Tutorial 18: Probabilistic Capture Zone

1Monte Carlo Backward Particle Tracking

Step 1 — Enter Synthetic Mode

Click 'Go to Synthetic Case Area' to create a blank domain.

Step 2 — Add River Boundaries

Click to add river zones on left (prescribed head = 0 m) and right (prescribed head = -10 m) edges. The head difference drives regional flow from left to right.

Step 3 — Add a Pumping Well with Particles

Click to add a pumping well near the right edge with a pumping rate of -2500 m³/day. Check the box next to 'Add Particle' — this automatically places particles around the well for backward (reverse) tracking. The particles will be traced backward through the flow field to identify where the well's water comes from.

Step 4 — Assign K as a Random Field

Click the 'Zone=DM' button to create a domain-wide zone. Assign hydraulic conductivity as a random field — same statistical parameters as Tutorials 15-17.

Step 5 — Enable Monte Carlo Simulation

Click to open Solver Options. Check 'Monte Carlo Simulation' with the default 10 realizations. Each realization will generate a new K field, solve flow, and trace particles backward from the well.

Step 6 — Configure Time Settings

Still in Simulation Settings, set the tracking duration:

Time step: 50 days
Simulation length: 1095 days (3 years)

This defines the 3-year time-of-travel capture zone — the area that contributes water to the well within 3 years. Longer tracking times produce larger capture zones.

Step 7 — Enable Capture Zone Display

Click to access Display Settings. Check 'MCS Display' and ensure 'Capture Zone' is checked underneath. Change Main Display to 'Vectors Only' for a clear view of particle paths and the accumulating capture zone.

Step 8 — Run the Simulation

Submit the model. Watch each realization unfold:

Realizations 1-2: Flow vectors and backward particle paths for the current realization only — the capture zone is unique to that K field
Realization 3+: The current realization's particles AND the accumulating mean capture zone are displayed — you watch the probabilistic capture zone converge as more realizations are added

Step 9 — View the Probabilistic Capture Zone

After all 10 realizations complete, the map shows the probabilistic capture zone — a color-coded probability map where darker regions have higher probability of being within the capture zone. The core area near the well has ~100% probability; the fringes have lower probability, reflecting uncertainty about where exactly the capture zone boundary lies.

Monte Carlo capture zone setup showing synthetic domain with river boundaries, pumping well with particle release enabled, domain-wide random K zone, and solver options configured for 10 realizations — Figure 2-3: Setup — river boundaries, pumping well (-2500 m³/day) with 'Add Particle' checked for backward tracking, random K zone, and Monte Carlo enabled for 10 realizations over 1095 days.

Display settings showing MCS Display with Capture Zone option checked and Vectors Only selected — Figure 3 (settings): MCS Display with Capture Zone enabled — the platform will accumulate the probabilistic capture zone across realizations.

Early realizations showing backward particle paths from the pumping well through two different K fields — the capture zone shape is different in each realization, with particles following different high-K channels backward to different source areas — Figure 4: Early realizations — backward particle paths trace from the well to different source areas in each K field. One realization's capture zone extends far to the left; another is wider but shorter. This variability IS the uncertainty.

Completed Monte Carlo probabilistic capture zone showing the overlay of all 10 realizations as a color-coded probability map — dark core area near the well with ~100% capture probability, gradual transition to lighter fringe areas with lower probability, mean flow vectors overlaid, demonstrating how the probabilistic capture zone is wider and more irregular than any single deterministic capture zone — Figure 5: The probabilistic capture zone — 10 realizations overlaid. The dark core has near-100% capture probability (water always comes from here). The fringe shows 20-80% probability (water sometimes comes from here, depending on the K field). This gradient of certainty replaces the false precision of a single deterministic boundary — giving regulators and water managers a risk-proportional tool for wellhead protection.

Key Concepts

Backward tracking = "where does my water come from?": Forward tracking (Tutorial 3) answers "where does water go?" Backward tracking reverses the question — particles are released at the well and traced upstream against the flow direction. The area they sweep defines the capture zone — the land surface area that contributes water (and potentially contamination) to the well.

Time-of-travel capture zones: The 1095-day simulation length defines a 3-year time-of-travel capture zone. Particles traced for 3 years delineate where water entering the well TODAY originated 3 years ago. Regulators commonly require 1-year, 5-year, and 10-year capture zones — each progressively larger — for tiered wellhead protection.

Capture probability vs. deterministic boundary: A deterministic model draws one boundary — inside or outside. The probabilistic approach assigns a probability to every location. A site at 90% probability needs immediate protection. A site at 10% may only need monitoring. This proportional approach is more scientifically honest and more economically efficient than the binary deterministic alternative.

Convergence with more realizations: With 10 realizations, the probability map is rough — 10% increments. With 100 realizations, you get 1% resolution. With 1000, the map becomes smooth and stable. IGW-NET's constant-memory approach makes large realization counts feasible — the probability map converges without running out of memory.

2What's Next

The stochastic chapter is complete. Continue the learning path:

Tutorial 19: Automatic Parameter Estimation — systematic calibration using optimization algorithms
Tutorial 20: Theis Solution — verify your model against analytical solutions
Tutorial 21: Unstructured Grid — flexible mesh for complex geometries

This tutorial covers