def alpha_nse(obs: DataArray, sim: DataArray) -> float:
# verify inputs
_validate_inputs(obs, sim)
# get time series with only valid observations
obs, sim = _mask_valid(obs, sim)
return float(sim.std() / obs.std())
def kge(obs: DataArray,
sim: DataArray,
weights: List[float] = [1., 1., 1.]) -> float:
r"""Calculate the Kling-Gupta Efficieny [#]_
.. math::
\text{KGE} = 1 - \sqrt{[ s_r (r - 1)]^2 + [s_\alpha ( \alpha - 1)]^2 +
[s_\beta(\beta_{\text{KGE}} - 1)]^2},
where :math:`r` is the correlation coefficient, :math:`\alpha` the :math:`\alpha`-NSE decomposition,
:math:`\beta_{\text{KGE}}` the fraction of the means and :math:`s_r, s_\alpha, s_\beta` the corresponding weights
(here the three float values in the `weights` parameter).
Parameters
----------
obs : DataArray
Observed time series.
sim : DataArray
Simulated time series.
weights : List[float]
Weighting factors of the 3 KGE parts, by default each part has a weight of 1.
Returns
-------
float
Kling-Gupta Efficiency
References
----------
.. [#] Gupta, H. V., Kling, H., Yilmaz, K. K., & Martinez, G. F. (2009). Decomposition of the mean squared error
and NSE performance criteria: Implications for improving hydrological modelling. Journal of hydrology, 377(1-2),
80-91.
"""
if len(weights) != 3:
raise ValueError("Weights of the KGE must be a list of three values")
# verify inputs
_validate_inputs(obs, sim)
# get time series with only valid observations
obs, sim = _mask_valid(obs, sim)
if len(obs) < 2:
return np.nan
r, _ = stats.pearsonr(obs.values, sim.values)
alpha = sim.std() / obs.std()
beta = sim.mean() / obs.mean()
value = (weights[0] * (r - 1)**2 + weights[1] * (alpha - 1)**2 +
weights[2] * (beta - 1)**2)
return 1 - np.sqrt(float(value))
def kge(obs: DataArray, sim: DataArray, weights: list = [1, 1, 1]) -> float:
if len(weights) != 3:
raise ValueError("Weights of the KGE must be a list of three values")
# verify inputs
_validate_inputs(obs, sim)
# get time series with only valid observations
obs, sim = _mask_valid(obs, sim)
r, _ = stats.pearsonr(obs.values, sim.values)
alpha = sim.std() / obs.std()
beta = sim.mean() / obs.mean()
value = (weights[0] * (r - 1)**2 + weights[1] * (alpha - 1)**2 +
weights[2] * (beta - 1)**2)
return 1 - np.sqrt(float(value))
def alpha_nse(obs: DataArray, sim: DataArray) -> float:
r"""Calculate the alpha NSE decomposition [#]_
The alpha NSE decomposition is the fraction of the standard deviations of simulations and observations.
.. math:: \alpha = \frac{\sigma_s}{\sigma_o},
where :math:`\sigma_s` is the standard deviation of the simulations (here, `sim`) and :math:`\sigma_o` is the
standard deviation of the observations (here, `obs`).
Parameters
----------
obs : DataArray
Observed time series.
sim : DataArray
Simulated time series.
Returns
-------
float
Alpha NSE decomposition.
References
----------
.. [#] Gupta, H. V., Kling, H., Yilmaz, K. K., & Martinez, G. F. (2009). Decomposition of the mean squared error
and NSE performance criteria: Implications for improving hydrological modelling. Journal of hydrology, 377(1-2),
80-91.
"""
# verify inputs
_validate_inputs(obs, sim)
# get time series with only valid observations
obs, sim = _mask_valid(obs, sim)
return float(sim.std() / obs.std())
