Partially scanned interferogram methodology applied to IASI for the retrieval of CO, CO2, CH4 and N2O

Giuseppe Grieco; Guido Masiello; Marco Matricardi; Carmine Serio

doi:10.1364/OE.21.024753

1. Introduction

Fourier Transform Spectroscopy with Partially Scanned Interferograms (PSI) for the retrieval of trace gases from Infrared Atmospheric Sounding Interferometer (IASI [1]) observations has been recently investigated by [2–5]. PSI is used to compute the difference between spectra of atmospheric radiances at two different spectral resolutions. This differentiation of the spectrum acts as a high pass filter, which eliminates from the spectrum the low pass components, which include the surface emission in atmospheric window spectral regions. This property is particularly useful for nadir-looking instruments, where we need to separate the atmospheric windows emission component, which conveys information about atmospheric gases in the lower troposphere, from the surface emission.

PSI was first introduced by [6] for the retrieval of atmospheric parameters. Later on, [7] proposed a correlation interferometer for the observation of atmospheric trace gases, whereas [8] further analysed and applied the PSI methodology to the direct inversion of small segments of interferometric radiances for the purpose of temperature retrieval.

When we apply PSI to the retrieval of total column amounts of trace gas species we exploit what is known as the multiplex or Fellgett gain of Fourier transform spectrometers. Each single interferogram sample is a linear combination of the entire set of spectral radiances forming the original spectrum. The peak contribution to top of atmosphere radiances comes from altitudes that change with wave number. Consequently, in the spectral domain we need to sample a relatively large portion of the spectrum if we want to retrieve information for an atmospheric column ranging from the Earth’s surface to the top of the atmosphere. Conversely, because in the interferogram domain each data point conveys information from any region of the spectrum, the vertical portion of the atmospheric column covered by any individual interferogram sample is much larger than the portion covered by any spectral sample at a given wave number. In addition, the IASI spectral sampling of 0.25 cm⁻¹ allows us to resolve the specific periodic patterns that characterize the spectra of linear molecules such as CO₂, CO and N₂O. Due to the properties of the Fourier transform, these periodic patterns in the spectra result in well defined sharp signatures in the interferogram. This means that a small interval of the interferogram domain contains most of the information contained in the whole radiance spectrum. For instance, CO₂ absorption lines are typically characterized by a regular spacing of ≈ 0.8 cm⁻¹, this results in a sharp resonance feature in the interferogram. The resonance can be found at an optical path difference equal to the inverse of two times the spacing, i.e. ≈ 0.63 cm.

Following the PSI approach, [3–5] developed an estimation statistical method, which is based on a polynomial regression between interferogram radiance and the total column amount (TCA) of the trace gas. This parametric approach is computationally fast because does not require the calculation of Jacobian derivatives and allowed us to achieve accuracies, at the level of the single IASI observation (which has a footprint of 12 km radius at nadir), of about ±9 ppmv for CO₂, ≈ ±16 ppbv for CO, ≈ ±0.1 ppmv for CH₄ and ≈ ±30 ppbv for N₂O [3, 5].

In this paper we show that the introduction of the use of Jacobian derivatives allows us to utilize a non-parametric approach where the radiative transfer equation is directly inverted through a conventional Least Squares estimation. Using this procedure we can achieve an estimate where the final accuracy has been improved by a factor between 3 and 10, depending on the molecule. The fast computation of the Jacobian derivatives has been made possible by improvements to our forward model for IASI, hereafter referred to as σ-IASI [9, 10]. These improvements have allowed us to run the code 100 times faster than the previous version.

The limb-sounding of upper and lower stratosphere trace species is amongst the main goals of many satellite missions, e.g. Atmospheric Chemistry Experiment [11], MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) of the European Space Agency [12]. The objective of this study is to apply our methodology to the retrieval of trace gases from IASI, which is a nadir-looking instrument, with improved accuracy and horizontal spatial resolution.

The subject of remote sensing of atmospheric minor and trace gases from nadir looking instruments on board polar satellites is not a new subject. The sensors used for this scope include the Japanese IMG (Interferometric Monitoring of Greenhouse Gases) [13], the American AIRS (Atmospheric Infrared Radiometer Sounder) [14–16], the European IASI [3, 17–24] and the Japanese GOSAT (Greenhouse Gases Observing Satellite) [25].

In this paper we offer a different perspective focusing on the use of the PSI methodology and documenting its capability of achieving columnar contents of trace gases with an unprecedented accuracy. The PSI methodology has been applied to IASI data recorded during July 2010 over the Mediterranean sea. The July 2010 period has been selected because of the weather pattern over the Mediterranean, which has been characterized by above normal surface temperatures associated to a relatively high frequency of blocking days. Likewise, a particularly long blocking event has been experienced over Western Russia that has lead to the occurrence of anomalously high temperatures over this region. Thus, we have decided to use our methodology to investigate whether the quiescent weather and the high temperatures could have resulted in any detectable behaviour in the concentration of the trace gases considered in this paper.

The state vector (surface temperature, temperature, H₂O and O₃ atmospheric profiles), which is needed to initialize the estimation procedure for the total column amount of traces gases, has been retrieved directly from IASI radiances, through the forward/inverse package that we call φ-IASI. The mathematical aspects and validation of φ-IASI have been discussed in detail in various publications [9, 10, 26–32]. Ancillary information used to constrain the retrieval of the atmospheric state vector has been obtained from the European Centre for Medium range Weather Forecasts (ECMWF) analyses, collocated in time and space with the IASI soundings.

The paper is organized as follows. In section 2 we describe the IASI data and the new aspects of our forward model σ-IASI, whereas the description of the basic methods used in the PSI approach is presented in sections 3. The retrieval methodology for CO₂, CO, CH₄ and N₂O is discussed in sections 3.1 and 3.2. Section 3.1 covers the case of CO₂ and is mainly intended to give an example of the overall retrieval methodology. Results obtained from the use of IASI data are presented for the aforementioned Mediterranean basin case study in section 4, where we also show a comparison to AIRS data and IASI retrievals obtained with variational approaches in the spectral domain [23, 24]. Finally, conclusions are drawn in section 5.

2. Data

IASI observations used in this work have been recorded during the entire month of July 2010 over the Mediterranean sea. We concentrate on clear sky, sea surface soundings. However, the retrieval methodology can be applied to any kind of surface.

IASI, which is flying on board the Metop-A/B (Meteorological Operational Satellite) platforms, has been developed in France by the Centre National d’Etudes Spatiales (CNES) and is the first of three satellites of the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) European Polar System (EPS). The IASI instrument [1] covers the spectral range from 645 to 2760 cm⁻¹ (3.62 to 15.50 μm), with a sampling interval Δσ = 0.25 cm⁻¹. Thus, each single spectrum is formed by 8461 data points or channels. The calibrated IASI interferogram extends from 0 to a maximum optical path difference of 2 cm. IASI is an across track scanning system with a swath range of ±48°20′. The scan movement is symmetric with respect to the nadir direction and results in a scan line with thirty footprint positions on the Earth’s surface. The effective field of view (EFOV) is the useful field of view at each scan position or footprint. Each footprint consists of a 2 × 2 matrix of instantaneous fields of view (IFOV). Any single IFOV has a diameter of 14.65 mrad, which corresponds to a ground resolution of 12 km at nadir assuming a satellite altitude of 819 km. The 2 × 2 matrix is centred on the viewing direction.

The IASI spectra were screened for cloud contamination using the IASI stand alone cloud detection algorithm developed by the authors [28–31]. After cloud detection, a total of 34719 IASI spectra were selected.

For comparison purposes we have utilized AIRS level 2 CO₂ products (AIRS version 5) for the same area and dates [33]. The data are not gridded and their horizontal spatial resolution is 90 km, which is coarser than the IASI 12 km resolution. For the case of CO, we have also used IASI data utilizing a different retrieval scheme. This is the scheme developed at LATMOS-ULB (Laboratoire d’Optique Atmosphérique - Université libre de Bruxelles) [23, 24]. LATMOS-ULB IASI Level 2 CO data for the whole month of July 2010 over the Mediterranean basin have been downloaded from the Atmospheric Chemistry Data Center [34] site.

Sea level July averages of CO₂, CH₄ and N₂O concentrations obtained from a number of Global Atmosphere Watch (GAW) (World Meteorological Organization) WMO stations located in the Mediterranean basin have been also used.

To specify the water vapour and ozone background vectors and covariance matrices utilized in the inversion of the IASI spectra, we have used ECMWF atmospheric analysis fields at 00:00, 06:00, 12:00 and 18:00 UTC during July 2010. The version of the ECMWF model which was operational at that time was characterized by a vertical discretization of the atmosphere into 91 pressure levels with the model top at 0.01 hPa and a horizontal truncation of T1279. This truncation corresponds to a grid spacing of about 16km or, equivalently, to a horizontal grid box of 0.141° × 0.141°. The vertical coordinates of the model are surfaces of constant pressure in the upper stratosphere and lower mesosphere whereas they follow the earth’s surface in the lower and mid-troposphere. In terms of vertical resolution (measured in geometric height), this is highest in the planetary boundary and lowest in the stratosphere and lower mesosphere. The analysis fields were extracted from the ECMWF archive at the full T1279 resolution, interpolated to a grid of points with a separation of 0.3° × 0.3° and then collocated in both space and time to the IASI soundings used in this study.

For T (temperature profile) and T_s (surface temperature) our IASI retrieval algorithm does not use the ECMWF analyses. These two parameters are first directly estimated from IASI observations with an Empirical Orthogonal Function linear regression procedure and, finally, simultaneously retrieved with the other parameters through iterations with a physical inverse scheme. This final physical retrieval step retrieves simultaneously the state vector (T, Q, O, T_s, ε), where Q is the water vapour mixing ratio profile (units of g/kg), O is the ozone mixing ratio profile (units of ppmv) and ε the surface emissivity spectrum. The most recent version of the scheme can be found in [32]. Trace gases are not retrieved at this stage, their retrieval is performed sequentially using the PSI scheme utilizing the state vector (T, Q, O, T_s, ε) previously estimated from IASI.

2.1. Forward model

Radiative transfer calculations are based on our σ-IASI model [9]. The σ-IASI package consists of a monochromatic radiative transfer computer code designed for the fast computation of spectral radiances and their derivatives (Jacobians) with respect to a set of geophysical parameters. In its original formulation σ-IASI uses a vertical grid of sixty atmospheric layers bounded by pressure levels ranging from 1050 to 0.005 hPa. The model is based on a look-up table of optical depths computed using the line-by-line code LBLRTM [35]. The current optical depth look-up table is based on LBLRTM version 12 released on January 2011 in conjunction with the water vapour continuum model MT CKD version 2.5.2 and the line file aer v3.0 [36]. The σ-IASI model parameterizes the monochromatic optical depths using a second order polynomial. At a given pressure, the optical depth for the generic i-th molecule, is computed according to

χ_{σ, i} = q_{i} (c_{σ, 0, i} + c_{σ, 1, i} T + c_{σ, 2, i} T^{2})

where T is the temperature, q_i the molecule concentration and c_σ,j,i with j = 0, 1, 2, are the regression coefficients which are obtained using a Least Squares procedure and are themselves stored in the optical depth look-up-table. For water vapour, unlike other gases, in order to take into account effects depending on the gas concentration, such as self-broadening, a bi-dimensional look-up-table is used [37]. Thus, for water vapour, identified with i = 1, the optical depths is calculated according to

χ_{σ, 1} = q_{1} (c_{σ, 0, 1} + c_{σ, 1, 1} T + c_{σ, 2, 1} T^{2} + c_{σ, 3, 1} q_{1})

The subscript σ indicates the monochromatic quantities. In the original version of σ-IASI [9], the monochromatic optical depth was computed and parameterized at the spectral resolution of 10⁻⁴ cm⁻¹. A recent analysis of the trade-off between accuracy and computational efficiency of the code has shown that this spectral sampling can be reduced without sacrificing the robustness and accuracy of the inverse scheme. The analysis has shown that for IASI, the optical depth can be averaged and re-sampled at the lower rate of 10⁻² cm⁻¹. This is referred to as lut-coarse (look-up-table-coarse) sampling in contrast to the lut-fine sampling of 10⁻⁴ cm⁻¹. Also, in the case of the lut-coarse sampling interval, the optical depth can be parameterized with a low order polynomial where the regression coefficients are obtained as explained below. For each species i we can define an equivalent optical depth χ_〈σ〉,i, which can be parameterized with respect to temperature in the same way we do for lut-fine sampled quantities (Eqs. (1) and (2)). The equivalent optical depth is

χ_{〈 σ 〉, i} = q_{i} (c_{〈 σ 〉, 0, i} + c_{〈 σ 〉, 1, i} T + c_{〈 σ 〉, 2, i} T^{2})

where the angular brackets, 〈·〉 indicates the average operation over the wave number. In Eq. (3) the equivalent coefficients c_〈σ〉,j,i with j = 0, 1, 2, are obtained by fitting the layer transmittance averaged from the fine to the coarse spectral resolution

q_{i} (c_{〈 σ 〉, 0, i} + c_{〈 σ 〉, 1, i} T + c_{〈 σ 〉, 2, i} T^{2}) = - log (〈 τ_{σ, i} 〉) = - log [〈 exp (- χ_{σ, i}) 〉]

Due to the lut-coarse sampling and other optimizations, σ-IASI runs more than 100 times faster than the older version that used the fine-mesh look-up table. It is also to be stressed that the code with the lut-coarse sampling may not be appropriate for use in the upper stratosphere where the representation of the features of the CO₂ absorption would be as a result significantly degraded. The lut-coarse sampling does not affects, however, the results presented in this paper where we are mainly interested in the study of the lower atmosphere.

3. PSI basics and retrieval methodology

For a Fourier transform spectrometer such as IASI the quantity which is effectively measured is the interferogram, I(x), with x the OPD (optical path difference in units of cm). The spectrum, R(σ), with σ the wave number (in units of cm⁻¹) is recovered through a Fourier transform operation. For a calibrated, bandlimited spectrum, whatever its origin and measurement technique, the interferogram is simply computed as the Fourier transform of the symmetrized spectrum, r(σ)

I (x) = \int_{- \infty}^{+ \infty} r (σ) exp (2 π i σ x) d σ; with r (\pm σ) = {\begin{matrix} \frac{R (σ)}{2}; & σ_{1} < σ < σ_{2} \\ 0; & otherwise \end{matrix}

with i the imaginary unit and σ₁, σ₂ are the band endpoints. The bandwidth is σ₂ − σ₁ and both endpoints are positive. In this way, the interferogram can be thought of as a mathematical tool which can be applied to any kind of spectrum, either measured with a radiometer or an interferometer. A partial interferogram, I(x); x₁ ≤ x ≤ x₂, is the interferogram over a given optical path difference interval with endpoints, x₁ and x₂, respectively. Details about the properties of the partial interferogram can be found in [3]. For the present analysis, these properties are well illustrated by the case for CO₂ whose periodic pattern of absorption lines, superimposed on vibrational transitions, yields a typical interferogram resonance around x = 0.65 cm. This resonance is plotted in Fig. 1, which shows a typical interferogram for a tropical IASI sounding. The interferogram has been obtained by considering the IASI band 1 (645 to 1210 cm⁻¹) alone. In this band we have the ν₂ fundamental absorption band of CO₂ and the hot bands in the atmospheric window. It is important to stress that the partial interferogram shown in Fig. 1 conveys information from the entire IASI band 1. This means that due to the spectral characteristics of CO₂ lines, all the IASI band 1 information on CO₂ emission is compressed in a relatively small interval in the interferogram domain. This is all the more evident when we consider the sensitivity of the partial interferogram to the concentration of CO₂. The sensitivity is computed as the Jacobian derivative of the interferogram radiance, J_I with respect to the CO₂ atmospheric profile, that is

J_{I} (x, p) = \frac{\partial I (x)}{\partial q_{{CO}_{2}} (p)}

where q_CO₂ (p) (with p the pressure) is the mixing ratio profile of CO2. The Jacobian derivative is shown in the mesh surface of Fig. 2 for the range of OPD around the CO₂ resonance. From this figure we see that the sensitivity of I(x) to CO₂ extends throughout the entire atmospheric column, down below to the planetary boundary layer.

Fig. 1 a) IASI band 1 spectrum for a tropical sounding; b) its interferogram; c) partial interferogram over the range 0.6–0.7 cm, which evidences the beating due to the CO₂ line emission structure. The spectrum is in radiance units (1 r.u.=1 W m⁻² sr⁻¹ (cm⁻¹)⁻¹); the interferogram is in interferogram units (1 i.u.= 1 W m⁻² sr⁻¹).

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Fig. 2 Mesh surface of J_I: the Jacobian derivative of the interferogram radiance with respect to mixing ratio profile of CO₂ (1 i.u.= 1 W m⁻² sr⁻¹).

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3.1. The case of CO₂

For the retrieval of the total column amount of CO₂, we consider the partial interferogram which extends from x₁ = 0.55 cm to x₂ = 0.75 cm. This interferogram is derived from IASI radiances in band 1, which covers the range from 645 to 1210 cm⁻¹. The partial interferogram is shown in Fig. 3 for the case of a typical tropical air mass. The contribution to the signal due to the potential interfering molecules H₂O and O₃ is also shown in the figure. For the generic interfering factor, X, the contribution to the interferogram is computed by considering the difference, I(x) − I_X (x), where I(x) is the interferogram with the full state vector, and I_X (x) that with the state vector where X has been set to zero. It is seen that within the range 0.55–0.75 cm the interferogram signal is mostly due to CO₂. The effect of H₂O is significant, whereas that of O₃ can be considered to be an effect of second order.

Fig. 3 (left) Exemplifying the partial interferogram used for the retrieval of CO₂. The figure also shows the signal contributed from two possible interfering atmospheric gases (1 i.u.= 1 W m⁻²sr⁻¹). (right) Reference mixing ratio profiles for the trace gases analyzed in this paper.

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For the specific case of IASI, the number of interferogram samples within the range 0.55–0.75 cm is N = 227. Let I be the interferogram vector, I = (I₁,..., I_N)^T), where the super-script T stands for transpose and I_j stands for I(x_j), j = 1,...,N and let v = (q_CO₂, T, Q, T_s)^T be the state vector. We develop the interferogram in a Taylor series around a reference state vector, v_o truncated at the first order term,

I = I_{o} + J_{{CO}_{2}} (q_{{CO}_{2}} - q_{{CO}_{2}, o}) + J_{T} (T - T_{o}) + J_{Q} (Q - Q_{o}) + J_{s} (T_{s} - T_{so})

where, as usual, as before T_s is the surface temperature, T the temperature profile, Q the water vapour profile and q_CO₂ the CO₂ profile. The reference state vector, v_o, apart from the CO₂ profile, is that determined by physical inversion of the same IASI spectrum as that we use for the final retrieval of CO₂. The Jacobian derivatives are computed as usual at the reference state vector.

Because the reference atmospheric state v_o has been itself retrieved by using IASI observations, the assumption of linearity is reasonable, unless the retrieval failed. In addition, we do not need at this stage to retrieve the fine structures of the vertical profiles of T and Q. These parameters are included, along with T_s, to avoid that their residual uncertainty could bias the final estimate of the total column amount of CO₂. For this reason we assume that the true and the reference atmospheric parameters may be different up to a scaling factor, that is

\begin{array}{l} T_{s} = (1 + f_{T_{s}}) T_{so}; & T = (1 + f_{T}) T_{o} \\ Q = (1 + f_{Q}) Q_{o}; & q_{{CO}_{2}} = (1 + f_{{CO}_{2}}) q_{CO 2, o} \end{array}

With this assumption, Eq. (7) simplifies in

\begin{array}{l} I - I_{o} = a_{1} f_{{CO}_{2}} + a_{2} f_{T} + a_{3} f_{Q} + a_{4} f_{T_{s}} \\ a_{1} = J_{{CO}_{2}} q_{{CO}_{2}, o}; a_{2} = J_{T} T_{o}; a_{3} = J_{Q} Q_{o}; a_{4} = J_{s} T_{so} \end{array}

The four vectors a₁, a₂, a₃, a₄ are of size N, the same as the vector I. They can be horizontally concatenated to form the matrix, A = (a₁, a₂, a₃, a₄) of size N × M, where M = 4 is the number of scaling factors in Eq. (9). Then, Eq. (9) can be written as

Y = I - I_{o} = Af; with f = {(f_{{CO}_{2}}, f_{T}, f_{Q}, f_{T_{s}})}^{T}

In Eq. (10) we have M = 4 unknowns and N = 227 observations, therefore we can use Least Squares to seek for an optimal solution. We have checked that no further constraints have to be considered to get an estimate f̂ of f and its covariance matrix, S_f̂, therefore we can use unconstrained Least Square, this is important because it means that the final solution is not biased,

\hat{f} = {(A^{T} S_{I}^{- 1} A)}^{- 1} A^{T} S_{I}^{- 1} Y; and S_{\hat{f}} = {(A^{T} S_{I}^{- 1} A)}^{- 1}

where S_I is the observational covariance matrix of the interferometric radiances. The observational covariance matrix, S_I has been constructed by considering that for the IASI spectrum, S_R, which, in turn, is constructed on the basis of IASI radiometric noise. S_R is non-diagonal because the IASI spectrum is apodised. The transformation of S_R to S_I has been performed taking correctly into account the apodisation effect.

Finally, an estimate q̄_CO₂ of the total column amount of CO₂ is obtained by

{\bar{q}}_{{CO}_{2}} = (1 + {\hat{f}}_{{CO}_{2}}) \int_{p_{g}}^{0} q_{{CO}_{2}} (p) d p = (1 + {\hat{f}}_{{CO}_{2}}) {\bar{q}}_{{CO}_{2}, o}

where p_g is the ground pressure and with q̄_CO₂,o the total column amount of the CO₂ reference profile. The accuracy, e_CO₂ of the estimate is given by

e_{{CO}_{2}} = \sqrt{S_{\hat{f}} (1, 1)} {\bar{q}}_{{CO}_{2}, o}

We should observe that in the retrieval procedure we also need a reference mixing ratio profile of CO₂ for the retrieval algorithm. Using the same approach as that shown in [3], we have checked that the choice of either an uniform CO₂ profile (constant mixing ratio with the altitude) or a non-uniform profile is not critical. This sensitivity check has been performed by considering retrievals obtained with uniform profiles with a fixed mixing ratio value of 385 ppmv (see Fig. 3) and non-uniform CO₂ profiles obtained from ECMWF analysis (e.g., see Fig. 2 in ref [3]) colocated in time and space with the JAIVEx soundings. As a result we have a difference, (non-uniform)-(uniform), which does not exceed +1 ppmv.

The various scaling factors which are determined within the retrieval scheme also provide a good quality check of the final solution. We do not expect dramatic variations in the values corresponding to T_s, T and H₂O. The reference atmospheric parameters have been obtained by a physical inversion of the same spectra we use to retrieve CO₂. In case we find large variations, it is likely that the retrieval has failed due to some unknown source of additional error, most likely cloudiness. For temperature we expect at most to have variations below ±1 K, for water vapour we could expect some larger deviation from the reference, because the IASI retrieval may have a large uncertainty in the lower troposphere. However, variation larger than 20% are suspicious and the retrieval is flagged as of poor quality in this case.

To demonstrate the PSI methodology, we have applied it to a set of 22 clear sky, sea surface IASI soundings which were recorded during the 2007 JAIVEx experiment [38], which took place in the Gulf of Mexico. This set of IASI spectra has been already used to check the PSI retrieval for CO₂ by [3], which the reader is referred to for further details. Six of this spectra are nadir view spectra, whereas the remaining 16 correspond to an angle of ≈ 22.5°. Furthermore, the spectra have been recorded on different days. Six (those at nadir) on 29 April 2007, sixteen on 30 April 2007. For that period the global average value for CO₂ was 384.10 ppmv, according to the NASA Earth System Monitoring Laboratory (Global Monitoring Division) [39]. For the JAIVEx experiment, the reference atmospheric state, consisting of (T_s, T, Q, O) was retrieved by initializing the physical scheme with a first guess obtained by EOF regression. From a comparison with in situ dropsonde observations, we know that the final results for H₂O were determined with an accuracy not better than 15%. In contrast, the accuracy for T_s was within ±0.5 K and that for the temperature profile was within ±1 K in layers of 1 km width in the lower troposphere [32]. Figure 4 shows the retrieved values of q̄_CO₂ corresponding to the 22 IASI soundings. It is seen that the accuracy, computed through Eq. (13) of the estimate is ±3 ppmv (that is better than 1%) at the level of the single IASI IFOV, hence at a spatial resolution of 12 km. The average of the retrieval for 29 April 2007 is (383.0 ± 1.2) ppmv, whereas that for 30 April 2007 is (382.2 ± 0.8) ppmv to be compared to the global average value of 384.10 ppmv for that period. It is important to note that if we consider the standard deviation of the retrieval shown in Fig. 4 we get the value of ±3 ppmv, which is equal to the accuracy of each single observation. In other words, the variability we see in Fig. 4 is that of the random error of the IASI observations and is not due to an additional unknown source of random noise or bias. To further check the quality of the retrieval it is also interesting to look at the behaviour of the four scaling factors. These are shown in Fig. 4. It is seen that the effect of T_s and T is marginal. The scale factor for the skin temperature is almost zero, which attests to the accuracy of the reference value used for T_s in our scheme. The scaling for the temperature profile is in any case below 1%, which again is a sign of the quality of the reference we used for the retrieval. Conversely, as expected, the effect of H₂O is more conspicuous and the related scaling factor can attain variations as large as 14%.

Fig. 4 (left) Retrieved CO₂ for the JAIVEx experiment; (right) retrieved scaling factors for the JAIVEx experiment.

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Finally, the problem of the interdependence between the total column amount of CO₂ and the temperature profile is addressed. First, we note that through the scaling factor, f_T we retrieve a bulk temperature of the atmosphere and not a detailed temperature profile. The fact that we have independent information for both f_T and f_CO₂ is evidenced by the existence of the unconstrained Least Squares solution we get through Eq. (11). A strong interdependency between the two parameters f_T and f_CO₂ would yield a Kernel A highly ill-conditioned. However, normally the conditioning number of this Kernel is below 100, which means that the linear system expressed by Eq. (10) is made up with equations, which are largely independent. The interdependency between atmospheric parameters can be also analysed by looking at the a-posteriori covariance matrix, S_f or better at the correlation matrix, C_f defined according to

C_{f} (i, j) = \frac{S_{f} (i, j)}{\sqrt{S_{f} (i, i), S_{f} (j, j)}} i, j = 1, \dots, M = 4

Keeping in mind the definition of the f-vector in Eq. (10), a typical example of the correlation matrix C_f is shown in Eq. (15) below

C_{f} = (\begin{matrix} 1.000, & - 0.14, & 0.130, & - 0.49 \\ - 0.14, & 1.000, & 0.850, & 0.540 \\ 0.130, & 0.850, & 1.000, & 0.260 \\ - 0.49, & 0.540, & 0.260, & 1.000 \end{matrix})

From the first row of this matrix we learn that the correlation of the CO₂ total column amount with temperature and water vapour is very poor: the correlation is −0.14 with temperature and 0.13 with water vapour. Furthermore, these two correlations have opposite sign and tend to cancel out. In contrast, the correlation with surface temperature reaches the value of −0.5. This result says that for the retrieval of the total column amount of CO₂ a good reference value of the surface temperature is much more critical than a good reference value for temperature and water vapour profiles. Also from Eq. (15), second row, we note a relatively high interdependency between T and Q, and T and T_s.

In summary, for the retrieval scheme we have developed the interdependence between temperature profile and the total column amount of CO₂ is not a major concern, a source of possible bias is much more linked to T_s, for which we need a good reference value to initialize the inverse scheme to retrieve q̄_CO₂.

3.2. The case of CO, N₂O and CH₄

The retrieval methodology developed for CO₂ has been also applied to CO, N₂O and CH₄. Of course, the partial interferogram depends on the given gas and is selected in order to minimize interfering effects from other species.

For the case of CO, a linear molecule, its spectrum (at the IASI spectral resolution) has regularly spaced spectral lines in the atmospheric window between 2080 and 2200 cm⁻¹. The line spacing is ≈ 2 cm⁻¹ in the spectral domain, which yields a resonance in the interferogram space at the inverse of two times the line spacing, that is 0.25 cm. The partial interferogram we use for CO total column amount retrieval is obtained by Fourier transforming the IASI band 3 alone. The interferogram interval extends from 0.2230 to 0.3118 cm and is shown in Fig. 5(a) for the case of a tropical model of atmosphere. At the IASI sampling interval, we have a total of N = 136 data points. In this range, apart from the ubiquitous presence of water vapour, CO is the most important contributors to the spectrum, with N₂O and O₃ playing a secondary role.

Fig. 5 Partial interferogram used for a) CO, b) N₂O and c) CH₄. (1 i.u.= 1 W m⁻²sr⁻¹).

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N₂O is a linear molecule as well, with regularly spaced absorption lines at the spectral IASI resolution. The main N₂O absorption bands (ν₁ and ν₃ absorptions bands) are located in IASI band 1, 2 and 3. For this reason, to take advantage of the contribution from all lines, the interferogram from N₂O is obtained by Fourier transforming the whole IASI spectrum (band 1, 2 and 3). The partial interferogram for N₂O is shown in Fig. 5(b) and extends over two separate intervals from 1.0459 to 1.0499 cm and 1.1220 to 1.1270 cm, respectively, for a total of 40 data points. N₂O is the most difficult gas to retrieve. Its ν₁-absorption band overlaps that of methane at 1306.6 cm⁻¹, and the ν₃ in the short-wave region overlaps that of CO₂. The partial interferogram range we have selected is the only short portion of the whole interferogram where the main contributor is N₂O, whereas the contribution from interfering species, especially by CH₄ is minimized.

Finally, CH₄ is present in the IASI band 2 (ν₄ absorption band centred at 1306.2 cm⁻¹). Methane is not a linear molecule, however its spectrum also generates (at IASI spectral resolution) a characteristic wave-like structure in the interferogram domain. For the purpose of the retrieval of the total column amount of CH₄, the interferogram has been obtained by considering only the IASI band 2, which limits potential interfering effects mostly to N₂O alone. The partial interferogram we have selected for the retrieval of CH₄ is shown in Fig 5(c). It extends from 0.7399 to 1 cm for a total of 412 data points. In this range the contribution from N₂O is nearly zero.

The reference profiles we use for CO, CH₄, N₂O and CO₂ as well are summarized in Fig. 3. The total column amount from the reference profile yields 109 ppbv for CO, 306 ppbv for N₂O and 1646 ppbv for CH₄.

As for CO₂ we have that the sensitivity of our retrieval methodology extends to a large portion of the troposphere. Normally, the lower troposphere, which extends from 1000 to ≈ 800 hPa shows a very poor sensitivity, mostly for CH₄ and N₂O, as it is possible to see from Fig. 6, which shows mesh surfaces of the Jacobian derivative of the interferogram radiance with respect to the volume mixing ratio of CO, N₂O and CH₄, respectively.

Fig. 6 Jacobian derivative of I(x) with respect to the volume mixing ratio of CO (left); N₂O (middle); CH₄ (right) (1 i.u.= 1 W m⁻²sr⁻¹).

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For the set of 22 IASI spectra from the JAIVEx experiment, Fig. 7 shows the retrieval for the total amount of CO, N₂O and CH₄, respectively. The accuracy of the retrieval for a single IASI observations is ≈ ±1.5 ppbv, ≈ ±13 ppbv and ≈ ±0.015 ppmv respectively for CO, N₂O and CH₄. Figure 7 shows that the retrieval is largely in agreement with the global annual cycle of CO, CH₄ and N₂O, respectively (e.g., [40]). In addition, as already found for the case of CO₂, we also have that the standard deviation of the retrieved values for CH₄ and N₂O perfectly parallels the accuracy assessed trough the retrieval covariance matrix, Eq. (11), that is ±15 ppbv for CH₄ and 13 ppbv for N₂O. For CO the standard deviation is 3 ppbv, which is about two times the accuracy. This is quite compatible with the high variability of this atmospheric gas.

Fig. 7 Retrieval analysis for the JAIVEx experiment. a) CO; b) N₂O; c) CH₄.

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4. Application to IASI for the Mediterranean sea

To check the quality and reliability of the retrieval algorithm for trace gases when applied to a large set of IASI data, we have focused on the Mediterranean basin for the period of July 2010. We have a total of 34719 IASI soundings, which have been checked for clear sky using the IASI stand alone cloud detection scheme described in [28–31]. Each IASI sounding has been inverted for T_s and T, Q, O. These parameters have been used as the reference state in the sequential retrieval for trace gases.

The maps for the four trace gases considered in this study are shown in Fig. 8. The original IASI retrieval has been smoothed with a Wiener filter [41] and projected on 0.5×0.5 deg (lat × lon) grid. To a variable degree, all maps shows a positive gradient into the direction North-West to South-East. This is in agreement with the general circulation over the Mediterranean sea for the month of July. For the case of CO₂ we have that the total column amount is distributed over a range of values form 380 to 390 ppmv, with an average of 384.8 ppmv. This can be compared to the global average value of the annual cycle for the month of July 2010, which according to the NASA Earth System Monitoring Laboratory (Global Monitoring Division) [39] is equal to 387.21 ppmv.

Fig. 8 July 2010 maps derived from IASI soundings. From top left, clockwise, total column amount of CO₂, CO, CH₄ and N₂O, respectively.

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The average values for CH₄, N₂O, and CO are 1926 ppbv, 313 ppbv and 88 ppbv, respectively. The value observed for CH₄ is a bit higher of that credited to this gas from ground based observations at mid-latitude, that is 1874 ppbv [40], whereas for N₂O our average concentration of 313 ppbv is slightly smaller than the global value, which is 324 ppbv [40]. These differences have to be expected when we compare sea surface measurements with satellite observations, which are not sensitive to the planetary boundary layer (e.g. see Fig. 6). The observed differences just says that the volume mixing ratio of both N₂O and CH₄ is not uniform with the altitude. For N₂O aircraft observations tend to confirm that the concentration of N₂O in the boundary layer is some 10–15 ppbv larger than that in the open troposphere [42].

For the case of CO, we have to say that this is a gas which has a large time and space variability, so that the comparison with sea surface values makes less sense. What we can say is that sea surface observations also show a pronounced annual cycle with its minimum in the summer season. Also, aircraft records show that the summer vertical spatial distribution of CO concentration has a rapid decrease from the boundary layer to the free troposphere [43]. This behaviour is in agreement with our retrieval. We also stress that our CO retrieval results are in excellent agreement with those obtained with the LATMOS-ULB algorithm [23, 24]. The comparison to our CO retrievals is shown in Fig. 9. The LATMOS-ULB mean value for the month of July is 89.4 ppbv with a variability of 9.08 ppbv over the basin. This figure can be compared to our figure of 88.2 ppbv for the mean and 7.20 ppbv for the variability. The slightly lower mean and variability obtained using our retrieval is likely to be a result of the use of a more stringent cloud mask in the processing of the IASI data. Nevertheless, the two maps plotted in Fig. 9 show remarkably consistent features and display the same horizontal spatial gradients.

Fig. 9 July 2010 maps derived from IASI soundings. LATMOS-ULB retrieval scheme (left); this study (right).

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For the CO₂ case we have carried out a comparison with AIRS CO₂ level 2 products by projecting IASI and AIRS CO₂ fields on the same 2 × 2 deg (lat × lon) grid. Results are shown in the maps plotted in Fig. 10. It is evident that the results shown in the AIRS map display all the elements of a random behaviour. Furthermore, the AIRS CO₂ level 2 data give an average value of 391.5 ppmv with a variability (standard deviation) of 2.8 ppmv. This means that, even taking into account its variability, the AIRS estimate of the average value exceeds both the value of the annual cycle for the month of July (387.21 ppmv) and the annual trend for 2010 (388.58 ppmv [39]). In contrast, our scheme retrieves an average value of 384.8 ppmv, which, within a variability of 4.8 ppmv, is in agreement with both the cycle and the trend. Besides, this variability of 4.8 ppmv is not just random. It reflects a North-to-South gradient as shown in Fig. 10. This pattern is absent in the AIRS results which clearly show that the variability of the retrieval is fundamentally random.

Fig. 10 CO₂ monthly map on 2 × 2 deg grid. Left, IASI. Right, AIRS.

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As shown in Fig. 10, the North-to-South gradient retrieved by the IASI PSI scheme is in agreement with the observations of CO₂ and CH₄ at the sea surface level obtained from the GAW WMO network for the month of July 2010. For the case of CO₂ it is interesting to see that the IASI PSI retrieval is capable of capturing the local minimum around Filokalia station (see Fig. 11). The capability of the PSI methodology of capturing the correct horizontal gradients is also evident in the case of methane. These results support our claim of being able to retrieve the concentration of trace gases to an unprecedented accuracy. Also, we note that the North-West to South-East gradient for CO₂ and CH₄ is in agreement with the known biogenic activity of the Mediterranean sea. In summer the North-West part of the sea is a sink for CO₂, whereas the South-East part behaves like a source [44].

Fig. 11 Comparison of IASI retrieval with observations at sea surface stations. CO₂ (left); CH₄ (right).

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5. Conclusion

We have demonstrated that the technique of partial correlation interferometry applied to IASI observations is capable of improving the accuracy of trace gas retrieval to the unprecedented values of ±3 ppmv for CO₂, ±13 ppbv for N₂O, ±1.5 ppbv for CO and, finally ±15 ppbv for CH₄ for each single IASI observation with a horizontal spatial resolution of ≈ 12 km. The analysis of IASI data over the relatively small basin of the Mediterranean sea has shown that we can retrieve relatively small scale structures. This has allowed us to detect for the first time a summer North-West to South-East gradient in the concentration of trace gases of climatological importance. The pattern of CO₂ is consistent with the known biogenic activity of the Mediterranean sea in July. The global monthly maps of methane, carbon monoxide, carbon dioxide and nitrous oxide retrieved using IASI data are consistent with the known annual cycles of these trace gases. As an example, we were able to detect the strong decrease of carbon monoxide concentration in July, when the concentration of this gas in the open troposphere goes below 100 ppbv. It has also to be stressed that our scheme is a physical-based algorithm, which exploits the capability of the σ-IASI forward model to compute analytical Jacobian derivatives. Examples of analytical Jacobian have been provided that show the sensitivity of IASI to the vertical concentration of trace gases. Because of this capability, our scheme can be easily generalized to retrieve also information along the vertical. However, the important aspect of the present methodology is that it is based on unconstrained Least Square, which yields unbiased results. If we want to move to the retrieval of vertical profiles, we will need additional constraints, which inevitably will add bias to the final solution. To conclude, the vertical spatial resolution and the magnitude of the bias will depend on the background constraint, an effect which will be investigated in future work.

Acknowledgments

IASI has been developed and built under the responsibility of the Centre National d’Etudes Spatiales (CNES, France). It is flown onboard the Metop satellites as part of the EUMETSAT Polar System. The IASI L1 data are received through the EUMETCast near real time data distribution service. We thank Dr Stuart Newman (Met Office) for providing the JAIVEx data. The ground based measurements in Lampedusa and Sede Boker have been provided by NOAA/ESRL and have been downloaded from (http://www.esrl.noaa.gov/gmd/dv/iadv/). The ground based measurements in Begur and Finokalia have been provided by Laboratoire des Sciences du Climat et de l’Environnement (http://www.lsce.ipsl.fr/). The ground based measurements in Cairo have been provided by the Egyptian Meteorological Authority (http://ema.gov.eg/). The ground based measurements in Lampedusa for what concerns N₂O have been provided by the Italian Agency ENEA. Work supported by project Ritmare-Ricerca Italiana per il Mare (CNR-MIUR)

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Partially scanned interferogram methodology applied to IASI for the retrieval of CO, CO₂, CH₄ and N₂O

Abstract

1. Introduction