The Number in the Compact Is Not the Driver
The 1922 Colorado River Compact commits the Upper Basin to delivering 75 MAF to Lee Ferry over any 10-year period — an average of 7.5 MAF/yr. Every negotiation since 2007 has centered on this number. But this investigation asks a prior question: in the mathematical model of how the basin works, how much does changing that number actually matter for breach risk?
The answer, from a global sensitivity analysis across six key uncertain parameters, is: barely.
Two Analyses, One Question
Sobol Global Sensitivity Analysis — A Sobol sensitivity analysis (Saltelli 2010 estimator, N=512 Saltelli samples = 4,096 model evaluations) was run on the 30-year Lee Ferry Compact breach model. Six uncertain inputs were varied across their plausible ranges:
| Input Parameter | Low | High | Rationale |
|---|---|---|---|
| Mean annual inflow | 9.0 MAF/yr | 14.0 MAF/yr | Natural flow uncertainty across climate scenarios |
| Inflow CV (interannual variability) | 0.20 | 0.50 | Historical range; higher under increased volatility |
| Upper Basin demand growth | 0.0 MAF/yr added | 2.0 MAF/yr added by 2055 | Spans no-growth to full projected development |
| Temperature delta | 0.0°C | 2.5°C warming by 2055 | CMIP6 Upper Basin range (current to high-end) |
| Tribal exercise rate | 0.0 MAF/yr additional | 1.498 MAF/yr additional | Full unexercised senior tribal rights |
| Compact delivery obligation | 6.0 MAF/yr | 7.5 MAF/yr | Plausible renegotiation range |
Stochastic Dynamic Programming — A Stochastic Dynamic Program was solved over a state space of (decade mean inflow, system storage) to find the economically optimal delivery obligation at every system state. Objective: minimize expected total economic damage (shortage costs + over-allocation costs) over 30 years. Three climate scenarios were evaluated: current conditions, +1.5°C, and +2.5°C.
The Delivery Obligation Is the Wrong Variable
Saltelli 2010 estimator, N=512, 4,096 model evaluations. S₁ = first-order effect (variance explained by input alone). Sᵀ = total effect (includes all interactions). Note: S₁ for Temperature Delta exceeds 1.0 — a known numerical artifact when breach probability is near-saturated; the total-effect index is reliable. Vertical line at Sᵀ = 0.10 marks the first-order relevance threshold.
The implication is sharp. Reducing the Compact obligation from 7.5 to 6.5 MAF/yr changes breach probability by less than 7%. Reducing Upper Basin consumptive demand by 1 MAF/yr changes it by more than 22%. The political debate is calibrated to the wrong sensitivity.
The SDP Reduces Damage, Not Breach Probability
The adaptive Compact SDP finds the economically optimal annual delivery obligation at each system state. At current storage (14,412 KAF) and current inflow conditions, the SDP recommends maintaining the full 7.5 MAF obligation — because shortage costs dominate at current system stress. At full storage (36,000 KAF), the optimizer backs off to 7.0 MAF.
| Scenario | Fixed Compact P(Breach) | Adaptive Policy P(Breach) | Adaptive Damage vs. Fixed |
|---|---|---|---|
| Current | 89.8% | 93.8% | ≈ Fixed (−0.003%) |
| +1.5°C | 100% | 100% | 59% lower |
| +2.5°C | 100% | 100% | 24% lower |
The adaptive policy counterintuitively increases breach probability at current conditions by a small amount. This is because the SDP is optimizing economic damage — not breach probability — and sometimes accepts breach outcomes that reduce total damage. More importantly: reducing breach probability in the Lee Ferry sense requires changing the 75 MAF/decade legal standard, not just optimizing year-to-year obligations within it. The adaptive policy saves real economic value ($6.7M → $2.7M expected damage at +1.5°C, a 59% reduction), but it does so by accepting fewer delivery promises — not by finding more water.
Damage reflects modeled shortage + over-allocation costs over 30 years; not total economic impact. Fixed compact holds delivery obligation at 7.5 MAF/yr regardless of system state. Adaptive policy: SDP-optimal obligation by (inflow decade, system storage) state. Costs calibrated to representative shortage and over-allocation damage coefficients.
Change the Objective, Then Change the Number
The Sobol result reframes the entire Compact debate. The political argument centers on the delivery obligation number (7.5 MAF, 75 MAF/decade). The sensitivity analysis shows that number drives less than 8% of breach risk. The real drivers are hydrologic (mean inflow, temperature) and behavioral (Upper Basin demand growth). A successful renegotiation must address those — the obligation number is, in this analysis, a downstream consequence of the supply, not a primary control variable.
This connects directly to Investigation 3's finding: the SDP optimizer reproduces the current AOP. The math is correct. The objective function needs updating.
The practical implication for negotiators: Getting agreement on 6.5 MAF instead of 7.5 MAF is not the hard part — and it may not even be a useful part. The hard part is reducing the 2–4 MAF structural gap between current legal allocations and available supply under a warming climate. That gap is driven by inflow and temperature, not by the obligation number.
Model Boundaries
The cost function uses simplified shortage and over-allocation cost coefficients. A full implementation would use agency-specific damage functions calibrated to agricultural, municipal, and hydropower users separately. The Sobol analysis treats the 30-year breach metric as a scalar output — a richer analysis would examine sensitivity across percentiles of the output distribution, which could reveal different driver rankings at tail-risk levels. The SDP state space discretization (decade mean inflow, system storage) omits within-decade flow timing, which Investigation 7 shows contributes measurably to effective supply.