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Qobs,i is the observed flow for time step i
Qsimmod,i is the modelled flow for time step i
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Sensitive to extreme values and insensitive to small values. For example, the NSE is generally not suitable for evaluating the fit to low flows as the value will be dominated by the fit to high flows
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NSE of Log Data (NSE Log)
Definition
NSE Log is the standard NSE statistic (equation (1)) applied to the logarithm of flow data:
| Equation 2 |
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where
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c is a
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positive constant equal to the maximum of 1 ML and the 10th percentile of the observed flow
other terms are as defined in equation (1)
As with the standard NSE, the time step size is arbitrary. The NSE Log cannot be applied to time series with negative values, as the logarithm of a number less than or equal to zero is undefined.
Interpretation
Using the logarithm of flows has the effect of reducing the sensitivity of the statistic to high flows and increasing the sensitivity to low and mid-range flows. For this reason, NSE Log is often used where low-flow performance is important. The use of the constant c de-emphasises very small flows, which tend to be unreliable, and avoids numerical problems arising from attempting to calculate the logarithm of zero flows.
The NSE Log can range between -∞ and 1 and the interpretation is the same as for the NSE, but applied to log data.
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sNSE-Bias penalty (Nash-Sutcliffe coefficient of efficiency with penalised bias solutions), daily and monthly variants
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