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Nash Sutcliffe Coefficient of Efficiency (NSE)
NSE of Daily Flows
The traditional formula for the NSE is:
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Alternatively, the NSE may be written as:
| Equation 2 |
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This formulation obviates the necessity to calculate the average of the observed flows before evaluating the denominator in the traditional version.
NSE of Log Transformed Flows
NSE of Monthly Flows
This objective function uses equation for the NSE of daily flows (equation (1)), but applies it to monthly rather than daily data:
- If the model is run on a daily time step, Qobsi becomes the sum of the observed flows for month i and Qsimi becomes the sum of the modelled flow for month i. The NSE calculation ignores observed and modelled data for all months where there are one or more days of missing data in the observed flow series.
- If the model is run on a monthly time step, then the monthly values are unchanged.
Flow Duration
The flow duration objective function sorts the observed and modelled data values in increasing order and then calculates the NSE of the sorted data.
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The bias penalty objective function is described in Viney et al. (2009). The equation is given by:
| Equation 4 |
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where B is the absolute value of the relative bias, as defined in equation (3).
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Combinations of the NSE, Flow Duration and Bias Penalty Objective Functions
The following nine forms of objective function are available in Source:
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