Adding pumping wells#
Developed by R.A. Collenteur & M. Bakker
In this example notebook it is shown how to simulate the effect of a pumping well on the groundwater levels. We will first create a TFN model with the net recharge as the single stress used to explain the observed heads. Second, this model is extended to include the effect of a pumping well on the heads by adding another stress model. The simulated heads are compared and it can be clearly seen how the addition of the pumping well improves the simulation of the heads.
This example was also shown at the 2018 General Assembly of the European Geophysical Union:
Bakker, M., Collenteur, R., Calje, F. Schaars (2018) Untangling groundwater head series using time series analysis and Pastas. In EGU General Assembly 2018.
import matplotlib.pyplot as plt
import pandas as pd
import pastas as ps
ps.show_versions()
Pastas version: 1.8.0b
Python version: 3.11.10
NumPy version: 2.0.2
Pandas version: 2.2.3
SciPy version: 1.15.0
Matplotlib version: 3.10.0
Numba version: 0.60.0
DeprecationWarning: As of Pastas 1.5, no noisemodel is added to the pastas Model class by default anymore. To solve your model using a noisemodel, you have to explicitly add a noisemodel to your model before solving. For more information, and how to adapt your code, please see this issue on GitHub: https://github.com/pastas/pastas/issues/735
1. Read the time series from files#
All time series for this example have been prepared as csv-files, which are read using the Pandas read_csv- method. The following time series are available:
heads in meters above the Dutch National Datum (NAP), irregular time steps
rain in m/d
Makkink reference evaporation in m/d
Pumping extraction rate in m\(^3\)/d. The pumping well stopped operating after 2012.
head = pd.read_csv(
"data_notebook_5/head_wellex.csv", index_col="Date", parse_dates=True
).squeeze()
rain = pd.read_csv(
"data_notebook_5/prec_wellex.csv", index_col="Date", parse_dates=True
).squeeze()
evap = pd.read_csv(
"data_notebook_5/evap_wellex.csv", index_col="Date", parse_dates=True
).squeeze()
well = pd.read_csv(
"data_notebook_5/well_wellex.csv", index_col="Date", parse_dates=True
).squeeze()
# Make a plot of all the time series
ps.plots.series(head, [rain, evap, well]);
2. Create a Pastas Model#
A pastas Model is created. A constant and a noisemodel are automatically added. The effect of the net groundwater recharge \(R(t)\) is simulated using the ps.RechargeModel stress model. Net recharge is calculated as \(R(t) = P(t) - f * E(t)\) where \(f\) is a parameter that is estimated and \(P(t)\) and \(E(t)\) are precipitation and reference evapotranspiration, respectively.
# Create the time series model
ml = ps.Model(head, name="groundwater")
ml.add_noisemodel(ps.ArNoiseModel())
# Add the stres model for the net recharge
rm = ps.RechargeModel(
rain, evap, name="recharge", rfunc=ps.Exponential(), recharge=ps.rch.Linear()
)
ml.add_stressmodel(rm)
ml.solve()
ml.plot(figsize=(10, 4))
# Let's store the simulated values to compare later
sim1 = ml.simulate()
res1 = ml.residuals()
n1 = ml.noise()
Fit report groundwater Fit Statistics
=================================================
nfev 24 EVP 51.75
nobs 3869 R2 0.12
noise True RMSE 0.33
tmin 1995-01-14 00:00:00 AICc -26684.78
tmax 2018-01-12 00:00:00 BIC -26653.49
freq D Obj 1.95
warmup 3650 days 00:00:00 ___
solver LeastSquares Interp. No
Parameters (5 optimized)
=================================================
optimal initial vary
recharge_A 843.245727 203.104730 True
recharge_a 545.587646 10.000000 True
recharge_f -1.939062 -1.000000 True
constant_d 16.516759 15.975755 True
noise_alpha 281.509268 1.000000 True
Interpreting the results
As can be seen from the above plot, the observed heads show a clear rise whereas the simulated heads do not show this behaviour. The rise in the heads cannot be explained by an increased precipitation or a decreased evaporation over time, and it is likely another force is driving the heads upwards. Given the location of the well, we can hypothesize that the groundwater pumping caused a lowering of the heads in the beginning of the observations, which decreased when the pumping well was shut down. A next logical step is to add the effect of the pumping well and see if it improves the simulation of the head.
3. Add the effect of the pumping well#
To simulate the effect of the pumping well a new stress model is added. The effect of the well is simulated using the ps.StressModel, which convolved a stress with a response function. As a response function the ps.Hantush response function is used. The keyword-argument up=False is provided to tell the model this stress is supposed to have a lowering effect on the groundwater levels.
# Add the stress model for the pumping well
sm = ps.StressModel(
well / 1e6, rfunc=ps.Hantush(), name="well", settings="well", up=False
)
ml.add_stressmodel(sm)
# Solve the model and make a plot
ml.solve()
axes = ml.plots.decomposition(figsize=(10, 8))
axes[0].plot(sim1) # Add the previously simulated values to the plot
Fit report groundwater Fit Statistics
=================================================
nfev 32 EVP 74.72
nobs 3869 R2 0.74
noise True RMSE 0.18
tmin 1995-01-14 00:00:00 AICc -26721.24
tmax 2018-01-12 00:00:00 BIC -26671.19
freq D Obj 1.93
warmup 3650 days 00:00:00 ___
solver LeastSquares Interp. No
Parameters (8 optimized)
=================================================
optimal initial vary
recharge_A 741.450384 203.104730 True
recharge_a 462.668221 10.000000 True
recharge_f -1.861624 -1.000000 True
well_A -102.102544 -338.167845 True
well_a 226.196450 100.000000 True
well_b 0.099881 1.000000 True
constant_d 16.786339 15.975755 True
noise_alpha 83.938534 1.000000 True
This axis already has a converter set and is updating to a potentially incompatible converter
[<matplotlib.lines.Line2D at 0x7f8630171d50>]
Interpreting the results
The addition of the pumping well to simulate the heads clearly improved the fit with the observed heads. It can also be seen how the pumping well stops contributing to the lowering of the head after ~2014, indicating the pumping effect of the well has dampened out. The period it takes before the historic pumping has no effect anymore can be approximated by the length of the response function for the well (e.g., len(ml.get_step_response("well"))).
4. Analyzing the residuals#
The difference between the model with and without the pumping becomes even more clear when analyzing the model residuals. The residuals of the model without the well show a clear upward trend, whereas the model with a model does not show this trend anymore.
ml.residuals().plot(figsize=(10, 4))
res1.plot()
plt.legend(["Model with well", "Model without well"])
<matplotlib.legend.Legend at 0x7f862978b190>
