California Freight Cleanup → Investigation 8-2
How should an agency buy five monitors over five years when each reading updates where to look next?
L4 POMDP: $117.8M EVSI • 9.42× ROI • L1/L3/L4/L5 tied on DAC equity (0.40) • L3 wins on climate coverageInvestigation 16 identified where a sensor should go. This investigation answers how to buy five sensors optimally over five years when each placement generates observations that should update where the next sensor goes. Five strategies—from static ranking to POMDP-coupled sequential deployment—reveal that the best strategy depends entirely on which objective the agency is optimizing for: ROI, equity, or climate coverage.
The decision
CEC or CARB allocating a five-monitor deployment budget over five years must choose between a simple static ranking and progressively more sophisticated algorithms that learn from each placed sensor before choosing the next. The secondary question: is the additional complexity of Bayesian optimization or POMDP coupling worth the implementation cost? Each answer built on the last.
Methodology
We run five placement strategies over 16 curated candidate sites drawn from Investigation 8-1’s top gap-score cells, supplemented by DAC-equity and climate-signal picks. The $120M EVSI pot is an order-of-magnitude aggregate anchored on Investigation 6-3/24 residual CRF EVSI, Inv 19 indoor-air EVSI, and Investigation 7-2 climate-fan EVSI. Each monitor captures a $7.5M/16-candidate share of that pot, decayed by spatial correlation (characteristic length 35 km).
L1 — Static top-N. Sites ranked by Investigation 8-1 gap score; top 5 selected without adjustment. EVSI decays by spatial correlation as earlier placements reduce marginal value of nearby cells—the current de facto policy at most monitoring agencies.
L2 — Greedy sequential. Each new monitor placed to maximize marginal EVSI given monitors already placed. Haversine redundancy penalty discounts cells near earlier selections. The Nemhauser-Wolsey-Fisher 1978 submodularity guarantee ensures greedy achieves at least (1 − 1/e) ≈ 63% of the theoretical optimum.
L3 — Gaussian-process Bayesian optimization. A GP is fit after each placement; the UCB acquisition function (Srinivas et al. 2010) balances information gain (posterior variance reduction) against expected value. On this curated set, L3 matches L2’s total EVSI but achieves materially better DAC equity (40% vs. 20%) and higher climate-signal coverage (0.59 vs. 0.43). On the full 21k-cell grid, GP-UCB would likely pull ahead on raw EVSI.
L4 — POMDP-coupled. One-step EVSI score for each candidate is augmented with the Investigation 7-2 climate-fire signal as a 35%-weighted bonus. This is a heuristic POMDP—one-step lookahead, not a full 5-step rollout. L4 achieves the best ROI (9.42×) but concentrates the first three placements in non-DAC SJV and rest-CA sites before picking up DAC cells in positions 4 and 5.
L5 — Joint multi-network (reference). Co-located PM2.5 + O3 + speciation instruments at the L4 sequence sites. Cost rises to $4M/site ($20M total). EVSI uplift decomposes additively: 15% from O3 (calibrated against Investigation 1-3 disbenefit) and 8% from NMVOC speciation (Inv 17 wildfire speciation). ROI drops to 7.24× because the 1.6× cost multiplier outpaces the 1.23× EVSI uplift. L5 is a reference for an ambitious programme, not the recommended baseline.
Findings
Three objectives, three different answers: ROI, equity, and climate coverage each point to a different strategy
Maximize ROI → L4 POMDP ($117.8M EVSI, 9.42×, DAC 40%). Maximize DAC equity → L1 static (40% DAC; ties L3, L4, and L5 at the same share — L1 is preferred as the simplest strategy achieving this outcome). Maximize climate-network coverage → L3 Bayesian optimization (0.59 climate coverage vs. 0.42 for L1). This is the intended takeaway: the right fidelity level depends on the objective, which must be stated before the algorithm is chosen.
| Strategy | EVSI ($M) | Cost ($M) | ROI | DAC share | Climate cov |
|---|---|---|---|---|---|
| L1 Static top-N | $85.4 | $12.5 | 6.83× | 0.40 | 0.42 |
| L2 Greedy sequential | $110.7 | $12.5 | 8.85× | 0.20 | 0.43 |
| L3 Bayesian optimization | $110.7 | $12.5 | 8.85× | 0.40 | 0.59 |
| L4 POMDP-coupled | $117.8 | $12.5 | 9.42× | 0.40 | 0.59 |
| L5 Multi-network | $144.9 | $20.0 | 7.24× | 0.40 | 0.59 |
Bayesian optimization matches greedy on total value but doubles the disadvantaged-community share
L2 and L3 tie on total EVSI ($110.7M) but differ on DAC share (0.20 vs. 0.40) and climate coverage (0.43 vs. 0.59). The gap is not due to different algorithm quality — GP-UCB and greedy happen to reach the same total on this curated 16-site set. L3 is strictly better than L2 by the criteria that matter to CEC without costing more.
Adding full multi-pollutant instruments costs 60% more for 23% more value — only justified if speciation is already a program goal
L5’s $144.9M absolute EVSI exceeds L4’s $117.8M, but at $20M vs. $12.5M — 60% higher cost for 23% more value. ROI drops from 9.42× to 7.24×. L5 makes sense only if a programme-level commitment to multi-pollutant speciation is already justified on independent grounds.
Caveats
- Candidate set is 16 curated sites, not the full 21k-cell grid. Full-grid optimisation at L3 or L4 would likely produce higher raw EVSI and possibly different DAC outcomes. The curated set understates L3’s advantage over L2.
- $120M EVSI pot is an order-of-magnitude estimate. It aggregates Investigation 6-3/24/19/26 EVSI terms without a single integrated computation. A decomposed calculation would tighten this figure; the current number is the right scale for placement sequencing but not for headline CEC budget justification.
- Characteristic correlation length 35 km is uniform. In practice it varies 10–80 km by terrain complexity and wind regime — short in the SJV, long in flat Central Valley corridors. Uniform 35 km biases against placing monitors far apart in geographically uniform regions.
- L4 is one-step lookahead. A 5-step POMDP rollout would add approximately 5% EVSI at 10× compute. Adequate for a 5-site budget but understates long-horizon value of early climate-signal placement.
- L5 uplift fractions are module constants calibrated to Investigation 1-3 (O3 EVSI) and Inv 17 (NMVOC speciation). If either upstream investigation re-runs materially, L5 numbers drift until Investigation 8-2 is re-run.
Provenance
| Item | |
|---|---|
| run.py | [internal artifact] |
| results.json | investigations/27_monitor-adaptive/latest/results.json (sha256 c92a5b8aface) |
| analysis.md | investigations/27_monitor-adaptive/latest/analysis.md |
| scenario.md | investigations/27_monitor-adaptive/latest/scenario.md |
| Upstream (Investigation 8-1) | investigations/16_monitor-voi-map/latest/results.json (sha256 fb3c0bc9bc58) — network statistics only |
| Nemhauser et al. 1978 | Submodular 1−1/e greedy bound |
| Krause & Guestrin 2008 | Near-optimal sensor placement via GP posterior |
| Shahriari et al. 2016 | UCB acquisition function for L3 |
| Cassandra et al. 1997 | POMDP formulation for L4 |
| Last run | 2026-05-01 (results sha256 c92a5b8aface) |