In this subsection we give a very brief introduction to the principles of the optimal estimation retrieval method. It is a standard retrieval method in atmospheric remote sensing. For more details, please refer to , and for a general introduction on vector and matrix algebra, dedicated textbooks are recommended.

Atmospheric remote sensing means that the atmospheric state is retrieved from the radiation measured after it has interacted with the atmosphere. This interaction of radiation with the atmosphere is modelled by a radiative transfer model (also called the forward model, F), which enables the measurement vector and the atmospheric state vector to be related by y=F(x,b). We measure y (the measurement vector, e.g. a thermal nadir spectrum in the case of IASI) and are interested in x (the atmospheric state vector). Vector b represents auxiliary parameters (like surface emissivity) or instrumental characteristics (like the instrumental line shape) which are not part of the retrieval state vector. However, a direct inversion of Eq. () is generally not possible because there are many atmospheric states x that can explain one and the same measurement y.

For solving this ill-posed problem, a cost function J is set up that combines the information provided by the measurement with a priori known characteristics of the atmospheric state: J=y-F(x,b)TSy,noise-1y-F(x,b)+x-xaTSa-1x-xa. Here, the first term is a measure of the difference between the measured spectrum (represented by y) and the spectrum simulated for a given atmospheric state (represented by x), while taking into account the actual measurement noise (Sy,noise is the measurement noise covariance matrix). The second term of the cost function (Eq. ) constrains the atmospheric solution state (x) towards an a priori most likely state (xa), whereby the kind and strength of the constraint are defined by the a priori covariance matrix Sa. The constrained solution is reached at the minimum of the cost function (Eq. ). Due to the non-linear behaviour of F(x,b), the minimization is generally achieved iteratively. For the (i+1)th iteration it is xi+1=xa+Gi[y-F(xi,b)+Ki(xi-xa)].

K is the Jacobian matrix (derivatives that capture how the measurement vector will change for changes in the atmospheric state x). G is the gain matrix (derivatives that capture how the retrieved state vector will change for changes in the measurement vector y). G can be calculated from K, Sy,noise and Sa as G=KTSy,noise-1K+Sa-1-1KTSy,noise-1.

The averaging kernel is an important component of a remote sensing retrieval and it is calculated as A=GK.

The averaging kernel A reveals how a small change of the real atmospheric state vector x affects the retrieved atmospheric state vector x^: x^-xa=A(x-xa).

The propagation of errors due to parameter uncertainties Δb can be estimated analytically with the help of the parameter Jacobian matrix Kb (derivatives that capture how the measurement vector will change for changes in the parameter b). According to Eq. (), using the parameter b+Δb (instead of the correct parameter b) for the forward model calculations will result in an error in the atmospheric state vector of Δx^=-GKbΔb.

The respective error covariance matrix Sx^,b is Sx^,b=GKbSbKbTGT, where Sb is the covariance matrix of the uncertainties Δb.

Noise on the measured radiances also affects the retrievals. The error covariance matrix for noise can be analytically calculated as Sx^,noise=GSy,noiseGT, where Sy,noise is the covariance matrix for noise on the measured radiances y.

The MUSICA IASI retrieval is based on a nadir version of the retrieval code PROFFIT PROFile FIT and on the corresponding radiative transfer model PRFFWD PRoFit ForWarD model. The nadir code has been developed in support of the project MUSICA (MUlti-platform remote Sensing of Isotopologues for investigating the Cycle of Atmospheric water; http://www.imk-asf.kit.edu/english/musica.php, last access: 29 August 2018). The PRFFWD nadir code has been recently updated by including water continuum calculations according to the model MT_CKD v2.5.2 .

For the MUSICA IASI retrieval calculations, a single broad spectral window from 1190 to 1400 cm-1 is used. The spectral signatures of H216O, H218O, and H217O are fitted together as a single species (from now on called H2O) and 1H2H16O (from now on called HDO) as a separate species. Furthermore, the retrieval's spectral window contains spectroscopic features of CH4 and N2O as well as weak spectroscopic features of HNO3 and very weak spectroscopic features of CO2. All these trace gases are simultaneously fitted during the retrieval process, whereby the spectroscopic parameters are taken from the HITRAN 2016 database with small modifications for HDO parameters (similar to , the line intensity parameters of HDO have been increased by 10 %).

For the water isotopologues, CH4, N2O, and HNO3 profile retrievals are performed on a logarithmic scale. For CO2 the a priori profiles are scaled. A single a priori profile is used for all the retrievals for each of the different trace gases; i.e. the a priori profiles used are the same for all locations and time periods . For CH4, N2O, HNO3, and CO2 the a priori profiles are averaged low-latitude profiles from WACCM (Whole Atmosphere Community Climate Model-version 6, and are provided by NCAR (National Center for Atmospheric Research, James W. Hannigan, private communication, 2009). The water vapour isotopologue a priori data are averages obtained from the isotopologue incorporated global general circulation model LMDZ .

The retrieval also fits the surface temperature and the atmospheric temperature profile, whereby the a priori temperatures are taken from the EUMETSAT IASI level 2 (L2) products. There is no constraint on the surface temperature. The atmospheric temperature variations allowed are 1 K at the ground, 0.5 K in the free troposphere, and 0.75 K above the tropopause. This altitude dependency roughly follows the altitude dependency of uncertainties in the EUMETSAT IASI L2 atmospheric temperature profiles .

The MUSICA IASI water vapour retrieval only works for pixels that are not contaminated by clouds, whereby we rely on the IASI L2 cloud flag (we require zero for the flag “cldfrm”). Ground elevations are from GTOPO30 developed by the US Geological Survey and provided by the Oak Ridge National Laboratory Distributed Active Archive Center (ORNL DAAC). GTOPO30 is a global digital elevation model with a horizontal grid spacing of 30 arcsec (approximately 1 km). The land surface emissivities are from the global database of infrared land surface emissivity (IREMIS; http://cimss.ssec.wisc.edu/iremis/, last access: 29 August 2018; ), and the sea surface emissivities are calculated according to the model of and for an assumed surface wind speed of 5 m s-1.

Figure  depicts an example of a typical radiance spectrum in the retrieval's spectral range as measured by IASI (upper graph) and the corresponding differences compared to the simulated spectra (the residuals, lower graph). The residuals are mostly within the order of the instrument's 1σ measurement noise . However, there are also distinctive spectral signatures that are not well understood, specifically at 1250 and at 1280 cm-1.

For further information on the retrieval set-up and its evolution, more detailed descriptions are available in , , , and .

The output of the retrieval refers to the ln⁡H2O,ln⁡HDO basis system. In this basis system the state vector x consists of the vector for the H2O profile extended by the vector for the HDO profile: x=xH2OxHDO.

Correspondingly, the averaging kernel matrix A has 2×2 blocks A=A11A12A21A22. A11 and A22 describe how the retrieved H2O and HDO states depend on the actual atmospheric H2O and HDO variations, respectively, and A12 and A21 reveal the cross-dependencies of the retrieved H2O on the actual atmospheric HDO and of the retrieved HDO on the actual atmospheric H2O, respectively. Since H2O and HDO vary largely in parallel, in the following we use the A11+A12 as the kernel for H2O see also Sect. 4.3 in.

Similarly, retrieval error covariance matrices consist of 2×2 blocks, whereby the blocks in the diagonal represent the H2O and HDO covariances. For this study only the H2O covariance block is of interest (i.e. we are only interested in the H2O error covariances). The outer diagonal blocks represent the error covariances between H2O and HDO.

The Vaisala RS92 radiosonde is equipped with a wire-like capacitive temperature sensor (“Thermocap”), two polymer capacitive moisture sensors (“Humicap”), a silicon-based pressure sensor, and a GPS receiver to measure position, altitude, and winds. Each second the RS92 transmits sensor data, which are received, processed, and stored by the ground station equipment.

The Humicap consists of a hydro-active polymer thin film as the dielectric between two electrodes applied on a glass substrate. The humidity sensors are not covered by protective caps, but they are alternately heated to prevent icing. To prevent overheating, the heating of the humidity sensors is switched off below -60 ∘C, or above 100 hPa, whichever is reached first. Humicaps show good performance over a wide range of temperatures but suffer from systematic errors such as dry bias due to solar radiative heating and a response lag below -40 ∘C. Known main error sources affecting the humidity profile are daytime solar heating of the Humicaps introducing a dry bias, sensor time lag at temperatures below about -40 ∘C, and temperature-dependent calibration correction.

We work with Vaisala RS92 data that have been processed by the GRUAN lead centre (http://www.gruan.org, last access: 29 August 2018). The GRUAN data processing assures that the humidity, pressure, and temperature profiles obtained are well calibrated and highly accurate .

At Manus Island we have coincidences in 2011, 2012, and 2013 with 25 individual GRUAN radiosonde profiles. The collocation of IASI and GRUAN measurements has been performed by EUMETSAT in the framework of a planned IASI retrieval comparison study , allowing a spatial and temporal window of 25 km and 30 min respectively.

For our retrieval we use the a priori temperatures (atmosphere and surface skin) as well as surface emissivities from the EUMETSAT IASI L2 product generated with the IASI L2 PPF software version 5. Since most of the ground scenes are over the ocean surface, the emissivity values are mainly according to the model of . The satellite pixels have been careful examined for clouds by EUMETSAT according to the cloud flags as provided in the IASI L2 data and in addition by visual inspection .

For Lindenberg there are coincidences with 32 individual GRUAN profiles in 2008 (representative of all seasons). We performed the collocation and required that the satellite pixel has to be within a distance of 25 km with respect to the starting position of the radiosonde and that the satellite's pixel sensing time has to be within the sensing time period of the radiosonde.

As for Manus Island we rely on the IASI L2 data for our retrieval input data (surface and atmospheric temperatures, surface emissivity, cloud filter, etc.). However, while for the 2011–2013 time period (Manus Island) the IASI L2 data are generated with the IASI L2 PPF software version 5, for the 2008 retrievals we work with L2 data generated by the IASI L2 PPF software version 4. As shown in , there can be inconsistencies between the MUSCA IASI products that are generated using different IASI L2 PPF software versions.

In 2007 we have 26 individual GRUAN profiles for Lindenberg and 17 individual GRUAN profiles for Sodankylä (details on the Sodankylä campaign are available in ) that coincide with IASI observations. This data set is limited to the summer observations. We performed the collocation using the same criteria as for the Lindenberg 2008 coincidences; i.e. we required that the satellite pixel has to be within a distance of 25 km with respect to the starting position of the radiosonde and that the satellite's pixel sensing time has to be within the sensing time period of the radiosonde.

For summer 2007 IASI L2 data were not available for our retrieval input. Thus data from the radiosonde measurements were used as the a priori temperatures. Above the top altitude of the radiosonde we use zonally and monthly averaged temperature climatologies COSPAR International Reference Atmosphere. Using the GRUAN temperatures (and climatologies at higher altitudes) instead of the IASI L2 temperatures as the a priori values for the atmospheric temperatures might cause some inconsistency between the LI07 and SK07, on the one hand, and the MI and LI08 retrievals, on the other hand.

Surface emissivities are taken from the global database of infrared land surface emissivity (IREMIS; http://cimss.ssec.wisc.edu/iremis/, last access: 29 August 2018; ), i.e. in agreement to the retrievals for 2008 (IASI L2 emissivities are based on IREMIS for land surfaces and use the Masuda model for sea surfaces). Because there are no IASI L2 cloud products for summer 2007, we use the radiosonde measurements and the cloud detection algorithm according to the model of for identifying cloud-free situations.

Figure  illustrates examples of H2O row kernels (A11+A12, logarithmic state vector entries according to Sect. ) for the three reference sites. Grey lines show all row kernels, and the thick coloured lines highlight the kernels for some selected altitudes. The peaks of the row kernels for the altitudes of 1.8, 3.6, 6.4, and 9.8 km are close to their nominal altitudes, meaning that the values retrieved for these altitudes represent the situation at the nominal altitude well. In contrast, the row kernel for the ground altitude peaks typically 1 km above ground altitude, meaning that data retrieved at the ground level mainly represent the altitudes about 1 km above the ground level. The row kernel for the 13.6 km altitude only peaks close to its nominal altitude for the tropical site of Manus Island. At Lindenberg and Sodankylä, the respective kernels peak at 9–10 km altitude; i.e. at these sites variations in the 13.6 km retrieval data are mainly driven by the actual atmospheric variations at 9–10 km.

The thick black dashed line represents the sum along the row of the averaging kernel matrix and is a measure of the remote sensing system's sensitivity. This value is typically between 0.9 and 1.1 from 1 up to 11 km at Lindenberg and Sodankylä, and from 1 up to 13 km at Manus Island.

The seasonal dependency of the averaging kernels is indicated in Fig. , which depicts the seasonal variations in the degree of freedom for signal (DOFS) values. The DOFS values are calculated as the trace of the averaging kernel matrix, and the higher the DOFS values are, the more profile information is in the retrieved atmospheric state. In the tropics we observe no seasonal dependency. In the mid-latitudes the DOFS values are distinctively higher in summer than in winter. More details on this seasonal dependency are provided in Fig. , which depicts typical wintertime and typical summertime row kernels for Lindenberg. It seems that the seasonal variation is mostly a variation of the sensitivity at higher altitudes. In summer the remote sensing system can detect the actual atmospheric variations up to 11–12 km, whereas in winter the sensitivity is limited to altitudes below 8–9 km. This is connected to the variation of the tropopause altitude. As shown in , the averaging kernels depend strongly on the atmospheric temperature and humidity profiles (as well as on the surface temperature and emissivity).

In summary, at all three different sites, the MUSICA IASI retrieval provides H2O profile information from about 1 km above ground up to about the altitude of the tropopause.

The error Jacobians (Kb from Eqs.  and ) are calculated by the forward model PRFFWD as follows: PRFFWD is executed running on a vertical grid of 28 levels from the surface altitude to approximately 55 km above mean sea level. For every site reference, forward calculations are performed for all cloud-free situations. The input (i.e. temperature, trace gas concentrations, etc.) for the reference forward model runs is the same as the input used in the forward calculation of the last iteration step of the MUSICA IASI retrievals; i.e. the reference radiances are given by F(x^,b). Then for each reference scenario we make additional forward calculations with slightly modified parameters; i.e. we calculate F(x^,b+Δb). For a measurement vector y with m elements and a parameter vector b with n elements, the Jacobian matrix Kb will have the dimension m×n. The individual matrix elements are calculated as Kbk,l=Fk(x^,b+Δbl)-Fk(x^,b)Δbl, where k is the index for the kth element of the measurement state vector y (simulated by vector function F) and l is the index for the lth element of the parameter vector b, respectively.

Table  gives an overview of the uncertainty assumptions Δb used for calculating the Jacobians and for performing the error estimation. The calculations of the error Jacobians for water vapour continuum and clouds require specific treatment, which is detailed in the following two subsections.

Figure  depicts the spectral responses (i.e. KbΔb) for an example of different uncertainty sources for a typical situation at the tropical reference site. The left panel shows that lower tropospheric temperature uncertainties mainly affect the spectra between 1190 and 1250 cm-1 (which is also the spectral region of an “atmospheric window”), but are negligible for higher wavenumbers. This is in contrast to upper tropospheric temperature uncertainties, which have the highest spectral responses for wavenumbers larger than 1250 cm-1.

The right panel of Fig.  illustrates that uncertainties in dust layers and uncertainties due to cirrus clouds have the highest impact at the lower end of wavenumbers and that a cirrus cloud has a different dependency on wavenumber than a dust layer. Furthermore unrecognized clouds have the opposite effect on the spectrum than increasing the atmospheric temperatures although affecting the spectrum in the same order of magnitude.

Figure  shows a certain seasonal variability in the DOFS values (in particular at the mid-latitude site), indicating varying sensitivities of the remote sensing system. This variation is also present in the sensitivity with respect to uncertainty sources. For this reason we present the estimated errors for all the Manus Island and Sodankylä retrievals (MI and SK07) and for all the Lindenberg 2008 retrievals (LI08). The Lindenberg 2008 error estimations are representative of all seasons; hence they cover the full sensitivity variation with respect to uncertainty sources well.

Table  gives on overview of the different uncertainty sources we consider for our error estimation. We distinguish between random uncertainty sources (the uncertainty affecting an observation is uncorrelated with the uncertainty affecting another observation), systematic uncertainty sources (the uncertainty is the same for all observations), and uncertainty sources that are always positive but with a random amplitude (clouds: the sky is either cloud-free or covered by a random amount of cloud).

The in situ profiles have a high vertical resolution. This differs from the remote sensing profiles, which can only detect the major characteristics of the vertical H2O distribution. Before comparing the data we have to account for these different characteristics by regridding and smoothing the in situ profiles.

While the remote sensing retrieval provides atmospheric states and averaging kernels on a coarse atmospheric grid (between ground level and about 55 km a.s.l., 28 grid points are defined), the radiosonde reports data about every 5 m. Therefore, we have to regrid the radiosonde data to the coarse vertical grid used by the remote sensing retrieval. In order to guarantee that the regridding does not significantly affect the H2O partial columns, the regridding is performed in two steps.

First, the radiosonde data points between the 28 MUSICA retrieval grid points are averaged by using a triangle inverse-distance-weighted function resulting in a first estimate of the regridded radiosonde data. In the second step this first estimate is corrected by requiring that the partial columns between adjacent grid levels remain almost the same in the original high-resolution data and in the regridded data. In the correction process a constraint is put on the smoothness of the profile, thereby preventing the correction from producing strongly oscillating profiles. The results are regridded data consisting of reasonably smooth profiles with practically the same partial columns as the original high-resolved radiosonde profiles. For the high altitudes that are not detected by the GRUAN radiosonde, we use the retrievals' a priori data (xa).

The regridded GRUAN in situ profiles g may be smoothed according to the averaging kernels of the remote sensing retrieval. The regridded and smoothed GRUAN in situ profile g^ is then comparable to the remote sensing profile, whereby g^=(A11+A12)(g-xa)+xa. Here A11 is the H2O block of the averaging kernel matrix, A12 the block that describes the response of the retrieved H2O to atmospheric HDO (see Sect. ), and the vector xa is the a priori state vector. An example illustrating the effects of the regridding and the smoothing is given in Fig. .

We would like to note that by using Eq. () we assume that H2O and HDO variations are fully correlated. However, H2O and HDO do not vary fully in parallel; i.e. calculating g^ according to Eq. () implies an uncertainty that can be estimated by the uncertainty covariance matrix Sg^ according to see also Sect. 4.3 of Sg^=A12Sa,δDA12T. Here Sa,δD describes the actual atmospheric δD covariances. Because A12 and Sa,δD only have small entries, this uncertainty is below 1 % and can be neglected for our comparison.

For a better statistical quantification of the deviations of the remote sensing data from the GRUAN reference data, we introduce a skill score, DL, describing the difference of the logarithmic values of the respective water vapour concentrations. Because Δln(x)≈Δxx, we interpret the logarithmic-scale difference between IASI and GRUAN as the relative difference (and use the GRUAN data in the denominator). DL then becomes

DL=ln⁡H2Oretrieval-ln⁡H2OGRUAN≈H2Oretrieval-H2OGRUANH2OGRUAN, where H2OGRUAN is the regridded and smoothed radiosonde H2O data (i.e. g^ from Eq. ), and H2Oretrieval is the retrieved IASI H2O data. The skill score DL defined in this way is a good measure for the relative difference between the GRUAN and IASI data.

As a good measure for the mean relative difference between GRUAN and IASI, we can use the mean difference of logarithmic values (MDL): MDL=1N∑i=1NDLi=1N∑i=1Nln⁡H2Oretrieval-ln⁡H2OGRUANi≈1N∑i=1NH2Oretrieval-H2OGRUANH2OGRUANi.

Similarly, we can use the standard deviation of the logarithmic differences as a measure for the relative scatter between GRUAN and IASI, and introduce σMDL as σMDL=1N∑i=1NDLi-MDL2. For illustrating the variation of the atmospheric state, we introduce σg^ as σg^=1N∑i=1Nln⁡H2OGRUANi-ln⁡H2OGRUAN‾2.

We want to document to what extent the differences between GRUAN and MUSICA IASI data can be explained by the estimated errors. In Sect.  we estimate the error in the MUSICA IASI H2O profiles in detail for three different climate zones. Uncertainties in the GRUAN H2O profiles also have to be considered. In general the uncertainty of the GRUAN data increases with altitude. For the regridded and smoothed GRUAN profiles, Δg^ is about 3 %–5 % near the surface and 5 %–20 % at around 10 km altitude. For further details on the radiosonde uncertainty, we refer the reader to Appendix . If we assume that the MUSICA IASI and the GRUAN errors are uncorrelated random errors, we can calculate the 1σ scatter of DL around MDL as expected from the MUSICA IASI and GRUAN errors by ΔMDL=1N∑i=1NΔx^i2+Δg^i2. Here the index i stands for an individual observation and N is the number of all observations.

In this section we present the comparison between the regridded and smoothed GRUAN H2O profiles and the IASI H2O profiles using the metric as described in the previous subsection. The statistical quantifications are done individually for the four different ensembles as given in Table . The aim is to illustrate the remote sensing data quality for the three different climate zones.

Figure  depicts the vertical profiles of the data agreement skill score parameters for all coinciding observations without separating the different ensembles. This analysis is based on 100 individual comparisons.

Below 12 km altitude the MDL value oscillates between -10 % and +11 % and at around 14 km altitude it reaches -21 %. The scatter in MDL (σMDL) is almost 29 % close to the surface but generally smaller than 20 % above 1 km altitude. Above 5 km altitude this observed scatter is only slightly larger than the scatter predicted from the estimated errors (ΔMDL). At lower altitudes the predicted scatter is clearly smaller than the observed scatter. An explanation of the observed upper tropospheric bias and increased scatter at low altitudes is given in the previous section: the dry bias in the upper troposphere might have its origin in incorrect modelling of the spectroscopic line shapes, and the increased scatter near the surface might be due to uncertainties in the IREMIS emissivities.

The observed scatter between GRUAN and IASI (σMDL) is significantly smaller than the 1σ variation of the smoothed radiosonde data (σg^), which reaches about 50 % near the surface and more than 100 % in the middle and upper troposphere. This reflects the large variation in the atmospheric water vapour concentration data we use for our evaluation study (see also Fig. ). The MUSICA IASI data product does capture most of these variations well. For demonstrating this capability, Fig.  illustrates correlation between the MUSICA IASI retrieval products and the smoothed GRUAN data for selected altitudes. The respective altitudes are highlighted in Figs.  and , which document that at all sites the MUSICA IASI product for 1.8, 3.6, 6.4, and 9.8 km is independent and very sensitive to real atmospheric variations. Near the surface, the sensitivity is generally limited, and at 13.6 km, only the Manus Island data are reasonably sensitive to the actual atmospheric variations.

At the altitudes at which the MUSICA IASI product shows very good sensitivity (1.8, 3.6, 6.4, and 9.8 km), we observe a very good correlation and can demonstrate that the MUSICA IASI product can correctly capture the large variations that are present in atmospheric water vapour. For instance, at 3.6 km the mixing ratios range from below 200 to almost 20000 ppmv and at 9.8 km from 10 to more than 1000 ppmv. Please note that these large variations are reliably reproduced by the MUSICA IASI processor, although the retrieval works with a single humidity a priori value that is used at all sites and during all seasons (indicated by the yellow stars in Fig. ). Near the surface the correlation is a bit weaker than at higher altitudes, mainly due to some outliers belonging to the LI07 and SK07 ensembles (the ensembles representing the summer season over land). At 13.6 km altitude we observe a good correlation, which demonstrates the possibility of detecting H2O at Manus Island. However, at Lindenberg and Sodankylä, these variations are strongly driven by actual atmospheric variations that take place at lower altitudes (see magenta lines in Figs.  and ).

For our theoretical error analyses in Sect. , we assume that the relative errors have a component that is mostly random (Fig. ) and another component that is mostly systematic (Fig. ). For the comparison study we proceed similarly and examine bias and scatter, which means that we describe the variance in the MUSICA IASI data by the variance in the GRUAN data (σg^2) and the variance in the difference between MUSICA IASI and GRUAN (σMDL2). Using this description, we can calculate the R2 value that represents the portion of the MUSICA IASI variance that is in full agreement (fully correlated) with the GRUAN variance: R2=σg^2σg^2+σMDL2. Each panel of Fig.  contains the R2 value calculated for the respective altitude.

The error blue bars on the diagonal of the plots of Fig.  indicate the typical GRUAN errors (Δg^ as detailed in Appendix ) and the root square sum of the typical leading MUSICA IASI random errors (Δx^), whereby we have considered measurement noise, uncertainties in surface emissivity, and uncertainties in the GRUAN temperatures. The MDL and σMDL values are also written in each panel as bias (b) and scatter (s) values, respectively. They are the same as shown in Fig. .

Figure  resumes the capability of the MUSICA IASI retrieval product for capturing real atmospheric H2O variations at different altitudes by showing vertical profiles of the R2 values calculated according to Eq. () for the different ensembles individually and when considering all 100 individual comparisons together. Between 1 and 12.5 km altitude (and when considering all comparisons of the MUSICA IASI products together), the retrieval detects more than 90 % of the atmospheric variations in agreement with GRUAN.