Cumulative Frequency Graphs

Cumulative frequency graphs plot flow or concentration on the x-axis against the frequency of occurrence of that value or lower on the y-axis. This can be interpreted as the frequency of compliance with a given value. While time-series graphs provide an overview of behaviour, cumulative frequency graphs provide a more informative summary of treatment performance.

Setup and Accessing Cumulative Frequency Graph

To create the Cumulative Frequency Graph, the user needs to record a Flow Based Cumulative Frequency Graph (FBCFG) for the target nodes from the Parameters section in the Main Interface (Figure 1 (a)). Once the model is run, the graph can be accessed from the Results Manager (Figure 1 (b)).

Figure 1 Setup and Accessing Cumulative Frequency Graph

Creating Flow Based Cumulative Frequency Graph (FBCFG)

After running a scenario, the user can create an FBCFG from the Results Manager. Clicking on the recorded variable of FBCFG (Figure 1 (b)) will display the interface of the Flow Based Cumulative Frequency Graph (right panel in Figure 2)

Figure 2 The Interface of Flow Based Cumulative Frequency Graph (FBCFG)

Selecting the parameters shown on the graph

In the Property section (Figure 2), users can adjust the five avialable parameters displayed on the graph by selecting one of the following:

Flow
Gross Pollutants
Total Nitrogen
Total Phosphorus
Total Suspended Solids

Selecting the data source for the graph

The Node Selection Options (Figure 2) manage data sources for the current graph:

All other recorded nodes - Includes all nodes with recorded FBCFG data in the Node Selection section (Figure 3a).
Only this node – Displays only the FBCFG data from the currently selected node (Figure 3b).
Other nodes of this type – Includes nodes of the same type that have recorded FBCFG data (Figure 3 (c)). This option can be used to compare between pre-development and post- development results.

Additional Notes:

MUSICX allows multiple receiving nodes in a single scenario/model, enabling comparisons across different development stages.
By default, nodes only display their own data in the Selected Nodes Options section (Figure 3b). However, receiving nodes will have access to all other receiving nodes by default (Figure 3c).

Figure 3 The Data Sources for Flow Based Cumulative Frequency Graph (FBCFG)

Displaying Data in Chart and Table

The parameters at nodes in Nodes Selection cannot automatically appear in the chart and table, they must be manually updated. The user can click on the task node in Nodes Selection box to display selected parameters. The Nodes Selection box allows multiple selections and selected nodes in the box will change their background color to light blue. The Cumulative Frequency Graph of the selected parameter at selected nodes will be displayed in the chart and table (Figure 4).

Figure 4 The chart for Cumulative Frequency Graph (FBCFG)

Flow Bounds

There are substantial periods of zero flows. When the flow is zero, the concentration is undefined, leading to truncated curves of the form shown. The user can select the Upper and Lower Flow Threshold (e.g. 0.01 and 0.3 ML/day shown in Figure 4) from the Flow Bounds, and then the user must click on Apply Filter to apply. The thresholds modify the analysis at that point, but not the underlying simulation.

Note that although Flow Bounds are defined based on the flow data, all other parameters in the Property are re-analyzed also from the same bound data sample.

The use of Flow-Based Cumulative Frequency Graphs for the flow data in the above case is described here.

Application for the analysis

Cumulative Frequency Graphs are often used for the comparison between the different scenario results. For example, the user can compare pre-development and a post-development node data.

The page Results Manager provides a general user guide for the results manager. The details of some used tools for comparison in Figure 4 are described below:

Item	Icon	Discretion

Item	Icon	Discretion
The hint icon		after clicking on this icon, hovering the mouse over the graph will display the x, y values on UI
Edit graph propertied icon		The user can set up the graph properties such as line color, thickness, displayed name, etc. (Figure 5 from Figure 4))
Save options icon		Saves the graph as Image, Data file, or as Vector (Figure 5 from saved PNG image)
50, 98 per cent (%) lines		Displays reference lines for 50% and 98% respectively.
Tabel Tab		Shows graph data in tabular format including key percentage values (e.g. 50%, 98%)

MUSICX User Guide