Data Analysis

Data files in CSV format were analyzed using Microsoft Excel and Access 2010. Potable water consumption at each location was evaluated from March 11, 2012 through August 16, 2014 at each hourly time step for all locations.

Table 5.3: Summary of attributes used to evaluate diurnal water use curves.

Characteristic Notation Units Definition

Average hourly flow QA gph Average flow over a 24-hour day

Peak hourly flow QP gph Maximum flow observed in a one-hour period over a 24-hour day

Peak factor (peak to average factor)

FP/A - Ratio of maximum one-hour flow to average hourly flow

Time to peak flow tp hr Hour at which the PHF first occurs

Time to 50% consumption t50 hr Time in hours that it takes to reach half of the daily water use

Duration that hourly flow is greater than QA

TQ>QA hr Duration in non-consecutive hours when the hourly flow exceeds the MHF

Number of peaks exceeding QA

NP - The number of events in which a peak flow occurs and exceeds the MHF

Median hourly flow QM gph The median flow over a 24-hour day

Peak to median factor FP/M - Ratio of the maximum one-hour flow to median hourly flow

Standard deviation σ, S gph The variation in flows observed over a 24-hour day

Statistical values are necessary in order to describe and quantify the variability among diurnal water curves of different building types and temporal changes of diurnal curves produced by the same building. Attributes used to characterize diurnal patterns must represent unique traits of the resultant daily demand curves in terms of intensity, duration, and frequency (Buchberger and Wells, 1996). The attributes identified and developed for this study are listed in Table 5.3 and depend on the analysis of logged flowrates (Q) tagged for each date (d) and hour (h) denoted as Q(d,h) in gallons per hour (gph).

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5.4.2.1 Calculations Over 24-hour Periods

The calculations for the following attributes are developed using data for unique dates consisting of 24 flow values representing each sequential hour within that date, beginning with hour 1 representing the time between 12:00 AM and 1:00 AM. A value for each attribute was produced, when applicable, for each of the 889 dates from March 11, 2012 through August 16, 2014 and for demand curves representing the average flow at each hour for combined dates.

The total daily water demand is represented as a mean or average hourly flow (QA)

normalized over 24 hours as calculated by Q_A=1

n∑ Q(d,h)

n

h=1

(5.1)

where the flow for each hour on the given date is summed and divided by the total number of n hours (24). Although the QA does not describe diurnal changes for the building at the given

date, it is useful for evaluating seasonal trends in water use and comparing the intensity of daily water use for each building site. Furthermore, establishing a mean hourly value provides a baseline by which to compare hourly water use magnitudes in terms of deviation from the average throughout the day.

The peak hour flow (QP) is determined by identifying the maximum hourly flow value

within each date,

Q_P=max⁡{Q(d,h)}_h=1n _{. (5.2)}

Peak flows are important for the design of water supply systems in order to ensure that water successfully meets customer demands at all times. Identification of the QP within the diurnal

curve is essential to the sizing and operation of water network components such as pipe diameters and pressure thresholds.

The magnitude of the QP may be normalized by division with the QA in order to

accurately report the intensity of the peak for the building on that day as a peak to average factor (FP/A). While changes in the QA indicate a change in the magnitude of water use by the

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building, the FP/A tracks the significance of the peak event. A low FP/A indicates a steadier water

use pattern with less variance from the mean, whereas a high FP/A alludes to a fluctuating

profile.

The time at which the QP is reached, or the time to peak (TP), is marked by the hour at

which the QP occurs. In the event that the QP occurs more than once in the 24-hour period, the

first occurrence is marked as the TP. The appearance of a peak requires that the flow exceed

the average value, and thus TP values were not recorded for dates that did not record

measurable water flow.

Another term developed to indicate the intensity of water use is the time required to fulfill 50% of the date’s total daily water use (T50). Similar to the TP, the T50 marks the hour at which

at least 50% of the daily water use has been achieved. The hour value indicates both the time of day at which the T50 is achieved and the duration it took to reach the T50 value. By splitting

the day’s water use such that half is achieved before the T50 and half fulfilled afterward, the

value acts as a center of mass and is calculated as

T50=∑ Q(d,h)

n

h=1 h

∑n_h=1Q(d,h). (5.3)

Expanding the center of mass definition to a 2-dimesional area results in the intersection of the AHF and T50 summarizing the diurnal curve profile as a single point at time T50 with flow AHF. It

is expected that the T50 nears the TP as the FP/A ratio increases due to the increasing

concentration of water volume around the peak. Similar to the TP, the T50 was not recorded for

dates with no measurable water flow.

Another indicator of water use intensity is the amount of time that the hourly flow exceeds the QA (TQ>QA). This value is calculated by counting each hour in which Q(d,h) > QA.

The resulting count represents the amount of time in hours that the water use by the building exceeded the mean and may be consecutive or non-consecutive. In either instance, a shorter

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duration recorded as the TQ>QA indicates events with higher intensity. It is expected that short

T_Q>QA values correlate with higher FP/A ratios.

Identifying characteristics of the highest peak flow event provides designers and operators with the most severe event that the system must be able to accommodate, but the appearance of additional peak events, although not necessarily of the same intensity, increases the stress placed on the system by decreasing the amount of time available to respond and recover between events. A higher frequency of intense peak events requires increased buffering capacity in the water supply system in the form of storage and affects pressure within the pipe network. The frequency of high-intensity peak events (NP) is determined by counting

the number of peak events that exceed the QA and result in a FP/A greater than 1.

Additional diurnal curve attributes considered include the median hourly flow (QM) and

the peak to median factor (FP/M) representing the ratio of the QP to QM. Flow data that follows a

normal distribution will result in a QM near to the QA and consequently a FP/A close to the FP/M.

Disagreement between mean flow attributes and median flow attributes indicates the presence of extreme outliers in the data, such as short-term high-consumption events.

The amount of variation within each diurnal curve is represented by the standard deviation (σ) of the 24-hour flow data defined as

σ=√1

n∑ [Q(d,h)-QA(d)] 2 n

h=1 . (5.4)

Demand profiles with relatively constant water flow throughout the day have small standard deviation values, whereas the standard deviation will increase as the range of observed flows throughout the day increases.

5.4.2.2 Trend Calculations

Two methods exist for estimating the average value for each attribute based on the data. The first method is based on the demand pattern produced by averaging the flow across all

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dates in the data set for each hour in order to create an hourly-average diurnal curve. The flow at each hour of the hourly-average curve follows the equation

Q(d_i,h)=∑ Q(d,h)

m d=1

m (5.5)

where Q(di,h) is the average flow for hour h within the set of dates d associated within set i. Set

i may include all dates of the study or represent a subset of dates separated by day of the week

or month of the year. Computing each attribute based on this demand profile and using the procedures described in Section 5.4.2.1 results in a set of hourly-average values. In the second method, attribute values for each daily diurnal curve are calculated and subsequently averaged thereby producing a set of daily-average values. The daily-average attribute values depend on the number of dates included in the set and are calculated as

X_i=∑ Xi(d)

m d=1

m (5.6)

where Xi indicates the attribute i being evaluated for a set of dates d from 1 to m. The collected

water flow data represents a sample of all potential water flows, and thus the standard deviation for daily-average attributes was calculated as

S=√ 1

(n-1)∑[Q(d,h)-QA(d)]2

n

h=1

(5.7)

in order to capture variation within each attribute for the set of dates. By grouping dates into subsets separated by day of the week or month of the year, temporal trends regarding diurnal curve daily-average attributes will be evaluated.

When comparing the set of hourly-average attributes to the total daily-average attributes, QA and TP values should remain constant regardless of the calculation method because, by

definition, each value is an average of the water use (mean flow and mean time) of the entire date set. However, it is expected that the hourly-average diurnal curve will dampen the intensity

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and frequency of hourly flows and result in measurable differences between the remaining hourly-average and daily-average attributes.

5.5 Results and Discussion