dr

HydroErr.HydroErr.dr(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 the refined index of agreement (dr).

\[\text{Note:} \enspace ||S_i-O_i||=\sum_{i=1}^n|S_i-O_i|\]
\[\text{When} \enspace ||S_i-O_i|| \leq 2||O_i-\overline{O}||, \enspace d_r=1-\frac{||S_i-O_i||}{2||O_i-\overline{O}||}\]
\[\text{When} \enspace ||S_i-O_i|| > 2||O_i-\overline{O}||, \enspace d_r=\frac{2||O_i-\overline{O}||}{||S_i-O_i||}-1\]

Range: -1 ≤ dr < 1, does not indicate bias, larger is better.

Notes: Reformulation of Willmott’s index of agreement. This metric was created to address issues in the index of agreement and the Nash-Sutcliffe efficiency metric. Meant to be a flexible metric for use in climatology.

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 refined index of agreement.

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.dr(sim, obs)
0.847457627118644

References

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