mae

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

Compute the mean absolute error of the simulated and observed data.

../_images/MAE.png

Range: 0 ≤ MAE < inf, data units, smaller is better.

Notes: The ME measures the absolute difference between the simulated data and the observed data. For the mean abolute error, a smaller number indicates a better fit to the original data. Also note that random errors do not cancel. Also referred to as an L1-norm.

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 mean absolute error value.
Return type:

float

References

  • Willmott, Cort J., and Kenji Matsuura. “Advantages of the Mean Absolute Error (MAE) over the Root Mean Square Error (RMSE) in Assessing Average Model Performance.” Climate Research 30, no. 1 (2005): 79–82.
  • Willmott, Cort J., and Kenji Matsuura. “On the Use of Dimensioned Measures of Error to Evaluate the Performance of Spatial Interpolators.” International Journal of Geographical Information Science 20, no. 1 (2006): 89–102.

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, 6.8])
>>> he.mae(sim, obs)
0.5666666666666665