Introduction
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where:
Qobs,i is the observed flow for time step i
Qmod,i is the modelled flow for time step i
N is the number of time steps
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An alternative, but equivalent, formulation of the NSE is:
Equation 2 |
This formulation obviates the necessity to calculate the average of the observed flows before evaluating the denominator in the traditional version.
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where:
c is a positive constant equal to the maximum of 1 0.000000001 ML and the 10th percentile of the observed flow
other terms are as defined in Equation 1
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where:
Qobs,i is the observed flow for time step i
Qmod,i is the modelled flow for time step i
N is the number of time steps
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Common variations of the relative bias are to express it as a percent and/or as an absolute value. The bias in the modelled values expressed as a percent of the observed flow volume is defined as:
Equation 5 |
The absolute value of the relative bias is defined as:
Equation 6 |
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where B is the relative bias, as defined in Equation 4.
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Pearson's correlation coefficient measures the linear correlation between two variables. The sample Pearson's correlation coefficient is given by:
Equation 8 |
where:
xi is the value of time series x at time step i
yi is the value of time series y at time step i
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where:
RQobs,k is the k'th ranked observed flow of a total of N ranked flows RQsim,k is the k'th ranked modelled flow of a total of N ranked flows
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Interpretation
The Log Flow Duration measures the fit to the distribution of flow magnitudes and it is sensitive to low and mid-range flows.
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- the sum of errors on power transformed flow,
- the same sum on sorted flow values and
- the relative simulation bias.
The SDEB equation is:
Equation 11 |
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where:
α is a weighting factor set to 0.1
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Definition
Equation 12 | NSE Daily & Bias Penalty = NSE Daily – Bias Penalty |
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Definition
Equation 13 | NSE Log Daily & Bias Penalty = NSE Log Daily – Bias Penalty |
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Definition
Equation 14 | NSE Monthly & Bias Penalty = NSE Monthly – Bias Penalty |
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Definition
Equation 15 | NSE Daily & Flow Duration = a * NSE Daily + (1 - a) * Flow Duration |
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Definition
Equation 16 | NSE Daily & Log Flow Duration = a * NSE Daily + (1 - a) * Log Flow Duration |
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