Where should the next monitor go, not the whole network?
Phase 1 Inv 13 ranked California's 21,164 grid cells by static gap-score. That ranking assumes we will deploy a batch of sensors against a frozen prior and never update. Real monitor networks grow sequentially: each new PM2.5 sensor updates the belief about the exposure field, which changes where the next one should go.
This investigation takes a 5-monitor, $12.5M deployment budget and asks which sequencing policy extracts the most decision-relevant information. The pot of available EVSI is $120M, anchored on the portfolio-relevant residual from Inv 11 (CRF), Inv 19 (indoor air), and Inv 26 (climate fan).
This investigation climbs five levels from the Phase 1 static ranking to a POMDP-coupled policy that sequences monitor placement against portfolio decisions and the 2050 climate fan.
Scope caveat. All five levels run on a curated 15-site candidate pool (Inv 13 top-15 plus equity and climate picks), not the full 21,164-cell grid. The pool is fixed across levels so differences are pure method — but a full-grid rollout would likely widen L3’s lead on raw EVSI, not just DAC composition.
Five levels of sequencing policy
Each level adds a distinct mechanism: redundancy penalty, closed-form information gain, climate-signal coupling, multi-pollutant co-location. Exact EVSI comes from the same $120M pot across all five levels; differences are pure method.
All levels share a 5-monitor budget, $500K/year installed-plus-operate cost over a 5-year deployment window. Total cost $12.5M (L1–L4) or $20M (L5 multi-network).
What each policy picks, and what it costs
| Level | Total EVSI | Cost | ROI | DAC share | Climate signal |
|---|---|---|---|---|---|
| L1 | $85.4M | $12.5M | 6.8× | 0% | 0.62 |
| L2 | $110.7M | $12.5M | 8.9× | 20% | 0.67 |
| L3 | $110.7M | $12.5M | 8.9× | 40% | 0.55 |
| L4 | $118.9M | $12.5M | 9.5× | 0% | 0.84 |
| L5 | $146.3M | $20.0M | 7.3× | 0% | 0.84 |
Winners: best by ROI = L4, best by DAC equity = L3, best by climate signal = L4.
L1 static vs L4 POMDP: the top-5 diverge
The Phase 1 static ranking and the POMDP-coupled policy share only one site in the top 5 (sjv_merced). L1 is anchored on high-population LA Basin cells; L4 moves toward climate-signal corridors in the Sierra/North Coast that can discriminate the 2050 CMIP6 fan.
| # | Site | EVSI | Cum | |
|---|---|---|---|---|
| 1 | la_basin_E | $26.4M | $26.4M | |
| 2 | sjv_merced | $20.6M | $47.0M | |
| 3 | sjv_stanislaus | $16.1M | $63.1M | |
| 4 | la_basin_S | $12.5M | $75.6M | |
| 5 | sierra_plumas | $9.8M | $85.4M |
| # | Site | EVSI | Cum | |
|---|---|---|---|---|
| 1 | sjv_merced | $72.0M | $72.0M | |
| 2 | sierra_plumas | $30.6M | $102.6M | |
| 3 | shasta_redding | $10.9M | $113.5M | |
| 4 | sjv_stanislaus | $3.8M | $117.2M | |
| 5 | north_coast_mendocino | $1.7M | $118.9M |
15 candidate sites (Inv 13 top-15 + equity + climate picks)
| Site | Region | PM2.5 (µg) | Pop | Gap | Climate signal | |
|---|---|---|---|---|---|---|
| la_basin_E | la_basin | 14.0 | 13,747 | 1.00 | 0.35 | |
| sjv_merced | sjv | 16.0 | 9,371 | 0.83 | 0.80 | |
| sjv_stanislaus | sjv | 16.0 | 8,420 | 0.74 | 0.70 | |
| la_basin_S | la_basin | 14.0 | 11,414 | 0.65 | 0.32 | |
| sierra_plumas | rest_ca | 8.0 | 5,241 | 0.58 | 0.95 | |
| sjv_fresno | sjv | 16.0 | 7,951 | 0.52 | 0.55 | DAC |
| sjv_stanislaus_W | sjv | 15.0 | 6,820 | 0.50 | 0.60 | |
| imperial_brawley | imperial | 13.0 | 9,310 | 0.47 | 0.40 | DAC |
| sacramento_rancho | sacramento | 9.5 | 16,422 | 0.42 | 0.45 | |
| north_coast_mendocino | north_coast | 7.0 | 3,150 | 0.38 | 0.85 | |
| south_coast_pico_rivera | la_basin | 13.5 | 19,802 | 0.37 | 0.30 | DAC |
| sjv_bakersfield_S | sjv | 18.0 | 14,210 | 0.35 | 0.50 | DAC |
| shasta_redding | rest_ca | 9.0 | 9,145 | 0.32 | 0.90 | |
| bay_richmond | bay_area | 11.0 | 22,400 | 0.30 | 0.25 | DAC |
| inland_empire_fontana | la_basin | 13.0 | 18,500 | 0.28 | 0.28 | DAC |
A full rollout would run the optimization over all 21,164 cells; we subset to 15 candidates for interpretability. The climate_signal_proxy is a 0–1 score of a site's ability to discriminate the 2050 CMIP6 fan (Inv 26).
Start with L4, adapt after 2–3 years of observations
The CARB / air-district recommendation: deploy the top 2 L4 sites (sjv_merced and sierra_plumas) as permanent stations in year 1. Hold the remaining 3 sensors until 2–3 years of data reveal whether California is tracking SSP2-4.5 or SSP5-8.5. Then choose between:
- Climate-fan branch: shasta_redding + north_coast_mendocino + 1 SJV (L4 sequence) if VPD is above SSP5-8.5 median by 2028.
- Equity branch: sjv_bakersfield_S + imperial_brawley + bay_richmond (L3 sequence) if fan tightens toward SSP2-4.5 and DAC exposure gaps dominate.
- Hybrid: 1 climate + 2 DAC if political pressure requires visible equity outcomes regardless.
Methodological signature: the ROI climb from 6.8× to 9.5× (L1 to L4) is not coming from a fancier optimizer — it is from coupling placement to downstream decisions. A static ranking optimizes reconstruction error; a POMDP optimizes the decision you will make.
Where this model could be wrong
- Candidate set is a curated top-15 from Inv 13 plus equity/climate picks; a full optimization should run over all ~21k grid cells. On the full grid, GP-UCB (L3) would likely pull ahead of greedy on raw EVSI, not just on DAC composition.
- EVSI pot $120M is an order-of-magnitude anchor; a decomposed computation over CRF + indoor + climate EVSI would tighten it.
- Characteristic correlation length 35 km is uniform; in practice 10–80 km by terrain and wind regime.
- L4 POMDP rollout is one-step lookahead; a 5-step rollout adds ~5% EVSI at 10× compute.
- L3 BO uplift over L2 is 0 on this curated set because GP domain-variance reduction matches greedy's haversine penalty. L3 is differentiated on DAC equity (0.40 vs 0.20), not total EVSI magnitude.
- L5 uplift is decomposed into explicit O3 (0.15) and NMVOC speciation (0.08) fractions, anchored on Inv 18 (SB-32 O3 EVSI) and Inv 17 (wildfire NMVOC). Co-location cost multiplier 1.6× is site-dependent.
Sources: Nemhauser–Wolsey–Fisher 1978 (submodular), Krause & Guestrin 2008 (near-optimal sensor placement), Shahriari et al. 2016 (BO review), Cassandra–Kaelbling–Littman 1997 (POMDPs), RFAQ Phase 1 Inv 13, RFAQ Phase 2 Inv 26.
Curated-set disclosure: The L1–L5 comparison runs over a hand-curated 15-site shortlist (Inv 13 top-15 by MVI + DAC equity picks + climate-fan picks), not the full 21,164-cell CA grid. This was chosen deliberately so the ladder is interpretable (readers can inspect every candidate and every score), and because the submodular 1−1/e guarantee from Nemhauser–Wolsey–Fisher carries over to any downselected candidate set. But it does bias the L3 (GP-UCB) vs L2 (greedy) comparison: on the curated set GP-UCB's variance-reduction advantage is muted because the shortlist is already near-Pareto-optimal on haversine spacing. A full-grid rollout would likely widen L3's margin over L2 on raw EVSI, not just on DAC composition. Production CARB deployment should re-run the optimization over all 21,164 cells before committing siting dollars.