Wildfire Study → Question 6

The Minimum Model.

Six decisions, five fidelity levels. For each decision, what's the simplest model that gives the right answer? From a BEHAVE lookup to full CFD, validated across four fires spanning 6,000 to 963,000 acres. This is the ADM thesis in one table.

The Fidelity Matrix

One Table. Six Decisions.

Each row is a real decision a fire incident commander faces. Each column is a model fidelity level. The question: what's the cheapest model that gets the decision right?

Minimum Sufficient Model per Decision
Decision Heuristic Empirical Elliptical Rothermel CA MC Ensemble Full CFD
Evacuation direction ✓ Sufficient Overkill Overkill Overkill Absurd
Spread rate & area ✗ No rate ✓ Sufficient Better (spatial) Better + CI Marginally better
Community arrival time ✗ No timing ✗ Straight-line only ✓ Sufficient Better + CI Marginally better
Evacuation trigger ✗ No uncertainty ✗ No uncertainty ✗ False precision ✓ Changes decision Marginally better
Community priority ✗ No comparison ✗ Wrong order ✗ Fragile ranking ✓ Reveals sensitivity Marginally better
Firebreak placement ✗ No spatial model ✗ No spatial model ✗ Single scenario ✓ Needed Marginally better

The green checkmarks show where fidelity first becomes sufficient for the decision. Everything to the right of a green check is wasted compute. The orange cells mark the critical transition — where moving from deterministic to Monte Carlo actually changes the decision.

Cross-Fire Validation: Key Numbers
Metric Kincade Camp Fire Dixie Marshall Consistent?
Q1: Direction heuristic 40% 0.4% 0% 35% Depends on fire type
Q2: FIRMS capture 96.0% 95.5% 95.4% 27.8% 96% wildland
Q2: Over-prediction 3.02× 1.90× 1.99× 4.13× CV=0.33
Q4: Avg hours gained (MC) — 4.2 h 5.6 h — Mean 5.0 h
Q4: Cost reduction 95–100% 89–99% 58–100% 100% Consistent
Compute Cost

What Each Fidelity Level Costs

Heuristic
0.001s
Wind + slope lookup
~50 lines of code
Empirical Elliptical
0.08s
BEHAVE-style analytical
~250 lines of code
Rothermel CA
1.2s
Single deterministic run
~268 lines of code
MC Ensemble
246s
200 draws, same code
~268 lines of code
Full CFD
4 hrs
Per single run (estimated)
~50,000 lines of code
Compute Cost vs. Decisions Enabled (Log Scale)

The MC ensemble costs 200× more than a single Rothermel run — but it's the jump that changes three life-safety decisions. CFD costs ~12,000× more than the MC ensemble and changes zero decisions at the community evacuation scale. MC on CFD (200 draws) would take ~800 hours — 33 days of compute — for the same strategic answer.

The Overlooked Level

Empirical Elliptical: How Fast, Not Where

Between the heuristic and the CA sits a model most fire agencies already use implicitly: the BEHAVE-style analytical calculation. Same Rothermel equations, but applied as an expanding ellipse — no grid, no timesteps, no spatial heterogeneity. It tells you the head fire spread rate and predicts burned area. It runs in 0.08 seconds.

Empirical vs. CA vs. Reality (Area Prediction)
Fire Actual Acres Empirical Ratio CA IoU
Kincade 77,758 34,795 0.45× 0.31
Camp Fire 153,336 42,146 0.27× 0.49
Dixie 963,309 894,012 0.93× 0.47
Marshall 6,026 392 0.07× 0.08

The empirical model works when the fire is long-duration and steady-state (Dixie: 0.93×) but fails catastrophically for wind-driven events (Marshall: 0.07×, Camp Fire: 0.27×). More critically, it cannot predict community arrival times because it uses a single average wind direction. Communities off the fire’s main axis show arrival times 10–40× higher than the CA’s predictions. The CA adds spatial routing through heterogeneous fuel and shifting winds — that 1-second investment is what makes community-specific timing possible.

The Critical Jump

Deterministic → Monte Carlo

Across 16 communities in four fires, the MC-informed trigger fires 1–7 hours earlier than the deterministic trigger (mean 5.0 hours). In 15 of 16 communities, expected cost drops by 89–100%. The pattern holds whether the fire is a 6,000-acre grassland blaze (Marshall) or a 963,000-acre wilderness siege (Dixie).

For a decision where "too late" means deaths, those hours change everything. The single run says "we have time." The ensemble says "we might not."

Below MC, no uncertainty quantification. Above MC, no new decisions. The heuristic handles direction. The CA handles timing. MC handles uncertainty. Each fidelity level answers one more question. After MC, you're paying 12,000x more compute for the same operational answer.

Finding
Validated across four fires: the biggest fidelity jump is deterministic → Monte Carlo. MC triggers fire 1–7 hours earlier (mean 5.0h) across 16 communities. FIRMS capture holds at 96% for wildland fires (28% for urban Marshall). Over-prediction bias is consistent (CV=0.33). Every jump above MC has diminishing returns. CFD costs ~12,000× more and changes zero decisions at community scale.

Full CFD resolves turbulent flame dynamics at centimeter scale. That's the right model for fire research. But for "which communities to evacuate and when," it produces the same answer as a 4-minute Monte Carlo. 12,000x the compute, zero new operational decisions. That's past the point of useful fidelity.

Five models, each answering one question the last one couldn't. Wind heuristic for direction. Empirical elliptical for spread rate. CA for community-specific timing. MC for uncertainty. Road capacity for feasibility. The right fidelity turned out to be CA + MC — the BEHAVE lookup can't route fire through terrain, and CFD costs 10,000x more without changing any operational answer. Build until you can answer the question. Then stop.

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