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You might often hear the terms “diurnal flow” or “diurnal pattern” when referring to water or sewer system flows. This post provides a short overview of what those terms mean and how they are derived from flow measurements.

#### Diurnal Pattern Defined

For starters, let’s examine the Wikipedia definition: “A diurnal cycle is any pattern that recurs every 24 hours as a result of one full rotation of the Earth with respect to the Sun.” The article provides a simple example of the diurnal temperature cycle, which can be approximated as a repeating sinusoidal curve with a high temperature and a low temperate. In metered data from water or sewer systems, the diurnal patterns looks like the example in the image below generated with a diurnal model tool in H2Ometrics.

Diurnal for a week.

The image shows the diurnal pattern for each day of the week derived from from three years of data for a typical residential community. The first five days on the plot are the weekdays Monday – Friday, and the last two days are the weekend days of Saturday and Sunday. The diurnal pattern for each day of the week are derived from taking the median flow value for each time step of the week. For example the median of all of the Mondays at midnight is computed, then the median of all of the Mondays at 1:00 am, and so on, until the pattern for each day of the week is developed. The median is a useful function for computing diurnal patterns because it results in the filtering of outliers or occasional high flow spikes from rain events.

#### Interpreting the Diurnal Pattern

Each weekday contains two spikes in the flow – one in the morning and one in the evening. These spikes are often referred to as the “morning flush” and “evening flush”, reflecting the higher levels of activity and water use as people start their day and end their day. The flow typically reaches a minimum flow in the middle of the night, when few people are awake and using water. Also note that the last two days on the plot are the weekend days of Saturday and Sunday. The weekend days exhibit a sightly different pattern than weekdays. The differences in these patterns can be seen by overlaying the diurnal patterns for all the days on a single plot as shown below.

Diurnal flow for each day of the week.

From this plot, we can discern several interesting observations about the diurnal pattern, and the behavior of the residents of this area. These are common patterns that occur for most residential areas:

• The weekdays of Monday – Thursday (black line) have similar diurnal patterns with people generally following the same morning and evening routine for these days.
• Friday (red line) trends with other weekdays in the morning, but in the evening, Friday trends with Saturday night (blue line), indicating that people in this area tend to use less water on Friday and Saturday nights. This might indicate that they go out to eat more on those nights, or perhaps postpone doing evening chores until Sunday night.
• On Saturday and Sunday (blue and green lines), the morning flush tends to start a few hours later than it does on weekdays, indicating that people sleep in or get started on the daily activities later in the day on weekends. The spike of the morning flush is also higher than on weekdays, probably because people are catching up on weekly laundry, dish washing and cleaning.
• Sunday night (green line) behaves more like a weekday (black line), indicating that people are getting back into their weekday routines on Sunday night as the work week approaches.

#### Diurnal Pattern Tools in H2Ometrics

H2Ometrics contains a modeling module that allows users to create many model types including diurnal patterns, meter correlations, meter math, rainfall-runoff models and many others. The diurnal model creates a diurnal pattern from flow data using all of the data or a user-defined subset of the data. The diurnal model is useful for the following functions: