nse

HydroErr.HydroErr.nse(simulated_array: ndarray[tuple[Any, ...], dtype[floating | integer]] | Sequence[int | float], observed_array: ndarray[tuple[Any, ...], dtype[floating | integer]] | Sequence[int | float], replace_nan: float | None = None, replace_inf: float | None = None, remove_neg: bool = False, remove_zero: bool = False) → floating[Any]

Compute the Nash-Sutcliffe Efficiency.

\[NSE=1-\frac{\sum_{i=1}^{n}(S_i-O_i)^2}{\sum_{i=1}^{n}(O_i-\overline{O})^2}\]

Range: -inf < NSE < 1, does not indicate bias, larger is better.

Notes: The Nash-Sutcliffe efficiency metric compares prediction values to naive predictions (i.e. average value). One major flaw of this metric is that it punishes a higher variance in the observed values (denominator). This metric is analogous to the mean absolute error skill score (MAESS) using the mean flow as a benchmark.

Parameters:

  • simulated_array – An array of simulated data from the time series.

  • observed_array – An array of observed data from the time series.

  • replace_nan – If given, indicates which value to replace NaN values with in the two arrays. If None, when a NaN value is found at the i-th position in the observed OR simulated array, the i-th value of the observed and simulated array are removed before the computation.

  • replace_inf – If given, indicates which value to replace Inf values with in the two arrays. If None, when an inf value is found at the i-th position in the observed OR simulated array, the i-th value of the observed and simulated array are removed before the computation.

  • remove_neg – If True, when a negative value is found at the i-th position in the observed OR simulated array, the i-th value of the observed AND simulated array are removed before the computation.

  • remove_zero – If true, when a zero value is found at the i-th position in the observed OR simulated array, the i-th value of the observed AND simulated array are removed before the computation.

Return type:

The Nash-Sutcliffe Efficiency value.

Examples

>>> import HydroErr as he
>>> import numpy as np

>>> sim = np.array([5, 7, 9, 2, 4.5, 6.7])
>>> obs = np.array([4.7, 6, 10, 2.5, 4, 7])
>>> he.nse(sim, obs)
0.922093023255814

References

  • Krause, P., Boyle, D., Bäse, F., 2005. Comparison of different efficiency criteria for hydrological model assessment. Advances in geosciences 5 89-97.

  • McCuen, R.H., Knight, Z., Cutter, A.G., 2006. Evaluation of the Nash-Sutcliffe Efficiency Index. Journal of Hydraulic Engineering.

  • Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I — A discussion of principles. Journal of Hydrology 282-290.

  • Willmott, C.J., Robeson, S.M., Matsuura, K., 2012. A refined index of model performance. International Journal of Climatology 32(13) 2088-2094.