Aggregate Hourly-average vs Daily-average Attributes

As expected, a range of individual daily diurnal curves is produced from the collected data and results in an hourly-average demand profile that describes each building type. Box plots are used in Figures 5.2 and 5.3 to illustrate the distribution of flows for each hour of the day for each building type with the composite hourly-average demand profile drawn on top of the distribution. Figure 5.3 limits the distribution sets between the 10th and 90th percentile ranges for better clarity. For all sites, the distributions plotted in Figure 5.2 are for all days during the study period, and therefore aggregate usage patterns may be different depending on day and month. The median flow at each hour is generally lower than the average flow for each of the four building sites due to high-flow outlier events that drive up the average. The effect of outliers on the average is best presented at the commercial site in Figure 5.2 where at least 75% of values indicate no flow during the early morning hours (hours 1-9 and 19-24). However, infrequent water use events presumably due to irrigation during this time period result in an average flow that represents the presence of a relatively constant use of water which is not correct. The outlier flow values cause the largest difference in median and average flows in the community center throughout the 24-hour period, thereby indicating wide fluctuations in the time and magnitude of peak flows. Fluctuating water use in the community center is a result of the dynamic population that utilizes the building’s many amenities; scheduled events that influence building occupancy and water use vary seasonally, monthly, and day-by-day. The distribution of water use for the commercial site is assumed to be the result of the transient occupants comprised of people visiting the building for only a short amount of time to complete business transactions. The number of full-time occupants in the building has remained relatively constant throughout the study period. The hourly-average demand profile and median hourly flows best

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align at the multi-residential site and result in the expected diurnal curve. However, the high distribution of values outside of the 50% of values about the mean indicate intense flow events that greatly exceed those within the average pattern.

Figure 5.2: Box plots showing distribution of all flows by hour for each of the four building sites – multi-residential (RES), commercial (COM), elementary school (ELM), and community center (CTR).

Figure 5.3: Box plots showing distribution between the 10th and 90th percentiles of flows by hour for each of the four building sites.

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The irregularities normally observed in daily demand profiles for all building sites are lost when the flows are averaged at each hour. An example is shown in Figure 5.4 where the daily diurnal curve for a singular 24-hour day is compared to the hourly-average diurnal curve. The single-day curves for the multi-residential and elementary school sites follow the general trend of each hourly-average curve. Contrarily, the single-day curves for the commercial building and community center locations do not align with the relatively plateaued features of the hourly- average curves. In all cases, the single-day curves indicate that water use includes peak flow rates higher than those captured by the hourly-average curve and that additional curve attributes greatly differ between the two curves.

The resultant hourly-average diurnal curve for each study site is unique to the building it describes. The multi-residential location hourly-average curve follows the pattern expected for residential water use where peak flows are observed once during the morning hours and again in the evening. The highest peak occurs at hour 11 (between 10:00 AM and 11:00 AM) with the second peak occurring at hour 21 (between 8:00 PM and 9:00 PM). The hourly-average curve for the commercial site may be defined by either low-flow or high-flow durations. Water use is low during the closed hours between hours 1 – 8 (12:00 AM – 8:00 AM) and 21 – 24 (8:00 PM – 12:00 AM). During hours of normal operation, water use increases in the morning and plateaus to a relatively constant high-flow state between hours 11 – 17 (10:00 AM – 5:00 PM) before decreasing back to the low-flow state. Similar to the commercial site, the elementary school hourly-average water use pattern has the highest usage during school hours when the majority of occupants consist of students. A steep increase in water use is observed in the morning between hours 8 – 10 (7:00 AM – 10:00 AM) which coincides with the arrival of the students. Water use continues to increase until the peak at hour 13 (12:00 PM – 1:00 PM) during the lunchtime hour and then sharply decreases between hours 15 – 17 (2:00 PM – 4:00 PM). Gradually decreasing low flow values are still observed through the evening hours which may correspond to after-school programs or teachers working beyond the scheduled school day.

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The hourly-average diurnal curve for the community center does not have restricted water use during the normal hours of operation. Water flow is low during the early morning hours, but sharply increases beginning near the opening time at hour 8 (7:00 AM – 8:00 AM) and plateauing near hour 12 (11:00 AM – 12:00 PM). Water flow begins to gradually decrease at hour 16 (3:00 PM – 4:00 PM) and continues a gradual downward trend through the end of the day and into the early morning. A considerable amount of water flow remains after the 9:00 PM closing hour for the community center. Water use outside of normal operating hours may be attributed to events that are scheduled beyond regular closing times or cleaning and maintenance activities undertaken during off-hours.

Figure 5.4: The differences illustrated between hourly-average diurnal curves (top row) compared to the diurnal curve for a single day (bottom row) for all four building locations.

The difference between attributes calculated based on the hourly-average diurnal curve and collection of daily-average diurnal curves is shown in Table 5.4. The percent error

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evaluates the deviation of the values from the hourly-average diurnal curve from the daily- average values. The QP was underestimated by the hourly-average diurnal curve by 20%, 59%,

14%, and 63% for the multi-residential (MR), commercial building (COM), elementary school (ELM), and community center (CTR), respectively. Consequently, the FP/A was also

underestimated by between 22% and 76% for all locations. The peak flow is an important design element for designing water supply systems in order to ensure the delivery of water, and underestimating this value compromises the ability of the system to fulfill the demand with water at the proper magnitude and pressure. The time at which the peak flow occurs is equally as important for system design because it dictates when the system must be ready to accommodate extreme events. The combination of the QP and TP indicates the amount of

storage that may be required for the system to meet the high-demand event and when that storage amount must be ready for use. The hourly-average TP diverged from the daily-average

by -15%, -2%, 10%, and -0.3% for the RES, COM, ELM, and CTR sites, respectively. Deviation in the T50 values is attributed to the exclusion of days with no flow for the daily-average

calculation but values remain in close agreement. There is a lack of correlation between the duration that flows exceed the QA and the number of peaks greater than the QA (NP). For all

four building sites, the hourly-average overestimates the duration when the flow is above the QA, but for three sites (RES, ELM, and CTR) the hourly-average underestimates the number of

peak flow events above the QA. These cases indicate that the daily diurnal patterns are

fluctuating above and below the QA more frequently than expected, but maintaining high flows

for shorter durations. The appearance of more peaks in the diurnal curve means there is less time available between peaks for the system to recover and prepare to meet the next event, and therefore, increased storage capacities may be necessary to fulfill the water demand through times of multiple peaks within short time periods.

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Table 5.4: Attribute values for the hourly-average diurnal curve compared to the average attribute values for all daily-average diurnal curves. Shown are all four building locations– multi- residential (RES), commercial (COM), elementary school (ELM) and community center.

Building QA QP FP/A TP T50 TQ>QA NP QM FP/M σ

RES Hourly-average 600 850 1.4 11.0 13.9 15.0 2.0 662 1.3 197.4 Daily-average 600 1064 1.8 13.0 13.9 12.6 4.1 617 1.7 240.4 Percent error 0% -20% -20% -15% 0% 19% -51% 7% -26% -18% COM Hourly-average 14 24 1.7 13.0 13.4 10.0 2.0 12 2.0 6.0 Daily-average 14 58 6.9 13.3 14.3 7.2 1.9 9 2.8 13.8 Percent error 0% -59% -76% -2% -6% 38% 7% 36% -27% -56% ELM Hourly-average 85 322 3.8 13.0 12.6 8.0 1.0 20 16.0 109 Daily-average 85 373 4.8 11.9 12.4 7.8 2.7 20 28.6 118 Percent error 0% -14% -22% 10% 2% 2% -63% -1% -44% -8% CTR Hourly-average 24 50 2.1 15.0 15.1 12.0 2.0 23 2.2 18.2 Daily-average 24 134 5.8 15.1 14.9 8.5 3.5 14 15.0 32.6 Percent error 0% -63% -64% -0.3% 1% 42% -44% 68% -86% -44%