Assignment # 8 : Water water everywhere but not a drop to drink.

Neelakantan TR, Pundarikanthan NV (2000) “Neural network-based simulation-optimization model for reservoir operation,” Journal of Water Resources Planning and Management, 126(2) pg. 57-64.

Summary

This paper aims at solving the water supply problems of the city of Chennai India by proposing a reservoir operation policy that has been optimized using a back program neural network as a subprogram with Hooke's and Jeeves main model. The city of Chennai is a metropolitan city located at the south of India at the East coast facing the Bay of Bengal. This city is the home of 4.5 million people. The city gets its water supply from three reservoirs which are fed by three different rivers. The city receives rainfall from the returning North-west monsoon in the months of November and December. The rainfall most of the times is not enough to refill the reservoirs. Periods of droughts and drinking water shortage are common in the city. Sometimes industries have to shut down to meet the city's drinking water needs. At times of water shortage water is transported to locations by rail and water trucks. To improve this situation of water shortage it is proposed to bring water through an open channel from the river Krishna which is a perennial river flowing in the neighbouring state. Two more reservoirs are also to be constructed to accommodate the access water.
For this particular problem we are considering deficit indices. Its now a well established fact that the city is facing shortage of water during the drought periods. During the periods of drought there is going to be deficiency but the it is preferred that the deficit is spread over a long duration with lesser magnitude. A sequence of deficit should be such that it gives a minimum of sum of the squared deficits which is than termed as the deficit index. Deficit index is also an important term while measuring equity at the reservoir level. Equity can be achieved by maintaining the deficit ratios of terminal reservoirs as 1:x2 where 1:x is the ratio of demand for the two parallel reservoirs. For single terminal reservoir the deficit in the time domain is taken as outcomes. For multiple terminal reservoirs to achieve equity scaled deficit indices that is computed from the percentage of deficit with respect to target and this is used to compute the objective function. Thus the objective is to minimize the overall deficit in a way so that the equity is maintained and the deficit indices of the terminal reservoirs are minimized individually.
A back program neural network is used as the simulation model that describes the system. The model includes constraints like canal capacity, minimum storage, evaporation losses etc and the management decision variables include the storage capacity of the different zone of the reservoirs which has to be controlled in a way such that it minimizes deficit and maintains constraint. The back program neural network maps the input vectors to output vectors, it doesn't have a feedback connection but errors are back propagated during training. Training includes adjusting the weights between the layers and recalculating the output in an iterative process and continued till the error is below the tolerance level. Pairs of input and output vectors in this case deficit index values are chosen to train the network . Once training is completed and the weights are fixed the network can be used to determine outputs for new value of inputs. The simulation is linked with the Hooke's and Jeeves model. The simulation model passes different configuration of the management decision vector and receives back a value of the objective function. Based on the new value of the objective function the Hooke's and Jeeves model decides to move to the new configuration of the management decision vector. This is repeated until no further improvement is possible.

Discussion

Based on the climate of the locality the a year is divided in 6 time periods and in each time period the release target values are the same. Thus for six time periods there are 3 storage values that makes it 18 decision variables. So there are 18 input units in the neural network and deficit index is the output index. A 100 starting policies are considered and for each starting point the local optimum is obtained. The best policy and few optimal policy that give close to optimal results is selected. The Simple Operating policy (SOP) gives optimum results when we are trying to minimize the deficit. In the case of SOP however there is no saving water for future times. In case of the optimal operating policy proposed by the model much consideration is given to storing water by rationing the water supply and thus storage is more but there will be looses due to evaporation. Due to the new reservoirs being shallow it doesn't improve the system performance in terms of reducing the deficit but it helps to reduce the spill.
The use of a neural network made the time required for computation much less compared to a conventional simulation model. Thus by selecting the neural network an added advantage is obtained in terms of computation time. However training the neural network requires considerable time.
This paper was the first paper we read on neural networks. To comment about it one needs to know what and how are neural networks developed so in this point I have limited knowledge about the process so I will just say that it is good to know that such kind of algorithms can also be used to solve problems related to water resources. However I am keen to know if this solution was actually able to solve the problem of water scarcity in the city of Chennai. To me this paper is an attempt to justify the use and performance of back propagation neural network model than to solve the issue of water problem. At the beginning of the paper the author describes various incidents of water problem in the city and I know they are true because I have lived in the city for an year. The model proposes that building extra reservoirs is not going to improve the system in terms of minimizing the deficit index. I want to raise a question here, is deficit index the only way to optimize a release schedule for reservoirs. The author accounts evaporation loss to be the reason which is difficult to visualize. Here we are increasing the supply so how can it not improve the system.Otherwise I found this paper the most difficult paper that has been asigned to us.

Optimal Location of Infiltration based Best Management Practices for Storm Water management

Pedini-Perez .Christina, Limbrunner.F.James, Vogel.M.Richard(2005). " Optimal Location of Infiltration based Best Management Practices for Storm Water management", Journal of Water Resorces Planning and Management, Vol 131(2005), Pg 441-448.

Summary

 Storm water management in urban areas has become critical in recent times. Development in a watershed results in greater impervious areas which in turn results in greater runoff thus causing flood. Best Management Practices (BMP) are introduced to minimize the effect of watershed development by reducing the peak flow. This paper aims at determining optimal locations of infiltration based BMPs for storm water management by using Genetic Algorithm (GA) in a distributed hydrologic model of an urban watershed. Although detention based water basins are highly effective in controlling peak flows they are expensive to construct and there is no systematic basin wide approach to their implement. This paper deals with infiltration based BMPs which are collectively called as low impact development (LID). To apply BMPs to a watershed it is first modeled as a network of 4553 Hydrologic Response unit (HRU) which can have a BMP. HRUs were modeled as square cells of 120 m. The SCS Curve Number method for calculating runoff is selected to estimate the flow from each HRU unit and it is than directed to the most negative slope. The spatial characteristics of the HRUs like its slope, position and curve number is developed using ARCGIS and the flow connectivity from cell to cell is built using the D8 algorithm. Each HRU drains to a single adjacent HRU and may receive flow from maximum seven upstream HRU’s. The rainfall that falls on a HRU is partly lost as infiltration that enters the ground storage and the rest contributes to runoff that is routed to the adjacent downstream HRU. The flow continues downstream till it enters a stream network. Stream network cell collects water from its adjacent HRU’s and routes it to the watershed outlet with a lag time that is equal to the stream travel time. The BMP is introduced as a binary integer decision variable which says that if a BMP is introduced in a HRU than its curve number will decrease by 5. The model does not consider the type of BMP that is introduced in a particular HRU as a part of the problem. A single type of BMP is introduced in the HRU and it is assumed that implementation costs are same irrespective of land use and surface conditions. This model is calibrated to real time data to estimate values of initial conditions like α1 (scaling term for curve number method) and So ( Storage capacity) and basin parameters like Coefficient of Initial abstraction (α2), fraction of inactive ground water (h) and groundwater outflow rate constant (r). Thus the goal of the optimization model is to locate those HRUs which if BMPs are applied will lead to maximum reduction in peak flow at the watershed outlet. The number of BMPs applied will be equal to the to the total project cost. A GA called Evolver is used to generate different groups of BMP location with the above objective. To minimize the search space the BMPs were restricted to HRUs that had higher curve number and were located further from the stream network. 2629 HRUs were excluded which has marginal effect on peak flow reduction. This model was applied to the Aberjona River watershed a 6400 ha urban catchment located northwest of Boston,Massachusetts.   

Discussions

Project budget reduction and peak flow reduction are considered as separate objectives and a trade off are obtained between the two objectives. A trade off curve was developed which showed the marginal benefits of reduced flood damage as a function of the number of BMPs that are applied. Thus less return is observed in terms of watershed peak flow reduction with increasing number of BMPS applied.  The GA identified four critical regions for our model and as the budget was increased it spread out to other locations which shows that optimal solution are not obtained by merely placing BMPs in HRUs with the greatest impervious areas. The regions in which BMPs have maximum effect coincide with industrial and commercial developments near major highway intersections. The solution generated for a larger budget is not necessarily inclusive of the smaller budget solution but quite near to it. This indicates that the GA may not find the global optimum solution but it helps to identify a wide range of near optimal solutions.  It is important that the solutions be inclusive so that a phase wise implementation of the BMP can be applied as the budget is increased over a period time.An attempt to find the optimal solution of the BMPS without resorting to a distributedhydrologic model and GA algorithm was made. However the relationship between thepeak outflow reduction due to BMP and HRU s characteristics are highly complicatedand dependent upon multiple factors which makes it necessary that we use the above described approach. The approach in this paper is simple and it also makes uses of one of the most commonlyused methods to calculate runoff. This kind of effort can easily be translated into practical uses. The objective is to reduce the peak flow but it also takes care of the budget limits. The solutions for smaller sets are inclusive of the larger set makes it convenient to plan step wise. The BMPs can be applied to critical HRUs first and than when more funds are available BMPs can be applied to less critical areas.  

Sensor Placement in Municipal Water Networks

Berry.W.Jonathan, Fleischer Lisa, Hart E. William, Phillips A.Cynthia, Watson Paul Jean(2005). " Sensor Placement in Municipal Water Networks", Journal of Water Resources Planning and Management, Vol 131(2005), Pg 237-243.

Summary

This paper deals with optimizing the placement of sensors in the municipal water system with the objective of protecting the general population from extreme events of water contamination which can be accidental or intentional. In order to protect the general public from consuming potentially poisonous water the US EPA in collaboration with community water system decided to incorporate real time early warning systems by planting sensors at locations in the network such that it ensures coverage of the networks flow for detection of contamination. The deployment cost should be minimized while maximizing the level of protection. The placement of the sensor is enforced with the objective to minimize the fraction of the population that will be exposed to a contaminant. The event of a contamination is modeled as a fixed probability distribution across the junctions.
The sensor placement problem is solved using a combinatorial optimization formulation considering models that can be solved as integer programs. Several assumptions are made to formulate the sensor placement problem as integer problem. Temporal effects and concentration affects are ignored. Temporal models are very large and difficult to apply to large scale problems. Concentration affects are not relevant in a non temporal model and however less information was known on how contaminant concentration describes contaminant detection. Thus this problem is modeled describing an attack to be single point event while the objective function is defined to minimize the fraction of the population affected by a contamination. The model also takes no consideration about the water patterns in terms of demands. The demand patterns are assumed to be constant. The direction of water is considered while the water velocity is ignored. Each junction is weighed based on the number of people consuming water from that junction.
Thus the problem is formulated using the Mixed Integer Programming. The network is modeled as a graph where pipes are represented as edges; nodes are represented as vertices which can also denote sources and sinks. The input data includes the network structure with its nodes and vertices, the probability of attack at a particular node, the population density at each node, direction of flow and the maximum number of sensor that can be placed. We also have a decision variable for each node which takes the binary form of 0 and 1 which decides if a sensor is placed at a node and a derived variable which decides if the node is contaminated at the event of an attack. The set of constraints ensures the single point attack theory previously discussed, also ensures that a single sensor covers flow in both directions. The other constraints propagate the contamination flow and limit the number of sensors. We also consider integrality constraints so that mixed integer programming can be used.

Discussion

Three networks were evaluated with the model. Two of the networks were example networks derived by using EPANET 2.0. The third network was a real world network. The model also considers changes in population density and attack risks. The results show that the percentage of population that is at risk decreases as we increase the number of sensors. For each dataset different scenarios are considered and the result is summarized as the percentage of population at risk for a specific number of sensors. Also from the evaluation it was shown that change in population density and attack risk did not affect the optimal population at risk however it did affect the configuration of sensor location. From the results it is worthwhile noticing the regime changes with the number of sensor used. The sensor placement sensitivity to noise rises and then drops for a specific number of sensors used. However verifying this regime changes and predicting sensor location is out of scope of this paper. This model gives us the population at risk as the optimized output on an event of contamination. However much is not discussed about the location of the sensors and how the model helps to identify which node the sensor has to be placed. The sensor location should be able to cover maximum part of the network, however in this case the demand pattern is not considered in the model. Also the model considers extreme scenarios like an accident or sabotage as the cause for placing the sensor. It relies on the probability distribution to decide the crucial assets in the water networks. Some events of contamination may take place every day in a water system and the question is will the system be effective enough to monitor such contamination.

Optimal Locations of Monitering Stations in Water distribution System.

Lee.H.Byoung, Deininger A. Rolf.(1992)." Optimal Locations of Monitering Stations in Water distribution System.", Journal of Environmental Engineering, Vol 118(1992).

Summary

This paper shows us an ideal case where integer programming has been used to solve a water distribution problem. EPA requires all drinking water authorities to closely monitor the quality so as to ensure that safe water reaches everyone. Thus sampling stations has to be set up and the location of the station is the criteria as cost is involved in setting them up. The best set of station is the one that maximizes the coverage. The first step is to analyze the flow distribution pattern and determine the pressures which can be easily determined using hydraulic modeling. Each node is associated with a demand and the fraction of the local demand to the total demand defines its coverage. We must therefore select our stations in such a way that they have maximum coverage. Water reaches the sampling station from upstream nodes and flows out to downstream nodes. If the water quality at the sampling node is good it can be safely assumed that the water quality of the upstream node is better than the sampling station. Thus coverage ensures that the water quality at one node can be inferred from measurements taken from another node.
The steps to solving this problem are well explained by considering a small network which consists of 7 nodes where each node is assumed to be the sampling station. The local demands at each node are known. The coverage is determined for the nodes with respect to other nodes. Thus the coverage for each node with respect to other node is determined and termed as water fraction and can be summarized in the water fraction matrix. Than the knowledge carrying matrix is determined from the water fraction matrix. The knowledge matrix determines whether the knowledge from the current node can be carried to upstream nodes or not. The knowledge carrying matrix will be entered as zero if the information from the current node cannot be carried to the upstream node. The next step is to obtain the coverage matrix which is determined from the knowledge matrix by converting all its nonzero entity to one. The optimization statement is simple. We have to maximize the demand fraction for each of the node to be considered as a possible station location and subjected to constraints. Now this simple problem is taken as the foundation and the same principle is applied to solve for multiple real water distribution systems.

Discussion

The first problem solved with the above consideration is of the monitoring stations in a medium sized city called Flint in Michigan. It receives its water from Lake Huron through a pipeline by the Detroit water and Sewerage Board. It has 337 pipes and 211 nodes. At present times there are 14 monitoring stations which cover 18.3% of the demand. This problem was formulated as an integer programming problem with 211 constrains and 422 variables. This problem was computed using two programs and the result was an increase of demand coverage to 54% from the old 18.3% for the new stations. However in real case there are multiple demand patterns which change hourly or daily. Thus demand patterns are identified and for each demand pattern there is a different coverage matrix. Thus the different coverage matrix has be considered for computation.
This kind of procedure was also applied for the city of Cheshire which is a part of South Central Connecticut Water Authority. The pattern of water demand for this system varies significantly over time and has to be taken into consideration. Four significant water demand patterns were selected. The problem had 245 variables and 197 constraints and solved using the LINDO integer programming code. The optimal solution was three nodes with a coverage of 45 % which is better than present 3 locations and coverage of 29.7%.
Thus this paper shows how pure integer programming can be used to solve the problem of locating a sampling station for water quality test. Coverage and demand is the taken as the only criteria for consideration. Cost can be another one which is not considered. However the paper is a demonstration of how integer programming can be used to solve a real problem of deciding locations for a sampling station in order to get better solution.

The Tragedy of the Commons

Hardin Garret.(1968)," The Tragedy of the Commons", Science, Vol .162(1968):1243-1248.

According to the author of this article there are certain problems that don’t have solutions that could be reached by applying technology. This genre of problems has more of human values and morality attached to it that cannot be gauged by using technology. Thus this type of problems can be classified as problems with no technical solutions. Such are problems that have no straightforward conventional solution. The population problem is one such problem which cannot be solved by using a technical approach.

Population growth is seen as exponential and if we consider our resources to be limited than a finite source can support us only if population growth tends to zero. This condition cannot be fulfilled because that would mean that the human race survive merely to stay alive and cut down on any activity that incorporates extra energy. The human race is not programmed to live life for the mare sake of existence. Our kind likes to explore new opportunities and search for new quest. Thus given a finite source of energy the population problem cannot be solved by applying technical methods. Thus when it comes to the population problem the optimum solution is something that is less than the maximum. How much less and what is a good number is difficult to comprehend because it doesn’t have a common basis or any standard comparison. The problem remains unsolved because we haven’t seen any population that has attained zero population growth but we need exercise control on population by some means because in most cases we have seen that the world’s fastest growing population are the ones that are in miserable condition.

After much consideration it is seen the root cause of such problems are related to something which the author calls the tragedy of the commons. This is a situation where an individual thinks good for him and his cumulative actions ruins the society in which he is also a part. It is like a vicious cycle where each individual thinks for momentary benefits for him and his family but his decisions causes him to suffer as a part of the society. The pollution problem is one of them. Each individual thinks that it is profitable for him to discharge untreated waste into a river which belongs to the commons thereby polluting it. His momentary benefit causes him and others to suffer as the source of water is polluted and rendered unusable for future. Thus freedom of the common brings the tragedy. This may be controlled by imposing taxes and taking proper control measures at the administrative level but again the administrative body consists of men who are liable to corruption.

The author points out that some of the measures taken to control the population have been rendered futile because one needs to understand the human society and its psychology before appealing to control population. Ours is a welfare state where there is a freedom to breed and every born has an equal right of survival. Such a policy is dreadful. A combination of freedom and welfare causes it impossible to control population and such are the policies that are endorsed by the world’s largest welfare organization “The United Nations”. One must see the loopholes of such a decision and understand its implications. Another failed approach has been appealing to conscience. There will be a mixed reaction, some will yield to it and some will not. Seems like those who don’t yield will produce more offspring’s and they in turn form larger part of the population with a conscience that does not yield to appealing. One can see this is a futile approach to control population. It is like the one who responds to the appealing is at the greatest disadvantage while others reap benefits from exploiting the society. His solo action gets him no profit and also doesn’t benefit the society.

So can such problems be controlled by force? In today’s world any forceful action even though rightful may be considered not appropriate. Thus a forceful action which is non voluntary but has been approved by all can be applied. Like in the case of taxes, we don’t like to pay taxes we complain and wish we don’t have to pay taxes but we also agree that it is for the betterment of the society and although involuntary we do end up paying taxes.

The evil of the commons exist in many social problems of today. One has to carefully analyzed them. We must exercise our freedom responsibly and understand that in certain cases we need to curb the freedom of commons to get a better society. Thus the population problem can be controlled if we curb the freedom to breed. This may sound very controversial to many and one may argue it from humanitarian and religious aspects but this is a basic and most fruitful solution. It is role of education to expose this idea so that at one point it will be mutually agreed upon and we may finally overcome the evils of overpopulation.

This article is an interesting collection of solid facts which are right in front of our eyes but we tend to overlook them probably because of their simplicity. I come from an overpopulated country which has like the highest population density and being the victim of overpopulation I do agree it is required that we control the rate of breeding. One can understand the storm of controversies that will be created as we even think of such a possibility but the question is how long can the human race survive with the pressure of this ever increasing population? It will be interesting to think of probable means by which a check can be imposed on the freedom to breed and also survive the wave of protest that will follow.

Hydraulic Gradient Control for Groundwater contaminant removal

Fisher Atwood D, Gorelick S.M.(1985)." Hydraulic Gradient Control for Groundwater Contaminant Removal", Journal of Hydrology, Vol 76(1985) 85-106.

Summary

This article provides the insight as to how linear programming was used to optimize the selection of wells for groundwater purification. The Rocky Mountain Arsenal near Denver Colorado was selected as the site for groundwater purification. The Arsenal which is a military base also process toxic chemicals. Poor disposal techniques over decades have resulted in contamination of the water table. A system of wells removes contaminated water. The optimization routine selects the best wells and their pumping and recharge schedule while controlling the hydraulic gradient.

Much of the study at the initial stages was concentrated to determine the hydrological parameters like the hydraulic head distribution, transmissivity, effective porosity and storage coefficients of the Arsenal. The key requirement of the groundwater pumping is that it should be hydraulic gradient controlled. This prevents the contaminant plume boundary from migrating beyond its original boundaries. If there is no hydraulic control while pumping studies showed that over the years the plume will move outside the model area selected for the study. However optimization for hydraulic control introduces non-linearity to the problem and thus it could not be solved in a single linear programming attempt. The pumping/recharge rate which is a decision variable which is unknown. The groundwater velocity is also an unknown and the non linearity is introduced by multiplying unknown velocities and concentrations in the advection dispersion equation. Thus a two step process was introduced to deal with the non linearity issue.

The first stage consisted of tracking the plume boundary. This was done by assuming a velocity vector as the true velocity is an unknown. This was derived by observing the effects of a successful hydraulic control. The speed at which a contaminant is removed depends on the number of the pumps, their placement and the pumping rates. So next the location of the most effective well was identified. The plume geometry is derived from experimentation. The second stage consisted of identifying optimal well selections and rates. The objective was to minimize the pumping rates. The hydraulic gradient control is the first constraint. The pumping rate and the non negativity of the velocity vectors are the other constraints. The process was to be completed in equal length time periods of pumping and each time period was associated with a certain specific position of the plume. A time period of 18 yrs was identified to complete the process and further divided in 8 yrs and it consisted of a total of 32 pumping periods. During trial runs proper location of wells were selected by mixed integer programming. Drawdown responses for each well location was derived and converted into a gradient. The resulting constrain matrix was evaluated with a convergence criteria of 1.10^-9 was solved using MINOS.

Discussion

The two stage optimization problem was solved by two optimization technique’s namely global optimization and sequential optimization, and comparisons were drawn between the two techniques. The sequential strategy would require periodically updating the plume configuration and determining new well locations for management problem 2 but for an accurate comparison identical well locations were used. The result from global optimization showed that recharge rates are relatively high for the first half year. Than the rates drop in the next 1 to 2 yrs thus indicating that lower rates are suitable for maintain the inward hydraulic gradient. As the target gradient increases with time for the rest of the management stage 1 the recharge rates show a steady rise. The results of the management problem II differs in case of global optimization from the first period. For pumping rates there is a steady rise but however this is not the case with recharge rates. For the last pumping period the pumping or recharge rates increase or decrease dramatically and there is an uncertainty in the explanations. The result from the sequential optimization differs from that of the global optimization. The well selection and pumping schedules are different. For stage I the entire hydraulic gradient is controlled by recharge wells alone and pumping wells are used only during the second stage. However the cumulative rates show that the global solution is better than the sequential solution. Although the values are mostly same during stage I they differ in stage II. The global rates are much less at the last stages of the pumping period. However other criteria like economic and social if considered might give sequential method an edge over global method.

The process described for the Arsenal ground water purification is general and can be applied to other locations as well. A future line of work for this model could be by introducing constrains related to economy and other factors affecting the system. It would be interesting to see and compare the results from the two optimization techniques.

Water Supply Planning Simulation Model Using Mixed Integer Linear Programming "ENGINE"

Dean Randall, leasa Cleland, Catherine S Kuene, George W Link, Daniel P Sheer.(1997) " Water Supply Planning Simulation Model Using Mixed Integer Linear Programming "ENGINE"" , Journal of Water Resources Planning and Management , Vol 123 pp 116- 124

Summary:

The purpose of this paper is to describe the development of a water simulation model that uses a mixer integer Linear programming approach and to show that this approach is superior to other network formulations. The model was developed for the Alameda County water district of California which supports consumers of cities like Fremont, Newark and Union city with a demand of 159 million Litres/day. The approach described in the paper has an linear program embedded in the system that acts as a router to direct water into the system for each time step. The use of LP allows certain constrains to be handled easily without iterative approach thus reducing the solve time as compared to network formulation.
The Alameda County water district (ACWD) imports 85% of its water from Sate Water Project (SWP) and San Fransisco Water Department (SFWD) and the rest 15% comes from it local resources. Irrespective of its consumption ACWD pays fixed rate to SWP and SFWD. Thus it becomes necessary for ACWD to use maximum from its allocation. Moreover ever increasing water demand , changing state regulations has made it a necessity that ACWD makes best possible use of its supplies or else it will fail to meet its ever increasing demand.
The storage in ACWD is both in the form of surface reservoirs and two ground acquifiers. A percolation pond feeds to the two underground basins. The surface water resource has lower and upper bounds. The region from level 0 to lower bound is called the dead zone. Thus one of the primary constrains is that the water should not be supplied from the dead storage. The water level is allowed to recede to the dead storage only by evaporation. Thus the Creek water is diverted to the percolation pond or the reservoirs based on dry or wet period and this is done by inflatable dams. Inflatable dams direct water into the percolation pond which feeds it to the two underground water basins when the flow is exceeded. Dams are deflated when the flow recedes. Also there are 2 treatment plants. Because of high hardness content the SWP water is mixed with ground water to meet water quality standards.
Node arc nomenclature is used to develop this model where a node is point of interest like a reservoir, diversion point, demand and arc is any flow of water like an hydraulic connection , stream or a reach. The objective function for the LP was designed based on priority assigned to decision variables. Its a weighted approach that allows more flexibility and operational control. There were both positive and negative values assigned. positive values encourages an operation and vice versa. The priorities are as follows

1. Meet all demands.
2. Recharge the ground water as much as possible.
3. Keep water in surface/reservoir storage.
4. Use surface supplies rather drawing down from aquifers.
5. Minimize spill on Alameda creek.
6. Minimize pumping and treatment costs.

The LP is designed such that water is pumped based on these priorities which are also the decision variables. Thus maximum water flows to the facility that has highest priority. The constrains were listed and two special constrains primary the Alameda ground water recharge based on flow and blending water at the treatment plant to maintain the quality was incorporated to the LP. Thus the priorities combined with the constrains make the model more realistic and feasible.
The ACWD model was developed in C programming using the XA Callable library. Each LP had 50 constrains and 85 variables. It was written in a modular form so that changes can be incorporated later. The first step was to evaluate the potential magnitude and frequency of shortages from the year 2000 to 2030. The best case scenarios were developed and grouped as best middle and worst case scenarios. The model was run for each set of assumptions for different demands in different years. It was seen for the current capacity ACWD will fail to meet its demand by 2010. The model was tested with various alternatives and combinations to eliminate seasonal capacity constrains and decrease the magnitude and frequency of drought year shortages.

Discussion

Several alternatives from different prospective were considered to obtain the best result.

1. Supply side alternatives

• Additional storage: Enhancement of ground water recharge capability, construction of surface reservoir whose size was optimized by the LP.
• Water Reclamation: Using reclaimed water reduced the possibility of a drought.
• Ground water desalination: The desalination facility size was considered for optimizing water supply benefit.
• Treatment plant modifications: The capacity of the current treatment plant was increased until peak season shortages were eliminated.
  
• Water Purchase: Water purchases in the drought year from area irrigation district was considered profitable

2. Supply side operational alternatives:

• Water quality variations: Increasing hardness from base hardness of 150 ppm to 175 ppm eliminated peak season shortages.
• Conjunctive use variations: SFWD demand was decreased in off peak demand months and increased in peak demand months.
  
• Ground water management alternatives: Several ground water management alternatives were run to optimize min and max ground water levels.
  

Several demand side alternatives were also considered. This paper is a good example of how to approach a water resources problem using linear programming. The model can be used as a base to approach other water systems and there is a brilliant scope of future work.