lm_index¶

Compute the Legate-McCabe Efficiency Index.

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

Range: 0 ≤ E1’ < 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 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.lm_index(sim, obs)
0.6949152542372882

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.