def fdc_flv(obs: DataArray, sim: DataArray, l: float = 0.3) -> float:
"""Low flow bias derived from the flow duration curve.
Reference:
Yilmaz, K. K., Gupta, H. V., and Wagener, T. ( 2008), A process‐based diagnostic approach to model evaluation:
Application to the NWS distributed hydrologic model, Water Resour. Res., 44, W09417, doi:10.1029/2007WR006716.
"""
# verify inputs
_validate_inputs(obs, sim)
# get time series with only valid observations
obs, sim = _mask_valid(obs, sim)
if (l <= 0) or (l >= 1):
raise ValueError(
"l has to be in range ]0,1[. Consider small values, e.g. 0.3 for 30% low flows"
)
# get arrays of sorted (descending) discharges
obs = _get_fdc(obs)
sim = _get_fdc(sim)
# for numerical reasons change 0s to 1e-6. Simulations can still contain negatives, so also reset those.
sim[sim <= 0] = 1e-6
obs[obs == 0] = 1e-6
obs = obs[-np.round(l * len(obs)).astype(int) :]
sim = sim[-np.round(l * len(sim)).astype(int) :]
# transform values to log scale
obs = np.log(obs)
sim = np.log(sim)
# calculate flv part by part
qsl = np.sum(sim - sim.min())
qol = np.sum(obs - obs.min())
flv = -1 * (qsl - qol) / (qol + 1e-6)
return flv * 100
def fdc_flv(obs: DataArray, sim: DataArray, l: float = 0.3) -> float:
r"""Calculate the low flow bias of the flow duration curve [#]_
.. math::
\%\text{BiasFMS} = -1 \frac{\sum_{l=1}^{L}[\log(Q_{s,l}) - \log(Q_{s,L})] - \sum_{l=1}^{L}[\log(Q_{o,l})
- \log(Q_{o,L})]}{\sum_{l=1}^{L}[\log(Q_{o,l}) - \log(Q_{o,L})]} \times 100,
where :math:`Q_s` are the simulations (here, `sim`), :math:`Q_o` the observations (here, `obs`) and `L` is the lower
fraction of flows of the FDC (here, `l`).
Parameters
----------
obs : DataArray
Observed time series.
sim : DataArray
Simulated time series.
l : float, optional
Fraction of lower flows to consider as low flows of range ]0,1[, be default 0.3.
Returns
-------
float
Low flow bias.
References
----------
.. [#] Yilmaz, K. K., Gupta, H. V., and Wagener, T. ( 2008), A process-based diagnostic approach to model
evaluation: Application to the NWS distributed hydrologic model, Water Resour. Res., 44, W09417,
doi:10.1029/2007WR006716.
"""
# verify inputs
_validate_inputs(obs, sim)
# get time series with only valid observations
obs, sim = _mask_valid(obs, sim)
if len(obs) < 1:
return np.nan
if (l <= 0) or (l >= 1):
raise ValueError(
"l has to be in range ]0,1[. Consider small values, e.g. 0.3 for 30% low flows"
)
# get arrays of sorted (descending) discharges
obs = _get_fdc(obs)
sim = _get_fdc(sim)
# for numerical reasons change 0s to 1e-6. Simulations can still contain negatives, so also reset those.
sim[sim <= 0] = 1e-6
obs[obs == 0] = 1e-6
obs = obs[-np.round(l * len(obs)).astype(int):]
sim = sim[-np.round(l * len(sim)).astype(int):]
# transform values to log scale
obs = np.log(obs)
sim = np.log(sim)
# calculate flv part by part
qsl = np.sum(sim - sim.min())
qol = np.sum(obs - obs.min())
flv = -1 * (qsl - qol) / (qol + 1e-6)
return flv * 100