Presentation by Mark Bakker (Delft University of Technology, Netherlands) at the Hydrology Suite User Days (Day 3) - Groundwater modelling, during the Delft Software Days - Edition 2023 (DSD-INT 2023). Thursday, 30 November 2023, Delft.

1. Challenges and developments in groundwater modeling
Mark Bakker

2. Solving Groundwater Problems with Time Series
Analysis
Mark Bakker and the Pastas Developers

3. Questions that a groundwater engineer may get
(All these questions concern transient flow)
How high will heads rise after a
period of high rainfall?
How long will it take before heads
recover after a long period of
drought?
What is the effect of changes in
rainfall pattern (e.g., climate
change)?
What is the drawdown caused by
a pumping station?
Has there been a change in the
groundwater system?

4. The classic approach: Make a groundwater model (MODFLOW, AEM, …)
1. Aquifer system description (including aquifer parameters)
2. Boundary conditions (given head, given flow)
3. Transient stresses (rainfall, pumping, surface water levels)
4. Measurements (time series of heads at observation well)
5. Calibrate model (vary aquifer parameters)
And then finally: Answer the groundwater question

5. But ultimately, a classic groundwater model gives you the
response of a one-day stress at an observation well

6. Why make such a complicated model?
Why not select a response function with a few parameters?
Simplified modeling approach:
1. Transient stresses (rainfall, pumping, surface water levels)
2. Measurements (time series of heads at observation well)
3. Select respons function(s) with a few parameters each
4. Calibrate model (vary parameters)
Lumped-parameter model
Reduced-order model
Time series model

7. Time series analysis with response functions:
Select response function with 2 or 3 parameters
Scaled Gamma response
3 parameters: A, a, n

8. The head variation is obtained through the convolution of
the response function with the stress
10 10

9. Example Convolution

10. Example series
linear model
recharge = rainfall - potential evaporation

11. Fitted model
Fitted response function

12. Pastas: Open source package for time series analysis of
groundwater heads
github.com/pastas/pastas
pastas.readthedocs.io

13. Example multiple
input series Head
Rainfall
Potential evaporation
Pumping

14. Results
Model fit
Contribution of rainfall
and evaporation
Contribution of pumping well

15. Response
functions
Recharge
Pumping

16. Application example: Drawdown caused by multiple well fields

17. Extraction rate of the 4 pumping stations

18. Contribution of precipitation excess, river stage, and pumping
of three pumping stations at one observation well
Step response
functions

19. Example results for one pumping station.
Steady drawdown vs. Distance from the well.
All observation wells analyzed separately

20. Second example:
Detection of a change in the groundwater system

21. Measurements (blue)
Fit over entire period 1982-2005
Fit over 1982-1997 (purple)
Fit over 1997-2005 (green)
Something happened in 1997…
1997

22. Solution: Use different response
function before and after 1997
Two separate response functions
with smooth transition
Fit

23. Physical explanation:
Dredging of the river in 1997

24. Why model head time series?
System Characterization: Which driving forces and processes
are impacting the aquifer under study?
Prediction and forecasting: Make a predictive model to
predict and/or forecast the heads.
Quantification of input-response relations: Quantify the
relationship between different stresses and the heads.
Support GW models: time series models can be used to
support the development of numerical groundwater models.

25. Applications across Europe
Pastas is an open-source package for time series analysis

26. github.com/pastas/pastas
Take home messages
• Many groundwater problems can be solved
with time series analysis
• If using classing groundwater model: Do time
series analysis before you start
Pastas is an open-source package
for time series analysis
mark.bakker@tudelft.nl