Characterization and evaluation of AIRS-based estimates of the deuterium content of water vapor

Abstract. Single-pixel tropospheric retrievals of HDO and H2O concentrations
are retrieved from Atmospheric Infrared Sounder (AIRS) radiances using the
optimal estimation algorithm developed for the Aura Tropospheric Emission
Spectrometer (TES) project. We evaluate the error characteristics and
vertical sensitivity of AIRS measurements corresponding to 5 d of TES data
(or five global surveys) during the Northern Hemisphere summers between 2006
and 2010 (∼600 co-located comparisons per day). We find that the
retrieval characteristics of the AIRS deuterium content measurements have
similar vertical resolution in the middle troposphere as TES but with
slightly less sensitivity in the lowermost troposphere, with a typical
degrees of freedom (DOFS) in the tropics of 1.5. The calculated measurement
uncertainty is ∼30 ‰ (parts per
thousand relative to the deuterium composition of ocean water) for a
tropospheric average between 750 and 350 hPa, the altitude region where AIRS
is most sensitive, compared to ∼15 ‰ for the TES data.
Comparison with the TES data also indicates that the uncertainty of a single
target AIRS HDO ∕ H2O measurement is ∼30 ‰.
Comparison of AIRS and TES data between 30∘ S and 50∘ N
indicates that the AIRS data are biased low by ∼-2.6 ‰ with a
latitudinal variation of ∼7.8 ‰. This latitudinal variation is
consistent with the accuracy of TES data compared to in situ measurements,
suggesting that both AIRS and TES have similar accuracy.



Introduction
Measurements of the isotopic composition of water can help identify the source of the water and provide knowledge about its condensation and evaporation history (e.g., Galewsky et al., 2016, and references therein). Through most of the twentieth century, most isotopic measurements of water have been of precipitation (e.g., Craig, 1961). Near global measurements of the isotopic composition of water vapor became possible with the advent of spectroscopic techniques applied to in situ measurements (e.g., Noone et al., 2011) using lasers and for passive ground-based and satellite measurements (e.g., Worden et al., 2006;Frankenberg et al., 2009;Schneider et al., 2012;Lacour et al., 2012). These data have in turn been used to evaluate the role of convection, largescale dynamics, and evapotranspiration in the tropical water cycle (e.g., Worden et al., 2007;Frankenberg et al., 2009;Wright et al., 2017) and tropical convection (e.g., Lacour et al., 2018, and refs therein) and the role of plants in global evapotranspiration (Good et al., 2015).
In this paper we demonstrate a retrieval algorithm, based upon the Aura TES optimal estimation retrieval algorithm (e.g., Worden et al., 2012) that can provide robustly characterized measurements of the deuterium content of water vapor (HDO and H 2 O) from the AIRS measurements. Our goal is to create a multi-decadal Earth Science Data Record (ESDR) using the AIRS and TES data; the TES global record spans ∼ 6 years (2005)(2006)(2007)(2008)(2009)(2010) and the AIRS data span 17+ years starting in 2002. This ESDR could potentially be used for evaluating the changing water cycle (e.g., Bailey et al., 2017) and its coupling to the carbon cycle (e.g., Zhou et al., 2014;Wright et al., 2017).
We first characterize the vertical resolution and uncertainties for estimates of HDO and H 2 O, and their ratio, using AIRS radiance observations corresponding to boreal summertime TES global survey's between 2006 and 2010, which is the time period when TES observations sample the (near) global atmosphere, and the calibration approach for TES measurements remained the same. We make only these comparisons due to current processing limitations but expect additional overlap between TES and AIRS data sets in the coming years. We then compare the AIRS and TES data to evaluate the calculated uncertainties of the AIRS data.

Description of AIRS and TES instruments
The AIRS instrument is a nadir-viewing, scanning infrared spectrometer Pagano et al., 2003;Irion et al., 2018;DeSouza-Machado et al., 2018) that is on board the NASA Aqua satellite and was launched in 2002. AIRS measures the thermal radiance between approximately 3 and 12 µm with a resolving power of approximately 1200. For the 8 µm spectral range used for the HDO/H 2 O retrievals, the spectral resolution is ∼ 1 cm −1 with a gridding of ∼ 0.5 cm −1 ; the signal-to-noise ratio (SNR) ranges from ∼ 400 to ∼ 1000 over the 8 µm region for a typical tropical scene. A single footprint has a diameter of ∼ 15 km in the nadir; with the ∼ 1650 km swath, the AIRS instrument can measure nearly the whole globe in a single day. The Aqua satellite is part of the "A-Train" that consists of multiple satellites, including TES, in a Sun-synchronous orbit at 705 km with an approximately 13:30 Equator crossing time.
The Aura TES instrument is a Fourier transform spectrometer that originally was designed to measure the thermal infrared (IR) radiances in both the limb and nadir viewing in order to obtain vertically resolved trace gas profiles of ozone, CO, CH 4 , HDO, and H 2 O and several ozone pre-cursors such as ammonia, methanol, and PAN (e.g., Beer et al., 2001;Worden et al., 2004Worden et al., , 2006Worden et al., , 2012Luo et al., 2007;Beer et al., 2008;Payne et al., 2014). Several of these trace gases, such as CO, CH 4 , and ammonia, have also been quantified using AIRS radiances (e.g., McMillan et al., 2010;Xiong et al., 2008;Warner et al., 2016). In comparison to the AIRS instrument, TES has a spectral resolution of ∼ 0.12 cm −1 (apodized) with a spectral gridding of 0.06 cm −1 . The SNR is ∼ 300 in the 8 µm spectral region. The Aura TES instrument, after the summer of 2005, observes one nadir scene every 100 km along the orbit path. The effective length of the record is approximately 5 years, between September 2005 and November 2009, after which instrument degradation problems resulted in interruptions and a decrease in sampling. The AIRS instrument has nearly 1000 times the sampling of TES and near-continuous operation between 2002 and the present and therefore can be used to construct several composition-based ESDRs.

Description of the radiative transfer forward model
The radiative transfer forward model used for this work is the optimal spectral sampling (OSS) fast radiative transfer model (RTM) (Moncet et al., 2008(Moncet et al., , 2015. The OSS approach is integrated in the operational Cross-Track Infrared Sounder (CrIS; Han et al., 2013) processing system (Divarkala et al., 2014) and has also been utilized for trace gas retrievals from CrIS (e.g., Shephard and Cady-Pereira, 2015). OSS uses a series of approximations tailored to a specific frequency range and spectral resolution to increase the radiative transfer calculation performance by approximately a factor of 20-100 relative to a line-by-line calculation (http://rtweb.aer.com, last access: 8 April 2019). OSS can be trained to user-defined accuracy relative to the line-by-line model used for training. Here, the training threshold was set to 20 % of the AIRS noise level. The line-by-line model used as a reference in the training and to build the absorption coefficient look-up tables (LUTs) used by the fast RTM is the Line-By-Line Radiative Transfer Model (LBLRTM) (Clough et al., 2005;Alvarado et al., 2013). The OSS version used in this work is based on LBLRTM v12.4, using the TES_v2.0 spectroscopic line parameter database. The TES_v2.0 line parameter database follows the HITRAN 2012 compilation (Rothman et al., 2013), with the following exceptions. -CH 4 includes first-order line mixing coefficients (as supplied in the aer_v_3.4 line parameter database). These were calculated using the approach of Tran et al. (2006).
-CO 2 line parameters are from the database of Lamouroux et al. (2015). This database takes most of its line positions, intensities, and lower state energies from the HITRAN 2012 database, but the values for airbroadening half-widths and their temperature dependences are adjusted from the HITRAN 2012 values to be consistent throughout the bands, and the air-induced pressure shifts (not given for a majority of transitions in HITRAN 2012) were added. The TES_v2.0 database includes first-order line mixing coefficients (as supplied in the aer_v_3.4.1 line parameter database), calculated using the software of Lamouroux et al. (2015).
Further information on the AER line parameter databases can be found at http://rtweb.aer.com (last access: 8 April 2019). OSS is adapted for use with AIRS radiances using the version 4 AIRS spectral response function (SRF)  that is interpolated to a uniform grid of 0.004 cm −1 centered on the channel center frequencies. The OSS radiative transfer code provides speedup of 20-100× over the original TES operational radiation transfer model .

Description of the retrieval approach
The optimal estimation algorithm used in this analysis for quantifying CH 4 , HDO, H 2 O, temperature, cloud properties, and emissivity is extensively discussed in Worden et al. (2004 and Bowman et al. (2006). We therefore refer the reader to those papers for a description of the retrieval algorithm, with a suggestion that they start with the Worden et al. (2012) paper; however, we will briefly summarize the retrieval approach here. This retrieval algorithm, now called the MUlti-SpEctra, MUlti-SpEcies, MUlti-Sensors (MUSES) algorithm Fu et al., 2013Fu et al., , 2016Worden et al., 2013), can use radiances from multiple instruments including TES, CrIS, OMI, OMPS, TROPOMI, and MLS to quantify geophysical observables that affect the corresponding radiance.
For the AIRS retrievals discussed here, we simultaneously estimate not just CH 4 , CO, HDO, and H 2 O but also temperature (surface and atmosphere), emissivity (if over land), and a spectrally varying gray body cloud (e.g., Eldering et al., 2008). As in Worden et al. (2006Worden et al. ( , 2012 the constraint matrix used to regularize the HDO and H 2 O components of the retrieval includes off-diagonal components that reflect a priori knowledge about the variability of HDO with respect to H 2 O in order to ensure that retrieval of the ratio of HDO to H 2 O is optimized, as opposed to either HDO or H 2 O alone. The prior information used for this covariance is derived from monthly climatologies using the NCAR Global Climate Model as discussed in . The a priori profile used for the HDO/H 2 O ratio is set to be constant over the whole globe, and represents the mean tropical a priori profile from the NCAR model. However, the H 2 O a priori profile is allowed to vary by latitude and is based on reanalysis ; therefore the HDO profile is the mean tropical profile of the HDO/H 2 O ratio from the NCAR model multiplied by the H 2 O a priori profile. We use single-pixel radiances that have not been transformed through "cloud clearing" in order to preserve the original well-characterized radiance noise characteristics for use in our estimates DeSouza-Machado et al., 2018) and because we find that single-pixel AIRS radiances have sufficient information about cloud pressure and optical depth to be retrieved jointly with the trace gases, as demonstrated empirically through validation of these AIRS-based composition retrievals with TES retrievals (e.g., Figs. 1-4). We assume the noise in any given pixel is uncor- related with that from adjacent pixels. However, these correlations are known to exist (e.g., Pagano et al., 2008) and the impact of ignoring them is that our calculated uncertainties will be larger than expected and therefore our noise-related uncertainty should be considered a conservative estimate.
A primary difference between the retrieval approach shown in this paper versus the TES methane and HDO retrievals  and those from previous efforts using AIRS radiances (e.g., Xiong et al., 2008) is that we retrieve these trace gas profiles using the AIRS radiances from ∼ 8 and ∼ 12 µm instead of radiances from the 8 µm region alone in order to provide a stronger constraint on atmospheric temperature and hence reduce uncertainty from knowledge of temperature on the HDO and H 2 O retrievals. The 8 µm region used (∼ 1217 to 1315 cm −1 ) for these retrievals has the most sensitivity to HDO and H 2 O, whereas the 12 µm band (∼ 650 to 900 cm −1 ) is primarily sensitive to temperature and H 2 O. All channels are used within this spectra unless flagged as poor during calibration.

Characterization of HDO/H 2 O profiles
While H 2 O is quantified using radiances from both the 12 and 8 µm spectral regions, the primary absorption lines used here to quantify HDO are in the 8 µm region. There are other HDO (and H 2 O) lines available to use from the AIRS radiance but for now we only use the 8 µm region to ensure consistency between AIRS and TES data. Figure 1a shows the 8 µm radiance and the Jacobian, or sensitivity of the radiance to variations in the (log) H 2 O and (log) HDO, respectively (Fig. 1b, c). These Jacobians are normalized by the instrument noise. For example, a value of 1 means that it would take a 100 % change in the corresponding species to distinguish between two similar radiances (everything about the observed scene and radiance is the same except for the species of interest) above the noise level. A value of ∼ −50 therefore means that only a 2 % variation is required (or 1/50). Figure 2 shows the averaging kernel matrix for the HDO component of the joint retrieval. The averaging kernel describes the response of the estimate, or log(HDO), relative to variations in the true state; consequently it can also be used to evaluate the vertical resolution and sensitivity of the estimate. For example, if HDO varies by 100 % at 908 hPa, then the AIRS estimate would be able to observe about 30 % of the variability because the averaging kernel is approximately 0.3 at that level. The averaging kernel at 908 hPa also depends on the deuterium content at several other pressure levels below and above, indicating that the estimate at 908 hPa depends on the deuterium content variations at these other levels. Not shown are the dependencies of the (log) HDO estimate on those from the (log) H 2 O estimate. These dependencies between the HDO averaging kernels and with the H 2 O averaging kernels are accounted for when constructing the HDO/H 2 O ratio; however a residual uncertainty called the "smoothing" error is imparted when comparing the HDO/H 2 O ratio to independent data; this smoothing error is part of the error budget shown in Fig. 3. As discussed in Worden et al. (2012) and Schneider et al. (2012), the sensitivity of the estimated HDO/H 2 O ratio is limited by the sensitivity of the estimate to HDO. Users of these data should note that this ratio is typically used with that of H 2 O in order to better evaluate their joint variation (HDO/H 2 O, H 2 O) against simple mixing and rainfall models . However, the sensitivity of the radiance to H 2 O variations is much stronger than that for HDO, although the altitude region of the HDO sensitivity typically overlaps with the H 2 O sensitivity. Schneider et al. (2012) discuss how to created HDO/H 2 O, H 2 O pairs to mitigate this component of the smoothing error when comparing these data against the simple models described in Noone et al., (2011). For comparison to more complex global climate models the user of these data also needs to apply the HDO and H 2 O averaging kernels to the corresponding model fields (e.g., Risi et al., 2012). Figure 3a shows the tropospheric deuterium content (or HDO/H 2 O ratio) derived from AIRS observations on 1 July 2006. Despite the improved computational performance of the OSS radiative transfer calculation relative to the TES algorithm line-by-line calculation (Clough et al., 2005), the retrieval is still sufficiently expensive such that we can only process a subset of the AIRS retrievals. Considering the computational cost, for the purpose of constructing a record we currently only process AIRS retrievals from between 45 • S and 65 • N that coincide with the nearest TES observation but with an additional two observations within 100 km of the TES track over the continents; this ad hoc sampling strategy is based on experience with previous studies using the TES deuterium and methane measurements. The traditional notation for this quantity is called "delta-D" , or "δ-D" with units of "per mil" or parts per thousand relative to the Standard Mean Ocean Water (SMOW) deuterium content, which is 3.11×10 −4 molecules of HDO per molecule of H 2 O. The observations shown represent the deuterium content for the pressures between 750 and 350 hPa, where we find the AIRS and TES observations have maximal overlap in their vertical resolution.
The errors are calculated during the optimal estimation retrieval Worden et al., 2012) and depend on the expected noise of the AIRS radiances and the parameters that are co-retrieved with the AIRS HDO/H 2 O ratio such as temperature, surface emissivity, clouds, and methane. As noted in Worden et al. (2012) these co-retrieved parameters affect both the precision and accuracy whereas the noise only affects the precision. The total error (Fig. 3b) is given in units of per mil and ranges between 25 ‰ and 30 ‰. The DOFS, or trace of the averaging kernel, are shown in Fig. 3c and indicate that many of the HDO/H 2 O retrievals can resolve different parts of the troposphere, at least in the tropics, because (as demonstrated in Fig. 2) the rows of the averaging kernels are separated between the boundary layer region (surface to ∼ 750 hPa) and the free troposphere (∼ 600 to 300 hPa). However, these observations cannot completely resolve the total variability in these two regions of the atmosphere because the total DOFS is typically 1.5 or less and for the measurement to be able to resolve the variability (to within the calculated error) of the two regions there would need to be at least 2 DOFS.   Fig. 4 overlap as retrievals may be rejected due to poor quality. We therefore compare all data that are within 200 km in the free troposphere. We do not expect substantive error to occur due to spatial mismatch of 2 • or less because air parcels in the free troposphere have length scales that are several hundred kilometers long (e.g., Worden et al., 2013). The average between approximately 750 and 350 hPa is shown for when the DOFS are larger than 1 for this altitude region. There is a slight bias of −2.7 ± 1.5 ‰ between TES and AIRS as shown in Fig. 4a. The calculated and actual (RMS difference between AIRS and TES) uncertainties are shown and are approximately 30 ‰, primarily driven by the uncertainty in the AIRS-based estimates as the TES-based estimates have an uncertainty of approximately 15 ‰. Figure 5 shows a direct comparison of the AIRS and TES data. The correlation is about 0.89 and the one-to-one line (solid line) overlaps this distribution. However the lowest values likely diverge from the one-to-one line, possibly because the vertical distribution in the sensitivity depends on the amount of HDO and hence we should expect differences between the TES and AIRS deuterium measurements for these lower-sensitivity retrievals.
A comparison of the AIRS and TES HDO/H 2 O ratio for five single global surveys taken between 2006 and 2010 (one global survey per year during boreal summer) is shown in Table 1 and indicates that the overall bias varies between  −2.7 ‰ and 3.7 ‰. Using all five TES global surveys that are summarized in Table 1 we can construct how AIRS and TES compare as a function of latitude as shown in Fig. 6. Figure 6 is constructed by averaging the difference between TES and AIRS observations within 5 • latitudinal bins. The mean bias across latitudes is ∼ −2.6 ‰. The error bars shown on the difference is the error on the mean, which is the root mean square (RMS) of the differences divided by the square root of the number of co-located observations; as this error bar is a measure of precision for each latitude bin, this comparison demonstrates that there are variations in the comparison that are larger than the precision and are therefore related to systematic errors in either the TES data or AIRS data or both. Variations in these systematic errors can be seen in the latitudinal variability, which has an RMS variation of ∼ 7.8 ‰ for the different latitude bins but can vary by as much as ∼ −15 ‰ to ∼ +15 ‰ in the tropics. Typically these variations are due to a combination of uncertainties in the spectroscopy along with temperature, water vapor, and surface properties; they may also be due to smoothing error, which is related to how differences in the vertical resolution affect the tropospheric average of the deuterium content shown in these figures (e.g., Worden et al., 2004). This 7.8 ‰ variation across latitudes is about the same as the reported accuracy of the Aura TES delta-d observations that are based on comparisons of TES data with surface and aircraft measurements Herman et al., 2014). We therefore report the current accuracy of the AIRS data to be ∼ 7.8 ‰.
We expect future comparisons between these data and those from aircraft or revisions to the AIRS retrieval approach will modify this estimate of the accuracy.

Conclusion
This paper describes the vertical resolution and error characteristics of retrievals of the deuterium content (or the HDO/H 2 O ratio) of water vapor using AIRS radiances and then evaluates the consistency between AIRS and TES retrievals of HDO and H 2 O. We find that the AIRS and TES deuterium content for the lower troposphere (750-350 hPa) is consistent, or within their calculated uncertainties, for the 5year period in which TES observations span the globe (2006)(2007)(2008)(2009)(2010). We find the total uncertainty for a single AIRS observation is ∼ 30 ‰ with an accuracy of ∼ 7.8 ‰. These uncertainties can be compared to the observed total variability, which can range from approximately −350 ‰ to −50 ‰ over the whole globe, as observed by the Aura TES data  and shown in Fig. 3 for AIRS data. While only 5 d of comparisons are shown here for the purpose of evaluating the retrieval approach and error characteristics of these AIRS retrievals, we expect to produce a record of the AIRS-based deuterium content retrievals from the start of the mission (2002) through the present. Because of computational limitations, we expect to process data from 45 • S to 65 • N at approximately 4 times the sampling of the Aura TES measurements and with increased sampling (∼ 3×) over the continental regions with the goal of increasing this sampling once the initial record is completed and as additional resources become available.
Data availability. The Aura TES data are publicly available on the Langley Atmospheric Research Center Data Archive https:// eosweb.larc.nasa.gov/ (NASA, 2019). We expect the AIRS-based deuterium data to be publicly released by January 2020. Files in IDL format of the data shown are available from the author upon request: john.r.w.worden@jpl.nasa.gov.
Author contributions. JRW led the study and made the comparisons between TES and AIRS. SSK and DF provided the AIRS retrievals. VHP, KWB and RLH supported initial evaluation of the OSS forward model and HDO/H 2 O retrievals. AEL, IP, YH, KCP and JLM provided the OSS forward model needed for the HDO/H 2 O retrievals. FWI of the AIRS team supported the adoption of the AIRS data.
Competing interests. The authors declare that they have no conflict of interest.