Comparison of Methane Detection Using Shortwave and Longwave Infrared Hyperspectral Sensors Under Varying Environmental Conditions

Methane is a prevalent greenhouse gas with potent heat trapping capabilities, but methane emissions can be difficult to detect. Hyperspectral imagery is an effective method of detection which can be used to locate methane emission sources, as well as provide accountability for reaching emissions reduction goals. Because of methane's absorption features, both shortwave infrared (SWIR) and longwave infrared (LWIR) hyperspectral sensors have been used to accurately detect methane plumes. However, surface, environmental, and atmospheric background conditions can cause methane detectability to vary, and there have not been previous studies which evaluate this variability over a wide range of conditions. To assess this variation, this trade study compared methane detectability for two airborne hyperspectral sensors: AVIRIS-NG in the SWIR and HyTES in the LWIR. We modeled methane plume detection under a wide range of precisely known conditions by making use of synthetic images which were comprised of MODTRAN-generated radiance curves. We applied a spectral matched filter to these images to assess detection accuracy, and used these results to identify the conditions which have the most significant impact on detectability in the SWIR and LWIR. We then computed the specific boundaries on these conditions which make methane most detectable for each instrument; these novel results explore methane detectability over a broader range of conditions and sensors than previous studies. This trade study and methodology can aid decision-making about which sensors are most useful for various types of methane emission analysis, such as leak detection and emission rate quantification.


I. INTRODUCTION
G REENHOUSE gas emissions are a pervasive issue; there are a wide variety of sources emitting various heattrapping gases at accelerating rates, many of which are not accurately monitored, and thus, cannot be mitigated. Methane is the second most prevalent greenhouse gas in the atmosphere, but it has heat trapping capabilities approximately 21 times greater than carbon dioxide, the most prevalent greenhouse gas [1]. Methane emissions reduction policy is currently a global focus, Manuscript  and one example is recent legislation in the United States, part of which imposes a fee on entities which report excessive methane emissions [2]. These are primarily oil and natural gas production companies, which account for 25%-40% of U.S. methane emissions [3], [4]. Methane leak tracking is crucial to emissions reporting, but there are still inaccuracies in various methods of methane monitoring. For example, the EPA's greenhouse gas inventory has been estimated to undervalue greenhouse gas emissions by a factor of 1.7 [4]. Satellite and airborne hyperspectral sensors, though, have been shown to accurately detect methane emissions; their high spectral resolution allows them to resolve methane absorption features, and being mounted on an airborne or satellite platform can provide a view of the full extent of a methane plume. Hyperspectral sensors detecting methane can operate in both the shortwave infrared (SWIR) and longwave infrared (LWIR), as methane has absorption features in both of these wavelength ranges. Satellite-mounted hyperspectral instruments are effective for methane detection, and they have advantages of continuous monitoring and a wide swath. They are specifically useful for monitoring diffuse methane sources over a large land area, such as wetlands and agriculture. One such example is the Tropospheric Monitoring Instrument, or TROPOMI, which operates in the SWIR and has been used for urban methane monitoring [5], [6]. Another satellite-mounted sensor is the Greenhouse Gas Observing Satellite, or GOSAT. GOSAT has bands in the SWIR and the LWIR as well as pointing capabilities, which have allowed it to both monitor diffuse emissions and identify a large natural gas leak [7], [8]. Most of these satellite-mounted hyperspectral sensors are limited by spatial resolution, so future sensors aim to retain the advantages of satellite systems while also improving spatial resolution. MethaneSAT is a planned satellite sensor with a goal of detecting up to 80% of methane point source emissions in the United States [9]. Carbon Mapper is a future satellite constellation which is based on the design of AVIRIS-NG, an existing airborne sensor [10], [11].
Satellite methane monitoring can be effective for diffuse methane emissions, but airborne instruments have proven more successful at detecting and quantifying methane point sources, or high concentration methane gas leaks. Two of these instruments are the airborne visible and infrared imaging spectrometer next generation (AVIRIS-NG) in the SWIR and the hyperspectral thermal emission spectrometer (HyTES) in the LWIR. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ AVIRIS-NG has a spectral range of 0.35-2.51 μm, covering both methane absorption features in the SWIR, and HyTES has a spectral range of 7.5-12.0 μm that covers the absorption feature in the LWIR. These sensors have been capable of methane plume detection, flux rate quantification, and concentration retrieval [12], [13], [14], [15], [16].
Despite the success of various hyperspectral instruments at detecting methane, previous research has indicated that hyperspectral sensors in the SWIR and LWIR can be limited by the environmental, atmospheric, and surface background conditions of the scene. There have been studies that have explored some aspects of these limitations using synthetic data, which is similar to the use of synthetic data in our methodology. A study using AVIRIS-NG synthetic data assessed the impact of surface reflectance on methane retrievals, and showed that retrieval errors for a methane plume over water were greater than 175% [17]. A study on the multiband uncooled radiometer imager (MURI), an LWIR sensor with only six bands, used synthetic data to model methane detection at a variety of surface and plume temperatures. Methane detectability was lowest when the temperatures of the plume and the ground were equal or similar to each other, and high water vapor concentration was shown to decrease methane detectability as well [18]. These studies suggest that SWIR and LWIR instruments may have limitations for methane detection under specific background conditions. However, these studies assessed detectability only over a limited range of background conditions, and did not allow for comparison between SWIR and LWIR sensors.
Understanding the impacts of a wide range of conditions on methane detectability is of high importance and interest, as methane-emitting fossil fuel production facilities are located in a wide variety of climates. Being able to directly compare instrument capabilities in the SWIR and LWIR can also be useful for deciding which type of sensor to use based on known background conditions. In order to expand the results of previous studies and draw a comparison between various hyperspectral sensors, the goal of this study was to assess the specific limits on environmental, surface background, and atmospheric conditions which make methane most detectable for SWIR and LWIR instruments. The primary results of this comparison were boundaries on scene environmental conditions which make methane most detectable. Based on these results, we drew novel conclusions about conditions under which SWIR or LWIR sensors are most effective. To perform this analysis, we generated synthetic data in order to model hyperspectral data collected over a wide range of precisely known conditions. We specifically modeled the sensors AVIRIS-NG and HyTES; these sensors are representative of current and future SWIR and LWIR sensors, and the conclusions we have drawn for these sensors can be extended to other instruments.

II. METHODOLOGY
To conduct a full trade study on methane detectability, our general approach was to generate synthetic image hypercubes which model methane detection using a hyperspectral instrument. We then applied the matched filter as a detection algorithm, and compared methane detectability between images of varying environmental conditions. In order to perform this analysis of methane detectability for a wide variety of background conditions, it was necessary to devise a method of generating synthetic data. In this section, we will detail the process for generating SWIR and LWIR synthetic image hypercubes containing enhanced methane.
An example synthetic image is shown in Fig. 1; this shows a cross section of the image hypercube at the 2.2 μm band for the SWIR and the 7.7 μm band for the LWIR. This section will fully expand on the way in which radiance curves and image hypercubes were generated, the basis of the synthetic images in real data, and the application of the matched filter as a methane detection algorithm. The section is organized based on the following steps in the synthetic image generation methodology: 1) generate radiance curves; 2) compile radiance curves into synthetic image hypercubes; 3) add instrument noise; 4) apply spectral matched filter and compute detection metric. These steps demonstrate the full process of developing synthetic images. In Section II-E, we also describe a validation study we conducted to ensure our synthetic data was representative of real data.

A. Generate Radiance Curves
The basis of the synthetic images is MODTRAN-generated radiance curves, which make up the image hypercube. MOD-TRAN is a radiative transfer code which models an atmosphere with user-defined environmental conditions, and models detection of radiance moving through that atmosphere based on sensor specifications [19]. MODTRAN performs radiative transfer calculations for this modeled atmosphere and sensor, computes at-sensor radiance for a variety of paths through the atmosphere, and provides the outputted at-sensor radiance curves for many paths. We utilized MODTRAN differently to generate radiance curves for AVIRIS-NG and HyTES due to the computational time required for MODTRAN to generate radiance curves in the SWIR. For AVIRIS-NG, we computed the total at-sensor radiance using two different MODTRAN path terms. One term was the radiance for a path reflected from the ground to the sensor, which we will represent as L grndref (λ). The other term was the path which is single-scattered to the sensor, represented as L singlescattered (λ). We computed these two terms for a scene with a 100% reflective surface, and then computed the total at-sensor radiance using the wavelength-dependent surface reflectance. This method is described by the following: L grndref100% is the radiance reflected off a 100% reflective surface, ρ is the applied surface reflectance, and L singlescattered is the single scattered radiance MODTRAN output. This radiance curve computation method allowed us to use a single MOD-TRAN run to generate curves for many surface reflectances.
To generate HyTES radiance curves, we did not do the same calculation as the AVIRIS-NG radiance curves; the radiance curve computation method utilized for AVIRIS-NG is The region on the left hand side of the image is the on-plume region, which contains radiance curves passing through a methane plume. The region on the right hand side is the off-plume region, which contains only ambient methane concentration, and has surface variation. not straightforward in the LWIR due to the influence of surface temperature on surface-emitted radiance, and MODTRAN computational times are faster in the LWIR. As a result, for HyTES, we utilized the MODTRAN-generated total at-sensor radiance term. This MODTRAN output is the total radiance reaching the sensor from many atmospheric paths, including ground reflected, thermal emitted, single and double scattered path radiance, and many more terms [19]. The HyTES radiance curves were computed in MODTRAN and were not postprocessed outside of MODTRAN.
To simulate radiance curves passing through a methane plume, we used the MODTRAN 6 local chemical plume model. This MODTRAN 6 capability models a methane plume of specified concentration and height as a uniform layer of the atmosphere, and computes radiance curves passing through and not passing through the plume. We utilized this feature to generate on-plume radiance curves, or radiance curves passing through a methane plume; the off-plume radiance curves pass through an otherwise identical atmosphere, but it contains only ambient methane concentration (1.8 ppm as opposed to 500-2500 ppm for an average plume). Example on-and off-plume radiance curves for HyTES are shown in Fig. 2. The effects of the methane absorption feature in the 7.6-8.5 μm region can be seen on the left-hand side of the figure. The remainder of the radiance curves from 8.5-12 μm are identical, as the only difference in radiance is due to the methane plume.

B. Compile Radiance Curves Into Synthetic Image Hypercubes
After radiance curves were created, they were compiled into an image with spatial structure containing two regions: an on-plume region and an off-plume region, as shown in Fig.  1. The on-plume region contains radiance curves which pass through a methane plume, and it is located on the left hand side of the images shown in Fig. 1. The off-plume region is comprised of radiance curves that do not pass through a methane plume, and this region also contains natural surface variation. The full image contains 210 000 pixels, and the on-plume region contains 3000 pixels. Because a spectral matched filter was applied to these images to assess detection, the separation of on-and off-plume regions was important to the analysis. The matched filter is sensitive to the presence of target pixels in the region over which the covariance is taken; this is called signal contamination [20]. As a result, we avoided signal contamination by separating the on-and off-plume regions. More detail on the matched filter formulation is provided in Section II-D.
The natural variation shown in the off-plume region is also important to producing an accurate matched filter result. The matched filter algorithm is based on the image covariance, so the variation in an image will impact the matched filter output. As a result, it was necessary to create variation in the background region of the image, or the region over which the covariance was taken. It was important that this variation be realistic so that the results from this study can be applied to real images and methane emissions scenarios. As a basis for the natural variation in the synthetic image, we used retrieved data from a simultaneous AVIRIS-NG and HyTES study. In this study, AVIRIS-NG and HyTES were flown near simultaneously over a known methane leak in the Four Corners region of the U.S. [21]. This study retrieved the surface reflectances at every pixel of the image for each band of AVIRIS-NG, as well as the surface temperature at every pixel. We used the retrieved surface reflectances and surface temperatures from this study in order to create synthetic images that had similar surface variation to what would be present in a real scene.
For AVIRIS-NG, this surface background variation was created using retrieved reflectance curves from the Four Corners study. For each pixel of the Four Corners image, there was a retrieved reflectance curve, and we used these reflectance curves as the surface MODTRAN inputs for our synthetic images. All other MODTRAN inputs, including atmospheric and environmental conditions such as water vapor concentration and solar zenith angle, remained static throughout the on-and off-plume regions of the image.
For HyTES, the background variation was based on the surface temperatures which were retrieved from the Four Corners study; we utilized radiance curves generated from surfaces of varying temperatures in order to create variation in the scene. We generated radiance curves for seven different surface temperatures: the on-plume surface temperature ± 3 K. This range of surface temperatures was the average range of all temperatures retrieved in the Four Corners study. All other surface and atmospheric parameters were constant for each radiance curve within a single image. To ensure that the distribution of these temperatures was realistic, we arranged the radiance curves spatially using the same surface temperature map as the retrieved data from the study. This methodology allowed for the assessment of methane detectability over a surface of a singular temperature, and modeled realistic temperature variation in the surface area of the image which surrounds the methane plume.
Surface variation was selected as the source of realistic variation because in a real scene, the atmosphere can be expected to be reasonably uniform across a moderately sized area. The ground surface, both in reflectance and in temperature, would be the largest source of variation in at-sensor radiance, and would thus contribute most strongly to scene covariance. The imagery from the Four Corners study was chosen as a basis to simulate realistic data. This is because it was a simultaneous AVIRIS-NG and HyTES collection, as well as because it was conducted in a region that commonly contains enhanced methane; the surface properties and variation in the scene are representative of a common methane emission location. This provided a realistic basis for the synthetic images, but through our simulation approach we were able to extend the scene conditions from the Four Corners data to fully explore methane detectability limits.

C. Add Instrument Noise
After radiance curves were compiled into an image, we added instrument noise. As an overview, instrument noise was computed by calculating the NEdL for each instrument, randomizing the NEdL at each wavelength band, and adding that randomized NEdL into the image radiance. This computation was done at each pixel and each wavelength band of the image. We based the computation of the AVIRIS-NG NEdL curve on a previously reported instrument SNR, which was assumed to be constant over the range of radiance values we used [22], [23], [24]. The NEdL was computed from a representative radiance curve in an image divided by the wavelength-dependent SNR. For HyTES, the NEdL was assumed to be constant with signal level, and was based on a HyTES test flight [25]. Noise was added to both images by scaling each band of the NEdL by numbers from a random Gaussian distribution centered at 0 with standard deviation 1 (X ∼ N (0, 1)), and then adding this scaled NEdL term to each band of the image. This process for adding noise to an image of radiance L N (λ) with N pixels and n wavelength bands at a single pixel is represented by the following: is a vector of length n of Gaussian distributed random variables. This method models instrument noise and has been employed in previous studies which utilized synthetic images [17], [26]. Fig. 3 shows examples of the HyTES and AVIRIS-NG NEdL curves, as well as example Gaussian random noise.

D. Apply Spectral Matched Filter and Compute Detection Metric
After the synthetic image was created, the spectral matched filter was applied. To calculate the spectral matched filter, an estimate of the covariance (Σ) was computed over mean centered and normalized n band by N pixel radiance data, K.
The scaled covariance and the target spectrum b were used to compute the matched filter output MF [27] The target spectrum was the methane absorption spectrum from the HITRAN database, which was convolved to AVIRIS-NG and HyTES sensor responses [28]. We used only the regions of the absorption spectrum with a methane feature present, which was 75 out of 432 bands for AVIRIS-NG and 35 out of 256 bands for HyTES. The absorption spectra and the regions which were used for the matched filter are shown in Fig. 4.
The use of the methane absorption spectrum as the target signature allows this detection algorithm to be used without a priori knowledge of scene atmospheric conditions; as a result, this method is commonly used for methane detection from radiance data [12], [18], [27], [29].
After the matched filter was applied, ROC curves were plotted for each synthetic image, and the area under the ROC curve was computed. Using area under the ROC curve as the detection metric prevented the need for thresholding the matched filter image and allowed for comparison of methane detectability for each synthetic image. Detectability is the highest when the area under the ROC curve is close to 1, and methane is not detectable when area under the ROC curve is close to 0.5.

E. Validation
In order to ensure that our methods of synthetic image generation could produce accurate representations of real AVIRIS-NG and HyTES data, we conducted a validation study. This consisted of comparing MODTRAN-generated data with real data in two parts: comparing radiance curves, and comparing methane detectability for a full image.
1) Real Data Basis for Validation: We used data from a simultaneous AVIRIS-NG and HyTES study conducted in the Four Corners region of northwest New Mexico to compare with our MODTRAN-generated data (the same study which provided the surface temperature and reflectance retrievals used in Section II-B). In this study, AVIRIS-NG and HyTES were flown near-simultaneously over a coal mine vent shaft with a known methane leak. Matched filters were used to detect methane in the data from both instruments, and a retrieval algorithm was applied to the AVIRIS-NG data, with the highest concentration of retrieved methane being 3500 ppm-m [21]. The data from this study and the retrieved quantities allowed us to compare our MODTRAN-generated radiance curves and the methane detectability trends for a full synthetic image.
2) Validation: Radiance Curves: The first step in the validation was to ensure that MODTRAN-generated radiance curves could represent radiance curves from real data. We used retrieved data, such as surface reflectance and surface temperature, and known parameters from the observed scene in order to produce MODTRAN radiance curves that modeled the conditions in the Four Corners study. We compared these radiance curves for both AVIRIS-NG and HyTES, and example results are shown in Fig. 5. The average percent difference between real and MODTRAN-generated radiance curves over all bands was 0.5%  for AVIRIS-NG and 0.3% for HyTES. This discrepancy could be due to imprecise knowledge of the specific environmental conditions of the observed scene, retrieval errors in the surface emissivity and reflectance, instrument noise, or calibration error.
3) Validation: Methane Detectability for Full Images: The next step in the validation analysis was to compare methane detectability for a full synthetic image with methane detectability for a full real image. We accomplished this by modeling real images as closely as possible using our image generation methodology. The MODTRAN atmospheric input parameters were representative of real conditions from the Four Corners study, and the MODTRAN surface inputs came from the retrieved reflectance curves and surface temperatures. We then compared these synthetic images with a real subset of the full AVIRIS-NG and HyTES images from the Four Corners study. This resulted in images with visually similar surface variation, as shown in Figs. 6 and 7. The real images were not altered other than augmentation with a methane plume. The augmentation process consisted of taking a single radiance curve from the AVIRIS-NG or HyTES data which had a methane plume of approximately 500 ppm-m concentration, and repeating it in an on-plume region of the image with added instrument noise. This allowed the real and synthetic data to be structured in the same way, enabling a more direct comparison between real and synthetic images, as well as allowing us to use a straightforward truthmask on the real data.
We applied a matched filter to the real and synthetic images for AVIRIS-NG and HyTES, and the ROC curves are displayed in Fig. 8. We compared the area under the ROC curves because this was the detection metric that we used to report our results. For AVIRIS-NG, the percent difference between area under ROC curves of real and synthetic images was less than 1%, and for HyTES the percent difference was 3%. These differences are within the margin of uncertainty introduced by instrument noise. This demonstrates that our method of synthetic image generation can accurately model methane detectability from real data.

III. RESULTS
Using the methodology presented in Section II and validated in Section II-E, we assessed the impacts that environmental, atmospheric, and surface background conditions have on methane detectability for AVIRIS-NG and HyTES. We conducted initial studies in order to identify the conditions which have the most significant impact on methane detectability for each sensor, and to identify the limits on background conditions which allow methane to be detectable. This process allowed us to define specific scene environmental boundaries which make methane most detectable using AVIRIS-NG and HyTES. Our primary result was the computation of these specific detectability boundaries, and these boundaries can be further interpreted to make general recommendations for when to use an SWIR or an LWIR sensor; this will be discussed in Section V. The following sections detail our process of generating results for AVIRIS-NG and HyTES, according to the outlined steps.
A. Results: AVIRIS-NG 1) Define Tradespace: For AVIRIS-NG, we identified the background conditions which have the most significant impact on methane detectability by conducting many trade studies which evaluated a wide range of background conditions. The conditions which we identified to most strongly impact detectability for AVIRIS-NG were surface reflectance directly below the methane plume, referred to as "on-plume surface reflectance," and average surface reflectance of the adjacent background region, or "off-plume surface reflectance." The off-plume region is the portion of the image over which the covariance was computed for the matched filter. In a scene where methane is being emitted over a uniform surface, these quantities will be equal, but there are also scenarios where these quantities can differ; for example, the on-and off-plume reflectances could be significantly different if methane were emitted over an industrial facility, but the surrounding area was comprised of vegetation. Solar zenith angle also had a minor impact on detection and is addressed in this section, but the other background conditions tested had a negligible impact on methane detectability.
2) Generate Images: We generated 720 synthetic images with varying on-and off-plume reflectances, but kept all other background conditions constant; these conditions are outlined in Table I. The conditions in the top three rows of the table change in each synthetic image, while the remainder of the conditions are constant throughout the study.
We modeled plumes that are 500 and 2500 ppm-m in concentration and 1 m in height. Because the plumes have a 1 m height, the point concentration measurement of the methane plume is also 500 and 2500 ppm at any location in the 1 m column. As a result, we refer to the plume concentrations as 500 and 2500 ppm, but in this case, the ppm and ppm-m units are interchangeable. These concentrations represent reasonable low and high concentration plumes that may be emitted from the fossil fuel production industry.
3) Compute Detection Metric: The next step in the analysis is to apply the matched filter and assign a detection metric to the image. Fig. 9 shows heatmaps of the results for methane plumes of two different concentrations detected using AVIRIS-NG. The color of each square on the heatmap corresponds to the area under the ROC curve for a single image with a methane plume present, and its location on the x-and y-axes determines the reflectances in the on-and off-plume regions of the image. The on-plume region of the image had a constant reflectance curve in order to keep these results general and applicable for different surface types. The background region of the image was comprised of a variety of retrieved reflectance curves, so the reported reflectance on the y-axis is the average reflectance in the 1.6-2.4 μm region. Fig. 9(a) is the heatmap for a lower concentration plume of 500 ppm, and Fig. 9(b) is heatmap for a plume of 2500 ppm concentration. 4) Interpret Results: Lastly, we drew conclusions on methane detectability as a function of varying background conditions. The general trend for both concentrations of methane shows that on-and off-plume reflectance must be within a certain margin of each other in order to maximize area under the ROC curve and optimize methane detectability. Area under the ROC curve has a maximum of 1 for perfect detection. For the 500 ppm plume as shown in Fig. 9(a), methane was most detectable when on-plume reflectance was 1.2-1.7 times greater than off-plume reflectance, but even in this region, the area under the ROC curve was not higher than 0.85. This shows that, for AVIRIS-NG detecting a 500 ppm plume, methane was not highly detectable no matter the surface background conditions, as the area under the ROC curve never approached 1. For a 2500 ppm plume, as shown in Fig. 9(b), detectability increased significantly over the full trade space. The region for which methane was detectable encompassed on-to off-plume reflectance ratios of 0.6-2.9. In part of this region, the area under the ROC curve exceeded 0.9, showing that methane was highly detectable under these conditions.
A noticeable feature of these figures is the low area under the ROC curve when the on-plume reflectance was much lower than the off-plume reflectance. The matched filter is an anomaly detector, so when the on-plume reflectance is much lower than off-plume average reflectance, the matched filter output will flag those pixels as an anomaly with a positive detection score, rather than a region that has a methane absorption with a low detection score. These effects could be mitigated in future studies by doing additional data preprocessing, which is discussed further in Section IV.

B. AVIRIS-NG Results: Bounding Box
An objective of this study is to define specific ranges of background conditions under which methane is detectable for AVIRIS-NG and HyTES. In order to do this, we used the results shown in Fig. 9 and implemented an area under the ROC curve threshold. If the area under the ROC curve was at least 0.8, we determined that the correct detection to false alarm ratio would be high enough to accurately detect a plume and map its spatial structure. Using this threshold, we created bounding boxes for AVIRIS-NG and HyTES which help predict the capabilities of each sensor depending on the environmental variables which impact methane detection the most.
For AVIRIS-NG, the detectability limits are bound by onplume surface reflectance, off-plume surface reflectance, and solar zenith angle. Fig. 10(a) is the bounding box for a 500 ppm plume. When the conditions on the axes of the figure fall inside the box, methane is detectable above a 0.8 area under the ROC curve threshold. For a 500 ppm plume, our results indicated that the on-plume reflectance needed to be 1.2-1.7 times the average off-plume reflectance in order for methane to be detectable at a low solar zenith angle. This range narrowed slightly as solar zenith angle increased. Fig. 10(b) is the bounding box for a 2500 ppm plume. The volume inside of this bounding box increased significantly from the 500 ppm plume bounding box, showing that the on-plume  C. Results: HyTES 1) Define Tradespace: For HyTES, we determined that the conditions which impact methane detectability the most were surface temperature, methane plume temperature, and atmospheric water vapor concentration. Similar to AVIRIS-NG, we determined this by conducting many smaller trade studies which evaluated a wide variety of background conditions.
2) Generate Images: The next step in the analysis was to create synthetic images which spanned a wide range of the conditions identified in step 1; this amounted to 2500 images in total. The experimental conditions used for the HyTES study are outlined in Table III. The methane plume temperature for all simulated images was set to be the same temperature as the ambient air. This is partly because we found that the temperature contrast between the ambient air and the methane plume did not have a significant impact on methane detectability; the impact of this factor was negligible in comparison to the temperature contrast between the plume and the surface. Additionally, we modeled the temperatures this way in order to model realistic methane emission scenarios. Methane emissions from the fossil fuel industry can be at a variety of temperatures compared to ambient air; steam extraction causes methane plumes to be very hot when released, whereas leaks or venting from underground storage could cause methane to be cooler than the ambient temperature. However, for all methane emissions scenarios, the temperature of the methane will eventually match the surrounding air temperature as the plume diffuses into the ambient air. As a result, this is the most common methane detection scenario and is explored here in the greatest detail.
3) Compute Detection Metric: After generating 2500 synthetic images and applying a matched filter, we computed the area under the ROC curve for each. Fig. 11 shows area under the ROC curve heatmaps for a 500 ppm plume detected by HyTES. Structured the same as the AVIRIS-NG heatmaps, each square represents the area under the ROC curve for an image with the conditions specified on the x-and y-axes. Fig. 11(a) has lower column water vapor concentration than Fig. 11(b). Fig. 12 shows these same results, but for a 2500 ppm plume.

4) Interpret Results:
Following computation of the area under the ROC curve, we were able to draw conclusions about methane detectability. Our results showed that detectability was very low when plume temperature and surface temperature were close to being equal, but detectability increased with temperature contrast increase. For a 500 ppm plume, higher column water vapor also slightly decreased detectability, as the central diagonal region of low detectability increased in size when total column water vapor was 3 cm rather than 1 cm. For 1 cm column water vapor, the minimum temperature contrast for detectability was 12 K for high temperature plumes and surfaces, and 15 K for low absolute temperature. For 3 cm column water vapor, a plume to surface temperature contrast of 16-17 K produced an area under the ROC curve greater than 0.8.
For a 2500 ppm plume, as shown in Fig. 12, the region where methane was detectable increased in comparison to a 500 ppm plume. To reach the area under the ROC curve greater than 0.8 detectability limit, only 3-4 K temperature contrast between the plume and the surface was necessary. Area under the ROC curve rapidly increased to higher than 0.9 as temperature contrast increased.

D. HyTES Results: Bounding Box
For HyTES, it is most reasonable to define the bounding box in terms of the conditions where methane is not detectable, as there was a discrete set of surface and plume temperatures in our results for which methane was not detectable. The conditions under which methane is detectable are technically an infinite set, although there are boundaries on how cool or hot the surface and the plume would reasonably be. So, in the box shown in Fig. 13(a) and (b), the conditions for which HyTES are detectable fall outside of the box. This is the opposite of the AVIRIS-NG bounding box, for which the conditions for a detectable plume fell inside of the box. Fig. 13(a) shows the boundaries on detectability for a 500 ppm plume detected using HyTES. The three conditions which limit detectability are surface temperature, plume temperature, and water vapor concentration, which are represented on each axis of the bounding box. The range of conditions here are reasonable temperature and water vapor extremes, but technically the walls of this box could extend infinitely. The top and bottom face of the box could be infinite planes, describing any possible combination of plume temperature, surface temperature, and water vapor. But these boundaries provide reasonable guidelines for the conditions that may be found in fossil fuel production regions of the United States. For a 500 ppm plume of 1.0 cm column water vapor at low surface and plume temperatures (265-280 K), the temperature difference between the plume and the surface needed to be at least 15 K for methane to be detectable (with area under ROC curve greater than 0.8). If the plume and surface temperatures were high (300-315 K), then the requisite temperature contrast for detectability was at least 12 K. If the column water vapor increased to 3.0 cm, then the temperature contrast needed to be at least 16 K for high temperatures and at least 17 K for low temperatures. Fig. 13(b) shows the detectability boundaries for a 2500 ppm plume. The distance between the top and bottom faces of the box is more narrow than the 500 ppm case, expanding the conditions under which methane was detectable. For a 2500 ppm plume with 1.0 cm column water vapor, 3 K temperature difference between the ground surface temperature and the plume temperature produced a detectable result. For 3.0 cm column water vapor, the difference in surface and plume temperatures was 4 K for detectability. Unlike the 500 ppm concentration plume, the absolute temperature of the surface and the plume did not have a significant impact on the detectability boundary.  Table IV provides an overview of the detectability ranges for HyTES methane detection, based on our results.

E. Uncertainty Analysis
We assessed the uncertainty in our area under the ROC curve results based on factors which could have a significant impact on detectability, but were outside the realm of environmental conditions. We identified two of these quantities: the amount of radiance due to instrument noise, and signal contamination. Signal contamination refers to the percentage of the region over which the covariance was taken (the off-plume region) which contained plume-present pixels. Our error analysis was based on the following formulation for error in a function f(x) due to the variable x [30]: We utilized this equation to analyze the uncertainty in area under the ROC curve due to factors outside of the trade space. Therefore, f was area under the ROC curve, and x was a source of uncertainty: either the noise level or the signal contamination. For the case of uncertainty due to noise, (6) becomes where AUC = area under ROC curve, L noise =radiance due to noise, and σ L noise = standard deviation of radiance due to noise. The radiance due to noise was a randomly scaled instrument NEdL, as detailed in Section II-C. For the case of uncertainty due to signal contamination, (6) becomes where AUC = area under ROC curve and signal % = percentage of the image containing signal contamination. Signal contamination in our images consists of pixels containing methane which are located in the background region of the image, which is the region over which the covariance was taken for the matched filter. We computed the percentage of the image over which these pixels were present to obtain signal % .
To compute the change in area under the ROC curve as a function of noise or signal contamination, we first computed areas under the ROC curve for images with a range of noise levels and signal contamination levels. We approximated the change in area under the ROC curve due to both of these conditions as linear, and used this rate of change as ∂AUC ∂L noise and ∂AUC ∂signal % . The range of noise levels we used were 50%-150% of the baseline noise used in the reported results. For signal contamination, we varied the percentage of pixels in the image covariance region containing a target methane signature from 0% to 3.5%.
To report the results of the uncertainty analysis, we show point measurements of area under the ROC curve for AVIRIS-NG and HyTES at a few points in the trade space. The uncertainty in area under the ROC curve for different background conditions can be extrapolated from the results shown. Fig. 14 shows the errorbar results for AVIRIS-NG. The x-axis is the ratio of on-to offplume surface reflectance; these are the same results as shown in Section III-A, but represented in 1 dimension. The errorbars in Fig. 14(a) and (b) represent the uncertainty introduced if noise level or signal contamination vary, respectively. The average uncertainty in area under the ROC curve due to noise was 0.1 for a 500 ppm plume and 0.03 for a 2500 ppm plume. Signal contamination had a significant impact on area under the ROC curve for AVIRIS-NG, with an average uncertainty of 0.15 for a 500 ppm plume and 0.28 for a 2500 ppm plume. Fig. 15 shows the results of the uncertainty analysis for HyTES. The x-axis is the temperature contrast between the surface and the methane plume. Like the AVIRIS-NG uncertainty results, this figure shows the same results as shown in Figs. 11 and 12, but represented in 1 dimension. The average uncertainty due to noise level was 0.08 for a 500 ppm plume and 0.03 for a 2500 ppm plume. The average uncertainty due to signal contamination was less than 0.01 for both 500 and 2500 ppm plumes.
General conclusions from the uncertainty analysis show that AVIRIS-NG was highly sensitive to signal contamination, whereas the impact of signal contamination on methane detection with HyTES was negligible. For both instruments, uncertainty due to noise level was lowest when the area under the ROC curve was near 1. Therefore, for conditions under which methane is highly detectable, noise level may not have a significant impact on detection, but it may contribute to uncertainty for conditions that are less conducive to detectability. This demonstrates that our model was sensitive to changes in noise level, so future use of the methodology would be best implemented with precise knowledge of the noise for the instrument being modeled.

IV. DISCUSSION
The detectability trends in our results agree with point measurements in previous work, while also providing novel extensions of previous work. To contribute to the understanding of methane detectability, we extended the scope of conditions that have been previously evaluated and provided a comparison of detectability between an SWIR and an LWIR instrument. For AVIRIS-NG, Thorpe et al. [27] evaluated the performance of the IMAP-DOAS retrieval algorithm for methane detection on real AVIRIS-NG data. They found that retrievals in regions of a real image with darker reflectance than the remainder of the image produced over-estimations of methane concentration. Despite our use of a different detection algorithm, this result is in agreement with our general trends, which show that having significant variation in reflectance curves throughout the scene can decrease methane detection accuracy. Another study on detectability trends for AVIRIS-NG was conducted by Ayasse et al. [17], and utilized synthetic data to evaluate the performance of the IMAP-DOAS algorithm for varying surface reflectances. Similar to the results of Thorpe et al., they found that retrieval errors were highest when methane was located over a surface with low reflectance. This study utilized a background of uniform reflectance, so there was no reflectance contrast to evaluate, but our results agree with the phenomenon that methane emitted over a low reflectance surface can be more conducive to detection inaccuracies than methane emitted over higher reflectance surfaces. Our results also show similar trends to published studies in the LWIR. Frankenberg et al. [21] applied a matched filter to real HyTES data where a plume traveled over a surface of varying temperature. It appeared that methane detectability decreased when the methane plume was over a surface of similar temperature to the plume, while detectability remained high in the portions of the plume for which surface-to-plume temperature contrast was approximately 10-20 K. For another LWIR methane sensor, Webber [18] utilized synthetic data to identify a similar trend in detectability using a matched filter. He showed that low temperature contrast between the plume and the surface resulted in low methane plume detectability, which was the same trend that is shown in our results.
All of these studies have demonstrated the dependence of methane detectability on background conditions for a variety of retrieval and detection algorithms, and our results agree with the general trends. The previous studies, however, evaluated detectability only over a limited set of conditions, and for only one sensor. Our study contributes new results to the field by comparing methane detectability over a wide range of background conditions as well as by comparing detectability between instruments in the SWIR and LWIR. This study helps to extend and tie together previous studies to gain a more comprehensive understanding of methane detection. By encompassing a much more broad range in our trade study, we have reported results that can be used to make decisions on whether to use an SWIR or LWIR sensor for methane detection under a specific set of background conditions; previous studies did not provide this capability, as they encompassed more narrow ranges of background conditions and did not compare between the SWIR and LWIR.
In order to further refine possible recommendations for sensor use and gain a more comprehensive understanding of environmental conditions' impact on methane detectability, future work could utilize our methodology to expand the trade space or test detectability for different sensors and detection algorithms. The results that we have presented are specifically for AVIRIS-NG and HyTES, but these instruments are representative of other instruments which operate in the SWIR and LWIR to detect methane. These results would be more generalizable if future work included applying the methodology to other sensors in the SWIR and LWIR; this would indicate whether the trends are consistent for various instruments, and would determine how the detection boundaries change when instrument parameters change. Another useful future objective which would provide more comprehensive results is to expand the trade space to conditions that we did not include in this study. Expanding the trade space to conditions such as partial cloud cover, high water vapor concentrations within the methane plume, or varying vertical plume structure could provide a more full picture of methane detectability for varying conditions. Our trade space included only environmental conditions, but the trade space could also be expanded to include different detection algorithms. This could make our results more widely applicable and provide insight into how detection algorithms impact methane detectability. This methodology could also be expanded to satellite sensors detecting diffuse methane concentrations rather than highly concentrated, low spatial area plumes. In general, the methodology that we have developed could have a variety of applications which would aid in understanding the impact of environmental conditions on greenhouse gas detection.

V. CONCLUSION
This trade study compared the methane detection capabilities of AVIRIS-NG and HyTES under varying environmental conditions by generating many synthetic images, applying a matched filter, and computing a detection metric. Using this methodology, we determined the primary result of the study: specific boundaries on scene environmental conditions which make methane most detectable for both instruments. These results were defined in terms of the background conditions which have the most significant impact on detectability for each instrument: for AVIRIS-NG, this is the ratio of on-plume to off-plume surface reflectance, and for HyTES, this is atmospheric water vapor concentration and the plume to surface temperature differential. Based on these results, we can make general recommendations on whether to use AVIRIS-NG or HyTES for specific methane detection applications; these general recommendations are discussed in this section.
Our results indicate that HyTES may be more useful for low concentration plume detection and mapping, while AVIRIS-NG may have more accurate applications in high concentration plume detection. Our results for a low concentration plume showed that the area under the ROC curve for AVIRIS-NG did not surpass 0.85. Therefore, low concentration plumes were never highly detectable for AVIRIS-NG, but they were for HyTES; if the temperature contrast was roughly 20 K, the plume was highly detectable. This shows that for a low concentration plume, HyTES has a broader range of conditions for which methane is highly detectable than AVIRIS-NG.
In contrast, AVIRIS-NG may be more accurate at detecting high concentration plumes. AVIRIS-NG had a very broad range of conditions for which methane was highly detectable: ratios of on-to off-plume reflectances from 0.6 to 2.9. It would be reasonable to expect that a methane plume would be located over a surface that is similar in reflectance to the adjacent surface. Therefore, AVIRIS-NG may be highly accurate at detecting high concentration methane plumes under a wide variety of conditions. For HyTES, even if the plume has a high concentration, it will still not be detectable in the case that the methane temperature is equal to the surface temperature.
In summary, our results indicate that HyTES may be most useful for mapping lower concentration methane plumes, as a temperature contrast of only 12-17 K between plume and surface caused methane to be highly detectable in our study. AVIRIS-NG may be most useful for detection of high concentration methane plumes, as the ratio of on-to off-plume reflectance can be as wide as 0.6-2.9 for a high concentration plume to be detectable. Low concentration plume mapping can be useful for flux rate quantification and to gain a full picture of the extent of a methane plume, while high concentration detection is useful for identification of methane leaks. These specific boundaries may not be applicable to all SWIR and LWIR instruments in general, but the detectability trends that we determined for AVIRIS-NG and HyTES can be extended to other SWIR and LWIR hyperspectral methane detecting sensors.
An important extension of this research is for these results and this methodology to be useful for future decision-making on sensor deployment and development. These results could be used to make decisions on whether to use an SWIR or LWIR sensor for methane monitoring in a specific region with known environmental conditions, or this methodology could be employed to help decide what region of the infrared should be used for a future sensor. Both the developed methodology and the specific detectability boundaries expand the current understanding of methane detectability using hyperspectral instruments in the SWIR and LWIR.