An observing system simulation experiment (OSSE)-based assessment of the retrieval of above-cloud temperature and water vapor using hyperspectral infrared sounder

. Measuring atmospheric conditions above convective storms is challenging. This study ﬁnds that the uncertainties in cloud properties near the top of deep convective clouds have a non-negligible impact on the TOA infrared radiances which cannot be fully eliminated by adopting a slab-cloud assumption. To overcome this issue, a synergetic retrieval method is developed. This method integrates the infrared hyperspectral observations with cloud measurements from active sensors to retrieve atmospheric temperature, water vapor, and cloud properties simultaneously. Using an observation system simulation 5 experiment (OSSE), we found that the retrieval method is capable of detecting the spatial distribution of temperature and humidity anomalies above convective storms and reducing the root-mean-square-errors in temperature and column integrated water vapor by more than half.

on the BT difference between a water vapor channel (BT 1419 cm −1 at 7.0 µm) and BT 1231 (8.1 µm, Aumann and Ruzmaikin, 2013). 9941 overshooting DCC profiles are identified using this criterion, their locations are marked in Figure 1. From the GEM outputs, these profiles are confirmed to be precipitating, with continuous clouds extending from near-ground to vertical levels above 120 hPa, the level of tropopause. We use the BT-based criterion to select retrieval locations, instead of examining GEM-simulated cloud and precipitation fields, to mimic the scenario of using infrared radiance measurements only to identify overshooting DCCs, as performed in Feng and Huang (2018). Among the identified overshooting clouds, 100 profiles are 95 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 simulation profiles, in the number of O(10 6 ), regardless of cloud conditions, are used to construct an a priori dataset to define the prior knowledge used in the retrieval in Section 2.3.

Radiative transfer model
This study uses the MODerate spectral resolution TRANsmittance, version 6.0 (MODTRAN 6.0) (Berk et al., 2014) to simulate 100 the infrared radiances observed by satellite. MODTRAN 6.0 provides a line-by-line (LBL) algorithm that calculates radiance at 0.1 cm −1 spectral steps. This algorithm is validated against a benchmark radiation model, LBLRTM, showing less than 0.005 differences in atmospheric transmittance throughout most of the spectrum (Berk and Hawes, 2017). MODTRAN 6.0 implements a spherical refractive geometry package and the DISORT discrete ordinate model to solve the radiative transfer equation accounting for both absorptive and scattering media in the atmosphere (Berk and Hawes, 2017). 105 In this study, we use MODTRAN 6.0 to simulate the all-sky radiances with user-defined atmospheric profiles including cloud information. The model has 80 fixed atmospheric pressure levels. Above the GEM model top, the values from a standard tropical profile (McClatchey, 1972) are placed between 13 and 0.1 hPa. The prescription of the cloud information is based on an optical library of Yang et al. (2013). The cloud optical library provides a look-up table for the single-scattering properties of ice particles of different habit shapes, roughness, and sizes. Following Bani Shahabadi et al. (2016), we assume a gamma 110 distribution of particle sizes and calculate the single-scattering properties of each ice habit for the effective radius range between 1 to 100 µm. The effect of effective radius and ice habit on the simulated infrared radiance is discussed in Section 2.2.1, over the spectral ranges from 200 to 2700 cm −1 . Liquid clouds at lower levels are neglected because their infrared emissions are completely attenuated by ice clouds in the DCC samples concerned here.
In this OSSE, to mimic the retrieval using existing measurements, we follow the instrument specifications of AIRS, an 115 infrared hyperspectral infrared sounder onboard the Aqua satellite since 2002. This instrument has 2378 channels from 650 to 2665 cm −1 with a noise equivalent temperature difference (NEdT) around 0.3 K (at 250K reference level). Using AIRS spectral response function, synthetic radiances are generated using MODTRAN 6.0 from the atmospheric profiles of the GEM test set described above, and then are added with random, spectrally uncorrelated noise based on the NEdT of AIRS. These infrared radiance spectra are used as the simulated observations in the OSSE.  5 https://doi.org/10.5194/amt-2020-518 Preprint. Discussion started: 16 March 2021 c Author(s) 2021. CC BY 4.0 License.

Cloud induced uncertainties
In the following, we evaluate the radiance variability that results from 1) the variability in cloud microphysics properties, especially the effective radius of ice particles, and 2) the variability in the vertical distribution of the IWC profile. The surface roughness of ice particles is neglected as it mainly affects the scattering angle which plays a minor role in the infrared channels.
We focus on tropical cyclone events for their relevance to the OSSE case here.

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To gain the knowledge of cloud ice particles and their impacts on the infrared radiance spectrum and also to prescribe relevant information in the UTLS retrieval (see the descriptions below), DARDAR-cloud, a synergic lidar-radar retrieval product, is sampled to form a cyclone overpasses dataset based on the CloudSat 2D-TC data (Tourville et al., 2015). This overpass dataset identifies satellite overpasses within 1000km from the cyclone centers. From these overpasses, profiles with overshooting First, based on the identified OT-DCC profiles, we calculate the probability distribution function of the effective radius of ice particles at the cloud top. Fig .2 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. According to Heymsfield (1986) and Baum et al. (2011), over 80% of the small ice particles at tropical high-altitudes are solid columns. Hence, in the following, we consider the ice 135 particles to be solid column only, with a rough surface but varying effective radius.
Then, we randomly select 100 profiles from identified OT-DCCs to evaluate the effects of varying IWC and effective radius on the infrared radiance spectra. We calculate the upwelling infrared radiances R(Re, IW C 0 ) using IW C 0 , the mean IWC of OT-DCCs, and effective radius Re of every profile. Fig. 3 (a) shows the mean and the standard deviation (STD) of the equivalent brightness temperature of R(Re, IW C 0 ) caused by effective radius variations. Similarly, the mean and STD of 140 R(Re 0 , IW C) caused by IWC variations are shown in Fig. 3 (b). Note that a 0.1 cm −1 spectral resolution is used in radiative transfer calculation for this evaluation.
As shown in Fig.3 (a,b), the mean spectra of OT-DCCs show cold, and relatively uniform, brightness temperatures in the window and weak absorption channels that largely result from the emission of the cloud top. While the varying effective radius and IWC have a weak effect on the strong absorption channels, it greatly impacts the cloud emission, thus leading to large 145 radiance variations in the window and weak absorption channels. In the mid-infrared, the standard deviation of brightness temperatures due to effective radius, as shown by the red curve in Fig. 3 (a), is around 1 K, and the standard deviation due to IWC profile, as shown in Fig. 3 (b), is around 4 K. Therefore, the infrared radiances are more sensitive to the IWC than the effective radius.
It is interesting to note that despite the similarity between the two STD spectra in Figure 3  there are noticeable differences in the far-infrared channels (wavenumbers smaller than 500 cm −1 ), suggesting that far-infrared channels, e.g., from future instruments, such as FORUM (https://www.forum-ee9.eu) and TICFIRE (Blanchet et al., 2011), may be advantageous for the UTLS retrieval, which is beyond the scope of this OSSE but warrants future investigations.
Here, in Fig. 3 (c) we investigate what spectral uncertainties may be caused by the slab-cloud assumption. Similarly, R(Re, IW C), the radiances corresponding to the effective radius and IWC of individual profiles, are computed for the 100 155 profiles selected earlier. For each radiance spectrum, we calculate the brightness temperature of a window channel at 1231 cm −1 , BT 1231 . Following the slab-cloud assumption used by Feng and Huang (2018), we then place at the vertical layer where the atmospheric temperature differs the least from BT 1231 , a 500-m thick cloud layer with uniform IWC of 1.5 g/m 3 . The temperature of this vertical layer is adjusted to BT 1231 . With this prescribed cloud layer, radiances are calculated again for each profile, denoted as R(Re 0 , slab) ; note that the BT 1231 values of R(Re, IW C) and R(Re 0 , slab) are identical. The difference 160 between R(Re, IW C) and R(Re 0 , slab) at other frequencies can be interpreted as radiance residuals not explained by the slab-cloud assumption. The mean bias and STD of the residuals, as well as the root-mean-square of the residuals (RMSE), are shown in Fig. 3 (c). Fig. 3 (c) shows that the slab-cloud assumption cannot fully account for the spectral variations of cloud emission. The assumption leads to a spectrally tilted mean radiance bias as shown by the blue curve in Fig. 3 (c). The STD of the radiance 165 residual is of a similar magnitude to the mean bias, suggesting that removing the mean bias would not significantly reduce the errors in the simulated spectra. The RMSE of R(Re 0 , slab) shows minimum errors of around 0.1 K in the mid-infrared window and maximum errors over 0.5 K in the far-infrared channels. This RMSE spectrum, referred to as ε cld , is also calculated using an AIRS-like spectral response function to represent the radiance uncertainty induced by slab-cloud assumption in Section 2.3.

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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 radiances. 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 radiances observation, 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. ε is the residual that includes the measurement error and the forward 180 model error.
Following the optimal estimation method (Rodgers, 2000, Eq. 5.9), the 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 185 the observation vector, respectively. S ε is set to be a diagonal matrix because the observation errors in different channels are considered to be uncorrelated.
Thex can then be iteratively solved through: Where the subscript i refers to the ith iteration step.

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The equations described above are adopted from Feng and Huang (2018), where the state vector x includes temperature and 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 to Feng and Huang (2018) is in the prescription of S ε . While S ε in Feng and Huang (2018) is the square of NESR (noise equivalent spectral radiances), S ε in this study for slab-cloud retrieval contains the sum of the square of NESR and the square of ε cld , as depicted 195 in Figure 3, to account for the radiance uncertainties induced by slab-cloud assumption.  The blue curves represent the mean of the radiances, R(Re, IW C0) and R(Re, IW C0), driven by Re and IWC variations, respectively; the grey areas, as well as the red curves (corresponding to the right y-axis), denote the STD of the radiances. (c) The mean bias, STD, and RMSE of the radiances simulated with the slab-cloud assumption, R(Re0, slab) . The brightness temperature spectra are convolved and presented at a spectral resolution of 5 cm −1 .

Synergetic-cloud retrieval
The radiance uncertainty due to the slab-cloud assumption, ε cld , can be largely eliminated by incorporating collocated observations of cloud profile, 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 200 the work of Turner and Blumberg (2018), we include relevant cloud variables in a synergetic retrieval. Turner and Blumberg (2018) demonstrated that the additional observation vector, such as atmospheric and cloud profiles from other instruments and NWP products, can improve the precision of the retrieval and also the convergence in cloudy scenes. Following this idea, the observation vector y in Eq.1 is formulated as: [y rad , y other ], where y rad is the infrared radiances observation, and y other includes elements other than radiances observation that we refer to as additional observation vector. Specifically, we include 205 collocated cloud observations, [y iwc , y Re ], which mimics those from the DARDAR-cloud product, in the observation vector y and also add [x iwc , x Re ] to the state vector x. At every iteration step (Eq. 5), [x iwc , x Re ] is updated along with temperature and humidity profiles. This retrieval method is referred to as the synergetic-cloud retrieval method in the following.
In this OSSE, y iwc is set to be the logarithm of the IWC profile to be consistent with the retrieval of active cloud sensors within the field of view of the infrared sounder. For example, the DARDAR-cloud product provides effective radius and IWC 210 retrieval based on observation from CloudSat and CALIPSO. The uncertainty in IWC measurements is estimated by averaging the posterior uncertainty of IWC, provided by DARDAR-cloud product for every footprint, in the OT-DCC profiles identified in Section 2.2.1. This estimated precision is denoted as ε iwc , which corresponds to an around 20% uncertainty in IWC at vertical levels near the tropopause. Then, we account for the IWC observation uncertainty by randomly perturbing the y iwc so that the y iwc deviates from the truth by an error that has a standard deviation of ε iwc . Similarly, the effective radius observation y Re 215 is obtained by assuming an uncertainty of 5 um. We note that this uncertainty prescription is higher than the typical value in the DARDAR-cloud product (1.6 µm) as we aim to account for sampling differences of the instruments. Because the satellitemeasured infrared radiances are most sensitive to cloud emission near the cloud top, we only keep the top 1.5 km of IWC profile in y iwc , which corresponds to six model layers in the radiative transfer calculations.
The diagonal elements of S ε for y iwc and y Re are then set by conservatively quadrupling the square of the uncertainty ranges 220 of these variables specified above.
In the state vector, x iwc contains the six layers of the logarithm of IWC at the same model layers as y iwc . Note that x iwc and y iwc are not required to have the same vertical resolution; in practice, the vertical resolution of y iwc can be much finer than model layers. The first guess and covariance matrix of x iwc are calculated using the same a priori dataset described in the previous section, although the cross-correlation between IWC and other atmospheric variables is neglected. Consequently, 225 the forward model for relating x iwc to y iwc is a matrix that linearly interpolates the pressure level of x iwc to match the level of y iwc .

Additional atmospheric observations
Besides the cloud observations, other products that provide collocated atmospheric profiles can be useful in improving the precision of the posterior estimation. These additional products may include the atmospheric observations from other instruments 230 that are in the same satellite constellation as the hyperspectral infrared sounder or from a NWP model. In this study, we investigate the effect of additional atmospheric observations by adding an observation vector y atm , which contains the temperature and the logarithm of specific humidity at a later time step: 810 minutes after the initial time, in the GEM simulation.
The distribution of retrieval variable fields is shown in Figure 6. As inferred by the brightness temperature, the massive spatial coverage of DCCs is evident at the time step used as the 'Truth' (410 minutes after the initial time in the GEM simulation).

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At the later time step (810 minutes), the atmospheric data used as y atm are taken from the same locations but deviate from the 'Truth' as they are not directly above the convective overshoots at this later time step. The RMSE between atmospheric profiles from the two time steps (410 and 810 minutes) defines the uncertainties in y atm . To be conservative, the uncertainty of y atm is set by quadrupling the square of the RMSE in the corresponding diagonal elements of S ε .

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Five retrieval cases are designed to assess the retrieval performance of the slab-cloud and synergetic cloud retrieval methods.
Among them, Cases 1 and 2 use the slab-cloud retrieval method; Cases 3 and 4 use the synergetic cloud retrieval method that incorporates cloud observations. Cases 2 and 4 differ from Cases 1 and 3 in that they add y atm in the retrieval. The components of state vectors and observation vectors for the four cases are listed in Table 1. Case 5 is added to ascertain the improvements attributable to infrared radiances (as opposed to other sources of information). In this case, we estimate the state vector without 245 using infrared radiances y rad in the synergetic cloud retrieval. Case 5 is relatively uniform in space and it is therefore not included in the figures but listed in Tables 1 and 2 for comparison.
Before conducting the retrieval experiments, the capability of retrieval methods is investigated 1) by comparing the spectral signal of atmospheric anomalies to the radiance uncertainties, and 2) by calculating the information content for each element of the state vector. 250 Feng and Huang (2018) demonstrated that the spectral signal of water vapor perturbations emerges above the noise level defined by instrument NEdT. Here, we are interested in whether the atmospheric variations, as simulated by the NWP model and depicted in Figure 1, produce spectral signals that are not obscured by radiance uncertainty due to slab-cloud assumption (ε cld ). DCCs. The mean profile of this region is denoted as t cold and q mois for temperature and water vapor, respectively. The spectral signals of water vapor are then obtained by differencing R(t 0 , q mois ) -R(t 0 , q 0 ), where t 0 and q 0 are the mean of the a priori dataset. The strength of signals under different spectral specifications was depicted in Feng and Huang (2018) and are not repeated here. The spectral signals are then compared to radiance uncertainties in Figure 4. Figure 4 shows that the radiance uncertainty from the slab-cloud assumption, ε cld , does not completely obscure the signal of 260 temperature or water vapor. In the CO 2 and water vapor channels where the signal mainly comes from, the TOA radiances are not sensitive to cloud emission due to a stronger atmospheric attenuation at these channels. ε cld becomes larger in the wings of absorption channels, where the signals are already masked by the instrument NEdT. Therefore, the information content in temperature and water vapor is not expected to be lost due to the uncertainty caused by the slab-cloud assumption.
We next examine the DFS [degree of freedom for signal (Rodgers, 2000)] of temperature and water vapor in the four retrieval 265 cases (Table 1). DFS is defined as the trace of averaging kernel A, which relates the retrieved statex i+1 to the true state x 0 , as derived from Equation 5 at the end of the iteration: For a proper comparison, only the infrared radiance observation is included to calculate the DFS, so that a higher DFS 270 indicates higher information content brought by infrared radiances y rad . Because the DFS depends on the cloud distribution, we calculate the average of DFS in the 100-profile test set with individual IWC profiles.
As expected from Figure 4 (a,b), the DFS of temperature and water vapor differ, although not substantially, between Cases 1 and Case 3. The DFS of temperature increases from 3.31 to 4.15 by adopting the synergetic-cloud method owing to the improved sounding near the cloud top, where sparse ice cloud particles do not fully attenuate the atmospheric emission. In 275 comparison, the slab-cloud retrieval method fails to capitalize the information near the cloud top, as it neglects the contributions to satellite radiances from the vertical layers around the assumed sharp cloud boundary. Therefore, the synergetic retrieval method is expected to achieve a better result in temperature.
Moreover, a significant DFS of IWC (1.93 out of 6, on average) is found. The DFS suggests the sensitivity of infrared radiances to the IWC profile near the cloud top, which is consistent with the large spectral variations caused by perturbation 280 in the IWC profile simulated from the DARDAR-cloud product (Figure 4 (b)). Hence, the retrieval method can improve the precision in IWC products provided by collocated cloud observations. Note that the DFS for IWC varies from 0.96 to 2.71 in the test set, depending on the optical depth near the cloud top. Low ice density near the cloud top leads to higher DFS of IWC.
For example, the DFS in IWC increases from 0.99 to 2.44 in Figure 7 (f) compared to Figure 7 (c). On the other hand, the DFS in effective radius is very limited (0.01). It can be expected from Figure 3 (a,b) which shows that effective radius has a smaller 285 impact on infrared radiances compared to IWC.
In the following, retrieval is performed for the 100 profiles in the test set using Eq. 5 and following the OSSE framework described above. We then evaluate the retrieval performance through the mean bias and RMSE in temperature, humidity, and IWC between the retrieved profiles and the truth, as shown in Figure 5. The retrieval performance is also evaluated with regard to these quantities at selected levels and with regard to CIWV integrated from 110 to 70 hPa.

Slab-cloud retrieval
To recap, Cases 1 and 2 use the slab-cloud retrieval method. Improving upon Feng and Huang (2018), Case 1 accounts for the radiance uncertainties due to the slab-cloud assumption, while Case 2 further incorporates additional atmospheric observations to improve the precision of the method.
The results of Case 1 are shown in red solid curves in Figures 5 and 7. The major improvement in Case 1, compared to the 295 prior (blue solid curves), is the temperature profile from 100 to 75 hPa. Although there are some DFS values for water vapor, Case 1 does not improve much from the first guess.
Case 2 improves from Case 1 owing to the information carried by the additional atmospheric observation, y atm . Case 2 is represented by the red dotted curves in Figures 5 and 7. It approaches the truth more than Case 1, despite the warm/dry biases in the first guess and y atm (See Figure 5 (a,c)). Noticeably, it increases the retrieved water vapor concentration by around 1 300 ppmv on average and reduces the RMSE from 2.4 ppmv to 1.0 ppmv, as shown in Figure 5 (c,d) and Table 2. For the CIWV, Case 2 reduces the RMSE by half, compared to Case 1.
To demonstrate how well the retrieved atmospheric field represents the spatial variability in the truth, namely a moister and colder UTLS region above the cyclone center as shown in Figure 1, the distributions of water vapor, temperature, and CIWV are presented in Figure 6. It shows that the 'true' spatial patterns are well reproduced by Case 2 retrieval.

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Furthermore, individual profiles from two clusters of overshooting DCCs, which includes 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 vertical variability in temperature and water vapor. The all-sky optical depth from TOA, along with the IWC profile, at the two locations is shown in Figure 7 (c,d). Less than 13.5% of the atmospheric emission transmits to the TOA is from layers where all-sky optical depth is higher than 2. Therefore, the retrievable radiative signals come from the atmospheric column above thick cloud 310 layers, i.e., where optical depth is less than 2. Figure 7 (a-c) shows the results in a location close to the cyclone center. At this location, the slab-cloud method prescribes the cloud layer at the cold-point due to the strong cloud emission. Atmospheric anomalies above 86 hPa have an 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 produces moistening in a board vertical 315 range which, as explained in 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 its temperature profile similar to Case 1. Figure 7 (d-f) shows the results in a location south 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 320 be inferred from the optical depth (Figure 7 (f)), leading to a large radiance residual that cannot be explained by 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, it approaches the y atm in lower altitudes that lead to unrealistic vertical oscillation in temperature near 100 hPa.

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Using the synergetic-cloud retrieval method, Case 3 becomes more sensitive to water vapor and temperature compared to Case 1, as indicated by the reduced RMSE in Table 2 and the better resemblance of the truth in Figure 6. It retrieves higher water vapor concentration from 110 to 70 hPa, in comparison with Case 1. Owing to the radiative emission from in-cloud layers between 110 to 95 hPa, Cases 3 and 4 become sensitive to temperature profile near the cloud top. Hence, Cases 3 and 4 reduce the RMSE compared to other cases.

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The advantage of the synergetic retrieval method, especially when IWC near the cloud top is relatively small, is illustrated in Figure 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 produces the enhanced water vapor in Figure 7 (e) and approaches the truth cloud-top temperature much better than Cases 1 and 2. Case 4 further benefits from y atm which constrains the profile in the vertical ranges below 110 hPa and above 80 hPa. Case 4 reproduces the oscillating temperature feature in Figure 7 (d), correcting the warm bias found in both 335 y atm and the first guess around 90 hPa.
In addition, Figure 5 (e,f) shows that the synergetic retrieval method can improve upon the collocated cloud observations by reducing the mean biases in the IWC profile. At 90 hPa, where the retrieved 1.5 km cloud layer overlaps the most between the test set, the retrieval reduces the RMSE and mean biases in the y iwc by half. This can be beneficial considering the sampling difference between the active sensor and infrared instruments.

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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 is important as the uncertainty range in y atm constrain 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 the y atm , so that the square root of S ε of y atm is equivalent to a doubling of RMSE shown in Figure 5 (b,d) blue dot line.

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Although the additional measurement vector, y atm , itself does not contain the spatial variability pattern as seen in Figure   6, the corresponding covariance in S ε properly accounts for its variability (uncertainty) by prescribing a large value around 80 hPa but smaller values at other vertical ranges. Therefore, it increases the confidence to the posterior at levels where the thermodynamic variables are relatively constant. The increased confidence in turn enhances the degree 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 350 the truth, including y atm in optimal estimation can still improve the posterior estimation. In reality, the uncertainty in available atmospheric products can be estimated by inflating the precision of the product to account for sampling size differences through comparison with NWP models and collocated observations.

Conclusion and Discussion
Sounding the UTLS thermodynamical conditions has been a challenge. Using simulation experiments, we aim to understand 355 whether the variability in temperature and humidity field, especially above convective storms, can be detected by hyperspectral infrared sounders. Our focus is to investigate and constrain the uncertainties induced by clouds. Two retrieval schemes are tested, including a slab-cloud scheme that uses mainly the infrared radiance measurements and a synergic cloud retrieval scheme that combines cloud observations from collocated active sensors.
First, we find that uncertainties in cloud properties near the top of overshooting deep convective clouds have a non-negligible 360 impact on the TOA infrared radiances (Figure 3). The variation in brightness temperature of the TOA radiances due to vertical distribution of IWC may amount to about 4 K. It is the largest in window channels and weak absorption channels which are sensitive to cloud emission. Adopting a slab-cloud assumption, which locates a clear-cut cloud top using the brightness temperature of the window channel, alleviates, but does not fully eliminate, the cloud effect on the radiance spectrum (Figure 3 (c)). This remaining radiance uncertainty is accounted for in this study and is found to not significantly obscure the temperature 365 and humidity signals in the retrieval. Therefore, it is affirmed that the cloud-assisted retrieval as proposed by Feng and Huang (2018), can improve the sounding of UTLS temperature and water vapor compared to the 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 Figure 7 (c), the slab-cloud retrieval fails to reproduce the oscillating temperature anomalies, although it still detects the moistening water vapor anomalies above convective storms.

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Second, we find that the synergetic-cloud retrieval method, especially after incorporating additional atmospheric observations y atm , is sensitive to temperature, water vapor, and also IWC profile, near and above the cloud top. 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. It is capable of producing the strong moistening feature of the individual profile (as shown by Figure 7 (b)) and detecting the oscillating temperature anomalies (as shown by Figure 7 (c)). The retrieved distributions of temperature and humidity 375 also best resemble the horizontal distribution patterns in the truth at a fixed pressure level ( Figure 6).
In conclusion, the OSSEs here suggest that it is promising to apply the synergetic-retrieval method, using the infrared hyperspectra and cloud profiles from the existing instruments: AIRS, CloudSat, and CALIPSO, to retrieve the UTLS temperature and water vapor above the deep convective clouds. One suitable application is the tropical cyclone events which generate massive upper tropospheric thick clouds that provide a favorable condition for the retrieval technique developed here, which we will 380 address in an accompanying paper (Feng and Huang., 2021). Although not explicitly discussed in this study, similar results shown in Figures 5 to 7 can be obtained using other hyperspectral infrared sounders, e.g., IASI and CrIS, due to their similar spectral specifications to AIRS. As discussed in Feng and Huang (2018), the sensitivity to water vapor and cloud microphysics properties (see Section 2.2.1) can be further improved by including a far-infrared coverage provided by future instruments, .e.g., FORUM and TICFIRE. While a limited number of samples is available for the synergetic retrieval to perform, instruments in 385 geostationary orbit, such as IRS (Infrared Spectrometer) and GIIRS (Geostationary Interferometric Infrared Sounder) (Schmit et al., 2009;Holmlund et al., 2021), can greatly increase the collocation with other spaceborne active sensors over convective region. It may also benefit the understanding of convective impacts by providing time-continuous observations (Li et al., 2018) in future research. The ability of the synergetic retrieval method in using hyperspectral infrared observations to improve the NWP outputs (y N W P ) also suggests the advantage of including cloudy-sky observations in the global data assimilation system 390 as performed in 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.
Author contributions. YH conceived the cloud-assisted retrieval idea; JF implemented this idea with improvements using the synergeticretrieval method. ZQ carried out the NWP simulation. JF and YH co-designed the OSSE and wrote this paper with contributions from