Representing Groundwater in Management Models

Julien Harou

University College London

2010 International Congress on Environmental Modelling and Software

July 4-8 2010 Ottawa, Canada

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Goal: represent groundwater in regional conjunctive use model

CV-RASA1 USGS Groundwater Model (1989)

• Finite-Difference Groundwater model: 529 100 km2 cells, 4 layers• Upscaling: vertical aggregation into 1 layer model by summing depth-average transmissivity and storage coefficient parameters

Regional Scale Discretization: groundwater Subbasins

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Two approaches

• Response function method:

Use external groundwater model to compile a database of responses at control locations caused by stresses at management locations

• Embedding method:

Numerical approximations of the flow equation are embedded into an optimization model as equality constraints

Embedding 3 groundwater model formulations

1. Sequential time-marching method (STM)

Implicit scheme finite-difference groundwater model, analogous to MODFLOW

2. Eigenvalue method (EV)

Efficient numerical scheme solves spatially discretized but time-continuous version of groundwater flow partial differential equations; allows aggregation into control variables (e.g. mean head per sub-basin)

3. Storage coefficient method (SC)

Storage coefficient equation relates volume of water released (or absorbed) from (into) storage per unit surface area of aquifer per unit change in hydraulic head.

Simulation Results Comparison:CVRASA1 vs. STM

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Monthly FD Model

Layers1-4

Regions 1,2,4,5

Simulation Results Comparison:CVRASA1 vs. EV

Regions 1,2,4,5

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EV

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EV

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EV

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EV

Layers1-4

EV method using 9 control variables, 9 basic stresses.

Simulation Results Comparison:CVRASA1 vs. SC

Regions 1,2,4,5

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Stor. Coeff.

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Stor. Coeff.

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Stor. Coeff.

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H = Stress / (storage coeff. * area)

Optimization formulations

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Subject to:

STM

EV

SC

STM Optimization Results (Cells)

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SVGMSVGM-EB

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EV Optimization Results (Basins)

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SVGMSVGM-EV

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SC Optimization Results (Basins)

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Subbasin 6

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Computational Comparison

MATLAB GAMS Simulation Simulation Optimization

Sequential time-marching (STM) method

0.72 sec. stable

7.2 sec. stable

3.6 min. moderate stability

Eigenvalue (EV) method

~ 0.02 sec. stable

3.4 sec. stable

2.9 min. (init. sol.) poor stability

Storage coefficient (SC) method

~ 0.01 sec. stable

0.003 sec. stable

0.003 sec. stable

Computational Comparison

MATLAB GAMS Simulation Simulation Optimization

Sequential time-marching (STM) method

0.72 sec. stable

7.2 sec. stable

3.6 min. moderate stability

Eigenvalue (EV) method

~ 0.02 sec. stable

3.4 sec. stable

2.9 min. (init. sol.) poor stability

Storage coefficient (SC) method

~ 0.01 sec. stable

0.003 sec. stable

0.003 sec. stable

Conclusions

• Groundwater simulation can efficiently be included in management models, particularly if only flows or heads in certain cells or aggregations of cells are of interest

• Optimization can be problematic:

Embedding spatially discretized groundwater models in mathematical program constraint sets can lead to significant numerical errors