Question About the CRPS Calculation Method in crepes

[zryao]

Dear Boström,

I hope this message finds you well. I have encountered some confusion regarding in the algorithm. From my understanding, there are multiple ways to compute CRPS, and the results I obtained using other methods differ from those generated by crepes. In fact, some of the results seem contradictory.If the norm method is introduced, the CRPS obtained in crepes tends to be smaller; otherwise, the resulting CRPS remains unchanged.

Could you please clarify which specific method for calculating CRPS is used in crepes, and why there might be differences compared to other methods? I would greatly appreciate your guidance on this matter.

here is my code to caculate CRPS:

def crps_my_without_Fy(y_vals, x_obs):
    """
    Parameters:
    -----------
    y_vals : array-like
        Forecasted values (ensemble members).
    x_obs : float
        The observed value.

    Returns:
    --------
    crps : float
        The calculated CRPS value.
    """
    N = len(y_vals)

    # First term: Average absolute difference between forecasts and observation
    T1 = np.mean(np.abs(y_vals - x_obs))

    # Second term: Half the average absolute difference between all pairs of forecasts
    pairwise_diffs = np.abs(y_vals.reshape(-1, 1) - y_vals)
    T2 = 0.5 * np.mean(pairwise_diffs)

    crps = T1 - T2
    return crps

Thank you for your time and assistance.