Changing response functions#

R.A. Collenteur, University of Graz, 2021

In this notebook the new ChangeModel is tested, based on the work by Obergfjell et al. (2019). The main idea is to apply different response functions for two different periods. As an example we look at the the groundwater levels measured near the river the Mur in Austria, where a dam was recently built.

[1]:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import pastas as ps

ps.set_log_level("ERROR")
ps.show_versions()

Python version: 3.10.8
NumPy version: 1.23.5
Pandas version: 1.5.3
SciPy version: 1.10.0
Matplotlib version: 3.6.3
Numba version: 0.56.4
LMfit version: 1.1.0
Pastas version: 0.23.0

1. Load the data#

[2]:

prec = pd.read_csv("data_step/prec.csv", index_col=0, parse_dates=True).squeeze()
evap = pd.read_csv("data_step/evap.csv", index_col=0, parse_dates=True).squeeze()
head = pd.read_csv("data_step/head.csv", index_col=0, parse_dates=True).squeeze()
river = pd.read_csv("data_step/river.csv", index_col=0, parse_dates=True).squeeze()
river -= river.min()

axes = ps.plots.series(
    head=head,
    stresses=[prec, evap, river],
    tmin="2000",
    labels=["Head\n[m]", "Prec\n[mm/d]", "Evap\n[mm/d]", "River [m3/d]"],
)

../_images/examples_16_changing_responses_3_0.png

2. The weighting factor#

The stress is convoluted two times with different response functions. Then, a weighting function is used to add the two contributions together and compute the final contribution.

[3]:

npoints = 100

tchange = 50 / npoints
t = np.linspace(0, 1, npoints)
color = plt.cm.viridis(np.linspace(0, 1, 10))

for beta, c in zip(np.linspace(-1, 1, 10), color):
    beta1 = beta * npoints
    omega = 1 / (np.exp(beta1 * (t - tchange)) + 1)
    plt.plot(omega, color=c, label="$beta$={:.2f}".format(beta))

plt.ylabel("$\omega$ [-]")
plt.xlabel("Time [t]")
plt.legend()

[3]:

<matplotlib.legend.Legend at 0x7f30bebf7430>

../_images/examples_16_changing_responses_5_1.png

3. Make a model#

We now make two models:

one model where we assume the response of the heads to the river level remains the same
and one model where the response to the river levels changes.

[4]:

# Normal Model
ml = ps.Model(head, name="linear")

sm = ps.StressModel(river, ps.Exponential(), name="test")
step = ps.StepModel("2012-01-01", rfunc=ps.One(), name="step")

ml.add_stressmodel([sm, step])
ml.solve(report=False, tmin="2004", tmax="2018", noise=True)
ml.plots.results(figsize=(10, 6))

# ChangeModel
ml2 = ps.Model(head, name="linear")

cm = ps.ChangeModel(
    river, ps.Exponential(), ps.Exponential(), name="test", tchange="2012-01-01"
)

ml2.add_stressmodel([cm, step])
ml2.solve(report=False, tmin="2004", tmax="2018", noise=True)
ml2.plots.results(figsize=(10, 6));

/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
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  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)
/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)

../_images/examples_16_changing_responses_7_1.png

../_images/examples_16_changing_responses_7_2.png

The second model shows a better fit, but also the step trend changed.

[5]:

print("RMSE for the first model:", ml.stats.rmse().round(2))
print("RMSE for the second model:", ml2.stats.rmse().round(2))

RMSE for the first model: 0.17
RMSE for the second model: 0.13

/home/docs/checkouts/readthedocs.org/user_builds/pastas/envs/v0.23.0/lib/python3.10/site-packages/pastas/stressmodels.py:1717: RuntimeWarning: overflow encountered in exp
  omega = 1 / (np.exp(beta * (t - sigma)) + 1)

[6]:

ml2.parameters

[6]:

	initial	name	optimal	pmin	pmax	vary	stderr
test_1_A	1.00000	test	0.428229	1.000000e-05	100.0	True	1.161801e-02
test_1_a	10.00000	test	1.930607	1.000000e-02	1000.0	True	1.026588e-01
test_2_A	1.00000	test	0.881949	1.000000e-05	100.0	True	9.400251e-03
test_2_a	10.00000	test	1.272092	1.000000e-02	1000.0	True	4.395104e-02
test_beta	0.00000	test	-88821.869586	-inf	inf	True	1.249071e-16
test_tchange	734503.00000	test	734503.000000	6.124110e+05	825914.0	False	NaN
step_d	1.00000	step	1.130025	0.000000e+00	NaN	True	1.750601e-02
step_tstart	734503.00000	step	734503.000000	6.124110e+05	825914.0	False	NaN
constant_d	330.18797	constant	329.256815	NaN	NaN	True	1.046843e-02
noise_alpha	7.00000	noise	24.476225	1.000000e-05	5000.0	True	1.370049e+00

4. Compare the response functions#

We can also look at the response to the river before and after,

[7]:

plt.plot(
    cm.rfunc1.step(p=ml2.parameters.loc[["test_1_A", "test_1_a"], "optimal"].values)
)
plt.plot(
    cm.rfunc2.step(p=ml2.parameters.loc[["test_2_A", "test_2_a"], "optimal"].values)
)

plt.legend(["Before", "After"])

[7]:

<matplotlib.legend.Legend at 0x7f30bc5444c0>

../_images/examples_16_changing_responses_12_1.png

5. Another way#

We can also add the stress twice, saving one parameter that needs to be estimated.

[8]:

ml3 = ps.Model(head, name="linear")

river1 = river.copy()
river1.loc["2012":] = 0

river2 = river.copy()
river2.loc[:"2011"] = 0

r1 = ps.StressModel(river1, rfunc=ps.Exponential(), name="river", settings="level")
r2 = ps.StressModel(river2, rfunc=ps.Exponential(), name="river2", settings="level")
step = ps.StepModel("2012-01-01", rfunc=ps.One(), name="step")

ml3.add_stressmodel([r1, r2, step])
ml3.solve(report=False, tmin="2004", tmax="2018", noise=True)
ml3.plots.results(figsize=(10, 6));

../_images/examples_16_changing_responses_14_0.png

How do the results compare?#

[9]:

plt.plot(
    cm.rfunc1.step(p=ml2.parameters.loc[["test_1_A", "test_1_a"], "optimal"].values)
)
plt.plot(
    cm.rfunc2.step(p=ml2.parameters.loc[["test_2_A", "test_2_a"], "optimal"].values)
)

ml3.get_step_response("river").plot()
ml3.get_step_response("river2").plot()

plt.legend(["Before", "After", "Before (method 2)", "After (method 2)"])

[9]:

<matplotlib.legend.Legend at 0x7f30bc81b250>

../_images/examples_16_changing_responses_16_1.png

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