Skip to main content
Studies · CA Air Quality · Investigation 27 · Phase 2

Adaptive monitor placement: where should the next sensor go?

Phase 1 gave a static ranking. A POMDP-coupled policy on the same $12.5M budget lifts EVSI by 39% — but L3 wins on DAC equity. Three objectives, three winning strategies.

$119M
L4 EVSI
9.5×
L4 ROI
40%
L3 DAC coverage
$12.5M
5-sensor budget
Decision context

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.

Findings at a glance
L1 static ROI
6.8×
$85M EVSI on $12.5M — Phase 1 baseline
L4 POMDP ROI
9.5×
$119M EVSI — +39% over L1 at same cost
L3 DAC equity
40%
40% DAC coverage vs 0% at L1
Key finding — three objectives, three winners
Total EVSI rises 85 → 119M from L1 to L4 at constant $12.5M cost, but the best level depends on what you're optimizing: L4 wins on ROI (9.5×) and climate signal (0.84), L3 wins on DAC equity (40%). No dominating strategy — CARB's priorities set the right fidelity.
Fidelity ladder

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.

L1
Static top-N EVSI ranking Phase 1 Inv 13 produced a gap-score ranking of 21,164 CA grid cells. L1 simply picks the top 5. No update after each placement; no redundancy penalty. The classical one-shot design.
$85M
EVSI • 6.8× ROI
L2
Greedy sequential placement Adds a haversine redundancy penalty (35 km correlation length) and places sites one-at-a-time. Submodular EVSI means this greedy policy has a guaranteed 1−1/e ≈ 0.63 fraction of the optimal batch (Nemhauser–Wolsey–Fisher 1978).
$111M
EVSI • 8.9× ROI
L3
Gaussian-process Bayesian optimization UCB acquisition balancing analytic GP information gain with the intrinsic site value. On this curated 15-site set, GP domain-variance reduction matches greedy's haversine penalty (both resolve ~42% of prior variance), so L3 ties L2 on total EVSI ($111M). Its value is site composition: L3 picks sjv_bakersfield_S + imperial_brawley (DAC share 0.40 vs L2's 0.20).
$111M
EVSI • DAC 40%
L4
POMDP-coupled placement Per-step climate bonus = 0.25 × site.climate_signal_proxy × pot, integrated over the 5-placement sequence. Top-2 picks shift to sjv_merced and sierra_plumas — sites that see wildfire transport and climate-driven VPD shifts directly. Trades DAC share (0.00) for climate coverage (0.84 vs 0.62 at L1).
$119M
EVSI • 9.5× ROI
L5
Joint PM2.5 + O3 + speciation multi-network Co-locate O3 and NMVOC speciation at the L4 sites. EVSI rises +23% explicitly decomposed: +15% O3 (resolves Inv 07 ozone disbenefit) + +8% NMVOC speciation (resolves Inv 17 wildfire NMVOC). Cost rises 1.6× (co-location multiplier), so ROI falls below L4. Useful when the portfolio includes O3-sensitive decisions.
$146M
EVSI • 7.3× ROI

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).

Cross-level comparison

What each policy picks, and what it costs

LevelTotal EVSICostROI DAC shareClimate signal
L1$85.4M$12.5M6.8×0%0.62
L2$110.7M$12.5M8.9×20%0.67
L3$110.7M$12.5M8.9×40%0.55
L4$118.9M$12.5M9.5×0%0.84
L5$146.3M$20.0M7.3×0%0.84

Winners: best by ROI = L4, best by DAC equity = L3, best by climate signal = L4.

Sequences side by side

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.

L1 — Static top-5
#SiteEVSICum
1la_basin_E$26.4M$26.4M
2sjv_merced$20.6M$47.0M
3sjv_stanislaus$16.1M$63.1M
4la_basin_S$12.5M$75.6M
5sierra_plumas$9.8M$85.4M
L4 — POMDP-coupled
#SiteEVSICum
1sjv_merced$72.0M$72.0M
2sierra_plumas$30.6M$102.6M
3shasta_redding$10.9M$113.5M
4sjv_stanislaus$3.8M$117.2M
5north_coast_mendocino$1.7M$118.9M
Candidate pool

15 candidate sites (Inv 13 top-15 + equity + climate picks)

SiteRegionPM2.5 (µg) PopGapClimate signal
la_basin_Ela_basin14.013,7471.000.35
sjv_mercedsjv16.09,3710.830.80
sjv_stanislaussjv16.08,4200.740.70
la_basin_Sla_basin14.011,4140.650.32
sierra_plumasrest_ca8.05,2410.580.95
sjv_fresnosjv16.07,9510.520.55DAC
sjv_stanislaus_Wsjv15.06,8200.500.60
imperial_brawleyimperial13.09,3100.470.40DAC
sacramento_ranchosacramento9.516,4220.420.45
north_coast_mendocinonorth_coast7.03,1500.380.85
south_coast_pico_riverala_basin13.519,8020.370.30DAC
sjv_bakersfield_Ssjv18.014,2100.350.50DAC
shasta_reddingrest_ca9.09,1450.320.90
bay_richmondbay_area11.022,4000.300.25DAC
inland_empire_fontanala_basin13.018,5000.280.28DAC

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).

Decision implication

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.

Validation & caveats

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.