def slope_fdc(da: DataArray,
lower_quantile: float = 0.33,
upper_quantile: float = 0.66) -> float:
# sort discharge by descending order
fdc = da.sortby(da, ascending=False)
# get idx of lower and upper quantile
idx_lower = np.round(lower_quantile * len(fdc)).astype(int)
idx_upper = np.round(upper_quantile * len(fdc)).astype(int)
value = (np.log(fdc[idx_lower].values +
1e-8)) - np.log(fdc[idx_upper].values +
1e-8) / (upper_quantile - lower_quantile)
return value
def slope_fdc(da: DataArray,
lower_quantile: float = 0.33,
upper_quantile: float = 0.66) -> float:
"""Calculates flow duration curve slope.
Slope of the flow duration curve (between the log-transformed `lower_quantile` and `upper_quantile`) [#]_ (Eq. 3).
Parameters
----------
da : DataArray
Array of flow values.
lower_quantile : float, optional
Lower quantile to use in slope calculation.
upper_quantile : float, optional
Upper quantile to use in slope calculation.
Returns
-------
float
Slope of the flow duration curve.
References
----------
.. [#] Sawicz, K., Wagener, T., Sivapalan, M., Troch, P. A., and Carrillo, G.: Catchment classification: empirical
analysis of hydrologic similarity based on catchment function in the eastern USA.
Hydrology and Earth System Sciences, 2011, 15, 2895--2911, doi:10.5194/hess-15-2895-2011
"""
# sort discharge by descending order
fdc = da.sortby(da, ascending=False)
# get idx of lower and upper quantile
idx_lower = np.round(lower_quantile * len(fdc)).astype(int)
idx_upper = np.round(upper_quantile * len(fdc)).astype(int)
value = (np.log(fdc[idx_lower].values +
1e-8)) - np.log(fdc[idx_upper].values +
1e-8) / (upper_quantile - lower_quantile)
return value
def _get_fdc(da: DataArray) -> np.ndarray:
return da.sortby(da, ascending=False).values
