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Challenges and developments in groundwater modeling
Mark Bakker
Solving Groundwater Problems with Time Series
Analysis
Mark Bakker and the Pastas Developers
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?
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
But ultimately, a classic groundwater model gives you the
response of a one-day stress at an observation well
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
Time series analysis with response functions:
Select response function with 2 or 3 parameters
Scaled Gamma response
3 parameters: A, a, n
The head variation is obtained through the convolution of
the response function with the stress
10 10
Example Convolution
Example series
linear model
recharge = rainfall - potential evaporation
Fitted model
Fitted response function
Pastas: Open source package for time series analysis of
groundwater heads
github.com/pastas/pastas
pastas.readthedocs.io
Example multiple
input series Head
Rainfall
Potential evaporation
Pumping
Results
Model fit
Contribution of rainfall
and evaporation
Contribution of pumping well
Response
functions
Recharge
Pumping
Application example: Drawdown caused by multiple well fields
Extraction rate of the 4 pumping stations
Contribution of precipitation excess, river stage, and pumping
of three pumping stations at one observation well
Step response
functions
Example results for one pumping station.
Steady drawdown vs. Distance from the well.
All observation wells analyzed separately
Second example:
Detection of a change in the groundwater system
Measurements (blue)
Fit over entire period 1982-2005
Fit over 1982-1997 (purple)
Fit over 1997-2005 (green)
Something happened in 1997…
1997
Solution: Use different response
function before and after 1997
Two separate response functions
with smooth transition
Fit
Physical explanation:
Dredging of the river in 1997
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.
Applications across Europe
Pastas is an open-source package for time series analysis
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

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DSD-INT 2023 Challenges and developments in groundwater modeling - Bakker

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