The first study presented here investigates the potential contrast for a single thermal infrared spectral band centered on the CH4 absorption feature present at 7.68 µm. Here, a narrow bandpass of 100 nm is considered. The goal of the study is to determine under what scenarios a single band allocated to CH4 detection is capable of detecting the temperature difference indicative of an enhanced level of atmospheric CH4.

In order to accomplish this, sensor-reaching radiances were calculated using radiative transfer models produced with MODTRAN6. This modeling code provides the ability to define a background surface, surface temperature, and atmosphere to calculate the spectral radiance that reaches a single pixel at the system's height. Utilizing the local chemical plume model option in MODTRAN6, spectral radiances, Lspec were calculated for a background case – or a case without enhanced levels of CH4 – and a plume-present case – or a case with enhanced levels of CH4 .

Effective radiances, the amount of light energy that the system is responsive to, can be calculated from the spectral radiance: 1Leff=∫λiλjLspecRdλ∫λiλjRdλ, where R is the responsivity of the pixel, and λi and λj are the wavelength limits . Note that this effective radiance is normalized by the responsivity curve of the spectral channel of the instrument. From effective radiance, the brightness or effective temperature can be calculated, which is the temperature perceived from the imaging system with reference to a blackbody. 2Tbrightness=hcλcenterkblog⁡hcLeffλcenter5, where h is Planck's constant, c is the speed of light, kb is the Stephan Boltzmann constant, and λcenter is the center wavelength of the band . By calculating a brightness temperature for both the background and plume-present case and then taking the difference of the resultant brightness temperatures, a brightness temperature difference was found. Comparing this brightness temperature difference to the noise-equivalent delta temperature (NEdT) – the minimum brightness temperature difference the system is capable of detecting – reveals if the system would be able to detect the increased concentration of CH4 utilizing only the CH4 band.

In order to better assess the system's methane detection capabilities, an approach proven to work for hyperspectral imagery was considered. The study presented here utilizes a matched-filter approach to assess MURI's capability of detecting enhanced levels of atmospheric CH4. While this method has been proven capable of detecting CH4 using thermal infrared HyTES data, applying the matched filter here is to investigate the viability of this method with a system with considerably fewer spectral bands (6 compared to 256) and only a single band allocated to the thermal infrared CH4 absorption feature.

The objective of developing a matched filter is to create a weighting function that when applied to an N spatial pixel by n spectral channel radiance matrix, L, the output is a new image where intensity correlates with the presence of the signal of inquiry. Application of the matched filter begins with the assumption that there exists a signal, in this case a methane plume absorption or emission signal, b, that is linearly superimposed on a background of the image, which can be written as 3r=αb+c, where r is the sensor-reaching radiance, α is the strength of the spectral signal, and c is a combination of noise and background signal . A realistic model of c considers the correlation between spectral channels, which can be described in terms of the covariance matrix K: 4K=<c′c′T>=1NL′L′T, where L′ is mean subtracted radiance over all the pixels from matrix L. Knowing, K, the covariance of the image, the optimal matched filter can be matched to both the desired signal b and the background, i.e., “clutter”. This clutter matched filter is defined as 5q=K-1bbTK-1b

It should be noted that q is normalized so that if the signal is not present in the original image, the resultant matched-filter image will prove to have a variance of 1. By applying the matched filter q to the N by n matrix of radiances L, the clutter matched-filter image is created, 6CMFI=qTL.

After computing the CMFI, a simple threshold is applied to determine if the signal is present . For this study, the threshold was varied in order to produce a receiver–operator characteristic (ROC) curve to assess the effectiveness of the method, rather than the effectiveness of a single threshold.

The study presented here provides a comparison between the six-channel multispectral MURI instrument and the 256-channel hyperspectral HyTES instrument when applying the matched filter to simulated imagery containing enhanced levels of atmospheric CH4.

The final study described here aims to determine if detection of enhanced atmospheric CH4 is possible using information from a pair of thermal spectral channels. This method has seen use in vegetation-based studies in the form of the normalized difference vegetation index, i.e., NDVI . Here, a normalized difference methane index, i.e., NDMI, is calculated using the following equation: 7NDMI=SB2-SB1SB2+SB1, where SB2 and SB1 are the radiance values recorded by two different spectral bands from the instrument which cover the same spatial pixel area, one that includes a CH4 feature (SB1) and one that does not (SB2). The result is an image of intensity values that can be compared to threshold to determine if CH4 is present. If the plume is absorbing more thermal energy than passes through and is emitted by it, higher values for NDMI indicate a stronger likelihood of enhanced CH4. If the plume is emitting more thermal energy than it absorbs, which is characteristic of hotter plumes, lower values of NDMI indicate a stronger likelihood of enhanced CH4. All cases considered for this study included plumes that produced spectral absorption features, and therefore higher NDMI values were indicative of a stronger likelihood of enhanced CH4.

For this study, two different band combinations were chosen to be compared. SB1 for each combination was MURI band 1. Centered at 7.68 µm, this band contains the strongest CH4 absorption feature. Two different bands were chosen for SB2 for comparison, the first was MURI band 2. This band was chosen as this band contains less CH4 absorption features than band 1 and covers a spectral region that has comparatively higher atmospheric transmission than band 1. The other band chosen for SB2 was MURI band 6. This band was chosen because CH4 has the weakest effect on this band. After calculating the NDMI, a threshold varying from the lowest value pixel to the highest value pixel of the NDMI image was used to create ROC curves, which inform on how well the NDMI is an indicator of enhanced CH4 presence.

In order to create a realistic data set of sensor-reaching radiances for these studies, a scenario in which a rogue emission source has been detected was chosen as a reference in order to produce a more realistic simulated model. Data from HyTES collections are fitting for this purpose as the system's 256 spectral channels roughly cover the same region in the thermal infrared as the MURI design and collects over the CH4 absorption feature at 7.68 µm. The chosen HyTES collection is shown in Fig. 1 and was recorded over Kern River oil fields on 5 February 2015 . The data set provided by the Jet Propulsion Laboratory includes a flagged image, shown in Fig. 2, that identifies pixels that a matched filter predicted contained enhanced CH4 concentrations. Figure 3 shows typical on- and off-plume spectra, as well as a simulated recreation of the data using MODTRAN6. Surface level air temperature was retrieved from Weather Underground (https://www.wunderground.com/, last access: 2 July 2019) and was set to 293.5 K. The concentration of the plume was determined by to be 6 ppm . A list of notable model inputs is recorded in Table 2. The model was able to recreate the HyTES spectra with a RMSE of 0.25 W m-2 sr-1 µm-1 for the CH4 present case and 0.15 W m-2 sr-1 µm-1 for the background case. Recreation of this data provided confidence that realistic scenes could be reproduced in MODTRAN6 and helped inform the input parameters for the other simulated data sets.

To evaluate the multiband methods, a simulated MURI image was created using higher-spectral-resolution HyTES imagery. By applying the MURI spectral response to the HyTES data, a six-channel image with MURI's spectral channels was created. It should be noted that HyTES data do not fully cover the bandpass of MURI's band 6. The synthetic MURI image was created using a subset of HyTES images recorded over Kern County, California, on 8 July 2014, which can be seen in Fig. 4. The chosen subset was determined to contain no detected enhanced CH4 pixels .

The images created by applying MURI's spectral response initially had less noise than the predicted noise for MURI. The noise in this image is defined as 8Nsimulated=NHyTES(#ofHyTESBands). This means that additional noise needed to be simulated in the image in order to better estimate a MURI image. The amount of additional noise can be defined as 9Nadd=sqrt(NMURI2-(NHyTESimage(#ofHyTESBands))2).

This additional noise was calculated from the noise-equivalent delta temperature by first calculating noise-equivalent delta radiance: 10NEdL=NEdT⋅dBdT, where dBdT is the derivative of Planck's blackbody function with respect to temperature. The noise was then added to the image by multiplying the difference in quadrature of the NEdLs with a Gaussian random number with mean 0 and standard deviation of 1.

The simulated data set was created to determine the ability of MURI to detect higher-concentration CH4 plumes. The data set for this investigation required an image with realistic variation and a known presence of CH4. In order to accomplish this, a set of CH4 present HyTES images were created. These images were created using the local chemical plume model of MODTRAN6, which outputs an on-plume and off-plume curve for at sensor radiance . Both the off-plume and on-plume simulations were run with a limited atmosphere with only small amounts of CO2. The off-plume simulation contained only background levels of CH4, while the on-plume model contained an enhanced concentration plume, ranging from 1 to 20 ppm above ambient methane. Then a radiance difference was calculated between the off-plume and on-plume spectral curves, removing the effects of the small amount of CO2 and background CH4 levels. The differences were then added to copies of the background HyTES image to create a set of plume-present images with realistic background variation and known methane quantity. The MURI images were then created by applying MURI's spectral response to the HyTES data set. Additional noise was added to the images by the same method stated above. The final data set consists of five images derived from the scene depicted in Fig. 4. The first image has no enhanced levels of methane present, and the rest of the images have only enhanced levels of methane present across the entire image. Each image has a plume of constant concentration ranging from 1 to 20 ppm and plume temperature difference of -10 K from ambient atmospheric temperature. This also provides a simple truth map, as a perfect accuracy method would indicate the background image as having no methane present pixels (zero false alarms) and the plume-present images as having every pixel be indicated as plume present (hit rate of 1).

For this study, a low-altitude plume is considered. Spectral radiances in the CH4 band were simulated using MODTRAN6, as described in Sect. 3. Table 3 contains a list of notable constants and their values, which were derived from examining HyTES images, metadata, and the conditions under which the images were recorded . Ambient atmospheric temperature was estimated from Weather Underground, which was recorded by the Meadows Field Station in Bakersfield, California, on 8 July 2014 at 11:54 am. Modern estimates of ambient atmospheric CH4 concentration are at about 1.8 ppm , while the lower explosive limit is around 50 000 ppm . For this experiment, the CH4 concentration within the plume was varied from 1 to 50 ppm or 0.1% of the lower explosive limit. The plume temperature was defined by a temperature difference from ambient temperature. The plume for this study varied from -10 to +10 K of ambient temperature at the plume height. This is a range of -27 to -7 K to the background surface. Brightness temperature differences between the plume-present and background cases were calculated. These differences were compared to the NEdT computed by DRS, which is 0.256 K for band 1, i.e., the CH4 feature band. The results of the low-altitude plume model can be seen in Fig. 5 (see Fig. S1 in the Supplement for low-altitude plume model results described using the temperature difference between the methane plume and the surface).

The results here indicate that a plume with a temperature difference as high as +10 K from ambient temperature is absorbing energy, which is consistent with knowledge that the background surface temperature is 17 K higher than the ambient atmospheric temperature. The higher-temperature plumes require higher concentrations to detect, with the hottest in this study requiring a plume of more than 45 ppm to provide a detectable contrast (about 25 times background levels). At ambient temperature, a plume of about 17 ppm (about 10 times background levels) is required for the temperature difference to have a detectable contrast, and for the coldest plume temperature, a concentration of 10 ppm creates a high enough temperature difference to display a detectable contrast. This study gives a baseline for detection for a single band allocated to CH4 absorption features.

For the purposes of this study, a low-temperature plume (-10 K from ambient atmospheric temperature or -27.6 K from background surface temperature) with various concentrations of CH4 were simulated in the column and added to the background image containing only background levels of CH4. Table 4 contains a list of notable constants and their values. Ambient atmospheric temperature was retrieved from Weather Underground, which was the daily high temperature recorded by the Meadows Field Station in Bakersfield, California, on 8 July 2014. Surface temperature was determined by matching a blackbody to a selection of random pixels from the HyTES imagery. The signal, b in Eq. (5), was defined as an absorbing CH4 plume and was extracted from the HITRAN data set. The ROC curves in Fig. 6 provide an understanding of how well the system distinguishes CH4 present pixels and background clutter using a the matched-filter approach. The probability of false alarm (Pfa) indicates the fraction of background clutter pixels incorrectly categorized as CH4 present pixels, while the hit probability (Phit) indicates the fraction of pixels correctly identified as CH4 present pixels. In the perfect detection case, an ideal circumstance, there exists a threshold value where Phit is 1, and Pfa is zero. A straight line with a slope of 1 indicates that the detection scheme is performing as well as chance. Otherwise, a high hit rate and low false alarm rate indicate a reliably detectable scenario.

Utilizing the matched-filter approach shows HyTES is capable of detecting as low as 5 ppm with a low false alarm rate. The hyperspectral system is even capable of detecting an additional plume of 1 ppm above background levels with a hit rate of 70% and a false alarm rate of 30%. MURI's matched-filter approach shows that an additional plume of 10 ppm can be detected with 80% accuracy and about 23% false alarm rate. Utilizing the matched filter on the two systems reveals that the narrow-band hyperspectral system is outperforming the broader-band multispectral system.

The result of applying the normalized differential methane index method for MURI data simulated from HyTES imagery and MODTRAN6 can be seen in Figs. 7 and 8.

The results indicate the MURI system performs better using the NDMI using bands 1 and 6 compared to bands 1 and 2. The NDMI method performed on MURI bands 1 and 6 performs as well as the matched-filter approach being applied to all MURI bands, as the NDMI method shows 80% accuracy and about 17% false alarm rate for a scenario with an enhanced CH4 plume of 10ppm. This provides evidence indicating that given a high enough concentration and temperature contrast, a simple two-band approach can be used to detect enhanced levels of atmospheric CH4 with similar accuracy to a six-band approach.