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**Atmospheric Measurement Techniques**
An interactive open-access journal of the European Geosciences Union

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**Research article**
13 Jul 2020

**Research article** | 13 Jul 2020

Instrumental characteristics and potential greenhouse gas measurement capabilities of the Compact High-Spectral-Resolution Infrared Spectrometer: CHRIS

- Univ. Lille, CNRS, UMR 8518 – LOA – Laboratoire d'Optique Atmosphérique, 59000 Lille, France

- Univ. Lille, CNRS, UMR 8518 – LOA – Laboratoire d'Optique Atmosphérique, 59000 Lille, France

**Correspondence**: Hervé Herbin (herve.herbin@univ-lille.fr)

**Correspondence**: Hervé Herbin (herve.herbin@univ-lille.fr)

Abstract

Back to toptop
Ground-based high-spectral-resolution infrared measurements are an
efficient way to obtain accurate tropospheric abundances of different
gaseous species, in particular greenhouse gases (GHGs) such as
CO_{2} and CH_{4}. Many ground-based spectrometers are used
in the NDACC and TCCON networks to validate the Level 2 satellite
data, but their large dimensions and heavy mass make them inadequate
for field campaigns. To overcome these problems, the use of portable
spectrometers was recently investigated. In this context, this paper
deals with the CHRIS (Compact High-Spectral-Resolution Infrared
Spectrometer) prototype with unique characteristics such as its high
spectral resolution (0.135 cm^{−1} nonapodized) and its wide
spectral range (680 to 5200 cm^{−1}). Its main objective is
the characterization of gases and aerosols in the thermal and
shortwave infrared regions. That is why it requires high radiometric
precision and accuracy, which are achieved by performing spectral and
radiometric calibrations that are described in this paper. Furthermore,
CHRIS's capabilities to retrieve vertical CO_{2} and CH_{4}
profiles are presented through a complete information content
analysis, a channel selection and an error budget estimation in the
attempt to join ongoing campaigns such as MAGIC (Monitoring of
Atmospheric composition and Greenhouse gases through multi-Instruments
Campaigns) to monitor GHGs and validate the actual and future
space missions such as IASI-NG and Microcarb.

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How to cite.

El Kattar, M.-T., Auriol, F., and Herbin, H.: Instrumental characteristics and potential greenhouse gas measurement capabilities of the Compact High-Spectral-Resolution Infrared Spectrometer: CHRIS, Atmos. Meas. Tech., 13, 3769–3786, https://doi.org/10.5194/amt-13-3769-2020, 2020.

1 Introduction

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Remote-sensing techniques have gained a lot of popularity in the past few decades due to the increasing need of continuous monitoring of the atmosphere (Persky, 1995). Greenhouse gases and trace gases as well as clouds and aerosols are detected and retrieved, thus improving our understanding of the chemistry, physics and dynamics of the atmosphere. Global-scale observations are achieved using satellites, and one major technique is infrared high-spectral-resolution spectroscopy (IRHSR). This technique offers radiometrically precise observations at high spectral resolution (Revercomb et al., 1988) where quality measurements of absorption spectra are obtained. TANSO-FTS (Suto et al., 2006), IASI (Clerbaux et al., 2007) and AIRS (Aumann et al., 2003) are examples of satellite sounders covering the thermal infrared (TIR) region. The observations acquired from such satellites have many advantages: day and night data acquisition, possibility to measure concentrations of different gases, the ability to cover land and sea surfaces (Herbin et al., 2013a), and the added characteristic of being highly sensitive to various types of aerosol (Clarisse et al., 2010). These spectrometers also have some disadvantages: local observations are challenging to achieve due to the pixel size that limits the spatial resolution, and the sensitivity in the low atmospheric layers, where many short-lived gaseous species are emitted but rarely detected, is weak.

To fill these gaps, ground-based instruments are used as
a complementary technique, and one famous high-precision Fourier-transform spectrometer is the IFS125HR from Bruker^{™},
which is briefly discussed in Sect. 3.5 (further
details can be found in Wunch et al., 2011). More than 30 instruments
are currently deployed all over the world in two major international
networks: TCCON (https://tccondata.org/, last access: 22 June 2020) and NDACC (https://www.ndsc.ncep.noaa.gov/, last access: 22 June 2020). This particular instrument
has a very large size ($\mathrm{1}\phantom{\rule{0.125em}{0ex}}\mathrm{m}\times \mathrm{1}\phantom{\rule{0.125em}{0ex}}\mathrm{m}\times \mathrm{3}$ m) and a mass well
beyond 100 kg, therefore achieving a long optical
path difference and leading to a very high spectral resolution (0.02 and
$\mathrm{5}\times {\mathrm{10}}^{-\mathrm{3}}$ cm^{−1} for TCCON and NDACC,
respectively). Despite its outstanding capabilities, this spectrometer
is not suitable for field campaigns, so it is mainly used to validate
Level 2 satellite data, thus limiting the scientifically important
ground-based extension of atmospheric measurement around the world.

One alternative is the new IFS125M from Bruker (Pathatoki et al., 2019),
which is the mobile version of the well-established IFS125HR
spectrometer. This spectrometer provides the highest resolution
available for a commercial mobile Fourier-transform infrared (FTIR) spectrometer, but it still has
a length of about 2 m and requires on-site realignment by
qualified personnel. Another alternative is the use of several compact
medium- to low-resolution instruments that are currently under
investigation, such as a grating spectrometer (0.16 cm^{−1}),
a fiber Fabry–Pérot interferometer (both setups presented in
Kobayashi et al., 2010) and the IFS66 from Bruker (0.11 cm^{−1})
described in Petri et al. (2012). The EM27/SUN is the first instrument to
offer a compact, optically stable, transportable spectrometer (Gisi et al., 2012) with a high signal-to-noise ratio (SNR) and that operates in the SWIR
(short-wavelength infrared) region. A new prototype called CHRIS
(Compact High-Spectral-Resolution Infrared Spectrometer) was conceived
to satisfy some very specific characteristics: high spectral
resolution (0.135 cm^{−1}, better than TANSO-FTS and the
future IASI-NG) and a large spectral band (680–5200 cm^{−1}) to
cover the current and future infrared satellite spectral range and
optimize the quantity of the measured species. Furthermore, this
prototype is transportable and can be operated for several hours by
battery (>12 h), so it is suitable for field campaigns. The full
presentation of the characteristics and the calibration of this
instrumental prototype is presented in Sect. 2.

Since carbon dioxide (CO_{2}) and methane (CH_{4}) are the
two main greenhouse gases emitted by human activities, multiple
campaigns have been launched, such as the MAGIC (Monitoring of
Atmospheric composition and Greenhouse gases through multi-Instruments
Campaigns) initiative, to better understand the vertical exchange of
these greenhouse gases (GHGs) along the atmospheric column and to contribute to the
preparation and validation of future space missions dedicated to GHG
monitoring. CHRIS is part of this ongoing mission, and this work
presents for the first time the capabilities of such a setup in
achieving GHG measurements. Analysis of the forward model, state vector and
errors is explained in Sect. 3.

In this context, we present in Sect. 3.5 a complete
information content study for the retrieval of CO_{2} and
CH_{4} of two other ground-based instruments that also
participated in the MAGIC campaign: a comparison study with the
IFS125HR instrument and, since CHRIS and the EM27/SUN have a common band
in the SWIR region, a study to investigate the spectral synergy in
order to quantify the complementary aspects of the TIR–SWIR–NIR (NIR stands for near-infrared)
coupling for these two instruments. Moreover, Sect. 4
describes the channel selection made in this study. Finally, we
summarize our results and perspectives for future applications, in
particular the retrieval of GHGs in the MAGIC framework.

2 The CHRIS spectrometer

Back to toptop
CHRIS is an instrumental prototype built by Bruker^{™} and
used in different domains of atmospheric optics. Its recorded
spectra contain signatures of various atmospheric constituents such
as GHGs (H_{2}O, CO_{2}, CH_{4}) and trace gases. The
capacity to measure these species from a technical point of view as
well as the characterization of this prototype in terms of spectral
and radiometric calibrations is presented in the following
subsections.

CHRIS is a portable instrumental prototype with a mass of approximately 40 kg and dimensions of $\mathrm{70}\phantom{\rule{0.125em}{0ex}}\mathrm{cm}\times \mathrm{40}\phantom{\rule{0.125em}{0ex}}\mathrm{cm}\times \mathrm{40}$ cm, making it easy to operate in the field. The tracker, which is similar to the one installed on the EM27/SUN and described in detail in Gisi et al. (2012), leads the solar radiation through multiple reflections on the mirrors to a wedged fused-silica window.

An internal look at CHRIS is shown in Fig. 1, where the optical path of the solar beam is represented with red arrows: after multiple reflections
on the tracker's mirrors, the solar radiation enters the spectrometer
through the opening and is then reflected by the first mirror, where
the charge-coupled device (CCD) camera verifies the collimation of the beam on the second
mirror, which has a solar filter. At this level, CHRIS has a filter wheel
that can be equipped with up to five optical filters with a diameter of
25 mm. Filters are widely used when making solar measurements
to reduce noise and nonlinearity effects. After reflection on the
second mirror, the beam enters the RockSolid^{™} Michelson
interferometer, which has two cube-corner mirrors to ensure the optical
alignment stability of the beam and a KBr beam splitter. After that,
the radiation is blocked by an adjustable aperture stop, which can be
set to between 1 and 18 mm. This limits the parallel beam
parameter and can be used to reduce the intensity of the incoming
sunlight in case of saturation of the detector. The remaining
radiation falls onto an MCT (mercury cadmium telluride) detector; then it
is digitized to obtain the solar absorption spectra in arbitrary
units. This detector uses a closed-cycle Stirling cooling system
(a.k.a. cryocooler), so no liquid nitrogen has to be used. As the
vibrations of the compressor may introduce noise in the spectra (see
Sect. 2.6), a high scanning velocity (120 KHz) is
needed.

A standard nonstabilized He–Ne laser controls the sampling of the interferogram. The condensation of the warm, humid air on the beam splitter due to its transportation between cold and warm environments is the main reason a dessicant cartridge is used, so the spectrometer can operate under various environmental conditions. CHRIS also has an internal blackbody, which can be heated up to 353 K to make sure that there is no drift in the TIR region, and it also serves as an optical source to regularly verify the response of the detector.

CHRIS's method of data acquisition is explained as follows: the
interferograms are sampled and digitized by an analog-to-digital
converter (ADC) and then numerically resampled at constant intervals
of optical path difference (OPD) by a He–Ne reference laser signal
controlled by the aperture stop diameter. In order to determine
a suitable compromise between the latter and to avoid the saturation
of the signal, measurements must be done in a clear (no clouds or
aerosols) and nonpolluted (no gases with high chemical reactivity)
atmosphere. For this purpose, a field campaign was carried out at El Observatorio Atmosférico de Izaña (28.30^{∘} N,
16.48^{∘} W) on the island of Tenerife. This particular observatory
site is high in altitude (2374 m), away from pollution sites
and has an IFS125HR listed in both the NDACC and TCCON
networks. Saturation of CHRIS's detector is reached at a value of
32 000 ADC. The MCT detector is known for its high
photometric accuracy, but it also exhibits a nonlinear response with
regard to the energy flux in cases of high incident energy. This led
us to choose an aperture stop of 5 mm, which is the best
compromise between saturation and incoming energy flux.

Each spectrum corresponds to the solar transmission light in the total
atmospheric column in a field of view (FOV) of 0.006 mrad. The
spectral range spans the region from 680 to 5200 cm^{−1} (1.9 to
14.7 µm), which corresponds to the middle-infrared region
(MIR). The water vapor causes the saturation we see between the bands,
thereby explaining the zero signal. Therefore, we divided the spectrum into four
distinctive spectral bands presented in Table 3: TB (thermal
band; 680–1250 cm^{−1}), B1 (1800–2300 cm^{−1}), B2
(2400–3600 cm^{−1}) and B3 (3900–5200 cm^{−1}). This
annotation is used for the rest of the paper.

A technical study was conducted on this prototype in order to evaluate
its optical and technical properties with a constant aperture stop
diameter of 5 mm. One of the most important findings is the
effect of the number of scans on the measured spectra. In practice,
a scan is the acquisition of a single interferogram when the mobile
mirror of the Michelson interferometer begins data collection at the
zero path difference (ZPD) and finishes at the maximum length,
therefore achieving the highest resolution required. In
Fig. 2, the spectrum with 10 scans has a higher amplitude
than those with 50 and 100 scans. On the other hand, the spectra with 50
and 100 scans are clearly less noisy than that with 10 scans. This
is due to the fact that the increase in the number of scans causes an
increase in the SNR, which leads to a decrease in noise. However,
there is a limit to the number of scans beyond which no improvement of
the SNR is obtained. The SNR is proportional to the square root of the
acquisition time (number of scans), also known as Fellgett's
advantage, and since the detector is dominated by shot noise, the
improvement of the SNR with the number of scans is blocked at
a certain value. This is why the spectra of 100 and 200 scans do
not show a significant difference. The SNR is an estimation of the
root-mean-squared noise of the covered spectral domain and can be
calculated in OPUS (the running program for CHRIS) using the function
SNR with the “fit parabola” option; it is estimated to be approximately
780. An optimized criterion is chosen to select the appropriate number
of scans: when the wanted species has a fast-changing concentration,
such as volcanic plumes, a relatively small number of scans is needed
to be able to follow the change in the atmospheric
composition temporally. In contrast, when measurements of relatively stable
atmospheric composition are made, for example GHGs (CO_{2} and
CH_{4}), the number of scans can be increased to 100. For
instance, the time needed for one scan with a scanning velocity of
120 KHz is 0.83 s, so 100 scans take approximately
83 s, which is low in comparison to the variability of
CO_{2} and CH_{4} in the atmosphere.

Another important feature is the effect of the gain amplitude (and preamplifiers, which amplify the signal before digitization) on the spectra. Those parameters should be chosen in a way that the numeric count falls in a region where no detector saturation occurs. If the gain is increased by a certain amount, the background noise is increased by the same amount. The use of such an option in the measurement procedure might be considered in cases where the signal is very weak, like lunar measurements. Note that there are other ways to increase the intensity of the signal, like using signal amplifying filters (see Sect. 2.1) or increasing the aperture stop diameter.

In the following section, the spectral and radiometric calibrations are discussed in order to convert spectra from numeric counts (expressed in arbitrary units) to radiance ($\mathrm{W}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{\mathrm{sr}}^{-\mathrm{1}}\phantom{\rule{0.125em}{0ex}}\mathrm{cm}$).

Despite the fact that CHRIS has an internal blackbody, radiometric
calibration cannot be overlooked because of its narrow spectral
coverage (only the TIR region), and since the radiometric noise and the time- and wavelength-dependent calibration errors are magnified in
the inversion process, high radiometric precision is required to
derive atmospheric parameters from a spectrum. We calibrate our
spectra using the two-point calibration method explained in
Revercomb et al. (1988). This method consists of using the observations
of hot and cold blackbody reference sources, which will be used as the
basis for the two-point calibration at each wave number. A cavity
blackbody was acquired by the LOA (Laboratoire d'Optique Atmosphérique) to perform regular radiometric
calibrations. The latter is an HGH/RCN1250N2, certified by the LNE
(Laboratoire National de métrologie et d'Essais) as having an
emissivity greater than 0.99 in the spectral domain spanned by CHRIS,
a stability of 0.1 at 1173 K and an opening diameter of up to
50 mm (corresponding to that of CHRIS) and as covering
temperatures from 323 to 1523 K. This cavity blackbody is
mounted on an optical bench and used before and after each campaign to
perform absolute radiometric calibrations through open-path
measurements and to make sure that this calibration is stable across the
whole spectral range. These two blackbody temperatures are viewed to
determine the slope *m* and offset *b* (Eqs. 1 and 2), which define the linear instrument response at each
wave number. The slope and the offset can be written following
Revercomb et al. (1988):

$$\begin{array}{}\text{(1)}& {\displaystyle}m& {\displaystyle}={\displaystyle \frac{{S}_{\mathrm{c}}-{S}_{\mathrm{h}}}{{B}_{\mathit{\nu}}\left({T}_{\mathrm{c}}\right)-{B}_{\mathit{\nu}}\left({T}_{\mathrm{h}}\right)}}\text{(2)}& {\displaystyle}b& {\displaystyle}={\displaystyle \frac{{S}_{\mathrm{c}}\cdot {B}_{\mathit{\nu}}\left({T}_{\mathrm{h}}\right)-{S}_{\mathrm{h}}\cdot {B}_{\mathit{\nu}}\left({T}_{\mathrm{c}}\right)}{{B}_{\mathit{\nu}}\left({T}_{\mathrm{h}}\right)-{B}_{\mathit{\nu}}\left({T}_{\mathrm{c}}\right)}},\end{array}$$

where *S* is the blackbody spectrum recorded, and *B*_{ν} corresponds to the calculated Planck blackbody radiance. The subscripts h and c correspond to the hot (1473 K) and cold (1273 K) blackbody temperatures, respectively. Finally, the calibrated spectrum expressed in watts per square meter steradian centimeter is obtained by applying the following formula:

$$\begin{array}{}\text{(3)}& L={\displaystyle \frac{S-b}{m}},\end{array}$$

where *S* is the spectrum recorded by CHRIS.

One open-path measurement using the calibrated HGH blackbody as source
was performed, similar to the one previously described in
Wiacek et al. (2007), to record a spectrum without applying any
apodization. Our colleagues in the PC2A laboratory provided us with
a 10 cm long cell with a free diameter of 5 cm, where
the pressure inside is monitored by a capacitive gauge. With the help
of the line-by-line radiative transfer algorithm ARAHMIS (atmospheric
radiation algorithm for high-spectral measurements from infrared
spectrometer) developed at the LOA laboratory, a maximum optical path difference (MOPD) of
4.42 cm was determined, corresponding to a spectral resolution
of 0.135 cm^{−1} using a sinc function with a spectral
sampling every 0.06025 cm^{−1} to satisfy the Nyquist
criterion. In FTIR spectroscopy, a poor instrumental line shape (ILS) determination generates
a significant error in the retrieval process, so we are currently
modifying the optical bench in order to perform an ILS determination
at the same time as the radiometric and spectral calibrations before
each field campaign.

The sampling of the interferogram is controlled by a standard, non-frequency-stabilized He–Ne laser with a wavelength of 632.8 nm,
which serves as a reference while converting from the distance scale
to the wave number scale. The instrument is subjected to changes in
pressure and temperature since it operates in different locations and
therefore under different meteorological conditions. This will cause
a change in the refractive index and as a consequence a change in the
reference wavelength of the laser, which will lead to an instability in
the conversion process and therefore the need for a spectral
calibration to reduce this error. The ILS line defined above is used
to resimulate isolated absorption lines from the high-resolution transmission molecular absorption (HITRAN) database
(Gordon et al., 2017) considering nonapodized spectra, which allows the
exploitation of the full spectral resolution. In short, we choose an
intense unsaturated H_{2}O absorption line that is always present in the spectra; then we compare the central wave number (*ν*) with
the calculated one (*ν*^{*}) following the equation

$$\begin{array}{}\text{(4)}& {\displaystyle}{\displaystyle}{\mathit{\nu}}^{*}=\mathit{\nu}(\mathrm{1}+\mathit{\alpha}),\end{array}$$

where *α* is the calibration factor. Equation (4)
is limited by a precision of 0.038 cm^{−1}, corresponding to
roughly half of the spectral sampling, estimated from the standard
deviation between the theoretical HITRAN spectroscopic lines and the
measured ones by CHRIS. Figure 3 shows the comparison
between a calibrated and a noncalibrated spectrum along with the
solar Planck function explained in Sect. 3.1. The spectral
and radiometric calibration procedure is automated using a MATLAB
code to convert the spectra instantly from numeric counts to absolute
radiance.

During campaigns and after long transportation, constant measurement of the internal blackbody, which can be heated up to 353 K, is carried out in the thermal infrared region (most affected by drifts). Figure 4 shows the variations of the internal blackbody during multiple field campaigns: a little fluctuation in function of the measurement conditions can be seen, but depending on the locations and even years, no systematic drift can be detected, so we can safely say that the instrument is quite stable between each laboratory calibration.

There are commonly several well-known spectral artifacts: aliasing, the picket fence effect (also known as the resolution bias error) and phase correction. These are well controlled in CHRIS.

Aliasing is the result of the missampling of the interferogram at the
*x*-axis locations, which leads to errors in the retrieved column
abundances due to its overlap with the original spectrum. The He–Ne laser,
having a wavelength *λ* of 632.8 nm, generates the sampling
positions of the interferogram at each zero crossing. No overlap will
occur if the signal of the spectrum is zero above a maximum wave number
*ν*_{max} and if *ν*_{max} is smaller than the folding
wave number ${\mathit{\nu}}_{\mathrm{f}}=\mathrm{1}/(\mathrm{2}\cdot \mathrm{\Delta}x)$. Since Δ*ν* is related to the
sample spacing Δ*x*, the minimum possible Δ*x* is
1∕31 600 cm since each zero crossing occurs every
*λ*∕2. This corresponds to a folding wave number of
15 800 cm^{−1}, i.e., the maximum bandwidth that can be measured
without overlap has a width of 15 800 cm^{−1}. This source error
is of special relevance to the spectra acquired in the near-infrared
region. However, for the MIR, the investigated bandwidth is much smaller
than 15 800 cm^{−1}, where *ν*_{max} is less than
5200 cm^{−1}, so CHRIS's spectra are not affected by this problem
(Dohe et al., 2013).

The picket fence effect, or the resolution bias error, becomes evident when the interferogram contains frequencies that do not coincide with the frequency sample points, but this is overcome in our spectra by the classical method of the zero filling factor (ZFF), where zeros are added to the end of the interferogram before the Fourier transform is performed, thereby doubling the size of the original interferogram.

Phase correction is necessary while converting the interferogram into a spectrum, which is relevant to single-sided measurements, similar to those acquired by CHRIS. Mertz phase correction is the method used for CHRIS to overcome this problem; it relies on extracting the real part of the spectrum from the complex output by multiplication of the latter by the inverse of the phase exponential, therefore eliminating the complex part of the spectrum generated.

Besides these classical FTIR artefacts, we noticed during our tests that when using a scan speed of 160 KHz, we drastically increase the nonlinearity effect of the detector (see Fig. 5). However, we identified a ghost signal for low scanning velocities (for example 40 KHz as shown in Fig. 6). This ghost is specific to CHRIS because it is caused by the noise introduced from the vibrations of the compressor used in the closed-cycle Stirling cooler as mentioned in Sect. 2.1. The choice of a scanning velocity of 120 KHz is a compromise between two important features: the elimination of the ghost signal, which appears at scanner velocities below 80 KHz, and the increase in the detector nonlinearity at a velocity of 160 KHz.

3 Information content analysis

Back to toptop
Since CHRIS is an instrumental prototype, its ability to retrieve GHGs
is unknown; therefore it is important to perform an information
content study to quantify its potential
capability to retrieve GHGs as a first attempt. In this context, CHRIS is one of the
instruments deployed in the MAGIC project alongside satellites, lidar,
balloons and ground-based measurements. MAGIC is a French
initiative supported by the CNES (Centre National d'Etudes Spatiales),
which aims to implement and organize regular annual campaigns in order
to better understand the vertical exchange of GHGs (CO_{2} and
CH_{4}) along the atmospheric column and establish a long-term
validation plan for the satellite Level 2 products.

Accurate calculations of the radiances observed by CHRIS are achieved
with the line-by-line radiative transfer algorithm ARAHMIS over the
thermal and shortwave infrared spectral range (1.9–14.7 µm). Gaseous
absorption is calculated based on the updated HITRAN 2016 database
(Gordon et al., 2017). The absorption lines are computed assuming a sinc
line shape, and no apodization is applied, which allows the exploitation
of the full spectral resolution. In this study, the term “all bands”
refers to the use of the CHRIS bands TB, B1, B2 and B3 simultaneously (see Sect. 2.2). Absorption continua for
H_{2}O and CO_{2} are also included from the Mlawer–Tobin–Clough–Kneizys–Davies (MT-CKD) model
(Clough et al., 2005). The pseudotransmittance spectra corresponding to
direct sunlight from the center of the solar disk reported by
Toon (2015) is used as the incident solar spectrum interpolated on
the spectral grid of CHRIS. The effective brightness temperature
depends strongly on the wave number; thus the Planck function is
calculated in each spectral domain of CHRIS determined from
Trishchenko (2006), who combined the work of four recent solar
reference spectra. Two of these reference spectra with 0.1 %
relative difference are taken into consideration and then adjusted by
a polynomial fit (solid line in Fig. 3). In the gaseous
retrieval process, the spectrometer's line of sight (LOS) has to be
known for calculating the spectral absorption of the solar radiation
while passing through the atmosphere. For this, the time and the
duration of each measurement are saved, from which the required
effective solar elevation (and the solar zenith angle, SZA)
is calculated based on the routine explained in Michalsky (1988).

As mentioned in Sect. 3.3.2, Izaña offers clear
nonpolluted measurements since it is high in altitude and away from major
pollution sites, so calculations are performed based on the concentration
of the desired atmospheric profile with the corresponding profile
information: the temperature, pressure and relative humidity are derived
from the radiosondes
(http://weather.uwyo.edu/upperair/sounding.html); CO_{2} and
CH_{4} profiles are derived from the TCCON database, whereas
O_{3}, N_{2}O and CO concentrations are calculated from
a typical midlatitude summer profile. Figure 7 shows the
results of the forward model simulation superimposed with the four
infrared bands measured by CHRIS. For each band, we present the influence
of the solar spectrum, the GHGs (CO_{2} and CH_{4}) and the major
interfering molecular absorbers. We can see good agreement between the
ARAHMIS simulations and the CHRIS measurements under clear sky conditions.

Once the forward model is calculated, we rely on the formalism of Rodgers (2000) that introduces the optimal estimation theory used for the retrieval, which is widely described elsewhere (e.g., Herbin et al., 2013a) and summarized hereafter.

In the case of an atmosphere divided into discrete layers, the forward
radiative transfer equation gives an analytical relationship between
the set of observations *y* (in this case the radiance) and the
vector of true atmospheric parameters ** x** (i.e., the variables to be retrieved: vertical concentration profiles of CO

$$\begin{array}{}\text{(5)}& \mathit{y}=F(\mathit{x};\mathit{b})+\mathit{\epsilon},\end{array}$$

where *F* is the forward radiative transfer function (here the ARAHMIS code), ** b** represents the fixed parameters affecting the measurement (e.g., atmospheric temperature, interfering species, viewing angle), and

In the following information content study, two matrices fully
characterize the information provided by CHRIS: the averaging kernel
**A** and the total error covariance **S**_{x}.

The averaging kernel matrix **A** gives a measurement of the sensitivity of the retrieved state to the true state and is defined by

$$\begin{array}{}\text{(6)}& \mathbf{A}=\partial \widehat{\mathit{x}}/\partial \mathit{x}=\mathbf{GK},\end{array}$$

where **K** is the Jacobian matrix (also known as the weighting function). The *i*th row contains the partial derivatives of the *i*th measurement with respect to each (*j*) element of the state vector ${\mathit{K}}_{ij}=(\partial {\mathit{F}}_{i}/\partial {\mathit{x}}_{j})$, and **K**^{T} is its transpose.

The gain matrix **G**, whose rows are the derivatives of the retrieved state with respect to the spectral points, is defined by

$$\begin{array}{}\text{(7)}& {\displaystyle}{\displaystyle}\mathbf{G}=\partial \widehat{\mathit{x}}/\partial \mathit{y}=({\mathbf{K}}^{\mathrm{T}}{\mathbf{S}}_{\mathit{\epsilon}}^{-\mathrm{1}}\mathbf{K}+{\mathbf{S}}_{\mathrm{a}}^{-\mathrm{1}}{)}^{-\mathrm{1}}{\mathbf{K}}^{\mathrm{T}}{\mathbf{S}}_{\mathit{\epsilon}}^{-\mathrm{1}},\end{array}$$

where **S**_{a} is the a priori covariance matrix describing our knowledge
of the state space prior to the measurement, and **S**_{ϵ}
represents the forward model and the measured signal error covariance
matrix.

At a given level, the peak of the averaging kernel row gives the
altitude of maximum sensitivity, whereas its full width at half
maximum (FWHM) is an estimate of the vertical resolution. The total
degrees of freedom for signal (DOFSs) is the trace of **A**, which
indicates the number of independent pieces of information that one can
extract from the observations with respect to the state
vector. A perfect retrieval resulting from an ideal inverse method
would lead to an averaging kernel matrix **A** equal to the identity
matrix with a DOFS value equal to the size of the state vector. Therefore,
each parameter we want to retrieve is attached to the partial degree
of freedom represented by each diagonal element of **A**.

The second important matrix in the information content (IC) study is the error covariance
matrix **S**_{x}, which describes our knowledge of the state space
posterior to the measurement. Rodgers (2000) demonstrated that this
matrix can be written as

$$\begin{array}{}\text{(8)}& {\displaystyle}{\displaystyle}{\mathbf{S}}_{x}={\mathbf{S}}_{\text{smoothing}}+{\mathbf{S}}_{\text{meas.}}+{\mathbf{S}}_{\text{fwd.mod.}}\end{array}$$

From Eq. (8), the smoothing error covariance matrix **S**_{smoothing} represents the vertical sensitivity of the measurements to the retrieved profile:

$$\begin{array}{}\text{(9)}& {\displaystyle}{\displaystyle}{\mathbf{S}}_{\text{smoothing}}=(\mathbf{A}-\mathbf{I}){\mathbf{S}}_{\mathrm{a}}\phantom{\rule{0.25em}{0ex}}(\mathbf{A}-\mathbf{I}{)}^{\mathrm{T}}.\end{array}$$

**S**_{meas.} gives the contribution of the measurement
error covariance matrix through **S**_{m}, which
illustrates the measured signal error covariance matrix, to the
posterior error covariance matrix
**S**_{x}. **S**_{m} is computed from the
spectral noise:

$$\begin{array}{}\text{(10)}& {\displaystyle}{\displaystyle}{\mathbf{S}}_{\text{meas.}}={\mathbf{GS}}_{\mathrm{m}}{\mathbf{G}}^{\mathrm{T}}.\end{array}$$

At last, **S**_{fwd.mod.} gives the contribution of the
posterior error covariance matrix through **S**_{f}, the forward model
error covariance matrix, which illustrates the imperfect knowledge of
the nonretrieved model parameters:

$$\begin{array}{}\text{(11)}& {\displaystyle}{\displaystyle}{\mathbf{S}}_{\text{fwd.mod.}}={\mathbf{GK}}_{b}{\mathbf{S}}_{b}({\mathbf{GK}}_{b}{)}^{\mathrm{T}}={\mathbf{GS}}_{\mathrm{f}}{\mathbf{G}}^{\mathrm{T}},\end{array}$$

with **S**_{b} representing the error covariance matrix of the
nonretrieved parameters.

The IC analysis uses simulated radiance spectra of CHRIS in the bands TB, B1, B2 and B3. The CO_{2} and CH_{4} vertical concentrations of the a priori state vector *x*_{a} are based on a profile that follows the criteria described in
Sect. 3.1 and discretized by 40 vertical layers, extending
from the ground to 40 km height with 1 km steps. In
addition, the vertical water vapor profile, the temperature and the
SZA are included in the nonretrieved parameters and are discussed in
Sect. 3.3.3. The a priori values and their variabilities are
summarized in Table 1 and are described in the following
sections.

In situ data and climatology can give us an evaluation of the a priori
error covariance matrix **S**_{a}. Since the use of
diagonal a priori covariance matrices is common for retrievals
from space measurements (e.g., De Wachter et al., 2017), and since this
study is dedicated to information coming from measurement rather
than climatology or in situ observations, we assume firstly that
**S**_{a} is a diagonal matrix with the *i*th diagonal
element (**S**_{a,ii}) defined as

$$\begin{array}{}\text{(12)}& {\displaystyle}{\displaystyle}{\mathbf{S}}_{\mathrm{a},ii}={\mathit{\sigma}}_{\mathrm{a},i}^{\mathrm{2}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\text{with}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}{\mathit{\sigma}}_{\mathrm{a},i}={x}_{\mathrm{a},i}.{\displaystyle \frac{{p}_{\text{error}}}{\mathrm{100}}},\end{array}$$

where *σ*_{a,i} stands for the standard deviation in the Gaussian statistics formalism. The subscript *i* represents the *i*th parameter
of the state vector. The CO_{2} profile a priori error is
estimated from Schmidt and Khedim (1991). The CH_{4} a priori error is
fixed to *p*_{error}=5 %, similar to the one used in
Razavi et al. (2009) for the retrieval of the methane obtained from IASI and
also to be consistent with the previous study concerning the TANSO-FTS
instrument (Herbin et al., 2013a).

Nevertheless, the correlation of the vertical layers is more expressed by the off-diagonal matrix elements. This is the reason we also use an a priori covariance matrix similar to the one used in Eguchi et al. (2010), where the climatology derived from TCCON is used to construct this matrix. The study with these two covariance matrices is presented for CHRIS in the following sections.

The measurement error covariance matrix is computed knowing the instrument
performance and accuracy. The latter is related to the radiometric noise
expressed by the SNR already discussed in Sect. 2.3. This error
covariance matrix is assumed to be diagonal, and the *i*th diagonal
element can be computed as follows:

$$\begin{array}{}\text{(13)}& {\displaystyle}{\displaystyle}{\mathbf{S}}_{\mathrm{m},ii}={\mathit{\sigma}}_{\mathrm{m},i}^{\mathrm{2}}\phantom{\rule{1em}{0ex}}\text{with}\phantom{\rule{1em}{0ex}}{\mathit{\sigma}}_{\mathrm{m},i}={\displaystyle \frac{{\mathit{y}}_{i}}{\text{SNR}}},\end{array}$$

where *σ*_{m,i} is the standard deviation of the *i*th measurement (*y*_{i}) of the measurement vector ** y**, representing the noise-equivalent spectral radiance. The SNR for CHRIS is estimated to be 780, and it is reported with other instrumental characteristics in Table 3.

The effects of nonretrieved parameters are a complicated part of an error description model. In our case these uncertainties are limited to the interfering water vapor molecules due to their important existence in the spectra and the effect of the temperature, where a vertically uniform uncertainty is assumed in both cases. It is important to note that in this study water vapor is considered as a nonretrieved parameter for the sake of comparison with Herbin et al. (2013a), but it will be part of the retrieved state vector in the inversion process, which will be the subject of a future study.

On the one hand, we assumed a partial column with an uncertainty
(*p*_{Cmol}) of 10 % instead of a profile error for
H_{2}O. On the other hand, we assumed a realistic uncertainty of
*δ**T*=1 K on each layer of the temperature
profile, which is compatible with the typical values used for
the European Centre for Medium-Range Weather Forecasts (ECMWF) assimilation. Moreover, we assumed a realistic uncertainty of 0.35^{∘}
on the SZA, corresponding to the difference in the solar angle during
the acquisition of a measurement corresponding to 100 scans. All these
variabilities are reported in Table 1.

The total forward model error covariance matrix
(**S**_{f}), assumed to be diagonal in the present study, is
given by adding the contributions of each diagonal element, and the
*i*th diagonal element (**S**_{f,ii}) is given by

$$\begin{array}{}\text{(14)}& {\displaystyle}{\displaystyle}{\mathbf{S}}_{\mathrm{f},ii}=\sum _{j=\mathrm{1}}^{n\text{level}}{\mathit{\sigma}}_{\mathrm{f},{T}_{j},i}^{\mathrm{2}}+{\mathit{\sigma}}_{\mathrm{f},{\mathrm{H}}_{\mathrm{2}}\mathrm{O},i}^{\mathrm{2}}+{\mathit{\sigma}}_{\mathrm{f},\text{SZA},i}^{\mathrm{2}}.\end{array}$$

Here, the spectroscopic effects such as the line parameter, the line
mixing and the continua errors are not considered, but they are
discussed with the *X*_{G} column estimation in Sect. 3.4.2.

An information content analysis is performed on the whole spectrum for
CO_{2} and CH_{4} separately to quantify the benefit of the
multispectral synergy. Separately means that the state vector comprises only one of the above gas concentrations at each level
between 0 and 40 km to match the altitudes reached by TCCON
and the MAGIC instruments (balloons and planes reaching altitudes of
more than 25 km). This corresponds to the case in which we
estimated each gas profile alone when all other atmospheric parameters
and all other gas profiles are known from ancillary data with
a specific variability or uncertainty. Two different SZAs (10 and
80^{∘}) are chosen to demonstrate the effect of the solar
optical path on the study since the sensitivity is correlated to the
viewing geometry. Furthermore two different a priori covariance
matrices are used to show the effect of using climatological data
describing the variability of GHG profiles. In the following
subsections, we explain in detail the averaging kernel, error budget
and total column estimations.

Figure 8 shows the averaging kernel **A** and total
posterior error **S**_{x} for CO_{2} for an angle of
10^{∘}. The figures of the second SZA (80^{∘}) are not shown
since the vertical distribution of the kernels and errors is quite
similar and exhibits only slight differences in the amplitude with
respect to the other angle. However, the results are different; they are discussed in order to quantify the information
variability with the viewing geometry. **A** is obtained for CO_{2}
independently using the variability introduced in
Sect. 3.3.1 and considering an observing system composed
of the band BT, B1, B2 or B3 separately and all the bands together to
quantify the contribution of each of the spectral bands and show the
benefits of the TIR–SWIR spectral synergy. Each colored line
represents the row of **A** at each vertical grid layer. Each peak of
**A** represents the partial degree of freedom of the gas at each level
that indicates the proportion of the information provided by the
measurement. In fact, if the value is close to unity, it means that
the information comes predominantly from the measurement, but a value
close to zero means that the information comes mainly from our prior
knowledge of the a priori state. We can clearly see that at lower
altitudes and up to 10 km, the kernels are close to unity,
suggesting that the measurement improved our knowledge, while at
higher altitudes (beyond 10 km) the kernels are close to
zero. It is also important to note that when using all the bands
simultaneously, the information distribution of the kernels is
improved and is more homogeneous along the vertical profile.

The measurement may provide information about CO_{2} from the ground
up to 20 km high in the atmosphere (all bands), while at much
higher altitudes the information comes mainly from the a priori profile due to
a smaller sensitivity of these gases in the upper troposphere. This is
clearly represented in the error budget study: the a posteriori total
error (solid black line) is significantly smaller than the a priori error
(red line) in the lower part of the atmosphere (between 0 and
20 km), which means that the measurement improved our knowledge of
the CO_{2} profile. Beyond 20 km, the total
a posteriori error is equal to the a priori error, suggesting a very poor
sensitivity at high altitudes. Furthermore, one can notice that the
measurement error stays very weak regardless of the band used, which proves
that the error related to the SNR is negligible. Furthermore, the forward model
error depending on the nonretrieved parameters remains quite
modest. However, the smoothing error predominates over the other errors and
becomes preponderant beyond 20 km, which means that the
information is strongly constrained by the a priori profile at high
altitudes, and little information is introduced from the measurement. To
overcome this problem, another similar study was conducted but with
a nondiagonal a priori covariance matrix (Eguchi et al., 2010). The vertical
distribution is more homogeneous through all the layers. The shape of the
error budget is very similar to that of the variance; however, the
a priori and a posteriori errors are significantly reduced. The
measurement and forward model errors remain weak, but it is important to
note that despite the fact that the smoothing error is smaller, the
constraint is stronger. This has the effect of decreasing the uncertainty but also increasing the propagation of the smoothing error along the vertical
layers, which explains the smaller values of the DOFSs.

Finally, the total DOFSs for CO_{2} are shown in
Table 4 for angles of 10 and 80^{∘}. It shows
that for a diagonal a priori covariance matrix, one might be able to
retrieve between two and three partial tropospheric columns for
CO_{2}, and as expected the DOFS value is slightly higher at 80^{∘}
since the optical path of the sun in every layer is longer. However, when
using a nondiagonal a priori covariance matrix, one less partial
tropospheric column is retrieved but with significant improvement in the
error budget estimation.

The same reasoning is followed for CH_{4}: **A** is obtained for
CH_{4} independently using the variability introduced in
Sect. 3.3.1 and considering an observing system composed of
the band TB, B1, B2 or B3 separately and all the bands
together. Figure 9 shows that the vertical distribution of
CH_{4} is more homogeneous than that of CO_{2}, and we can see
that the **A**'s are broader than those of CO_{2}, suggesting a very
important correlation between layers. The use of all the bands
simultaneously, just like CO_{2}, improves the information
distribution along the vertical profile. The forward model error is larger
than that of CO_{2} since methane is more affected by the
interfering species. The smoothing error is significantly larger than
CO_{2} since it is constrained by a much higher a priori profile variability, which
suggests a more direct effect on the retrieval of CH_{4}. Similar
to CO_{2}, when using a nondiagonal a priori covariance matrix, the
vertical distribution is very analogous to that of the variance
only. However, the a priori and a posteriori errors are significantly
reduced. The total DOFSs for CH_{4} are shown in
Table 5 for both SZAs. This parameter shows that, for
a diagonal a priori covariance matrix, three partial tropospheric columns and one additional partial column for an SZA of
80^{∘} can be retrieved. Finally, while using a nondiagonal a priori covariance
matrix the DOFSs show that one less partial column is retrieved.

As a general result, the simultaneous use of all the bands instead of
using each one separately increases the total DOFSs and systematically reduces the total errors of the two species. Moreover, using
a climatological a priori covariance matrix shows the importance of
reducing the error of the retrieved partial columns. Finally, the total
profile error is derived from the relative values of the diagonal matrix
of **S**_{x} (see Tables 4 and 5),
which are discussed in detail in the following section.

Ground-based instruments like the one used in the TCCON network and the
EM27/SUN operate in the NIR, where the column-averaged dry-air mole
fractions (denoted *X*_{G} for gas G) are calculated by monitoring the
observed O_{2} columns. *X*_{G} is calculated by rationing the gas-retrieved slant column to the O_{2}-retrieved slant column for the
same spectrum. Especially among the NDACC
community, another method is used to calculate *X*_{G} without using the oxygen reference. Based on
the formula given in Wunch et al. (2011) and used in Zhou et al. (2019), we can
calculate *X*_{G} for CO_{2} and CH_{4}:

$$\begin{array}{}\text{(15)}& {\displaystyle}{\displaystyle}{X}_{\mathrm{G}}={\displaystyle \frac{{\text{column}}_{\mathrm{G}}}{\text{column dry air}}}\end{array}$$

$$\text{column dry air}={\displaystyle \frac{{P}_{\mathrm{s}}}{{g}_{\text{air}}{m}_{\text{air}}^{\text{dry}}}}-{\text{column}}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}{\displaystyle \frac{{m}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}{{m}_{\text{air}}^{\text{dry}}}},$$

where ${m}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ and ${m}_{\text{air}}^{\text{dry}}$ are the mean molecular
masses of water and dry air, respectively; *P*_{s} is the surface pressure; and
*g*_{air} is the column-averaged gravitational
acceleration. Therefore, the calculation of *X*_{G} is possible if all these
parameters are available, particularly within the MAGIC framework, where we
have access to the balloons and
radiosondes data (temperature, surface pressure, relative humidity
etc.) along with all the instruments involved. Thus, for these particular
campaigns, *X*_{G} values will be calculated for CHRIS using ARAHMIS, and
the results will be compared with the other instruments involved,
especially the IFS125HR of the TCCON network and the EM27/SUN. This
will be the subject of an upcoming paper. However, the two equations for
the calculation of *X*_{G} are not strictly similar since the EM27/SUN
eliminates the systematic errors that are common to the target gas and
O_{2} column retrievals, which will not be possible for us since the
O_{2} band is not detected by CHRIS.

In addition, the total column uncertainty is calculated by adding the
concentration of each layer along the profile, weighted by the column
of dry air based on Figs. 8 and
9. Table 2 lists the propagated uncertainties
of the total column for both SZAs using a diagonal a priori covariance
matrix: the uncertainty of the total CO_{2} column is 2.89 %
and 2.6 % for 10 and 80^{∘}, respectively, while
the uncertainty for the total CH_{4} column is 4.4 % and
4.19 % for 10 and 80^{∘}, respectively. The
uncertainties are smaller for an SZA of 80^{∘} because the
information distribution is improved with a longer OPD. Furthermore,
these results show that the total profile error for CH_{4} is
almost 2 times higher than that of CO_{2}, but this is explained
by the fact that our profile error is limited by the a priori profile
error, which is much higher for CH_{4} than for CO_{2}. The
dominating component of the uncertainty comes from the smoothing, which
predominates over the other uncertainties for both GHGs and is the major
contributor to the total profile error. H_{2}O, temperature and
SZA are the most important parameters contributing to the forward
model; they are represented by the nonretrieved parameter
uncertainty. Additionally, it is important to note that there is
a supplementary uncertainty associated with the spectroscopy unaccounted
for in our study, which is purely systematic. It is not simple to
evaluate in this case because we use different spectral domains, each
having different spectroscopic uncertainties listed in the HITRAN
database.

During the MAGIC campaigns, several EM27/SUN and two IFS125HR instruments from the TCCON network were operated alongside CHRIS. An information content analysis is presented in the following sections for both of these instruments in order to compare and complement the study performed on CHRIS in Sect. 3.4.

In this section, an IC study is performed for the EM27/SUN instrument
in order to compare it with our results and to investigate the
possibility of complementing the data we obtained from CHRIS,
especially for MAGIC. The bands of the EM27/SUN used in this study are
denoted as follows: B3 is the common band with CHRIS and has a spectral
range of 4700–5200 cm^{−1}, B4 goes from 5460 to
7200 cm^{−1}, and B5 spans the spectral region between 7370
and 12 500 cm^{−1}.

Firstly, a similar study to CHRIS is performed on the EM27/SUN for
CO_{2} and CH_{4} separately. As mentioned in
Sect. 3.4, the state vector comprises only one of
the gas concentrations with the same profile at a layer going from 0
to 40 km; however, we took into account the SNR and spectral
resolution specific to this instrument (see
Table 3). Similar to the reasoning for CHRIS followed in
Sect. 3.4, this study shows that using all the EM27/SUN
bands together leads to an improvement of the a posteriori error
profile of CO_{2} concentrations, especially in the lower part of
the atmosphere. Table 4 shows the DOFSs for CO_{2}
of the EM27/SUN: using a diagonal a priori covariance matrix for an angle
of 10^{∘}, the total DOFSs for bands B3 (common band with CHRIS) and
B4 as well as all bands together are 2.95, 1.63 and 3.03, respectively. If
only band B3 is taken into consideration, which is the common band
between the two instruments, the DOFSs of CHRIS in this band are, as
stated before, 2.62 and 3.34 for an angle of 10 and 80^{∘},
respectively, compared to 2.95 and 3.17 for the EM27/SUN. Therefore, the
same number of partial columns can be retrieved using CHRIS (see
Sect. 3.4) for CO_{2} in this band. Furthermore,
similar to CHRIS, the total error is reduced with a more
propagated smoothing error on the profile and a reduction in the
DOFSs when using a nondiagonal a priori covariance
matrix (Eguchi et al., 2010). As for CH_{4} and referring to Table 3, band 3
in this instrument begins (4700 cm^{−1}) where the CH_{4}
band ends (4150–4700 cm^{−1}) in the IFS125HR and CHRIS. This is
important because TCCON networks begin their measurements at
4000 cm^{−1}, which allowed for the comparison with band 3 of
CHRIS (for both CO_{2} and CH_{4}). However, the EM27/SUN
instruments have no exploitable signal before 4700 cm^{−1}
(Gisi et al., 2012); therefore the CH_{4} absorption lines do not
show in the common band between CHRIS and the EM27/SUN, so the results
are not discussed here.

Secondly, a simultaneous IC study was performed on all the channels
of both CHRIS and the EM27/SUN in order to analyze the complementary
aspect of these two instruments. The results of this study are shown
in Fig. 10. The DOFSs obtained for CO_{2} are
3.67 and 3.93 for angles 10 and 80^{∘}, respectively; for CH_{4} they are 3.99 and 4.43. This indicates a significant
improvement of the retrieval when the spectral synergy between TIR, SWIR and NIR
is used, but it is less than the one obtained from space (for example
TANSO-FTS in Herbin et al., 2013a) since the measurement is obtained
from the same optical path.

As mentioned before, the IFS125HR is a ground-based high-resolution
infrared spectrometer used at NDACC and TCCON stations around
the world. We performed a similar information content study only
on the TCCON instrument since this network is involved in the
MAGIC campaigns; therefore the results can be compared. For
simplicity, the same annotation of the bands is kept for this
section. The same methodology described in Sect. 3.4
is used here: the state vector comprises only CO_{2}
and CH_{4} concentrations at a layer going from 0 to
40 km, where the SNR and the spectral resolution specific
to the IFS125HR are taken into consideration (see
Table 3).

We follow the same reasoning as in the sections before:
Fig. 11 shows the averaging kernel **A** and
the total posterior error **S**_{x} for CO_{2} and
CH_{4} for an angle of 10^{∘}. We can see that the
vertical distribution is more homogeneous than CHRIS and the EM27/SUN,
suggesting a high sensitivity at high altitudes, although in the
lower atmosphere the a posteriori error **S**_{x} is
significantly reduced. This is also shown in the error budget
study: we can still distinguish the a posteriori total error
(solid black line) from the a priori error (red line) even in the
higher atmosphere. This is explained by the fact that the IFS125HR
has a spectral resolution higher than both CHRIS and the EM27/SUN, so
the measurement always improves our knowledge of the profile all
along the atmospheric column. Furthermore, when using a nondiagonal
a priori covariance matrix, the total profile error is
significantly reduced, especially for CH_{4}; however, the
DOFSs are also reduced.

The DOFSs of CO_{2} and CH_{4} are shown in
Table 4 for both viewing angles and a priori covariance
matrices. On the one hand, one additional partial tropospheric column for
CO_{2} can be retrieved with respect to CHRIS for an angle of
10^{∘} and with respect to the EM27/SUN for both angles if all the bands are used. On
the other hand, one additional partial tropospheric column can be
retrieved for CH_{4} with respect to CHRIS for both angles if all the bands are used.

4 Channel selection

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Using all the channels in the retrieval process has two
disadvantages. First of all, it requires a very large computational
time. Secondly, the correlation of the interfering species increases
the systematic error. In this case, the a priori state vector
*x*_{a} and the error covariance matrix
**S**_{a} are very difficult to evaluate. Channel
selection is a method described by Rodgers (2000) to optimize
a retrieval by objectively selecting the subset of channels that
provides the greatest amount of information from high-resolution
infrared sounders. L'Ecuyer et al. (2006) offer a description of this
procedure based on the Shannon information content. Firstly, we create
an “information spectrum” in order to evaluate the information
content with respect to the a priori state vector. The channel with
the largest amount of information is then selected. A new spectrum is
then calculated with a new a posteriori covariance matrix that is
adjusted according to the channel selected in the first iteration to
account for the information it provides. In this way a second channel
is chosen, based on this newly defined state space. This channel provides
maximal information relative to the new a posteriori covariance
matrix. This process is repeated, and channels are selected
sequentially until the information in all the remaining channels falls
below the level of measurement noise. As stated by the Shannon information
content and noted in Rodgers (2000), it is convenient to work on
a basis on which the measurement errors and prior variances are
uncorrelated in order to compare the measurement error with the
natural variability of the measurements across the full prior
state. Therefore, it is desirable to transform the Jacobian matrix **K**
(see Sect. 3.2) into $\stackrel{\mathrm{\u0303}}{\mathbf{K}}$ using

$$\begin{array}{}\text{(16)}& {\displaystyle}{\displaystyle}\stackrel{\mathrm{\u0303}}{\mathbf{K}}={\mathbf{S}}_{y}^{-\mathrm{1}/\mathrm{2}}{\mathbf{KS}}_{\mathrm{a}}^{\mathrm{1}/\mathrm{2}},\end{array}$$

which offers the added benefit of being the basis on which both the a priori and the measurement covariance matrices are unit matrices. Furthermore, Rodgers demonstrates that the number of singular values of $\stackrel{\mathrm{\u0303}}{\mathbf{K}}$ greater than unity defines the number of independent measurements that exceed the measurement noise defining the effective rank of the problem.

Letting **S**_{i} be the error covariance matrix for the state space after *i* channels have been selected, the information content of channel *j* of the remaining unselected channels is given by

$$\begin{array}{}\text{(17)}& {\displaystyle}{\displaystyle}{H}_{j}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{log}}_{\mathrm{2}}\left(\mathrm{1}+{\stackrel{\mathrm{\u0303}}{\mathit{k}}}_{j}^{\mathrm{T}}{\mathbf{S}}_{i}{\stackrel{\mathrm{\u0303}}{\mathit{k}}}_{j}\right),\end{array}$$

where ${\stackrel{\mathrm{\u0303}}{\mathit{k}}}_{j}$ is the *j*th row of $\stackrel{\mathrm{\u0303}}{\mathbf{K}}$. *H*_{j}
constitutes the information spectrum from which the first channel is
selected. Taking the chosen channel to be channel *l*, the covariance
matrix is then updated before the next iteration using the following
statement:

$$\begin{array}{}\text{(18)}& {\displaystyle}{\displaystyle}{\mathbf{S}}_{i+\mathrm{1}}^{-\mathrm{1}}={\mathbf{S}}_{i}^{-\mathrm{1}}+{\stackrel{\mathrm{\u0303}}{\mathit{k}}}_{l}{\stackrel{\mathrm{\u0303}}{\mathit{k}}}_{l}^{\mathrm{T}}.\end{array}$$

In this way, channels are selected until 90 % of the total
information spectrum *H* is reached in a way that the measurement noise
is not exceeded.

After that, *H*, expressed in bits, is converted to DOFSs to obtain Fig. 12, which represents the total DOFS evolution for CO_{2} and CH_{4} as a function of the number of selected channels for all spectral bands and for an SZA of 10^{∘}. CHRIS has 75 424 channels in total; 13 800 are unusable because of the water vapor saturation between the bands, which leaves us with 61 624 exploitable
channels. A preselection of these channels, based on
Fig. 7, is done where the number of exploitable channels is
reduced to the spectral areas where we find CO_{2} and
CH_{4} (13 447 and 19 751 preselected channels,
respectively). In Fig. 12, the DOFSs for each
gas increase sharply with the first selected channels at first glance and then more
steadily. The number of channels required to reach 90 % and
99 % of the total information is represented in
Table 6. For CO_{2}, out of the 1329 channels,
55.76 % of the information comes from B3 (common band with
the EM27/SUN), 37.24 % from TB and 6.99 % from B1. As for CH_{4}, out of the 1387 channels, 46.86 % of the information comes from B2, 28.19 % from TB and 24.9 % from B3. This result shows that most of the information for CO_{2} and CH_{4} comes from B3 and TB,
respectively, which indicates that the synergy between TIR and SWIR
observations is confirmed.

Furthermore, the 1329 and 1387 selected channels represent 2.15 % and 2.25 % of the 61 624 exploitable channels, respectively, so a retrieval process that uses selected channels corresponding to 90 % of the total information content would give comparable results to the one using the entire set of channels since almost 98 % of the information is redundant. Hence, these results indicate the interest of determining an optimal set of channels for each gas separately. This is why this channel selection will be used in the retrieval process, making it easier and less time consuming.

5 Conclusions

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In conclusion, this paper presents the characteristics of the new
infrared spectrometer CHRIS, which allows the retrieval of GHGs and trace
gases. This instrumental prototype has unique characteristics such as
its high spectral resolution (0.135 cm^{−1}) and wide spectral
range (680–5200 cm^{−1}), covering the MIR region. In the
context of its exploitation to retrieve GHGs, spectral and radiometric
calibrations were performed using a calibrated external blackbody
reaching a temperature of 1523 K. Additionally, between
laboratory calibrations and during field campaigns the radiometric
stability is monitored through measurements of the internal
blackbody. Within the MAGIC framework, an extensive information content
analysis is performed, showing the potential capabilities of this
instrument to retrieve GHGs using two different SZAs (10 and
80^{∘}) to quantify the improvement of the information
with the solar optical path. Furthermore, two a priori covariance
matrices were used: one diagonal and another derived from
climatological data. The total column uncertainty is estimated, showing
that when using a diagonal a priori covariance matrix the error for an
angle of 10^{∘} is of the order of 2.89 % for
CO_{2} and 4.4 % for CH_{4} for all the bands;
however, when using a climatological distribution the total column
error for the same angle and for all the bands is reduced to
1.01 % for CO_{2} and 1.5 % for CH_{4} but
with a significant decrease in the DOFSs (from 2.95 to 2.38 for
CO_{2} and from 3.34 to 2.57 for CH_{4}). Furthermore, a comparison
study with the IFS125HR of the TCCON, which is widely used in the
satellite validation process, is performed, illustrating the benefits
of its high spectral resolution for GHG retrievals. Moreover,
a complementary study is carried out on the EM27/SUN to investigate
the possibility of a retrieval exploiting the synergy between
TIR, SWIR and NIR observations, which showed that a significant improvement
can be obtained. For example, with an SZA of 10^{∘} the DOFSs are
increased from 2.95 to 3.67. Finally, a channel selection is
implemented to remove the redundant information. The latter will be
used in future work dedicated to the CO_{2} and CH_{4}
total column retrievals for the MAGIC campaigns.

Data availability

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Data availability.

All CHRIS data are available by contacting the authors.

Author contributions

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Author contributions.

MTEK and HH wrote the paper and produced the main analysis and results. FA, HH and MTEK designed the calibration study, performed the laboratory measurements and participated in the field campaigns. All authors read and provided comments on the paper.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

We acknowledge Fabrice Ducos for providing IT support and extensive expertise that greatly assisted this work and most of all for his great work on the ARAHMIS algorithm development. We would also like to thank the Ecole Centrale de Lille for its help on the radiometric calibration. Finally, we acknowledge Denis Petitprez from the PC2A laboratory for his experimental help on the ILS characterization.

Financial support

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Financial support.

This research has been supported by the CNES (Centre National d'Etudes Spatiales) TOSCA-MAGIC project.The CaPPA (Chemical and Physical Properties of the Atmosphere) project is funded by the French National Research Agency (ANR) through the PIA (Programme d'Investissement d'Avenir) (contract no. ANR-11-LABX-0005-01) and by the regional council Nord Pas de Calais-Picardie and the European Funds for Regional Economic Development (FEDER).

Review statement

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Review statement.

This paper was edited by Alyn Lambert and reviewed by two anonymous referees.

References

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Short summary

This paper is submitted as part of my thesis project. It highlights the importance of ground-based measurements for future satellite validations. This paper represents the characteristics of a new prototype called CHRIS, which is the MIR version of the EM27/SUN. Our primary concern is the exploitation of the data of the MAGIC campaign, which is a French initiative in collaboration with the CoMet project, to monitor greenhouse gases.

This paper is submitted as part of my thesis project. It highlights the importance of...

Atmospheric Measurement Techniques

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