Goal Oriented Hydrogeological Site Characterization: A Framework and Case Study in Contaminant Arrival Time

Bradley Harken1,2 Uwe Schneidewind3 Thomas Kalbacher2 Peter Dietrich2 Yoram Rubin1

1University of California, Berkeley, USA2Helmholtz Centre for Environmental Research—UFZ, Leipzig, Germany3RWTH Aachen University, Aachen, Germany

Groundwater Contamination

Prevention, Regulation, Risk Assessment, Remediation– Will maximum concentration exceed Maximum Contaminant Levels?– Will a plume reach water supplies before it degrades?– Is a waste disposal site safe?

Use hydrogeological models to answer these questions– How to cope with uncertainty?

http://www.huffingtonpost.com/2013/01/12/tap-water-catches-fire-methane-debby-jason-kline_n_2462981.html

Uncertainty in Hydrogeological Models

Conceptual model uncertaintyUncertainty in parametersDifficulty in characterization

– Determination of necessary parameters (e.g. Hydraulic Conductivity)– Description of spatial variability of parameters (mean, drift, covariance structure, …)– Costs and logistics of field campaigns– Measurement Errors

How to account for this uncertainty while answering questions relevant to remediation, regulation, risk assessment, etc.?

– Decisions often made by non-hydrologists

Hypothesis Testing Framework

Modeling Predictions: Hypotheses, amenable to statistical treatment

Null Hypothesis (): “dangerous” scenario, fallback assumption

– Example: contaminant arrives at water supply before it degrades

Alternative Hypothesis (): “desirable” scenario, requires convincing evidence

– water supply is safe from contamination

Possible Errors:– Type I () Error: Accidentally expose population to

contaminants– Type II () Error: Unnecessarily find alternative

supply

Account for all uncertainty in a simple, easy to understand manner

– Enable risk-based decision making– Subjectively defined accepted level of uncertainty

Role of Field Data

More field data less uncertainty

Different field campaign designs result in different levels of uncertainty

– Field campaign design: specifies quantity, type, and spatial location of field measurements

Which design will best meet uncertainty requirements, subject to other constraints?

– Cost– Field Logistics

Characterization Forward Modeling Decision Making

Prior Information

Field Data

Parameter Estimates

Parameter Estimates

(e.g. K)

Inverse Modeling

Modeling Predictions

(e.g. , )

Modeling Predictions

Water resources management, policy, or regulation decision

Find new water source?

Remediate contaminated site?

UNCERTAINTY

UNCERTAINTY

UNCERTAINTY

Hypothesis Testing: allows us to account for all sources of uncertainty in a simple, easy to communicate manner

Enables us to examine the link between field data and uncertainty in decisions

Hypothesis Testing: Summary

Allows us to make risk-based, defensible decisions in face of uncertainty

– Easily communicate uncertainty to decision-makers (not hydrologists)

Next: use HT framework to “optimize” field campaign designs in order to best support decision-making

Use HT Framework to Assess Field Campaign Design

Simulate Baseline Field or true?

Simulate Field

Campaign

Conditional Simulations

Accept or Reject

Correct? Error? Error?

Baseline field simulated according to prior knowledge

Physical models with baseline field synthetic “truth”

“Data” collected from baseline field according to field campaign design

Simulate fields conditional only to collected “data”

Simulate decision making

Would we have made the correct decision?

Repeat on numerous baseline fields &

Simulate Baseline Field

Correct? Error? Error?

Simulate Baseline Field

Correct? Error? Error?

Simulate Baseline Field

Correct? Error? Error?

Simulate Baseline Field

Correct? Error? Error?

Synthetic Case Study

Budget allows for 8 measurements of hydraulic conductivity– Measurements used for:

• Estimation of geostatistical parameters • Conditioning values in forward model

What is the best spatial configuration of measurements?

Issue alert if contaminant will arrive at target before a critical amount of time passes

Measurements: Possible Spatial Configurations

Option 1: Spread measurements throughout domain for improved estimate of geostatistical parameters and global trends

Alternatively, focus on travel path for stronger conditioning

Option 2: Spread along whole path

Option 3: Clustered close to source

Option 4: Clustered close to target

Results

Conclusion: Best spatial configuration of measurements depends on “how early” are the early arrivals we’re trying to predict

𝑃𝛼=Pr [𝛼𝑒𝑟𝑟𝑜𝑟 ]=Pr [ 𝑓𝑎𝑙𝑠𝑒𝑙𝑦 𝑎𝑠𝑠𝑢𝑚𝑒𝑠𝑎𝑓𝑒𝑡𝑦 ]

This is when . What if was smaller?

𝜏𝑐𝑟𝑖𝑡=350𝑑𝜏𝑐𝑟𝑖𝑡=230𝑑

Summary

• Hypothesis Testing enables risk-based decision making in face of uncertainty– Better communicate relationship between uncertainty in

data, parameters, models, etc. and uncertainty in questions we ultimately want to answer

– Improve link between hydrologists and managers/regulators

• Hypothesis Testing allows us to “optimize” our data collection– Uncertainty in final prediction as quantitative measure of

data effectiveness

THANK YOU!

References:

Nowak, W., Y. Rubin, and F. P. J. de Barros (2012), A hypothesis-driven approach to optimize field campaigns, Water Resour. Res., 48, W06509, doi:10.1029/2011WR011016.

Nowak, W., F. P. J. de Barros, and Y. Rubin (2010), Bayesian geostatistical design: Task driven optimal site investigation when the geostatistical model is uncertain, ‐Water Resour. Res., 46, W03535, doi:10.1029/2009WR008312.