d1_p

HydroErr.HydroErr.d1_p(simulated_array: ndarray[tuple[Any, ...], dtype[floating | integer]] | Sequence[int | float], observed_array: ndarray[tuple[Any, ...], dtype[floating | integer]] | Sequence[int | float], obs_bar_p: float | None = None, replace_nan: float | None = None, replace_inf: float | None = None, remove_neg: bool = False, remove_zero: bool = False) → floating[Any]

Compute the Legate-McCabe Index of Agreement.

\[d_{1}^{'} = 1-\frac{\sum_{i=1}^{n}\left|S_i-O_i\right|}{\sum_{i=1}^{n} \left| S_i - \overline{O_i^{'}} \right| + \left| O_i - \overline{O_i^{'}} \right| }\]

Range: 0 ≤ d1’ < 1, does not indicate bias, larger is better.

Notes: The obs_bar_p argument represents a seasonal or other selected average.

Parameters:

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

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

  • obs_bar_p – Seasonal or other selected average. If None, the mean of the observed array will be used.

  • 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 Legate-McCabe Efficiency 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.d1_p(sim, obs)
0.8434782608695652

References

  • Legates, D.R., McCabe Jr, G.J., 1999. Evaluating the use of “goodness-of-fit” Measures in hydrologic and hydroclimatic model validation. Water Resources Research 35(1) 233-241. Lehmann, E.L., Casella, G., 1998. Springer Texts in Statistics. Springer-Verlag, New York.