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Single result

If a single time series is selected from the left-hand tree menu of the Results Manager window, the statistics tab will show univariate statistics (Figure 1). 522039484Univariate statistics provide information on a single result and are intended to summarise and reveal patterns in that result.

For statistics for a single result, you can:

• Choose the period type (Table 1) used to calculate the statistics from the drop-down menu;
• Change the Water Year Start from the default date (the default is set in Project Options);
• View the result used to calculate the statistics under Data;
• View the statistics themselves.

Multiple results

For multiple results in a custom chart, the statistics tab shows both univariate comparison (Figure 2) and bivariate statistics (Figure 3) for two of the results in the chart:

• Univariate comparison statistics are the same as univariate statistics for a single result, except that by default the statistics are only calculated from data that overlaps between the two results (see Table 2). To calculate univariate statistics for all data in each result, disable Calculate using overlapping data only.
• 522039484Bivariate statistics compare two results for the purpose of determining empirical relationships between them.

For statistics of multiple results, you can also:

• Toggle on or off two Statistics Options for how the two results are compared (Table 3);
• View and change the result used as the X Data (reference) and the Y Data for statistic calculations (in Figure 2, this is Downstream Flow Volume); and
• Select to view either Univariate Comparison or Bivariate statistics for the two results.

Table 1. Basic statistical analysis, period types

Table 2. Multiple results, parameters

Figure 1. Univariate statistics, single result.

Figure 2. Univariate statistics, multiple results, yearly summary

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NamingConventions NamingConventions

Naming conventions of difference, double mass and scatter statistics

If you have a custom chart with a chart type of difference, double mass or scatter, then the following naming conventions are used in the statistics tab (Figure 3):

• Each result in the custom chart is given a letter. This is shown in a Legend in the bottom left of the statistics tab.
• The series used as a reference in the chart is always given letter A. To change the reference series, go to the Chart view then select Chart Settings » Charts and modify Chart Type Reference Series.
• Under X Data (Reference) and Y (Data), the results are listed using the letters to represent each result.

For example, in Figure 3, A - B corresponds to the difference between Crab Creek's Downstream flow volume (result A) and Fish Creek's Downstream Flow Volume (result B). 

Figure 3. Statistics, Difference Chart Type

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UnivariateStatistics UnivariateStatistics

Univariate statistics

You can view univariate statistics for a single result (as shown in Figure 1) or for each individual result when multiple results are combined (Figure 2). A brief description of each univariate statistic is given in Table 1, for more detailed information see Univariate Statistics SRG.

Table 1. Univariate Statistics

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BivariateStatistics BivariateStatistics

Bivariate statistics

When two or more results are in a custom chart, a set of bivariate statistics is automatically generated and can be viewed on the Bivariate Statistics tab (Figure 4). A brief description of each bivariate statistic is given in Table 4, where:

• NSE (Nash-Sutcliffe Efficiency) measures the relative magnitude of the model error variance compared to the measured data variance. It can be applied at any time step size (eg. daily, monthly). See Bivariate Statistics SRG - Nash-Sutcliffe Efficiency
• The NSE of Flow Duration measures the NSE of the modelled and observed flow duration curves. It can be applied at any time step size (eg. daily, monthly). See Bivariate Statistics SRG - Flow Duration.
• Relative Bias measures the magnitude of the model errors relative to the magnitude of the observations. See Bivariate Statistics SRG - Relative Bias.
• Bias Penalty is log transformation of the absolute value of the relative bias. In Source, the bias penalty is always used in combination with the NSE and is not available on its own. It is designed to be used in model calibration to penalise biased solutions. See Bivariate Statistics SRG - Bias Penalty.
• Kling-Gupta Efficiency (KGE) measures several aspects of model performance such as correlation, bias and variance. It can also be applied to any time step. 
• Trotter is used to ensure capturing of both high and low flow aspects of a hydrograph and also to obtain minimal volumetric bias. Trotter is a composite bivariate statistics involving the KGE. Split Trotter and  Split Trotter Weighted are other modified Trotter objective functions. 

For more detailed information on bivariate statistics, see Bivariate Statistics SRG.

Parameter selection for bivariate statistics is the same as for a univariate comparison. If you select any period type other than Total, or you have disabled Calculate using overlapping data only and your start and/or end dates do not match, a subset of the statistics are available:

• Pearson's Correlation (r);
• NSE Daily;
• Volume Bias (%);
• Values used; and
• Values not used.

Table 4. Bivariate Statistics

Figure 4. Bivariate statistics, Total period

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