In situ instruments analyse a clearly defined air mass and from the H2O and HDO measurements the ratio (δD) can be directly calculated. This is more complicated for remote sensing observations. There, the amount of H2O and HDO along the line of sight is retrieved from the measured spectra. The sensitivity of the retrieval depends on the noise in the spectra and on the shape and strength of the different spectral lines. Typically, the sensitivity for H2O is different to the sensitivity for HDO and the retrieved H2O value represents a different altitude range than the retrieved HDO value (H2O and HDO have different averaging kernels). In consequence, the δD values calculated from individual H2O and HDO retrievals can be rather misleading. Instead of individual retrievals, a combined H2O and HDO retrieval is needed.

A logarithmic-scale retrieval of H2O and HDO together with a constraint of ln⁡[HDO]-ln⁡[H2O] has been proposed by and for generating δD values by remote sensing techniques. This approach means actually an optimal estimation of (ln⁡[H2O]+ln⁡[HDO])/2 and ln⁡[HDO]-ln⁡[H2O], which are good proxies for H2O and δD ; i.e. it is a quasi-optimal estimation of H2O and δD. However, it is an individual optimal estimation of H2O and δD, and thus such a product is still not comparable to the {H2O,δD} pairs obtained from the in situ measurements. The reason is that the remote sensing system is more sensitive to atmospheric H2O than to atmospheric δD and in addition there is a slight cross-dependency of the retrieved δD on atmospheric H2O e.g..

The aforementioned problems can be overcome by an a posteriori processing of the retrieval output. The result of the a posteriori processing is an estimation of {H2O,δD} pairs that are comparable to the {H2O,δD} pairs obtained from in situ measurements. In the following, we give a very brief explanation of the necessity and functionality of the a posteriori processing.

The remote sensing retrievals produce state vectors x, averaging kernels A, error covariance matrices S, etc., for the {ln⁡[H2O],ln⁡[HDO]} basis system (or for the {ln⁡[H216O],ln⁡[H218O],ln⁡[HD16O]} basis system, if isotopologues with different oxygen atoms are distinguished). However, besides H2O (99.7 % in form of H216O), we are actually interested in δD, and eventually deuterium excess (d=δD-8δ18, with δ18=H218O/H216OVSMOW-1). These parameters, their variations and uncertainties can be captured and characterized in an elegant manner by using the {H2O,δD} (or {H2O,δD,d}) proxy basis system: the basis {(ln⁡[H2O]+ln⁡[HDO])/2} (or {(ln⁡[H216O]+ln⁡[H218O]+ln⁡[HD16O])/3}, if we distinguish between the isotopologues with different oxygen atoms) well captures the parallel variations of the different isotopologues and is thus a good proxy for the dominant H2O variations. Variations in δD are 1 order of magnitude smaller, for which the basis {ln⁡[HDO]-ln⁡[H2O]} (or {ln⁡[HD16O]-ln⁡[H216O]}) is a good proxy. Variations in deuterium excess are a further order of magnitude smaller, for which we can use the proxy basis {7ln⁡[H216O]-8ln⁡[H218O]+ln⁡[HD16O]} .

The transformation of this proxy basis system can easily be realized by a transformation operator P, and the transformed state vector, averaging kernel and any covariance matrix (x′, A′ and S′) are then given by x′=PxA′=PAP-1S′=PSPT.

In the proxy basis system, the different sensitivities with respect to H2O and δD and the cross-dependencies become clearly visible. We can remove these deficits by the a posteriori processing, which consists of simple matrix multiplications (using the a posteriori correction operator C). The a posteriori corrected state vector, averaging kernel and any covariance matrix (x∗, A∗ and S∗) can be calculated as x∗=C(x′-xa′)+xa′A∗=CA′S∗=CS′CT.

In the MUSICA papers, this a posteriori processed product is also often called the Type 2 product, and since it is most useful for isotopologue studies (H2O and δD have almost the same averaging kernels), it will be the product that is generally used in this work. In addition, MUSICA offers a Type 1 product which is not a posteriori processed and it is the kind of product that is generally distributed by other data producers. It consists of optimal H2O data, but has limited possibilities for isotopologue studies (see discussion in Sect. ).

Readers that are interested in more details about the proxy state method, the a posteriori correction and the operators P and C as used in Eqs. () and () are recommended to study , and . However, we would like to note that the MUSICA remote sensing data users do not have to be concerned about details of the a posteriori processing. The processing does not have to be performed by the data users because the data are provided as an a posteriori processed product (Type 2) and also in the form of the direct retrieval output (H2O and HDO or H2O and δD products that have not been a posteriori processed, Type 1 product).

The MUSICA ground-based remote sensing retrieval uses the PROFFIT retrieval code and the middle-infrared spectra recorded within the NDACC (www.acom.ucar.edu/irwg/). The NDACC spectra are of very high spectral resolution (0.005 cm-1) and offer H216O, H218O and HD16O absorption lines of similar strength.

For the final MUSICA retrieval version (v2015), we perform an optimal estimation of (ln⁡[H216O]+ln⁡[H218O]+ln⁡[HD16O])/3, ln⁡[HD16O]-ln⁡[H216O] and 7ln⁡[H216O]-8ln⁡[H218O]+ln⁡[HD16], which are good proxies for H2O, δD and d (deuterium excess). In addition to the cross-constrained fit of the water vapour isotopologues H216O, H218O and HD16O, we perform simultaneous but individual fits (no cross-constraints) for profiles of the water vapour isotopologue H217O, the temperature and the interfering species CO2, O3, N2O, CH4 and HCl. The code PROFFIT uses the root mean square value of the residual (difference between simulated and measured radiances) as noise level for constraining the retrievals. We use HITRAN 2012 parameters optimized for speed-dependent Voigt line parameterization. Details on the general retrieval set-up are given in and the modifications made for v2015 are summarized in .

The Type 1 MUSICA NDACC/FTIR product provides water vapour profiles for the lower, middle and upper troposphere (DOFS, degree of freedom of signal, of almost 3). The Type 2 product (the a posteriori corrected product) offers consistent {H2O,δD} pairs, which are sensitive to the lower and the middle troposphere, whereby it is possible to reasonably separate both altitude regions (DOFS of about 1.7). This is illustrated in Fig. , which shows the rows of the averaging kernel matrix (A∗) in the {H2O,δD,d} proxy basis system and after applying the a posteriori correction (see Eq. ). The full averaging kernels matrix consists of nine blocks, each of which is a {nol×nol} matrix, whereby {nol} is the number of the vertical atmospheric grid points used for the retrieval. In total, A∗ has the dimension {(nol×3)×(nol×3)}: A∗=A11∗A12∗A13∗A21∗A22∗A23∗A31∗A32∗A33∗.

The three blocks along the diagonal describe the direct responses; i.e. they represent the averaging kernels for the H2O, δD and d proxies. Figure  demonstrates that the sensitivity with respect to H2O and δD is very similar (compare plots showing the entries of A11∗ and A22∗), which is achieved by the a posteriori processing. The outer diagonal blocks describe the cross-responses, whereby in Fig.  the respective x axes are scaled, thereby accounting for the different magnitudes of the H2O, δD and d variations. Concerning the cross-responses between H2O and δD, we have to consider that ln⁡[H2O] variations are 1 order of magnitude larger than δD variations. This means that the entries in the A12∗ block must be 10 times larger than entries in the A11∗ block in order to be of similar importance. Vice versa, entries in the A21∗ block can be 1 order of magnitude smaller than entries in the A22∗ block and still have a similar importance. The blocks A31∗, A32∗ and A33∗ describe how the retrieved d proxy responds to real atmospheric variations. Although there is sensitivity with respect to real atmospheric deuterium excess (see entries of A33∗), the retrieved d signals are mainly caused by variations in H2O and δD (significant entries in blocks A31∗ and A32∗). The situation can be improved by an alternative a posteriori processing being dedicated to {H2O,δD,d} triplets see Sect. 4.4.2 in, which is, however, not subject of this paper. For this paper and in order to understand the {H2O,δD} pair signals, it is sufficient to work with the kernel blocks A11∗, A12∗, A21∗ and A22∗.

Error estimations are discussed in detail in . The random error is about 2 % for H2O and 25 ‰ for δD, whereby the leading error source is uncertainty in the atmospheric temperature profiles and artefacts in the spectral baseline (like channelling or offset). Systematic errors are dominated by uncertainties in the spectroscopic parameters. Already for small uncertainties of 1 and 2 % for line intensity and pressure broadening parameters, the systematic errors in H2O and δD “profiles” can reach 10 % and 150 ‰, respectively. An empirical study indicates that for the v2015 data, the bias is actually much smaller (see Sect. ). In addition, for an atmosphere with fine vertical structures, the δD cross-dependency on H2O can reach 15 ‰ see Fig. 9 in.

For the MUSICA MetOp/IASI retrievals, a nadir version of PROFFIT is used. The basic retrieval set-up is presented and analysed in detail in and . It has been developed in consistency with the NDACC/FTIR retrieval. It uses a broad spectral window (1190–1400 cm-1), and performs an optimal estimation of the humidity and δD proxies ((ln⁡[H2O]+ln⁡[HDO])/2 and ln⁡[HDO]-ln⁡[H2O]). Simultaneously, we retrieve surface skin temperature and atmospheric temperature, as well as the interfering species CH4, N2O, CO2 and HNO3. Our MetOp/IASI retrieval does not distinguish between H216O and H218O because the spectroscopic signatures of the latter are very weak in the IASI spectra. So, we treat all water molecules with two hydrogen atoms as a single molecule (in the following referred to as H2O), whose variability is mainly the one of H216O. For our atmospheric temperature fit, we constrain strongly towards the EUMETSAT L2 atmospheric temperature. The root mean square value of the residual (difference between simulated and measured radiances) is used as noise level for constraining the retrievals.

The previous version of the MUSICA MetOp/IASI retrieval worked with HITRAN 2008 spectroscopic water vapour line parameters . For the final MUSICA retrieval version (v2015) we use the HITRAN 2012 parameters and modified the line intensities (S) for the HDO absorption signatures by +10 %. We also tested modifications of S for the H2O signatures and changes of γair (pressure broadening parameter), but finally found that a modification of S of HDO works most effectively for correcting biases in δD. In this context, we would like to remark that the bias correction as suggested for TES is also consistent with a positive change of S of HDO.

The retrieval provides a Type 1 product of H2O profiles that is sensitive to variations between the surface and about 15 km altitude (DOFS of about 4). The Type 2 product (consistent {H2O,δD} pairs) has a typical DOFS of 0.7–1.0 (after filtering according to Sect. ), whereby the sensitivity is mainly limited to the middle troposphere. This is illustrated in Fig. , which plots the rows of the averaging kernel matrix (A∗) in the {H2O,δD} proxy basis system and after applying the a posteriori correction. For the MetOp/IASI retrieval we have no deuterium excess basis and the dimension of A∗ is {(nol×2)×(nol×2)} A∗=A11∗A12∗A21∗A22∗.

As for the NDACC/FTIR kernels, A11∗ and A22∗ describe the sensitivities with respect to H2O and δD, and A12∗ and A21∗ their cross-responses, respectively.

The random error is about 5 % for H2O and 20 ‰ for δD, whereby atmospheric temperature uncertainties, thin elevated clouds and noise in the spectra are the leading uncertainty sources. The systematic error is dominated by uncertainties in the spectroscopic parameters. It can easily reach 5 % and 50 ‰ for H2O and δD, respectively (in case of a 5 % uncertainty in the spectroscopic line intensity parameters). However, an empirical study as shown in Sect.  reveals that for v2015 the bias is actually much smaller. In addition, for an atmosphere with fine vertical structures, the δD cross-dependency on H2O can occasionally be larger than 40 ‰ see Fig. 5 in.

For v2015, we work with the same globally constant water vapour isotopologue a priori data for all ground-based retrievals (different globally distributed NDACC/FTIR stations) and for all MetOp/IASI retrievals (for the whole globe). Thereby, we assure that observations at different locations are not affected by the use of different a priori data, and therefore an interpretation of regional differences (e.g. latitudinal gradients) becomes rather straightforward. This is a further development of the previous retrieval version, where we used different a priori data for the (sub)tropics, the midlatitudes and the polar regions.

The a priori profiles used are mean values of LMDZiso calculations and are as depicted in Fig. 2 of . As H2O a priori variability, we assume 75 % in the boundary layer, 150 % in the middle and upper troposphere and 30 % in the stratosphere. For δD, the respective variability values are 60 ‰, 120 and 50 ‰. The a priori covariances are then calculated by assuming a correlation length of 2 km in the boundary layer, 4 km in the middle and upper troposphere and 8 km in the stratosphere.

In a first study with data from the previous MUSICA NDACC/FTIR retrieval version, we found a bias of 25–70 ‰ for δD with respect to the profile references see right panels in Figs. 9 and 10 of. That study was done with a limited data set (only one exemplary remote sensing observation per day). For the v2015 product we perform a comprehensive empirical bias assessment and compare the ground-based FTIR data obtained for all optimal coincidences (about 10 observations each day between 08:15 and 09:45 UT) with the reference data (one profile per day: 21 Jul 2013, 22 Jul 2013, 24 Jul 2013, 25 Jul 2013, 30 Jul 2013 and 31 Jul 2013).

Figure  shows the plots for the correlations between the reference and the FTIR data. The upper panel depicts the comparison for the lower free troposphere and the bottom panel for the middle free troposphere. The references are constructed from the in situ profile measurements (surface up to ceiling altitude of 6–7 km) and a climatology for higher altitudes by convolution with the FTIR averaging kernels. The climatology above the ceiling altitude is the same as the a priori data as discussed in Sect. . The technical details for this comparison, like the need for applying the averaging kernels to the reference profiles, are the same as for the exemplary study of . The error bars on the reference data are largely due to the unknown humidity and δD values above the aircraft's ceiling altitude. This can easily be understood from the averaging row kernels of the matrix blocks A11∗ and A22∗ as shown in Fig. . They reveal that the atmospheric state above 6–7 km does affect the retrieval for lower altitudes. Appendix  provides a brief discussion on the importance of reaching high ceiling altitudes.

We observe a reasonable correlation and no significant bias between the reference data and the MUSICA NDACC/FTIR v2015 data. We also see variations in the FTIR data measured between 08:15 and 09:45 UT on a single day, which cannot be attributed to changes in the averaging kernels because there is no similar variation seen in the smoothed reference data (there is only a single reference profile per day). This variation is seen in the lower free troposphere and in the middle free troposphere and is very likely a true variation in the free tropospheric humidity and δD fields.

The relatively high variability of the atmospheric state is a problem when comparing the different measurements because we do not know whether the different measurements detect air masses with the same atmospheric characteristics well. Our experience is that in the surroundings of Tenerife, the middle tropospheric humidity fields can be reasonably compared if they are made within 2 h and within a horizontal distance of about 100 km . For these coincidence criteria, the mismatch between lower and middle tropospheric H2O and δD can be assumed to be within 10 % and 10 ‰, respectively. However, the comparison of aircraft measurements (free troposphere) with measurements made at Izaña (on a mountain ridge) is more difficult due to the local thermal circulation that starts on the island during the morning hours . For that reason, we compare the in situ aircraft references with FTIR data measured in the early morning hours (between 08:15 and 09:45 UT) and define these measurements the optimal coincidences with the free tropospheric aircraft measurements made between 10:30 and 13:30 UT. As a consequence the mismatch uncertainty for the comparison between aircraft and FTIR data will be larger (within 30 % for H2O and very likely within 30 ‰ for δD). For a detailed discussion on optimal coincidences between the aircraft-based in situ and the remote sensing measurements, please refer to Appendix .

The Tables  and  resume the results of the empirical validation and bias assessment. The reference and the NDACC/FTIR products detect the same variations to a large extent (R2 values of about 70 % for the lower and almost 90 % for the middle troposphere). The calculated mean NDACC/FTIR biases are not significant if we take the confidence range of these assessments into account. The confidence range is calculated as the standard deviation of the bias divided by NR-1 (with NR being the number of independent reference observations). For the lower troposphere, we are able to determine the bias with a confidence of 12.4 % and 16.6 ‰ for H2O and δD, respectively. In the middle troposphere, the assessment is even more reliable. There, the confidence ranges are 8.2 % and 7.4 ‰ for H2O and δD, respectively. These confidence ranges are in good agreement with the estimated mismatch uncertainties. In summary, the lower tropospheric bias is very likely somewhere between -10 and +15 % for H2O and between -30 and +5 ‰ for δD. The middle tropospheric bias is very likely between -10 and +8 % for H2O and between -10 and +5 ‰ for δD.

In an exemplary study with the previous MUSICA MetOp/IASI retrieval version, reported a bias between the IASI δD product and the δD reference of about 60 ‰ (see Fig. 11 therein). For the comprehensive bias assessment of the v2015 data, we follow the procedure as described in the context of that exemplary study.

Figure  shows the correlation plots between the reference and the MetOp/IASI v2015 data. The data points plotted by smaller symbols and by black error bars are for non-ideal coincidences, and the rest of the data points are for good coincidences (Appendix  gives more details on the coincidences and the error bars). For this comparison, we smooth the reference profile data (in situ measurements and climatological data above ceiling altitude, as described in Sect. ) with the respective IASI averaging kernels. Since there is only one reference profile per day, the small variations in the smoothed reference data on an individual day must be due to varying averaging kernels (for instance, the small variability of the green dots for 24 Jul 2013 in parallel to the x axis). The respective variations of the IASI data (variations in parallel to the y axis) are due to variations in the sensitivity of IASI (variation in the kernels) and due to variations in the real atmospheric state encountered at the different observational pixels. The in situ data and the remote sensing data observed for good coincidences are well correlated. We estimate a mismatch uncertainty of about 10 % and 10 ‰ for the H2O and δD comparisons, respectively (for more details see discussions in Sect.  and Appendix ).

We are able to assess the bias for the middle tropospheric IASI data with a confidence of 3.7 % and 7.9 ‰ for H2O and δD, respectively (see Table ). The confidence ranges are in agreement with the expected mismatch uncertainties. The obtained mean bias values lie within these confidence ranges (for H2O) or are only very slightly outside this range (for δD), meaning that the actual biases are very likely between -2.5 and +5 % for H2O and between 0 and +15 ‰ for δD.

In the surroundings of Tenerife there are three distinct moisture transport pathways that control free tropospheric humidity. showed that these three pathways have a distinct {H2O,δD} pair distribution, which offers a unique opportunity for validating the different {H2O,δD} pair data sets.

Generally, the free troposphere in the subtropics receives air that has been transported from higher latitudes and altitudes and subsides to the subtropics e.g.. In the following, we call this pathway “ATL, desc”. However, the summertime free troposphere close to West Africa is often affected by the Saharan air layer (SAL). The SAL is a well-mixed planetary boundary layer that can expand up to 6–7 km and has its origin in the strong vertical mixing (dry convection) over the summertime Sahara. This dry convection process mixes boundary layer air with free tropospheric air. The SAL is then often advected westward over the Atlantic, where it can be identified by high dust concentrations and increased humidity levels. The free troposphere above Tenerife is also particularly humid when the air has been transported from lower altitudes over the tropical/subtropical Atlantic . This mainly occurs in the late summer and early autumn. We call this pathway “ATL, asc” in the following. The three distinct moisture transport pathways, their identification methods and the prevailing occurrences are summarized in Table  and discussed in great detail in .

For our validation purpose we sort the {H2O,δD} observations according to the moisture pathway that has been prevailing during the observation. The sorting is done according to the identification method as given in Table  and for all the different data sets independently: the Picarro surface-based in situ observations (at 2390 and 3550 m a.s.l.), the NDACC/FTIR measurements made from Izaña and the MetOp/IASI observations made close to Tenerife. Then we calculate the {H2O,δD} pair density distribution for each observational technique and each moisture pathway ensemble. The results are the {H2O,δD} pair contour plots as depicted in Fig.  (from the left to the right for the different data sets as described in the panels). We present these plots on a logarithmic scale for H2O and maintain the scale for δD (the δD scale is in a first approximation the same as a ln⁡[HDO]-ln⁡[H2O] scale). These are the scales on which the optimal estimation of the remote sensing products is performed. This largely facilitates the interpretation of the remote sensing data because then the Type 2 kernels are very similar on the x and y scales. Furthermore, on these scales a Rayleigh process will become visible by a straight line.

For air descending from the Northern Atlantic (ATL, desc, blue contours), the data points are well distributed between a typical Rayleigh line (gradual dehydration due to condensation) and mixing lines (mixing of two end members with {H2O,δD} on the exemplary Rayleigh line). These water masses have gone through different condensation and mixing processes.

For air ascending from the tropical/subtropical Atlantic (ATL, asc, green contours), the air is more humid and the {H2O,δD} pairs generally group around the Rayleigh line with some data points lying significantly below the Rayleigh line. These water masses are strongly depleted in HDO, which indicates rain re-evaporation or gradual dehydration (Rayleigh distillation) after evaporation over a warm ocean.

For SAL conditions (red contours), the air is also humid but HDO is significantly enriched when compared to the typical Rayleigh distribution. This can be well explained by the mixing of planetary boundary layer humidity with middle/upper tropospheric humidity.

We observe that the three different data sets reveal very similar {H2O,δD} pair distributions depending on the history of the detected air mass. The study is statistically very robust, since it uses several hundred individual observations (number given by parameter N in the legends of Fig. ) made on many different days (number given by parameter D). This confirms that the v2015 MUSICA remote sensing data are reasonably well bias corrected and proves that they are capable of tracking different moisture pathways. The smaller variability in the remote sensing data is due to the fact that they represent averages for layers of several kilometres (see averaging kernel plots of Figs.  and ). For the MetOp/IASI data the variability is particularly small for dry air (blue contours) because the drier the atmosphere, the lower IASI's sensitivity for middle tropospheric {H2O,δD} pairs.

Figure  shows validations of {H2O,δD} pairs for a subtropical site. In order to perform a similar study for other sites, we would need respective middle tropospheric in situ references, which are not available. The ISOWAT profile and surface-based Izaña and Teide Picarro in situ references as observed in the surroundings of Tenerife are unique and a generation of similar data sets for middle or high latitudes would be expensive (it would require a large number of aircraft campaigns).

Here, we show a comparison between NDACC/FTIR, MetOp/IASI-A and MetOp/IASI-B, which is of global validity. Our argument is that a global agreement between the different remote sensing data sets would suggest that the in situ validations made for Tenerife are of global validity.

For this kind of validation, we work with {H2O,δD} extremes. For this purpose, we identify anomalous or extreme {H2O,δD} distributions in one remote sensing data set and document to what extent these extremes are seen in another remote sensing data set (by comparing coincident observations). The validation approach with {H2O,δD} extremes was first presented by , which should be consulted for more details.

The number of stations contributing to the MUSICA activities is gradually increasing and the data sets have been updated. Table  gives an overview of the 12 NDACC/FTIR sites that currently contribute to the MUSICA activities and the available data records. The stations are well distributed from the Arctic to the Antarctic and in some occasions have provided data since the late 1990s a plot of time series until 2012 is given in Fig. 12 of. A further extension of the data set to other sites or for some stations to measurements made in the beginning of the 1990 is feasible, but has not been possible with the funds available for the MUSICA project.

All the data pass through a quality filter with different criteria. First, we require total DOFS for the three water vapour isotopologues (H216O, HD16O and H218O) of at least 4.0. Second, we analyse the position of solar lines with respect to terrestrial lines and require a Δν/ν within 5×10-6 (Δν is the difference in the line shift of solar and terrestrial lines and ν the position of the solar line, both given in cm-1). This method allows observations made with incorrect pointing of the solar tracker to be excluded . Third, we require that the fitted phase error of the instrumental line shape does not change by more than 0.02 rad during the period of the data record. Thereby, we exclude data that have been measured under anomalous instrumental characteristics. Fourth, we perform XCO2 retrievals using the same spectra as for the water vapour isotopologue retrievals. We compare the retrieved XCO2 values with XCO2 as obtained from a multi-parameter model for XCO2 . We require that the measured and modelled XCO2 data agree within 2 %.

Figure  gives an example of the seasonal cycles in the {H2O,δD} distributions (around 5 km altitude) obtained from the observations made on Tenerife in the subtropical North Atlantic (14 years: 2001–2014) and in Addis Ababa in East Africa (4 years: 2009–2013).

For the subtropical North Atlantic (upper panels), the seasonal cycle can be explained by the seasonality of the prevailing moisture pathways as summarized in Table , so the {H2O,δD} pair distribution plot shown here is very similar to the one shown in Fig.  (central panel). The right panels show typical row kernels for the three different seasons and for the altitude of 4.9 km. Due to the a posteriori processing, the sensitivity with respect to H2O and δD is almost identical (compare row kernels of A11∗ and A22∗). However, the sensitivities slightly depend on the season. It seems that during winter and late summer the 4.9 km retrieval is more sensitive to the lower troposphere than to the middle troposphere, whereas the situation is vice versa for retrievals of midsummer observations.

Over East Africa (bottom panel) the air is generally more humid and less depleted in HDO than over the subtropical North Atlantic. Furthermore, we observe different {H2O,δD} distributions for the different seasons. Directly after the rain season (mid-October–December, green contours) the vapour is most depleted in HDO. In January and February (blue contours) the air remains similarly dry, but becomes more enriched in HDO. Then, before the rain season (March–June, purple contours), the air gets more humid, but δD gets only slightly enriched in HDO. The typical row kernels depicted in the right panels, reveal very similar sensitivities for all the different seasons.

The main intention of this figure is to briefly demonstrate the potential of the NDACC/FTIR data for climatological {H2O,δD} pair distribution analyses. A deeper scientific discussion of the climatological signals would need model calculations and is beyond the scope of this paper.

For one morning or evening overpass the IASI-B swaths typically complement the area left out by the IASI-A swaths, and vice versa. Since the MUSICA IASI-A and IASI-B data are very consistent (see Fig. ), we can treat them as a uniform data set and create extremely dense global data point maps for each daily morning and evening overpass. Figure  depicts typical maps for single day morning and evening overpasses during boreal winter and summer, respectively. The areas with missing data are cloudy areas or correspond to scenarios where the retrieval has rather low sensitivity.

Currently, MUSICA MetOp/IASI-A and MetOp/IASI-B data (Type 1 and Type 2 products) are available on a global scale for 6 days in February 2014 and for the whole months of August 2014. In addition, we have retrievals' results for longer time periods and for 2∘ × 2∘ areas around the three ground-based FTIR sites, Izaña (Tenerife), Karlsruhe and Kiruna. More MUSICA MetOp/IASI retrievals are planned, but depend on future funding.

The height region around 5 km altitude (about 500 hPa) is generally most sensitive with respect to the {H2O,δD} pairs. However, occasionally (e.g. for an extremely dry or humid troposphere) the sensitivity peaks at other altitudes.

To filter out data with low sensitivity at a certain altitude, we set up a matrix in representation of the atmospheric covariances (the matrix's elements represent the different altitude levels). This matrix (Sc∗) has unity values on the diagonal, and the outer diagonal elements are obtained by assuming an inter-level correlation length of 5 km. Then we calculate the error covariance in the retrieved data as Sϵ∗=(A∗-I)Sc∗(A∗-I)T. Here, A∗ is the averaging kernel matrix (see Eq.  and Fig.  for an example) and I the identity matrix. If we are interested in data that represent the atmosphere at altitude X, we do not consider retrievals, for which the respective diagonal element of Sϵ∗ is larger than 0.52, thereby requiring that at least 50 % of the atmospheric variation at altitude X is seen in the retrieved data. In Fig.  we only plot data points for which this sensitivity criterion is fulfilled for the altitude of 4.9 km (i.e. it only shows data that reflect variations of a relatively deep layer at about 5 km altitude).

We filter out poor quality observational data by only considering retrievals for which the root mean square value of the residuals (difference between measured and simulated radiances) relative to the maximum value of the radiances is smaller than 0.0065.

The cloud, retrieval quality and sensitivity filter for 4.9 km altitude leaves us with about 120 000  and 110 000 valid data points for each single morning and evening overpass in August, respectively. In February there are typically 100 000 and 95 000 valid morning and evening observations for each day, respectively. Each of these data points represents the middle tropospheric situation of a small area (12 km diameter at nadir).

In order to demonstrate the high potential of IASI for a daily detection of regional-scale moisture transport pathways, we analyse the {H2O,δD} pair distribution measured on 16 August 2014 in different regions during the morning overpass. We investigate observations over land (two distinct locations: Alaska and South Africa) and sea (two distinct locations: subtropical North Atlantic and Gulf of Persia). The analysed regions are marked by a bluish colour in Fig.  and the respective {H2O,δD} pair density distributions are plotted in the upper left panel of Fig. .

IASI detects very distinct {H2O,δD} pair distributions for the different regions. The air over Alaska and South Africa is similarly dry; however, the δD values differ systematically by more than 150 ‰. A look on the row kernels (right panels) reveals that in both regions, IASI has a very similar sensitivity, which peaks between 2 and 5 km altitude. An apparent explication is that in Alaska, the drying happens by condensation (via Rayleigh distillation), while in South Africa, the drying is due to mixing with very dry air (subsidence from the upper troposphere).

The air over the North Atlantic and the Gulf of Persia is similarly humid, but there is a clear difference in δD. A reason for the difference in δD might be that over the North Atlantic, rain re-evaporation is important, whereas the air over the Gulf of Persia is strongly affected by dry convection processes (vertical mixing) over the Arabian peninsula. The row kernels for both scenes are not the same however, both show peak sensitivities for altitudes between 4 and 8 km, meaning that for both regions, IASI should be able to consistently capture variations in the {H2O,δD} pair distributions that take place within a deep middle tropospheric layer.

The bottom panels of Fig.  demonstrate IASI's potential for detecting seasonal- and diurnal-scale signals in the {H2O,δD} pair distribution. This is done by analysing the {H2O,δD} pair distributions over the Sahara (22.5 to 32.5∘ N and 10∘ W to 30∘ E, region marked by a reddish colour in Fig. ) for six consecutive winter and summer days and for morning and evening overpasses. Morning overpasses of the IASI instruments are at about 10:00 LT and evening overpasses at about 22:00 LT.

In the context of Fig.  we discussed the SAL events that can be observed during July and August over the Atlantic Ocean. Actually, the dry convection process that is responsible for the distinct {H2O,δD} pair distribution under SAL conditions in the surroundings of Tenerife takes place over the Sahara. The strong heating of the Earth's surface during the day in summer is the main driver of these processes, which should be manifested by a pronounced diurnal cycle over the Sahara in August. Indeed, for August we observe such diurnal signals in the MUSICA {H2O,δD} pair data. For the morning overpasses we observe a fractionation that is similar to the situation in winter (δD values between -300 and -200 ‰), whereas for the evening overpass the δD values veer away from the Rayleigh line and group around a line that simulates mixing between the planetary boundary layer air and middle free tropospheric air (δD values between -250 and -140 ‰). This evening distribution is very similar to the distribution that IASI typically observes over the Atlantic under SAL conditions (red contours in the right panel of Fig. ). For February, the surface heating is much weaker than in summer and dry convection processes are unlikely. As a result, we observe no significant difference between the morning and evening {H2O,δD} pair distribution.

Regarding the morning data, the moistening from winter to summer does not happen perfectly parallel to a Rayleigh line. This is probably because in summer the evaporation takes place over a warmer ocean than in winter and we have to consider different Rayleigh lines for winter and summer.

The main intention of Fig.  is to give examples of the large potential of IASI {H2O,δD} products. A more profound scientific study of these {H2O,δD} pair distribution patterns can only be done with model calculations and is out of the scope of this paper.

Figure  shows exactly the same as Fig. , but for data that have not undergone the a posteriori processing. In MUSICA we call them the Type 1 products and they represent individual optimal estimations of H2O and δD. For the Type 1 product, H2O and δD are not sensitive for the same air mass and the retrieval response is much more sensitive to atmospheric H2O than to δD variations. This is revealed by the typical row kernels as depicted on the right panels. There is clearly a higher sensitivity for H2O than for δD (compare the row kernels of the matrix blocks A11∗ and A22∗).

The different sensitivities affect the slopes in the {H2O,δD} distribution plots. Concretely, the NDACC/FTIR Izaña Type 1 data for winter (blue contour lines in upper panel of Fig. ) show a {H2O,δD} pair distribution where dry air can occasionally be weakly depleted (significant number of data points with H2O concentrations below 102.7ppmv≈500ppmv and δD above -400 ‰). It is very likely that these data points only appear there because of the H2O sensitivity being higher than the δD sensitivity. Actually, when accounting for the different H2O and δD sensitivities, this observation is not made (see Fig. ). For midsummer, the Type 1 data show a {H2O,δD} pair distribution that is reasonably parallel to a Rayleigh line (red contour lines in upper left panel of Fig. ), whereas the distribution when H2O and δD have almost identical sensitivities is more along a mixing line (red contour lines in upper left panel of Fig. ).

Concerning East Africa (lower panel of Fig. ), the Type 1 {H2O,δD} pairs are generally distributed around a line with a slope being less steep than the slope of a Rayleigh line. However, the conclusion that mixing with dry air is the dominating drying process might be wrong because when analysing the a posteriori processed {H2O,δD} pair distribution, the slope is steeper and in parallel to a Rayleigh line (see Fig. ).

The risk of such defective interpretations is larger the more pronounced the difference between the H2O and δD sensitivities is. For the MetOp/IASI products the sensitivity difference is especially important. Figure  shows exactly the same as Fig. , but for data that have not undergone the a posteriori processing. We observe completely changed {H2O,δD} pair distribution patterns. These changed patterns reveal the risk of a defective interpretation of the real atmospheric situation when using H2O and δD data that have significantly different averaging kernels. The row kernels are plotted in the right panels, and the very different entries in the matrix blocks A11∗ and A22∗ can be clearly observed.

The cyan contour lines in the upper panel of Fig.  are reasonably close to the exemplary Rayleigh line. This means that the moisture above the Gulf of Persia might be defectively interpreted as being partly dried by Rayleigh distillation processes. This is in contrast to what is indicated by the more reliable {H2O,δD} pair distribution pattern from Fig. . There the cyan contour lines are close to a mixing line, revealing that mixing with dry air is actually much more important than dehydration by condensation. Vice versa, for Alaska a δD value of -300 ‰ for H2O concentrations below 102.8ppmv≈630ppmv (see purple contour lines in the upper panel of Fig. ) indicates drying by mixing with dry air; however, when considering the different sensitivities in H2O and δD it seems that drying by mixing is rather unlikely. Instead, dehydration by condensation is suggested (see corresponding contour line in Fig. ).

A further example for defective interpretations is the seasonal cycle over the Sahara. The {H2O,δD} pair distributions as depicted in the bottom panel of Fig.  suggest strong differences between the summer and winter humidity levels, but only small differences in δD. Whereas during summer the {H2O,δD} pairs are reasonably close to the exemplary Rayleigh line, they are far away from this line in winter. When removing the inconsistencies between the H2O and δD sensitivities, this behaviour is very different. Then, the seasonal variation happens much closer to the exemplary Rayleigh line (see bottom panel of Fig. ).

Already the few examples discussed here clearly demonstrate that the interpretation of {H2O,δD} pair remote sensing data has to be done with great care. It is important to have a look at the sensitivities of H2O and δD (as well as at their cross-sensitivities). The transformation of the {H2O,δD} proxy basis system helps to gain insight into the complex characteristics of these remote sensing data products (see the discussions in Sect.  and the references cited therein). In order to reduce the risk of defective data interpretation, we strongly recommend the a posteriori data processing, which provides {H2O,δD} pair distributions that can be interpreted in a straightforward manner (see Figs.  and ).

A profound interpretation of the {H2O,δD} pair distributions is only possible in combination with isotopologue models. In this context and if model data are available, it might be argued that the a posteriori processing is actually not needed because one can compare Type 1 data with model outputs that have been convolved with the Type 1 averaging kernels, thereby simulating the effect of the different H2O and δD kernels. However, model data that have been convolved with Type 1 averaging kernels will be strongly different from the original model data and they will, to a large extent, reflect averaging kernel properties instead of real atmospheric signals (e.g. the slopes of the {H2O,δD} pair distributions will strongly depend on the differences between the Type 1 H2O and δD kernels). It will be difficult to understand what {H2O,δD} pair signals are introduced by the averaging kernels and what {H2O,δD} pair signals are actually modelled. Furthermore, the differences between the Type 1 H2O and δD kernels depend on the atmospheric and geophysical conditions (surface and atmospheric temperatures, atmospheric humidity concentrations, etc.; see, for instance, the example row kernels of the A11∗ and A22∗ matrix blocks in Fig. ), and since modelled and measured atmospheric state often differ significantly (high small-scale variability of tropospheric humidity), there is a high risk when using inadequate Type 1 H2O and δD kernels when convolving the model data. Under such circumstances it will be very difficult to compare the remote sensing data with the model because the modelled {H2O,δD} pair distributions can be strongly camouflaged by averaging kernels properties.

The different issues with the averaging kernels are less important when using a posteriori processed data because the respective kernels are less complex and have less of an effect on the {H2O,δD} pair distributions (e.g. the slopes of the {H2O,δD} pair distributions are not significantly affected by the kernels). Then the application of the averaging kernel to the model data is less critical and a first-order comparison between modelled and measured {H2O,δD} pair distributions is even possible without applying the averaging kernels to the model (if variations of deep layers are of interest). This possibility becomes evident from Fig. . There, the in situ data as depicted in the left panel correspond to point measurements made at 2390 and 3550 m a.s.l., whereas the NDACC/FTIR and MetOp/IASI data reflect the middle troposphere according to their averaging kernels (A11∗ and A22∗ in Figs.  and ). The {H2O,δD} pair distributions of the a posteriori processed NDACC/FTIR and MetOp/IASI data compare well with the in situ data that are not affected by averaging kernels, suggesting that a posteriori processed remote sensing data can be used as a direct reference for a first-order validation of modelled {H2O,δD} pair distributions (there is no need for applying the kernels to the model as long as the dominating {H2O,δD} pair signal of a deep layer is of interest).

A further improved integration of model and remote sensing {H2O,δD} pairs might be achieved by the development of a {H2O,δD} pair remote sensing retrieval simulator (the principle idea of a retrieval simulator is presented in ).