Identifiability-Aware Source Apportionment in City-Scale Advection-Diffusion Systems

2026-07-25

AI Summary

This study addresses the challenge of source apportionment in urban sparse sensor networks, where limited sensor placement, wind-driven transport, background variability, and observational noise render candidate sources difficult to distinguish. The authors propose an Identifiability-Aware Source Apportionment (IASA) framework that models time-varying emissions via low-dimensional non-negative temporal bases, formulates a lagged inverse problem conditioned on wind fields using emission inventories, and removes background interference through subspace projection. Innovatively integrating identifiability metrics—such as matrix rank, singular values, and coherence—into non-negative coefficient estimation and uncertainty quantification, IASA provides a conservative merging strategy for indistinguishable sources. Experiments on PM2.5 data from New Delhi demonstrate that IASA significantly outperforms existing methods in recovery accuracy, robustness to background interference, and inventory resilience, reliably delivering defensible source resolution under given observational constraints.

Abstract

Source apportionment from sparse urban air-quality sensors is an inverse problem limited by sensor placement, wind-driven transport, background variation, and noise. Known or proxy emission inventories make attribution meaningful by restricting the unknown source field to a finite set of candidate groups, but do not guarantee those groups are distinguishable from the observations. We represent time-varying source activity with a low-dimensional nonnegative temporal basis and formulate inventory-based apportionment as a wind-conditioned lagged inverse problem in which each source--basis coefficient produces a sensor-time fingerprint. After projecting out a separate low-dimensional background space, the relevant object is the projected lagged response matrix $\widetilde H_Φ$: exact identifiability at the chosen basis resolution requires its full column rank, while noise-robust attribution is controlled by its singular values, coefficient visibility, background absorption, pairwise coherence, and ray distance. We propose an identifiability-aware apportionment (IASA) framework that estimates nonnegative source--basis coefficients, reconstructs activity trajectories, and reports uncertainty and conservative grouping recommendations for indistinguishable sources. We instantiate it on a New Delhi platform built from government PM$_{2.5}$ and wind records, regulatory sensor locations, and four proxy source groups, and define controlled and observed evaluations of recovery, ambiguity, wind diversity, background stress, transport error, inventory robustness, and residual adequacy. IASA reports the attribution resolution defensible under the declared inventories, transport, background, lag, and noise rather than the most detailed possible vector.

Problem

• source apportionment
• identifiability
• advection-diffusion systems
• urban air quality
• inverse problem

Innovation

• identifiability-aware
• source apportionment
• advection-diffusion inverse problem
• low-dimensional temporal basis
• projected lagged response matrix