def watt_m(simulated_array, observed_array, replace_nan=None, replace_inf=None,
           remove_neg=False, remove_zero=False):
    """Compute Watterson's M (M).

    .. image:: /pictures/M.png

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

    **Notes:**

    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
    -------
    float
        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.
    """

    # Treats data
    simulated_array, observed_array = treat_values(
        simulated_array,
        observed_array,
        replace_nan=replace_nan,
        replace_inf=replace_inf,
        remove_neg=remove_neg,
        remove_zero=remove_zero
    )

    a = 2 / np.pi
    b = np.mean((simulated_array - observed_array) ** 2)  # MSE
    c = np.std(observed_array, ddof=1) ** 2 + np.std(simulated_array, ddof=1) ** 2
    e = (np.mean(simulated_array) - np.mean(observed_array)) ** 2
    f = c + e
    return a * np.arcsin(1 - (b / f))
Compute Watterson's M (M).

    .. image:: /pictures/M.png

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

    **Notes:**

    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
    -------
    float
        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.