dmod

HydroErr.HydroErr.dmod(simulated_array: ndarray[tuple[Any, ...], dtype[floating | integer]] | Sequence[int | float], observed_array: ndarray[tuple[Any, ...], dtype[floating | integer]] | Sequence[int | float], j: float = 1, replace_nan: float | None = None, replace_inf: float | None = None, remove_neg: bool = False, remove_zero: bool = False) → floating[Any]

Compute the the modified index of agreement (dmod).

\[d_{mod}=1-\frac{\sum_{i=1}^{n}|S_i-O_i|^j}{\sum_{i=1}^{n}(|S_i-\overline{O}|+|O_i-\overline{O}|)^j}\]

Range: 0 ≤ dmod < 1, does not indicate bias, larger is better.

Notes: When j=1, this metric is the same as d1. As j becomes larger, outliers have a larger impact on the value.

Parameters:

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

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

  • j – Optional input indicating the j values desired. A higher j places more emphasis on outliers. j is 1 by default.

  • 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 modified index of agreement.

Examples

Note that using the default is the same as calculating the d1 metric. Changing the value of j modification of the metric.

>>> 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.dmod(sim, obs)  # Same as d1
0.8434782608695652
>>> he.dmod(sim, obs, j=1.5)
0.9413310986805733

References

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