Statistical Gaussian Plume Inversion Improves Satellite Methane Emission Rate Quantification

Researchers at the Jet Propulsion Laboratory have introduced a statistical inversion technique called Statistical Plume Imaging Inversion for Rate Estimation, or SPIIRE, to quantify trace gas emission rates from imaging spectrometers. Operating through a maximum likelihood estimation framework applied to a physical two-dimensional Gaussian plume model, the method infers emission rates directly from gas enhancement imagery without depending on subjective plume boundaries. By comparing physical plume simulations against overhead trace-gas observations, SPIIRE evaluates the statistical likelihood that measured data represents a noisy realization of a Gaussian plume. The development addresses a persistent bottleneck in greenhouse gas monitoring, where traditional algorithms rely heavily on manual operator choices and empirical thresholds that vary across sensor designs. Demonstrated on NASA’s orbital EMIT instrument and airborne AVIRIS-3 passes, the algorithm automates plume interpretation while demonstrating enhanced noise resilience.

Quantification of point-source emissions through imaging spectroscopy has historically depended on the Integrated Mass Enhancement approach across airborne campaigns and orbital monitoring missions. Under standard formulations, analysts convert column gas concentration length measurements into mass enhancements for each spatial pixel across a detected plume. The sum of these pixel enhancements yields the integrated mass, which is multiplied by wind speed and divided by estimated plume length to derive an emission rate. However, this classical framework introduces notable vulnerabilities, as defining plume boundaries requires subjective manual input and thresholding algorithms. Plume length calculations similarly fluctuate depending on whether analysts measure the longest dimension of the plume mask or compute the square root of the mask area. Consequently, traditional methods depend on tuned parameters that require continuous recalibration across different instruments, observation geometries, and atmospheric conditions.

To eliminate empirical parameter tuning, SPIIRE grounds its mathematical formulation in the physical equations of atmospheric dispersion. A classical three-dimensional Gaussian plume model describes gas released from a continuous point source into a uniform wind field, assuming turbulent diffusion expands the plume downwind according to dispersion coefficients. Because remote imaging spectrometers record vertically integrated column concentration lengths, researchers integrated the three-dimensional transport equation along the vertical axis, assuming that all emitted gas resides above the ground surface. The resulting two-dimensional concentration model relies on a downwind spreading parameter formulated as a power-law function of distance normalized by a reference scale of one thousand meters. Rather than assigning fixed spreading parameters from historical Pasquill-Gifford stability classes, the SPIIRE fitting procedure retrieves both the power-law amplitude and exponent directly from observed data, adapting the physical dispersion curve to local atmospheric conditions.

Standard Gaussian dispersion models strictly presume a constant wind vector across the spatial domain, an assumption frequently violated by real-world atmospheric motion, local topography, and surface heating. To accommodate natural plume meander and directional shifts without sacrificing physical grounding, SPIIRE incorporates cross-wind flexibility by adjusting the lateral center of the Gaussian profile as a function of downwind distance. The research team parameterized this cross-wind displacement using a continuous piecewise linear function defined by spatial parameters spaced at intervals equal to three times the sensor ground sampling distance along the wind axis. This formulation allows the synthetic plume trajectory to bend smoothly along the observed centerline of gas enhancement, reflecting localized shifts in wind direction. Because lateral displacement parameters scale dynamically from the plume origin to the retrieval domain boundary, the inversion maintains flexibility to fit curved plumes without introducing numerical instability.

A central pillar of the SPIIRE framework is its probabilistic maximum likelihood formulation, which systematically incorporates instrument noise characteristics and observational artifacts from spectral retrieval processing. In this approach, each spatial pixel’s measured concentration length is treated as a Gaussian random variable whose expected value equals the two-dimensional Gaussian plume model scaled by local pixel sensitivity. This sensitivity factor accounts for systematic biases caused by variable surface albedo and atmospheric conditions, while a molar-to-mass conversion factor calibrated for methane at standard temperature and pressure scales the model. In the likelihood exponent, the squared difference between the observed concentration length and sensitivity-scaled model is weighted inversely by the product of squared sensitivity and squared measurement uncertainty. By explicitly incorporating pixel uncertainty into the denominator, the objective function downweights noisy pixels, preventing surface transitions and albedo anomalies from distorting the retrieved emission rate.

To optimize the likelihood function, SPIIRE defines an objective retrieval window that extends beyond visible plume boundaries, circumscribing the manual plume detection mask with a ten-pixel buffer along all four rectangular edges. This expanded optimization window serves two vital functions: it eliminates subjective edge delineation by allowing the mathematical solver to determine plume extent independently, and it captures diffuse gas enhancements trailing downwind that escape human visual identification. To prevent the mathematical singularity inherent to point-source Gaussian equations where spreading approaches zero at the origin, the algorithm places the emission source along an excluded pixel boundary. The optimization executes within the jaxopt scientific computing library using bounded numerical minimization applied to the negative log-likelihood function. To stabilize numerical gradients across diverse physical scales, the solver optimizes the natural logarithms of both the wind-normalized emission rate and the horizontal spreading amplitude.

The predictive accuracy of SPIIRE was evaluated against controlled-release experimental trials in Casa Grande, Arizona, and Evanston, Wyoming, where metered methane was discharged from a stack seven point three meters above ground. During testing, AVIRIS-3 completed one hundred ten overpasses at Evanston and thirty-four at Casa Grande, while surface sonic anemometers recorded wind vectors at two meters. For each flightline, researchers paired the retrieved wind-normalized emission rate with thirty-second averaged wind speeds to generate absolute emission rates and analytical uncertainties. Across both airborne datasets, SPIIRE demonstrated robust agreement with metered release rates. When evaluating analytical error bounds, fifty percent of SPIIRE estimates in Arizona and sixty-two percent in Wyoming fell within one standard deviation of metered rates, outperforming traditional Integrated Mass Enhancement methods, which achieved corresponding success rates of forty-four and forty percent.

Validation efforts extended to spaceborne platforms using observations collected by NASA’s EMIT spectrometer over the Arizona controlled-release facility. While high wind speeds during initial trials dispersed gas enhancements below detection limits, EMIT captured five successful overpasses corresponding to active releases. Because releases commenced only minutes prior to satellite overpass, plumes remained exceptionally short, spanning between eight and sixteen EMIT pixels over distances under one kilometer. To prevent unphysical model fitting across empty buffer pixels downwind, investigators adapted the cost function to restrict optimization to a circular domain matching visible plume length. Despite the reduced pixel count, SPIIRE demonstrated high reliability, placing four of the five orbital estimates within analytical uncertainty of metered ground values. By comparison, traditional Integrated Mass Enhancement calculations placed only two of the five overpasses within uncertainty bounds, illustrating SPIIRE’s capacity to maintain precision across platforms without sensor-specific recalibration.

Beyond providing point-source emission estimates, the adapted Gaussian inversion provides critical physical insight into visually complex plumes previously mischaracterized by manual screening. However, application of SPIIRE demonstrated that these intricate plume geometries could be reproduced using a steady-state physical plume model when modulated by local surface sensitivity corrections. Apparent gaps and localized concentration peaks were shown to correspond directly to high-contrast surface albedo boundaries across the terrain rather than genuine fluctuations in atmospheric transport. By smoothing over turbulent eddies through spatial integration and correcting for optical reflectance variations, the statistical model prevents false attribution of visual anomalies to physical intermittency, yielding more reliable mass rate estimates where traditional thresholding algorithms suffer substantial bias.

The researchers expanded SPIIRE to address complex multi-source environments that historically defeated single-source quantification techniques, specifically overlapping plume complexes and broad distributed area sources. Rather than attempting subjective pixel allocation, SPIIRE executed a simultaneous numerical inversion of five distinct Gaussian plume models, optimizing their combined emission footprint across the shared domain. In a parallel demonstration over an eight-hundred-meter-wide landfill in northwestern China, the algorithm modeled diffuse emissions as a cluster of individual point plumes across an area polygon with shared spreading dynamics. The optimization converged to identify localized primary vents within the landfill footprint, estimating a total emission rate of approximately eleven thousand kilograms per hour compared to sixty-two hundred kilograms per hour produced by standard area-integration methods.

Despite its analytical advantages, the authors outlined physical and computational limitations that govern SPIIRE’s present operational implementation. Because standard Gaussian plume formulations express concentration solely through the ratio of emission rate to wind speed, the mathematical model cannot independently untangle wind magnitude from mass release rates without auxiliary meteorological data. Attempts to infer wind speed by correlating retrieved spreading parameters with empirical Pasquill-Gifford atmospheric stability classes proved unfeasible, as fitted dispersion values frequently exceeded published experimental boundaries. Furthermore, applying multi-source inversions across vast geographic regions demands accurate prior knowledge of source coordinates to prevent exponential growth in optimization parameters. Nevertheless, by releasing the open-source software implementation and establishing a mathematically objective inversion protocol, the authors provide a scalable framework capable of ingesting high-volume data streams from forthcoming orbital imaging spectrometers, establishing a standardized foundation for global greenhouse gas accounting that eliminates operator subjectivity and refines remote trace gas quantification.

Subject of Research: Statistical Gaussian plume inversion for quantifying trace gas emission rates from imaging spectroscopy

Article Title: Plume emission rate estimation using Gaussian plumes in remote imaging spectroscopy with SPIIRE

Article References: Fahlen, J. E., Brodrick, P. G., Thompson, D. R., Thorpe, A. K., & Green, R. O. (2026). Plume emission rate estimation using Gaussian plumes in remote imaging spectroscopy with SPIIRE. Atmospheric Measurement Techniques, 19(21), 7217-7229. https://doi.org/10.5194/amt-19-7217-2026

Image Credits: AI Generated

DOI: 10.5194/amt-19-7217-2026

Keywords: SPIIRE, imaging spectroscopy, methane emission quantification, Gaussian plume model, maximum likelihood estimation, EMIT, AVIRIS-3, integrated mass enhancement, remote sensing, controlled release experiment, atmospheric dispersion, point source emissions, plume complexes, landfill methane, surface albedo sensitivity, trace gas detection, emission rate uncertainty, atmospheric measurement techniques