# IASI's sensitivity to near-surface carbon monoxide (CO): Theoretical analyses and retrievals on test cases

Sophie Bauduin, Lieven Clarisse, Michael Theunissen, Maya George, Daniel

Hurtmans, Cathy Clerbaux, Pierre-François Coheur

► To cite this version:

Sophie Bauduin, Lieven Clarisse, Michael Theunissen, Maya George, Daniel Hurtmans, et al. IASI's sensitivity to near-surface carbon monoxide (CO): Theoretical analyses and retrievals on test cases. Journal of Quantitative Spectroscopy and Radiative Transfer, 2017, 189, pp.428-440. 10.1016/j.jqsrt.2016.12.022. insu-01422581

HAL Id: insu-01422581

https://insu.hal.science/insu-01422581v1

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# IASI's sensitivity to near-surface carbon monoxide (CO): Theoretical analyses and retrievals on test cases

Sophie Bauduin<sup>a</sup>, Lieven Clarisse<sup>a</sup>, Michael Theunissen<sup>a</sup>, Maya George<sup>b</sup>, Daniel Hurtmans<sup>a</sup>, Cathy Clerbaux<sup>a,b</sup>, Pierre-François Coheur<sup>a</sup>

<sup>a</sup>Université libre de Bruxelles (ULB), Atmospheric spectroscopy, Service de Chimie Quantique et Photophysique CP 160/09, Avenue F.D. Roosevelt 50, Bruxelles, Belgium.
<sup>b</sup>LATMOS/IPSL, UPMC Univ. Paris 06 Sorbonne Universités, UVSQ, CNRS, Paris, France

## Abstract

Separating concentrations of carbon monoxide (CO) in the boundary layer from the rest of the atmosphere with nadir satellite measurements is of particular importance to differentiate emission from transport. Although thermal infrared (TIR) satellite sounders are considered to have limited sensitivity to the composition of the near-surface atmosphere, previous studies show that they can provide information on CO close to the ground in case of high thermal contrast. In this work we investigate the capability of IASI (Infrared Atmospheric Sounding Interferometer) to retrieve near-surface CO concentrations, and we quantitatively assess the influence of thermal contrast on such retrievals. We present a 3-part analysis, which relies on both theoretical forward simulations and retrievals on real data, performed for a large range of negative and positive thermal contrast situations. First, we derive theoretically the IASI detection threshold of CO enhancement in the boundary layer, and we assess its dependence on thermal contrast. Then, using the optimal estimation formalism, we quantify the role of thermal contrast on the error budget and information content of near-surface CO retrievals. We demonstrate that, contrary to what is usually accepted, large negative thermal contrast values (ground cooler than air) lead to a better decorrelation between CO concentrations in the low and the high troposphere than large positive thermal contrast (ground warmer than the air). In the last part of the paper we use Mexico City and Barrow as test cases to contrast our theoretical predictions with real retrievals, and to assess the accuracy of IASI surface CO retrievals through comparisons to ground-based in-situ measurements.

Preprint submitted to Journal of Quantitative Spectroscopy and Radiative transfer December 13, 2016
*Keywords:* IASI, carbon monoxide, thermal contrast, vertical sensitivity, planetary boundary layer

# 1. Introduction

At a time when air quality is a major concern for our society, monitoring concentrations of pollutants is crucial. More particularly, measuring the vertical distributions of these gases is required to properly distinguish emission plumes from transported plumes, and to better understand their reactivity in the atmosphere. Satellite remote sensing measurements are optimally suited to this purpose because of their global coverage and high temporal frequency. Carbon monoxide (CO) is a good example to illustrate the need for vertically resolved measurements. As a primary pollutant, it is emitted at the surface from different sources [1], such as fossil fuel combustion and biomass burning. In the background atmosphere (i.e., not polluted by any local surface sources), CO is formed by methane oxidation. Its destruction leads to the formation of ozone ($O_3$) in the presence of nitrogen oxides ($NO_x$); it also produces carbon dioxide ($CO_2$). Because it reacts with the OH radical, CO has a direct impact on the oxidation capacity of the atmosphere [2]. Finally, because of its relatively long lifetime (a few weeks to a few months), CO can be transported on continental scale distances, which makes it an excellent atmospheric tracer [e.g., 3].

Nadir thermal infrared (TIR) satellite sounders have shown their ability to monitor the variability and trends of CO at global scale [e.g., 4, 5, 6, 7]. These instruments are known to present their maximum sensitivity in the mid-troposphere, and have a lower sensitivity close to the surface. This is linked to the generally low thermal contrast (TC) between the ground and the air above it. It has been previously shown though, that in cases of high TC, TIR instruments are able to observe CO close to the ground [7, 8, 9, 10, 11, 12]. The influence of TC on the capabilities of such instruments to measure near-surface CO has been up to now investigated mostly qualitatively, with no systematic assessment of the TC value needed to allow sensitivity near the ground. Moreover, only restricted TC values have been generally considered, mostly in the positive range. Less attention has been given to negative TC values, which have previously been shown to enhance IASI's sensitivity near the surface to short-lived species (sulfur dioxide and ammonia, [13, 14, 15]) and CO [15]. In contrast, negative TC values have been reported to have
small impact or even to degrade near-surface CO retrievals from MOPITT (Measurements of Pollution in the Troposphere) observations [9].

In this work, we investigate in a systematic and quantitative way the influence of thermal contrast on the capabilities of IASI (and, by extent, of other TIR instruments) to retrieve near-surface CO concentrations (see [16, 17] for details about the IASI instrument). First, we calculate the differences between spectra simulated for a variety of near-surface CO burdens and for a large range of TC values, and we explore the capability of IASI to detect the spectral signal coming from the near-surface CO enhancement (section 2). Then, using the optimal estimation formalism, we evaluate theoretically the influence of TC on the error budget and information content of CO retrievals from IASI observations (section 3). This second approach follows the one presented by [9] for the MOPITT instrument, but differs in the way of calculating averaging kernel functions (we do not perform retrievals in this case) and is performed for a significantly larger range of TC values. Lastly, we contrast our theoretical predictions with real retrievals performed over Mexico City and Barrow (section 4). The accuracy of these real retrievals is also assessed by comparison with ground-based in-situ measurements. All the forward simulations and retrievals of this work have been performed with the line-by-line Atmosphit software [18, 19], using most of the retrievals settings of the fast operational FORLI algorithm, developed at ULB for retrieving CO profiles from IASI observations in near-real time [20].

## 2. Radiative transfer and IASI sensitivity to near-surface CO

### 2.1. Radiative transfer theory

TIR radiative transfer describes the transmission of radiation emitted by the Earth through the atmosphere. This description takes into account the absorption and scattering by atmospheric constituents, and the thermal emission of the atmosphere itself. With a perfect knowledge of the atmospheric state, and by solving the radiative transfer equation, the upwelling radiance at the top of the atmosphere (TOA), $I^{\uparrow}(\tilde{\nu}, \theta, \text{TOA})$, can be calculated. Assuming local thermodynamic equilibrium and clear sky, the monochromatic upwelling radiance at the TOA measured by IASI can be expressed as [21]

$$ I^{\uparrow}(\tilde{\nu}, \theta, \text{TOA}) = I^{\uparrow}(\tilde{\nu}, \theta, 0) t(\tilde{\nu}, \theta, 0, \text{TOA}) + \int_{0}^{\text{TOA}} B(\tilde{\nu}, T) \frac{\partial t(\tilde{\nu}, \theta, z', \text{TOA})}{\partial z'} dz' \quad (1) $$
where $\theta$ is the zenith angle of the satellite, $I^{\uparrow}(\tilde{\nu}, \theta, 0)$ is the radiance emitted at the surface of the Earth at wavenumber $\tilde{\nu}$, $t(\tilde{\nu}, \theta, 0, \text{TOA})$ is the transmittance of the atmosphere, $t(\tilde{\nu}, \theta, z', \text{TOA})$ is the transmittance from the altitude $z'$ to TOA, and $B(\tilde{\nu}, T)$ accounts for the emission of the atmosphere, which is approximated as that of a black body at temperature $T$. Because we assume a non-scattering medium, the scattering contribution can be neglected. For simplicity, the angular and wavenumber dependences will be omitted hereafter.

Calculating the TOA radiance from equation 1 usually requires the discretization of the atmosphere in a number of layers, for which averaged parameters are calculated (temperature, pressure, and partial columns of molecular species, among other). The upwelling radiance is evaluated for each layer according to

$$I_i^{\uparrow} = B(\bar{T}_i) + (I_{i-1}^{\uparrow} - B(\bar{T}_i))\tilde{t}_i \quad (2)$$

where $I_i^{\uparrow}$ is the upwelling radiance at the top of layer $i$, $B(\bar{T}_i)$ is the emission of layer $i$ approximated as a black body at temperature $\bar{T}_i$. $\tilde{t}_i$ represents the effective transmittance of layer $i$, and is calculated as

$$\tilde{t}_i = \exp \left[ - \sum_j PC_{i,j} \sum_{j,k} \alpha_{j,k}(\tilde{\nu}, \bar{P}_i, \bar{T}_i) \right] \quad (3)$$

where $j$ refers to the molecular species and $k$ refers to the relevant absorption lines at the chosen $\tilde{\nu}$. $PC_{i,j}$ represents the partial column of the species $j$ in the layer $i$ and $\alpha_{j,k}(\tilde{\nu}, \bar{P}_i, \bar{T}_i)$ is the absorption coefficient of that species (cm$^2$/molecules) calculated for the mean parameters of layer $i$. A more detailed description of the radiative transfer implementation in Atmosphit can be found in [18] and [19].

## 2.2. Sensitivity to near-surface CO

The sensitivity of TIR sounders (IASI among them) to near-surface CO is largely driven by TC. We define TC as the difference between the temperature of the surface ($T_S$) and the mean temperature of the air in the first discrete layer ($\bar{T}_1$), calculated using the Curtis-Godson approximation [22, 23]. To illustrate the effect of TC on IASI's near-surface sensitivity, and following equation 2, we can express the change in radiation, $\Delta I$, after going through the first layer of a discretized atmosphere ($i = 1$) as

$$\Delta I = I_1^{\uparrow} - I_0^{\uparrow} = (1 - \tilde{t}_1)(B(\bar{T}_1) - B(T_S)) \quad (4)$$
where $B(T_S)$ is the emission of a black body at temperature $T_S$, calculated using Planck's function. Because we consider the surface to behave as a perfect black body (i.e., surface emissivity= 1), both the downwelling reflected term and the solar incoming term are zero. We can similarly express the emission of a black body at temperature $\bar{T}_1$ as $B(\bar{T}_1)$. Thus, equation 4 reveals the TC (the difference between $B(\bar{T}_1)$ and $B(T_S)$) in the right term. Three scenarios are possible, depending on the relative magnitudes of $T_S$ and $\bar{T}_1$:

1. $T_S = \bar{T}_1$; TC= 0

The radiance emitted by the atmospheric layer closest to the ground is equal to that of the ground ($\Delta I=0$). CO spectral features are absent in $I_1^\uparrow$ and, thus, retrieving CO in that layer is not possible.

2. $T_S > \bar{T}_1$; TC> 0

This is true in general for daytime observations. $\Delta I$ is negative; the outgoing radiance $I_1^\uparrow$ will show CO absorption lines.

3. $T_S < \bar{T}_1$; TC< 0

This is the scenario encountered for thermal inversion. $\Delta I$ is positive; the outgoing radiance $I_1^\uparrow$ reveals CO emission lines.

The TC directly influences the sensitivity of IASI to near-surface CO. The larger the absolute value of TC is, the larger $\Delta I$, and the better the sensitivity. The sensitivity also depends on the abundance of CO in the first layer, as expressed by the $1 - \tilde{t}_1$ term (the absorptance of the layer; see equation 3).

At global scale, CO is present in the whole troposphere, and IASI allows monitoring both polluted and background columns [7, 11]. Near-surface CO enhancements occur locally close to sources. Following the discussion above, it is instructive to evaluate the capability of IASI to detect such enhancements as a function of TC. To do this, spectra have been simulated for two representative atmospheres, under varying conditions of TC. We use two CO reference vertical profiles representative of background and polluted conditions, respectively. To simulate background conditions we use the single a priori profile utilized by the FORLI algorithm (Figure 1.a; [19]), derived from representative measurements and modeling results. The two reference profiles differ only in the 0–1 km layer, where the background VMR is scaled to build the polluted profile. A series of CO VMRs has been considered for the 0–1 km layer, leading to various polluted profiles. Figure 2 presents the range of CO VMRs considered at the surface for these (Table 1 includes the
corresponding 0–1 km mean VMRs). The forward simulations have been performed considering an atmosphere discretized in 1 km thick layers (0–60 km). The parameters chosen for these simulations are given in Table 1. From simulated spectra, a normalized radiance difference (NRD) is calculated as

$$NRD(\tilde{\nu}) = \frac{I^{\uparrow}(\tilde{\nu}, \theta, \text{TOA})_{\text{polluted}} - I^{\uparrow}(\tilde{\nu}, \theta, \text{TOA})_{\text{background}}}{RN(\tilde{\nu})} \quad (5)$$

where $I^{\uparrow}(\tilde{\nu}, \theta, \text{TOA})_{\text{polluted}}$ and $I^{\uparrow}(\tilde{\nu}, \theta, \text{TOA})_{\text{background}}$ are respectively the polluted and the background radiance spectra, for which the satellite zenith angle $\theta$ was set to 0°, and $RN(\tilde{\nu})$ is the IASI radiometric noise [16]. The NRD($\tilde{\nu}$) thus represents the difference in the spectral signal detected by IASI due to an enhancement of CO abundance in the 0–1 km layer relative to the noise. A NRD($\tilde{\nu}$) larger than 1 characterizes a situation for which IASI detects at wavenumber $\tilde{\nu}$ a spectral signature above its noise level, which is due to the enhancement.

A range of NRD values have been calculated by applying equation 5 to a number of cases using the following constraints: increasing TC values from -20 K to +20 K in 1 K steps, keeping the background CO profile fixed, and increasing CO VMR in the 0–1 km layer, according to the values shown in Figure 2. These conditions are summarized in Table 1. As an example, Figure 3.a represents the NRD values calculated for a CO enhancement of around 200 ppb in the 0–1 km layer as a function of TC, and Figure 3.b presents the NRD values calculated for TC=10 K as function of the CO enhancement. In Figure 3.a, NRD and TC have opposite signs: if the latter is positive (negative), absorption (emission) occurs in the 0–1 km layer and the NRD is negative (positive). For the example shown in Figure 3.a, we conclude that 200 ppb CO enhancement is detected by IASI from TC=3 K (absolute value) in most channels corresponding to the center of CO lines with low $J^1$ values (between 2080 and 2190 cm$^{-1}$). For weaker lines, mainly those at high J in both P and R branches, the detection is possible only for larger TC. As expected, in case of no thermal contrast, NRD is 0 and CO detection is not possible. For the example shown in Figure 3.b, for the strongest CO lines, if TC= 10 K, then IASI is capable of detecting CO enhancements around 80 ppb. This value has to be higher (> 150 ppb) for the weaker lines.

<footnote n="1">¹Quantum number that characterizes the rotational levels of a molecule.</footnote>
Such calculations are useful to infer a detection threshold for CO enhance-
ment in the boundary layer. To do this, for each IASI spectral channel and
for each TC value, the minimum CO enhancement resulting in a NRD larger
than 1 (i.e., CO enhancement signal greater than radiometric noise) was cal-
culated. The results are presented in Figure 4.a, plotted as a function of TC
and wavenumber. As expected, smaller CO enhancements can be detected
for larger TC, either positive or negative (note that in the next section, we
will show that the retrieval of independent information on the near-surface
CO concentration is favoured by large negative TC). For example, for most
channels centered on the strongest CO lines, if the absolute value of TC is
over 15 K, then IASI can detect near-surface CO enhancements below 60
ppb. When moving away from the line centers towards the line wings, the
CO enhancement threshold rapidly increases. For lower TC, the sensitivity
of IASI to near-surface CO decreases and only larger enhancements can be
detected.

The detection thresholds discussed above are defined for individual spec-
tral channel. We can expect lower thresholds if all the channels in the CO
band are used. We have estimated this new threshold (TH) following the
same method described above, but applying the more general relation [24]:

$$
TH = (\mathbf{K}_{01}^{\mathrm{T}} \mathbf{S}_{\epsilon}^{-1} \mathbf{K}_{01})^{-1} \qquad (6)
$$

where **K**<sub>01</sub> is the derivative of the TOA radiance with respect to CO in
the 0–1 km layer, and **S**<sub>ε</sub> is the covariance matrix of the measurement; the
diagonal elements of **S**<sub>ε</sub> represent the square of the measurement noise. T
indicates the transposed matrix. **K**<sub>01</sub>, calculated for each IASI channel in
the 2000–2250 cm<sup>-1</sup> spectral range, is a measure of the spectral response in
the 0–1 band of CO due to a given change in CO concentration in the 0–1
km layer. Figure 4.b shows *TH* as a function of TC. Consistent with what
was observed for a single channel, *TH* decreases for increasing TC (absolute
value). It drops below 10 ppb for TC larger than 10 K (absolute value),
which is significantly lower than the 80 ppb calculated for a single channel.
The detection threshold reaches very large values when TC approaches 0
(about 500 ppb), i.e., IASI hardly detect CO in the 0–1 km layer under these
circumstances.

The results presented above provide theoretical constraints on the capa-
bility of IASI to detect the radiance contribution of near-surface CO enhance-
ments. However, they rely on spectral differences and do not quantify the
sensitivity of individual measurements to near-surface CO. Moreover, they do not provide information on the IASI sensitivity to near-surface CO with respect to mid-tropospheric CO. While these tests are not sufficient to evaluate how many independent pieces of information can be retrieved from the measurements, they can be obtained using the optimal estimation method, as discussed in the next section.

### 3. Theoretical characterization of CO retrievals from IASI observations

#### 3.1. Inversion - optimal estimation method (OEM)

The radiative transfer equation (Eq. 1) can be expressed in a more general way as

$$y = F(\mathbf{x}, \mathbf{b}) + \epsilon \quad (7)$$

where $y$ is the vector of measured radiances, $\mathbf{x}$ is the atmospheric state vector containing the parameters to be retrieved, $\mathbf{b}$ represents fixed atmospheric variables (such as for example the spectroscopic parameters) that have an impact on the measured radiances, $\epsilon$ is the measurement noise and $F$ is the forward radiative transfer model. Atmosphit solves the inversion problem by using the optimal estimation method (OEM). The OEM aims at finding an approximate state vector $\hat{\mathbf{x}}$ of the true state $\mathbf{x}$ which is the most consistent with both the measurement and with the a priori atmospheric state $\mathbf{x}_a$ [24]. This is achieved by minimizing the following cost function

$$J = (y - F(\mathbf{x}, \mathbf{b}))^{\mathrm{T}} \mathbf{S}_{\epsilon}^{-1} (y - F(\mathbf{x}, \mathbf{b})) + (\mathbf{x} - \mathbf{x}_{a})^{\mathrm{T}} \mathbf{S}_{a}^{-1} (\mathbf{x} - \mathbf{x}_{a}) \quad (8)$$

where the error and a priori covariance matrices ($\mathbf{S}_{\epsilon}$ and $\mathbf{S}_a$, respectively) weight the contribution of the measurement and a priori atmospheric state in the derivation of $\hat{\mathbf{x}}$.

The OEM offers a very adequate framework to characterize the retrieval in terms of errors and vertical sensitivity, which can be used as diagnostics for the IASI sensitivity to near-surface CO. This characterization uses the total error covariance matrix $\hat{\mathbf{S}}$ associated with $\hat{\mathbf{x}}$ and the averaging kernels matrix $\mathbf{A}$, which can be calculated as [24]

$$\hat{\mathbf{S}} = (\mathbf{K}^{\mathrm{T}} \mathbf{S}_{\epsilon}^{-1} \mathbf{K} + \mathbf{S}_{a}^{-1})^{-1} \quad (9)$$

$$\mathbf{A} = (\mathbf{K}^{\mathrm{T}} \mathbf{S}_{\epsilon}^{-1} \mathbf{K} + \mathbf{S}_{a}^{-1})^{-1} \mathbf{K}^{\mathrm{T}} \mathbf{S}_{\epsilon}^{-1} \mathbf{K} \quad (10)$$
where **K** is the Jacobian matrix of the forward model, whose rows contain the derivatives of **y** with respect to the retrieved variables (CO in each vertical layer, in this case). The square root of the diagonal elements of **Ŝ** corresponds to the standard deviation of each retrieved variable in **x̂**. The **A** matrix represents the sensitivity of the retrieved state to the true state. Its rows define one averaging kernel function (AVK) for each variable. In case of the CO profile, for each retrieved layer, the averaging kernel functions peak at the altitude containing most information on the profile: the AVK thus provides an estimation of the altitude of maximum sensitivity. The trace of the **A** matrix, represents the number of independent pieces of information or degrees of freedom for signal (DOFS) in the retrieved profile.

## 3.2. Theoretical characterization of CO retrievals

Using Eq. (9) and (10) with specific precalculated Jacobians describing different TC conditions, we have derived theoretical **Ŝ** and **A** matrices. These can then be used to analyze the influence of TC on both error budget and information content of the retrieved CO profile. Table 2 summarizes the parameters used in the simulations. The atmosphere has been divided in 60 layers of 1 km thickness (0–60 km). The a priori profile and associated covariance matrix are the same as described in section 2.2 (Figure 1). Also the spectral range and noise constraint are the same as those used in FORLI. Accordingly, the results described next and summarized in Figure 5 are applicable to the characterization of the FORLI-CO products.

It is important to note that the precalculated Jacobians depend on the chosen settings (see Table 2). Thus, these results are strictly representative for retrievals made under these same conditions. However, the general patterns of the error budget and of the vertical sensitivity of IASI to near-surface CO retrievals are more general.

### 3.2.1. Reduction of prior uncertainty

The reduction of prior uncertainty for the 0–1 km CO column, calculated using the square root of the diagonal elements of the **Ŝ** and **S**<sub>a</sub> matrices, is shown Figure 5.a. The lowest reduction of uncertainty for the 0–1 km layer is around 20% and occurs for TC = −7 K. This reduction increases for increasing TC values (absolute value), and reaches 53% for TC = −20 K and even a larger value for TC = +20 K (the most extreme TC values considered). Note that the prior uncertainty is around 63%.
According to the results shown in section 2.2, one would have expected the lowest uncertainty reduction to occur for TC = 0 K. The fact that it is found at a non-zero TC value (-7 K) is explained by the correlation between layers, which is introduced in the a priori covariance matrix $S_a$ by the non-diagonal elements. To demonstrate this, we have calculated the reduction of prior uncertainty for the 0–1 km CO column considering a diagonal $S_a$ matrix (Figure 5.a). The results show that in the absence of correlation between the layers, the lowest error reductions occur near TC = 0 K, and are around 0%. This experiment shows that in case of no TC (hence with no physical information on the CO concentrations in the 0–1 km layer), the error reduction is brought by the correlation with the upper layers, where the sensitivity of IASI is larger. This correlation, and the dependence of the boundary layer sensitivity on the value of TC, is of crucial importance when analysing CO retrieved columns, their spatial distributions and time evolution. They are important as well to properly assess the values of the IASI surface CO measurements in comparison with co-located measurements (see section 4).

### 3.2.2. Near-surface sensitivity

In Figure 5.b, the 0–1 km AVK functions are represented for a series of TC conditions. Figure 5.b shows that for extreme TC values (e.g., -20 K, -15 K, +15 K and +20 K), these AVK peak at the surface (values respectively of 0.57, 0.42, 0.28 and 0.32), meaning that the maximal sensitivity is at the surface. Their values drop close to 0 above 3 km in case of negative TC and above 6 km in case of positive TC, showing some correlation with the upper layers. The surface value of the 0–1 km AVK decreases with decreasing TC (absolute value). For low TC, their maximal value is found higher in the atmosphere, showing that the IASI sensitivity to CO is maximal in the middle troposphere (most common case, [e.g., 7]). Most of the information on CO in the lowest layers is thus inferred from higher up in the atmosphere in case of low TC values, especially in the range -5 K to +5 K.

The total and 0–1 km DOFS values presented in Figure 5.c confirm that increasing TC values favour the sensitivity to surface CO. For large absolute values of TC, the total DOFS is close to 2, which means that we extract two independent pieces of information in the CO vertical profile. Figure 6 shows predicted averaging kernels (VMR/VMR) for three different TC values: -15 K (left), 0 K (middle) and 15 K (right). The right and left panels show that the AVKs peak at two different heights: close to the surface and in the 5-10
km range, consistent with two separate pieces of information. For $TC = -15$ K, these pieces seem to correspond to the 0–3 km and the 3–19 km mean VMRs. For $TC = +15$ K, they are the 0–5 km and the 5–19 km mean VMRs. The total DOFS decreases with decreasing absolute values of TC and drops to 1.23 at -5 K. The AVKs, shown in Figure 6.b for $TC = 0$ K, peak in case of no sensitivity at a single height (around 5 km), meaning that only one independent piece of information is retrieved, and this is consistent with the DOFS value. In this case, IASI would be mostly sensitive to CO in the mid-troposphere. As explained above, the smallest DOFS does not occur at $TC = 0$ K because of correlation between layers.

A similar behavior characterizes the 0–1 km DOFS (Figure 5.c), which reaches its largest values of 0.57 and 0.32 for respectively high negative and positive TC, and its smallest value at -4 K of TC.

An important result that comes out from this analysis is that large negative TC values allow the best decorrelation between the low and the high troposphere. This can be seen from the 0–1 km DOFS, and from the shape of the AVKs (Figure 6). This result seems to contradict what was said on negative TCs in [9] for MOPITT. However, in that study, the largest negative TC values considered were only around -10 K. We find, indeed, that error reduction and DOFS at $TC = -10$ K are worst than those at positive TC values of similar magnitude (Figure 5). The large decorrelation between the low and the high troposphere is found only for lower negative TC values and is due to the emission of radiation in the first atmospheric layers. This is illustrated in Figure 7.a and 7.b, which show the radiance contribution of the 0–1 km and 1–2 km layers to IASI spectrum for $TC = -15$ K. Absorption occurs in the higher layers of the troposphere (Figure 7.c and 7.d), and generally counterbalances the emission, resulting in net absorption at TOA, as shown in Figures 8.a and 8.b. Note however that, for $TC = -15$ K, some spectral features appear in emission; they correspond to $H_2O$ lines, for which the surface contribution is very large.

In summary, our simulations show that it is the transition from emission to absorption that brings the decorrelation between the low and the high troposphere. This is illustrated in Figure 7, and Figures 8.c and 8.d, which represent the Jacobians for $TC = -15$ K and $TC = +15$ K as a function of altitude. In case of high positive TC (Figure 8.d), the Jacobians are negative, which means that an increase of CO concentration increases the strength of absorption in the TOA spectrum. They have constant high values and shape from ground to 6–7 km of height; this means that an identical change in
CO concentration in one of these layers would produce a similar effect in the IASI spectrum. In other words, the IASI sensitivity to CO is almost constant from the ground up to 6–7 km in case of large positive TC. For TC = –15 K (Figure 8.c), there is clear contrast (at around 3 km) in the shape of the Jacobians between low (0–2 km) and mid-upper troposphere (> 3 km). Below 3 km, the Jacobians are positive due to emission in these layers (Figures 7.a and 7.b); an increase of CO concentration below 3 km decreases the strength of absorption in the TOA spectrum. Above 3 km, the Jacobians are negative due to the dominance of absorption; an increase in CO concentrations above 3 km increases the strength of absorption in the TOA spectrum. To sum up, a change of CO concentration below or above 3 km produces different spectral responses in the IASI spectrum. It is the latter, which comes from the transition between emission and absorption regimes, that allows decorrelating the low and the high troposphere in case of large negative TC.

**4. Test cases of near-surface CO retrievals**

In the previous section, CO retrievals from a IASI-type instrument were characterized theoretically, and retrieval errors for the 0–1 km mean VMRs were assessed. However, these theoretical errors depend on the constraint applied to the retrieval of the CO profile and are insufficient to evaluate the accuracy of IASI CO retrievals for real observations. To remedy this, we compared IASI near-surface retrievals to spatially and temporally co-located ground measurements. To include a large range of TC values, this evaluation is performed above two regions: Mexico City, which provides mostly positive TC cases, and Barrow (Alaska), which encounters large thermal inversions in winter. These are discussed separately in the following.

4.1. *Mexico City - Positive TC*

The region of Mexico City was chosen because: 1) it encounters persistent air pollution [25, 26, 27], 2) its TC encompasses a large range of values year-round, and 3) a dense local network of ground-based stations (RAMA, Red Automática de Monitoreo Atmosférico, http://www.aire.df.gob.mx) provides hourly measurements of various pollutants, CO among them [28]. In the next sections we describe the retrieval procedure applied to IASI spectra, discuss the characterization of the retrieved profiles, according to the theoret-
ical analysis described in section 3.2, and compare the retrieved near-surface
concentrations to ground measurements.

4.1.1. *Retrieval procedure*

Retrievals of CO profiles have been performed on IASI observations taken
during 2013 using the Atmosphit software. Only measurements for which
the cloud fraction is less than 20% and with available meteorological EU-
METSAT L2 data have been considered. Table 3 summarizes the retrieval
settings; most are those also used in the FORLI software. Mexico City is lo-
cated in a basin of around 100 km of diameter, where the pollution remains
trapped because of the surrounding high mountains (on South, West and
East, see Figure 9). Therefore, to remove IASI observations located outside
the polluted basin, only those having their centers inside the red rectangle
(99.35–98.85°W/19.2–19.75°N) indicated in Figure 9 have been analysed. In
total, 952 spectra have been analysed, covering all months of 2013.

Moreover, the region of Mexico City is located at an altitude of around
2 km above sea level. To compare the theoretical results from section 3 to
those obtained from real IASI measurements, the ground height is considered
as the 0 level, i.e., the a priori CO profile shown in Figure 1 starts at the
ground height instead of 0 km and the scale height of the associated S_a has
been modified accordingly.

4.1.2. *Characterization of the retrievals*

Figure 10 (a-c) shows the reduction of the prior uncertainty on the re-
trieved 0–1 km CO VMRs, the DOFS for the entire profiles and for the 0–1
km layers (red dots). These three quantities are plotted against the TC,
revealing a clear relation, consistent with the results from the previous sec-
tions. The error reduction increases with increasing TC (absolute value),
from around 25% for TC close to 0 K to more than 50% above 15 K. The
DOFS increases from 1.2 to 1.9 (for the entire profile) and from 0 to 0.35 (for
the 0–1 km layer) for TC varying from below 5 K to 30 K. These patterns
can all be traced back to an increase of the IASI sensitivity to near-surface
CO. Furthermore, these can be compared to those predicted in section 3.2
(Figure 5). A good consistency is found for both predicted prior uncertainty
reduction and DOFS (total and 0–1 km).

To complete the evaluation, two IASI measurements over Mexico City
representative of low and high TC conditions were analysed. The resulting
retrieved CO profiles and their associated averaging kernels functions are
shown in Figures 11 and 12. From Figure 11.a, we see that, in case of low
TC (here 3.17 K), the retrieved profile stays close to the a priori from the
surface up to 19 km. The sensitivity of IASI to near-surface CO is limited in
this case, as seen by the averaging kernels peaking at the same altitude of 6
km for all layers. The DOFS for the entire profile is 1.28, and expresses the
fact that the retrieved CO VMR in the low troposphere is not independent
at all on the one in the high troposphere.

The case of high positive TC (around 23.5 K, shown in Figure 12) shows
CO peaking at the surface with a retrieved VMR of 510 ppb. The two first
averaging kernels (0–1 and 1–2 km) peak at the surface, indicating that the
information coming from the surface layer contribute indeed most to the
retrieval of CO VMR in these layers. The total DOFS equals 1.85, which
means that almost two pieces of information on the vertical profile of CO
are retrieved independently. According to the shape of the averaging kernels
 panel b), these would correspond to the 0–5 km and 5–19 km mean VMRs.
Note that these AVK are in a good agreement with those derived theoretically
in the previous sections (see Figure 12.c).

4.1.3. *Comparisons to RAMA ground measurements*

For the comparison, we have used the CO VMRs hourly recorded ev-
eryday by 20 stations, which are identified in Table 4. These stations are
disseminated in the area (as shown in Figure 9) at distances of up to 30 km
from the city center. This distribution lead to very variable measured CO
VMRs, which can differ of up to thousands ppb between the stations. This
is shown in Figure 9 for the example of 1st February 2013 at 10:00 AM local
time (LT), where we have 3000 ppb for the largest VMR difference. For this
reason, IASI observations, which cover a large area, have been compared to
the mean CO VMR calculated for RAMA stations within the central part the
footprint of the instrument (distance< 5 km). If no RAMA station is found
within the footprint, the closest one is selected for the comparison, with a
maximum distance, of 25 km from the pixel center, allowed. Moreover, Mex-
ico City encounters a strong diurnal cycle of surface CO VMRs, as reported
by [29], [30], and [31]. A time window of ±30 minutes on IASI overpass has
thus been applied for the selection of the RAMA reference measurements.

Figure 13.a shows the correlation between IASI and co-located RAMA
surface CO measurements as a function of TC. Two linear regressions have
been calculated using 1) all data (black), and 2) IASI observations with
TC > 15 K (pink). We find that IASI significantly underestimates the sur-
face CO VMRs in the majority of the cases. The largest underestimation is observed for low TC values (between 0 and 5 K in absolute value), for which IASI provides 0–1 km VMRs around 100 ppb (≈a priori) whereas the RAMA stations report VMRs up to 2000 ppb. Observations associated with TC > 15 K tend to be less underestimated, as shown by the small improvement observed for the linear regression using only IASI observations with TC > 15 K. This is better seen with Figure 13.b, which shows the relative difference between the two sets of CO measurements ((IASI-RAMA)/RAMA) as a function of TC. We find a clear decrease in the percent bias with increasing TC values. The averaged relative differences calculated per bin of 5 K of TC between -5 K and 25 K (indicated by red lines) decrease from averages up to 80% for TC lower than 15 K, to 60% for the 15-20 K bin and 40% for TC larger than 20 K. This decrease in the percent bias (absolute value) for increasing TC is consistent with the gain of IASI sensitivity to near-surface CO, which allows a more accurate estimation of its concentration close to the ground. Note finally that a correlation coefficient of 0.48 is calculated between the percent bias and the TC, showing some correlation between these two quantities.

Although the agreement between IASI and RAMA data is improved in case of large TC, the CO VMRs measured by IASI are still significantly underestimated. This could be related in part to the fact that IASI and RAMA surface measurements are different quantities. For IASI, we provide an averaged 0–1 km VMR calculated from the retrieved 0–1 km partial column of CO. Depending on the shape of the CO profile in the 0–1 km layer, this averaged retrieved VMR can be smaller than the surface VMR measured by the stations. This especially depends on the height of the mixing layer: low mixing height leads to accumulation of CO close to the ground (the 0–1 km VMR retrieved from IASI would be biased low compared to RAMA surface measurement), while a growth of the mixing layer is followed by a decrease of CO concentrations at the surface (RAMA and IASI VMRs would be more comparable quantities). [30] report strong diurnal variations of this height in Mexico City, which is the lowest during the early morning (and associated to the largest CO VMRs at the surface) and increases during the afternoon. The morning overpass time of IASI above Mexico City is around 10:00-11:00 LT, for which [30] measure a mixing height around 500 m. This narrow mixing layer could therefore partly explain the large discrepancies observed between IASI and RAMA datasets. Deeper investigation is however needed to confirm this effect.
Another possible origin of the underestimation of CO surface concentra-
tions can be the choice of the a priori profile, which is not representative of a
high CO pollution at the surface but rather describes a typical background
concentration profile. Preliminary results tend to show that the choice of a
more polluted a priori profile has significant impact on CO retrievals (see
also [7]). Further investigations are needed here to also estimate the gain
in accuracy provided by a selection of a priori profile (and associated S<sub>a</sub>)
representative of polluted megacities. Other retrieval adaptations could be
also envisaged in high polluted cases, such as the use of more retrieved layers
close to the surface. Finally, alternative minimization approaches could be
considered (e.g., Tikhonov-Phillips [32]).

4.2. Barrow - Negative TC

To verify the theoretical results for large negative TC cases (section 3.2),
retrievals have been performed on IASI observations taken during the win-
ter in Barrow for several years and for daytime and nighttime overpasses.
Only measurements for which the cloud fraction is less than 20% and with
available meteorological EUMETSAT L2 data have been considered. As for
Mexico City, the retrieval settings are summarized in Table 3. Moreover, a
NOAA station (http://www.esrl.noaa.gov/gmd/obop/brw/) is located in
the region and provides CO surface measurements that can be used for com-
parison [33]. Only IASI observations located within 20 km from the NOAA
station (71.32°N, 156.61°W) are therefore analysed.

4.2.1. *Characterization of the retrievals*

The blue dots in Figure 10 (a-c) show the reduction of the prior uncer-
tainty on the retrieved 0-1 km CO VMRs, the DOFS for the entire profiles
and for the 0-1 km layers for the Barrow region as a function of TC. These
three quantities show a clear dependence on TC values, which is consistent
with theoretical results. More particularly, we find a very good agreement
with the theoretical curves obtained for these three quantities in section 3.2,
when Barrow and Mexico City results are combined. The minimal error re-
duction (DOFS) is obtained around TC = -7 K and is equal to 10% (0.9) on
average. The maximal error reductions (DOFS) of 60% (1.8) are reached for
the extreme TC cases. The combination of Barrow and Mexico City results
shows especially an asymmetry for the 0-1 km DOFS between large negative
and large positive TCs, which was revealed theoretically; for instance, for
TC = -20 K, the 0-1 km DOFS is 0.5 whereas it is 0.3 for TC = 20 K.
This is the demonstration, with real IASI observations, that large negative
TCs allow better decorrelation of the CO VMRs in the low and in the high
troposphere. This demonstration is also supported by the AVK functions
shown in Figure 14.a for an example case with large negative TC (-13.5 K).
These reach maximal values of around 0.45 between 0 and 2 km, revealing a
constant maximal sensitivity to the 0–2 km VMR. This is also well seen with
Figure 14.b, which shows that the associated Jacobians present their largest
values between 0 and 2 km. This maximal sensitivity in the 0–2 km layer
is linked to the presence of a 2 km thick inversion layer above ground (Fig-
ure 14.c). Note finally that, despite this difference, the general shapes of the
AVK functions are in good agreement with the theoretical ones (Figure 6).

4.2.2. *Comparison to NOAA ground measurements*

For the comparison, the NOAA ground-based station provides one or
two CO measurements for some specific days, which are recorded at various
times. For each of these, the IASI observation recorded in a time window
of ±6 hours and located within 20 km from the station is selected. In total,
28 pairs of co-located measurements have been found. The correlations are
represented in Figure 15.

As for Mexico City, Figure 15.a shows the correlation between IASI and
NOAA measurements as a function of TC. The correlation is poor and in-
sensitive to the TC. This is further seen in Figure 15.b, for which the relative
difference between the two datasets is calculated (IASI-NOAA/NOAA). A
mean percent bias of -21% is found, showing an underestimation of IASI CO
retrievals, which was already revealed with the Mexico City case. In contrast,
no clear relation is found between the percent bias and the TC values for Bar-
row. The most probable reason for this is that near-surface CO VMRs in this
region are close to the FORLI a priori value. CO surface VMRs retrieved
for low TC conditions stay close to the a priori values and are, as for large
TCs, in good agreement with NOAA measurements. Another possible rea-
son is the low number of co-located observations. Note finally that the mean
percent bias calculated for Barrow is smaller (in absolute value) than for
Mexico City. However, retrievals performed above these two regions cannot
be compared as they are associated to very different levels of pollution.
5. Conclusions

In this work, we have evaluated the performance of the IASI TIR sounder to measure near-surface CO concentrations, and more particularly, the influence of TC on this performance. Three different approaches have been used, combining theoretical analyses and retrievals for Mexico City and Barrow, chosen as test regions respectively for large positive and large negative TC conditions.

First, by computing differences between spectra simulated for polluted and background conditions of CO in the 0–1 km layer, we have shown that the three main factors driving IASI sensitivity to the near-surface CO enhancement are: 1) the TC, 2) the concentration of CO in the 0–1 km layer, and 3) the wavenumber. We have shown that IASI is more sensitive to near-surface CO at the center of the rotational lines, where CO enhancements smaller than 80 ppb can be observed from 10 K (in absolute value) of TC. For lower TC, e.g. at 4 K, the smallest detectable enhancement is about 150 ppb. These thresholds significantly decrease by exploiting the whole 1–0 band of CO: CO enhancement as low as 10 ppb can be detected, which is much more favourable than what is usually assumed for TIR sounders.

Using the general framework of the optimal estimation method we have shown that IASI becomes sensitive to near-surface CO from 5 K of TC (in absolute value) and that values of TC larger than 10–15 K (in absolute value) favour the decorrelation between two tropospheric layers. In case of high negative (positive) TC, we have demonstrated that it was possible to independently retrieve the 0–3 (0–5) km and 3–19 (5–19) km mean VMRs. An important result was to show that large negative TC, corresponding to temperature inversions, are in fact the most favourable conditions for this decorrelation of two tropospheric layers, contrary to what was shown for the MOPITT instrument [e.g. 9]. This was explained by the transition between emission in the first atmospheric layers and absorption in higher layers. Another important result is the shift of minimal error reduction/DOFS from vanishing TC towards negative values, when using a non-diagonal $S_a$ matrix. This has been attributed to the correlation between the atmospheric layers, which have therefore to be taken into account carefully when interpreting the error budget and information content of real retrievals of CO abundance in the near-surface atmosphere.

The profile retrieval and characterization for the set of real IASI measurements above Mexico City and Barrow have confirmed these findings.
We found in particular very good consistence in the error budget and vertical sensitivity diagnostics (AVK and DOFS) for both positive and negative TCs. The comparisons of the retrieved surface VMRs with those from co-located measurements of the RAMA ground-based stations (Mexico City) has allowed assessing the accuracy of the retrievals at near-surface level in case of high pollution. As expected, we found that the agreement depends strongly on the TC: IASI retrieved CO VMRs were shown to be underestimated systematically by 80% on average for TC values smaller than 15 K (absolute value), and by 40% on average above TC = 20 K. The same could not be shown in the Barrow analysis, either because of insufficient co-located samples or because retrievals were too similar to the a priori.

The results presented in this work are valuable for all applications using the CO distributions from the operational L2 CO IASI product delivered by EUMETSAT (FORLI-CO), as the retrieved settings are similar. The CO-FORLI product has previously been validated, but mostly total columns are currently used in applications. In this work, we show that favourable conditions of TC increase the accuracy of low tropospheric CO from FORLI. These favourable conditions (both positive and negative TC) are encountered in different polluted regions of the world, suggesting a possible use for air quality monitoring. However, we reveal that the surface CO retrievals tend to be systematically underestimated when compared to surface in-situ measurements, especially in case of high pollution. Different explanations have been proposed, including 1) the effect of the mixing layer height (and thus the vertical distribution of CO in the 0–1 km layer) on the comparison, and 2) the choice of the a priori settings. The impacts of these should be investigated in future works for a better characterization of the near-surface CO retrievals from IASI.

Finally, knowing the capabilities of current TIR instruments is of particular importance to prepare and develop future satellite TIR missions. The proposed analyses have the advantage of being adaptable to any other instruments and/or any other atmospheric species, and could be used to complete the evaluation of the performances of future TIR sounders, such as IASI-NG [34].

## 6. Acknowledgements

IASI has been developed and built under the responsibility of the Centre National d'Etudes Spatiales (CNES, France). It is flown on board 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. The research in Belgium was funded by the F.R.S-FNRS, the Belgian State Federal Office for Scientific, Technical, and Cultural Affairs, and the European Space Agency (ESA-Prodex arrangements). S. Bauduin and L. Clarisse are respectively Research Fellow and Research Associate with F.R.S.-FNRS. C. Clerbaux is grateful to CNES for scientific collaboration and financial support. The authors acknowledge support from the EU-FP7 project QA4ECV (grant agreement 607405). This work is also part of the EUMETSAT/O3M-SAF project. Finally, the authors would like to thank the Sistema De Monitoréo Atmosférico of Mexico City and the Earth System Research Laboratory (NOAA) for freely providing in-situ ground measurements of CO.

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<figure><img src="image_2.png" /><figcaption>Figure 1: (a) A priori vertical profile of CO ($x_a$) used in the FORLI algorithm. The red dashed lines represent the $1\sigma$ associated variability (square root of the diagonal elements of $S_a$). (b) A priori covariance matrix ($S_a$, in %$^2$/100) used in the FORLI algorithm.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>Figure 2: CO vertical profiles representative of background (blue) and polluted atmospheres (red). The background profile is the a priori profile of FORLI. For the polluted atmosphere, a variety of surface VMRs has been considered and these are represented by the red dots (the corresponding 0–1 km VMRs are included in Table 1). For display purposes, only the profile associated to the largest surface VMR (1500 ppb) is shown.</figcaption></figure>
<table><caption>Table 1: Range of atmospheric situations considered for the forward simulations used to calculate the normalized radiance difference (NRD) between polluted and background conditions of near-surface CO. Only the VMR of CO at the 0 km level has been varied, and the averaged VMR for the 0–1 km layer are given.</caption><thead><tr><th>Parameter</th><th>Values</th><th>Background</th></tr></thead><tbody><tr><td>Spectral range</td><td>2000–2250 cm<sup>-1</sup></td><td></td></tr><tr><td>Satellite zenithal angle</td><td>0°</td><td></td></tr><tr><td>0–1 km VMR (ppb) of CO</td><td>107.4–247.4, 10 ppb step<br>247.4–297.4, 25 ppb step<br>297.4–547.4, 50 ppb step<br>647.4 and 797.4</td><td>FORLI a priori<br>(mean VMR<br>of 98.2 ppb)</td></tr><tr><td>TC (K)<sup>1</sup></td><td>-20 to +20, 1 K step</td><td></td></tr><tr><td>Temperature profile</td><td>US Standard model<sup>2</sup></td><td></td></tr><tr><td>CO<sub>2</sub>, H<sub>2</sub>O and N<sub>2</sub>O profiles</td><td>US Standard model<sup>2</sup></td><td></td></tr><tr><td>O<sub>3</sub> profile</td><td>FORLI a priori profile<sup>3</sup></td><td></td></tr><tr><td>Emissivity</td><td>1</td><td></td></tr></tbody></table>

<footnote n="1">¹ TC has been varied by changing the surface temperature.</footnote>

<footnote n="2">² [35].</footnote>

<footnote n="3">³ [20].</footnote>
<figure><img src="image_4.png" /><figcaption>Figure 3: NRD($\tilde{\nu}$) (color scale) calculated from the difference between polluted spectra and background spectra (a) as function of TC (constant CO enhancement in the 0–1 km layer of 199.2 ppb) and, (b) as function of CO enhancement in the 0–1 km layer (constant TC of 10 K)</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 4: (a) Minimum CO enhancement in the 0–1 km layer (ppb, colorscale), calculated from the FORLI a priori background conditions, detectable by IASI as a function of TC and wavenumber. (b) Detection threshold (ppb) for CO enhancement in the 0–1 km layer, calculated considering the spectral signal in the whole CO band, as a function of thermal contrast.</figcaption></figure>
<table><caption>Table 2: Forward simulations parameters used for the calculations of Jacobians, and theoretical $\hat{S}$ and $A$ matrices. Those corresponding to the retrieval settings of the FORLI algorithm are indicated.</caption><thead><tr><th>Parameter</th><th>Values</th><th>FORLI settings</th></tr></thead><tbody><tr><td>Spectral range</td><td>2143–2181.25 cm<sup>-1</sup></td><td>✓</td></tr><tr><td>Satellite zenithal angle</td><td>0°</td><td></td></tr><tr><td>Instrumental noise</td><td>2×10<sup>-7</sup> W/(m<sup>2</sup> sr m<sup>-1</sup>)<br>diagonal S<sub>ε</sub></td><td>✓</td></tr><tr><td>Background:<br>0–1 km layer CO VMR<sup>1</sup></td><td>98.2 ppb</td><td>✓</td></tr><tr><td>TC (K)<sup>2</sup></td><td>-20 to +20, 1 K step</td><td></td></tr><tr><td>Temperature profile</td><td>US Standard model<sup>3</sup></td><td></td></tr><tr><td>CO<sub>2</sub>, H<sub>2</sub>O<br>and N<sub>2</sub>O profiles</td><td>US Standard model<sup>3</sup></td><td></td></tr><tr><td>O<sub>3</sub> profile</td><td>FORLI a priori profile<sup>4</sup></td><td>✓</td></tr><tr><td>Emissivity</td><td>1</td><td></td></tr></tbody></table>

<footnote n="1">¹ The FORLI a priori profile is considered above the 0-1 km layer.</footnote>

<footnote n="2">² TC has been varied by changing the surface temperature.</footnote>

<footnote n="3">³ [35].</footnote>

<footnote n="4">⁴ [20].</footnote>
<figure><img src="image_6.png" /></figure>

Figure 5: Theoretical characterization of CO retrievals from IASI at near-surface level: (a) Retrieval errors (%) of CO in the 0–1 km layer as a function of TC; the green line represents the prior uncertainty (square root of the diagonal element of the S_a) for the same layer; the black dashed line corresponds to the retrieved errors for the 0–1 km layer in case of a diagonal S_a. (b) Averaging kernels (VMR/VMR) of the 0–1 km layer for different TC (K) conditions; (c) Total and 0–1 km DOFS as a function of TC.

<figure><img src="image_7.png" /></figure>

Figure 6: Predicted averaging kernels (VMR/VMR) for the ten first layers and for three different values of TC: -15 K (a), 0 K (b), and +15 K (c).
<figure><img src="image_8.png" /></figure>

Figure 7: From top to bottom: contributions to TOA radiance of the 0–1 km layer, the 1–2 km layer, the 2–3 km layer and the 7–8 km layer, calculated for a TC = −15 K and considering the CO a priori profile of FORLI. They are expressed in brightness temperature (K). The contributions have been calculated following a method similar to the one presented in [13].
<figure><img src="image_9.png" /></figure>

Figure 8: Simulated IASI spectrum at TOA in brightness temperature (K) for -15 K (a) and +15 K (b) values of TC, the surface temperature is indicated in red; Jacobians (expressed here in W/(m² sr m⁻¹) per scaling factor, color scale) for the spectral range 2143-2181.25 cm⁻¹ and as function of height for -15 K (c) and +15 K (d) values of TC.
<table><caption>Table 3: Settings used in the retrieval of CO profiles from IASI observations recorded in the region of Mexico City. Note that the 0 km indicated here corresponds to the ground height (see text).</caption><thead><tr><th>Parameter</th><th>Values/A priori</th><th>Layers and variability</th></tr></thead><tbody><tr><td>Spectral range</td><td>2143–2181.25 cm<sup>-1</sup></td><td></td></tr><tr><td>Instrumental noise</td><td>2×10<sup>-7</sup> W/(m<sup>2</sup> sr m<sup>-1</sup>)<br>diagonal S<sub>ε</sub></td><td></td></tr><tr><td>CO profile</td><td>FORLI (Figure 1)</td><td>S<sub>a</sub> FORLI (Figure 1)</td></tr><tr><td>Surface temperature</td><td>L2 EUMETSAT</td><td>2%</td></tr><tr><td>Temperature profile</td><td>L2 EUMETSAT</td><td>Fixed</td></tr><tr><td>CO<sub>2</sub></td><td>380 ppm constant</td><td>5% on the total column</td></tr><tr><td>H<sub>2</sub>O</td><td>L2 EUMETSAT</td><td>30% for the layers:<br>0–2 km, 2–4 km<br>4–6 km, 6–8 km<br>8–10 km, 10–15 km<br>15–20 km</td></tr><tr><td>N<sub>2</sub>O</td><td>Tropical model<sup>2</sup></td><td>Fixed</td></tr><tr><td>O<sub>3</sub></td><td>FORLI a priori<sup>3</sup></td><td>Fixed</td></tr><tr><td>Emissivity</td><td>[36]</td><td>Fixed</td></tr></tbody></table>

<footnote n="2">² [35].</footnote>

<footnote n="3">³ [20].</footnote>
<figure><img src="image_10.png" /></figure>

Figure 9: Location of the RAMA ground-based stations (1 to 20), which provide hourly CO in-situ measurements, in the Mexico City basin. The name list of the stations is given in Table 4. The color scale indicates the CO VMRs (ppb) measured at each station for 1st February 2013 at 10:00 local time. The contour on the plot shows the terrain height in meters. The red rectangle defines the region for which IASI spectra have been selected.
<figure><img src="image_11.png" /><figcaption>Figure 10: Characterization of CO retrieval above Mexico city (red) and Barrow (blue) regions as function of TC: (a) Reduction of prior uncertainty (%) on the derived 0–1 km CO VMR; (b) DOFS for the entire profile; (c) DOFS for the 0–1 km layer.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 11: (a) Retrieved vertical profile of CO (blue, ppm) and a priori profile of CO (red, ppm) for a IASI measurement taken in low TC condition (3.17 K) above Mexico. The error bars correspond to the retrieval error (blue) and the prior uncertainty (red). (b) Averaging kernel functions (VMR/VMR) for the ten first retrieved layers. (c) Predicted averaging kernels (VMR/VMR) for the ten first layers for a TC of 4 K. The IASI observation has been taken the 24/09/2013 at a distance of 27 km from Mexico City center. The DOFS of the retrieval is 1.28 and the ground-based measured VMR of CO is 0.98 ppm (relative difference of -91%).</figcaption></figure>
<figure><img src="image_13.png" /></figure>

Figure 12: Same as Figure 11 for a IASI measurement, taken in high TC condition (23.45 K). In panel (c), the predicted averaging kernels (VMR/VMR) are for a TC of 20 K. The IASI observation has been taken the 09/03/2013 at a distance of 7.2 km from Mexico City center. The DOFS of the retrieval is 1.85 and the CO VMR measured by the ground stations is 1.76 ppm (relative difference of -71%).
<table><caption>Table 4: RAMA stations used for comparison with IASI CO measurements. They are represented in Figure 9 with the corresponding number.</caption><thead><tr><td>Name</td><td>Number on map</td><td>Longitude</td><td>Latitude</td></tr></thead><tbody><tr><td>Acolman (ACO)</td><td>1</td><td>-98.912°</td><td>19.6355°</td></tr><tr><td>Camarones (CAM)</td><td>2</td><td>-99.1698°</td><td>19.4684°</td></tr><tr><td>Cuajimalpa (CUA)</td><td>3</td><td>-99.2917°</td><td>19.3653°</td></tr><tr><td>FES Acatlán (FAC)</td><td>4</td><td>-99.2435°</td><td>19.4824°</td></tr><tr><td>Hospital General de México (HGM)</td><td>5</td><td>-99.1522°</td><td>19.4116°</td></tr><tr><td>Iztacalco (IZT)</td><td>6</td><td>-99.1176°</td><td>19.3844°</td></tr><tr><td>La Presa (LPR)</td><td>7</td><td>-99.1177°</td><td>19.5347°</td></tr><tr><td>Merced (MER)</td><td>8</td><td>-99.1196</td><td>19.4246°</td></tr><tr><td>Nezahualcóyotl (NEZ)</td><td>9</td><td>-99.0282°</td><td>19.3937°</td></tr><tr><td>Pedregal (PED)</td><td>10</td><td>-99.2041°</td><td>19.3251°</td></tr><tr><td>Santa Fe (SFE)</td><td>11</td><td>-99.2629°</td><td>19.3574°</td></tr><tr><td>San Juan Aragón (SJA)</td><td>12</td><td>-99.0861°</td><td>19.4526°</td></tr><tr><td>Santa Ursula (SUR)</td><td>13</td><td>-99.15°</td><td>19.3145°</td></tr><tr><td>Tlahuac (TAH)</td><td>14</td><td>-99.0106°</td><td>19.2465°</td></tr><tr><td>Tlalnepantla (TLA)</td><td>15</td><td>-99.2046°</td><td>19.5291°</td></tr><tr><td>Tultitlán (TLI)</td><td>16</td><td>-99.1772°</td><td>19.6025°</td></tr><tr><td>UAM Xochimilco (UAX)</td><td>17</td><td>-99.1036°</td><td>19.3044°</td></tr><tr><td>UAM Iztapalapa (UIZ)</td><td>18</td><td>-99.0739°</td><td>19.3608°</td></tr><tr><td>Villa de las Flores (VIF)</td><td>19</td><td>-99.0966°</td><td>19.6582°</td></tr><tr><td>Xalostoc (XAL)</td><td>20</td><td>-99.0824°</td><td>19.526°</td></tr></tbody></table>
<figure><img src="image_14.png" /></figure>

Figure 13: (a) Comparison between 0–1 km CO VMRs (ppb) retrieved from IASI obser-
vations with surface RAMA CO VMRs (ppb), as a function of TC (K, color scale). The
black and pink lines correspond to the linear regressions calculated considering respectively
1) all data and 2) IASI measurements with TC > 15 K. The equations and correlation
coefficients are indicated (inset). The dashed red line is the one-to-one line. (b) Relative
difference (%) between the IASI and RAMA sets of surface measurements as a function
of TC. The red lines indicate the mean differences calculated per bins of 5 K.
<figure><img src="image_15.png" /><figcaption>Figure 14: For an example of IASI observation recorded at TC = -13.5 K: (a) Averaging kernel functions (VMR/VMR) for the ten first retrieved layers. (b) Associated Jacobians (in W m⁻² sr⁻¹ m per scaling factor (MF)) as a function of height. (c) Temperature profile retrieved by the EUMETSAT L2 PPF for this specific IASI observation.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 15: (a) Comparison between 0–1 km CO VMRs (ppb) retrieved from IASI observations with surface NOAA CO VMRs (ppb), as a function of TC (K, color scale). The dashed red line is the one-to-one line. (b) Relative difference (%) between IASI and NOAA sets of surface measurements as a function of TC.</figcaption></figure>