Goal Oriented Hydrogeological Site Characterization:
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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, USA 2Helmholtz Centre for Environmental Research—UFZ, Leipzig, Germany 3RWTH Aachen University, Aachen, Germany Groundwater Contamination http://www.huffingtonpost.com/2013/01/12/tap-water-catches-fire-methanedebby-jason-kline_n_2462981.html 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? Uncertainty in Hydrogeological Models Conceptual model uncertainty Uncertainty in parameters Difficulty 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 (π»0 ): “dangerous” scenario, fallback assumption – Example: contaminant arrives at water supply before it degrades Alternative Hypothesis (π»π ): “desirable” scenario, requires convincing evidence – water supply is safe from contamination Possible Errors: – Type I (πΌ) Error: Accidentally expose population to contaminants – Type II (π½) 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 ο 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 Prior Information Field Data Inverse Modeling Forward Modeling Parameter Estimates Modeling Predictions (e.g.UNCERTAINTY π, πΆπππ₯ ) Decision Making Modeling Predictions Water resources management, policy, or regulation decision Find new water source? Parameter Estimates (e.g. K) UNCERTAINTY Remediate contaminated site? 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 π»0 or π»π Simulate Baseline Field true? Simulate Baseline Field Simulate Baseline Field Simulate Baseline Field Baseline Field Simulate Field Campaign Baseline field simulated according to prior knowledge Physical models with baseline field ο synthetic “truth” “Data” collected from baseline field according to field campaign design Simulate fields conditional only to collected “data” Conditional Simulations Accept or Reject π»0 Simulate decision making Correct? Correct? πΌ Error? Correct? πΌ Error? Correct? π½ Error? πΌ Error? Correct? π½ Error? πΌ Error? π½ Error? πΌ Error? π½ Error? π½ Error? Would we have made the correct decision? Repeat on numerous baseline fields ο Pr[πΌ πππππ] & Pr[π½ πππππ] Synthetic Case Study Issue alert if contaminant will arrive at target before a critical amount of time passes 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? 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 ππΌ = Pr πΌ πππππ = Pr[ππππ πππ¦ ππ π π’ππ π ππππ‘π¦] πππππ‘ = 230π πππππ‘ = 350π This is when πππππ‘ = 350 π. What if πππππ‘ was smaller? Conclusion: Best spatial configuration of measurements depends on “how early” are the early arrivals we’re trying to predict 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: Taskβdriven optimal site investigation when the geostatistical model is uncertain, Water Resour. Res., 46, W03535, doi:10.1029/2009WR008312.
