Using the Statistics tab of the Results Manager, you can carry out several types of statistical analyses on scenario results. For simplicity, they can be categorised into two groups:
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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 #3). A brief description of each bivariate statistic is given in Table 1, for more detailed information4, 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 Nash-Sutcliffe Efficiency
- The NSE of Flow Duration 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 Flow Duration.
- Relative Bias measures the magnitude of the model errors relative to the magnitude of the observations. See 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 Bias Penalty.
For more detailed information on bivariate statistics, see Bivariate Statistics - SRG. Parameter
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:
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Table 4. Bivariate Statistics
Statistic | Definition | Range | SRG entry |
|---|---|---|---|
Values Used | The number of time steps for which there are complete data pairs ie. both the X data and Y data time series have values. These pairs are used to calculate the bivariate statistics. Time steps where either series has missing values are not used. | 0 to +∞ | |
Values not used from X | The number of time steps in the X Data series that are not used in bivariate statistics calculations because either the X data or the Y data have missing values for those time steps. | 0 to +∞ | |
Values not used for Y | The number of time steps in the Y Data series that are not used in bivariate statistics calculations because either the X data or the Y data have missing values for those time steps. | 0 to +∞ | |
Pearson's Correlation (r) | Pearson's correlation coefficient measures the linear correlation between two variables. Pearson's correlation coefficient is symmetric, meaning that the value will be the same regardless of which time series is defined as X data (reference) and which as the Y data. See Pearson's Correlation Coefficient. | -1 to 1 |
Volume Bias (%) | Relative bias expressed as a percentage. See Relative Bias. | 0 to 100 | |
Minimise Absolute Bias | The absolute value of the relative bias |
. See Relative Bias. | 0 to +∞ |
| NSE |
| Daily | The NSE for using a daily time step. See Nash-Sutcliffe Efficiency. | -∞ to 1 | |
NSE Daily & Bias Penalty | The difference between NSE daily and the Bias Penalty. See NSE Daily & Bias Penalty. | -∞ to 1 | |
NSE Daily & Flow Duration | Combines the NSE Daily and Flow Duration using a user-defined weighting factor. See NSE Log Daily & Bias Penalty. | -∞ to 1 | |
| NSE Daily & log Flow Duration | Combines the NSE Daily and log Flow Duration using a user-defined weighting factor. Log flow duration is the NSE of flow duration of the logarithm of data, calculated using a daily time step. See NSE Daily & log Flow Duration. | -∞ to 1 | |
| NSE Log Daily | The NSE of the logarithm of data, using a daily time step. See NSE of Log Data. | -∞ to 1 | |
| NSE Log Daily & Bias Penalty | The difference between NSE Log daily and the Bias Penalty. See NSE Log Daily & Bias Penalty. | -∞ to 1 | |
| NSE Monthly | The NSE using a monthly time step. See Nash-Sutcliffe Efficiency. | -∞ to 1 | |
| NSE Monthly & Bias Penalty | The difference between NSE monthly and the Bias Penalty. See NSE Monthly & Bias Penalty. | -∞ to 1 | |
| Square-root Daily, Exceedance and Bias | Combines three terms, the sum of errors on power transformed flow, the same sum on sorted flow values, and the relative simulation bias. See Sum of Daily Flows, Daily Exceedance (Flow Duration) Curve and Bias. | 0 to +∞ |
Figure #3. Bivariate statistics, Total period
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where xi is the ith value of the flow series x, xt is the user-defined threshold value for x, yj is the jth value of the flow series y, and yt is the user-defined threshold for y. This statistic can be used to calculate several useful parameters such as Volumetric runoff coefficients and Stream Erosion Index(SEI). To calculate SEI, it is necessary to know the flow threshold (critical flow) below which no erosion is expected to occur within a waterway. This threshold can be represented (EarthTech, 2005) as a percentage of the pre‐development two-year ARI peak flow at the location in question. The percentage depends on the stream bed material and usually varies between 10 – 50%. The pre-development two-year ARI peak discharge can be estimated using flood frequency analysis or the rational method as described in Australian Rainfall and Runoff (Pilgrim, D.H., 2001). Flux Files containing the pre- and post-development outflows can be generated from MUSIC model run. SEI can be calculated by creating a custom chart in Results Manager where X data is the post-development outflow, Y data is the pre-development outflow, and both the X data and Y data threshold values are manually set to the value of critical flow using the appropriated fields next to the volumetric ratio. Although Results Manager can calculate a volumetric ratio for any two data series, currently this statistic supports data expressed as either volume (eg. ML) or rate (eg. m3/s). |
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