data for the numerical interpretation of a

Ensemble Kalman filter assimilation of ERT data for the numerical interpretation of a saltwater intrusion laboratory experiment

Workshop on Data Assimilation in Terrestrial Systems, Bonn, 19 September 2016

Véronique Bouzaglou

, Matteo Camporese

, Erwan Gloaguen

, Elena Crestani

, Paolo Salandin

aCentre Eau Terre Environnment, Institut National de la Recherche Scientifique, Canada

bDepartment of Civil, Environmental and Architectural Engineering, University of Padua, Italy

Agenda

1 Motivation

2 Laboratory experiment 3 Numerical model

4 Data assimilation 5 Results

6 Summary

1 Motivation

Increasing relevance due to overexploitation of coastal aquifers and climate changes Development of projects to limit saltwater

intrusion (underground barriers)

Numerical models are fundamental to test scenarios and possible solutions…

How to improve model performance and reliability?

Data assimilation is a possible answer!

2 Laboratory experiment: setup

Specifically designed plexiglass sandbox

500 cm 30 cm

60 cm

ρ ≈ 1000 kg/m

ρ

≈ 1033 kg/m

V

= 2 m

V

= 0.5 m

2 Laboratory experiment: setup

ρ ≈ 1000 kg/m

ρ

≈ 1033 kg/m

H

= 42.8 cm 0.4% gradient h

= 40.7 cm

2 Laboratory experiment: setup

ρ ≈ 1000 kg/m

ρ

≈ 1033 kg/m

H

= 42.8 cm 0.4% gradient h

= 40.7 cm

Auxiliary upstream tank for recirculation and constant supply

Auxiliary downstream tank for volumetric discharge measurement

2 Laboratory experiment: setup

2 Laboratory experiment: monitoring

(cm)

Saltwater wedge evolution visualized with red dye

2 Laboratory experiment: monitoring

•

72 gold-plated electrodes

•

2.13 m coverage, 3 cm spacing

•

measures every 20’ (5’ 24’’ duration)

•

pole-dipole configuration

3 Numerical model: SUTRA [Voss, 1984]

Calibrated model with fine grid - Mesh: 237500 elements

- Discretization: 0.0025 m × 0.01 m and 0.0025 m × 0.0025 m

- Permeability (measured): k = 1.3 × 10

m

- Dispersivity (calibrated): α

= 0.001 m, α

= 0.0001 m Model with coarse grid for data assimilation

- Mesh: 24000 elements

- Discretization: 0.01 m × 0.01 m - Permeability: tbc

- Dispersivity: tbc

Boundary

conditions

3 Numerical model: calibration

20 h since the beginning of the experiment

(m)

Forward simulation of flow and transport:

NMC distributions of concentration C at time t

Forward simulation of dynamic ER data:

NMC vectors of modeled transfer resistance R

Convert concentration to electrical resistivity ρ (Archie’s law parameters

are assumed known)

Update of the NMC vectors θ = [k α

] values through the EnKF

Measured transfer resistance R at t

(from the

experiment) i = i + 1

4 Data assimilation: EnKF direct approach

f

H

Forward simulation of flow and solute transport:

NMC distributions of concentration C at time t

Measured transfer resistance R at each time t

(from the experiment)

Convert concentration to electrical resistivity ρ (Archie’s law parameters

are assumed known)

Update of the NMC vectors θ = [k α

] values through the EnKF

Electrical inversion:

Spatial distribution of electrical resistivity ρ at t

i = i + 1

4 Data assimilation: EnKF by inversion

f

H

4 Data assimilation: dual-step update

C

= f(C

, θ

)

θ

= θ

+ K

(C

– C

) C

= C

+ K

(d

– HC

)

d

= measured resistance (R

) or

resistivity (ρ

)

i = i + 1

Updated

concentration (C

)

Includes estimation of error due to wall effect (2.5D electrical model vs 3D reality)

5 Results: EnKF direct approach

log-permeability (m

)

5 Results: EnKF direct approach

log-dispersivity (m)

5 Results: EnKF by inversion

log-permeability (m

)

5 Results: EnKF by inversion

log-dispersivity (m)

update step update step

5 Results: performance summary

Average absolute error and ensemble spread of log-permeability

update step update step

5 Results: performance summary

Average absolute error and ensemble spread of log-dispersivity

6 Summary

 Assimilation of ERT data seems a promising approach for improving model predictions and parameter estimation in saltwater intrusion problems;

 Permeability can be effectively estimated by assimilating either raw or inverted ERT data;

 Dispersivity is more difficult to estimate, as it mainly controls the transition zone (higher resolution probably required);

 The approach with inverted ERT data seems affected by filter inbreeding (need reliable covariance matrix of measurement errors!);

 Future work:

• consider soil heterogeneity;

• fully three-dimensional ERT inversions;

• test the methodology in a real field experiment.