watt_m

HydroErr.HydroErr.watt_m(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 Watterson’s M (M).

\[M=\left(\frac{2}{\pi}\right)sin^{-1}\left(1-\frac{MSE}{\sigma^2_s+\sigma^2_o+(\overline{S}-\overline{O})^2}\right)\]

Range: -1 ≤ M < 1, does not indicate bias, larger is better.

Notes:

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:

Watterson’s M 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.watt_m(sim, obs)
0.8307913876595929

References

• Watterson, I.G., 1996. Non-dimensional measures of climate model performance. International Journal of Climatology 16(4) 379-391.