"""This module contains all the stress models available in Pastas.
Stress models are used to translate an input time series into a
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
import numpy as np
from pandas import DataFrame, Series, Timedelta, Timestamp, concat, date_range
from scipy.signal import fftconvolve
from .decorators import njit, set_parameter
from .recharge import Linear
from .rfunc import Exponential, HantushWellModel, One
from .timeseries import TimeSeries
from .utils import check_numba, validate_name
logger = getLogger(__name__)
__all__ = ["StressModel", "StressModel2", "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
Dataframe containing the parameters.
"""
_name = "StressModelBase"
[docs] def __init__(self, name, tmin, tmax, rfunc=None):
self.name = validate_name(name)
self.tmin = tmin
self.tmax = tmax
self.freq = None
self.rfunc = rfunc
self.parameters = DataFrame(
columns=['initial', 'pmin', 'pmax', 'vary', 'name'])
self.stress = []
@property
def nparam(self):
return self.parameters.index.size
[docs] def set_init_parameters(self):
"""Set the initial parameters (back) to their default values."""
@set_parameter
def _set_initial(self, name, value):
"""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, value):
"""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, value):
"""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, value):
"""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, **kwargs):
"""Method to update the settings of the individual TimeSeries.
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(**kwargs)
if "freq" in kwargs:
self.freq = kwargs["freq"]
[docs] def dump_stress(self, series=True):
"""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:
data.append(stress.to_dict(series=series))
return data
[docs] def get_stress(self, p=None, tmin=None, tmax=None, freq=None,
istress=None, **kwargs):
"""Returns the stress or stresses 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, series=True):
"""Method to export the StressModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the
StressModel object.
"""
data = {
"stressmodel": self._name,
"name": self.name,
"stress": self.dump_stress(series)
}
return data
[docs] def get_nsplit(self):
"""Determine in how many timeseries the contribution can be split."""
if hasattr(self, 'nsplit'):
return self.nsplit
else:
return len(self.stress)
def _get_block(self, p, dt, tmin, tmax):
"""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]class StressModel(StressModelBase):
"""Time series model consisting of the convolution of one stress with one
response function.
Parameters
----------
stress: pandas.Series
pandas Series object containing the stress.
rfunc: rfunc class
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.
cutoff: float, optional
float between 0 and 1 to determine how long the response is (default
is 99% of the actual response time). Used to reduce computation times.
settings: dict or str, optional
The settings of the stress. This can be a string referring to a
predefined settings dict, or a dict with the settings to apply.
Refer to the docstring of pastas.Timeseries for further information.
metadata: dict, optional
dictionary containing metadata about the stress. This is passed onto
the TimeSeries object.
meanstress: float, optional
The mean stress determines the initial parameters of rfunc. The initial
parameters are chosen in such a way that the gain of meanstress is 1.
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, rfunc, name, up=True, cutoff=0.999,
settings=None, metadata=None, meanstress=None):
if isinstance(stress, list):
stress = stress[0] # TODO Temporary fix Raoul, 2017-10-24
stress = TimeSeries(stress, settings=settings, metadata=metadata)
if meanstress is None:
meanstress = stress.series.std()
rfunc = rfunc(up=up, cutoff=cutoff, meanstress=meanstress)
StressModelBase.__init__(self, name=name,
tmin=stress.series.index.min(),
tmax=stress.series.index.max(), rfunc=rfunc)
self.freq = stress.settings["freq"]
self.stress = [stress]
self.set_init_parameters()
[docs] def set_init_parameters(self):
"""Set the initial parameters (back) to their default values."""
self.parameters = self.rfunc.get_init_parameters(self.name)
[docs] def simulate(self, p, tmin=None, tmax=None, freq=None, dt=1.0):
"""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=True):
"""Method to export the StressModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the
StressModel object.
"""
data = {
"stressmodel": self._name,
"rfunc": self.rfunc._name,
"name": self.name,
"up": self.rfunc.up,
"cutoff": self.rfunc.cutoff,
"stress": self.dump_stress(series)
}
return data
[docs]class StressModel2(StressModelBase):
"""Time series model consisting of the convolution of two stresses with one
response function. The first stress causes the head to go up and the second
stress causes the head to go down.
Parameters
----------
stress: list of pandas.Series or list of pastas.timeseries
list of two pandas.Series or pastas.timeseries objects containing the
stresses. Usually the first is the precipitation and the second the
evaporation.
rfunc: pastas.rfunc instance
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.
cutoff: float, optional
float between 0 and 1 to determine how long the response is (default
is 99.9% of the actual response time). Used to reduce computation
times.
settings: Tuple with two dicts, optional
The settings of the individual TimeSeries.
settings: list of dicts or strs, optional
The settings of the stresses. This can be a string referring to a
predefined settings dict, or a dict with the settings to apply.
Refer to the docstring of pastas.Timeseries for further information.
Default is ("prec", "evap").
metadata: list of dicts, optional
dictionary containing metadata about the stress. This is passed onto
the TimeSeries object.
Notes
-----
The order in which the stresses are provided is the order the metadata
and settings dictionaries or string are passed onto the TimeSeries
objects. By default, the precipitation stress is the first and the
evaporation stress the second stress.
See Also
--------
pastas.rfunc
pastas.timeseries.TimeSeries
"""
_name = "StressModel2"
[docs] def __init__(self, stress, rfunc, name, up=True, cutoff=0.999,
settings=("prec", "evap"), metadata=(None, None),
meanstress=None):
# First check the series, then determine tmin and tmax
stress0 = TimeSeries(stress[0], settings=settings[0],
metadata=metadata[0])
stress1 = TimeSeries(stress[1], settings=settings[1],
metadata=metadata[1])
# Select indices from validated stress where both series are available.
index = stress0.series.index.intersection(stress1.series.index)
if index.empty:
msg = ('The two 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)
# First check the series, then determine tmin and tmax
stress0.update_series(tmin=index.min(), tmax=index.max())
stress1.update_series(tmin=index.min(), tmax=index.max())
if meanstress is None:
meanstress = (stress0.series - stress1.series).std()
rfunc = rfunc(up=up, cutoff=cutoff, meanstress=meanstress)
StressModelBase.__init__(self, name=name, tmin=index.min(),
tmax=index.max(), rfunc=rfunc)
self.stress.append(stress0)
self.stress.append(stress1)
self.freq = stress0.settings["freq"]
self.set_init_parameters()
[docs] def set_init_parameters(self):
"""Set the initial parameters back to their default values."""
self.parameters = self.rfunc.get_init_parameters(self.name)
self.parameters.loc[self.name + '_f'] = \
(-1.0, -2.0, 0.0, True, self.name)
[docs] def simulate(self, p, tmin=None, tmax=None, freq=None, dt=1, istress=None):
"""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
istress: int, optional
Returns
-------
pandas.Series
The simulated head contribution.
"""
b = self._get_block(p[:-1], dt, tmin, tmax)
stress = self.get_stress(p=p, tmin=tmin, tmax=tmax, freq=freq,
istress=istress)
if istress == 1:
stress = p[-1] * stress
npoints = stress.index.size
h = Series(data=fftconvolve(stress, b, 'full')[:npoints],
index=stress.index, name=self.name, fastpath=True)
if istress is not None:
if self.stress[istress].name is not None:
h.name = h.name + ' (' + self.stress[istress].name + ')'
return h
[docs] def get_stress(self, p=None, tmin=None, tmax=None, freq=None,
istress=None, **kwargs):
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:
if p is None:
p = self.parameters.initial.values
return self.stress[0].series.add(p[-1] * self.stress[1].series)
elif istress == 0:
return self.stress[0].series
else:
return self.stress[1].series
[docs] def to_dict(self, series=True):
"""Method to export the StressModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the
StressModel object.
"""
data = {
"stressmodel": self._name,
"rfunc": self.rfunc._name,
"name": self.name,
"up": self.rfunc.up,
"cutoff": self.rfunc.cutoff,
"stress": self.dump_stress(series)
}
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.RfuncBase class, optional
Pastas response function used to simulate the effect of the step.
Default is rfunc.One, an instant effect.
up: bool, optional
Force a direction of the step. Default is None.
cutoff: float, optional
float between 0 and 1 to determine how long the response is (default
is 99.9% of the actual response time). Used to reduce computation
times.
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, name, rfunc=One, up=True, cutoff=0.999):
rfunc = rfunc(up=up, cutoff=cutoff, meanstress=1.0)
StressModelBase.__init__(self, name=name, tmin=Timestamp.min,
tmax=Timestamp.max, rfunc=rfunc)
self.tstart = Timestamp(tstart)
self.set_init_parameters()
[docs] def set_init_parameters(self):
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, tmin=None, tmax=None, freq=None, dt=1):
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, series=True):
data = {
"stressmodel": self._name,
'tstart': self.tstart,
'name': self.name,
"up": self.rfunc.up,
'rfunc': self.rfunc._name
}
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 to impossible to estimate from the data.
"""
_name = "LinearTrend"
[docs] def __init__(self, start, end, name="trend"):
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):
"""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, tmin=None, tmax=None, freq=None, dt=1):
"""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, series=None):
data = {
"stressmodel": 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. E.g. The minimum of the
observed series.
"""
_name = "Constant"
[docs] def __init__(self, name="constant", initial=0.0):
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=None):
return p
[docs]class WellModel(StressModelBase):
"""Convolution of one or more stresses with one response function.
Parameters
----------
stress: list
list containing the stresses timeseries.
rfunc: pastas.rfunc
this model only works with the HantushWellModel response function.
name: str
Name of the stressmodel.
distances: list or list-like
list of distances to oseries, must be ordered the same as the
stresses.
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.
cutoff: float, optional
float between 0 and 1 to determine how long the response is (default
is 99.9% of the actual response time). Used to reduce computation
times.
settings: str, list of dict, optional
settings of the timeseries, by default "well".
sort_wells: bool, optional
sort wells from closest to furthest, by default True.
Notes
-----
This class implements convolution of multiple series with a the same
response function. This can be applied when dealing with multiple
wells in a time series model. The distance from an influence to the
location of the oseries has to be provided for each stress.
Warnings
--------
This model only works with the HantushWellModel response function.
"""
_name = "WellModel"
[docs] def __init__(self, stress, rfunc, name, distances, up=False, cutoff=0.999,
settings="well", sort_wells=True):
if not issubclass(rfunc, HantushWellModel):
raise NotImplementedError("WellModel only supports the rfunc "
"HantushWellModel!")
logger.warning("It is recommended to use LmfitSolve as the solver "
"when implementing WellModel. See "
"https://github.com/pastas/pastas/issues/177.")
# 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])]
if isinstance(settings, list):
settings = [s for _, s in sorted(zip(distances, settings),
key=lambda pair: pair[0])]
distances = np.sort(distances)
if settings is None or isinstance(settings, str):
settings = len(stress) * [settings]
# convert stresses to TimeSeries if necessary
stress = self.handle_stress(stress, settings)
# 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.name for s in stress],
data=distances,
name="distances")
meanstress = np.max([s.series.std() for s in stress])
rfunc = rfunc(up=up, cutoff=cutoff, meanstress=meanstress,
distances=self.distances.values)
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)
self.stress = stress
self.freq = self.stress[0].settings["freq"]
self.set_init_parameters()
[docs] def set_init_parameters(self):
self.parameters = self.rfunc.get_init_parameters(self.name)
[docs] def simulate(self, p=None, tmin=None, tmax=None, freq=None, dt=1,
istress=None, **kwargs):
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.iteritems():
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
[docs] @staticmethod
def handle_stress(stress, settings):
"""Internal method to handle user provided stress in init.
Parameters
----------
stress: pandas.Series, pastas.TimeSeries, list or dict
stress or collection of stresses
settings: dict or iterable
settings dictionary
Returns
-------
stress: list
return a list with the stresses transformed to pastas TimeSeries.
"""
data = []
if isinstance(stress, Series):
data.append(TimeSeries(stress, settings=settings))
elif isinstance(stress, dict):
for i, (name, value) in enumerate(stress.items()):
data.append(TimeSeries(value, name=name, settings=settings[i]))
elif isinstance(stress, list):
for i, value in enumerate(stress):
data.append(TimeSeries(value, settings=settings[i]))
else:
logger.error("Stress format is unknown. Provide a Series, "
"dict or list.")
return data
[docs] def get_stress(self, p=None, tmin=None, tmax=None, freq=None,
istress=None, squeeze=True, **kwargs):
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=None):
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=None):
""" 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 : np.array
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 to_dict(self, series=True):
"""Method to export the WellModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the
WellModel object.
"""
data = {
"stressmodel": self._name,
"rfunc": self.rfunc._name,
"name": self.name,
"up": True if self.rfunc.up else False,
"distances": self.distances.to_list(),
"cutoff": self.rfunc.cutoff,
"stress": self.dump_stress(series),
"sort_wells": self.sort_wells
}
return data
[docs]class RechargeModel(StressModelBase):
"""Stressmodel simulating the effect of groundwater recharge on the
groundwater head.
Parameters
----------
prec: pandas.Series or pastas.timeseries.TimeSeries
pandas.Series or pastas.timeseries object containing the
precipitation series.
evap: pandas.Series or pastas.timeseries.TimeSeries
pandas.Series or pastas.timeseries object containing the potential
evaporation series.
rfunc: pastas.rfunc class, optional
Response function used in the convolution with the stress. Default
is Exponential.
name: str, optional
Name of the stress. Default is "recharge".
recharge: pastas.recharge instance, optional
String with the name of the recharge model. Options are: Linear (
default), FlexModel and Berendrecht. These can be accessed through
ps.rch.
temp: pandas.Series or pastas.timeseries.TimeSeries, optional
pandas.Series or pastas.TimeSeries object containing the
temperature series. It depends on the recharge model is this
argument is required or not.
cutoff: float, optional
float between 0 and 1 to determine how long the response is (default)
is 99.9% of the actual response time). Used to reduce computation
times.
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, or a dict with the settings to apply. Refer to the
docstring of pastas.Timeseries for further information. Default is (
"prec", "evap").
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)
Warning
-------
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, evap, rfunc=Exponential, name="recharge",
recharge=Linear(), temp=None, cutoff=0.999,
settings=("prec", "evap", "evap"),
metadata=(None, None, None)):
# 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])
# Check if both series have a regular time step
if self.prec.freq_original is None:
msg = "Frequency of the precipitation series could not be " \
"determined. Please provide a time series with a regular " \
"time step."
raise IndexError(msg)
if self.evap.freq_original is None:
msg = "Frequency of the evaporation series could not be " \
"determined. Please provide a time series with a regular " \
"time step."
raise IndexError(msg)
# 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
meanstress = self.get_stress(p=p, tmin=index.min(), tmax=index.max(),
freq=self.prec.settings["freq"]).std()
rfunc = rfunc(up=True, cutoff=cutoff, meanstress=meanstress)
StressModelBase.__init__(self, name=name, tmin=index.min(),
tmax=index.max(), rfunc=rfunc)
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):
"""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, **kwargs):
"""Method to update the settings of the individual TimeSeries.
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(**kwargs)
self.evap.update_series(**kwargs)
if self.temp is not None:
self.temp.update_series(**kwargs)
if "freq" in kwargs:
self.freq = kwargs["freq"]
[docs] def simulate(self, p=None, tmin=None, tmax=None, freq=None, dt=1.0,
istress=None):
"""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=None, tmin=None, tmax=None, freq=None,
istress=None, **kwargs):
"""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
if self.temp is not None:
temp = self.temp.series.values
else:
temp = None
if p is None:
p = self.parameters.initial.values
stress = self.recharge.simulate(prec=prec, evap=evap, temp=temp,
p=p[-self.recharge.nparam:])
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=None, tmin=None, tmax=None, freq=None):
"""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).
Warning
-------
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=True):
data = {
"stressmodel": self._name,
"prec": self.prec.to_dict(series=series),
"evap": self.evap.to_dict(series=series),
"rfunc": self.rfunc._name,
"name": self.name,
"recharge": self.recharge._name,
"recharge_kwargs": self.recharge.kwargs,
"cutoff": self.rfunc.cutoff,
"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
----------
oseries: pandas.Series or pastas.TimeSeries, optional
A series of observations on 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
this model only works with the Exponential response function.
See Also
--------
pastas.recharge
Notes
-----
The Threshold autoregressive self-exciting open-loop (Tarso) model
[knotters_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.
References
----------
.. [knotters_1999] Knotters, M. & De Gooijer, Jan G.. (1999). TARSO
modeling of water table depths. Water Resources Research. 35.
10.1029/1998WR900049.
"""
_name = "TarsoModel"
[docs] def __init__(self, prec, evap, oseries=None, dmin=None, dmax=None,
rfunc=Exponential, **kwargs):
check_numba()
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))
o = TimeSeries(oseries).series
dmin = o.min()
dmax = o.max()
elif dmin is None or dmax is None:
msg = 'Please specify either oseries or dmin and dmax'
raise (Exception(msg))
if not issubclass(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):
# parameters for the first drainage level
p0 = self.rfunc.get_init_parameters(self.name)
one = One(meanstress=self.dmin + 0.5 * (self.dmax - self.dmin))
pd0 = one.get_init_parameters(self.name).squeeze()
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=None, tmin=None, tmax=None, freq=None, dt=1):
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=True):
data = super().to_dict(series)
data['dmin'] = self.dmin
data['dmax'] = self.dmax
return data
@staticmethod
def _check_stressmodel_compatibility(ml):
"""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, r, dt):
"""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: rfunc class
response function used in the convolution with the stress.
rfunc2: rfunc class
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.
cutoff: float, optional
float between 0 and 1 to determine how long the response is (default
is 99% of the actual response time). Used to reduce computation times.
settings: dict or str, optional
the settings of the stress. This can be a string referring to a
predefined settings dict, or a dict with the settings to apply.
Refer to the docstring 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 Obergfjell et al. (2019).
References
----------
Obergfell, C., Bakker, M. and Maas, K. (2019), Identification and
Explanation of a Change in the Groundwater Regime using Time Series
Analysis. Groundwater, 57: 886-894. https://doi.org/10.1111/gwat.12891
"""
_name = "ChangeModel"
[docs] def __init__(self, stress, rfunc1, rfunc2, name, tchange, up=True,
cutoff=0.999, settings=None, metadata=None):
if isinstance(stress, list):
stress = stress[0] # TODO Temporary fix Raoul, 2017-10-24
stress = TimeSeries(stress, settings=settings, metadata=metadata)
StressModelBase.__init__(self, name=name, rfunc=None,
tmin=stress.series.index.min(),
tmax=stress.series.index.max())
self.rfunc1 = rfunc1(up=up, cutoff=cutoff)
self.rfunc2 = rfunc2(up=up, cutoff=cutoff)
self.tchange = Timestamp(tchange)
self.freq = stress.settings["freq"]
self.stress = [stress]
self.set_init_parameters()
[docs] def set_init_parameters(self):
"""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., -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, tmin=None, tmax=None, freq=None, dt=1.0):
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] * npoints
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]class ReservoirModel(StressModelBase):
"""Time series model consisting of a single reservoir with two stresses.
The first stress causes the head to go up and the second stress causes
the head to go down.
Parameters
----------
stress: list of pandas.Series or list of pastas.timeseries
list of two pandas.Series or pastas.timeseries objects containing the
stresses. Usually the first is the precipitation and the second the
evaporation.
name: str
Name of the stress
settings: list of dicts or strs, optional
The settings of the stresses. This can be a string referring to a
predefined settings dict, or a dict with the settings to apply.
Refer to the docstring of pastas.Timeseries for further information.
Default is ("prec", "evap").
metadata: list of dicts, optional
dictionary containing metadata about the stress. This is passed onto
the TimeSeries object.
Notes
-----
The order in which the stresses are provided is the order the metadata
and settings dictionaries or string are passed onto the TimeSeries
objects. By default, the precipitation stress is the first and the
evaporation stress the second stress.
See Also
--------
pastas.timeseries
"""
_name = "ReservoirModel"
[docs] def __init__(self, stress, reservoir, name, meanhead,
settings=("prec", "evap"), metadata=(None, None),
meanstress=None):
# Set resevoir object
self.reservoir = reservoir(meanhead)
# Code below is copied from StressModel2 and may not be optimal
# Check the series, then determine tmin and tmax
stress0 = TimeSeries(stress[0], settings=settings[0],
metadata=metadata[0])
stress1 = TimeSeries(stress[1], settings=settings[1],
metadata=metadata[1])
# Select indices from validated stress where both series are available.
index = stress0.series.index.intersection(stress1.series.index)
if index.empty:
msg = ('The two 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)
# First check the series, then determine tmin and tmax
stress0.update_series(tmin=index.min(), tmax=index.max())
stress1.update_series(tmin=index.min(), tmax=index.max())
if meanstress is None:
meanstress = (stress0.series - stress1.series).std()
StressModelBase.__init__(self, name=name, tmin=index.min(),
tmax=index.max(), rfunc=None)
self.stress.append(stress0)
self.stress.append(stress1)
self.freq = stress0.settings["freq"]
self.set_init_parameters()
[docs] def set_init_parameters(self):
"""Set the initial parameters back to their default values."""
self.parameters = self.reservoir.get_init_parameters(self.name)
[docs] def simulate(self, p, tmin=None, tmax=None, freq=None, dt=1, istress=None):
"""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: float, time step
istress: int, not used
Returns
-------
pandas.Series
The simulated head contribution.
"""
stress = self.get_stress(tmin=tmin, tmax=tmax, freq=freq)
h = Series(data=self.reservoir.simulate(stress[0], stress[1], p),
index=stress[0].index, name=self.name, fastpath=True)
return h
[docs] def get_stress(self, p=None, tmin=None, tmax=None, freq=None,
istress=0, **kwargs):
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, self.stress[1].series
[docs] def to_dict(self, series=True):
"""Method to export the StressModel object.
Returns
-------
data: dict
dictionary with all necessary information to reconstruct the
StressModel object.
"""
pass
def _get_block(self, p, dt, tmin, tmax):
"""Internal method to get the block-response function.
Cannot be used (yet?) since there is no block response"""
pass