Challenges in Methane Column Retrievals from AVIRIS-NG Imagery over Spectrally Cluttered Surfaces: A Sensitivity Analysis

Abstract

A comparison between efforts to detect methane anomalies by a simple band ratio approach from the Airborne Visual Infrared Imaging Spectrometer-Classic (AVIRIS-C) data for the Kern Front oil field, Central California, and the Coal Oil Point marine hydrocarbon seep field, offshore southern California, was conducted. The detection succeeded for the marine source and failed for the terrestrial source, despite these sources being of comparable strength. Scene differences were investigated in higher spectral and spatial resolution collected by the AVIRIS-C successor instrument, AVIRIS Next Generation (AVIRIS-NG), by a sensitivity study. Sensitivity to factors including water vapor, aerosol, planetary boundary layer (PBL) structure, illumination and viewing angle, and surface albedo clutter were explored. The study used the residual radiance method, with sensitivity derived from MODTRAN (MODerate resolution atmospheric correction TRANsmission) simulations of column methane (XCH₄). Simulations used the spectral specifications and geometries of AVIRIS-NG and were based on a uniform or an in situ vertical CH₄ profile, which was measured concurrent with the AVIRIS-NG data. Small but significant sensitivity was found for PBL structure and water vapor; however, highly non-linear, extremely strong sensitivity was found for surface albedo error. For example, a 10% decrease in the surface albedo corresponded to a 300% XCH₄ increase over background XCH₄ to compensate for the total signal, less so for stronger plumes. This strong non-linear sensitivity resulted from the high percentage of surface-reflected radiance in the airborne at-sensor total radiance. Coarse spectral resolution and feedback from interferents like water vapor underlay this sensitivity. Imaging spectrometry like AVIRIS and the Hyperspectral InfraRed Imager (HyspIRI) candidate satellite mission, have the advantages of contextual spatial information and greater at-sensor total radiance. However, they also face challenges due to their relatively broad spectral resolution compared to trace gas specific orbital sensors, e.g., the Greenhouse gases Observing SATellite (GOSAT), which is especially applicable to trace gas retrievals over scenes with high spectral albedo variability. Results of the sensitivity analysis are applicable for the residual radiance method and CH₄ profiles used in the analysis, but they illustrate potential significant challenges in CH₄ retrievals using other approaches.

1. Introduction

1.1. Methane

The potent greenhouse gas (GHG), methane (CH₄) is the second most important anthropogenic gas affecting the global radiative balance after carbon dioxide (CO₂). CH₄ is 34 times stronger as a heat-trapping gas than CO₂ on a 100-year timescale (86 times on a 20-year timescale) [1]. About 60–70% of global CH₄ emissions arise from anthropogenic sources including rice agriculture, fossil fuel industrial (FFI) production, waste handling, and domestic ruminants [2]. Important natural CH₄ sources include wetlands, termites, and geological seepage [3].

Given that CH₄’s atmospheric residence time is only ~8.5 years [4]—i.e., far shorter than the century timescale of CO₂, there are advantages to addressing global warming through CH₄ emission regulations compared to CO₂ [5]. Since pre-industrial times, CH₄ concentrations have risen, with the increase rate slowing and then almost stopping between 1999 and 2006, but growth has resumed since 2007 [6,7]. A number of mechanisms have been proposed to underlie these trends [6,8,9]; however, high uncertainty in emissions complicates interpretations. For example, a recent study suggested that FFI emissions are one and a half times greater than previous inventory estimates [10], while those of husbandry also appear to be underestimated significantly [11]. Given that accurate inventories are key to effective mitigation strategies, there is a critical need for new approaches to assess emissions to improve inventories.

The National Oceanic and Atmospheric Administration (NOAA) tower network provides in situ, highly accurate CH₄ measurements. Still, it cannot improve inventories at the regional (or national in many cases), local, or facility scale due to the scarcity of the observing stations [12]. In contrast, satellites provide global coverage and repeat measurements at high data density allowing effective monitoring of CH₄ concentrations at regional to local scales, if the sensor has sufficient resolution [13]. Necessarily, retrieval algorithm validation for current and future satellite missions is required to enable satellite data to improve inventories. Airborne remote sensing data can play a critical validation role.

1.2. Methane Remote Sensing

Only satellite remote sensing provides the global coverage to address emissions on the global scale needed to address factors underlying greenhouse warming. The first global map of tropospheric CH₄ was provided by the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) instrument launched in 2002 [14], which operated through 2012 at a 30 × 60 km resolution. More recently, the currently operational Greenhouse gases Observing SATellite (GOSAT) operated by Japan Aerospace Exploration Agency (JAXA), provides global column CH₄ (XCH₄, see definition in

Table 1. Nomenclature.

Symbol	Definition	Unit
Ar	Asphalt road	N/A
Bsl	Brown sandy loam	N/A
Rbl	Reddish-brown fine sandy loam	N/A
GOSAT	Greenhouse gases Observing SATellite	N/A
i	Band number	N/A
k	Scaling factor forXCH4_p	N/A
Lt(α, λ)	at-sensor radiance in wavelength λ for a ρs relative error of α	mW cm−2 μm−1 sr−1
S(XCH4_b, α)	Albedo sensitivity with a scenario, XCH4_b and the relative error, α, in ρs	dimensionless
XCH4	Methane column ratio	ppm
XCH4_A	Background methane column ratio	ppm
XCH4_P	Plume methane column ratio	ppm
XCH4_b	Base XCH4	ppm
XCH4_err	XCH4 from trial and error	ppm
XCH4_GOSAT	Mean XCH4 over subpixels in GOSAT pixel	ppm
θs	Solar zenith angle	degree
θv	Viewing zenith angle	degree
ϕ	Relative sun-sensor azimuth angle	degree
λ	Wavelength	nm
ρs(λ)	Surface albedo	dimensionless
ρt(λ)	At-sensor reflectance	dimensionless
Lt(λ)	At-sensor radiance	mW cm−2 μm−1 sr−1
Lt_GOSAT(λ)	Mean Lt(λ) over subpixels in GOSAT pixel	mW cm−2 μm−1 sr−1
Lt_AO(λ)	Mean Lt over the subpixels	mW cm−2 μm−1 sr−1
Lt_OA(λ)	Lt for the mean surface albedo over subpixels	mW cm−2 μm−1 sr−1
Lt_err	Lt for the original albedo and XCH4 with 10% underestimation	mW cm−2 μm−1 sr−1
ρs_err	ρs corresponding to Lt_err and the original XCH4	dimensionless
XCH4_M	XCH4 corresponding to Lt_GOSAT and mean albedo over GOSAT subpixels	ppm
NEδL	Noise equivalent delta radiance	mW cm−2 μm−1 sr−1
NEδLa	NEδL adjusted to the band average	mW cm−2 μm−1 sr−1
α	Relative error in surface albedo	%
β	Relative error in Lt	%
γ	Underestimate of XCH4 resulted from the subpixel heterogeneity of CH4	ppm
σ	ρt(2298)/ρt(2058)	dimensionless
Δ	Average residual radiance	mW cm−2 μm−1 sr−1
Pc	Percentage of area in one GOSAT pixel covered by XCH4 plume	%

) by means of proxy and physics-based algorithms [15,16,17]. GOSAT observes at 10 × 10 km spatial resolution and is a sampling mission. The Thermal And Near infrared Sensor for carbon Observation (TANSO)—Fourier Transform Spectrometer (FTS) onboard GOSAT uses spectral absorption features near 1.6 μm for CH₄ retrieval with 0.2 cm⁻¹ spectral intervals and 0.27 cm⁻¹ spectral resolution. The coarse spatial resolution of these satellite instruments (and sampling nature of GOSAT) challenges facility-level monitoring sources with their data. The Sentinel 5 precursor mission, TROPOspheric Monitoring Instrument (TROPOMI), is scheduled to launch in 2017 with a 7 km spatial resolution, followed by the Sentinel 5 mission in 2021, to provide daily global mapping coverage of XCH₄ and XCO₂ [18].

Existing airborne systems can remotely sense CH₄ at finer than satellite scales, using either non-imaging or imaging spectrometers. Airborne non-imaging sensors have higher sensitivity to CH₄, an example being the Methane Airborne MAPper (MAMAP) sensor [19], whereas imaging sensors have lower sensitivity, but include contextual information, examples being the instrument Mako [20] and HyTes [21] that use the thermal infrared (TIR), and Airborne Visual InfraRed Imaging Spectrometer-Classic (AVIRIS-C) [22] and AVIRIS-Next generation (AVIRIS-NG) [23] spectrometers that use the short-wave infrared (SWIR). AVIRIS-C and AVIRIS-NG specifications are provided in Section 2.1.

A number of approaches have been developed to retrieve XCH₄ from airborne and satellite data. These approaches include qualitative ones such as band-ratio approach [24], cluster-tuned matched filter (CTMF) approach [25], and quantitative ones such as the Weighting Function Modified (WFM) Differential Optical Absorption Spectroscopy (DOAS) algorithm [14], and the Iteratively Maximum a Posteriori DOAS (IMAP-DOAS) algorithm [26].

1.3. Study Motivation

Real-world applications of radiative transfer models to atmospheric simulations almost always incorporate imperfect information given that in situ profile data and surface spectral data generally are unavailable. Imperfect information propagates into biases in the trace gas retrievals. This study is developed out of a scoping study that compared XCH₄ for two scenes of comparable emission strength, one marine and one terrestrial—i.e., different radiative transfer characteristics and surface spectral complexity. The scoping study used a simple band-ratio method [24], which is computationally fast and can screen large datasets to identify spatial subsets for more sophisticated analysis. Specifically, the scoping study analyzed AVIRIS-C acquired 19 June 2008 for the Coal Oil Point (COP) marine seep field and 6 June 2013 for the Kern Front oil field (terrestrial) (Figure 1). This is a producing oil field and is located near Bakersfield, California, in the central San Joaquin Valley, California. Emissions have been estimated at ~1.0–1.5 ×10⁵ m³ day⁻¹ (25 Gg year⁻¹) [27] for the COP seep field. Emissions for the Kern Front oil field were estimated at ~60 Gg year⁻¹ in September 2014, decreasing exponentially to ~30 Gg year⁻¹ by late 2015 [28].

The scoping study revealed a dramatic performance difference for XCH₄ retrievals (Figure 1). Strong CH₄ plumes were easily detected for the marine source, but were highly challenged for the terrestrial source. The main purpose of the present study was to better understand these differences through a series of sensitivity studies testing different factors that could influence the XCH₄ retrievals including albedo, water vapor, observational geometry, aerosol, and surface spectral heterogeneity. Findings are evaluated with respect to implications for airborne and spaceborne remote sensing sensors. Sensitivity was studied through forward modeling using MODTRAN, the spectral specifications and geometries of AVIRIS Next Generation (AVIRIS-NG), and the residual radiance, also termed the residual radiance method. The residual radiance method has been used for successful trace gas detection of the offshore emissions from the COP seep field [29]. For simplicity, the modeling is for a uniform surface, despite the fact that in reality many surfaces can exhibit complicated effects in their Bi-directional Reflectance Distribution Functions (BRDF). The study focused on understanding factors leading to the band ratio’s poor performance for the Kern oil fields and how they also impact a more sophisticated approach, the residual radiance method. These sensitivity study results are directly applicable only to the residual radiance method for XCH₄ retrievals. Still, the findings have implications for other retrieval methods due to common radiative transfer challenges, such as spectral clutter, particularly for moderate spectral resolution instruments.

2. Materials and Methods

2.1. Imaging Spectrometers

AVIRIS-C is a whiskbroom sensor that collects radiance from 380 to 2500 nm in 224 channels with a ~10 nm bandwidth and 1 milliradian [30]. AVIRIS-NG is the successor instrument to AVIRIS-C and is a pushbroom sensor that collects spectra in 432 bands at a sampling interval of 5 nm and a Full Width at Half Maximum (FWHM) varying from 5.6 to 6.0 nm. AVIRIS-NG has improved geo-location and signal to noise ratio (SNR) over AVIRIS-C (SNR > 1000 @ 600 nm and > 800 @ 2200 nm, at an input reflectance level of 25%) [31]. A Gaussian function was employed to describe the slit function. The cross-track swaths of the AVIRIS-C and AVIRIS-NG are 892 and 795 pixels, respectively, with an angular swath width of 30°.

Dennison et al. [32] reported that the NEδL of AVIRIS-NG is one third that of AVIRIS-C, which Green & Pavri [33] estimated at 0.001 mW cm⁻² μm⁻¹ sr⁻¹. For this study, the NEδL is taken as 0.00035 mW cm⁻² μm⁻¹ sr⁻¹ for AVIRIS-NG. Important geometric parameters include solar zenith angle (θ_s), sensor viewing zenith angle (θ_v) and relative sun-sensor azimuth angle (φ). Jet Propulsion Laboratory provided geo-referenced radiance data and observation geometries.

2.2. Study Area

The sensitivity study used the observation geometry, surface albedo from AVIRIS-NG imagery acquired for the Kern River oil field (Figure 2), located immediately north of Bakersfield, CA. CH₄ leakage plumes have been documented by remote sensing for this active oil field [20], as well as by in situ observations [28].

Supporting this study are data collected during the CO₂ and Methane EXperiment (COMEX) [34]. COMEX combined in situ airborne and surface data, with airborne imaging and non-imaging spectroscopy to explore synergies between these remote sensing approaches for GHG emission estimation. COMEX investigated southern California CH₄ sources including husbandry, landfills, natural geology, and FFI refining and production, the latter being the strongest among the COMEX foci.

This study leveraged the availability of simultaneous in situ profile and AVIRIS-NG data, to understand the impact of erroneous vertical CH₄ profile on XCH₄. Two profile cases were simulated, in situ profile and a uniform profile (see Figure 3B). The two profiles have the same column-averaged CH₄ within a boundary layer of 2.0 km. In situ data were collected in a data curtain (Figure 3A and Figure A1) by the CIRPAS Twin Otter airplane (www.cirpas.org) above the Kern Front oil field [19].

The CIRPAS acquisition was concurrent (to a few hours) with the AVIRIS-NG acquisition. In situ CH₄ concentrations were measured by an onboard Cavity Ringdown Spectrometer (Picarro Inc., Mountainview, CA, USA). Data in the survey plane were segregated as in the plume or outside, averaged at each altitude level, and then interpolated linearly between levels. Data identified the Planetary Boundary Layer (PBL) at ~1.2 km (Figure 3B and Figure A2). Additional details on the measurement and derivation of the in situ profile are provided in Appendix A.1. The “uniform profile” presumed a well-mixed atmosphere (vertically uniform) to 2.0 km altitude. For all two cases, the profile above 2.0 km was that of a typical mid-latitude summer atmosphere.

2.3. Radiative Transfer Simulations—Residual Radiance Method

MODTRAN has a long history of being applied to trace gas retrievals, e.g., Roberts et al. [29] and Thorpe et al. [25]. In this study, we use MODTRAN5.3.2 to model L_t for the AVIRIS-NG sensor viewing and illumination geometries and bandwidth (5 nm). Gaussian slit functions were used in the simulations. Two plume simulation scenarios were considered, a uniform profile and an in situ profile (Section 2.2). The atmosphere simulated was a typical mid-latitude summer atmosphere. Thus, the default mid-latitude CH₄ profile was used for above 2.0 km. Visibility was derived from the atmospheric correction of AVIRIS-NG using the Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH) module in Environment for Visualizing Images (ENVI) for an urban aerosol. Water vapor column was derived from the water absorption feature that overlaps the 1135 nm band. AVIRIS-NG data provided the land cover spectra and observation geometries for the sensitivity analysis.

The residual radiance method for CH₄ retrieval is detailed in Roberts et al. [29], and summarized briefly below. In this study, the method was used in forward modeling to evaluate whether two modeled total radiance spectra (using different input parameters) agreed with each other. First, the at-sensor radiance (L_t) was simulated for a surface albedo (ρ_s) of 0.1 and the aerosol and water vapor derived using the method described above. The true ρ_s was approximated by comparing the simulated L_t with the observed L_t for 2139 nm, under the assumption that L_t increases linearly with ρ_s. The 2139 nm band was used to estimate ρ_s because it is the band closest to the CH₄ spectral absorption feature (2239–2299 nm) that also is free of CH₄ absorption (Figure 4A). ρ_s in the wavelength range of 2239–2299 nm was assumed to be equal to ρ_s for 2139 nm—a spectral flatness assumption. Spectral flatness may not be a valid assumption for some land surface types, introducing biases in XCH₄. A new radiative transfer simulation was carried out using the newly calculated ρ_s and a background XCH₄, from which a new set of L_t were derived. The average residual radiance (Δ) was calculated by averaging the subtraction of the AVIRIS-NG observed L_t from the simulated L_t (denoted by L_tsim) for bands from 2239 to 2299 nm, where CH₄ had stronger absorption than water vapor (Figure 4B).

$$\Delta =\frac{1}{N}{\displaystyle \sum }_{i=1}^N(L_{t_{sim}}\left({\lambda }_i\right)-L_t\left({\lambda }_i\right))$$

(1)

Note, a large ∆ corresponds to high CH₄ absorption—i.e., high XCH₄. It should be noted that the residual radiance method for XCH₄ retrieval was presented in this paper by forward simulations for calculating residual radiance that was used to derive the sensitivity.

2.4. Sensitivity Studies

The sensitivity of XCH₄ to surface albedo was based on the hypothesis that errors in surface albedo propagate through the MODTRAN calculations manifesting as an error in XCH₄ that produces the same measured L_t. Because of the underlying key importance of surface albedo, sensitivity studies were referenced to the spectra of three common scene elements in the Kern Front oil field imagery: Asphalt road, Brown sandy loam, and Reddish-brown sandy loam, noted as Ar, Bsl, and Rbl, respectively (Figure 5). These three scene elements span a range of occurrence probabilities in the AVIRIS-NG imagery, with Rbl being dominant (Figure A3 in Appendix A.2). The three surface types differ in terms of both magnitude and shape of the spectral reflectance, which deviate slightly from a spectrally flat behavior (see Figure 5B).

Within the CH₄ absorption feature, increases (decreases) in XCH₄ will decrease (increase) L_t. Thus, inaccurate ρ_s biases XCH₄. The retrieved XCH₄ sensitivity to ρ_s was evaluated through MODTRAN simulations for a XCH₄ “base-scenario”, denoted XCH_{4_b}, with respect to relative error in ρ_s, denoted α, which spanned from −50% to 50%. L_t(λ_i) for different values of α was derived for the 13 AVIRIS-NG bands from 2239 to 2299 nm, denoted L_t(α, λ_i). Using the original ρ_s, the increase (for α < 0) or decrease (for α > 0) in XCH₄ relative to XCH_{4_b} was determined by error minimization, which minimized the average residual radiance ($∆$) until convergence, defined as $∆$ < NEδL_a, where NEδL_a is the average over the N bands spanning the feature, i.e.,

$$∆=\frac{1}{N}{\displaystyle \sum }_{i=1}^N\left|L_t\left(0,{\lambda }_i\right)-L_t\left(\mathsf{\alpha },{\lambda }_i\right)\right|$$

(2)

$$NE\delta L_{\mathrm{a}}=\frac{NE\delta L}{\sqrt{N}}$$

(3)

where N is 13, and i is the band number. For convenience, we denoted XCH_{4_err} for the residual-radiance minimized XCH₄ for ρ_s with respect to α. Finally, we defined the sensitivity to α for the CH₄ column, S(XCH_{4_b}, α):

$$S(XC{H}_{4\_\mathrm{b}}, \alpha )=\frac{XC{H}_{4\_\mathrm{err}}-XC{H}_{4\_\mathrm{b}}}{XC{H}_{4\_\mathrm{b}}}$$

(4)

A negative (positive) α means underestimation (overestimation), which causes an overestimation (underestimation) of XCH₄ and as a result S(XCH_{4_b}, α) is positive (negative).

Taking a negative α as an example, the error minimization was carried out as follows. XCH₄ is increased from XCH_{4_b} by a specified interval (e.g., 0.01 ppm). For each increase, L_t was simulated and applied to Equation (2) to calculate Δ. The increase continues until $\Delta$ in Equation (2) is smaller than NEδL_a.

Using the same method for deriving the sensitivity to albedo as described above, sensitivities to water vapor and to spectral flatness were also investigated. The sensitivity to scene geometry (or aerosol, vertical profile) was derived by calculating S(XCH_{4_b}, α) using the method described above for different geometries (or aerosols, vertical profiles) while other parameters were kept unchanged.

3. Results

3.1. Sensitivity Studies

The sensitivity study investigated the relative importance of the various differing factors between the scenes to understand the relative importance of the factors underlying the difference between the band ratio analysis of the Kern versus the COP scenes. Sensitivity studies are for the residual radiance method. Factors include surface albedo, vertical profile, scene geometry, spectra flatness, water vapor, and aerosols.

3.1.1. Sensitivity to Albedo Error

The simulations showed that XCH₄ exhibited an extremely strong and non-linear sensitivity to ρ_s error (α), with the relative error in L_t(λ) (β) for the plume simulation exhibiting a significant but linear sensitivity—note how β(α) lies on the 1:1 line (Figure 6A). The albedo error sensitivity with respect to XCH₄ was explored by varying the plume strength from k = 0 (background, XCH_{4_A}) to k = 1 (in situ profile) to k = 10 (factor of 10 stronger plume than observed), i.e.,

XCH₄ = XCH_{4_A} + k × XCH_{4_P}

(5)

Here, XCH_{4_P} is the plume anomaly, such that XCH_{4_A} + XCH_{4_P} is the vertical plume profile. Simulations revealed a significant and non-linear XCH₄ error resulted from the error in ρ_s for the observed plume (k = 1), a sensitivity that was close to invariant with land cover types (Figure 6B). This albedo error sensitivity in XCH₄ was explored further for the dominant scene element, Rbl by varying the plume anomaly strength from k = 0 to k = 10 (Figure 6C). S(XCH_{4_b}, α), is highly nonlinear (Figure 6C), albeit less so for stronger plumes (k > 1). For example, for α = −5% for pixel Rbl, S decreased from 144.3% to 18.5% for XCH₄ increasing from background (k = 0) to a very strong plume (k = 10). XCH₄ could not be retrieved for α higher than 5% for XCH₄ plumes of k = 0, 0.1, 0.25. For the k = 10 plume, XCH₄ could not be retrieved for α higher than 45%. This means no XCH₄ could be found that would meet the convergence requirements of Equations (2) and (3).

S(XCH_{4_b}, α) is much larger for small plumes than for strong plumes, as shown in Figure 6C, simply because approximately the same amount of XCH₄ must compensate for the same albedo error, but that this constant amount is divided by a smaller or a larger value of XCH₄ (see Figure 7).

3.1.2. Variation of Albedo Sensitivity with Vertical CH₄ Profile

Comparison between the simulations showed that the measured profile, with a shallower PBL, reduced sensitivity (S(XCH_{4_b}, α)) by 9–12% compared to a uniform profile (Figure 8). The sensitivity difference resulting from the difference in vertical CH₄ distribution indicated that path dependency was a factor that should be considered in the CH₄ retrieval. This showed that at a minimum, the importance of using appropriate PBL thicknesses for retrievals in different regions, using realistic profiles, if available, is naturally the best option.

3.1.3. Variation of Albedo Sensitivity with Scene Geometry

Scene geometry sensitivity was investigated by simulations for the k = 1 plume, with solar zenith angle (θ_s) varied from 30° to 50°, sensor viewing zenith angle (θ_v) varied from 0° to 20°, and relative sun-sensor azimuth angle (φ) varied from 0° to 180°. With respect to observation geometry, S(XCH_{4_b}, α) exhibits the strongest angular sensitivity to θ_s (Figure 9A), with little difference between scene elements. S(XCH_{4_b}, α) is related inversely to increases in θ_s and θ_v but is constant with φ due to the simulations’ Lambertian surface characterization (Figure 9). The relatively strong angular sensitivity to θ_s and θ_v is probably due to that the relative contribution from the surface scattering versus from atmospheric scattering decreases with increasing θ_s or θ_v.

3.1.4. Variation of Albedo Sensitivity with Aerosol Type and Visibility

Given the similarity in S(XCH_{4_b}, α) between surface spectral composition for the parameters studied, aerosol sensitivity was studied only for Rbl pixel and showed no significant difference in S(XCH_{4_b}, α) between the two highly distinct aerosol types considered, urban and marine (Figure 10)—163% vs. 160% for urban compared to the marine atmosphere. Thus, the discrepancy between clearly detected plumes in the marine environment (Figure 1B) and no detectable plumes for the urban terrestrial environment (Figure 1D) was not due to the significant differences between marine and terrestrial aerosol. The overestimation changed from 160.8% for a 16-km visibility to 157.7% for 2-km visibility.

3.1.5. Sensitivity to Spectral Flatness

The residual radiance method [29] has an underlying important spectral flatness assumption. In reality, ρ_s(λ) varies with λ for a water surface in the spectral range of the CH₄ absorption feature, decreasing from 2139 to 2299 nm. Simulations showed that the flat spectra assumption led to an overestimation of the calculated L_t compared with the true albedo spectra (Figure 11). The overestimation in L_t increased with, longer λ and resulted in a non-negligible underestimation of XCH₄.

Table 2. S(XCH_{4_b}, α = 0) resulting from constant ρ_s assumption for wavelengths 2239 to 2299 nm.

XCH4_b	Underestimation (%)
	Ar	Rbl	Bsl
k = 0	-	−79.77	−73.72
k = 0.1	−120.73	−70.35	−63.97
k = 1	−79.68	−35.81	−30.95
k = 10	−30.18	−10.65	−8.08

further quantified this underestimation, which decreased with brighter surface pixels. Furthermore, this underestimation in L_t increased with a decrease in XCH_{4_b}. In fact, for the background (k = 0), XCH₄ could not be retrieved for the pixel Ar with XCH_{4_A} for the constant surface albedo assumption based on albedo at 2139 nm (Table 2). The underestimation decreased to 30% for Ar and to 8.1% for Bsl as XCH₄ increased from background to the k = 1 plume.

3.1.6. Sensitivity to Water Vapor

Water vapor was retrieved from Moderate Resolution Imaging Spectroradiometer (MODIS) data using a ratio of radiance in a band with water vapor absorption (905 or 940 nm) to that in a band free of the absorption (865 nm). The retrieved water vapor has been validated by in situ data, with a relative error estimated at ~7% [35]. In a study by Albert et al. [36], MODIS retrieved water vapor by means of a differential absorption technique was compared with the field measurements taken by microwave water radiometer. A relative deviation of 9.4% was derived from the comparison.

A sensitivity study based on a 9% uncertainty in AVIRIS-NG, water vapor retrievals (Figure 12) showed a detectable S(XCH_{4_b}, α = 0) overestimation. Specifically, S(XCH_{4_b}, α = 0) increased with the increase of water vapor while it decreased with increasing XCH₄. Overall, S(XCH_{4_b}, α = 0) varied little with the land cover types.

3.2. Space-Based Retrieval Sensitivity to Subpixel Spectral and CH₄ Heterogeneity

To investigate the sensitivity of XCH₄ to subpixel spectral heterogeneity, simulations were conducted for a simplified GOSAT pixel—a 10 × 10 km square (rather than round)—for 666 km altitude. The GOSAT pixel was divided into 160 × 160 subpixels with spatial resolution of 62.5 m, approximately the spatial resolution of the Hyperspectral Infrared Imager (HyspIRI) mission, which has a planned 10-nm spectral resolution [37]. For this simulation, the albedos of a 100 km² subset of the AVIRIS-NG data, subset into 160 × 160 pixels, was derived from imagery acquired on 4 September 2014 (Figure 2, red box). Note, concurrent GOSAT data were unavailable for the Kern area on 4 September 2014.

L_t for the GOSAT pixel was simulated for the in situ profile (i.e., k = 1, Figure 3) by two approaches. In the first case, denoted L_{t_AO}, L_t was simulated for each of the 160 × 160 pixels using each pixel’s ρ_s, and the orbital L_t then was averaged to produce the GOSAT pixel L_t. In the second case, denoted L_{t_OA}, the average ρ_s for the 160 × 160 pixels was calculated first, from which the GOSAT pixel L_t then was derived. The notation reflected whether spatial averaging occurred before or after extending AVIRIS-NG ρ_s to the orbital sensor, respectively. The calculated L_{t_AO} and L_{t_OA} across the spectral area of interest were essentially identical (Figure 13), demonstrating linearity for the response of L_t to ρ_s.

Although in some conditions, e.g., a well-mixed background PBL, GOSAT pixels were approximated reasonably well on the sub-pixel level as having homogeneous XCH₄; for many GOSAT pixels, XCH₄ was spatially heterogeneous. On the GOSAT size-scale, this heterogeneity was dominated by the overall plume dimensions; however, even on the vastly finer AVIRIS-NG size scale, strong heterogeneity exists due to plume structure, including puffiness [23].

The importance of spatial XCH₄ heterogeneity was investigated by simulations over a pixel of the same size as GOSAT, which was divided into 160 × 160 subpixels with a spatial resolution of 62.5 m. The L_t and albedo for these subpixels were from the AVIRIS-NG imagery acquired on 4 September 2014 (Figure 2, red box). The mean L_t and XCH₄ over the pixel are denoted by L_{t_GOSAT} and XCH_{4_GOSAT}, respectively. Then, using the average albedo for all the subpixels, simulations were carried out by varying XCH₄ to minimize the average residual radiance between the simulated L_t and L_{t_GOSAT} until it was smaller than the band-averaged NEδL (NEδL_a). The error minimized XCH₄ is denoted XCH_{4_M}. It is important to note that XCH_{4_M} was smaller than XCH_{4_GOSAT}. Figure 14 shows the XCH₄ underestimation (γ) with respect to percentage area coverage by the CH₄ plume in a pixel of the same size as GOSAT (Pc). Note the pixel size is fixed while Pc is varied.

Variations in Pc change for the average XCH₄. For example, a pixel with the mean XCH₄ = 0.5 ppm, a 5% variation of Pc implies that 5% of the 160 × 160 subpixels were covered by a plume with XCH₄ = 10 ppm. In this case, the forward simulation indicates that a XCH₄ of 0.35 ppm can be observed over the pixel (γ is equal to 0.15 ppm). As Pc decreases, γ increases but γ also increases for increasing XCH₄ plume strength, e.g., γ increases from 0.01 to 0.15 ppm when Pc decreases from 60% to 5% for an anomaly of 0.5 ppm. Thus, biases can become significant if the pixel percent coverage by a strong plume is small.

4. Discussion and Conclusions

4.1. Scoping Study

The scoping study identified a surprising difference in performance of the band ratio approach for similar strength sources from the COP marine seep field and for Kern Front oil field (Figure 1). The band ratio approach clearly detected plumes for the marine source, while plumes were not apparent for the terrestrial source. Key differences between these settings include water vapor, aerosol, and surface albedo heterogeneity—often termed spectral clutter.

Using a forward simulation and a residual radiance approach (as in the CH₄ detection algorithm in Roberts et al. [29]), sensitivity of XCH₄ to a variety of factors was investigated. The greatest sensitivity was from surface albedo (Figure 6, Figure A4 and Figure A5). A −5% error in surface albedo could cause a relative error up to 144.3% depending on the CH₄ concentration. Such a strong sensitivity arises from the high percentage of the surface reflected radiance in the total radiance received by AVIRIS-NG. Even a small error in surface albedo requires a large XCH₄ to compensate in the total radiance spectrum. Sensitivity to scene-differing factors other than surface albedo error, such as scene geometry, aerosols, and water vapor was small, although some were important in terms of accurate retrievals. For example, sensitivity to water vapor showed a 9% overestimation of water vapor (equivalent to 1.9 g cm⁻²) results in a 4.6% overestimation for background XCH₄. Despite significant differences in aerosol between a marine atmosphere (COP) and a terrestrial atmosphere (Kern Front), aerosol was found to be of negligible importance to the different scene retrieval performances. As a result, the non-albedo sensitivity factors cannot explain the difference in retrieval performance between the scenes.

Surface albedo error also induces uncertainty in retrieved trace gas column in a second manner due to spectral non-flatness. Specifically, the assumption of spectral flatness in Roberts et al. [29] was investigated and found to introduce significant uncertainty in XCH₄, up to over 100%, depending on the plume strength and the underlying pixel surface type. This spectral factor occurs in synergy with albedo error, and illustrates the importance of accurately retrieving the surface albedo spectra, within and across the CH₄ absorption feature.

Above all, the non-linear sensitivity of XCH₄ to the albedo error could explain most of the difference in the retrieval performance between two different scenes. It should also be noted from Noël et al. (2012) that the distortion of the slit function for an inhomogeneously illuminated slit could also be another reason for the difference in retrieval performance [38].

4.2. In Situ Versus Uniform Profile

The simplest profile is a well-mixed PBL—i.e., uniform with altitude; which was quite distinct from the real profile where concentration decreased rapidly with altitude in the upper PBL, with a sharp decrease above (Figure 3). In the simulations, the column was held the same for the two, to test sensitivity to albedo error, and found a 9–12% increase in albedo error sensitivity. In other words, the realistic profile improved retrieval performance against artifacts resulting from surface albedo error.

4.3. Interferents

Accurate surface albedo is critical to any retrieval method, and this study found it to be highly sensitive for the residual radiance retrieval approach. In part, this non-linearity arose from radiative interaction between water vapor and CH₄ column, both of which depend on surface albedo. Finer spectral resolution would enable better deconvolution of these factors (AVIRIS-NG versus AVIRIS-C), decreasing the albedo error sensitivity. In the limit, extremely fine spectral resolution sensors, e.g., SCHIAMACHY, that resolve individual absorption lines, avoid most of the problems of assumed spectral flatness, which, while potentially significant over tens of nanometers, are minimal across a single line.

4.4. Retrieval Method and Future Work

This sensitivity study used the forward simulation and residual radiance; thus the results are directly applicable only to the residual radiance method for XCH₄ retrieval. As noted above, surface albedo is critical to any retrieval method, particularly if the cluttered surface includes material with spectral features in the wavelengths of the trace gas. For example, carbonates have spectral features in the 2.4 µm CH₄ feature. Thorpe et al. [22], found that the IMAP-DOAS approach, which succeeded at CH₄ retrievals for AVIRIS imagery for the COP seep field, was challenged by retrievals for a terrestrial scene. Specifically, they noted that “disentangling surface spectral signatures from the methane absorption features is complicated”. Some approaches are likely to be less sensitive, such as the singular value decomposition hybrid IMAP-DOAS approach adopted by Thorpe et al. [22] to address complex terrestrial scenes. Higher spatial resolution may or may not reduce sub-pixel element heterogeneity, depending on how the end members are organized spatially. Albedo error uncertainty is largest if the spectral contrast in the absorption feature between end members is large; thus pixels at water/ice-land boundaries present very strong contrasts that will introduce relatively larger uncertainty. Specifically, the different pixel end members introduce positive and negative biases that are non-linear and thus do not cancel when combined to calculate XCH₄ for the pixel. This would not be true if the biases were linear, in which case they would cancel when combined. One approach is to statistically model surface composition outside the plume, as an application for plume pixels. This approach is challenged by non-statistical surfaces such as river banks and urban areas where natural laws do not govern pixel end member component distributions.

These simulations were for a uniform surface; however, many surfaces exhibit complicated BRDF. The importance of realistic scene BRDF should be explored in further studies.

In any case, the fundamental importance of surface albedo to retrievals shows a need for investigating the sensitivity of different retrieval algorithms, to better understand the advantages and limitations of each approach, with respect to different applications. This is particularly important for broad spectral resolution instruments like AVIRIS-C, AVIRIS-NG, and the candidate HyspIRI orbital mission, as well as for spectrometers with finer spatial resolution.