochemical oxygen Demand BOD, Dissolved Oxygen DO, and pH.), and Scenarios S2 and S3 with 10% and 20% increase in EC,TDS,and BOD, respectively.The adopted acceptable limits are 1500,1000, 6,4 and 7, while the penalty factors are 1,0.8,0.8,0.8,and0.2 for EC,TDS,BOD,DO,and pH respectively

The Proposed Optimization Model:
The proposed optimization model is to minimize the water quality function represented by the following function:

During normal years
Where: Acceptable limit of water quality parameter k. = k p Relative penalty weight for the k quality parameter.
For the upper limit acceptable concentration of the water quality parameter k p will be positive and: For the lower limit acceptable water quality parameter k p will be negative,and: J= 1, 2, 3 ….12,represent the month starting from October and ending at September, respectively, as the water year of Tigris river.Qi, j: are the optimum water release from the river i, at the month j.
Di, j: are the demand along the river i, at month j for the area located between the upstream of regulator to the location where the river i, enters Maissan river.Qi, j min: are the minimum flow from river i at month j(Dry Year).
Qi, j max: are the maximum flow from river i at month j(Wet Year).
Qi, j ave: are the average flow from river i at month j(Normal Year).
Ci, j, k: Is the average values of the river i, at month j of the k water quality parameter.

Demand Analysis:
The demand data were collected from different authorities that had conducted demand calculations during the most recent years (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011).These data were collected from the demand sheets recorded by the general management of water resources, and the office of environmental of Maissan governorate (unpublished records).Table (2) shows the estimated demand values for the three rivers.

WATER QUALITY DATA USED IN THE OPTIMIZATION MODEL:
The available records of the water quality data for Al-Areed, Al-Bittera and Al-Majar Al-Kabeer rivers are inadequate for the purpose of the proposed optimization model.Hence, a water quality-testing program was conducted in some selected points to get the required additional data.
The criteria of the selection adopted for those points is for each river two points were selected at the upstream side (downstream of the regulator existing on the river), while the other point is at the downstream side of the river, just before its outfall to Maissan river.The water quality parameters gathered are TDS, EC, pH, DO, BOD water temperature and air temperature.Tables (3), ( 4) and ( 5) show the measured and estimated average monthly values of (EC, TDS, BOD, DO and pH) for Al-Areed, Al-Bittera and AL-Majar Al-Kabeer rivers respectively.

APPLICATION OF THE OPTIMIZATION MODEL:
In this study, a MATLAB program was used to find the optimum flow values for Al-Areed, Al-Bittera and Al-Majar Al-Kabeer rivers using genetic algorithm optimization .The optimum flow values and the objective function are obtained for the three scenarios and the three flow cases wet , normal and dry years.Tables (3,4,  and 5) show the water quality parameters for scenario S1,while tables (6,7, and 8) show these values for scenario S2.For scenario S3 these values are shown in tables (9,10, and 11).Hence the total cases analyzed are 9 cases S1(Wet, Normal, and Dry),S2 (Wet, Normal, and Dry), and S3 (Wet,Normal, and Dry).

RESULTS AND DISCUSSION:
For the optimization process a MATLAB code is written.The adopted cross over and mutation rates are 0.8 and 0.2 respectively.The number of population is found by trial and error procedure until obtaining a stable optimum solution.It is increased from 100 to 1000 in a step of 100, at 1000 a stable solution is found .Table(12) shows the optimum monthly flow values for the three rivers for Scenarios S1 for the three flow cases.Figures (4,5, and 6) show these values with the adopted average water quality parameters and the estimated flows and demands.It is shown that in general as the flow case changes from wet to normal and dry year the optimum flow decreases.Table(13) shows the optimum monthly flow values for the three rivers for Scenarios S2 for the three rivers with the three flow cases.Figures (7,8, and 9) show these values with the adopted 10% increase in water quality parameters (EC,TDS, and BOD)and the estimated flows and demands.It is shown that in general as the flow case changes from wet to normal and dry year the optimum flow decreases.Table(14) shows the optimum monthly flow values for the three rivers for Scenarios S2 for the three flow cases.Figures (10,11, and 12) show these values with the adopted 20% increase in water quality parameters (EC,TDS, and BOD) and the estimated flows and demands.It is shown that in general as the flow case changes from wet to normal and dry year the optimum flow decreases.Table(15) shows the obtained minimum objective function for the 9 cases adopted in the analysis.It is shown that the values do not exhibit a certain trend with the changes of flow case or the change in the scenario.
2. The demand analysis indicates low variation with little increase in summer months.
3. The Genetic algorithm optimization model that use a 0.8 and 0.2 cross over and a mutation rates, required a minimum population of 1000 to obtain a stable optimum solution.
4. In general as the flow case changes from wet to normal and dry year , the optimum flow values required decreases, however for few months sometimes the optimum flow for normal year exceeds the corresponding value for the wet year.This conclusion is true for all of the three scenarios analyzed.
5. The comparison between the optimum monthly flow values for different scenarios for a given case flow , indicates in general the highest flow are for S3,however it is not always the case since so many values exhibits high flow values for S2 and/or S1. 6.The minimum observed objective function obtained for the 9 cases analyzed exhibits no certain trends with the change in case flow or with the change in the water quality scenario.

Al
consists of interconnected small marshes.The central marshes are bounded by Tigris river to the east and the Euphrates river to the south.The central marshes are roughly located between Nasiriyah, Maimona, Qalat Saleh and Al-Qurna Cities, and cover of about 3000 square Kilometers during flood season.This area reduced to 600 square Kilometers during normal season.The main sources of the water for the central marshes are the Tigris river tributaries within Ammara governorate.These tributaries are Al-Areed, Al-Bittera and Al-Majar Al-Kabeer rivers.Figure (1) and (2) shows the Mesopotamian marshes before and after the drying process respectively, (Al-Suhiaili and Hraize‫و‬ 2006).

Firas
reservoir.Mussab(1998) had presented an optimization model for Saddam and Dokan reservoir and their effect on Tigris River water Quality.Hassan(2001) had pointed out the environmental effects of marshes drying process.
Examination of those data indicates a remarkable decrease in the available water for Al-Areed, Al-Bittera and Al-Majar Al-Kabeer rivers as shown in figure (3).Hence, the flow data for the first six years were excluded and the analysis were performed on the flow of the most resent years (2000-2011), for the three rivers.If we, consider the flow data as normally distributed with mean value µ and standard deviationσ , so the data can be divide into three categories for each river.I. Normal year: represents the average of flow values that Figure(13) shows the comparison between the obtained optimum flow values for each of the three rivers, for Scenario S1, for wet, normal and dry years .It is found that the dry case flow gives the minimum flow values, while the maximum values are obtained for the wet year flow cases, the normal flow case are in between the wet and dry values ,however some few values exceed the corresponding values for the wet case flow.Figures(14 and 15) show the comparison between the obtained optimum flow values for each of the three rivers, for Scenarios S2, and S3 for wet, normal and dry years .Similar observation can be deduced as those for Figure (13).
Figure(16) shows the comparison between the obtained optimum flow values for each of the three rivers, for a wet year and the different scenarios.It is observed that for scenario S3 the optimum flow are almost the highest, however for few monthly optimum flow it becomes lower than that for S2 and/or S1 flow values.Figures(17 and 18) show the comparison between the obtained optimum flow values for each of the three rivers, for a normal and a dry year respectively and each for the different three scenarios.Similar observations can be deduced as those observed from Figure(16).

Fig( 14 )
Fig(14) Optimum Flow for the Three Rivers for Wet , Normal and Dry Years,for Scenario S2.

Fig.( 17 )
Fig.(17) Optimum Flow for the Three Rivers for all Scenarios for Normal Year Flow.