Comparison of optimal estimation HDO/H2O retrievals from AIRS with ORACLES measurements

In this paper we evaluate new retrievals of the deuterium content of water vapor from the Aqua Atmospheric InfraRed Sounder (AIRS), with aircraft measurements of HDO and H2O from the ObseRvations of Aerosols above Clouds and their intEractionS (ORACLES) field mission. Single-footprint AIRS radiances are processed with an optimal estimation algorithm that provides vertical profiles of the HDO/H2O ratio, characterized uncertainties and instrument operators (i.e., averaging kernel matrix). These retrievals are compared to vertical profiles of the HDO/H2O ratio from the Oregon State University Water Isotope Spectrometer for Precipitation and Entrainment Research (WISPER) on the ORACLES NASA P-3B Orion aircraft. Measurements were taken over the southeastern Atlantic Ocean from 31 August to 25 September 2016. HDO/H2O is commonly reported in δD notation, which is the fractional deviation of the HDO/H2O ratio from the standard reference ratio. For collocated measurements, the satellite instrument operator (averaging kernels and a priori constraint) is applied to the aircraft profile measurements. We find that AIRS δD bias relative to the aircraft is well within the estimated measurement uncertainty. In the lower troposphere, 1000 to 800 hPa, AIRS δD bias is −6.6 ‰ and the root-mean-square (rms) deviation is 20.9 ‰, consistent with the calculated uncertainty of 19.1 ‰. In the mid-troposphere, 800 to 500 hPa, AIRS δD bias is −6.8 ‰ and rms 44.9 ‰, comparable to the calculated uncertainty of 25.8 ‰.


Introduction
The deuterium content of tropospheric water vapor is sensitive to the different types of atmospheric moisture sources, such as evaporation from the ocean or land, and the processing that occurs during transport, such as mixing or condensation (e.g., Craig, 1961;Dansgaard, 1964;Galewsky et al., 2016). Condensation and precipitation preferentially remove the heavier HDO isotopologue from the gas phase relative to the parent isotopologue H 2 O, whereas evaporation of precipitation at lower altitudes in the atmosphere can enrich HDO relative to H 2 O vapor. These unique, isotopic properties allow the HDO/H 2 O ratio to be a tracer for the origin, condensation and evaporation history of an air parcel, and thus be useful for evaluating changes to the water cycle (e.g., Noone, 2012;Galewsky et al., 2016).
In the last decade, satellite retrievals of tropospheric water vapor isotopic composition (HDO and H 2 O) have been developed, including Envisat/SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography) (Frankenberg et al., 2009), IASI (Infrared Atmospheric Sounding Interferometer) aboard the MetOp satellites (Herbin et al., 2009;Schneider and Hase, 2011;Lacour et al., 2012) and TES (the Tropospheric Emission Spectrometer) on the Aura spacecraft . More recently, Worden et al. (2019) developed HDO retrievals from the Aqua Atmospheric InfraRed Sounder (AIRS) single-footprint Level 1B radiance data. These AIRS retrievals are the subject of the present comparison with aircraft data.
Satellite HDO measurements have been utilized to study tropical carbon-water feedbacks (Wright et al., 2017), moist processes in deep convection (e.g.,  and the global partitioning of transpiration to evapotranspiration (Good et al., 2015). A decadal record of HDO has promise for characterizing global shifts in moisture sources and atmospheric water balance in response to warming, climactic variability, and land use. For example, Bailey et al. (2017) show that a record of free tropospheric HDO/H 2 O would provide an observational constraint on changes in the tropical water balance (evaporation minus precipitation) in response to shifts in ocean temperature. Wright et al. (2017) also show that free tropospheric deuterium measurements provide a fundamental new constraint in carbon-water dynamics in the Amazon. They use the TES isotope measurements to show that dry-season evapotranspiration is critical for initiating southern Amazon rainfall, which in turn is critical towards sustaining the Amazon rainforest (R. . For these reasons a record of the deuterium content of water vapor from the long (17 years and continuing) record from AIRS holds significant potential to evaluate changes in the global water cycle. This paper presents detailed comparisons between new AIRS measurements of the deuterium content of water vapor (or HDO/H 2 O ratio) and accurate in situ HDO/H 2 O measurements from an aircraft sensor during the NASA Ob-seRvations of Aerosols above Clouds and their intEractionS (ORACLES) field mission. In this paper, we denote the volume mixing ratios q D for HDO and q H for H 2 O. By standard convention, we report the isotopic abundance as δD (per mil or ‰) = (q D q H ) obs (q D /q H ) std − 1 × 1000, where (q D /q H ) std = 3.11 × 10 −4 , based on the HDO/H 2 O standard ratio for Vienna Standard Mean Ocean Water (SMOW).

AIRS instrument description
The Atmospheric InfraRed Sounder (AIRS) on the NASA Aqua satellite is a nadir-viewing, scanning thermal infrared grating spectrometer that covers the 3.7 to 15.4 µm spectral range with 2378 spectral channels (Pagano et al., 2003. Launched on 4 May 2002, Aqua is in a sun-synchronous orbit at 705 km, with an approximately 13:30 UTC Equator crossing time, as part of the A-Train satellite constellation. AIRS continues to make daily measurements of most of the globe with its wide cross-scanning swath of coverage. For HDO retrievals, the single-footprint AIRS Level 1B (L1B) radiances are utilized. These footprint observations have a horizontal resolution of approximately 13.5 km at nadir. Absolute radiometric accuracy between 220 and 320 K at all observation angles is better than 0.2 K (Pagano et al., 2003(Pagano et al., , 2008. The algorithm applied to AIRS radiances to yield HDO is described below in Sect. 3.1.

WISPER system for aircraft measurements
Aircraft measurements were made on the NASA P-3B Orion aircraft during the NASA ORACLES field mission. ORA-CLES is a 5-year Earth Venture Suborbital (EVS-2) investigation with three Intensive Observation Periods (IOPs) designed to study key processes that determine the climate impacts of African biomass burning aerosols in 2016, 2017 and 2018. The ORACLES experiment provided multiyear airborne observations from the NASA P-3B Orion and ER-2 aircraft over the complete vertical column of the key parameters that drive aerosol-cloud interactions in the southeastern Atlantic Ocean region. The focus of the ORACLES field measurements was a biomass burning plume that advected west from the African continent to the Atlantic Ocean at 2 to 5 km altitude above sea level (a.s.l.). Here we use data from the ORACLES 2016 IOP (ORACLES Science Team, 2017), and report on aircraft versus satellite comparisons from eight flights ( Fig. 1 Henze et al., 2020;Henze and Noone, 2017), which uses a modified commercial Picarro L2120-i δD/δ 18 O Ultra-High-Precision Isotopic Water Analyzer. The measurement technique is cavity ring-down (CRD) spectroscopy (O'Keefe and Deacon, 1988;Berden et al., 2000;Gupta et al., 2009). The majority of measurements analyzed in this paper are located within the biomass burning plume, characterized by elevated H 2 O (approximately 6000 ppmv) and elevated δD (−100 ‰ to −70 ‰). At these abundances of HDO/H 2 O, the 1 Hz precision (1σ ) of the measurements of δD is ±3 ‰ and the accuracy is ±6.5 ‰.   Table 1. The map is the NASA new blue marble, a true-color Earth image from Stockli et al. (2011), ©NASA. Superimposed on the map are the September 2016 monthly mean 700 hPa winds (white vectors) and surface pressure (white isobars), along with the approximate biomass burning region (green rectangle).

Retrieval algorithm
The single-footprint AIRS HDO profile data used in this work were produced using the retrieval algorithm, named the MUlti-SpEctra, MUlti-SpEcies, MUlti-Sensors (MUSES) algorithm (D. Fu et al., , 2016Fu et al., , 2018Fu et al., , 2019Worden et al., 2019). The MUSES algorithm can use radiances from multiple instruments, including AIRS and other instruments (CrIS, TES, OMI, OMPS, TROPOMI, and MLS), to quantify geophysical observables that affect the corresponding radiance. The AIRS single-footprint HDO profile retrievals have been described by Worden et al. (2019), and have heritage from the TES algorithm (Worden et al., 2004(Worden et al., , 2011(Worden et al., , 2012Bowman et al., 2006Bowman et al., , 2002. The Optimal Spectral Sampling (OSS) fast radiative transfer model (Moncet et al., 2008(Moncet et al., , 2015 for single-footprint AIRS measurements has been integrated into the MUSES algorithm, in support of the operational data production towards the multi-decadal record of global HDO profiles. The Supplement discusses the sensitivity of the retrievals to the choice of the forward model. The retrieval uses the optimal estimation (OE) method to quantify atmospheric HDO and H 2 O (Worden et al., , 2012(Worden et al., , 2019. For both AIRS and TES retrievals, height discrimination of the HDO/H 2 O ratio in the troposphere is provided by spectral resolution of pressurebroadened and the temperature-broadened absorption features of their corresponding lines (Beer et al., 2002). The algorithms and spectral microwindows are described by Worden et al. (2019). Chemical species CH 4 , CO, HDO, and H 2 O are jointly retrieved along with atmospheric temperature, surface temperature, land emissivity and clouds (Worden et al., 2012). The retrieval optimizes the ratio of HDO to H 2 O, as opposed to either HDO or H 2 O alone (Worden et al., 2019(Worden et al., , 2012. AIRS radiances at wavelengths from 8 to 12 µm are used here, excluding the 9.6 µm ozone band. The parent molecule H 2 O is retrieved at both 8 and 12 µm, but HDO is retrieved primarily from strong absorption lines in the 8 µm region (particularly in the wavenumber range 1210 to 1270 cm −1 ). Cloud optical depth and cloud top pressure are jointly retrieved with the chemical species, using the approach described in . The cloud-clearing approach (Susskind et al., 2006), utilized in AIRS operational products up to and including AIRS version 6, where retrievals are reported on the 45 km Advanced Microwave Sounding Unit (AMSU) footprint, is not utilized here. As described by Worden et al. (2019), retrievals are performed on single AIRS 13.5 km footprints in order to preserve the Level 1B radiance noise characteristics DeSouza-Machado et al., 2018).
For H 2 O, the a priori constraint vectors come from NASA's Goddard Earth Observing System (GEOS) data assimilation system version 5.12.4 processing stream (Rienecker et al., 2008). These are produced by the Global Modeling and Assimilation Office (GMAO) at the NASA Goddard Space Flight Center (GSFC). The GMAO GEOS-5.12.4 water mixing ratios are linearly interpolated to the latitudes, longitudes and log(pressure) levels of the satellite retrievals to generate the a priori profiles.
For all HDO retrievals, the initial profile of the HDO/H 16 2 O isotopic ratio is set equal to a simulated tropical profile . In the AIRS HDO product files, a priori HDO is defined as the product of the local a priori H 2 O profile (GMAO GEOS-5.12.4) and one tropical a priori profile of the HDO/H 2 O isotopic ratio . The initial guess profiles for H 2 O are set equal to the a priori.

Method of comparison
The AIRS HDO/H 2 O retrievals are matched up in space and time with the aircraft in situ HDO/H 2 O measurements. A critical aspect of validating satellite retrievals is obtaining data that span the altitudes where the satellite has sensitivity to HDO/H 2 O. AIRS data are sensitive to the HDO/H 2 O ratio in the atmosphere from the surface up to approximately 10 000 m altitude. The aircraft samples HDO and H 2 O from the surface up to 6000 m altitude, spanning most of the altitudes where the AIRS data are sensitive and therefore allows us to validate AIRS HDO/H 2 O with in situ measurements.
For direct comparison of AIRS HDO/H 2 O with in situ HDO/H 2 O, the AIRS instrument operator (averaging kernel and a priori constraint) is applied to the in situ data (see Eq. 1 below), as described by Rodgers (2000). This has the effect of smoothing the in situ data to the same resolution as the satellite retrievals. The averaging kernel matrix A is the sensitivity of the AIRS estimate to the true concentration in the atmosphere (Rodgers, 2000). The in situ profile with applied averaging kernel x insituw/AK is calculated jointly for HDO and H 2 O using the AIRS operator: (1) Joint HDO/H 2 O retrievals are performed on the logarithm of the volume mixing ratios, x D = ln(q D ) and x H = ln(q H ) (Worden et al., 2012. The data structure for AIRS HDO files is similar to TES HDO, with details provided by Herman et al. (2014). For comparison with AIRS, the in situ HDO and H 2 O profiles are extended to cover the full range of AIRS levels. In the boundary layer, from the surface up to the lowest-altitude aircraft data, we assume constant values of HDO and H 2 O set equal to the first aircraft measurement. In the range of aircraft data (up to 6000 m flight ceiling), the aircraft in situ HDO and H 2 O data are interpolated to the levels of the AIRS forward model, smoothing fine-scale features. In the layers above the aircraft maximum altitude, the profile is extrapolated using a scaled a priori profile. In this paper, all comparisons have been completed by applying Eq. (1).

Validation
Validating the accuracy of AIRS HDO and H 2 O retrievals is important for studies of the hydrologic cycle, exchange processes in the troposphere and climate change. Comparisons of AIRS and TES over 5 years (2006)(2007)(2008)(2009)(2010) indicate that the retrieval characteristics of the AIRS HDO/H 2 O measurements have similar vertical resolution and uncertainty in the middle troposphere but slightly less sensitivity in the lower troposphere (Worden et al., 2019). Worden et al. (2019) reported that the calculated uncertainty of AIRS HDO/H 2 O is ∼ 30 ‰ for a tropospheric average between 750 and 350 hPa, with a mean bias between TES and AIRS (TES minus AIRS) for the HDO/H 2 O ratio of ∼ −2.6 ‰ and a latitudinal variation of ∼ 7.6 ‰.

Comparison of AIRS with aircraft measurements
ORACLES 31/08/2016 to 25/9/2016 data comparison In this section, we describe comparisons between AIRS and ORACLES aircraft HDO measurements. First, time segments of each aircraft flight are identified where the aircraft profiled from the boundary layer up to approximately 6000 m altitude. To minimize the impact of atmospheric spatial and temporal variability, same-day AIRS measurements are selected for the same latitude-longitude rectangle as each aircraft profile (Fig. 2). These matched pairs are compared by the method described in Sect. 3.2. The loose constraint (Table 1, column 2; Fig. 2, open circles; and Fig. 4a) is that, for an aircraft vertical profile (∼ 100 to 300 km in length), all AIRS geolocations within the same rectangle of maximum to minimum latitude and maximum to minimum longitude are selected. The only exceptions were the aircraft flights of 2 and 14 September 2016, which had different flight patterns and used smaller shapes to constrain AIRS geolocations. The tighter constraint (Table 1,  The standard data retrieval quality flags for the retrieval are used in this analysis, which are based on the Aura TES data retrieval quality flags (Herman and Kulawik, 2018). For closer spatial coincidence, we also selected AIRS-aircraft measurement pairs within 0.3 • (Fig. 2). Following  and Brown et al. (2008), we filter data for a reasonable threshold of standard nadir data product degrees of freedom for signal (DOFS) > 1.1 but include all values of average cloud effective optical depth. The data product DOFS is the trace of the averaging kernel, and is a measure of the number of independent parameters for the retrieved HDO/H 2 O profile. Average cloud effective optical depth is the retrieved cloud mean optical depth at wavenumbers from 975 to 1200 cm −1 from the final retrieval step (i.e., the same for all species) . Figure 3a shows a representative 31 August 2016 comparison between aircraft water vapor δD from WISPER and the coincident AIRS retrieval. Figure 3b shows the corresponding averaging kernels.

AIRS bias correction
TES HDO/H 2 O ratios are biased compared to model and in situ measurements (Worden et al., , 2011. We assess whether AIRS HDO has a bias relative to in situ mea- surements. As described above, AIRS and TES show a small bias for the HDO/H 2 O ratio of ∼ −2.3 ‰ (Worden et al., 2019) after a bias correction is applied, so it is reasonable to see how well in situ and AIRS data agree if the TES bias correction is applied to the AIRS HDO. Herman et al. (2014) estimated the TES bias δ bias by minimizing the difference between bias-corrected TES and in situ δD with TES operator applied: We apply the TES δ bias to the AIRS data to evaluate against ORACLES aircraft data. There are 446 matched profiles of AIRS and ORACLES within the same latitude-longitude boxes and 110 closely matched profiles within 0.3 • or approximately 30 km (Fig. 2). Comparisons with an averaging kernel applied are shown in Fig. 4 and Table 2. Over the range of aircraft data, 0 to 6 km altitude, AIRS δD has a mean bias of −6.7 ‰ relative to the aircraft profiles, well within the estimated measurement uncertainty of both AIRS and the WISPER calibration. This is consistent with TES δD (Worden et al., 2019;Herman et al., 2014). AIRS lowertroposphere δD bias is −6.6 ‰ and rms 20.9 ‰ (surface to 800 hPa). In the mid-troposphere, 800 to 500 hPa, AIRS δD bias is −6.8 ‰ and rms 44.9 ‰.

Error estimation
In this section we characterize the a posteriori error budget for AIRS HDO/H 2 O and assess this error by comparison with the ORACLES aircraft measurements. Error analysis in OE has been described in detail in the literature (Worden et al., 2004Bowman et al., 2006;Rodgers, 2000). The errorx in the estimate of HDO/H 2 O is defined as the true state x minus the linear estimatex retrieved by AIRS (e.g., Worden et al., 2006, Eq. 15): Similar to Herman et al. (2014), we define the estimated error of the AIRS isotopic ratio HDO/H 2 O, (Eq. 4) as the observation error covariance : where is the gain matrix of the HDO/H 2 O retrieval, S n is the measurement error covariance, and S i b is the error covariance due to systematic errors and Table 2. Summary of satellite-aircraft comparisons for 110 matched pairs in 2016 (Fig. 2, closed circles). Bias and rms (standard deviation) of AIRS δD relative to ORACLE aircraft, with averaging kernel applied ("BiasAK", "rmsAK"), and for AIRS relative to mapped ORACLES aircraft, with no averaging kernel ("Bias", "rms"). The reported rms here is the standard deviation, not including the bias.  interference errors. Interference errors are due to CH 4 , N 2 O, surface emissivity, effects of temperature and clouds. The estimated error is given by the square roots of the diagonal elements of S, the best estimate of the AIRS observation error covariance for the HDO/H 2 O retrieval. The estimated error (Eq. 4) is compared to the empirical error calculated from the AIRS-aircraft comparisons. It is seen that the error varies from ∼ 20 ‰ to ∼ 40 ‰ (Fig. 5). The empirical error (AIRS versus aircraft rms) is similar in magnitude to the estimated error but exceeds the estimated Figure 5. Plot of AIRS error analysis for coincident AIRS and OR-ACLES δD on 31 August 2016, which shows that the empirical error is comparable to the AIRS-estimated error. The empirical error is obtained from the statistics of the satellite-aircraft comparison, while the estimated error is obtained from optimal estimation retrieval theory. Plotted here are the AIRS δD-estimated error, also known as AIRS observation error (dashed red line), and the AIRS δD empirical error (black line). error at 500 to 600 hPa in the free troposphere. These differences between the OE-estimated error and the empirical error are likely due to uncertainties in atmospheric variability in space and time and in the collocation between satellite retrieval and aircraft measurements. The instrument operator (Eq. 1) accounts for error due to the mismatch in "vertical" sensitivity between the satellite retrieval and aircraft in situ vertical profiling. In the cases where AIRS is compared to in situ measurements without the instrument operator, there is an additional smoothing error ( Table 2). The instrument operator does not account for error due to "horizontal" mismatch. The close coincidences are all within 30 km (0.3 • ), but given the time differences, AIRS 15 km nadir footprint and limited in situ measurement, the satellite and aircraft are not necessarily measuring the same air mass. There is a collocation error on the order of ∼ 10 ‰ due to horizontal collocation and representativeness uncertainty.

Conclusions
HDO/H 2 O estimates from AIRS single-footprint radiances been compared to coincident in situ airborne measurements on the P-3B Orion aircraft by the Oregon State Water WIS-PER system over the southeastern Atlantic Ocean. On 8 d between 31 August and 25 September 2016, there are collocated measurements between AIRS and the P-3B aircraft. We have shown that AIRS-only retrievals have sensitivity to HDO from the middle troposphere to the lower troposphere. We demonstrate that AIRS δD has a mean bias of −6.7 ‰ relative to aircraft, well within the estimated measurement uncertainty. In the lower troposphere, 1000 to 800 hPa, AIRS δD bias is −6.6 ‰ and the rms 20.9 ‰, consistent with the calculated uncertainty of 19.1 ‰. In the mid-troposphere, 800 to 500 hPa, AIRS δD bias is −6.8 ‰ and rms 44.9 ‰, comparable to the calculated uncertainty of 25.8 ‰. The errors are sufficiently small that the AIRS HDO/H 2 O ratio retrievals are useful for scientific analysis. This long-term global data record has considerable potential utility.
Code and data availability. The AIRS HDO data used in this analysis are publicly available from the following link: https://avdc.gsfc.nasa.gov/pub/data/satellite/Aura/TES/.AIRS/ (Worden et al., 2019, last access: 27 March 2020. The OR-ACLES aircraft data used in the data analysis can be freely downloaded from the following Digital Object Identifier: (https://doi.org/10.5067/Suborbital/ORACLES/P3/2016_V1 OR-ACLES Science Team, 2017, last access: 22 April 2017). Files in Interactive Data Language (IDL) format of the AIRS data shown and the forward model output are available from coauthor John Worden upon request: john.r.worden@jpl.nasa.gov.
Author contributions. RLH carried out all steps of aircraft validation, from matching data and quality filtering to applying observation operator and statistics, while JW provided satellite-to-satellite validation. JW developed the retrieval strategies for both AIRS and TES HDO/H 2 O retrievals. DF and SSK built the strategies of single AIRS footprint HDO/H 2 O retrievals into the MUSES algorithm. KCP, RLH and VHP evaluated the sensitivities of retrievals to the choice of forward model. RLH, VHP, JW, SSK, DF, DN, DH and KB contributed to the text and interpretation of the results. JW and SSK helped in the estimation of HDO/H 2 O measurement uncertainty, quality flagging and knowledge of the retrieval process. DN and DH provided ORACLES data, aircraft measurement uncertainty, and identified profiles in the aircraft data. All authors participated in writing the manuscript.
Competing interests. The authors declare that they have no conflict of interest.
Special issue statement. This article is part of the special issue "New observations and related modelling studies of the aerosolcloud-climate system in the Southeast Atlantic and southern Africa regions (ACP/AMT inter-journal SI)". It is not associated with a conference.