Can the assimilation of water isotopologue observation improve the quality of tropical diabatic heating and precipitation?

The strong coupling between atmospheric circulation, moisture pathways and atmospheric diabatic heating is responsible for most climate feedback mechanisms and controls the evolution of severe weather events. However, diabatic heating rates obtained from current meteorological reanalysis show significant inconsistencies. Here, we theoretically assess with an Observation System Simulation Experiment (OSSE) the potential of the MUlti-platform remote Sensing of Isotopologues for investigating the Cycle of Atmospheric water (MUSICA) Infrared Atmospheric Sounding interferometer (IASI) 5 mid-tropospheric water isotopologue data for constraining uncertainties in meteorological analysis fields. For this purpose, we use the Isotope-incorporated General Spectral Model (IsoGSM) together with a Local Ensemble Transform Kalman Filter (LETKF) and assimilate synthetic MUSICA IASI isotopologue observations. We perform two experiments consisting each of two ensemble simulation runs, one ensemble simulation where we assimilate conventional observations (temperature, humidity and wind profiles obtained from radiosonde and satellite data) and a second one where we assimilate additionally to the con10 ventional observations the synthetic IASI isotopologue data. In the second experiment, we perform one ensemble simulation where only synthetic IASI isotopologue data are assimilated and another one where no observational data at all are assimilated. The first experiment serves to assess the impact of the IASI isotopologue data additional to the conventional observations and the second one to assess the direct impact of the IASI isotopologue data on the meteorological variables, especially on the heating rates and vertical velocity. The assessment is performed for the tropics in the latitude range from 10◦S to 10◦N. When the 15 synthetic isotopologue data are additionally assimilated, we derive in both experiments lower Root-Mean-Square Deviations (RMSDs) and improved skills with respect to meteorological variables (improvement by about 8-13%). However, heating rates and vertical motion can only be improved throughout the troposphere when additionally to IASI δD conventional observations are assimilated. When only IASI δD is assimilated the improvement in vertical velocity and heating rate is minor (up to a few percent) and restricted to the mid-troposphere. Nevertheless, these assimilation experiments indicate that IASI isotopologue 20 observations have the potential to reduce the uncertainties of diabatic heating rates and meteorological variables in the tropics and in consequence offer potential for improving meteorological analysis, weather forecasts and climate predictions in the tropical regions. 1 https://doi.org/10.5194/wcd-2021-49 Preprint. Discussion started: 3 August 2021 c © Author(s) 2021. CC BY 4.0 License.

Only IASI data of high quality is used, e.g measurements at 4.2 km, the altitude where IASI δD has the highest sensitivity and filtering of the data by applying several quality filters (e.g. measurements response, cloud-free scenes). The data are spatially resampled to the IsoGSM grid at one vertical sigma level corresponding to 4.2 km (Toride et al., 2021).

IsoGSM model and data assimilation
For our assimilation experiments we use the isotope-incorporated Global Spectral Model (IsoGSM). This model is based on the Scripps Experimental Climate Predictions Center's (ECPC) Global Spectral Model (GSM) that has been used by NCEP 95 to perform operational analyses and medium-range forecasts (Kanamitsu et al., 2002). Gaseous forms of stable water isotopes (HDO and H 18 2 O) are incorporated as prognostic variables in addition to water vapour into GSM (Yoshimura et al., 2008). Simulations with IsoGSM have been used together and also evaluated with both, ground-based (Schneider et al., 2010;Uemura et al., 2008) and space-borne observations (Frankenberg et al., 2009;Yoshimura et al., 2011) of water isotopologues.
Here, we use IsoGSM ensemble simulations performed with a T62 horizontal resolution (1.9 • × 2 • , ∼200×200 km) and 100 28 vertical sigma levels from the surface up to ∼2.5 hPa. The sea surface and sea ice temperature distribution from the National Centers of Environmental Prediction/Department of Energy Reanalysis 2 (NCEP-DOE, Reanalysis 2) have been used as lower boundary condition. The data assimilation is performed with a Local Ensemble Kalman Transform Filter (LETKF, Hunt et al. (2004Hunt et al. ( , 2007) which is a parallel-efficient update of the traditional Ensemble Transform Kalman Filter (ETKF, Bishop et al. (2001)). For the data assimilation a relaxation-to-prior spread (RTPS) method (Whitaker and Hamill, 2012) 105 is used with a relaxation parameter of 0.4 to maintain an appropriate ensemble spread and to avoid filter divergence. The horizontal localisation scale is set to be 500 km (influence radius of 1826 km for best assimilation performance). The used ensemble size is 96. This large ensemble size is needed to derive results of satisfying quality as was shown by Toride et al. (2021). A detailed description on the data assimilation with LETKF and IsoGSM is provided in Yoshimura et al. (2014) and Toride et al. (2021). 110

Observation System Simulation Experiment
To investigate the potential impact of the assimilation of satellite data an Observation System Simulation Experiment (OSSE) is performed. In an OSSE, a model simulation is regarded as "truth" ("Nature run") and several data assimilation experiments with synthetic observations derived from the Nature run are conducted that aim to reproduce the Nature run as closely as possible (Schröttle et al., 2020). The synthetic data mocks therefore the data that would be obtained if satellites or ground-based sensors 115 were actually operated (Yoshimura et al., 2014).
For the OSSEs performed in this study the characteristics of the IASI δD observations generated by the MUSICA IASI retrieval processor are mocked. For generating the synthetic MUSICA IASI data set the spatial coverage and the observational error statistics of the real data are used. Our mocked "truth" data set has been derived from an IsoGSM simulation and is used as reference for assessing the impact of our assimilation experiments on the meteorological variables. The synthetic observational 120 data set is then generated by adding Gaussian noises with the actual error statistics of the IASI observations to the Nature run (Toride et al., 2021).

Experimental set-up
Two experiments consisting in total of four ensemble simulations (two per experiment) were performed to investigate the potential impacts of assimilating IASI water vapour isotopologues observations. Thereby, three OSSEs and one ensemble simulation 125 without any data assimilation were performed to assess the potential impact of the IASI δD data on the meteorological fields.
In the first OSSE synthetic conventional observations of temperature, humidity and wind profiles obtained from radiosonde and satellite data are assimilated, in the second OSSE synthetic IASI observations are assimilated additionally to the conventional observations and in the third OSSE synthetic IASI data are assimilated alone. The former two OSSEs serve to assess the additional benefit one gets if to the conventional assimilation procedure used in numerical weather prediction IASI data 130 would be assimilated. The third one serves to investigate what impact the assimilation of the IASI δD data alone has on the meteorological fields, e.g. on the diabatic heating rates. Therefore, this OSSE is compared to an ensemble simulation without assimilation of any observations. The Nature run is generated by an IsoGSM simulation over two years, covering the time period from 2015 to 2016. The model run was started on 1 June 2015 at 00 UTC. The first year has been discarded as spin-up period to minimize the possibility 135 of the model's drift. The initial conditions for the 96 ensemble members were taken from the Nature run. The first initialisation was done on 1 June 2016 at 00 UTC and then all other ensemble members were initialised with the following consecutive 6hour time steps. Therefore, the initial conditions can be considered as being independent from the Nature run, but representing similar climatological conditions. The following two months, thus from 1 July 2016 to 1 September 2016 have then been used as the experimental period and the results of our assimilation experiments are then evaluated for the latter one-month period (1 140 August to 31 August 2016).
The synthetic conventional observations (radiosondes, wind profilers, aircrafts, ships, buoys, surface stations, and wind data derived from satellites and radar) are generated based on a data set used in the NCEP operational system (known as PREPBUFR, i.e. preprocessed and quality controlled observations of the Binary Universal Form for the Representation of meteorological data (BUFR), https://rda.ucar.edu/datasets/ds337.0/). PREPBUFR is a commonly used data set in data assimilation 145 studies (e.g. Koshin et al., 2020). The conventional observations are also spatially resampled to the IsoGSM grid.
In the following the ensemble simulation with the assimilation of the conventional observations is called DA_prepbufr, the one where additionally to the conventional observations IASI δD is assimilated is called DA_prepbufr_IASI, the one with the assimilation of IASI δD alone is called DA_IASI and the ensemble simulation without any data assimilation is called noDA. When we later in Section 3.3 compare the former two with the latter two ensemble simulations we call the first 150 assimilation experiment (consisting of the ensemble simulations DA_prepbufr and DA_prepbufr_IASI) PREPBUFR and the second assimilation experiment (consisting of the ensemble simulations DA_IASI and noDA) noDAvsDA. An overview over our assimilation experiments is given in Table 1.
The assessment of the idealized assimilation experiment is then done by using each experiments ensemble mean, the mean difference between each ensemble mean of the respective assimilation run and the Nature run, the root-mean-square deviation 155 (RMSD) between each experiments ensemble mean and the Nature run and the RMSD skill. The ensemble mean and the mean difference between the assimilation run and the Nature run are calculated by: and 160 where x denotes the assessed meteorological variable (e. g. T , u, v) of the assimilation experiment and x n the respective meteorological variable of the Nature run. The RMSD is calculated as follows: The skill (in %) is calculated by: where CTRL denotes the assimilation with the conventional observations (DA_prepbufr in case of the PREPBUFR experiment) and the ensemble simulation without any data assimilation (noDA in case of the noDAvsDA experiment), respectively. RMSD and skill are typical measures for the quality of a simulation that are commonly used in Numerical Weather Prediction (NWP, e. g. Bauer et al. (2015))

IsoGSM output and derived parameters 170
For the assessment of the assimilation experiments we use the IsoGSM output of the following parameters: temperature (T ), zonal (u) and meridional wind (v), vertical velocity (ω), specific humidity (q) and precipitation. The water isotopologues δD and δ 18 O are derived from converting the model output of HDO and H 18 2 O from mixing ratios to the delta notation in per mille. The apparent heat flux of the large scale motion system Q 1 and the apparent moisture sink Q 2 which is due to the net condensation and vertical divergence of the vertical eddy transport of moisture are calculated based on the equations given in Yanai et al. (1973).
where s is the dry static energy, ω the vertical velocity, L is the latent heat of net condensation, q the specific humidity, V the 180 horizontal wind vector and p the pressure.

Assessment of the performance in the tropics
The assessment is performed for the tropics in the latitude range from 10 • S to 10 • N and for the one month period of August 2016. In the following this experiment is called PREPBUFR and the assimilation run with the conventional observations is 185 called DA_prepbufr and the one with the additional assimilation of IASI δD data is called DA_prepbufr_IASI. Figure 1 (left) shows the spatial and temporal averaged vertical profiles of the ensemble mean for δD, moisture sink (Q 2 ) and vertical velocity (ω) for the tropics (one month average over all longitudes). The spatially and temporally averaged ensemble mean profiles reflect the characteristics of the tropics, mainly upwelling (ω), drying above 800 hPa and moistening below and heating (Q 2 ) in most parts of the troposphere. In the spatial and temporally averaged ensemble mean profiles differences between the Nature 190 and the assimilation runs are quite low and become only visible when the mean difference between the assimilation run and the Nature run is considered ( Fig. 1 right). Generally, for the assimilation with additionally IASI δD (DA_prepbufr_IASI) the mean differences are lower than for the assimilation run with conventional observations only (DA_prepbufr).
Considering the corresponding RMSD and skill, which are shown in Fig. 2 for δD, Q 2 and ω, we find a clear decrease in the RMSD for the assimilation run where IASI δD is assimilated (DA_prepbufr_IASI). A decrease in the RMSD and improvement 195 in skill is also found for all other parameters ( Fig. S2 and S3). The highest decrease in the RMSD and highest skill is found for all parameters at ∼500-600 hPa, corresponding to the approximate altitude level where the IASI data has been assimilated. The improvement in the skill for δD is about 6 % at the lowest altitudes and increases to almost 40 % at 600 hPa and then decreases to 6 % at 300 hPa and remains at this value up to 100 hPa. For Q 2 the improvement in skill ranges between 8-10 % up to 400 hPa and decreases then to 5 %. Although the improvement in skill is mostly decreasing with altitude, this comparisons show that at all altitudes in the troposphere the assimilation of the IASI data additionally to the conventional observations leads to an improvement in the RMSD of the analysis variables. That this holds not only for the tropical mean profile, but also for all longitudes in the tropics can be seen from the cross sections.   Moisture Sink Skill (%) Figure 3. Cross sections of the RMSD for δD (left) and Q2 (right) from the assimilation experiment with the conventional observations alone (DA_prepbufr, top row), the one with assimilation of the mocked IASI data additionally to the conventional observations (DA_prepbufr_IASI, second row), the absolute difference between these two (third row) and the skill (bottom row) for the tropics (10 • S to 10 • N).
are found in δD and Q 2 , but the RMSD in these areas is significantly reduced in the DA_prepbufr_IASI assimilation run. This is also clearly reflected in the absolute difference of the RMSD (with positive values showing an improvement) and also the skill for both parameters is significantly improved. For δD the highest improvement in the skill is found at around 500 hPa which is approximately the altitude where the IASI data has been assimilated (while however the highest RMSD in δD is found in the upper troposphere at around 200-300hPa). For Q 2 the highest RMSD is found at the lowest atmospheric layers 210 Figure 4 shows the cross sections for Q 1 , Q 2 and ω for the tropics (monthly mean for August 2016). The longitudinal distribution is strongly tied to the equatorial Walker circulation which consists of several east-west circulation cells spanning different longitudinal sectors along the Equator; whereby having it's major cell above the tropical Pacific (Peixoto and Oort, 1992). Regions of diabatic heating (Fig. 4) are located in the convective regions over Asia (around 120 • E), South America 215 (around 60 • W) and western and central Africa (near 20 • E). Conversely, the absence of convection over the eastern Pacific leads to strong subsidence (Wright and Fueglistaler, 2013). When comparing the longitudinal regions where the high RMSD in δD is found with the vertical velocity and Q 1 (see Fig. 4 top panel) we find that these regions of high RMSD coincide with regions where strong upward/downward motion and diabatic heating/cooling is dominant. For Q 2 these regions coincide with the regions where upward motion and heating is dominant.

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The Comparison of the regions where the high RMSD is found in the cross sections ( Fig. 3) with the underlying map of the monthly mean distribution of Q 2 and precipitation ( Fig. 5) reveals the regions where the high RMSD is found in δD and Q 2 geographically. While the high RMSD in Q 2 is found over America, Asia and the Pacific, the high RMSD in δD is found over America and the Pacific. Based on this we select three regions in the tropics which will be analysed in the following in more detail. We selected the regions over land (Asia, America, Africa) since we are also interested in the performance of 225 the assimilation experiments with respect to precipitation and in the regions over land also the highest precipitation is found

Assessment of the performance by regions
We assess the performance of the assimilation experiments in specific tropical regions and selected therefore the three regions Asia (60 • E to 180 • E), America (120 • W to 30 • W) and Africa (30 • W to 60 • E). Figure 4 shows the cross sections for Q 1 , Q 2 and ω for the tropics and for the three selected regions separately these are shown in Fig. S4 in the supplement.
The Asian region is characterised by strong heating and upward motion. In the lowest layers (below the 800 hPa level) Q 2 235 shows a cooling (moistening) and heating (drying)    IsoGSM Nature (2016 08 indicating moistening due to evaporation. The quite similar shape of Q 1 and Q 2 but vertically shifted peaks indicate the occurrence of deep cumulus convection within the Asian monsoon (Yanai and Tomita, 1998). In the Asian region, the heating and upward motion are the highest of the three regions considered.
The American region is characterised by both strong upward motion and heating in the lowest layers as well as downward motion and radiative cooling in the mid to upper troposphere. Thus, showing some intermediate or balanced characteristic.

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The heating (Q 1 ) in the lowest layers can be explained by the vertical convergence of sensible heat flux from the surface. The moistening in the lowest layers (Q 2 ) is due to evaporation (Yanai and Tomita, 1998).
The Generally, the differences between the regions considered here can be described as follows: The strongest upward motion and associated heating is found in Asia, while the highest downward motion and cooling is found in the African region. The characteristics in heating and vertical motion are in America somewhere in between showing a mixture between heating/cooling and upward/downward motion. For Q 2 the moistening is highest in Africa and lowest in Asia. Considering the corresponding 260 MD, RMSD and skill (Fig. S5-Fig. S7) we find as for the entire tropics that the MD and RMSD is decreased and the skill improved and that thus the run DA_prebufr_IASI is generally closer to the Nature and thus the assimilation of IASI δD improves the diabatic heating rates and vertical motion. For example, for Q 2 the improvement in skill is in average throughout the troposphere about 7-9 % (7.65 % for Asia), 9.97 % for America and 5.29 % for Africa, see also Tab. S1). Similar values are derived for ω (7.61 % for Asia, 10.49 % for America, 5.27 % for Africa, Tab. S1 and Fig. 7).   (Fig. 7, bottom right), we also find an improvement in skill for all parameters where the highest improvement, as for the tropics, is found for Asia and Africa for the isotopologues (δD and δ 18 O). For America the highest improvement is derived for zonal (u) and meridional wind (v) and specific humidity (Q).

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The overall range in improvement in skill for the three regions is as follows: For Asia, except for δD and δ 18 O where the improvement is about 13 %, the improvement in skill is for the other parameters about 7-8 %. For America, the improvement is in the range of 9-14 %. For Africa the improvement in skill is about 10 % for the isotopologues (δD and δ 18 O) and 4-6 % for the other parameters (see Tab. S1). Also precipitation rates can be improved (Tab. S3). We find an improvement of 8.19 % for Asia, 13.65 % for America and 5.21 % for Africa. By region, for all here considered meteorological parameters the highest 275 improvement is therefore found for America while the lowest improvement is found for Africa.
This again shows the benefit of additionally assimilating IASI δD to the conventional observations. Irrespective if a specific region in the tropics or the tropics as a whole are considered, a improvement of about 10 % of the meteorological analyses due to the assimilation of IASI δD additional to the conventional observations can be achieved. In the following we are interested on the direct impact of IASI δD on the meteorological analysis. Especially, we are interested in answering the 280 following question: Can also the assimilation of only δD improve the heating and precipitation rates? Therefore, we performed an additional assimilation experiment, where only IASI δD is assimilated and derive the skill in comparison to an IsoGSM ensemble simulation without any data assimilation. The results will be discussed and compared to the previous experiment in the following section.

Assessment of the direct impact of IASI δD 285
To assess the direct impact of the assimilation of IASI δD on the meteorological analysis we performed an ensemble simulation with OSSE where only IASI δD is assimilated (called DA_IASI) and compare this simulation then to an IsoGSM ensemble simulation without any data assimilation (called noDA). This experiment is denoted in the following as "noDAvsDA" while the ensemble simulations where only conventional observations are assimilated and the one where IASI δD is assimilated additionally to the conventional observations (the two ensemble simulations discussed in the previous sections) are denoted as for all parameters except ω, Q 1 and Q 2 . For these three parameters a slight degradation (−2 to −7 % for ω, −3 to −8 % for Q 1 and −2 to −4 % for Q 2 ) is found ( Fig. 7 and Tab. S1). However, this degradation is mainly restricted to the lowest or highest pressure levels (above 150-200 hPa and for Q 1 below 700 hPa, Q 2 below 500 hPa and ω below 800 hPa). Inbetween, thus in the free troposphere, the assimilation of δD has either no impact (skill around 0 %) or causes a slight improvement 300 (see Fig. S10). The improvement for the other parameters is in the range of 4-9 % for Asia, 14-22 % for America, 12-20 % for Africa and 11-17 % for the tropics).
Additionally to the improvement throughout the troposphere derived from the vertical profile we also consider time series.
The time series have the advantage that it can be assessed how the assimilation experiment for a certain meteorological parameter at a certain altitude performs with respect to temporal variability of this parameter. Deriving the bar charts for the 305 improvement in skill from the time series at the 500 hPa level (Fig. 8), the level where approximately the IASI data has been assimilated, we derive for the tropics an improvement for all parameters. Here, although very small, an improvement is also found for ω, Q 1 and Q 2 . Separated by regions, at this level, a slight degradation of temperature (−3.14 %) is solely found for Asia and in Q 1 and Q 2 for Africa (−0.38 and −0.35 %, so small that is hardly visible in Fig. 8, therefore see Tab. S4 instead).
The improvement for the other parameters is in the range of 2-18 % for Asia, 3-27 % for America, 1-25 % for Africa and 2-21 % 310 for the tropics (see Tab. S4). As from the profiles, also from the time series the lowest improvement is found for Asia for all parameters except the isotopologues. For these here the highest improvement is found (27.44 % for δD and 25.28 % for δ 18 O).
The improvement in the precipitation rates ( Fig. 8 and Tab. S4) is 3.97 % for Asia, 13.45 % for America and 7.79 % for Africa.
We generally derive from this experiment (noDAvsDA) similar results by region as for the PREPBUFR experiment, namely that in the troposphere the highest improvement is found for America. In contrast to the PREPBUFR experiment the lowest 315 improvement is here found for Asia (Figure 7 and Tab. S2). However, for the degradation of ω, Q 1 and Q 2 it is the opposite than for the improvement: The degradation is lowest for Asia. The highest degradation in ω, Q 1 and Q 2 is found for Africa, although only slightly higher than for America (the average performance is about the same for these two regions). For the noDAvsDA experiment, we derive similar results from the time series at the 500 hPa level than from the vertical profiles, namely that the lowest improvement is found for all parameters for Asia except for the isotopes. Here, as for the PREBUFR 320 experiment, the highest improvement is found for America. for Q 1 , Q 2 and ω and for the three regions considered here. Here, especially in the noDAvsDA experiment ( Fig. 9) the positive impact of assimilating IASI δD is quite obvious. While the noDA simulation lacks the synoptic-scale temporal variations that 325 are found in the Nature run, the assimilation with IASI δD (DA_IASI) directly introduces these (see time series of the ensemble mean shown in Fig. S11). However, although these are not exactly the same as the one in the Nature run, especially for Asia and Africa, the agreement is quite reasonable.Therefore, the mean differences to the Nature run are for Asia and Africa larger for the assimilation run with IASI δD (DA_IASI). In contrast to these two regions, the DA_IASI assimilation is quite successful for America. The agreement for Q 1 , Q 2 and ω to the Nature run with just assimilating δD is impressive. This is reflected in the 330 mean differences by lower differences for DA_IASI than for noDA which also alternate much closer around zero. The good agreement found here in the time series for America is in agreement with the results concerning skill discussed above, where we also found the highest improvement in skill for America.
In the case of the PREPBUFR experiment ( Fig. 10 and Fig. S12), the assimilation of the conventional observations already brings the analysis close to the Nature run and is further improved when IASI δD is additionally assimilated as can be seen 335 from the RMSD and skill discussed a few paragraphs earlier (and shown in Fig. 8 and Tab. S3). In the mean differences this is reflected by lower differences from the Nature run for DA_IASI that alternate closer to zero than the assimilation run with conventional observations only.

Assessment by the δD-δ 18 O relationship and d-excess
Another example to demonstrate the benefit of the assimilation of IASI δD is when the relationship between δD and δ 18 O is 340 considered. Figure 11 shows the correlation of δD and δ 18 O of the 6-hourly data for August 2016 at 500 hPa for the noDAvsDA (Fig. 11 top) and the PREPBUFR (Fig. 11 bottom) experiment at the three selected regions in the tropics. Additionally, the global and local meteoric water line (GMWL and LMWL, respectively) are shown. The GMWL is defined by: To derive the local meteoric water line (LMWL) for the here chosen areas a linear fit is applied to the correlation of δD and 345 δ 18 O of the Nature run. We derive the following relationship for August 2016 at 500 hPa: Then δ 18 O is calculated based on the δD from the Nature and the assimilation runs, respectively. Figure 11 shows that the relationship between δD and δ 18 O is generally correct in IsoGSM, however, δD and δ 18 O show less variability and generally a relationship with more depleted δD and enriched δ 18 O. This deviation that is introduced by IsoGSM is most pronounced in 350 Africa and America. The assimilation of IASI δD alone helps to reduce this deviation and moves the correlation closer to the Nature. If the conventional observations are assimilated this deviation is also significantly reduced but an offset with respect to δD and δ 18 O still remains which can be corrected when additionally to the conventional observations IASI δD is assimilated.
For both, the PREPBUFR and noDAvsDA experiment, the best agreement in the δD-δ 18 O relation is found for Asia which x and y-scale ranges are used for the panels. may be due to the fact that here the deviation in δD and δ 18 O is also lowest. For Africa and America, although the deviation 355 can be significantly reduced, still a lot of scatter (noDAvsDA) and a slight offset (PREPBUFR) remains.
Comparing the three regions with each other we find that Africa is the region which is most depleted (lowest δD and δ 18 O) and America is the region that is most enriched (highest δD and δ 18 O). The δD-δ 18 O correlation for Asia is quite similar to the one for America, but is by ∼40 ‰ more depleted than America. Further, the correlation for Africa spans over a much larger value range than the correlation for America and Asia which is also reflected in a larger range of deuterium excess (d-excess) 360 values (see Fig. 12). The second-order isotope variable d-excess (Daansgard, 1964) is a tracer for moisture source conditions and is also a measurable constraint for processes involved in precipitation formation (Aemisegger et al., 2015;Aemisgger and Sjolte, 2018). It is defined as follows: d = δD − 8× δ 18 O. While the d-excess for Asia agglomerates around 15 ‰, the d-excess for Africa spans over a much larger value range (17−40 ‰) with much more depleted (thus drier) δ 18 O than in the other two regions. As larger the value range of the d-excess spans as larger also the differences between the assimilation experiments and 365 the Nature run get.

Discussion
The assimilation experiments described in the previous sections show that the assimilation of δD has the potential to improve the meteorological analysis in the tropics, both alone (noDAvsDA) and together with conventional observations (PREPBUFR).
However, heating rates and vertical motion can only be improved throughout the troposphere when additionally to IASI δD 370 conventional observations are considered. When only IASI δD is assimilated the improvement in ω, Q 1 and Q 2 is minor and restricted to the mid-troposphere. Further, there are differences in the performance of the assimilation experiments in the three regions in the tropics considered in this study (Asia, America and Africa). Thereby, we found the highest improvement for both experiments for America, while the lowest improvement was found for the PREPBUFR experiment for Africa and for the noDAvsDA experiment for Asia.

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High RMSDs of δD and Q 2 in the PREPBUFR experiment were found in the regions where the upward and downward branches of the atmospheric circulation are located ( Fig. 3 and Fig. 4). Thereby, we found that these regions of high RMSD  We generally find, in agreement with Toride et al. (2021), an improvement in the atmospheric circulation when IASI δD 385 is assimilated additionally to the conventional observations. However, for both experiments we do not see from the analyses performed here a better performance on either upward or downward branches. We rather find an improvement in the circulation cells dependent on region. For the PREPBUFR experiment, the highest improvement is found in the main Walker cell over  branches just confirms what we found before, namely that for both experiments the highest improvement is found for the respective upward/downward branches covered by the here defined American region and the lowest for the branches over the here defined African region (PREPBUFR) and Asian region (noDAvsDA). An exception are here ω, Q 1 and Q 2 for which at the 500 hPa level better results are derived for the upward than for the downward branches.
We cannot entirely rule out why we see differences in the assimilation experiments by region, but a possible explanation 395 may be the specific characteristics of these regions. The best agreement for both experiments was found for America, a region where moderate upward and downward motion prevails (ω alternating around zero), while the here defined Asian region is mostly dominated by strong upward motion and the African region by strong subsidence (Fig. 4 and Fig. S4). All three regions are affected by the respective monsoons, but in case of Asia and America the monsoon is located further north of our here defined tropical region, while the monsoon over Africa is located at this time of the year directly over the equator and thus 400 within the here defined region (Geen et al., 2020).
The above described intermediate behaviour of America is also reflected in the correlation of d-excess and δ 18 O (Fig. 12). precipitation rates, the lowest rates are found for Africa, while the highest are found for Asia (Fig. 15). D-excess can act as fingerprints of earlier processes and thus high d-excess values can be associated with air that has been dried while low d-excess values can be associated with air that has been moistened (Salmon et al., 2019). Thus, the Asian regions which is mostly covered by oceanic areas is probably mostly affected by ocean evaporation (Risi et al., 2013).

Asia
Additionally with the above high precipitation rates the isotope ratios are in equilibrium resulting in the agglomeration of the Considering all these differences we can conclude that we derive the best results for America because this region is affected 420 by moderate dynamics (moderate up and downward motion with ω alternating around zero) than it is the case for Asia and Africa. In these two regions, dynamical processes are much stronger than in America. Especially, Asia which is quite humid and wet (high precipitation rates) is also a region where rather deep convection is prevailing (see also ω profile Fig. 6). This could explain, why the performance for the noDAvsDA experiment was lowest for Asia. Due to the underlying dynamics the additional information from PREPBUFR is here more important than for the other two regions. Africa, on the other hand, 425 with its complex dynamics and interaction between moist tropical and dry subtropical air masses and thus according effects on the isotopic composition seems to be generally an area that is difficult to simulate, both in terms of dynamics and isotopic processes (e.g. Diekmann et al., 2021b). Thus, this may explain why we find the lowest improvement in this region for the PREPBUFR experiment.
Nevertheless, besides the above discussed regional differences also the amount of data availability of the conventional 430 observations and IASI δD in the respective areas for the assimilation experiments and the underlying model physics may definitely also play a role in the performance of the assimilation experiments in the three here considered tropical regions.

Conclusions
We performed idealized assimilation experiments where IASI δD data was mocked into an OSSE additional to conventional observations (PREPBUFR). The assessment of the impact of this assimilation experiment on the meteorological analysis was 435 performed for the tropics (10 • S to 10 • N). Thereby, additionally to the entire tropics also specific longitude regions in the tropics were considered, namely Asia (60 • E to 180 • E), America (120 • W to 30 • W) and Africa (30 • W to 60 • E).
The assimilation experiment with IASI δD shows that for all parameters the RMSD can be decreased and the skill improved when the IASI δD data is assimilated additionally to the conventional observations (PREPBUFR experiment). The highest improvement in skill and decrease in RMSD was found at ∼500-600hPa, the approximate altitude where IASI δD has the 440 highest sensitivity and was assimilated into the IsoGSM model. The improvement in skill for the PREPBUFR experiment is about 8-13 % for the tropical troposphere (up to the 100 hPa level). Separated by regions the improvement in the troposphere is about 7-13 % (Asia), 9-13 % for (America) and 4-10 % (Africa), respectively. Thus, the highest improvement is found for America and the lowest for Africa. Concerning the RMSD we found high RMSDs in δD, Q 1 , Q 2 in certain regions. We found that these regions of high RMSD in δD coincides with regions of upward/downward motion and heating/cooling while the high 445 RMSD in Q 2 coincides with regions of upward motion and heating.
In Addition to the PREPBUFR experiment, we performed another experiment consisting of an assimilation run where only IASI δD is assimilated and compared this to an IsoGSM ensemble simulation where no observations were assimilated to obtain the direct impact of the assimilation of IASI δD on the meteorological analysis fields (noDAvsDA experiment). In this experiment we find an improvement in skill in the tropical troposphere for all parameters except ω, Q 1 and Q 2 (from vertical 450 profiles up to the 100 hPa level). However, the degradation for these parameters is restricted to the lowest atmospheric layers (below ∼800 hPa). Above 800 hPa the improvement in skill is either around zero or slightly positive. The lowest improvement/highest degradation, thus lowest impact is found for Asia. From the time series at the 500 hPa level an improvement for all parameters is found except T (Asia) and Q 1 and Q 2 (Africa) where a minimal degradation is found. Although also here the lowest improvement is derived for Asia, for the isotopes it is here the opposite. Here, we find the highest improvement. From 455 the vertical profiles, the highest improvement is found for all parameters for America and from the time series at the 500 hPa level for America when all parameters are considered and for Africa when only the parameters are considered where an improvement is found. The noDAvsDA experiment shows that the assimilation of IASI δD alone cannot significantly improve the heating rates. However, the assimilation of δD has a positive effect on all other parameters. Furthermore, together with the conventional observations from PREPBUFR an additional improvement for all parameters, including the heating rates, can be achieved and shows the benefit of the IASI δD data.
Our study shows that the assimilation of IASI data has the potential (especially in combination with the conventional observations) to improve meteorological analysis and thus also weather forecasts and climate predictions. More promising results with OSSE can be derived if additionally to IASI δD also IASI H 2 O is assimilated (Toride et al., 2021). So far only idealized experiments were performed, but experiments with assimilating real IASI δD data are in progress. However, a lot of uncertain-465 ties concerning water isotope modelling and observations remain (as discussed in Toride et al. (2021)) that could hinder the realisation of the assimilation of real IASI data and/or compared to the idealised experiments lessen the impact of δD on the analysis fields. Nevertheless, in the future, when vapor isotopic fields will be measured more frequently and the modelling of isotopic processes will be more accurate, the assimilation of isotopic observations may play an important role in improving the analysis and forecast skill because isotopes provide unique information relevant to atmospheric circulation.