A simulation-experiment-based assessment of retrievals of above-cloud temperature and water vapor using a hyperspectral infrared sounder

Abstract. Measuring atmospheric conditions above convective storms using spaceborne instruments is challenging. The operational retrieval framework of current hyperspectral infrared sounders adopts a cloud-clearing scheme that is unreliable in overcast conditions. To overcome this issue, previous studies have developed an optimal estimation method that retrieves the temperature and humidity above high thick clouds by assuming a slab of cloud. In this study, we find that variations in the effective radius and density of cloud ice near the tops of convective clouds lead to non-negligible spectral uncertainties in simulated infrared radiance spectra. These uncertainties cannot be fully eliminated by the slab-cloud assumption. To address this problem, a synergistic retrieval method is developed here. This method retrieves temperature, water vapor, and cloud properties simultaneously by incorporating observations from active sensors in synergy with infrared radiance spectra. A simulation experiment is conducted to evaluate the performance of different retrieval strategies using synthetic radiance data from the Atmospheric Infrared Sounder (AIRS) and cloud data from CloudSat/CALIPSO. In this experiment, we simulate infrared radiance spectra from convective storms through a combination of a numerical weather prediction model and a radiative transfer model. The simulation experiment shows that the synergistic method is advantageous, as it shows high retrieval sensitivity to the temperature and ice water content near the cloud top. The synergistic method more than halves the root-mean-square errors in temperature and column integrated water vapor compared to prior knowledge based on the climatology. It can also improve the quantification of the ice water content and effective radius compared to prior knowledge based on retrievals from active sensors. Our results suggest that existing infrared hyperspectral sounders can detect the spatial distributions of temperature and humidity anomalies above convective storms.


L1B observations to construct an example. A retrieval method that incorporates such collocated cloud products is referred to as a synergistic method.
In this paper, we first quantify the uncertainty in infrared radiance spectra induced by cloud optical properties. The per-95 formance of retrieval strategies following the slab-cloud and synergistic methods is then evaluated following a simulation experiment, emulating an implementation based on the AIRS L1B and DARDAR-Cloud products. This simulation experiment simulates observational signals from realistic temperature, humidity, and cloud fields above a deep convective event simulated by an NWP model. Section 2 describes the main components of this simulation experiment. We then implement different retrieval strategies, as formulated in Section 2.3, to retrieve from synthetic observations. The results are evaluated in Section 100 3 by comparing retrievals to the prescribed truth. The application of the improved synergistic retrieval scheme to existing instruments is discussed in Section 4. 141°E, 16°N. All simulations use 67 vertical levels, with vertical grid-spacing ∆z ∼ 250 m in the UTLS region and a model top at 13.5 hPa (29.1 km). The simulation is initialized with conditions from the ECCC global atmospheric analysis at 00:00 UTC 16 May 2015. It runs for 24 hours until 00:00 UTC on 17 May 2015. The model spin-up time of 6 hours is used to assure 125 the correct formation of clouds. Model outputs at 1 km horizontal grid-spacing are saved every 10 minutes. The subdomains of the 1 km simulation near the cyclone are used in the simulation experiment.
For the two high-resolution simulations with 2.5-km and 1-km horizontal grid-spacing, the double-moment version of the bulk cloud microphysics scheme of Milbrandt and Yau (2010a, b; hereinafter referred to as MY2) is used. This scheme predicts the mass mixing ratio for each of six hydrometeors including non-precipitating liquid droplets, ice crystals, rain, snow, graupel, 130 and hail. Condensation (ice nucleation) is formed only upon reaching grid-scale supersaturation with respect to liquid (ice).
In addition to the MY2 scheme, the planetary boundary-layer scheme (Bélair et al., 2005) and the shallow convection scheme (Bélair et al., 2005) can also produce cumulus, stratocumulus, and other low-level clouds, which are of less relevance to our UTLS-centric simulation experiment.
A snapshot from the 1-km resolution GEM simulation, 410 minutes after the initial time step, is used for the radiance 135 simulation because a mature storm at this time has generated abundant convective clouds, which our retrieval approach targets. Figure 1 shows the atmospheric conditions at this time step, including the distributions of temperature and water vapor at 81 hPa, at which level the variance is largest. To mimic the satellite infrared image, we show the distribution of the brightness temperature in a window channel at 1231 cm −1 (8.1 µm, BT 1231 ). A cold BT 1231 suggests a deep convective cloud (DCC) that extends to the tropopause level. Overshooting DCCs are often identified from satellite infrared images based on a warmer BT in 140 a water vapor channel (BT 1419 cm −1 ) relative to BT 1231 , which can be attributed to water vapor emission above the cold point (Aumann and Ruzmaikin, 2013). The BT-based criterion is used to select retrieval samples, mimicking the scenario of using satellite infrared radiance measurements alone to identify overshooting DCCs, as performed in Feng and Huang (2018). Using the BT-based criterion, 9941 retrieval samples are identified, with their locations marked in Fig. 1. These samples are confirmed to be continuous, precipitating clouds that fully cover vertical ranges from near-ground to 380 K potential temperature. Among 145 these samples, 100 profiles are randomly selected to construct a test set. The size of the samples is verified to meet the convergence requirement of the statistical evaluation conducted in Section 3. The rest of the simulated profiles, regardless of cloud conditions, numbering O(10 6 ), are used to construct an a priori dataset to define the prior knowledge used in the retrieval in Section 2.3.

Radiative transfer model 150
This study uses the MODerate spectral resolution TRANsmittance, version 6.0 (MODTRAN 6.0) (Berk et al., 2014) to simulate infrared radiance spectra observed by satellite. MODTRAN 6.0 provides a line-by-line (LBL) algorithm that performs monochromatic calculations at the center of 0.001 cm −1 sub-bins. Within each 0.2 cm −1 spectral region, this method explicitly sums contributions from line centers while precomputing contributions from line tails. This algorithm has been validated against a benchmark radiation model, LBLRTM, showing less than 0.005 differences in atmospheric transmittance through 155 most of the spectrum (Berk and Hawes, 2017). MODTRAN 6.0 accounts for both absorptive and scattering media in the atmo- from 110 to 70 hPa. Solid color-coded dots mark the overshooting deep convective clouds sampled via BT-based criterion from which the test set is sampled to conduct the retrievals. Partially transparent colors show the rest of the simulated fields. The variable fields are taken at sphere by implementing a spherical refractive geometry package and the DISORT discrete ordinate model to solve the radiative transfer equation (Berk and Hawes, 2017).
In this study, we use MODTRAN 6.0 to simulate the all-sky radiances with user-defined atmospheric profiles. 80 fixed atmospheric pressure levels are used. Temperature, water vapor, and ice cloud (IWC) profiles from GEM simulations at 67 160 layers are input into the model. Above the GEM model top (13.5 hPa), the values from a standard tropical profile (McClatchey, 1972) are placed between 13.5 and 0.1 hPa. Other trace gases are fixed at a tropical mean value.
User-defined cloud extinction coefficients, single scatter albedo, and asymmetry factor (defined per unit mass of cloud ice) are added to the model, based on the cloud optical library of Yang et al. (2013). This cloud optical library provides a look-up table for the scattering, absorption, and polarization properties of ice particles of different habit shapes, roughness, whether the mass density of cloud ice and optical properties leave significant impacts on infrared radiance spectra. We also 190 evaluate uncertainties of the forward model in simulating infrared radiance spectra with simplified cloud inputs.
The cloud-induced uncertainties in infrared radiance spectra are evaluated with regard to three factors: 1) variation in IWC, 2) variation in cloud optical properties caused by column to column (horizontal) variation in effective radius, and 3) variation in cloud optical properties caused by variation in crystal habit mixture and layer-to-layer (vertical) variation in effective radius.
Uncertainties due to particle size distribution are not evaluated because of the lack of observation in its variability and its 195 smaller impact compared to the other cloud variables considered here. The surface roughness of ice particles is neglected because it mainly affects the scattering angle (Yang et al., 2013), which plays a minor role in the infrared channels. To gain knowledge of cloud ice particles and their impacts on the infrared radiance spectrum and also to prescribe relevant information in the UTLS retrieval (see Section 2.3), we use the DARDAR-Cloud product to form a dataset of observations close to tropical cyclones, due to their relevance to the simulation experiment. The moment when A-Train satellites pass over tropical cyclones 200 is identified by the CloudSat 2D-TC product (Tourville et al., 2015) for the year 2006 to 2016. Only overpasses in the western part of the Pacific are used. From these overpasses, we select DARDAR footprints that are within 1000 km of the cyclone center locations. Based on the CloudSat-CLDCLASS product, 98293 of these footprints contain OT-DCCs that penetrate beyond 16 km in altitude. Each profile consists of IWC (IW C) and effective radius (Re) at a vertical resolution of 60 m.
Using the identified OT-DCC profiles from DARDAR-Cloud, we calculate the probability distribution function (PDF) of 205 effective radii of ice particles at the topmost cloud layer. Figure 2 (a) shows that the ice particles are typically small, with an average effective radius of 21.5 µm and the 1st and 99th percentiles of 13.3 and 39.7 µm respectively. Using the same OT-DCC profiles, the mean and standard deviation (STD) of IWC profiles are shown in Fig.2  For tropical deep convective clouds, Baum et al. (2011) developed a habit mixture model as a function of ice particle sizes.

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Using this model, ice cloud optical properties are generated following the description in Section 2.2. A radiance spectrum calculated using this model is denoted with the subscript mix . Based on the habit mixture model, over 80% of small ice particles in tropical deep convection are solid columns. Therefore, we also generate radiance from ice cloud optical properties using solid columns alone, which are denoted with the subscript sc . 100 profiles are selected from OT-DCC samples. For each sample, we calculate the upwelling infrared radiance, R mix (Re, IW C), 215 using the IWC profile (IW C), effective radius profile (Re), and the habit mixture model developed by Baum et al. (2011). The mean temperature (t 0 ) and water vapor (q 0 ) profiles of the NWP simulation domain (Fig. 1) are used in the radiative transfer calculations.
Considering that the infrared radiance spectra may not be sensitive to vertical variations in cloud optical properties, we assume constant optical properties in all vertical layers of an atmospheric column and crystal habit of solid columns, to simplify 220 the input cloud variables to MODTRAN. Following this assumption, we calculate R sc (Re opt , IW C) using solid column alone and one effective radius value, Re opt , for all vertical layers of an individual profile. This Re opt is solved iteratively and it minimizes the brightness temperature difference between R mix (Re, IW C) and R sc (Re opt , IW C). The PDF of Re opt is shown by red in Fig. 2 (a), with an average of 34 µm (Re 0 ) and a STD of 11 µm. In practice, one may estimate the Re opt from the effective radius of a cloud layer where the optical depth measured from the cloud top reaches unity, with a root-meansquare-error (RMSE) of 1.6 µm (∼ 5%). RMSE spectra in R sc (Re opt , IW C) relative to R mix (Re, IW C) is shown by the red solid curve in Fig.3 (a). The magnitude of the RMSE spectrum in the mid-infrared is around 0.1 K, confirming that the midinfrared spectra are not sensitive to layer-to-layer variations in effective radius or mixtures of crystal habits differing from the solid column. Using constant cloud optical properties for the entire column of a tropical deep convective cloud can reasonably represent the mid-infrared emission spectra of the cloud. At wavenumbers higher than 1800 cm −1 , however, neglecting such 230 variations in effective radius and crystal habits induces significant RMSE, as shown in Fig. 3 (a). The RMSE spectrum is also computed adopting an AIRS-like spectral response function, denoted as ε synergistic , to represent the forward model uncertainty in the synergistic retrieval method introduced in Section 2.3.
In the following contents of this paper, Re opt determined for each profile as described above is used to represent the vertically constant effective radius value for characterizing cloud optical properties of a cloud column. It is also used to evaluate the 235 spectral differences caused by IWC and column-to-column variations in cloud optical properties. We calculate infrared radiance spectra with mean effective radius (Re 0 , 34 µm) or IWC profile (IW C 0 ), denoted as R sc (Re 0 , IW C) and R sc (Re opt , IW C 0 ), respectively. Then, perturbations of infrared spectra caused by variations in effective radius (Re opt ) are evaluated by the mean (blue curve) and the STD (grey shaded area) of the equivalent brightness temperature of R sc (Re opt , IW C 0 ), as shown in Fig.   3 (b). Using a mean effective radius leads to a RMSE spectrum in R sc (Re 0 , IW C) relative to R sc (Re opt , IW C), which is 240 shown by a red curve in Fig. 3 (b). Similar results are shown in Fig. 3 (c) for IWC. In Fig.3 (b,c), the mean spectrum of OT-DCCs shows cold and relatively uniform brightness temperatures in the window and weak absorption channels that largely correspond to the emission from the cloud top. While variations in effective radii (Re opt ) and IWC have a weak effect on the strong absorption channels, they greatly impact the cloud emission, thus leading to large radiance variations in the window and weak absorption channels. As a result, the two RMSE spectra are similar. The 245 RMSE due to column-to-column variations in effective radius (Re opt ) is around 1 K and the RMSE due to a varying IWC profile is around 3 K.
The RMSE spectra are further normalized with respect to the spectral mean, as shown in Fig.3 (d), to examine whether spectral signatures of effective radius and IWC are distinguishable from each other. Despite the overall similarity, effective radius affects the spectrally dependent extinction coefficients, leading to a tilted pattern across the infrared spectra, while 250 the RMSE due to IWC is relatively uniform across the infrared window. Therefore, it is possible to distinguish the radiative signals of effective radius from those of IWC with a mid-infrared coverage characteristic of existing instruments. Interestingly, differences in the two normalized RMSE spectra are more prominent at lower wavenumbers (∼ 200 cm −1 ), suggesting that far-infrared channels, e.g., from future instruments, such as FORUM (Palchetti et al., 2020) and TICFIRE (Blanchet et al., 2011), may be advantageous for the UTLS retrieval, which is beyond the scope of this simulation experiment but warrants 255 future investigation.
For a comparison, we follow Feng and Huang (2018) to obtain the infrared spectra using the slab-cloud method. For each R mix (Re, IW C), we calculate the brightness temperature of a window channel at 1231 cm −1 . The idea of slab-cloud method used by Feng and Huang (2018) is to minimize the infrared radiance residual at this window channel by placing a slab of cloud at the vertical layer where the atmospheric temperature differs the least from BT 1231 . This 500-m thick slab-cloud has uniform 260 IWC of 1.5 g/m 3 and an effective radius of 34 µm. The temperature of this vertical layer is adjusted to BT 1231 . With this prescribed cloud layer, radiance spectra are calculated again for each profile, denoted as R sc (Re 0 , slab). The BT 1231 values of R mix (Re, IW C) and R sc (Re 0 , slab) are identical. Consequently, differences between R mix (Re, IW C) and R sc (Re 0 , slab) in other channels highlight the radiance uncertainty due to the slab-cloud assumption. The RMSE in R sc (Re 0 , slab) relative to R mix (Re, IW C) are shown by the red dashed curve in Fig. 3 (a).  Fig. 3 (a) reveals that the slab-cloud assumption cannot fully account for spectral variations of cloud emission. The assumption leads to a spectrally tilted mean radiance bias as shown by the red curve in Fig. 3 (a). We note that this tilted pattern is related to the spectrally dependent extinction coefficients, which is affected by effective radius (variation in Re opt ), so that radiances at different wavenumbers are contributed by cloud emission at varying heights, which is in turn affected by the vertical distribution of ice mass. Therefore, the clear-cut cloud boundary in the slab-cloud and a constant effective radius (Re opt ) 270 collectively contribute to the radiance bias shown by a dashed blue curve in Fig. 3 (a). The RMSE of R sc (Re 0 , slab) shows a minimum of around 0.2 K in the mid-infrared window and a maximum over 4 K at the high wavenumbers (over 2000 cm −1 ).
This RMSE spectrum is also calculated adopting an AIRS-like spectral response function to represent the radiance uncertainty induced by the slab-cloud assumption in the retrieval described in Section 2.3 and is denoted as ε slab .

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The cloud-assisted retrieval proposed by Feng and Huang (2018) is an optimal estimation method (Rodgers, 2000) that retrieves atmospheric states above clouds using infrared spectral radiance. Similar to Eq.1 in Feng and Huang (2018), we express the relation between the observation vector, y, and the state vector, x, as follows: Following a similar definition to Feng and Huang (2018), the state vector includes temperature x t and the logarithm of specific humidity, x q , in 67 model layers.
x 0 refers to the first guess of the state vector, which is the mean of the a priori. y contains the infrared radiance observations, y rad . F is the forward model that relates x to y. Here, the forward model is the radiative transfer model, MODTRAN 6.0, configured with the spectral response function of the AIRS instrument. The forward model can be linearly approximated by the Jacobian matrix K, which is iteratively computed at every time step. ε is the measurement

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Following the optimal estimation method (Rodgers, 2000, Eq.5.16), an estimate of x,x, is expressed as: where S a and S ε are the covariance matrix of the state vector as given by the a priori dataset and that of the error in the observation vector, respectively. S ε is set to be a diagonal matrix because the observation errors in different channels are 295 considered to be uncorrelated.
x can then be iteratively solved through: where the subscript i refers to the ith iteration step.
The equations described above are adopted from Feng and Huang (2018), where the state vector x includes temperature and 300 the logarithm of specific humidity. For comparison, we adopt the slab-cloud retrieval scheme of Feng and Huang (2018) as described above and refer to the result as the slab-cloud retrieval in the following. The only difference from Feng and Huang (2018) is in the S ε . While S ε in Feng and Huang (2018) is the square of radiometric noise of AIRS instrument, S ε in this study for slab-cloud retrieval contains the sum of the square of radiometric noise and the square of ε slab , as schematically depicted by the red dashed curve in Fig. 3(a), to account for radiance uncertainties induced by slab-cloud assumption. Because ε slab is 305 relatively small, especially at absorption channels, we find that adding off-diagonal correlations to S ε does not improve the retrieval quality significantly. Therefore, S ε keeps its diagonal form.
We further examine whether the addition of ε slab masks spectral signals from atmospheric variations. Figure 1 depicts that strong cooling and hydration appears above overshooting DCCs near the cyclone center (141°E, 16°N). We denote the mean profiles of this region as t cold and q mois for temperature and water vapor, respectively, which are shown in Fig.4 310 (b,d) blue curves. A set of radiative transfer calculations is conducted to obtain R sc (Re 0 , t 0 , q 0 ), R sc (Re 0 , t cold , q mois ) and R sc (Re 0 , t cold , q 0 ) at 0.1 cm −1 spectral resolution, using an effective radius of 34 µm and a randomly selected IWC profile (cloud top at 100 hPa) of this region. The spectral signals of temperature and water vapor are then obtained from R sc (Re 0 t 0 , q 0 ) − R sc (Re 0 , t cold , q 0 ) and R sc (Re 0 , t 0 , q 0 ) − R sc (Re 0 , t 0 , q mois ), respectively. The strength of signals under different spectral specifications was examined by Feng and Huang (2018) and is not repeated here. The spectral signals are 315 then compared to radiance uncertainties in Fig. 4. The spectral range used in the retrieval tests (between 649.6 and 1613.9 cm −1 ) are enveloped by grey dotted lines in Fig. 4. Figure 4 shows that the radiance uncertainty from the slab-cloud assumption, ε slab , does not completely obscure the signal of temperature or water vapor. In the CO 2 and water vapor channels, where the signal is the strongest, the TOA radiance spectra are not as sensitive to cloud emission due to strong atmospheric attenuation at these channels. ε slab becomes greater in 320 the wings of absorption channels, where the signals are already masked by the instrument NEdT of ∼ 0.5 K.

Synergistic method
The radiance uncertainty due to the slab-cloud assumption, ε slab , can be largely eliminated by incorporating collocated observations of cloud profiles, from active sensors (CloudSat-CALIPSO) along the same track as the hyperspectral infrared sounder (such as AIRS). Instead of simply prescribing the cloud profile from the active sensors in the forward model, motivated by Table 1. State vector and observation vector of four cases of retrieval strategies. Case 5 is a posterior estimation of the state vector from a combination of yatm, yiwc, yRe opt , and a priori. DFS is compared to the number of vertical layers of the state vector. The DFS is counted from 130 hPa to 13.5 hPa for temperature and water vapor (20 model layers).
x y DFS

Slab-cloud
Case 1 x t ,x q y rad t: 3.15, q: 0.69 Case 2 x t ,x q y rad , y atm Same as Case 1

Synergistic
Case 3 x t ,x q , x iwc ,x Re opt y rad , y iwc , y Re opt t: 3.6, q :0.74, IW C :1.94, Re opt : 0.65 Case 4 x t ,x q , x iwc ,x Re opt y rad ,y atm , y iwc , y Re opt same as Case 3 Case 5 x t ,x q , x iwc ,x Re opt y atm , y iwc , y Re opt \

Slab-cloud retrieval
Improving upon Feng and Huang (2018), Case 1 accounts for the radiance uncertainties due to the slab-cloud assumption, The results of Case 1 are shown as red solid curves in Figures 5 and 7. The major improvement in Case 1, compared to the prior (blue solid curves), is the temperature profile from 100 to 75 hPa. Although DFS for water vapor reaches 0.69, Case 1 does not provide much improvement from the first guess in water vapor.
Case 2 improves from Case 1 owing to the information carried by the additional atmospheric constraints, y atm . Case 2 is 425 represented by the red dotted curves in Figures 5 and 7. It approaches the true state better than Case 1, despite warm and dry biases in the first guess and y atm (See Fig. 5 (a,c)). Notably, it increases the retrieved water vapor concentration by around 1 ppmv on average and reduces the RMSE from 2.4 ppmv to 1.0 ppmv, as shown in Fig. 5 (c,d) and Table 3.2. For the CIWV, Case 2 reduces the RMSE by half when compared to Case 1.
To demonstrate how well the retrieved atmospheric field represents the spatial variability in the true state (Fig. 1), namely a 430 moister and colder UTLS region in the cyclone center compared to the south of the domain, the distributions of water vapor, temperature, and CIWV are presented in Fig. 6. It shows that the 'true' spatial patterns are well reproduced by the Case 2 retrieval.
Furthermore, individual profiles from two clusters of overshooting DCCs, which include the DCCs near the cyclone center and those in the south of the domain, are randomly selected to investigate how well the retrieval reproduces the spatial vari-435 ability in temperature and water vapor. The all-sky optical depths from TOA and IWC profiles for the two locations are shown in Fig. 7 (c,d). The retrievable signals mainly come from the atmospheric column above thick cloud layers, i.e., where optical depth is less than 2 (only 13.5% of the infrared emission is transmitted through this cloud layer). Figure 7 (a-c) shows results for a location close to the cyclone center. At this location, the slab-cloud method prescribes the cloud layer to be located at the cold-point due to the strong cloud emission. Atmospheric anomalies above 86 hPa have an 440 impact on TOA infrared radiances. Around 80 hPa, the truth profile that we aim to retrieve is around 8 K colder than the prior and nearly 3 ppmv moister. While the result from Case 1 overcomes the bias in temperature, it increases the water vapor over a broad vertical range which, as explained by Feng and Huang (2018), is due to the strong smoothing (smearing) effect of the averaging kernel in this case. In comparison, Case 2 correctly produces a peak moistening around 80 hPa, while keeping a retrieved temperature profile similar to Case 1. Figure 7 (d-f) shows the results in a location in the southern part of the domain, where the slab-cloud method prescribes the cloud layer at 95 hPa. At this location, the cloud emission from the top 1.5 km cloud layer affects infrared radiances strongly, which can be inferred from the optical depth ( Fig. 7 (f)), leading to a large radiance residual that cannot be addressed under the slab-cloud assumption. Therefore, Case 1 fails to improve upon the prior. Case 2 leads to a moister posterior compared to the prior owing to the addition of y atm . However, Case 2 fails to update the temperature profile above the cloud layer. Instead, 450 it approaches y atm in lower altitudes, leading to an unrealistic vertical oscillation in temperature near 100 hPa.

Synergistic method
Using the synergistic method, Case 3 becomes more sensitive to water vapor and temperature compared to Case 1, as indicated by the reduced RMSE in Table 3.2 and a closer match between the retrieved field and the true state in Fig. 6. It retrieves higher water vapor concentrations from 110 to 70 hPa in comparison with Case 1. Owing to the radiative emission from in-cloud  layers between 110 and 95 hPa, Cases 3 and 4 become sensitive to the temperature profile near the cloud top. Hence, Cases 3 and 4 reduce the RMSE compared to other cases.
The advantage of the synergistic method, especially when IWC near the cloud top is relatively small, is illustrated in Fig.   7 (d-f). At this location, the radiative signal from the moistening near the cloud top can be transmitted to the TOA. As a result, Case 3 approaches the true cloud-top temperature much better than Cases 1 and 2 ( Fig. 7 (a,d)). It also produces higher 460 water vapor compared to Case 1 (Fig. 7 (e)). Case 4 further benefits from y atm which constrains the profile in the vertical ranges below 110 hPa and above 80 hPa. Case 4 overcomes the warm bias around 90 hPa in y atm and the first guess. It also reproduces the oscillating temperature feature in Fig. 7 (d).
Owing to the sensitivity to IWC and Re opt as suggested by DFS and Fig .3, the synergistic method can improve upon the collocated cloud observations by reducing RMSE in IWC profile and in Re opt (Fig. 5 and Table 2). Although adding 465 the y atm does not significantly improve the retrieval performance in case 4, it stabilizes the iterative retrieval process by constraining uncertainties in temperature. The improvement from infrared spectra and the addition of y atm is desirable to reduce measurement uncertainties due to sampling differences between active sensors and the infrared instrument.
While the improvement in Cases 2 and 4 shows the advantage of including additional atmospheric products, y atm , one caveat is in the proper evaluation of the uncertainty range, which is included in the covariance matrix of the observation vector. This 470 is important as the uncertainty range in y atm constrains the posterior uncertainty range of the retrieval at each vertical level.
In this study, we account for the difficulties in evaluating S ε by increasing the RMSE in y atm , so that the square root of S ε of y atm is equivalent to a doubling of RMSE shown by the blue dotted line in Fig. 5 (b,d).
Although the additional measurement vector, y atm , itself does not contain the spatial variability pattern as seen in Fig. 6, the corresponding covariance in S ε properly accounts for its variability (uncertainty) by prescribing a large value around 80 hPa but 475 smaller values at other vertical locations. Therefore, it increases confidence in the posterior at levels where the thermodynamic variables are relatively constant. The increased confidence in turn enhances the degrees of freedom in the ranges around 80 hPa, where the warm and dry signals mainly come from. Therefore, even though y atm itself deviates from the true state, including y atm in optimal estimation can still improve the posterior estimation. In practice, uncertainty in atmospheric products can be estimated by inflating the precision of the product to account for sampling size differences through comparison with NWP 480 models and collocated observations.

Conclusion and Discussion
Sounding UTLS thermodynamic conditions has long been a challenge. A simulation experiment has been conducted to simulate hypothetical radiance observations of AIRS by integrating a NWP model and a radiative transfer model, MODTRAN 6.0. By conducting the simulation experiment, this study evaluates the capability of existing hyperspectral infrared sounders 485 in detecting temperature and humidity fields above convective storms. Our focus is to investigate and constrain the uncertainties induced by clouds. Two retrieval methods are tested, including a slab-cloud method that uses mainly the infrared radiance measurements (i.e., AIRS) and a synergistic method that combines cloud products from collocated active sensors (i.e., DARDAR-Cloud).
First, we find that a radiative transfer model can simulate the TOA mid-infrared radiance spectra above tropical deep convec-490 tive clouds fairly accurate (RMSE around 0.1 K, characterized by ε synergistic ) by assuming constant cloud optical properties (per unit mass) in all vertical layers of a cloud column. Uncertainties in the infrared radiance spectra mainly comes from variations in IWC profile and column-to-column variations in effective radius (Fig. 3). The uncertainties are largest in window channels and weak absorption channels because they are sensitive to cloud emission. The slab-cloud assumption locates a clear-cut cloud top that matches the brightness temperature of the window channel. This assumption alleviates, but does not 495 fully eliminate, the cloud effect on the radiance spectrum ( Fig. 3 (a)). The remaining radiance uncertainty is accounted for in the retrieval framework of this study and is found to not significantly obscure the temperature and humidity signals in the retrieval. Therefore, the cloud-assisted retrieval as proposed by Feng and Huang (2018) is affirmed to improve the sounding of UTLS temperature and water vapor compared to prior knowledge. However, this retrieval neglects information content from the in-cloud atmosphere. As a result, it may lead to biases in individual temperature profiles. For example, as shown in Fig. 7 500 (c), the slab-cloud retrieval fails to reproduce oscillating temperature anomalies, although it still detects anomalous moistening above convective storms. Although not explicitly discussed here, a similar OE framework adopting the slab-cloud assumption is expected to detect moistening anomalies when applied to other hyperspectral infrared sounders, e.g., IASI and CrIS, due to their similar spectral specifications to AIRS.
Second, we find that the synergistic method, especially after incorporating additional atmospheric constraint, y atm , is sensi-505 tive to temperature, water vapor, the IWC profile, and column-to-column variation in effective radius. It substantially reduces the RMSE in temperature from 7.1 to 2.7 K compared to the prior. It also reduces the RMSE in column integrated water vapor by half. This method can capture strong moistening features in individual profiles (as shown by Fig. 7 (b)) and detect oscillating temperature anomalies (as shown by Fig. 7 (c)). The retrieved temperature and humidity fields by synergistic approach best match the true horizontal distribution patterns on a fixed pressure level (Fig. 6). Moreover, owing to the sensitivity of infrared 510 radiance spectra to cloud properties, the synergistic method is able to improve IWC and effective radius (Re opt ) relative to collocated active cloud observations.
In conclusion, our study suggests that the synergistic method holds promise for using hyperspectral infrared radiance and cloud profiles from the existing instruments (AIRS, CloudSat, and CALIPSO) to retrieve UTLS temperature and water vapor distributions above deep convective clouds. As discussed in Feng and Huang (2018), the sensitivity to water vapor and 515 cloud microphysics properties (see Section 2.2.1) can be further improved by including the far-infrared coverage provided by future instruments, e.g., FORUM and TICFIRE. While a limited number of samples is available for applying the synergistic retrieval, instruments in geostationary orbit, such as IRS (Infrared Spectrometer) and GIIRS (Geostationary Interferometric Infrared Sounder) (Schmit et al., 2009;Holmlund et al., 2021), can greatly increase collocation with other space-borne active sensors over convective regions. Such an approach may also benefit the understanding of convective impacts by providing 520 time-continuous observations (Li et al., 2018) in future research. The ability of the synergistic method to leverage hyperspectral infrared observations to improve the NWP outputs (y atm ) also suggests the advantage of including cloudy-sky observations in global data assimilation systems, as performed by Okamoto et al. (2020).
Data availability. Derived data supporting the findings of this study are available from JF on request. The data for assessing cloud-induced uncertainties is openly available at http://dx.doi.org/10.17632/fy3gg7ch42.1.

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Author contributions. YH conceived the cloud-assisted retrieval idea; JF implemented this idea with improvements using the synergistic method. ZQ carried out the NWP simulation. JF and YH co-designed the simulation experiment and wrote this paper with contributions from ZQ.
constructive comments. This work is supported by grants from the Canadian Space Agency (16SUASURDC and 21SUASATHC) and the Nat-