"""This module contains all the stress models available in Pastas.
Stress models are used to translate an input time series into contribution that
explains (part of) the output series.
Examples
--------
>>> sm = ps.StressModel(stress, rfunc=ps.Gamma(), name="sm1")
>>> ml.add_stressmodel(stressmodel=sm)
See Also
--------
pastas.model.Model.add_stressmodel
"""
from logging import getLogger
# Type Hinting
from typing import List, Optional, Tuple, Union
import numpy as np
from pandas import DataFrame, Series, Timedelta, Timestamp, concat, date_range
from scipy.signal import fftconvolve
from pastas.typing import ArrayLike, Model, Recharge, RFunc, TimestampType
from .decorators import njit, set_parameter
from .recharge import Linear
from .rfunc import Exponential, HantushWellModel, One
from .timeseries import TimeSeries
from .utils import validate_name
logger = getLogger(__name__)
__all__ = [
"StressModel",
"Constant",
"StepModel",
"LinearTrend",
"RechargeModel",
"WellModel",
"TarsoModel",
"ChangeModel",
]
[docs]class StressModelBase:
"""StressModel Base class called by each StressModel object.
Attributes
----------
name: str
Name of this stressmodel object. Used as prefix for the parameters.
parameters: pandas.DataFrame
The DataFrame containing the parameters.
"""
_name = "StressModelBase"
[docs] def __init__(
self,
name: str,
tmin: TimestampType,
tmax: TimestampType,
rfunc: Optional[RFunc] = None,
up: bool = True,
gain_scale_factor: float = 1.0,
) -> None:
self.name = validate_name(name)
self.tmin = tmin
self.tmax = tmax
self.freq = None
if rfunc is not None:
rfunc.update_rfunc_settings(up=up, gain_scale_factor=gain_scale_factor)
self.rfunc = rfunc
self.parameters = DataFrame(columns=["initial", "pmin", "pmax", "vary", "name"])
self.stress = []
@property
def nparam(self) -> Tuple[int]:
return self.parameters.index.size
[docs] def set_init_parameters(self) -> None:
"""Set the initial parameters (back) to their default values."""
@set_parameter
def _set_initial(self, name: str, value: float) -> None:
"""Internal method to set the initial parameter value.
Notes
-----
The preferred method for parameter setting is through the model.
"""
self.parameters.loc[name, "initial"] = value
@set_parameter
def _set_pmin(self, name: str, value: float) -> None:
"""Internal method to set the lower bound of the parameter value.
Notes
-----
The preferred method for parameter setting is through the model.
"""
self.parameters.loc[name, "pmin"] = value
@set_parameter
def _set_pmax(self, name: str, value: float) -> None:
"""Internal method to set the upper bound of the parameter value.
Notes
-----
The preferred method for parameter setting is through the model.
"""
self.parameters.loc[name, "pmax"] = value
@set_parameter
def _set_vary(self, name: str, value: float) -> None:
"""Internal method to set if the parameter is varied during optimization.
Notes
-----
The preferred method for parameter setting is through the model.
"""
self.parameters.loc[name, "vary"] = bool(value)
[docs] def update_stress(
self,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
) -> None:
"""Method to update the settings of the all stresses in the stress model.
Parameters
----------
freq: str, optional
String representing the desired frequency of the time series. Must be one
of the following: (D, h, m, s, ms, us, ns) or a multiple of that e.g. "7D".
tmin: str or pandas.Timestamp, optional
String that can be converted to, or a Pandas Timestamp with the minimum
time of the series.
tmax: str or pandas.Timestamp, optional
String that can be converted to, or a Pandas Timestamp with the maximum
time of the series.
Notes
-----
For the individual options for the different settings please refer to the
docstring from the TimeSeries.update_series() method.
See Also
--------
ps.timeseries.TimeSeries.update_series
"""
for stress in self.stress:
stress.update_series(freq=freq, tmin=tmin, tmax=tmax)
if freq:
self.freq = freq
[docs] def get_stress(
self,
p: Optional[ArrayLike] = None,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
istress: Optional[int] = None,
**kwargs,
) -> DataFrame:
"""Returns the stress(es) of the time series object as a pandas DataFrame.
If the time series object has multiple stresses each column represents a stress.
Returns
-------
stress: pandas.Dataframe
Pandas dataframe of the stress(es)
"""
if tmin is None:
tmin = self.tmin
if tmax is None:
tmax = self.tmax
self.update_stress(tmin=tmin, tmax=tmax, freq=freq)
return self.stress[0].series
[docs] def to_dict(self, **kwargs):
"""Method to export the stress model object."""
[docs] def get_nsplit(self) -> int:
"""Determine in how many time series the contribution can be split."""
if hasattr(self, "nsplit"):
return self.nsplit
else:
return len(self.stress)
def _get_block(
self, p: ArrayLike, dt: float, tmin: TimestampType, tmax: TimestampType
) -> ArrayLike:
"""Internal method to get the block-response function."""
if tmin is not None and tmax is not None:
day = Timedelta(1, "D")
maxtmax = (Timestamp(tmax) - Timestamp(tmin)) / day
else:
maxtmax = None
b = self.rfunc.block(p, dt, maxtmax=maxtmax)
return b
[docs] def get_settings(self) -> dict:
"""Method to obtain the settings of the stresses.
Returns
-------
settings: dict
Notes
-----
To update the settings of the time series, use the `update_stress` method.
"""
if len(self.stress) == 0:
settings = None
else:
settings = {stress.name: stress.settings for stress in self.stress}
return settings
[docs]class StressModel(StressModelBase):
"""Stress model convoluting a stress with a response function.
Parameters
----------
stress: pandas.Series
pandas.Series with pandas.DatetimeIndex containing the stress.
rfunc: pastas.rfunc instance
An instance of the response function used in the convolution with the stress.
name: str
Name of the stress.
up: bool or None, optional
True if response function is positive (default), False if negative. None if
you don't want to define if response is positive or negative.
settings: dict or str, optional
The settings of the stress. This can be a string referring to a predefined
settings dict (defined in ps.rcParams["timeseries"]), or a dict with the
settings to apply. Refer to the docs of pastas.Timeseries for further
information.
metadata: dict, optional
dictionary containing metadata about the stress. This is passed onto the
TimeSeries object.
gain_scale_factor: float, optional
the scale factor is used to set the initial value and the bounds of the gain
parameter, computed as 1 / gain_scale_factor.
Examples
--------
>>> import pastas as ps
>>> import pandas as pd
>>> sm = ps.StressModel(stress=pd.Series(), rfunc=ps.Gamma(), name="Prec",
>>> settings="prec")
See Also
--------
pastas.rfunc
pastas.timeseries.TimeSeries
"""
_name = "StressModel"
[docs] def __init__(
self,
stress: Series,
rfunc: RFunc,
name: str,
up: bool = True,
settings: Optional[Union[dict, str]] = None,
metadata: Optional[dict] = None,
gain_scale_factor: Optional[float] = None,
) -> None:
stress = TimeSeries(stress, settings=settings, metadata=metadata)
StressModelBase.__init__(
self,
name=name,
tmin=stress.series.index.min(),
tmax=stress.series.index.max(),
rfunc=rfunc,
up=up,
gain_scale_factor=stress.series.std()
if gain_scale_factor is None
else gain_scale_factor,
)
self.gain_scale_factor = gain_scale_factor
self.freq = stress.settings["freq"]
self.stress.append(stress)
self.set_init_parameters()
[docs] def set_init_parameters(self) -> None:
"""Set the initial parameters (back) to their default values."""
self.parameters = self.rfunc.get_init_parameters(self.name)
[docs] def simulate(
self,
p: ArrayLike,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
dt: float = 1.0,
) -> Series:
"""Simulates the head contribution.
Parameters
----------
p: array_like
array_like object with the values as floats representing the model
parameters.
tmin: str, optional
tmax: str, optional
freq: str, optional
dt: int, optional
Returns
-------
pandas.Series
The simulated head contribution.
"""
self.update_stress(tmin=tmin, tmax=tmax, freq=freq)
b = self._get_block(p, dt, tmin, tmax)
stress = self.stress[0].series
npoints = stress.index.size
h = Series(
data=fftconvolve(stress, b, "full")[:npoints],
index=stress.index,
name=self.name,
fastpath=True,
)
return h
[docs] def to_dict(self, series: bool = True) -> dict:
"""Method to export the StressModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the StressModel
object.
Notes
-----
Settings and metadata are exported with the stress.
"""
data = {
"class": self._name,
"rfunc": self.rfunc.to_dict(),
"name": self.name,
"up": self.rfunc.up,
"stress": self.stress[0].to_dict(series=series),
"gain_scale_factor": self.gain_scale_factor,
}
return data
[docs]class StepModel(StressModelBase):
"""Stressmodel that simulates a step trend.
Parameters
----------
tstart: str or Timestamp
String with the start date of the step, e.g. '2018-01-01'. This value is
fixed by default. Use ml.set_parameter("step_tstart", vary=True) to vary the
start time of the step trend.
name: str
String with the name of the stressmodel.
rfunc: pastas.rfunc instance
Pastas response function used to simulate the effect of the step. Default is
ps.rfunc.One(), an instant effect.
up: bool, optional
Force a direction of the step. Default is None.
Notes
-----
The step trend is calculated as follows. First, a binary series is created,
with zero values before tstart, and ones after the start. This series is
convoluted with the block response to simulate a step trend.
"""
_name = "StepModel"
[docs] def __init__(
self,
tstart: TimestampType,
name: str,
rfunc: Optional[RFunc] = None,
up: bool = True,
) -> None:
if rfunc is None:
rfunc = One()
StressModelBase.__init__(
self,
name=name,
tmin=Timestamp.min,
tmax=Timestamp.max,
rfunc=rfunc,
up=up,
)
self.tstart = Timestamp(tstart)
self.set_init_parameters()
[docs] def set_init_parameters(self) -> None:
self.parameters = self.rfunc.get_init_parameters(self.name)
tmin = Timestamp.min.toordinal()
tmax = Timestamp.max.toordinal()
tinit = self.tstart.toordinal()
self.parameters.loc[self.name + "_tstart"] = (
tinit,
tmin,
tmax,
False,
self.name,
)
[docs] def simulate(
self,
p: ArrayLike,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
dt: float = 1.0,
) -> Series:
tstart = Timestamp.fromordinal(int(p[-1]))
tindex = date_range(tmin, tmax, freq=freq)
h = Series(0, tindex, name=self.name)
h.loc[h.index > tstart] = 1
b = self._get_block(p[:-1], dt, tmin, tmax)
npoints = h.index.size
h = Series(
data=fftconvolve(h, b, "full")[:npoints],
index=h.index,
name=self.name,
fastpath=True,
)
return h
[docs] def to_dict(self, **kwargs) -> dict:
"""Method to export the StepModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct object.
"""
data = {
"class": self._name,
"tstart": self.tstart,
"name": self.name,
"rfunc": self.rfunc.to_dict(),
"up": self.rfunc.up,
}
return data
[docs]class LinearTrend(StressModelBase):
"""Stressmodel that simulates a linear trend.
Parameters
----------
start: str
String with a date to start the trend (e.g., "2018-01-01"), will be
transformed to an ordinal number internally.
end: str
String with a date to end the trend (e.g., "2018-01-01"), will be transformed
to an ordinal number internally.
name: str, optional
String with the name of the stress model.
Notes
-----
While possible, it is not recommended to vary the parameters for the start and
end time of the linear trend. These parameters are usually hard or even impossible
to estimate from the data.
"""
_name = "LinearTrend"
[docs] def __init__(
self, start: TimestampType, end: TimestampType, name: str = "trend"
) -> None:
StressModelBase.__init__(
self, name=name, tmin=Timestamp.min, tmax=Timestamp.max
)
self.start = start
self.end = end
self.set_init_parameters()
[docs] def set_init_parameters(self) -> None:
"""Set the initial parameters for the stress model."""
start = Timestamp(self.start).toordinal()
end = Timestamp(self.end).toordinal()
tmin = Timestamp.min.toordinal()
tmax = Timestamp.max.toordinal()
self.parameters.loc[self.name + "_a"] = (0.0, -np.inf, np.inf, True, self.name)
self.parameters.loc[self.name + "_tstart"] = (
start,
tmin,
tmax,
False,
self.name,
)
self.parameters.loc[self.name + "_tend"] = (end, tmin, tmax, False, self.name)
[docs] def simulate(
self,
p: ArrayLike,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
dt: float = 1.0,
) -> Series:
"""Simulate the trend."""
tindex = date_range(tmin, tmax, freq=freq)
if p[1] < tindex[0].toordinal():
tmin = tindex[0]
else:
tmin = Timestamp.fromordinal(int(p[1]))
if p[2] >= tindex[-1].toordinal():
tmax = tindex[-1]
else:
tmax = Timestamp.fromordinal(int(p[2]))
trend = tindex.to_series().diff() / Timedelta(1, "D")
trend.loc[:tmin] = 0
trend.loc[tmax:] = 0
trend = trend.cumsum() * p[0]
return trend.rename(self.name)
[docs] def to_dict(self, **kwargs) -> dict:
"""Method to export a dictionary to reconstruct the stressmodel.
Parameters
----------
kwargs
Returns
-------
data: dict
"""
data = {
"class": self._name,
"start": self.start,
"end": self.end,
"name": self.name,
}
return data
[docs]class Constant(StressModelBase):
"""A constant value that is added to the time series model.
Parameters
----------
name: str, optional
Name of the stressmodel.
initial: float, optional
Initial estimate of the parameter value. For example, the minimum of the
observed series.
"""
_name = "Constant"
[docs] def __init__(self, name: str = "constant", initial: float = 0.0) -> None:
StressModelBase.__init__(
self, name=name, tmin=Timestamp.min, tmax=Timestamp.max
)
self.initial = initial
self.set_init_parameters()
[docs] def set_init_parameters(self):
self.parameters.loc[self.name + "_d"] = (
self.initial,
np.nan,
np.nan,
True,
self.name,
)
[docs] @staticmethod
def simulate(p: Optional[float] = None) -> float:
return p
[docs] def to_dict(self, **kwargs):
"""Method to export the StressModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the StressModel
object.
"""
data = {
"class": self._name,
"name": self.name,
"initial": self.initial,
}
return data
[docs]class WellModel(StressModelBase):
"""Convolution of one or more stresses with a single scaled response function.
Parameters
----------
stress: list
list containing the stresses time series.
name: str
name of the stressmodel.
distances: array_like
array_like of distances between the stresses (wells) and the oseries
(monitoring well), must be in the same order as the stresses. This
distance is used to scale the HantushWellModel response function for
each stress.
rfunc: pastas.rfunc instance, optional
this model only works with the HantushWellModel response function, default is
None which will initialize a HantushWellModel response function.
up: bool, optional
whether a positive stress has an increasing or decreasing effect on the model,
by default False, in which case positive stress lowers e.g., the groundwater
level.
settings: str, list of dict, optional
The settings of the stress. By default this is "well". This can be a string
referring to a predefined settings dict (defined in
ps.rcParams["timeseries"]), or a dict with the settings to apply. Refer
to the docs of pastas.Timeseries for further information.
sort_wells: bool, optional
sort wells from closest to furthest, by default True.
Notes
-----
This class implements convolution of multiple series with the same response
function. This can be applied when dealing with multiple wells in a time series
model. The distance(s) from the pumping well(s) to the monitoring well have to be
provided for each stress.
Only works with the HantushWellModel response function.
"""
_name = "WellModel"
[docs] def __init__(
self,
stress: List[Series],
name: str,
distances: ArrayLike,
rfunc: Optional[RFunc] = None,
up: bool = False,
settings: str = "well",
sort_wells: bool = True,
metadata: Optional[list] = None,
) -> None:
# check response function
if rfunc is None:
rfunc = HantushWellModel()
elif not isinstance(rfunc, HantushWellModel):
raise NotImplementedError(
"WellModel only supports the rfunc HantushWellModel!"
)
# check if number of stresses and distances match
if len(stress) != len(distances):
msg = (
"The number of stresses does not match the number of distances "
"provided."
)
logger.error(msg)
raise ValueError(msg)
else:
self.distances = Series(
index=[s.squeeze().name for s in stress],
data=distances,
name="distances",
)
# parse settings input
if settings is None or isinstance(settings, str) or isinstance(settings, dict):
settings = len(stress) * [settings]
# if metadata is passed as dict -> convert to list
if metadata is not None and isinstance(metadata, dict):
metadata = [metadata]
# parse stresses input
stress = self._handle_stress(stress, settings, metadata)
# sort wells by distance
self.sort_wells = sort_wells
if self.sort_wells:
stress = [
s for _, s in sorted(zip(distances, stress), key=lambda pair: pair[0])
]
distances = np.sort(distances)
# estimate gain_scale_factor w/ max of stresses stdev
gain_scale_factor = np.max([s.series.std() for s in stress])
tmin = np.min([s.series.index.min() for s in stress])
tmax = np.max([s.series.index.max() for s in stress])
StressModelBase.__init__(
self,
name=name,
tmin=tmin,
tmax=tmax,
rfunc=rfunc,
up=up,
gain_scale_factor=gain_scale_factor,
)
self.rfunc.set_distances(self.distances.values)
self.stress = stress
self.freq = self.stress[0].settings["freq"]
self.set_init_parameters()
[docs] def set_init_parameters(self) -> None:
self.parameters = self.rfunc.get_init_parameters(self.name)
[docs] def simulate(
self,
p: Optional[ArrayLike] = None,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
dt: float = 1.0,
istress: Optional[int] = None,
**kwargs,
) -> Series:
distances = self.get_distances(istress=istress)
stress_df = self.get_stress(
p=p, tmin=tmin, tmax=tmax, freq=freq, istress=istress, squeeze=False
)
h = Series(data=0, index=self.stress[0].series.index, name=self.name)
for name, r in distances.items():
stress = stress_df.loc[:, name]
npoints = stress.index.size
p_with_r = np.concatenate([p, np.array([r])])
b = self._get_block(p_with_r, dt, tmin, tmax)
c = fftconvolve(stress, b, "full")[:npoints]
h = h.add(Series(c, index=stress.index, fastpath=True), fill_value=0.0)
if istress is not None:
if isinstance(istress, list):
h.name = self.name + "_" + "+".join(str(i) for i in istress)
elif self.stress[istress].name is not None:
h.name = self.stress[istress].name
else:
h.name = self.name + "_" + str(istress)
else:
h.name = self.name
return h
@staticmethod
def _handle_stress(stress, settings, metadata):
"""Internal method to handle user provided stress in init.
Parameters
----------
stress: pandas.Series, list or dict
stress or collection of stresses.
settings: dict or iterable
settings dictionary.
metadata : dict or list of dict
metadata dictionaries corresponding to stress
Returns
-------
stress: list
return a list with the stresses transformed to pastas TimeSeries.
"""
data = []
if isinstance(stress, Series):
data.append(TimeSeries(stress, settings=settings, metadata=metadata))
elif isinstance(stress, dict):
for i, (name, value) in enumerate(stress.items()):
if metadata is not None:
imeta = metadata[i]
else:
imeta = None
data.append(
TimeSeries(value, name=name, settings=settings[i], metadata=imeta)
)
elif isinstance(stress, list):
for i, value in enumerate(stress):
if metadata is not None:
imeta = metadata[i]
else:
imeta = None
data.append(TimeSeries(value, settings=settings[i], metadata=imeta))
else:
msg = "Cannot parse 'stress' input. Provide a Series, dict or list."
logger.error(msg)
raise TypeError(msg)
return data
[docs] def get_stress(
self,
p: Optional[ArrayLike] = None,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
istress: Optional[int] = None,
squeeze: bool = True,
**kwargs,
) -> DataFrame:
if tmin is None:
tmin = self.tmin
if tmax is None:
tmax = self.tmax
self.update_stress(tmin=tmin, tmax=tmax, freq=freq)
if istress is None:
df = DataFrame.from_dict({s.name: s.series for s in self.stress})
if squeeze:
return df.squeeze()
else:
return df
elif isinstance(istress, list):
return DataFrame.from_dict({s.name: s.series for s in self.stress}).iloc[
:, istress
]
else:
if squeeze:
return self.stress[istress].series
else:
return self.stress[istress].series.to_frame()
[docs] def get_distances(self, istress: Optional[int] = None) -> DataFrame:
if istress is None:
return self.distances
elif isinstance(istress, list):
return self.distances.iloc[istress]
else:
return self.distances.iloc[istress : istress + 1]
[docs] def get_parameters(self, model=None, istress: Optional[int] = None) -> ArrayLike:
"""Get parameters including distance to observation point and return as array
(dimensions = (nstresses, 4)).
Parameters
----------
model : pastas.Model, optional
if provided, return optimal model parameters, else return initial
parameters.
istress : int, optional
if provided, return specific parameter set, else return all parameters.
Returns
-------
p : array_like
parameters for each stress as row of array, if istress is used returns
only one row.
"""
if model is None:
p = self.parameters.initial.values
else:
p = model.get_parameters(self.name)
distances = self.get_distances(istress=istress).values
if distances.size > 1:
p_with_r = np.concatenate(
[np.tile(p, (distances.size, 1)), distances[:, np.newaxis]], axis=1
)
else:
p_with_r = np.r_[p, distances]
return p_with_r
[docs] def dump_stress(self, series: bool = True) -> list:
"""Method to dump all stresses in the stresses list.
Parameters
----------
series: bool, optional
True if time series are to be exported, False if only the name
of the time series are needed. Settings are always exported.
Returns
-------
data: dict
dictionary with the dump of the stresses.
"""
data = []
for stress in self.stress:
stress.name = validate_name(stress.name, raise_error=True)
data.append(stress.to_dict(series=series))
return data
[docs] def to_dict(self, series: bool = True) -> dict:
"""Method to export the WellModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the WellModel
object.
"""
data = {
"class": self._name,
"stress": self.dump_stress(series),
"rfunc": self.rfunc.to_dict(),
"name": self.name,
"distances": self.distances.to_list(),
"up": True if self.rfunc.up else False,
"sort_wells": self.sort_wells,
}
return data
[docs] def variance_gain(
self, model: Model, istress: Optional[int] = None, r: Optional[ArrayLike] = None
) -> float:
"""Calculate variance of the gain for WellModel.
Variance of the gain is calculated based on propagation of uncertainty using
optimal parameter values and the estimated variances of A and b and the
covariance between A and b.
Parameters
----------
model : pastas.Model
optimized model
istress : int or list of int, optional
index of stress(es) for which to calculate variance of gain
r : array_like, optional
radial distance(s) at which to calculate variance of the gain,
only considered if istress is None
Returns
-------
var_gain : float
variance of the gain calculated from model results for parameters A and b.
See Also
--------
pastas.HantushWellModel.variance_gain
"""
if model.fit is None:
raise AttributeError("Model not optimized! Run solve() first!")
if self.rfunc._name != "HantushWellModel":
raise ValueError("Response function must be HantushWellModel!")
if model.fit.pcov.isna().all(axis=None):
model.logger.warning("Covariance matrix contains only NaNs!")
# get parameters and (co)variances
A = model.parameters.loc[self.name + "_A", "optimal"]
b = model.parameters.loc[self.name + "_b", "optimal"]
var_A = model.fit.pcov.loc[self.name + "_A", self.name + "_A"]
var_b = model.fit.pcov.loc[self.name + "_b", self.name + "_b"]
cov_Ab = model.fit.pcov.loc[self.name + "_A", self.name + "_b"]
if istress is None and r is None:
r = np.asarray(self.distances)
elif isinstance(istress, int) or isinstance(istress, list):
if r is not None:
logger.warning("kwarg 'r' is only used if istress is None!")
r = self.distances.iloc[istress]
elif istress is not None and r is None:
raise ValueError("Parameter 'istress' must be None, list or int!")
return self.rfunc.variance_gain(A, b, var_A, var_b, cov_Ab, r=r)
[docs]class RechargeModel(StressModelBase):
"""Stressmodel simulating the effect of groundwater recharge on the head.
Parameters
----------
prec: pandas.Series
pandas.Series with pandas.DatetimeIndex containing the precipitation series.
evap: pandas.Series
pandas.Series with pandas.DatetimeIndex containing the potential evaporation
series.
rfunc: pastas.rfunc instance, optional
Instance of the response function used in the convolution with the stress.
Default is ps.Exponential().
name: str, optional
Name of the stress. Default is "recharge".
recharge: pastas.recharge instance, optional
Instance of a recharge model. Options are: Linear, FlexModel and Berendrecht.
These can be accessed through ps.rch. Default is ps.rch.Linear().
temp: pandas.Series, optional
pandas.Series with pandas.DatetimeIndex containing the temperature series.
It depends on the recharge model is this argument is required or not.
settings: list of dicts or str, optional
The settings of the precipitation and evaporation time series, in this order.
This can be a string referring to a predefined settings dict (defined in
ps.rcParams["timeseries"]), or a dict with the settings to apply. Refer to
the docs of pastas.Timeseries for further information.
metadata: tuple of dicts or list of dicts, optional
dictionary containing metadata about the stress. This is passed onto the
TimeSeries object.
See Also
--------
pastas.rfunc
pastas.timeseries.TimeSeries
pastas.recharge
Notes
-----
This stress model computes the contribution of precipitation and potential
evaporation in two steps. In the first step a recharge flux is computed by a
model determined by the input argument `recharge`. In the second step this
recharge flux is convoluted with a response function to obtain the contribution
of recharge to the groundwater levels.
Examples
--------
>>> sm = ps.RechargeModel(rain, evap, rfunc=ps.Exponential(),
>>> recharge=ps.rch.FlexModel(), name="rch")
>>> ml.add_stressmodel(sm)
Warnings
--------
We recommend not to store a RechargeModel is a variable named `rm`. This name is
already reserved in IPython to remove files and will cause problems later.
"""
_name = "RechargeModel"
[docs] def __init__(
self,
prec: Series,
evap: Series,
rfunc: Optional[RFunc] = None,
name: str = "recharge",
recharge: Optional[Recharge] = None,
temp: Optional[Series] = None,
settings: Tuple[Union[str, dict], Union[str, dict], Union[str, dict]] = (
"prec",
"evap",
"evap",
),
metadata: Optional[Tuple[dict, dict, dict]] = (None, None, None),
) -> None:
if rfunc is None:
rfunc = Exponential()
if recharge is None:
recharge = Linear()
# Store the precipitation and evaporation time series
self.prec = TimeSeries(prec, settings=settings[0], metadata=metadata[0])
self.evap = TimeSeries(evap, settings=settings[1], metadata=metadata[1])
# Store recharge object
self.recharge = recharge
# Store a temperature time series if provided/needed or set to None
if self.recharge.snow is True and temp is None:
msg = (
"Recharge model requires a temperature series. No temperature series "
"were provided"
)
raise TypeError(msg)
if temp is not None:
if len(settings) < 3 or len(metadata) < 3:
msg = "Number of values for the settings and/or metadata is incorrect."
raise TypeError(msg)
else:
self.temp = TimeSeries(temp, settings=settings[2], metadata=metadata[2])
else:
self.temp = None
# Select indices from validated stress where both series are available.
index = self.prec.series.index.intersection(self.evap.series.index)
if index.empty:
msg = (
"The stresses that were provided have no overlapping time indices. "
"Please make sure the indices of the time series overlap."
)
logger.error(msg)
raise Exception(msg)
# Calculate initial recharge estimation for initial rfunc parameters
p = self.recharge.get_init_parameters().initial.values
gain_scale_factor = self.get_stress(
p=p, tmin=index.min(), tmax=index.max(), freq=self.prec.settings["freq"]
).std()
StressModelBase.__init__(
self,
name=name,
tmin=index.min(),
tmax=index.max(),
rfunc=rfunc,
up=True,
gain_scale_factor=gain_scale_factor,
)
self.stress = [self.prec, self.evap]
if self.temp:
self.stress.append(self.temp)
self.freq = self.prec.settings["freq"]
self.set_init_parameters()
if isinstance(self.recharge, Linear):
self.nsplit = 2
else:
self.nsplit = 1
[docs] def set_init_parameters(self) -> None:
"""Internal method to set the initial parameters."""
self.parameters = concat(
[
self.rfunc.get_init_parameters(self.name),
self.recharge.get_init_parameters(self.name),
]
)
[docs] def update_stress(
self,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
) -> None:
"""Method to update the settings of the all stresses in the stress model.
Parameters
----------
freq: str, optional
String representing the desired frequency of the time series. Must be one
of the following: (D, h, m, s, ms, us, ns) or a multiple of that e.g. "7D".
tmin: str or pandas.Timestamp, optional
String that can be converted to, or a Pandas Timestamp with the minimum
time of the series.
tmax: str or pandas.Timestamp, optional
String that can be converted to, or a Pandas Timestamp with the maximum
time of the series.
Notes
-----
For the individual options for the different settings please refer to the
docstring from the TimeSeries.update_series() method.
See Also
--------
ps.timeseries.TimeSeries.update_series
"""
self.prec.update_series(freq=freq, tmin=tmin, tmax=tmax)
self.evap.update_series(freq=freq, tmin=tmin, tmax=tmax)
if self.temp is not None:
self.temp.update_series(freq=freq, tmin=tmin, tmax=tmax)
if freq:
self.freq = freq
[docs] def simulate(
self,
p: Optional[ArrayLike] = None,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
dt: float = 1.0,
istress: Optional[int] = None,
**kwargs,
) -> Series:
"""Method to simulate the contribution of recharge to the head.
Parameters
----------
p: array_like, optional
array_like object with the values as floats representing the model
parameters.
tmin: string, optional
tmax: string, optional
freq: string, optional
dt: float, optional
Time step to use in the recharge calculation.
istress: int, optional
This only works for the Linear model!
Returns
-------
pandas.Series
"""
if p is None:
p = self.parameters.initial.values
b = self._get_block(p[: self.rfunc.nparam], dt, tmin, tmax)
stress = self.get_stress(
p=p, tmin=tmin, tmax=tmax, freq=freq, istress=istress
).values
name = self.name
if istress is not None:
if istress == 1 and self.nsplit > 1:
# only happen when Linear is used as the recharge model
stress = stress * p[-1]
if self.stress[istress].name is not None:
name = f"{self.name} ({self.stress[istress].name})"
return Series(
data=fftconvolve(stress, b, "full")[: stress.size],
index=self.prec.series.index,
name=name,
fastpath=True,
)
[docs] def get_stress(
self,
p: Optional[ArrayLike] = None,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
istress: Optional[int] = None,
**kwargs,
) -> Series:
"""Method to obtain the recharge stress calculated by the model.
Parameters
----------
p: array_like, optional
array_like object with the values as floats representing the model
parameters.
tmin: string, optional
tmax: string, optional
freq: string, optional
istress: int, optional
Return one of the stresses used for the recharge calculation. 0 for
precipitation, 1 for evaporation and 2 for temperature.
kwargs
Returns
-------
stress: pandas.Series
When no istress is selected, this return the estimated recharge flux that
is convoluted with a response function on the simulate method.
"""
if tmin is None:
tmin = self.tmin
if tmax is None:
tmax = self.tmax
self.update_stress(tmin=tmin, tmax=tmax, freq=freq)
if istress is None:
prec = self.prec.series.values
evap = self.evap.series.values
temp = None
if self.temp is not None:
temp = self.temp.series.values
if p is None:
p = self.parameters.initial.values
stress = self.recharge.simulate(
prec=prec, evap=evap, p=p[-self.recharge.nparam :], **{"temp": temp}
)
return Series(
data=stress,
index=self.prec.series.index,
name="recharge",
fastpath=True,
)
elif istress == 0:
return self.prec.series
elif istress == 1:
return self.evap.series
else:
return self.temp.series
[docs] def get_water_balance(
self,
p: Optional[ArrayLike] = None,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
) -> DataFrame:
"""Method to obtain the water balance components.
Parameters
----------
p: array_like, optional
array_like object with the values as floats representing the model
parameters.
tmin: string, optional
tmax: string, optional
freq: string, optional
Returns
-------
wb: pandas.DataFrame
Dataframe with the water balance components, both fluxes and states.
Notes
-----
This method return a data frame with all water balance components, fluxes and
states. All ingoing fluxes have a positive sign (e.g., precipitation) and all
outgoing fluxes have negative sign (e.g., recharge).
Warnings
--------
This is an experimental method and may change in the future.
Examples
--------
>>> sm = ps.RechargeModel(prec, evap, ps.Gamma(), ps.rch.FlexModel(),
>>> name="rch")
>>> ml.add_stressmodel(sm)
>>> ml.solve()
>>> wb = sm.get_water_balance(ml.get_parameters("rch"))
>>> wb.plot(subplots=True)
"""
if p is None:
p = self.parameters.initial.values
prec = self.get_stress(tmin=tmin, tmax=tmax, freq=freq, istress=0).values
evap = self.get_stress(tmin=tmin, tmax=tmax, freq=freq, istress=1).values
if self.temp is not None:
temp = self.get_stress(tmin=tmin, tmax=tmax, freq=freq, istress=2).values
else:
temp = None
df = self.recharge.get_water_balance(
prec=prec, evap=evap, temp=temp, p=p[-self.recharge.nparam :]
)
df.index = self.prec.series.index
return df
[docs] def to_dict(self, series: bool = True) -> dict:
"""Method to export the RechargeModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the object.
Notes
-----
Settings and metadata are exported with the stress.
"""
data = {
"class": self._name,
"prec": self.prec.to_dict(series=series),
"evap": self.evap.to_dict(series=series),
"rfunc": self.rfunc.to_dict(),
"name": self.name,
"recharge": self.recharge.to_dict(),
"temp": self.temp.to_dict() if self.temp else None,
}
return data
[docs]class TarsoModel(RechargeModel):
"""Stressmodel simulating the effect of recharge using the Tarso method.
Parameters
----------
prec: pandas.Series
pandas.Series with pandas.DatetimeIndex containing the precipitation series.
evap: pandas.Series
pandas.Series with pandas.DatetimeIndex containing the potential evaporation
series.
oseries: pandas.Series, optional
A pandas.Series with pandas.DatetimeIndex of observations to which the model
will be calibrated. It is used to determine the initial values of the
drainage levels and the boundaries of the upper drainage level. Specify
either oseries or dmin and dmax.
dmin: float, optional
The minimum drainage level. It is used to determine the initial values of the
drainage levels and the lower boundary of the upper drainage level. Specify
either oseries or dmin and dmax.
dmax : float, optional
The maximum drainage level. It is used to determine the initial values of the
drainage levels and the upper boundary of the upper drainage level. Specify
either oseries or dmin and dmax.
rfunc: pastas.rfunc instance
this model only works with the Exponential response function.
See Also
--------
pastas.recharge
Notes
-----
The Threshold autoregressive self-exciting open-loop (Tarso) model
:cite:t:`knotters_tarso_1999` is nonlinear in structure because it incorporates
two regimes which are separated by a threshold. This model method can be used to
simulate a groundwater system where the groundwater head reaches the surface or
drainage level in wet conditions. TarsoModel uses two drainage levels, with two
exponential response functions. When the simulation reaches the second drainage
level, the second response function becomes active. Because of its structure,
TarsoModel cannot be combined with other stress models, a constant or a transform.
TarsoModel inherits from RechargeModel. Only parameters specific to the child
class are named above.
"""
_name = "TarsoModel"
[docs] def __init__(
self,
prec: Series,
evap: Series,
oseries: Optional[Series] = None,
dmin: Optional[float] = None,
dmax: Optional[float] = None,
rfunc: Optional[RFunc] = None,
**kwargs,
) -> None:
if oseries is not None:
if dmin is not None or dmax is not None:
msg = "Please specify either oseries or dmin and dmax"
raise (Exception(msg))
dmin = oseries.min()
dmax = oseries.max()
elif dmin is None or dmax is None:
msg = "Please specify either oseries or dmin and dmax"
raise (Exception(msg))
if rfunc is None:
rfunc = Exponential()
if not isinstance(rfunc, Exponential):
raise NotImplementedError("TarsoModel only supports rfunc Exponential!")
self.dmin = dmin
self.dmax = dmax
super().__init__(prec=prec, evap=evap, rfunc=rfunc, **kwargs)
[docs] def set_init_parameters(self) -> None:
# parameters for the first drainage level
p0 = self.rfunc.get_init_parameters(self.name)
initial = self.dmin + 0.5 * (self.dmax - self.dmin)
pd0 = Series(
{
"initial": initial,
"pmin": np.NaN,
"pmax": np.NaN,
"vary": True,
"name": self.name,
}
)
p0.loc[f"{self.name}_d"] = pd0
p0.index = [f"{x}0" for x in p0.index]
# parameters for the second drainage level
p1 = self.rfunc.get_init_parameters(self.name)
initial = self.dmin + 0.75 * (self.dmax - self.dmin)
pd1 = Series(
{
"initial": initial,
"pmin": self.dmin,
"pmax": self.dmax,
"vary": True,
"name": self.name,
}
)
p1.loc[f"{self.name}_d"] = pd1
p1.index = [f"{x}1" for x in p1.index]
# parameters for the recharge-method
pr = self.recharge.get_init_parameters(self.name)
# combine all parameters
self.parameters = concat([p0, p1, pr])
[docs] def simulate(
self,
p: Optional[ArrayLike] = None,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq=None,
dt: float = 1.0,
) -> Series:
stress = self.get_stress(p=p, tmin=tmin, tmax=tmax, freq=freq)
h = self.tarso(p[: -self.recharge.nparam], stress.values, dt)
sim = Series(h, name=self.name, index=stress.index)
return sim
[docs] def to_dict(self, series: bool = True) -> dict:
"""Method to export the TarsoModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the object.
Notes
-----
Settings and metadata are exported with the stress.
"""
data = super().to_dict(series)
data["dmin"] = self.dmin
data["dmax"] = self.dmax
return data
@staticmethod
def _check_stressmodel_compatibility(ml: Model) -> None:
"""Internal method to check if no other stressmodels, a constants or a
transform is used."""
msg = (
"A TarsoModel cannot be combined with %s. Either remove the TarsoModel or "
"the %s."
)
if len(ml.stressmodels) > 1:
logger.warning(msg, "other stressmodels", "stressmodels")
if ml.constant is not None:
logger.warning(msg, "a constant", "constant")
if ml.transform is not None:
logger.warning(msg, "a transform", "transform")
[docs] @staticmethod
@njit
def tarso(p: ArrayLike, r: ArrayLike, dt: float) -> ArrayLike:
"""Calculates the head based on exponential decay of the previous timestep
and recharge, using two thresholds."""
A0, a0, d0, A1, a1, d1 = p
# calculate physical meaning of these parameters
S0 = a0 / A0
c0 = A0
S1 = a1 / A1
c1 = A1
# calculate effective parameters for the top level
c_e = 1 / ((1 / c0) + (1 / c1))
d_e = (c1 / (c0 + c1)) * d0 + (c0 / (c0 + c1)) * d1
a_e = S1 * c_e
h = np.full(len(r), np.NaN)
for i in range(len(r)):
if i == 0:
h0 = (d0 + d1) / 2
high = h0 > d1
if high:
S, a, c, d = S1, a_e, c_e, d_e
else:
S, a, c, d = S0, a0, c0, d0
else:
h0 = h[i - 1]
exp_a = np.exp(-dt / a)
h[i] = (h0 - d) * exp_a + r[i] * c * (1 - exp_a) + d
newhigh = h[i] > d1
if high != newhigh:
# calculate time until d1 is reached
dtdr = -S * c * np.log((d1 - d - r[i] * c) / (h0 - d - r[i] * c))
if dtdr > dt:
raise (Exception())
# change parameters
high = newhigh
if high:
S, a, c, d = S1, a_e, c_e, d_e
else:
S, a, c, d = S0, a0, c0, d0
# calculate new level after reaching d1
exp_a = np.exp(-(dt - dtdr) / a)
h[i] = (d1 - d) * exp_a + r[i] * c * (1 - exp_a) + d
return h
[docs]class ChangeModel(StressModelBase):
"""Model where the response function changes from one to another over time.
Parameters
----------
stress: pandas.Series
pandas Series object containing the stress.
rfunc1: pastas.rfunc instance
The instance of the response function used in the convolution with the stress.
rfunc2: pastas.rfunc instance
The instance of the response function used in the convolution with the stress.
name: str
name of the stress.
tchange: str
string with the approximate date of the change.
up: bool or None, optional
True if response function is positive (default), False if negative. None if
you don't want to define if response is positive or negative.
settings: dict or str, optional
The settings of the stress. This can be a string referring to a predefined
settings dict (defined in ps.rcParams["timeseries"]), or a dict with the
settings to apply. Refer to the docs of pastas.Timeseries for further
information.
metadata: dict, optional
dictionary containing metadata about the stress. This is passed onto the
TimeSeries object.
Notes
-----
This model is based on :cite:t:`obergfell_identification_2019`.
"""
_name = "ChangeModel"
[docs] def __init__(
self,
stress: Series,
rfunc1: RFunc,
rfunc2: RFunc,
name: str,
tchange: Union[str, TimestampType],
up: bool = True,
settings: Optional[Union[dict, str]] = None,
metadata: Optional[dict] = None,
) -> None:
stress = TimeSeries(stress, settings=settings, metadata=metadata)
StressModelBase.__init__(
self,
name=name,
rfunc=None,
tmin=stress.series.index.min(),
tmax=stress.series.index.max(),
)
rfunc1.update_rfunc_settings(up=up)
self.rfunc1 = rfunc1
rfunc2.update_rfunc_settings(up=up)
self.rfunc2 = rfunc2
self.tchange = Timestamp(tchange)
self.freq = stress.settings["freq"]
self.stress.append(stress)
self.set_init_parameters()
[docs] def set_init_parameters(self) -> None:
"""Internal method to set the initial parameters."""
self.parameters = concat(
[
self.rfunc1.get_init_parameters("{}_1".format(self.name)),
self.rfunc2.get_init_parameters("{}_2".format(self.name)),
]
)
tmin = Timestamp.min.toordinal()
tmax = Timestamp.max.toordinal()
tchange = self.tchange.toordinal()
self.parameters.loc[self.name + "_beta"] = (
0.0,
-np.inf,
np.inf,
True,
self.name,
)
self.parameters.loc[self.name + "_tchange"] = (
tchange,
tmin,
tmax,
False,
self.name,
)
self.parameters.name = self.name
[docs] def simulate(
self,
p: ArrayLike,
tmin: Optional[TimestampType] = None,
tmax: Optional[TimestampType] = None,
freq: Optional[str] = None,
dt: float = 1.0,
) -> Series:
self.update_stress(tmin=tmin, tmax=tmax, freq=freq)
rfunc1 = self.rfunc1.block(p[: self.rfunc1.nparam])
rfunc2 = self.rfunc2.block(
p[self.rfunc1.nparam : self.rfunc1.nparam + self.rfunc2.nparam]
)
stress = self.stress[0].series
npoints = stress.index.size
t = np.linspace(0, 1, npoints)
beta = p[-2]
sigma = stress.index.get_loc(Timestamp.fromordinal(int(p[-1]))) / npoints
omega = 1 / (np.exp(beta * (t - sigma)) + 1)
h1 = Series(
data=fftconvolve(stress, rfunc1, "full")[:npoints],
index=stress.index,
name="1",
fastpath=True,
)
h2 = Series(
data=fftconvolve(stress, rfunc2, "full")[:npoints],
index=stress.index,
name="1",
fastpath=True,
)
h = omega * h1 + (1 - omega) * h2
return h
[docs] def to_dict(self, series: bool = True):
"""Method to export the ChangeModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the object.
Notes
-----
Settings and metadata are exported with the stress.
"""
data = {
"stress": self.stress[0].to_dict(series=series),
"rfunc1": self.rfunc1.to_dict(),
"rfunc2": self.rfunc2.to_dict(),
"name": self.name,
"tchange": self.tchange,
"up": self.rfunc1.up,
}
return data