mae

HydroErr.HydroErr.mae(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 mean absolute error of the simulated and observed data.

\[MAE = \frac{1}{n} \sum_{i=0}^{n} | S_i - O_i |\]

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 – 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 mean absolute error value.

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