Monitoring anthropogenic emissions is a crucial aspect in understanding the methane budget. Moreover, a reduction of methane emissions could help to mitigate global warming on a short timescale. This study compares various retrieval schemes for estimating localized methane enhancements around ventilation shafts in the Upper Silesian Coal Basin in Poland using nadir observations in the shortwave infrared acquired from the airborne imaging spectrometer HySpex. Linear and nonlinear solvers are examined and compared, with special emphasis put on strategies that tackle degeneracies between the surface reflectivity and broad-band molecular absorption features – a challenge arising from the instrument's low spectral resolution. Results reveal that the generalized nonlinear least squares fit, employed within the Beer InfraRed Retrieval Algorithm (BIRRA), can measure enhanced methane levels with notable accuracy and precision. This is accomplished by allowing the scene's background covariance structure to account for surface reflectivity statistics. Linear estimators such as matched filter (MF) and singular value decomposition (SVD) are able to detect and, under favorable conditions, quantify enhanced levels of methane quickly. Using

Methane (

The vast majority of anthropogenic

Satellite observations are typically used for continuous and global long-term monitoring of atmospheric composition, but also ground-based networks such as the Global Atmosphere Watch (GAW) Programme of the World Meteorological Organization (WMO) or the European Integrated Carbon Observation System (ICOS) are crucial assets.
Spaceborne spectrometers measuring shortwave infrared (SWIR) solar radiation reflected at the Earth's surface are
especially well suited to observe atmospheric

Operational

Another way to increase the sensitivity towards smaller sources is to increase the instrument's spatial resolution. This in turn
necessitates a trade-off in spectral resolution because the loss of photons caused by the smaller ground pixels reduces the signal-to-noise ratio (SNR) of the image, which has to be compensated for by broadening the width of the spectral channels. Imaging spectrometers for land surface remote sensing (often referred to as hyperspectral cameras) are typical
examples of instruments optimized for spatial resolution this way. Their technology matured over the last 30 years, and a variety
of airborne instruments and several spaceborne versions are either in orbit

One of the core challenges when retrieving methane from measurements with high spatial (

This study aims to compare concentration enhancements from different retrieval methods using measurements of the German Aerospace Center's (DLR) HySpex sensor system. The objective is to evaluate the retrievals' performance in terms of accuracy, precision, and speed and show advantages and drawbacks for each method. Another goal is to assess the latest BIRRA updates and its applicability to moderately resolved spectra from airborne sensors. Therefore, the paper is structured as follows.

First, the experimental setup is briefly described, followed by a quick review of atmospheric radiation and an introduction to the various BIRRA setups examined in this study. Afterwards, other simpler but faster retrieval schemes employed in this work are briefly discussed. The result section presents the

Both linear and nonlinear methane retrieval schemes are
examined. While the former are very fast but often lack sufficient
accuracy, nonlinear iterative solvers require more computing power and
time to come up with a best estimate. The study utilizes measurements
collected by the DLR airborne HySpex sensor system (see
Table

Summary of some important HySpex properties. The sensor is described in detail in

To compare the performance of various retrieval methods, we limit our analysis to the two flight lines shown in Fig.

(Left, top) Flight line 9 (dashed red line) was obtained around 09:55 UTC, while flight line 11 (solid red line) was acquired around 10:10 UTC (©

Figure

In the SWIR spectral range the radiative transfer through the atmosphere under clear-sky conditions (cloud and scattering free) is well described by Beer's law

The decision to exclude aerosol modeling for HySpex observations was encouraged by findings from

In Fig.

The model atmosphere's vertical extent ranges from 0–80 km with 39 levels in total. The atmosphere is composed of pure gaseous layers.
The highest vertical resolution is found in those layers below

The

The classical BIRRA level 2 processor, developed at DLR, uses the Generic Atmospheric Radiation Line-by-line Infrared Code

The mathematical forward model

The transmission is described by

This study examines various nonlinear retrieval schemes that are implemented in the BIRRA level 2 processor and are briefly introduced below. Nonlinear least squares methods are iterative and require calculating derivatives for each of the nonlinear state vector elements, represented by a Jacobian matrix

The nonlinear least squares fit minimizes the residual norm (

The SLS splits (separates) the state vector

A generalized least squares fit is used to account for correlated errors. The covariance matrix

The error covariance matrix

Scene 09 inverse square root matrix of

A scene-averaged background spectrum, excluding ground pixels around
the suspected

The state vector

The actual

In contrast to nonlinear fitting schemes, linear solvers for

Assuming that the increase in optical depth caused by the plume,

It is important to note that in this setup the reflectivity coefficient

Another aspect that should be kept in mind is that since

The MF is a well-established method for estimating molecular concentration enhancements from hyperspectral sensors, with numerous studies supporting its effectiveness

In order to improve accuracy, a per-measurement target spectrum is computed, which accounts for the pixel's albedo

However, the MF method has its limitations; for example, it suffers from a heterogeneous background and correlation between the plume and the background which limits the detection quality even for strong plumes

The retrieval of methane enhancements from hyperspectral AVIRIS data using singular vectors of the observed spectrum plus a target signature was first demonstrated by

The orthogonal singular vectors are obtained from HySpex spectra that are not impacted by the plume. The matrix containing the scene's log-space background spectra is decomposed into

The basic idea is analogous to the MF, i.e., to represent the general variability in spectral radiance by a linear combination of singular vectors and a target signal. The minimization problem is then given by

Standardized singular vectors

A straightforward approach to identify methane absorption is the SSD, which compares the ratio of spectral residual norms to produce a score. Unlike other methods, this approach does not require any radiative transfer calculations, lookup tables, or initial guess information – only calibrated sensor data for a specific interval.

The algorithm is based on a simple polynomial fit of spectral pixels and the calculation of spectral residuals. The idea behind this method is similar to the continuum interpolated band ratio (CIBR) from

The algorithm constitutes a fast scheme which can also be applied for real-time detection of enhancements, e.g., determine whether or not a

This section presents the results for the

Figure

Methane enhancements for

Mean and standard deviation (SD) for the background pixels of the

Figure

Methane plume depicted for the single-window covariance-weighted fits for scene 09. The background pixel concentration is rather stable in the 4K interval depicted in panel

Figure

Figure

In the single-pixel spectra depicted for

The albedo-normalized, cluster-tuned, and classical matched filters are examined for scene 09. Figure

The SVD-based retrieval method illustrated in Fig.

The linear least squares fit is able to identify

In Fig.

The ratio of the spectral residuals in the 6K range for the in-band and out-of-band pixel is depicted. In panel

It is important to note that the method yields better results for the 6K absorption since the 4K absorption features are distributed over a larger spectral range which causes more uncertainty in the out-of-band polynomial fit since many pixels need to be omitted.

In order to provide a more quantitative measure on the quality and confidence of the fits, a Student

The null hypothesis was rejected at the 1 % significance level, which can be considered a strong evidence. Although some fit results may ask for a tighter significance level in the

Figure

Plume pixels according to the Student

The Student

Plume pixels identified by the

In general the retrieval's fit quality is assessed with respect to the discrepancy between the measurement

The errors of the individual state vector parameters are represented in the square root of the diagonal elements of

Uncertainties in the estimated

Tables

Same as Table

Figure

Pearson correlation coefficients for inferred methane from scene 09 for the nonlinear and linear solvers in the two examined spectral intervals.

The study found that nonlinear setups which utilize background pixel covariance statistics (GLS) are suited to quantify

In order to scan for potential

The LLS fit ignores background statistics, and hence the inversion suffers from albedo correlations similar to its nonlinear counterparts. The fit also significantly underestimates enhancements, although it is able to capture parts of the pattern.

Polynomials up to the second order were able to capture the enhanced methane signal in the rather simple SSD method. The selection of an adequate polynomial needs to consider the width of the spectral interval and its surface reflectivity. Moreover, the method is not designed to quantify methane but only allows for the detection of anomalies in the spectral residuum.

Cluster tuning of linear retrieval setups can help to mitigate background clutter and surface-reflectivity-induced biases

While linear methods are well suited to survey vast datasets and pinpoint potential sources, iterative solvers such as BIRRA are adequate to quantify enhanced concentrations at known locations as the slower speed is not of much concern for some thousands of observations.

The study examines the feasibility of methane retrievals from hyperspectral imaging observations for various retrieval methods. It was found that localized

The BIRRA NLS and SLS fits were found to be sensitive to spectral variations in the albedo, leading to surface-type-dependent biases known from previous studies utilizing data from hyperspectral sensors. This effect is more pronounced for single spectral intervals but less evident when multiple intervals are combined.

The linear estimators proved to be highly efficient and effective for many cases, making them suitable in the survey of large hyperspectral datasets. The well-established SVD and MF method produced results that often agree well with the BIRRA inferred enhancements; however, the sensitivity is lower. The LLS method turned out to be the least sensitive one. For detection purposes the SSD was found to be a useful tool.

In conclusion, covariance-weighted methods are able to quantify methane enhancements from hyperspectral SWIR observations at high spatial resolution with good accuracy. In particular, the GLS solver is suited to capture enhancements with an accuracy that should allow for emission estimation. Considering the significant speedup and reasonable accuracy of the linear methods MF and SVD, both constitute a valuable tool in examining plumes on vast datasets.

The methods are also applicable to spaceborne sensors, which will be considered in a next step. Overall, the new Python version of the BIRRA code used in this study turned out to be a flexible toolbox for prototyping.

Parts of the code are published via the Py4CAtS software suite (see

The data used in this study are available from the corresponding author upon request.

PH developed and implemented the retrieval setups and analysis tools and wrote the manuscript. FS originally designed and developed the software package Py4CAtS and supported the data evaluation. CHK conceived the experimental setup and conducted the data acquisition of the airborne measurements. AB performed the instrument calibration and level 0–1 processing. CHK and AB contributed the experimental setup. DC gave valuable advice for the cluster-tuning approach and provided spectral unmixing data for the verification of the SVD and MF results. All authors reviewed the manuscript.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the special issue “CoMet: a mission to improve our understanding and to better quantify the carbon dioxide and methane cycles”. It is not associated with a conference.

We thank Thomas Trautmann and Peter Haschberger for valuable criticism of the manuscript. Furthermore, we thank Konstantin Gerilowski for initiating cooperation with the CoMet campaign and Andreas Fix, the campaign leader, for the support and coordination.

This paper was edited by Justus Notholt and reviewed by David R. Thompson and two anonymous referees.