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2021 HiMCM Problem B · Award-standard · Real USBR data

Tackling the Drought — Forecasting Lake Mead & Sizing Water Recycling

A complete 22-page modeling paper, produced end to end at the award-winning standard: a coupled pipeline from reservoir level to storage to budget to recycling, validated against real U.S. Bureau of Reclamation data, with a Monte-Carlo coverage analysis and a named decision flip under stress. This is the deliverable the seven-stage coaching method is built to reach.

Open the 22-page paper (PDF) → View the model code Watch the assistant work ← HiMCM coaching

The Paper

22 pages · read it in place

Deterministic compliance — all pass

Page countPASS22 pp (≤ 25)
Summary lengthPASS427 words (band 340–560)
Summary numericPASS27 results stated
AnonymityPASScontrol number only
ReferencesPASSpresent, in-text cited
AI-Use reportPASSpresent
FiguresPASS17 (target ~14)

Headline results — real data, validated

  • Volume curve validated to 0.19% against USBR Table 1
  • 2050 level: 1052 ft (Model 1, R²=0.90, back-test 8.3 ft) vs 976 ft under stress
  • 2050 shortfall 2.49 maf; recycling covers 100% to 2043, 83% by 2050
  • Monte-Carlo mean coverage 82% (p10 59%); full coverage needs recovery ρ ≥ 0.72
22 ppwithin the 25-page limit
17 figuresevery one from checked computation
0.19%volume curve validated vs. official tables
7 checksdeterministic compliance — all pass

Every Figure

17 figures · a coupled pipeline: level → storage → budget → recycling
Historical Lake Mead elevation record
Fig 1Historical elevation record
Seven detected drought periods
Fig 2Seven detected drought periods
Annual inflow band
Fig 3Annual inflow variability band
Volume curve fit
Fig 4Volume curve validated < 0.2%
Model 1 forecast
Fig 5Model 1 — trend forecast
Model 2 forecast
Fig 6Model 2 — stress forecast
Two forecasts diverge after 2030
Fig 7Forecasts diverge after 2030
Out-of-sample back-test
Fig 8Out-of-sample back-test
Volume projection
Fig 9Storage volume projection
Supply and demand
Fig 10Supply vs. demand budget
Recycling vs the shortfall
Fig 11Recycling against the shortfall
Tornado sensitivity chart
Fig 12Tornado — parameter sensitivity
Monte-Carlo coverage
Fig 13Monte-Carlo coverage
Decision flip at rho = 0.72
Fig 14Decision flip at ρ = 0.72
Named scenario comparison
Fig 15Named scenario comparison
Key-findings panel
Fig 16Key-findings panel
Residual diagnostics
Fig 17Residual diagnostics
※ How this was made

This paper was produced end to end through the same seven-stage method Tian2 uses to coach teams — decode, strategy, data & code, sensitivity, draft, summary, and a submission compliance pass — with every figure traced back to real, executed computation on public U.S. Bureau of Reclamation data. It is shown as a standard to aim for, not as a submission. To see the assistant run those stages live on a different problem, watch the assistant work.