the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Apr 2026
A Hybrid Ice Hydrometeor Retrieval Algorithm for (Sub)millimeter-Wave Radiometers in Support of the PolSIR and PMM Missions
Abstract. This paper presents an ice hydrometeor retrieval algorithm for submillimeter-wave radiometers in support of the upcoming PolSIR (Polarized Submillimeter Ice Cloud Radiometer) and PMM (Precipitation Measuring Mission) satellite missions. The algorithm employs a hybrid Bayesian Monte Carlo Integration (BMCI) and Optimal Estimation Method (OEM) approach, which leverages the strengths of the BMCI method but extends the retrieval capability beyond the limitations of the a priori database when BMCI alone fails to identify enough database cases matching the observations. To address the highly non-Gaussian nature of the a priori statistics, a method using cumulative distribution functions (CDFs) and empirical orthogonal functions (EOFs) is applied to enable effective implementation of the OEM algorithm. With the CDFs/EOFs method, the OEM can maximize the posterior probability density function using the a priori constraint that is largely consistent with that used in the BMCI step, ensuring that the entire retrieval operates under a nearly uniform prior constraint.
The algorithm is first applied to evaluate the PMM-C2OMODO (Convective Core Observations through MicrOwave Derivatives in the trOpics) radiometer using simulated observations. Retrieval accuracies for key microphysical parameters are presented. Also, the retrieval diagnostics, including the vertical resolution, Degrees of Freedom (DoF), and Shannon information content, are analyzed. The algorithm is further applied to real CoSSIR (Configurable Scanning Submillimeter-wave Instrument/Radiometer) observations during the IMPACTS (Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms) campaign, and the results are evaluated against the collocated triple-frequency radar retrievals from CRS (Cloud Radar System) and HIWARP (High-altitude Imaging Wind & Rain Airborne Profiler) observations. Multiple ice particle habits are examined, and both layer-resolved and column-integrated mass and size parameters are evaluated. Both simulated experiments and real-observation retrievals demonstrate that the hybrid BMCI-OEM method is highly effective in reducing simulated and observed brightness temperature (TB) discrepancies. With an appropriate selection of ice cloud particle habits, the TB simulations closely reproduce the observations. Using the logarithmic difference as the quantitative metric, the CoSSIR-retrieved ice water content, layer-resolved particle diameter, ice water path, and column-averaged mean mass diameter with the hybrid BMCI–OEM algorithm differ from triple-frequency radar retrievals by 3.75, 0.82, 2.53, and 0.55 dB, respectively, representing reductions of 0.21, 0.02, 0.85, and 0.13 dB relative to BMCI-only retrievals. The hybrid Bayesian framework also demonstrates high extensibility to other remote-sensing observations. As more information becomes available through multi-sensor integration or the use of hyperspectral measurements, the hybrid Bayesian algorithm shows increasing potential to better constrain cloud microphysical properties.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-1348', Anonymous Referee #1, 02 Aug 2026
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AC1: 'Reply on RC1', Yuli Liu, 20 Sep 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1348/egusphere-2026-1348-AC1-supplement.pdf
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AC1: 'Reply on RC1', Yuli Liu, 20 Sep 2026
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RC2: 'Comment on egusphere-2026-1348', Anonymous Referee #2, 03 Aug 2026
General comments
This manuscript presents a hybrid BMCI-OEM algorithm for retrieving ice cloud properties from (sub)millimeter-wave radiometer observations to support the planned PolSIR and PMM missions. BMCI serves as the primary retrieval method, while OEM is applied when too few cases in the a priori database adequately match the observed TBs. The primary retrieval products are ice water path and Dm, although the algorithm also explores the retrieval of vertical profiles of ice and liquid cloud properties and water vapor. The method is evaluated through a PMM-C2OMODO simulation and an application to real CoSSIR observations from IMPACTS, which are compared against collocated triple-frequency radar retrievals. The results show that the additional OEM step substantially reduces TB discrepancies and provides improvements in the retrieved microphysical properties compared with BMCI alone.
Overall, I found the manuscript very well written and easy to follow, especially considering the amount of work involved in developing and evaluating the retrieval method. The retrieval algorithm is clearly explained, and the experiments are carefully designed. The results are promising, and the study fits well within the scope of AMT. The topic is timely given the planned PolSIR and PMM missions, and I believe the proposed method will be useful for future (sub)millimeter-wave retrieval studies and other similar retrieval applications. I believe the manuscript is suitable for publication in AMT after the minor points listed below are addressed.
Specific comments
Minor comments
#1. (Lines 46-50)
This sentence mixes missions, satellite platforms, and instruments. Please revise the sentence for clarity.
#2. (Line 55)
Brath et al. (2018) uses an ensemble of standard neural networks and may not be an example of a quantile regression neural network. Could the authors please check whether this reference is appropriate here?
#3. (Line 124)
Because the previous sentence describes the synergistic CloudSat-CALIPSO 2C-ICE product, it would be helpful to clarify that 2B-CWC-RO is a radar-only product.
#4. (Lines 138-139)
Prigent et al. (2017) describes TESSEM2. Also, could the authors clarify whether TELSEM2 was used for land emissivity? Aires et al. (2011) describes the TELSEM, which does not cover frequencies above 200 GHz.
#5. (Line 159)
The right-hand side of Eq. (3) gives the variance. Please revise the text or equation accordingly.
#6. (Line 168)
I understand the point the authors are making, but inflating the NEDT does not change the actual measurement accuracy. It instead weakens the observational constraint in the retrieval. The term “measurement accuracy” may therefore be misleading. Please consider revising this wording.
#7. (Lines 180-181)
It is unclear what is meant by “mapped onto the CDF of a standard normal distribution.” Is the inverse standard normal CDF applied to the rank values?
#8. (Eq. 5)
The first K in Eq. (5) should be transposed.
#9. (Lines 227-228)
The term “cases” refers to profiles?
#10. (Lines 244-245)
The range from 0.5*IWP_true to 2*IWP_true corresponds to -50% to +100%
#11. (Line 265)
Please revise “, with most values falling below 10^1 and are ….” for grammatical consistency.
#12. (Eq. 6)
Eq. (6) seems to be incorrect. The first K should be transposed. If I understand correctly, K represents the sensitivity of the simulated TBs to the state vector. When K=0, the observations provide no information about the state, so the averaging kernel should also be zero. However, Eq. (6) gives the identity matrix in this case. This equation may need revision.
#13. (Line 309)
It seems that Sa and Sp are the covariance matrices, but the text describes them as PDFs.
#14. (Line 355)
CloudSat was launched in 2006, so data from winter 2005 would not be available.
#15. (Lines 395-402)
The interpretation based on excess ice mass looks reasonable, but I’m curious why the BMCI-only mismatch increases toward the centers of the water vapor absorption lines. Some explanation of this spectral pattern would be useful.
#16. (Line 406 and Figure 7)
Reflectivity differences should be expressed in dB.
#17. (Lines 459-460)
Since Xy^2 is dimensionless, I’m not sure what is meant by “fall below or close to the measurement uncertainties.”
Technical corrections
#1. (Line 16): HIWARP -> HIWRAP
#2. (Line 28): ice clouds properties -> ice cloud properties
#3. (Line 41): IceCube was launched in 2017, not 2016
#4. (Line 65): samplings -> samples
#5. (Line 221): The numbers of the 183.31 GHz and 325.15 GHz channels are reversed.
#6. (Line 294): from -> between
#7. (Line 295): corresponds -> correspond
#8. (Line 316): lowers -> decreases
#9. (Line 320): contributes -> contribute
#10. (Line 345): four subchannels near 325 GHz -> three subchannels near 325 GHz
#11. (Figure 11 caption): vertical -> vertically
#12. (line 515): HIWARP -> HIWRAP
Citation: https://doi.org/10.5194/egusphere-2026-1348-RC2 -
AC2: 'Reply on RC2', Yuli Liu, 20 Sep 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1348/egusphere-2026-1348-AC2-supplement.pdf
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AC2: 'Reply on RC2', Yuli Liu, 20 Sep 2026
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General comments
This manuscript presents an ice hydrometeor retrieval algorithm for sub-mm radiometers in support of the upcoming PolSIR and PMM satellite missions. The study proposes a hybrid BMCI-OEM retrieval framework that effectively integrates the advantages of both methods and evaluates its performance using both simulated and real observations. The topic is relevant to ongoing efforts in cloud and precipitation remote sensing, and the manuscript provides a detailed assessment of retrieval performance through a range of diagnostics and comparisons with independent radar retrievals.
Overall, I would like to commend the authors for the quality of this work. The manuscript is clearly written, the methodology is comprehensively described, and the analyses are thorough. I particularly appreciated the inclusion of the information-content analysis and retrieval diagnostics, especially the discussion based on the Shannon information content metric. I only have a few minor comments listed below and recommend publication after minor revisions.
Specific comments
(1) The manuscript highlights the advantages of the hybrid BMCI-OEM framework over a BMCI-only approach. Could the authors comment on the computational performance of the hybrid retrieval framework? While BMCI is described as computationally efficient, the OEM component requires iterative optimization and numerical Jacobian calculations. It would be useful to know how often the OEM step is triggered in practice and what additional computational cost it introduces compared to a BMCI-only retrieval.
(2) Please consider including the spatial resolution/footprint size of the various instruments used in the study, as well as the expected characteristics of the future missions (e.g., C²OMODO footprints <5 km have been reported in the literature). In addition, please provide the radar sensitivity (minimum detectable reflectivity, dBZ), as this information is essential for understanding the sensitivity of the reference retrievals.
(3) The manuscript demonstrates a notable sensitivity of the simulated brightness temperatures to the assumed ice particle habit. All simulations further assume randomly oriented particles and use only the first Stokes component. While polarization differences vanish at nadir, particle orientation can still modify the bulk scattering and extinction properties and therefore affect the simulated brightness temperatures. Given that the selected particle models are adopted from May et al. (2024), where orientation effects are also discussed, could the authors briefly comment on the potential implications of neglecting particle orientation for the retrieved ice microphysical properties? In addition, errors associated with neglecting particle orientation and polarization effects may become increasingly important at larger viewing angles, which are relevant for the planned cross-track satellite observations, particularly for future dual-polarization conically scanning radiometers.
(4) The current implementation assumes pencil-beam radiative transfer simulations and evaluates only nadir observations. Please provide information on the horizontal resolution of the simulations and discuss the extent to which the reported performance may be affected by the neglect of finite instrument footprints and off-nadir viewing geometries. Given that both PolSIR and PMM-C2OMODO are cross-track scanning radiometers, beam-filling effects may become increasingly important at submillimeter frequencies.
In this respect, please delete the word "slightly" from the following statement:
"All results presented here assume nadir-only observations: we acknowledge that both the PolSIR and PMM-C2OMODO radiometers are cross-track scanners, and results at off-nadir angles can be slightly different"
as differences are to be expected.
Suggestions for future work
The paper reports the largest residual brightness temperature discrepancies for the channels closest to 325 GHz and for the most strongly scattering cloud scenes. For future developments of the retrieval framework, the authors may wish to explore alternative particle model selections. For example, McEvoy et al. (2026, EGUsphere preprint) adopted the same particle habit framework as May et al. (2024), but introduced an additional ICON-hail particle model after identifying discrepancies between simulated and observed submillimeter brightness temperatures in strongly scattering deep convective conditions. In this context, analysing the joint behaviour of the 183 and 325 GHz channels (e.g., through scatterplot diagnostics) may provide a useful tool for evaluating and refining the choice of particle models used in the retrieval framework.
McEvoy, P., May, E., and Eriksson, P.: The Arctic Weather Satellite, introducing a new wavelength range for ice hydrometeor retrievals, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2026-2456, 2026.