The Hyperspectral Unmixing of Trace-Gases From ESA ... - IEEE Xplore

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 12, NO. 10, OCTOBER 2015

The Hyperspectral Unmixing of Trace-Gases From ESA SCIAMACHY Reflectance Data Pia Addabbo, Member, IEEE, Maurizio di Bisceglie, Member, IEEE, Carmela Galdi, Member, IEEE, and Silvia Liberata Ullo, Member, IEEE

Abstract—Atmospheric concentrations of trace-gases are retrieved from hyperspectral data using a blind source separation method. The algorithm relies on the assumption that the absorption cross sections of the gas components are weakly dependent on the overall atmospheric background. The unmixing of contributions from the logarithm of the spectral reflectance provides estimates of both individual trace-gas absorption cross sections and their concentrations. In the experimental analysis, nadir reflectances received by SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY are considered in two scenarios: the sulfur dioxide emissions from a volcanic eruption and the nitrogen dioxide production from anthropogenic pollution. In both cases, it is demonstrated that the algorithm performs very similarly to the Differential Optical Absorption Spectroscopy algorithm but with very little ancillary information. Index Terms—Blind source separation (BSS), SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY), trace-gas concentration retrieval.

I. I NTRODUCTION

T

HE SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) is a passive hyperspectral UV-VIS-NIR grating spectrometer observing backscattered, reflected, or emitted radiation from the atmosphere and the Earth’s surface [1]. The Differential Optical Absorption Spectroscopy (DOAS) exploits the narrow-band spectral absorption structures in the near UV, visible, and near infrared wavelength regions [2] and is the most widely used technique for retrieving trace-gas abundances in the open atmosphere. It has been successfully used for years to retrieve atmospheric columns of NO2 , BrO, SO2 , HCHO, and OClO from SCIAMACHY nadir measurements [3]–[6]. It is also known that, in some applications, results from standard DOAS are affected by spectral interference from other gases, as in sulfur dioxide (SO2 ) retrieval with a strong interference by the ozone in the narrow 260–340-nm vibrational band. To improve accuracy in this case, the Weighting Function DOAS (WFDOAS) has been developed with wavelength-dependent weighting functions used instead of the absorption cross sections [7]. Moreover, the main limitation of this technique is the need of a priori information about the trace-gas under analysis. Recent investigations, aimed at Manuscript received January 23, 2015; revised April 23, 2015; accepted June 18, 2015. Date of publication July 21, 2015; date of current version August 7, 2015. The authors are with the Department of Engineering, University of Sannio, 82100 Benevento, Italy (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2015.2452315

improving the SO2 retrievals, were developed using the principal component analysis (PCA) to characterize the effects caused by both the physical processes and the measurement artifacts in the absence of SO2 absorption [8]. A different unmixing approach has been recently proposed, based on blind source separation (BSS). Starting from the general rationale of the independent component analysis, this method replaces the constraint of perfect independence among sources with a minimum dependence criterion and represents an effective way for measuring the SO2 concentration from reflectance spectra measured by the ozone monitoring instrument [9]. In this contribution, it is shown that BSS can be also usefully applied to nadir SCIAMACHY reflectance spectra to produce trace-gas concentration maps in several observational conditions. Experiments have been carried out for SO2 from volcanic emission and nitrogen dioxide (NO2 ) from anthropogenic pollution. In both cases, the trace-gases are air pollutants that absorb solar radiation in the ultraviolet portion of the electromagnetic spectrum. In particular, the NO2 absorption is very well structured in the 420–450-nm wavelength range, whereas the SO2 exhibits a relatively strong absorption from 260 to 340 nm, where there is also a strong absorption by the ozone. A calibration approach for finding the optimal retrieval wavelength range has been considered by applying the proposed technique to spectra with known trace-gas concentrations, simulated with MODerate resolution atmospheric TRANsmission (MODTRAN) [10]. Comparisons with DOAS results are also carried out and discussed.

II. T RACE -G AS U NMIXING VIA S OURCE S EPARATION This section provides a short description of the BSS algorithm for trace-gas unmixing. Further details can be found in [9]. The main improvement presented in this section is the introduction of a contamination matrix that allows a rigorous and simple presentation of the observation model and a straightforward proof of a key property of the mixed linear model. A diagram of the processing scheme is reported in Fig. 1, and the analytical description of the algorithm is presented in the following sections.

A. Mixing Model According to the Beer–Lambert law, the negative natural logarithm of the reflectance spectrum D(λ), also known as optical density, can be modeled as the sum of the atmospheric cross sections σi of the gas components weighted by their

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ADDABBO et al.: HYPERSPECTRAL UNMIXING OF TRACE-GASES FROM ESA SCIAMACHY REFLECTANCE DATA

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Fig. 1. Scheme of the source separation method with the contaminated mixing model.

respective slant column densities Si , plus a polynomial function of the wavelength [11]. Thus D(λ)

N

Si σi (λ) + P (λ)

(1)

i=1

where N is the number of gas species. The polynomial P (λ) is a slowly varying function of the wavelength, accounting for Rayleigh and Mie scattering, and surface albedo [2]. Because the major influence of the atomic and molecular states is observed in the narrow-band structure of the absorption bands, the slowly varying component of the optical density should be separated by the received spectral waveform. This is a well-known issue in DOAS-based algorithms that was also introduced into the BSS procedure because the slowly varying polynomial component generates a correlation among sources in a context where we are searching for the least dependent sources. The interested reader may refer to [9] for further details. After high-pass filtering, (1) takes the form D (λ)

N

Si σi (λ)

(2)

i=1

where D (λ) is the high-pass-filtered version of D(λ), known as differential optical density, and σi (λ) is the fast-varying component of the absorption cross sections. The slowly varying component of the spectral waveform can be efficiently removed by using a high-pass Savitzky–Golay filter, as shown in the scheme of Fig. 1, which provides a least-squares smoothing of the noisy data, especially when the shape and amplitude of the waveform peaks must be preserved [12]. (λ), with m = From a collection of M optical densities Dm 1, . . . , M , corresponding to different observed instantaneous field of views (IFOVs), we get the stochastic mixing model D = Sσ.

(3)

To avoid heavy mathematical notations, since now, we refer to random vectors and variables without apex. Equation (3) should be interpreted as follows: each differential optical density is sampled at the wavelengths λ1 , . . . , λP ; the sampled values are modeled as realizations of the random variable Dm . Similarly, the sampled absorption cross sections σi (λ) are realizations of the random variables σi . Thus, D = [D1 , D2 , . . . , DM ]T , σ = [σ1 , σ2 , . . . , σN ]T are random vectors, and S = {Smn }, m = 1, 2, . . . , M , n = 1, 2, . . . , N is the M × N mixing matrix of the slant column densities, with M ≥ N . Equation (3) is in the form of a classical spectral unmixing problem, where the optical density spectra are expressed as a linear combination of endmembers, weighted by the corresponding abundances. If the sources are independent or weakly dependent, the BSS method

provides estimates of both the sources and the mixing matrix. However, a well-posed BSS problem requires that all sources appear in detectable concentrations in at least one observed IFOV, whereas in a gas mixture, the presence of a nonzero tracegas concentration is not generally ensured. In this case, the linear mixing model expressed by (3) is singular. To overcome the problem, a contaminated mixing model is introduced as described in the next section. B. Contaminated Mixing Model For the mixing model (3), let us define an ordering criterion such that the first N − 1 waveforms are the trace-gas cross sections of interest and the last waveform σN is a background term containing all remaining contributions. The N − 1 waveforms do not necessarily subsist in detectable concentrations; therefore, the matrix S is possibly singular. To regularize the problem and, at the same time, drive the solution toward the set of trace-gas components of interest, we define a contaminated mixing model, with M equal to N , as follows: the first observation D1 is the uncontaminated differential optical density of the IFOV under test; the remaining N − 1 observations Di , i = 2, . . . , N , are defined as the sum of the first observation D1 plus the differential absorption cross section σi−1 of the (i − 1)th trace-gas component of interest. The background component σN is not contaminated because it is always supposed different from zero. In matrix terms, contamination corresponds to adding the contamination matrix ⎞ ⎛ 0 0 ··· 0 ⎜C1 0 ··· 0 ⎟ ⎟ ⎜ (4) C=⎜ . . .. ⎟ . . . . ⎝ . . . . ⎠ 0 ··· CN −1 0 with Ci > 0, to the mixing matrix S = (1 . . . 1)T (S11 . . . S1N ) having all rows given by replicas of the first row. The stochastic contaminated model is therefore D = Qσ, where Q = (S + C) is the contaminated matrix, as shown in the second block of Fig. 1. It is easy to see that the contaminated model is nonsingular even if the atmospheric concentrations of the σ1 , . . . , σN −1 species are zero. This is shown in the following. Proposition 1: The contaminated matrix having identically zero cross section concentrations S11 , . . . , S1N −1 ⎞ ⎛ 0 0 ··· S1N ⎜C1 0 ··· S1N ⎟ ⎟ ⎜ Q=⎜ . ⎟ .. .. .. ⎠ ⎝ .. . . . 0

···

CN −1

S1N

and all positive contaminating components is nonsingular.

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Proof: The matrix Q can be transformed into an upper triangular matrix by simply shifting the first row in the last position. The proposition follows because the upper triangular matrices with nonzero diagonal elements are nonsingular. It is worth remarking here that one feature of the BSS method is the possibility of detecting one gas spectral waveform in a composite background. In this case, the mixing matrix is a 2 × 2 matrix, with the concentrations of the trace-gas of interest and background in the first row and the contaminated gas concentration and the uncontaminated background concentration in the second row. This simple scenario cannot be defined using DOAS algorithms, where the number of sources should be as large as to include all components of the standard atmosphere for an accurate estimate of concentration abundances. C. Source Separation Scheme The BSS problem can be posed as follows: Given the observables D, Find the matrix W, Such that the transformed sources W(S + C)σ are as independent as possible. The source separation method provides the least dependent sources σ and the matrix W = (S + C)−1 such that the gas concentrations can be found as S = W−1 − C. The transformation matrix for unmixing W is decomposed as the product of a whitening matrix V and a unitary rotation matrix R, namely, W = RV, where V is calculated from the estimated covariance matrix of the observables D as V = −1/2 ΛD UD T , where ΛD and UD are the eigenvalues and the eigenvector matrix of the estimated covariance matrix, respectively. Given that the whitening matrix is invariant with respect to rotations, the problem is reduced to finding a rotation in N dimensions such that the statistical independence of the sources is maximized. In N dimensions, the number of angles to consider for maximization is L = (1/2)N (N − 1), which increases as N 2 . Indeed, the procedure becomes quickly unfeasible and the most interesting cases are restricted to one or two sources. For what concerns the independence measure, it can be shown [13], [14] that minimizing the mutual information is equivalent to minimizing the sum of the Shannon entropies of the observed random variables with respect to the Euler rotation angles θ = (θ1 , . . . , θL ), or formally θ 0 = arg min θ

N

H(Yn ; θ).

(5)

n=1

Because the resulting quantities must be nonnegative, the additional constraint Yn ≥ 0 should be included in the minimization procedure to ensure that solutions are physically consistent [15]. III. R ETRIEVALS U SING MODTRAN-S IMULATED S PECTRA : C ALIBRATION AND B IAS C ORRECTION The SCIAMACHY instrument provides spectroscopic capabilities over a large spectral range with high spectral resolution, high radiometric accuracy, high dynamic range, and signalto-noise ratio. Nonetheless, achieving stringent performance results in terms of precision and accuracy of the trace-gas estimates is a challenging goal that requires careful calibration of the algorithms for the specific cases of interest. In the

Fig. 2. Absolute differences between estimated values for varying wavelength intervals. At the left, SO2 vertical column concentration in Dobson unit and, at the right, NO2 vertical column concentration in 1015 mol/cm2 .

following sections, calibration for the retrieval of SO2 and NO2 concentrations is obtained by an optimal choice of the wavelength range and by appropriate correction laws to be applied to the estimated concentrations. A. Calibration for SO2 Retrievals From Volcanic Eruptions Optimum bandwidths for DOAS retrievals, from SCIAMACHY data, have been carefully assessed so far [7]: they indicate that SO2 should be estimated in the [315–327] nm range. Given the different approach of the proposed algorithm, a new study for finding the optimal wavelength range is here presented. Synthetic spectra with known trace-gas concentration columns are simulated with MODTRAN software and used as a test-bed for the BSS retrieval algorithm. Atmospheric profiles are defined, differing only for the SO2 from the U.S. Standard Atmosphere [16]. The SO2 vertical column concentration profile models a volcanic eruption scenario and follows a Gaussian profile, centered at hc = 13 km, with a standard deviation calculated such that the concentration is reduced to 1/e fraction at hup = 3 km. The total concentration of the simulated profile is 10 Dobson units (DU). The synthetic spectrum is processed by the BSS algorithm, and the estimation error with respect to the true concentration value is evaluated as a function of the wavelength interval location and size. Subintervals of the SCIAMACHY second channel [309–405] nm are scanned with 0.26-nm resolution between a lower limit λmin in the [309–321] nm range and an upper limit λmax in the [323–335] nm range. Results are presented at the left side of Fig. 2, where the absolute values of the estimated concentration errors with respect to the true value (10 DU) are reported: the y-axis and the x-axis are, respectively, the minimum and maximum wavelengths in the range, and darker pixels indicate smaller errors. The optimum wavelength range is [309.8–327.2] nm, resulting in a close to 10−3 DU estimation error. It is worth to note that the wavelength range for the BSS algorithm is wider than the range for DOAS fitting. Another issue in trace-gas concentration retrieval is represented by the dependence of the absorption cross sections on atmospheric temperature profile, air mass factor, water vapor, pollution, and other anthropic or natural environmental conditions [17]. Even if the BSS method is intrinsically weakly dependent on changes in the spectral waveforms, a bias analysis is here considered to apply possible empirical laws for correction of systematic errors in the estimation process, which may induce an overestimation or underestimation of the tracegas abundances. To this end, MODTRAN synthetic spectra for

ADDABBO et al.: HYPERSPECTRAL UNMIXING OF TRACE-GASES FROM ESA SCIAMACHY REFLECTANCE DATA

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Fig. 3. Estimated errors for vertical column concentrations and bias correction laws for SO2 at the left and NO2 at the right.

varying SO2 concentration were simulated, and the estimated concentrations were compared with true values to produce an error correction law. SO2 simulated profiles with varying vertical column concentrations, in the range from 0 to 100 DU, are generated. All vertical profiles are centered at hc = 13 km, with hup = 3 km, as simulations have shown a weak influence on these two parameters. The differences between the estimated and true SO2 vertical column concentrations are shown at the left side of Fig. 3. The estimated values, for very low SO2 concentrations, are affected by a small positive offset (3 DU for zero concentration), whereas high SO2 concentrations are underestimated. The data are very well fitted by a parabolic function y = −0.0021x2 − 0.33x + 4.1, which represents the correction law to be applied to volcanic SO2 retrieval.

Fig. 4. (Left) SO2 concentration in Dobson unit over the Nyamuragira volcano eruption on August, 3, 2002. (Right) Scatter plot of DOAS versus BSS (black points) at the top and SO2 concentrations versus latitudes (red: BSS, blue: DOAS) at the bottom.

for stratospheric contribution, modeled by a Gaussian profile centered at hc = 24 km with hup = 8 km. The right side of Fig. 3 shows the estimated errors for NO2 vertical column concentration, where two linear interpolations y = −0.14x + 0.15 and y = −0.035x− 0.36 are also reported, representing the correction laws for the case at hand. The estimated errors range from −1.6 to 0.2 · 1015 mol/cm2 ; thus, bias corrections are, in absolute terms, smaller than those for the SO2. IV. T RACE -G AS R ETRIEVALS

B. Calibration for NO2 Retrievals From Pollution Due to the significant diurnal variability of stratospheric NO2 , the choice of a suitable height profile for the trace-gas concentration is more difficult than in the previous case. The simulated NO2 height profile is Gaussian-shaped, with hc = 24 km, hup = 8 km, and 5 · 1015 mol/cm2 vertical column density concentration, according to the NO2 1976 U.S. Standard Atmosphere profile. In DOAS retrievals from SCIAMACHY data, the optimum spectral interval for NO2 is the [426–451] nm range [18]. For the BSS algorithm optimization, we have analyzed the SCIAMACHY third channel [383–628] nm, with 0.44-nm spectral resolution. The lower limit λmin and the upper limit λmax for the calibration setup range in the [426–440] nm and [451–465] nm intervals, respectively. Results are presented in Fig. 2 at the right, where it is shown that the absolute errors range from 10−2 to 0.2 · 1015 mol/cm2 . The minimum error is achieved in the [437.12–451.40] nm spectral range; this interval is smaller than the nominal spectral window used in DOAS retrievals. The sensitivity with respect to spectral range in SO2 and NO2 retrievals can be compared from the analysis of Fig. 2. We note that the estimation error is, in any case, smaller in NO2 retrieval with respect to SO2 that, however, shows less sensitivity to the spectral range. The presence of systematic errors was investigated using different NO2 height profiles; the total vertical profiles are representative of situations from nonpolluted (0 − 5 · 1015 mol/cm2 ) to highly polluted (30 · 1015 mol/cm2 ) atmosphere and are composed of two profiles: the first, accounting for tropospheric contribution, represented by the half Gaussian profile centered at hc = 0 km with hup = 6 km, and the second accounting

Two case studies have been considered: SO2 concentration from volcanic emission during the Nyamuragira volcano eruption in Central Africa and NO2 concentration from anthropogenic pollution in northern Italy. Results are compared with DOAS vertical column concentrations provided by ESA products. A. Retrieval of SO2 : The Nyamuragira Volcano Emissions The Nyamuragira volcano is a shield volcano, one of the most active African volcanoes, located in the Virunga Mountains of the Republic of Congo. Fig. 4 at the left shows SO2 concentrations in Dobson unit retrieved with the BSS algorithm. Two consecutive orbits with six SCIAMACHY nadir states (12–17) are considered for the analysis. Red points represent areas of large SO2 concentration, whereas the lowest concentrations are indicated in blue color. The selected SCIAMACHY states intercept an SO2 polluted area over the Nyamuragira volcano. A large area around the volcano region shows large SO2 concentrations, extending into almost two consecutive SCIAMACHY orbits. Fig. 4 (right side) shows a comparison between BSS and DOAS. SO2 concentration estimates, versus latitudes for the six states of the second orbit, are reported at the bottom. The first two states, showing larger gas concentrations, intersect the SO2 plume. A good agreement between the results of the two algorithms is clearly shown, especially for high concentration values, whereas for SO2 background levels, results differ by about 0.5 DU on average. The same data are represented in a scatter plot, at the top, where the agreement between the results is more evident and demonstrated by a close to 0.91 correlation coefficient between data.

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Fig. 5. (Left) NO2 concentration in 1015 mol/cm2 over Europe in February, 19, 2003. (Right) Scatter plot of DOAS versus BSS at the top (black points) and NO2 concentrations versus latitudes (red: BSS, blue: DOAS) at the bottom.

B. Retrieval of NO2 : Anthropogenic Pollution in Northern Italy A small area in northern Italy, also known as the Po river valley, is considered for the experiment of anthropogenic NO2 emission. A polluted area is clearly visible in Fig. 5 at the left, where NO2 maximum estimated concentrations are even greater than 20 · 1015 mol/cm2 . The NO2 concentration map is normalized to 1015 mol/cm2 . It is interesting to point out that the algorithm is able to detect the higher concentrations that clearly emerge in the northern Italy region with respect to the background. In the same figure, BSS estimates are compared with DOAS retrievals at varying latitudes at the right-bottom and as a scatter plot at the right-top. A good agreement between the two methods is demonstrated by a correlation coefficient that is close to 0.96. Discrepancies between the two algorithms are located in the range of small concentrations, but in any case, results from the retrievals are in a very good agreement. V. D ISCUSSION AND C ONCLUSION This work is the first demonstration of applicability of the BSS method to ESA SCIAMACHY retrievals of SO2 and NO2 concentrations. Both cases depict interesting situations to test the effectiveness and potential of the proposed method with respect to DOAS for SO2 retrieval in the presence of ozone and for detection of small NO2 concentrations. The optimization of the wavelength range and the correction of systematic bias have been carried out using simulations of spectra with MODTRAN. Due to the wide variability of the environmental parameters and measurement conditions, the defined assessment in terms of calibration and bias correction represents the best choice for the addressed situations, but it is not automatically extendable to all cases. This limit is more relevant for NO2 retrievals because of many significant variations in the stratospheric gas profile. On the other hand, the advantages of the BSS technique with respect to the current standard spectroscopic techniques can be outlined as follows. 1) The model definition in the form of an unmixing problem provides, in a single shot, accurate estimates of the absorption waveforms and the mixing concentrations in the real environment. It is worth to notice that estimated spectral waveforms are different, in general, with respect to the uncontaminated waveform models.

2) It is also possible and easy to detect a single gas concentration by separating the gas spectral waveform from a composite background; this is not possible with DOAS methods because the number of fitting components should be as large as possible to include all of the constituent absorbers in the selected wavelength interval. 3) The need of a priori information about the trace-gas under investigation, such as temperature and pressure dependence, is strongly reduced in the BSS method. 4) Some common inaccuracies of DOAS-like methods are fixed. For example, the nonphysical negative concentrations, mainly due to random measurement noise in regions of zero or very low SO2 concentrations, are not displayed in BSS retrievals. R EFERENCES [1] M. Gottwald et al., “SCIAMACHY, Monitoring the Changing Earth’s Atmosphere,” Institut f’ur Methodik der Fernerkundung (IMF), Deutsches Zentrum fur Luft-und Raumfahrt (DLR), Wessling, Germany, 2006. [2] U. Platt and J. Stutz, Differential Optical Absorption Spectroscopy: Principles and Applications. Berlin, Germany: Springer-Verlag, 2008. [3] A. Richter, J. P. Burrows, H. Nusz, C. Granier, and U. Niemeier, “Increase in tropospheric nitrogen dioxide over China observed from space,” Nature, vol. 437, no. 7055, pp. 129–132, Sep. 2005. [4] O. T. Afe, A. Richter, B. Sierk, F. Wittrock, and J. P. Burrows, “BrO emission from volcanoes: A survey using GOME and SCIAMACHY measurements,” Geophys. Res. Lett., vol. 31, no. 24, Dec. 2004, Art. ID. L24113. [5] C. Lee et al., “Impact of transport of sulfur dioxide from the Asian continent on the air quality over Korea during May 2005,” Atmos. Environ., vol. 42, no. 7, pp. 1461–1475, Mar. 2008. [6] H. Oetjen et al., “Evaluation of stratospheric chlorine chemistry for the Arctic spring 2005 using modeled and measured OClO column densities,” Atmos. Chem. Phys., vol. 11, no. 2, pp. 689–703, 2011. [7] C. Lee, A. Richter, M. Weber, and J. Burrows, “SO2 retrieval from SCIAMACHY using the Weighting Function DOAS (WFDOAS) technique: Comparison with standard DOAS retrieval,” Atmos. Chem. Phys., vol. 8, pp. 6137–6145, 2008. [8] C. Li, J. Joiner, N. A. Krotkov, and P. K. Bhartia, “A fast and sensitive new satellite SO2 retrieval algorithm based on principal component analysis: Application to the ozone monitoring instrument,” Geophys. Res. Lett., vol. 40, no. 23, pp. 6314–6318, 2013. [9] P. Addabbo, M. di Bisceglie, and C. Galdi, “The unmixing of atmospheric trace gases from hyperspectral satellite data,” IEEE Trans. Geosci. Remote Sens., vol. 50, no. 1, pp. 320–329, Jan. 2012. [10] A. Berk, G. Anderson, P. Acharya, and E. Shettle, MODTRAN 5.2.0.0 User’s Manual, 2008. [11] V. V. Rozanov and A. V. Rozanov, “Differential Optical Absorption Spectroscopy (DOAS) and air mass factor concept for a multiply scattering vertically inhomogeneous medium: Theoretical consideration,” Atmos. Meas. Techn. Discuss., vol. 3, no. 1, pp. 697–784, 2010. [12] C. Ruffin and R. King, “The analysis of hyperspectral data using Savitzky–Golay filtering—Theoretical basis,” in Proc. IEEE Int. Geosci. Remote Sens. Symp., 1999, pp. 756–758. [13] E. G. Learned-Miller and J. W. Fisher, “ICA using spacing estimates of entropy,” J. Mach. Learn. Res., vol. 4, pp. 1271–1295, Dec. 2003. [14] M. van der Baan, “PP/PS wavefield separation by independent component analysis,” Geophys. J. Int., vol. 166, no. 1, pp. 339–348, Jul. 2006. [15] M. Plumbley, “Algorithms for nonnegative independent component analysis,” IEEE Trans. Neural Netw., vol. 14, no. 3, pp. 534–543, May 2003. [16] “U.S. Standard Atmosphere,” U.S. Gov. Printing Office, Washington, D.C., USA, 1976. [17] K. Bogumil et al., “Measurements of molecular absorption spectra with SCIAMACHY pre-flight model: Instrument characterization and reference data for atmospheric remote-sensing in the 230–2380 nm region,” J. Photochem. Photobiol., vol. 157, no. 1–3, pp. 167–184, May 2003. [18] A. Richter et al., “Satellite measurements of NO2 from international shipping emissions,” Geophys. Res. Lett., vol. 31, no. 23, 2004, Art. ID. L23110.