pastas.stats.metrics.kge
========================

.. py:function:: pastas.stats.metrics.kge(obs: pandas.Series, sim: pandas.Series, missing: str = 'drop', weighted: bool = False, max_gap: int = 30, modified: bool = False) -> float

   
   Compute the (weighted) Kling-Gupta Efficiency (KGE).

   :param sim: Series with the simulated values.
   :type sim: pandas.Series
   :param obs: The Series with the observed values.
   :type obs: pandas.Series
   :param missing: string with the rule to deal with missing values. Only "drop" is
                   supported now.
   :type missing: str, optional
   :param weighted: Weight the values by the normalized time step to account for
                    irregular time series. Default is False.
   :type weighted: bool, optional
   :param max_gap: maximum allowed gap period in days to use for the computation of the
                   weights. All time steps larger than max_gap are replace with the
                   max_gap value. Default value is 30 days.
   :type max_gap: int, optional
   :param modified: Use the modified KGE as proposed by :cite:t:`kling_runoff_2012`.
                    According to the article this ensures that the bias and variability
                    ratios are not cross-correlated, which otherwise may occur when inputs
                    are biased.
   :type modified: bool, optional

   .. rubric:: Notes

   The (weighted) Kling-Gupta Efficiency :cite:t:`kling_runoff_2012` is
   computed as follows:

   .. math:: \text{KGE} = 1 - \sqrt{(r-1)^2 + (\beta-1)^2 - (\gamma-1)^2}

   where :math:`\beta = \bar{x} / \bar{y}` and :math:`\gamma =
   \frac{\bar{\sigma}_x}{\bar{\sigma}_y}`. If modified equals True,
   :math:`\gamma = \frac{\bar{\sigma}_x / \bar{x}}{\bar{\sigma}_y /
   \bar{y}}`. If weighted equals True, the weighted mean, variance and
   pearson correlation are used.















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