Table of Contents          Next Section

SENSITIVITY ANALYSIS

OVERVIEW

Model parameter uncertainty and variability may occur because of spatial and temporal variability of data, incomplete or missing data, or measurement errors. Sensitivity analyses are typically conducted as part of a model calibration process to assess changes in simulation results when adjustments or modifications are made to certain model parameters (Walski et al. 2001). For example, a sensitivity analysis was conducted as part of the model calibration process for the present-day (1998) water-distribution system serving the Dover Township area and was used to assess changes in simulation results caused by variations in pipe diameters and pipe roughness coefficients (Maslia et al. 2001, p. 51). Sensitivity analyses conducted as part of the historical reconstruction of water-distribution system operations were designed to assess changes in the percentage of water contributed by a well or well field to pipeline locations (proportionate contribution) rather than to assess changes in the simulated hydraulics of the distribution system. Output from the source-trace analyses—the simulated proportionate contribution of water—will be considered as one of the risk factors in the epidemiologic case-control investigation. If large but reasonable variations in model parameter values result in correspondingly large variations in the percentage of water contributed by a well or well field to pipeline locations, the estimates of exposure to the different water sources may result in exposure misclassification. On the other hand, if changes in the simulated proportionate contributions are small regardless of the magnitude change in model parameters, then simulation variability will not greatly detract from the confidence assigned to exposure classifications. The bases of comparison for all sensitivity analysis results were the corresponding results obtained through the manual adjustment process—previously described in the section on "Historical Reconstruction Analysis."

VARIATION OF OPERATIONAL AND HYDRAULIC CONSTRAINTS

Four types of operational and hydraulic constraints were varied during sensitivity analyses in order to determine the effects of constraint changes on the simulated proportionate contribution results. The constraints subjected to variation were:

• pattern factors assigned to wells and supply nodes²⁴ (operational variation in value and time of day);
• minimum pressure requirements at model nodes;
• allowable storage tank water-level differences between the starting and ending time of a simulation (hour 0 and 24, respectively); and
• daily system operations represented by a "typical" 24-hour day over a month-long period.

Genetic Algorithm (GA) optimization methods²⁵ were used to conduct sensitivity analyses of the first three constraints or constraint sets. Proportionate contributions were simulated at all pipeline locations for each constraint change, and these results were compared with corresponding results obtained using the manual adjustment process. Sensitivity analyses of the fourth constraint were obtained using the manual adjustment process. Descriptions of constraints varied during the sensitivity analyses are listed in Table 20. The month and year for which sensitivity analyses results were obtained are listed in Table 21. For the sensitivity analyses that used the GA optimization methods (SENS0–SENS7), initial estimates for the on-and-off cycling patterns and pattern factors for the groundwater wells and supply nodes were derived from the manual adjustment process. This approach guaranteed that the GA simulation would begin with balanced flow conditions. Simulation SENS0 was conducted for every month of the historical period (420 months) which included the months shown in Table 21. Simulation SENS1 was conducted for every month of selected years 1962, 1965, 1971, 1978, 1988, and 1996. Sensitivity analyses SENS2–SENS7 were conducted for three selected months of the aforementioned selected years. The three selected months corresponded to the minimum-, maximum-, and average-demand months. (The rationale for conducting sensitivity analyses for selected months and years of the historical period for simulations SENS1–SENS7 will be discussed below.) Sensitivity analyses SENS8 were conducted solely for the three selected months of 1996 because hourly operational data were required to conduct the month-long simulations, and these data, obtained from the water utility (Flegal 1997), were only available for 1996.

Table 20. Description of operational and hydraulic contraints varied for sensitivity analyses¹
[GA, genetic algorithm optimization; MAP, manual adjustment process]

Well- and Supply-Node-Pattern Factors

Because of the variability and lack of definitive data regarding the hourly on-and-off cycling of wells and high-service and booster pumps for the historical period, testing changes in simulation results in conjunction with changes in on-and-off cycling of wells and pumps was considered a critical feature of the sensitivity analyses. As described above, GA optimization methods were used to develop alternative schedules for operating the water-distribution system for every month of the historical period. Sensitivity analyses SENS0 were designed to modify the EPANET 2 pattern factors in order to vary well- and supply-node-operating patterns. Hydraulically balanced and optimal or near optimal operating conditions were achieved using pressure and storage tank water-level criteria described by the "Master Operating Criteria" (Table 4 and Table 20). Following the simulation of an alternative balanced flow system using GA methods, source-trace analyses were conducted in the manner previously described (see "Water-Quality Modeling [Source-Trace Analysis"] section) to obtain proportionate contributions of water at all pipeline locations.

The effects of varying schedules and pattern factors on the simulated proportionate contributions of water at pipeline locations were unknown prior to conducting the sensitivity analyses SENS0. Accordingly, these simulations were conducted for every month of the historical period (Table 21). Subsequent analyses of SENS0 simulation results (see section on "Results of Sensitivity Analyses") indicated that the historical water-distribution system successfully operated only within a narrow range of conditions. Successful operation included maintaining a balanced flow condition and satisfying the "Master Operating Criteria" previously described (Table 4). Therefore, the remaining sensitivity analyses (SENS1–SENS7) were conducted solely for representative years and months listed in Table 21.

In response to recommendations from the external expert panel (ATSDR 2001e), sensitivity analyses using GA optimization methods were conducted to simulate a pattern of system operation as different as possible from the operating patterns developed by the manual adjustment process used for sensitivity analyses SENS0. Substantially different operating patterns were developed using GA optimization methods and were designated SENS1 (Table 20). The resulting pattern factors for SENS1 simulations were not as optimal as the results derived from sensitivity analyses SENS0, but nonetheless resulted in acceptable system operations that satisfied the "Master Operating Criteria." (See Aral et al. 2001b and Appendix E for details and a description of the development of the alternate set of pattern factors.) Sensitivity analyses SENS1 were conducted for every month of selected years 1962, 1965, 1971, 1978, 1988, and 1996 (Table 21). After reviewing results it was apparent that the complete range of results of the effects of constraint variation could be characterized by conducting sensitivity analyses just for the three annual demand conditions (minimum, maximum, and average). Therefore, all other sensitivity analyses (SENS2–SENS7) were conducted only for the minimum-, maximum-, and average-demand months of the aforementioned selected years (Table 21).

Pattern factors derived using the manual adjustment process as well as those obtained from sensitivity analyses SENS0 and SENS1 were allowing wells and supply nodes representing wells linked to storage tanks and high-service and booster pumps to operate at a fraction of their pumping capacities. In some instances, the resulting pattern factors were near zero in value. To limit this occurrence, pattern factors obtained from sensitivity analyses SENS2 were constrained to a minimum value of 0.25 (the default value for a pattern factor in EPANET 2 is 1.0). The pressure and storage tank water-level constraints imposed on the previous sensitivity analyses were also imposed on sensitivity analyses SENS2 (Table 20).

The final test of changes of well- and supply-node-pattern factors on simulation results was designated sensitivity analyses SENS3. Analyses SENS3 were conducted to test the operational status of wells and highservice and booster pumps; that is, pumps must be either "on" or "off." To address this issue, pattern factors for operating wells and supply nodes representing wells linked to storage tanks and high-service and booster pumps were constrained to values of 0.75–1.25. Otherwise, a value of 0.0 (indicating the well or supply node was in the "off" position) was applied. The pressure and storage tank water-level constraints imposed on the previous sensitivity analyses were also imposed on analyses SENS3 (Table 20).

Table 21. Identification of year and month for conducting sensitivity analysis simulations
[—, sensitivity analysis simulation not conducted for this month]

Minimum Pressure Criteria

The simulations of historical distribution-system operations based on the manual adjustment process were constrained by a minimum allowable pressure requirement of 15 psi and a maximum allowable pressure requirement of 110 psi at all model node locations (Table 4). Based on the configuration, hydraulics, and operations of the historical distribution systems, these pressure constraints were sufficient to ensure that, at all interior points of the model network, pressure was generally above 30 psi and less than 110 psi. The panel of experts who reviewed this simulation approach recommended that additional simulations be conducted where the pressure constraints were varied beyond the minimum and maximum constraints described by the "Master Operating Criteria" (Table 4). Because the minimum pressure constraint of 15 psi was the more difficult constraint to maintain during the manual adjustment process, and because minimum system pressure is required for fire and health protection, two sets of sensitivity analyses were conducted whereby the minimum pressure required at all interior points of the model network was varied and constrained to be 20 psi (SENS4) and 30 psi (SENS5)—Tables 20 and 21. While simulating the minimum pressure constraints of 20 and 30 psi, the maximum allowable pressure constraint of 110 psi and the storage tank water level requirement (no change over a 24-hour period) applied during the manual adjustment simulations were maintained. As with the previously described sensitivity analyses, the GA optimization methods were used to determine the operating schedule for wells and high-service and booster pumps, and the results of the manual adjustment process simulations were used as the bases for comparison.

Storage Tank and Water-Level Difference Criteria

The historical reconstruction simulations conducted using the manual adjustment process and sensitivity analyses SENS0–SENS5 applied the constraint that starting and ending water levels in storage tanks (over a 24-hour simulation period) were equal (Table 20). This constraint was imposed, in part, because of the simulation requirements of the source-trance analyses used to determine proportionate contributions. As previously described (see section on "Water-Quality Modeling [Source-Trace Analyses]"), prior to retrieving results form the source-trace analysis, the hydraulic features of the distribution system were simulated until a state of stationary water-quality dynamics was achieved, which for the historical networks was about 1,200 simulation hours.²⁶ If the water level in a storage tank at the end of a 24-hour simulation period (hour 24) varied signifi- cantly from the water level at the start of the simulation period (hour 0), then by the time a state of stationary water-quality dynamics was reached (if stationary water-quality dynamics could be reached under these conditions), the tank was either completely drained or was overflowing. Both of these conditions were in violation of the "Master Operating Criteria" (Table 4). To test the sensitivity of the simulated values of proportionate contribution by relaxing the storage tank water-level constraint, and in response to a recommendation from the panel of experts (ATSDR 2001e), two additional sensitivity analyses were conducted—SENS6 and SENS7 (Tables 20 and 21). For both analyses, the starting and ending water level in any storage tank was permitted to vary by as much as 3.0 ft over a 24-hour simulation period. Minimum pressure requirements of 20 psi (SENS6) or 30 psi (SENS7) were also maintained. As with all previous sensitivity analyses, GA optimization methods were used to determine the operating schedule for wells and high-service and booster pumps, and the results of the manual adjustment process simulations were used as the bases for comparison.

Daily System Operations

For the historical reconstruction analysis, the assumption was made that daily system operations over a period of one month could be represented by a "typical" 24-hour day for each month of the historical period, as previously described in the section on "System Operations." This assumption was the basis for conducting the simulations using the manual adjustment process and sensitivity analyses SENS0–SENS7 that used GA optimization methods. To test the validity of this assumption, and in response to recommendations from the external expert panel, additional sensitivity analyses were conducted—designated sensitivity analyses SENS8 (Table 20 and 21). To conduct these sensitivity analyses, historical hourly operational data were required, and the only time such data were available dur- ing 1996 (Flegal 1997). Therefore, sensitivity analyses SENS8 were conducted using the manual adjustment process for the minimum-, maximum-, and average-demand months of February, June, and October 1996, respectively. For each of these months, a simulation time was used corresponding to the number of hours in the month—696 hours (29 days) for February, 720 hours (30 days) for June, and 744 hours (31 days) for October. Simulations were conducted using the operating schedule information obtained from the water utility while still honoring the "Master Operating Criteria" (Table 4). The results of sensitivity analyses SENS8 were compared to simulations of the "typical" 24-hour day for each respective month (Table G-7 and Figure H-7).

RESULTS OF SENSITIVITY ANALYSES

Genetic Algorithm (GA) Optimization Simulations

An example of simulated proportionate contribution results obtained from sensitivity analyses SENS0 is shown in Figure 26. Simulated proportionate contribution results for model nodes (pipeline junctions) are shown for the maximum-demand month of July 1988 using the Parkway well field as the point of entry. Comparison of simulation results in Figure 26—obtained using the GA optimization methods—with the corresponding simulated proportionate contribution results obtained using the manual adjustment process (Figure 21), shows little difference. Results shown in Figures 21 and 26 are nearly identical. Results are also presented using the "stacked" column graph format.²⁷ For this method of presentation, simulation results obtained from sensitivity analyses SENS0 are shown for five geographically distinct pipeline locations (A–E). These graphs are used to show the spatial distribution of the simulated proportionate contribution of water from all operating wells and well fields for a specified historical time. Using 1988 as an example, a comparison of the simulated proportionate contribution of water from wells and well fields to the five selected pipeline locations derived from the manual adjustment process and sensitivity analyses SENS0 (Figure 27) indicate that results are nearly identical. The graphs in Figure 27 further demonstrate that, at specific historical pipeline locations in the Dover Township area, the difference between results obtained using the two simulation approaches is insignificant.

A comparison of simulation results—obtained from sensitivity analyses SENS0—to corresponding results obtained using the manual adjustment process for each month of the historical period, indicated that the simulated proportionate contributions of water were highly similar regardless of the simulation approach. Because of this, and, owing to space limitations, simulated proportionate contribution results, derived from sensitivity analyses will not be shown using the map format (except for the example shown in Figure 26). Rather, proportionate contribution results, obtained from sensitivity analyses SENS0 for each month of selected years 1962, 1965, 1971, 1978, 1988, 1995, and 1996, for the five pipeline locations (A–E) are provided in tabular format in Appendix I (Table I-1 through I-7). For the aforementioned years and for the selected months representing minimum-, maximum-, and average-demand conditions, the simulated proportionate contribution of water from wells and well fields to the five pipeline locations, obtained from sensitivity analyses SENS0, are shown in graphical format in Appendix J (Figures J-1 through J-7). A summary of the years and months for which simulated proportionate contribution results, derived using sensitivity analyses SENS0, is provided in Table 22. This table also indicates the location of simulation results in either Appendix I or J.

Table 22. Presentation of proportionate contribution results for wells and well fields for selected pipeline locations using sensitivity analyses SENS0, year, month of analysis, and location in report
[see Figure 26 or Plates 52–153 for pipeline locations; —, simulation results not presented in a graphical format for this month]

As described previously, GA optimization methods were used to develop alternate operating schedules that also resulted in the successful operation of the historical water-distribution system. Pattern factors of operating schedules derived from the application of the GA methods, and used to schedule the operation of wells and supply nodes²⁸ could be markedly different when compared to corresponding pattern factors derived using the manual adjustment process. An example of EPANET 2 pattern factors derived using the manual adjustment process and corresponding pattern factors from sensitivity analyses SENS0 are shown in Figure 28. The pattern factors schedule pumping at supply nodes representing Parkway wells 23 and 24, operating during July 1988. From Figure 28:

• Parkway well 23—from 0500 to 0600 hours, the pattern factor derived using the manual adjustment process is about 2; whereas, the pattern factor derived using sensitivity analyses SENS0 is about 5. From 1200 to 1300 hours, the pattern factor derived using the manual simulation approach is again about 2; whereas, the pattern factor derived from sensitivity analyses SENS0 is about 4.

• Parkway well 24—from 0900 to 1100 hours, the pattern factors derived using the manual adjustment process are about 6.5; whereas, the pattern factors derived using sensitivity analyses SENS0 are about 4 from 0900 to 1000 hours and less than 0.5 from 1000 to 1100 hours.²⁹

Although pattern factors for some hours of operation show marked differences (like those in Figure 28), the simulated proportionate contributions of water simulated using these different pattern factors for sensitivity analyses SENS0 show little difference throughout the Dover Township area when compared to corresponding proportionate contributions of water simulated using the manual adjustment process.

To assist in determining the differences between corresponding proportionate contribution results obtained using the manual adjustment process and sensitivity analyses SENS0, tabular values of the absolute value of these differences are provided in Appendix K (Tables K-1 through K-7). The differences between proportionate contribution results obtained using the manual adjustment process and corresponding results from sensitivity analyses SENS0 were computed according to the following:

DC_i,j = difference in the proportionate contribution of water for the ith study location and the jth operating source (well or well field), in percent;
(C_map)_i,j = simulated proportionate contribution of water for the ith study location and the jth operating source (well or well field), obtained using the manual adjustment process, in percent;
(^CGA₀)_i,j = simulated proportionate contribution of water for the ith study location and the jth operating source (well or well field), obtained from sensitivity analyses SENS0, in percent;
NSL = number of study locations; and
NS = number of operating sources of water (wells or well fields).

The absolute values of the differences were computed according to Equation (17) as follows:

where:

(DC_i,j)_abs = absolute value of difference computed using equation (16), in percent.

The tables in Appendix K list the absolute value of difference for each of the five pipeline locations (A–E) for every month of selected years 1962, 1965, 1971, 1978, 1988, 1995, and 1996.

In addition to sensitivity analyses SENS0, seven additional sensitivity analyses (SENS1–SENS7)—using GA optimization methods—were conducted to assess the effects of operating the historical water-distribution systems under alternate operating schedules and conditions (Tables 20 and 21). These sensitivity analyses were exhaustive with respect to the range of possible operating conditions for the representative historical networks (1962, 1965, 1971, 1978, 1988, and 1996). Examples of the resulting pattern factors from these sensitivity analyses are shown in Figures 29 and 30 for supply nodes representing Parkway wells 26 and 22, respectively.

Pattern factors derived from the manual adjustment process and corresponding factors from sensitivity analyses SENS1 are shown in Figure 29. Sensitivity analyses SENS1 were conducted to derive an alternate operating schedule that was not as optimal as the operating schedule derived from sensitivity analyses SENS0, but nonetheless resulted in a successful system operation that also honored the "Master Operating Criteria" (Table 20). The resulting pattern factors can be viewed in terms of seasonal variation by taking a certain year (for example, 1978, Figure 29) and comparing the results by moving vertically down the illustration from top to bottom. Historical variation is shown in Figure 29 by taking a certain demand condition (for example, average demand conditions occurring during the month of October) and comparing the results horizontally across the illustration from left to right.

Pattern factors derived using the manual adjustment process and corresponding pattern factors from all sensitivity analyses (SENS0–SENS7) are shown in Figure 30 for the supply node representing Parkway well 22. The pattern factors, derived for October 1996 demand conditions, show the effect of conducting the different sensitivity analyses with their respective constraints. For example, sensitivity analyses SENS3 were conducted to simulate the wells and high-service and booster pumps in either the "on" or the "off" position (Table 20). Therefore, the values of pattern factors were constrained to ranged between 0.75–1.25 for the "on" position or 0.0 for the "off" position. This constraint was in addition to the pressure and storage tank water-level constraints derived from the "Master Operating Criteria." As shown in Figure 30, the resulting pattern factors range between 0.75–1.25 for hours that the supply node is operational, and are 0.0 for simulation hours 0400 to 0500 and 1700 to 1900 when the supply node is not operational. The pattern factors resulting from all of the sensitivity analyses (Figure 30) also show some significant differences in terms of values and hours of operation when compared to the pattern factors derived using the manual adjustment process. However, regardless of the value or origin of the pattern factors derived using the sensitivity analyses, the simulated proportionate contributions of water when compared to corresponding results obtained using the manual adjustment process were highly similar.

It is also possible to assess the results of each the sensitivity analyses (SENS0–SENS7) in terms of differences in the simulated proportionate contribution of water from wells and well fields to locations in the Dover Township area with respect to corresponding simulation results obtained from the manual adjustment process—as was demonstrated with sensitivity analyses SENS0. However, because of the large number of model nodes representing pipeline junctions in the historical networks, an alternate method of summarizing results would be preferable. An alternative presentation method that facilitates evaluation of the magnitude of the difference in the proportionate contribution of water between simulation methods and between the different sensitivity analyses was developed.

Differences in proportionate contributions derived from all sensitivity analyses (SENS0–SENS7) are shown in Figure 31. The graphs were constructed by using Equations (16) and (17) to compute the absolute value of the difference between simulated proportionate contribution results using the manual adjustment process and a particular sensitivity analysis simulation for all wells and well fields (sources) that contributed water to each study location.³⁰ Then the percentage of study locations that exceeded a specified difference value was determined. The values of n in the graphs in Figure 31 represent the number of study locations where the contribution of water from a specified well or well field was greater than 0%. Figure 31 shows these results for minimum-, maximum-, and average-demand months of 1971, 1978, 1988, and 1996. Results shown on this figure can be used to assess the differences between simulated proportionate contributions of water to study locations derived using the manual adjustment process and each of the sensitivity analyses.

To determine the number of study locations receiving water from all operating wells and well fields where simulation results indicate a difference of 10% or less between results obtained using the manual adjustment process and sensitivity analyses SENS0 for 1978, the following procedure is used:

• on the 1978 graph in Figure 31, the 10% difference value on the x-axis of the graph is located,
• from that location, a vertical line is drawn until it intersects with the symbols used to plot the results of sensitivity analyses SENS0, and
• at the intersection of the vertical line and the SENS0 plotting symbols, a horizontal line is drawn until it intersects the y-axis of the graph; in this example, the intersection of the horizontal line with the y-axis corresponds to approximately 97%.

For this example, therefore, 97% is the percentage of study locations receiving water from all operating wells and well fields where the absolute difference in the simulated proportionate contribution of water between the manual adjustment process and sensitivity analyses SENS0 is 10% or less.

Alternatively, if information is desired on the difference between the manual adjustment process and the sensitivity analysis simulations for a specified percentage of study locations, then the procedure described above is reversed. For example, to determine the absolute difference in the simulated proportionate contributions of water between the manual adjustment process and sensitivity analyses SENS3 for 90% of study locations for the 1988 water-distribution system, the following procedure is used:

• on the 1988 graph in Figure 31, the 90% value is located on the y-axis of the graph,
• a horizontal line is drawn from the 90% location on the y-axis until it intersects with the symbols used to plot the results of sensitivity analyses SENS3, and
• at the intersection of the horizontal line with the SENS3 plotting symbols, a vertical line is drawn until it intersects with the x-axis of the graph; in this example, the intersection of the vertical line with the x-axis corresponds to a value of about 5.7%.

For this example (1988 and sensitivity analyses SENS3), the result is interpreted as indicating that, less than 10% of study locations (100%–90%), the absolute difference in the simulated proportionate contributions of water exceeds 5.7%. The absolute difference this example is derived using simulation results obtained from the manual adjustment process and corresponding results obtained from sensitivity analyses SENS3.

The procedures described above for evaluating the results of the sensitivity analyses and comparing them with the results from the manual adjustment process have to be repeated many tens or hundreds of times order to obtain an assessment of the overall range of differences in simulated proportionate contributions water for all sensitivity analyses. As an alternative, statistical analyses were conducted on these differences using results of the manual adjustment process as the bases of comparison. The statistical analyses assumed that the differences could be characterized by a normal distribution. Results of the statistical analyses are listed in Table 23 for all sensitivity analyses (SENS0–SENS7) for years 1962, 1965, 1971, 1978, 1988, and 1996. Table 23, values are listed for the following statistics:

• n (sample size)—number of study locations where the contribution of water from a specified well or well field is greater than 0%;
• DC_m(mean of the differences)—where the differences between the contribution of water derived using the manual adjustment process and the sensitivity analyses were computed using Equation (16);
• DC_o(mode of differences)—where the mode of the differences is the difference value that occurred with the greatest frequency (the most common value);
• DC_d(median of differences)—where the median of the differences is the middle value when the set of all differences for a specific sensitivity analysis is ordered; and
• ^sDC (standard deviation of the differences)— where the standard deviation of differences is used to express the "spread" or deviation of the differences from the mean or central value.

Mathematical definitions for the statistics listed in Table 23 can be found in any standard text on mathematics, statistics, or probability (Beyer 1986), and therefore will not be presented in this report.

If the differences between the simulated proportionate contributions of water derived by the manual adjustment process and sensitivity analyses are normally distributed, then the computed values for the mean, mode, and median of the differences in the proportionate contribution of water should be equal. As can be seen from Table 23, the computed values for these statistics are nearly always 0%. The standard deviation of differences in percent contribution is generally below 5 %, with the exception of 1962, which was the earliest historical network analyzed and the network with the fewest number of pipelines and study locations (compare the n-value for the 1962 network with the n-value for the other historical networks listed in Table 23).

For a graphical representation of the statistical results listed in Table 23, histograms are shown in Figure 32 for all sensitivity analyses (SEN0–SEN7) for years 1971, 1978, 1988, and 1996. In these graphs, the bars of the histograms represent the differences in simulation results, computed using Equation (16), between the manual adjustment process and the sensitivity analyses. The histograms in Figure 32 are compared with a normal or Gaussian distribution that was fitted using the difference data. The results shown in Figure 32 confirm that, in general, the differences in the simulated proportionate contribution of water derived by comparing results of the manual adjustment process with the results obtained from the sensitivity analyses are normally distributed, and that the differences tend to have a narrow "spread" or deviation and cluster around a mean difference value of 0%.

The last column in Table 23 shows statistics computed for all eight of the GA sensitivity analyses (SENS0–SENS7) for each of the years listed in the table. These statistics can be interpreted as providing a quantitative evaluation for the differences in the proportionate contribution of water for any plausible operational mode (consistent with hydraulic engineering principles and the "Master Operating Criteria") for the historical water-distribution system characterized by the years listed in Table 23. For example, for the more recent historical networks (1988 and 1996), the different methods of simulating the successful operation of the water-distribution system would result in differences of proportionate contribution of water to locations in the Dover Township area of approximately 3% to 4% when compared with the manual adjustment process. These results are well within accepted limits for engineering and scientific analyses. For all sensitivity analyses for all of the years listed in Table 23, the mean, mode, and median of the differences are 0% and the standard deviation of the differences of proportionate contributions of water is 3.9%. Thus, for the entire historical period, which can be characterized by the six selected years listed in Table 23, sensitivity analyses indicated that the differences in the proportionate contribution of water—simulated by the range of operating conditions and hydraulic constraints previously described (Table 20)—are insensitive to the manner in which the water-distribution system was operated over a 24-hour period. Thus, the minor differences in the simulated proportionate contribution of water between the manual adjustment process and the sensitivity analyses (Figure 31) indicate that there was a narrow range of conditions within which the historical water-distribution system could have successfully operated to maintain a balanced flow condition and satisfy the "Master Operating Criteria."

Table 23. Statistical summary of differences in simulated proportionate contributions of water derived by the manual adjustment process and sensitivity analyses
[n, number of study locations where the contribution of water from a specified source (well or well field) is greater than 0%; DC_m, mean of differences computed using difference using difference between contribution of water derived using the manual adjustment process and sensitivity analyses, in percent, see Equation (16) for definition of difference; DC_o, mode of differences, in percent; DC_d, median of differences; in percent; s_DC, standard deviation of differences]

Daily System Operations Simulations

For the historical reconstruction analysis, daily system operations over a period of one month were represented by a "typical" 24-hour day for each month of the historical period. This approach was the basis for conducting the simulations using the manual adjustment process and sensitivity analyses SENS0–SENS7. Daily operational variations including routine maintenance of system facilities, repair of pipeline breaks, emergency fire service, and other temporary interruptions of routine operations over a "typical" 24-hour period were considered insignificant using this approach. To test the validity of this approach, additional sensitivity analyses (SENS8) were conducted using hourly operational data obtained from the water utility for 1996 (Tables 20 and 21). Pattern factors used in these simulations represented actual on-and-off cycling of wells and high-service and booster pumps. The "Master Operating Criteria" (Table 4) were also honored. Simulations were conducted using the manual adjustment process for the minimum-, maximum-, and average-demand months of February, June, and October 1996, respectively. For each of these months, simulation time corresponded to the number of hours in the month—696 hours (29 days) for February, 720 hours (30 days) for June, and 744 hours (31 days) for October.

Results of the month-long simulations for February, June, and October are shown in Figure 33 using the "stacked" column graph format for the five selected pipeline locations (A–E) previously identified. Comparison of these simulation results to corresponding results obtained using the "typical" 24-hour day simulation for each respective month, indicate similar values of simulated proportionate contribution were obtained. For example, simulation results for the maximum-demand month of June indicate that differences in the proportionate contribution of water from the Parkway well field for the two methods of simulating daily system operations were 0% for location A, 1% for location B, 4% for location C, 2% for location D, and 3% for location E. Therefore, sensitivity analyses SENS8 assisted in confirming that the day-to-day operations of the waterdistribution system were highly consistent over a month-long period (based on available 1996 hourly data) and could be realistically represented by a "typical" 24-hour operational pattern.

The sensitivity analyses conducted as part of the historical reconstruction of the water-distribution system serving the Dover Township area indicate that: (1) only a narrow range of conditions existed within which the historical water-distribution system could have successfully operated and still satisfy hydraulic engineering principles and the "Master Operating Criteria" (Table 4), and (2) daily operational variations over a month did not appreciably change the simulated proportionate contribution of water from specific sources when compared to results from a typical 24-hour day pattern of operation representing the month. Thus, the reconstructed historical water-distribution systems and operating criteria—based on applying the "Master Operating Criteria" and using generalized water-utility information—are believed to be the most plausible and realistic scenarios under which the historical water-distribution systems were operated.

Table of Contents          Next Section