spearman_r

HydroErr.HydroErr.spearman_r(simulated_array, observed_array, replace_nan=None, replace_inf=None, remove_neg=False, remove_zero=False)

Compute the spearman rank correlation coefficient.

../_images/R_spearman.png

Range: -1 ≤ R (Pearson) ≤ 1. 1 indicates perfect postive correlation, 0 indicates complete randomness, -1 indicate perfect negative correlation.

Notes: The spearman r coefficient measures the monotonic relation between simulated and observed data. Because it uses a nonparametric measure of rank correlation, it is less sensitive to outliers compared to the Pearson correlation coefficient.

Parameters:
  • simulated_array (one dimensional ndarray) – An array of simulated data from the time series.
  • observed_array (one dimensional ndarray) – An array of observed data from the time series.
  • replace_nan (float, optional) – 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 (float, optional) – 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 (boolean, optional) – 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 (boolean, optional) – 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.
Returns:

The Spearman rank correlation coefficient.

Return type:

float

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.spearman_r(sim, obs)
0.942857142857143

References

  • Spearman C (1904). “The proof and measurement of association between two things”. American Journal of Psychology. 15: 72–101. doi:10.2307/1412159