🎓 Lesson 10
D5
From Conceptual Model to Numerical Simulation: Key Assumptions and Uncertainties
A conceptual model is a simplified picture of how groundwater moves underground, and turning it into a numerical simulation means using math and computers to predict what will really happen at a mine site after closure.
🎯 Learning Objectives
- ✓ Explain how conceptual model choices (e.g., aquifer geometry, boundary type) propagate uncertainty into numerical simulation outputs
- ✓ Analyze calibration residuals and quantify prediction uncertainty using sensitivity analysis techniques
- ✓ Design a tiered monitoring strategy aligned with model purpose and dominant uncertainty sources
- ✓ Apply parameter correlation and identifiability diagnostics to assess model structural adequacy
📖 Why This Matters
At mine closure, regulators require credible predictions of long-term water quality and quantity—especially for acid rock drainage (ARD) plumes, pit lake evolution, or seepage through reclaimed waste dumps. But models are not crystal balls: they’re tools shaped by assumptions made before a single line of code is written. A poorly conceived conceptual model—even with perfect software—can yield dangerously overconfident predictions. This lesson shows how to trace uncertainty from sketchpad to spreadsheet, so your closure plans are defensible, adaptive, and grounded in geologic reality.
📘 Core Principles
Hydrogeologic modelling begins with three interdependent layers: (1) the *conceptual model* — a geologically constrained narrative of flow systems, including stratigraphy, fault controls, recharge mechanisms, and geochemical domains; (2) the *numerical model* — a mathematical translation that discretizes space/time and solves governing equations (e.g., MODFLOW’s continuity equation); and (3) the *uncertainty framework* — explicit recognition of epistemic (knowledge-based) and aleatory (inherent variability) uncertainties across all layers. Key assumptions include: homogeneity vs. heterogeneity representation, steady-state vs. transient forcing, simplification of complex boundary conditions (e.g., treating fractured bedrock as equivalent porous media), and omission of key processes (e.g., mineral dissolution kinetics). Each assumption introduces bias or variance that compounds during calibration and prediction.
📐 Uncertainty Propagation Index (UPI)
The Uncertainty Propagation Index quantifies how parameter uncertainty amplifies prediction uncertainty for a given output (e.g., contaminant breakthrough time at a compliance point). It combines first-order sensitivity coefficients with parameter variance estimates to rank dominant uncertainty drivers.
Uncertainty Propagation Index (UPI)
UPI_i = |∂Y/∂θ_i| × σ_{θ_i}Quantifies contribution of parameter θ_i uncertainty to output Y uncertainty, assuming linear sensitivity and independent parameters.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| UPI_i | Uncertainty Propagation Index for parameter i | units of output Y | Magnitude of output uncertainty attributable to parameter i |
| ∂Y/∂θ_i | First-order sensitivity coefficient | units of Y / units of θ_i | Rate of change of model output Y with respect to parameter θ_i |
| σ_{θ_i} | Standard deviation of parameter θ_i | units of θ_i | Quantified uncertainty (epistemic or aleatory) in parameter estimate |
Typical Ranges:
Pit lake water level prediction: 0.02 – 0.8 m
Contaminant travel time to compliance point: 0.5 – 12 years
💡 Worked Example
Problem: Given: Sensitivity of pit lake pH prediction to hydraulic conductivity (K) = 0.45 pH units/(m/d); K standard deviation = 0.35 m/d; sensitivity to recharge rate (R) = −0.18 pH units/(mm/yr); R standard deviation = 25 mm/yr. Calculate UPI for K and R, then identify dominant uncertainty source.
1.
Step 1: Compute UPI_K = |Sensitivity_K| × σ_K = 0.45 × 0.35 = 0.1575
2.
Step 2: Compute UPI_R = |Sensitivity_R| × σ_R = 0.18 × 25 = 4.5
3.
Step 3: Compare values: UPI_R (4.5) >> UPI_K (0.1575) → recharge rate dominates pH prediction uncertainty
Answer:
The UPI for recharge (4.5) is 28× greater than for hydraulic conductivity (0.1575), confirming that recharge estimation—not K—is the critical uncertainty lever for pit lake pH prediction.
🏗️ Real-World Application
At the Mt. Pleasant Mine (New Brunswick, Canada), closure modeling initially assumed a uniform, isotropic aquifer beneath the waste rock facility. Calibration failed to reproduce observed seepage chemistry until the conceptual model was revised to include a discrete, low-permeability till layer acting as a perched aquifer—identified only after targeted geophysical surveys and piezometer nest data. Recalibration with the updated conceptual model reduced prediction error for sulfate flux by 73% and shifted the predicted ARD onset from year 12 to year 28. This case underscores that model failure is rarely due to software—it’s usually a conceptual misrepresentation awaiting geological validation.
🔧 Interactive Calculator
🔧 Open Mine Closure & Progressive Rehabilitation Engineering Calculator📋 Case Connection
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