Table of Contents          Next Section

METHODS OF ANALYSIS AND APPROACHES TO SIMULATION

OVERVIEW

The application of simulation methods to the historical reconstruction analysis (specifically the application of EPANET 2) using the specific network data for the Dover Township area was accomplished in two steps. First, hydraulic modeling was conducted whereby average network conditions were simulated for every month of the historical period (420 simulations). These simulations were completed under balanced flow conditions that honored hydraulic engineering principles and that conformed to the "Master Operating Criteria" (Table 4). Second, using the results of the monthly network hydraulic simulations, water-quality simulations (source-trace analysis) were conducted for each water source (point of entry) of the network in order to determine the monthly proportionate contribution of source water at all locations in the Dover Township area serviced by the water-distribution system.

Routinely, simulation of water-distribution systems, similar to the historical water-distribution system that serviced the Dover Township area, would require detailed descriptions of system operations, such as the on-and-off scheduling of high-service and booster pumps and groundwater wells for the entire period of simulation. In order to simplify these rigorous data requirements, a surrogate or alternative method was devised. Balanced flow conditions were maintained, and the measured volumes of monthly water production were used while avoiding the need for detailed system operations data, which were not available for most of the historical period. This surrogate method is described in detail in the following sections.

With respect to the scheduling of groundwater well operations, EPANET 2 utilizes "pattern factors" which correspond to the hourly operations of supply wells¹². These pattern factors along with the operational extremes of storage tank water levels were manually adjusted during each of the 420 monthly network simulations to achieve balanced flow conditions. This approach to simulation is designated in this report as the "manual adjustment process." All simulation results presented in the "Historical Reconstruction Analysis" section of this report were obtained using the "manual adjustment process."

A second simulation approach was also utilized to achieve balanced flow conditions for each of the 420 monthly networks of the historical period. This approach to simulation is designated the "genetic algorithm" or "GA optimization" approach and is an automated objective simulation technique. The GA simulations utilized the balanced flow conditions obtained by the manual adjustment process as starting conditions. Genetic algorithm techniques were utilized to simulate alternative and possibly optimal water-distribution system operations and to assess the effects of variations in system operations on the results of the proportionate contribution simulations. Results achieved using the GA optimization approach are presented in the "Sensitivity Analysis" section of this report.

HYDRAULIC MODELING

Simulation of water-distribution system hydraulics can be conducted by solving mathematical equations that characterize the physics of water movement through the pipeline network of the water-distribution system. Details of the mathematical formulation and solution technique can be found in numerous references including Bhave (1991), Lansey and Mays (2000), Todini and Pilati (1987), and the EPANET 2 Users Manual and, therefore, will not be repeated here. Requirements for model input data properties using the EPANET 2 software are also provided in the EPANET 2 Users Manual, and are specifically described for the present-day (1998) water-distribution system serving the Dover Township area in Maslia et al. (2000a p. 31).

Network hydraulic models can be used to analyze systems where demand and operating conditions are either static or are time varying. The former type of model is a "steady-state" model, and the latter is referred to as an "extended period simulation" or EPS model. Data gathered in the Dover Township area during March and August 1998 (Figure 4) clearly show the time-varying characteristics of the diurnal-demand patterns. Additionally, observations by ATSDR and NJDHSS staff of system operations during these field-data collection activities also indicated the time-varying characteristics of system operations (on-and-off cycling of wells and high-service and booster pumps). Therefore, all network simulations representing the historical period were conducted as EPS models. Each simulation was conducted for a representative (or "typical") 24-hour period and corresponded to a single month of the historical period. One-hour hydraulic time steps were used to achieve a balanced flow condition and a successful system operating schedule that met the "Master Operating Criteria" (Table 4). To assure that stationary water-quality dynamics were simulated (i.e., "dynamic equilibrium" was reached), the 24-hour operating schedule, which resulted in a balanced flow system, was extended to simulate a period of approximately 1,200 hours. For this extended simulation, the "Master Operating Criteria" requiring the ending water level to equal the starting water level in storage tanks (Table 4) was of critical importance. If this criterion was violated, then, at the end of 1,200 hours, the storage tanks would either be depleted of water or would overflow, causing an unbalanced flow condition and an unsuccessful system operation. Additional details regarding conducting simulations to achieve stationary water-quality dynamics for the present-day (1998) water-distribution system are provided in Maslia et al. (2000a).

To conduct the historical simulations, model parameter values input to EPANET 2 required variation that reflected the change in the historical data. For example, data documenting the installation year of network pipelines were available on an annual basis (Appendix A and Plates 3–37) and thus, model parameters describing the pipeline network were modified in the EPANET 2 simulations on an annual basis. Data documenting water production were available on a monthly basis (Appendix B) and thus, EPANET 2 model parameters associated with production were varied for each month of the historical period simulations. For other model parameters, such as the on-and-off cycling of wells, data were not available throughout the entire historical period (Table 12). Quantitative estimation and qualitative description methods (previously described in the section on "Data Availability, Quality, Methods, and Sources" and in Table 12) were used to derive values required to conduct the EPANET 2 simulations. A summary of model parameters, data availability, and the time-unit variation required to conduct the historical reconstruction simulations using EPANET 2 is provided in Table 13.

Table 13. Summary of model parameters, data availability, and time-unit variation for historical reconstruction analysis, Dover Township area, New Jersey

Representation of Wells, Storage Tanks, and High-Service and Booster Pumps

As noted previously, a surrogate method was used to simulate historical operations of groundwater wells and storage tanks linked to high-service and booster pumps. For the Holly, Parkway, and Windsor treatment plants¹³ (Figure 3 or Plate 2), the actual network consists of a groundwater well (or wells) pumping water and discharging the water into a storage tank. Then high-service or booster pumps discharge water from the storage tank into the distribution system based upon some predetermined operating schedule and demand requirements.¹⁴ This physical or "real-world" representation is shown in Figure 19A and was the method used to represent the distribution of water during simulation of the present-day system (Maslia et al. 2000a). This method is referred to as the "Well-Storage Tank-Pump" or WSTP simulation method and the corresponding distribution system is referred to as the WSTP system. Using this method (Figure 19A) to calibrate the model to present-day conditions required the following information:

• known operating schedules for groundwater well on-and-off cycling;
• observed storage tank water-level variations;
• realistic high-service and booster pump-characteristic curve; and
• known operating schedules for the on-and-off cycling of high-service and booster pumps.

Because data describing this information were available for the present-day system, simulation of the 1998 water-distribution system (Maslia et al. 2000a) was accomplished by using the WSTP simulation method.

Hourly operations data for the historical water-distribution systems are limited and, for most of the systems, such data are not available (Tables 12 and 13). Additionally, the model parameter that is of interest to both ATSDR and NJDHSS is the proportionate contribution of water from wells and well fields to locations throughout the historical pipeline networks. Thus, the distribution of water delivered to the pipeline locations was the item of interest rather than the specific operation of the WSTP combination which delivered the water. In order to simplify the simulation of the WSTP combination and, thus, reduce data requirements for simulation, a method of idealizing the WSTP combination was developed—designated the "Supply-Node-Link" or SNL simulation method. The SNL method eliminated the need for including the storage tank and high-service and booster pump combinations in the historical simulations. The corresponding water-distribution system is referred to as the SNL system. The Holly, Parkway, and Windsor Avenue treatment plants were represented in historical water-distribution system simulations using the SNL method.

To replace the WSTP method with the SNL method using EPANET 2, the WSTP system was idealized as shown in Figure 19B. Ideally, if measured hourly data for the high-service or booster pumps were available for the historical water-distribution systems, the total flow in surrogate link K over a 24-hour period (Figure 19B) would be equal to the total flow through link J over a 24-hour period from high-service or booster pumps P₁ and P₂ (Figure 19A)¹⁵. Accordingly, flow discharged to the distribution system by supply nodes S₁, S₂, and S₃ (Figure 19B) to meet demand should be equal to the flow that would have been supplied by pumps P₁ and P₂ shown in Figure 19A.

As previously discussed, groundwater-well production data were based on measurements using in-line flow meters at each well and were available for every month of the historical period (Appendix B and Table 13). These data are considered to be highly reliable. Supply from high-service and booster pumps, on the other hand, was estimated from notes provided by the water utility. These data were not available for most of the historical period (Table 9), and for the most part, were not obtained by direct measurement (Table 12). Accordingly, measured groundwater well production data were used as surrogate indicators of supply to the distribution system at sites where supply wells and storage tanks were linked to high-service and booster pumps, and the less reliable high-service and booster pump supply and operational data were used as guidelines.

Referring to the schematic of the WSTP or "real-world" simulation method shown in Figure 19A, production wells W₁, W₂, and W₃ are shown linked to a storage tank which, in turn, is connected to the distribution system through high-service or booster pumps P₁ and P₂. The production data listed in Table 14 for example wells W₁, W₂, and W₃ are for an arbitrary month of 31 days. The average daily operation for each well was computed using Equation (1). Note that the total monthly production for the distribution system was 41,217,000 gal. Continuing further with this example, using operational notes provided by a hypothetical water utility, supply volumes were computed for high-service or booster pumps P₁ and P₂, and these data also are listed in Table 14. The assumption was made that pumps P₁ and P₂ were operated in the same manner over the course of the month. Note that groundwater well production for the month (41,217,000 gal) exceeds high-service and booster pump production (39,060,000 gal) by 2,157,000 gal.

Table 14. Production and supply data for a hypothetical distribution system
[—, not applicable]

Referring to the schematic of the surrogate SNL simulation method (Figure 19B), the wells, storage tank, and high-service and booster pumps are eliminated and replaced by "supply nodes" S₁, S₂, and S₃. The number of hours that the combination of supply nodes S₁, S₂, and S₃ must operate in the model just to meet demand supplied by pumps P₁ and P₂ (39,060,000 gal in this example) had to be determined. Thus, consider the following equation:

where:

T_S = time of operation for supply nodes, in hours per day;
^QW_i = monthly production from the ith well, in gallons per month;
^CP_j = rated capacity of the jth high-service or booster pump, in gallons per minute;
nw = the number of groundwater wells producing water for the month;
np = the number of high-service or booster pumps supplying the distribution system for the month;
T_m = number of minutes per hour (60); and
T_d = number of days per month (for this example, 31).

The groundwater-well production and high-service and booster-pump capacity values from Table 14 are now substituted into Equation (11). Therefore, the average number of hours per day the supply nodes (S₁, S₂, and S₃) were operated to meet demand can be computed as:

Having determined the total number of hours per day of supply node operation, the volume of water supplied by the SNL system to the water-distribution system from individual supply nodes (S₁, S₂, and S₃) must next be computed. Although alternative methods of computing these volumes are possible, the method chosen for this investigation utilizes the pattern factor variation capabilities of EPANET 2.

As an initial estimate, each supply node in the SNL system was assumed to have operated for the same number of hours and to have supplied the same volume of water assigned to the corresponding groundwater well in the WSTP system. Thus, using the values listed in Table 14 for the groundwater wells W₁, W₂, and W₃ as initial estimates:

• Supply node S₁—operated daily for 10.0 hours supplying the distribution system with 13,020,000 gal during the month,
• Supply node S₂—operated daily for 9.45 hours, supplying the distribution system with 14,061,000 gal of water during the month, and
• Supply node S₃—operated daily for 7.6 hours, supplying the distribution system with 14,136,000 gal of water during the month.

However, according to Equation (12), the combined daily time of operation (T_S) for supply nodes S₁, S₂, and S₃ was 15 hours. Therefore, in the SNL method, for the supply nodes to supply the equivalent volume of water over a 24-hour period per the operation of wells W₁, W₂, and W₃ in the WSTP method, the hourly operation of the individual supply nodes have to be modified. In EPANET 2, this was accomplished by using a pattern factor (the default value in EPANET 2 being 1.0). The modified pattern factors for each supply node of the SNL system—reflecting a combined total of 15 hours of operation—were computed according to Equation (13):

where:

PF_j = Pattern factor for supply node j (dimensionless),
^Tavg_i = average time well i operated, in hours per day (Table 14),
T_S = total time of operation for supply nodes, in hours per day (Equation (11)),
nw = number of wells operating (Figure 19A), and
ns = number of supply nodes (Figure 19B).

Subsitituting in values for ^Tavg_i representing W₁, W₂, and W₃ from Table 14, and the value for T_S of 15 hours per day computed using Equation (11), the following pattern factors were computed for supply nodes S₁, S₂, and S₃, respectively:

Therefore, using the SNL method to simulate the equivalent volume of water contributed to the distribution system over a 24-hour period by the WSTP method, the supply nodes were operated according to the following schedule in EPANET 2:

• Supply node S₁—15 hours at a rated capacity of 700 gallons per minute, and a pattern factor of 0.667;
• Supply node S₂—15 hours at a rated capacity of 800 gallons per minute, and a pattern factor of 0.630; and
• Supply node S₃—15 hours at a rated capacity of 1,000 gallons per minute, and a pattern factor of 0.507.

The operational schedule and water supply information for the supply nodes using the SNL method for the hypothetical network in Figure 19 are summarized in Table 15.

Table 15. Water supply for a hypothetical distribution system computed using the Supply-Node-Link (SNL) method
[—, not applicable]

Over the entire 31-day month (for this example), the total combined volume from the three supply nodes is listed in Table 15 and also can be computed according to the following equation:

where:

^CS_i = capacity for supply node i, in gallons per minute.

The total monthly supply derived from the supply nodes using the SNL method was computed as 41,233,410 gal which is nearly identical to the total production of 41,217,600 gal obtained from the production data for the hypothetical distribution system (Table 14). Thus, in summary, a mechanism for representing the physical WSTP system (Figure 19A) with the idealized SNL system (Figure 19B) was developed that: (1) honors the measured groundwater-well production data, (2) approximates the operational schedule of the high-service and booster pumps, and (3) eliminates the need to include storage tanks and high-service or booster pumps linked to groundwater wells in the EPANET 2 model for historical reconstruction simulations.

To demonstrate that the idealized SNL simulation method supplies the distribution system with an equivalent amount of water when compared to the "real-world" WSTP simulation method, both simulation methods were applied to the present-day (1998) water-distribution system (Figure 3, Plate 2) for conditions existing in August 1998. As previously discussed, the WSTP simulation method requires: (1) known operating schedules for groundwater well and high-service and booster pump on-and-off cycling, (2) observed storage tank water-level variations, and (3) realistic high-service and booster pump-characteristic curves. Operating schedule data for wells and high-service and booster pumps and storage tank water-level variation data were collected in August 1998 as part of the field-data collection activities used to characterize the present-day water-distribution system (Maslia et al. 2000a). High-service and booster pump-characteristic curve data were obtained from the water utility (Flegal 1997) and refined during the calibration process These data and simulation results using the WSTP simulation method for the Holly and Parkway treatment plants were previously reported in Maslia et al. (2000a, Appendix N). Because measured data and results using the WSTP simulation method were available for a 48-hour period (August 14–15, 1998), an EPANET 2 simulation using the SNL method to represent the Holly and Parkway treatment plants was conducted using a 48-hour simulation time. Measured and simulated high-service pump flows—using the WSTP simulation method—are compared with simulated flows for the SNL method represents of the Holly and Parkway treatment plants in Figure 20. The results obtained using both the WSTP and the SNL methods produce nearly identical simulated flow. Additionally, the hourly pump flows for August 14–15, 1998 representing measured data and simulation results for the WSTP and SNL methods are listed in Table 16. Total simulated supply to the distribution system from the Holly treatment plant over the 48-hour period using the SNL method was 5.62 Mgal, which is nearly identical to the measured supply of 5.63 Mgal (Table 16). For the Parkway treatment plant, simulated flow using the SNL method was 8.53 Mgal which is less than 3% different from the measured flow of 8.32 Mgal. Thus, results obtained using both the WSTP and the SNL methods produce nearly identical simulated flows, thereby confirming the appropriateness of representing the "real-world" WSTP distribution system (Figure 19A) with the surrogate SNL distribution system (Figure 19B).

The application of the SNL method to simulate historical water-distribution system operations is identified in the operational notes listed in Appendix C. For example, in Table C-3, for the maximum-demand month of July 1971, the operational notes state that the Holly ground-level storage tanks are "in service" but "closed in EPANET 2." This wording indicates that the operation of Holly storage tanks was not explicitly accounted for during simulation of the hydraulics of the July 1971 water-distribution system, but rather, was replaced by supply wells of the surrogate SNL method as shown in Figure 19. The operational notes in Table C-3 also state that the Holly supply wells pump directly into the distribution system. The simulated discharge from the surrogate Holly supply wells represent the discharge from the Holly high-service pumps into the distribution system. From the notes in Table C-3, the total discharge from Holly high-service pumps 1 and 2 over a 24-hour period for July 1971 was estimated as 3.376 Mgal. The total flow from the surrogate supply wells representing Holly wells 14, 16, 18, 19, and 21 is also 3.376 Mgal. Thus, the simulated volume of water discharged to the distribution system using the SNL method (supply nodes representing the Holly wells linked to the Holly storage tanks and high-service pumps) was equivalent to the estimated discharge of the Holly high-service pumps. Descriptions of the SNL representation of other facilities in the water-distribution system, namely the Parkway and Windsor treatment plants, can also be found in the operational notes of Appendix C.

Manual Adjustment Process

As described previously, two simulation methods were used to achieve balanced flow conditions that honored hydraulic engineering principles and that conformed to the "Master Operating Criteria" (Table 4)—the manual adjustment process and the GA optimization method. Using the manual adjustment process, investigators manually adjusted and refined certain system physical and operational parameters in order to achieve balanced flow conditions and satisfy system operational requirements described by the "Master Operating Criteria" (Table 4) or described in water-utility operational notes. Model parameters that could have been adjusted during a simulation or calibration process are pipe roughness coefficients, pipe diameters (using nominal versus actual), point (nodal) demands, pump-characteristic curve data, and system operational data such as the on-and-off cycling of wells and high-service and booster pumps. Based on results of initial simulations, the model parameter that most affected water-distribution system pressures and hydraulic gradients was the pattern factor—the system operations parameter which controlled the on-and-off cycling of wells and high-service and booster pumps. The effects on simulation results of modifying other modeling parameters such as pipe roughness coefficient, pipe diameter, point demands, or pump-characteristic curves were minor in comparison. In fact, based on sensitivity analyses conducted using the calibrated model of the present-day (1998) network, the water-distribution system was found to be insensitive to variation in pipe roughness coefficient and diameter (Maslia et al. 2000a, p. 51). Therefore, only pattern factors were adjusted during simulations of the historical water-distribution systems. Pipe roughness coefficients, pipe nominal diameter values, and pump-characteristic curves were not adjusted and were the same as those determined from the model calibration and testing of the present-day water-distribution system (Maslia et al. 2000a). Point demands (nodal values) were varied on a monthly basis using the methods explained previously to derive monthly values (see section on "Estimation and Distribution of Historical Consumption)." A listing of model parameters and time-unit variation used for simulating the historical water-distribution systems is provided in Table 13.

Table 16. Comparison of measured high-service pump flows and the Well-Storage Tank-Pump and Supply-Node-Link simulation methods, Dover Township area, New Jersey, August 1998
[gmp, gallons per minute; WSTP, well-storage tank-pump; SNL, supply-node-link]

Genetic Algorithm (GA) Optimization

As shown in Tables 12 and 13, with the exception of the present-day (1998) and the 1996 water-distribution system, hourly-specific information regarding the operation of wells and high-service and booster pumps for the historical networks was not available¹⁶. Therefore, developing and investigating alternative operating schedules for the historical water-distribution systems and evaluating the effects of these alternative schedules with respect to results were considered critical parts of the historical reconstruction analysis¹⁷. The issues to be resolved were which alternative schedules would represent in a successful way the operation of the historical water-distribution systems and, if multiple alternatives were available, which ones should be chosen for investigation and analyses. Accordingly, the following questions were posed:

• If a balanced flow operating condition was achieved using the manual adjustment process, was the resulting operating condition the only way the system could have successfully operated?
• Could alternative or additional operating conditions be defined such that system operations would also be satisfactory or even "optimal?"

To answer these questions and address the issues raised by the external panel (ATSDR 2001e), a technique was required to "search" for and select a set of alternative operating conditions that, when applied, would result in the satisfactory operation of the historical water-distribution systems. Such a technique is the Genetic Algorithm (GA) optimization method. Simply put, a GA method refers to an optimization technique that attempts to find the best solution based on mimicking (in a computational sense) the mechanics of natural selection and natural genetics (Holland 1975, Goldberg 1989; Haupt and Haupt 1998, Walski et al. 2001). A complete description of the concept and application of GA methods is included in Appendix E.

Previously, the GA has been coupled with hydraulic network solvers to select a set of roughness coefficient values to automate the model calibration process (Savic and Walters 1995, 1997, Walters et al. 1998). A GA analysis begins with a trial solution using a set of assumed values for the decision variables. The decision variables are automatically adjusted to create additional trial solutions. Each trial solution is then used for an objective function that evaluates the "fitness" of the solution. Based on the evaluation of the fitness of the solution, the most recent set of decision variables is either (1) directly entered for the next solution ("direct selection"), (2) combined with values from other solutions ("crossover"), or (3) adjusted slightly by use of random changes ("mutated") to obtain a new trial solution. The GA method does not apply this process to just one trial solution, but rather, the approach is based on the consideration of many trials or a set of solutions ("a population") at any one time. The process described above continues for a specified number of solutions ("generations") until the solution cannot be improved very readily (or until some stopping criteria is met). Although this approach does not guarantee an optimal solution, it is usually a very good solution to the objective function. The technique of coupling a GA method with hydraulic network solvers is still in its infancy. However, results have demonstrated the GA method has the ability to greatly assist in the evaluation of complex water-distribution systems.

The GA method was applied to historical water-distribution systems that served the Dover Township area. In order to derive alternative on-and-off cycling patterns (and pattern factors) for every operating well, alternative sets of successful operating conditions were derived for every month of the historical period (January 1962–December 1996). The decision variables for the GA analyses were the hourly schedules of on-and-off cycling of wells and the well-pattern factors. The objective function was constrained by the pressure and storage tank water-level requirements described in the "Master Operating Criteria" (for example, minimum pressure at any pipeline node must be greater than 15 pounds per square inch (psi), maximum pressure at any pipeline node must not exceed 110 psi; see Table 4).

Owing to the complexity of the analysis, a new approach that embeds a GA in a progressive optimality algorithm was developed (Guan and Aral 1999a,b, Aral et al. 2001a,b,c). The resulting algorithm is identified as the Progressive Optimality Genetic Algorithm (POGA), which was applied to obtain solutions for alternative and optimal system-operation patterns for every network of the historical period (420 months). Initial estimates to start the POGA solution were obtained from the on-and-off cycling patterns derived from the manual adjustment process, previously described. This guaranteed that the POGA would begin with balanced flow conditions, although because of the robustness of this approach, such a requirement is unnecessary. A complete and detailed description of the POGA methodology and approach (Aral et al. 2001b) is included as part of this report (Appendix E). The reader that is interested in the developmental and computational aspects of the POGA should refer to Appendix E for details. In a subsequent section of the report (see section on "Sensitivity Analysis"), the proportionate contribution results obtained from the GA methodology are described and compared with proportionate contribution results obtained from the manual adjustment process.

WATER-QUALITY MODELING (SOURCE-TRACE ANALYSIS)

The fate of a dissolved constituent flowing through a distribution network over time is tracked by the EPANET 2 dynamic water-quality simulator. To model the water quality of a distribution system, EPANET 2 uses flow information computed from the hydraulic network simulation as input to the water-quality model. The water-quality model uses the computed flows to solve the equation for conservation of mass for a substance within each link. Details of the specific mathematical formulation of the water-quality simulator and the solution technique are provided in the EPANET 2 Users Manual, as are the model input data requirements.

Identifying the source of delivered water in a distribution system is necessary when trying to determine the exposure of water users to chemical or biological constituents. Males et al. (1985) developed a method using simultaneous equations to calculate the spatial distribution of variables such as percentage of flow, concentration, and travel times that could be associated with links and nodes, under steady-flow conditions. Grayman et al. (1988) developed a water-quality model that used flows previously generated by a hydraulic model and a numerical method to route contaminants—conservative and non-conservative—through a distribution system. This type of model has become known as a dynamic water-quality model. EPANET 2 is also a dynamic water-quality model, and has the ability to compute the percentage of water reaching any point in the distribution system over time from a specified location (source) in the network—the "proportionate contribution" of water from a specified source. To estimate the proportionate contribution of water, a source location is assigned a value of 100%. The resulting solution provided by the waterquality simulator in EPANET 2 then becomes the percentage of flow at any location in the distribution-system network (for example, a demand node) contributed by the source location of interest.

For the historical reconstruction analyses, a source-trace analysis was conducted for every month of the historical period. The list of EPANET 2 source-node identifications assigned to points of entry for the source-trace analyses is included in Appendix F (Table F-1 through F-35). These source nodes were assigned a value of 100% in order to estimate the proportionate contribution of water to locations in the historical distribution-system networks. Initial conditions must be "flushed out" of the distribution system before retrieving the proportionate contribution results (Maslia et al. 2000a, p. 55). Accordingly, the monthly historical network models were run for simulation periods of approximately 1,200 hours to reach a state of stationary water-quality dynamics ("dynamic equilibrium") as previously explained. The results of the source-trace analyses reported herein represent the last 24 hours of the 1,200 hours of the simulation period. Hydraulic time steps of 1 hour, and water-quality time steps of 5 minutes were used. For some monthly simulations in the 1980s, the water-quality time steps were reduced to 1 minute. These smaller water-quality time steps were necessary to ensure that the mass balance summed to 100%. Results of the source-trace analyses are presented and discussed in the next section of this report.

Table of Contents          Next Section