Collocated measurement is the occurrence where two or more sensors observe the same regions at the same time. One factor for the collocation window requirements is the specific observation target. Ice clouds are a fast-changing (minutes to hours) atmospheric phenomenon that requires a window of short time and small space. Another considered factor in defining the collocation window is the number of meaningful statistics for training.

The ascending node time of CloudSat is between 13:30 and 13:45 at local solar time (LST), which is close to that of FY-3B (13:30 LST). Because of the close orbits and the ascending time between FY-3B and CloudSat, the number of collocated measurements is large. In this study, a collocation dataset of MWHS and 2C-ICE was created by setting the collocation window to 15 min in time and 15 km in space. Since the footprint of MWHS is an order of magnitude larger than that of CPR, multiple 2C-ICE pixels can be found within 1 MWHS pixel. Therefore, the IWP values of 2C-ICE within a circular window (a radius of 7.5 km) were averaged to represent the mean IWP for the MWHS measurement pixel. According to this collocation strategy, 1 207 731 collocations were found between the FY-3B/MWHS and the CloudSat/2C-ICE for 2014. Due to the different observation methods (scan angle and footprint size) of MWHS and CPR/CALIOP, only 14 pixels of 2C-ICE were contained in the best-case collocations (see Fig. 1a). Therefore, the CloudSat footprints cover at most 13.75 % of the area of an MWHS footprint, an error from imprecise collocation was unavoidable, and the representation of the dataset must be considered.

Figure 1 illustrates the statistics of the 2C-ICE pixels within the MWHS footprints in the collocations. In most cases, more than 10 pixels of 2C-ICE were averaged in the corresponding MWHS pixel. However, there were still many MWHS pixels that covered only a small quantity of 2C-ICE pixels, which means that collocations were poorly represented. The coefficient of variation in each collocation pixel is shown in Fig. 1b. The coefficient of variation was used to represent the IWP dispersion of 2C-ICE pixels in each MWHS pixel. When the coefficient of variation is small, it means that the IWP of 2C-ICE pixels averaged in this MWHS pixel are homogeneous and represent a scene which MWHS observed relatively well. Since the collocation error cannot be estimated, the criteria discussed in Holl et al. (2010) was applied to reduce the sampling effect of collocations. In this study, an MWHS pixel with more than 10 pixels of 2C-ICE and less than 0.6 coefficients of variation was selected for subsequent processing. However, in the case of highly inhomogeneous clouds existing outside the CloudSat field of view, larger uncertainty for the IWP within MWHS pixels cannot be eliminated. After the reduction in inhomogeneous collocations, 665 519 collocations were retained.

Figures 2 and 3 give statistical information on the scan angle, latitude, and month of the MWHS measurements in this dataset. Since the dataset was used for global retrieval, it must have sufficient samples, and their distribution must represent the real world. According to the statistical results of the collocated MWHS pixels shown in Fig. 2, most of the collocations occurred on one side of the flight direction (from the 40th to the 90th scan pixel). In terms of observation latitude, the collocations near the nadir scan (the 49th pixel) cover the latitude from 80∘ S to 80∘ N, while at the edge of the observation (the 90th pixel), they only cover the tropical regions. In terms of observation time and latitude, Fig. 3 illustrates that there is an obvious lack of data above 60∘ S from April to September, and there are also limited data between 0∘ and 30∘ S in December. The data distribution suggested that the training in polar regions may be inadequate. Due to the high number of collocations near the poles, 121 500 observations at high latitudes were randomly excluded to obtain a balanced dataset. For IWP retrieval, collocations should be classified into two bins (clear-sky scene and cloudy scene), according to a specific IWP threshold. A threshold of IWP >100 g m-2 was preliminarily selected to classify cloudy scenes. Therefore, 81 490 collocations were recognized as cloudy scenes and 462 529 collocations were clear-sky scenes in this dataset.

The statistical information of TB and IWP for different channels (CH.2–CH.5) in the collocation dataset is given in Fig. 4. The TBs for CH.3 and CH.4 were mainly concentrated at approximately 250 K, indicating a small sensitivity to ice clouds. For CH.2 and CH.5, the TBs had a larger range of variation, which is due to the larger contribution of near-surface information to the window channels. However, it can be seen that, in the presence of ice clouds (IWP >100 g m-2), the surface information is blocked by clouds, making the TB range significantly smaller as the IWP becomes larger. The statistical relationship between the 150 GHz TB and IWP at different scan angles is given in Fig. 5. It can be found that there is a significant decrease in the measured TB with increasing IWP for large scan angles. As the scan angle decreases, especially in the case of nadir observations, many low TBs are appearing in clear-sky scenes because nadir observations have a very large number of collocation scenes in the polar regions (see Fig. 2b) where the surface lowers the measured TB. In contrast, collocation scenes with large scan angles are mainly located in the tropics, which makes the TB–IWP relationship very significant.

The density plots of the PD and TB at 150 GHz (clear-sky and cloudy scenes) and the corresponding IWP from 2C-ICE over the ocean and land are depicted in Figs. 6 and 7. Scan angles from ±41.28 to ±53.35∘ were selected to compare the results with observations from conical scanners. In the cloudy case, the TBs are distributed between 150 and 290 K, with the largest PD occurring at 230 K (corresponding to IWP >1000 g m-2). This is similar to the result of Gong and Wu (2017) and Gong et al. (2020). However, due to the quasi-polarization mode and the much larger footprint, the PD of MWHS is much lower than that of conical scanners (e.g. GMI). The lowest TB generally appears in the centre of deep convection clouds, and the PD is small due to the randomly oriented ice particles; the largest PD due to the horizontally oriented particles generally appears in the warmer clouds. Figure 6 shows that, the lower the TB, the larger the IWP, while the TB is also influenced by the local atmospheric temperature. Comparing Figs. 6 and 7, the TB of the clear sky is generally above 240 K. The PD from the ocean surface is relatively large, while the PD from land is small.

The network structure, training dataset, and cloud IWP threshold are discussed above. The sigmoid activation function can vary the output of the network from 0 to 1, which represents the probability of cloud occurrence. Therefore, a threshold value of cloud probability must be assigned to determine the cloudy scene. After testing, a threshold value of 0.4 was the most appropriate for this cloud filtering. To enhance the filtering capacity, scan angle, mask, latitude, and longitude were all used as auxiliary information. The cloud filtering performance for different channel combinations is listed in Table 2. The results showed that all three 183 GHz channels have cloud identification capability, and the addition of one 150 GHz channel enhances the POD of the network, while the two 150 GHz channels do not yield additional information. However, the detection of ice clouds using MWHS channels was still limited. The FAR and POD of the best network are 0.31 and 0.61, respectively.

For the global IWP retrieval, clear-sky scenes were excluded from the training data. Different combinations of the network input are compared to find the best retrieval strategy. The auxiliary information cases and their retrieval errors are listed in Table 3. In these cases, all five channels were used. Additional information, including latitude, scan angle, and ocean/land mask and their combinations, was added to train the networks.

Concerning the errors shown in Table 3, a significant improvement in retrieval performance is achieved by adding latitude or ocean/land mask information, while the contribution of just adding the scan angle to the retrieval is not significant. In MWHS measurements, the signal from ice clouds is a reduction in TB by the scattering effect. In the absence of latitude information and ocean/land mask, it is difficult to distinguish whether the decrease in TB is due to ice particles or the low radiance from the surface. According to cases 1, 2, and 4 in Table 3, CC is improved from 0.50 to approximately 0.62, and the RMSE and MAPE are also improved significantly. However, MAPE and BIAS are in conflict, and reducing MAPE will increase BIAS. Therefore, CC is an important metric for evaluating the model. The combination of auxiliaries can further improve the retrieval results, although the effect of using the scan angle alone is not obvious. Cases 5 and 6 in Table 3 indicate that the scan angle combined with latitude and ocean/land mask can also further improve the retrieval capability. The retrieval MAPE of each IWP bin is shown in Fig. 9a. The MAPE in different IWP bins gives a more detailed comparison. Compared to no auxiliary model, adding auxiliaries can significantly reduce retrieval errors, especially at IWP <200 g m-2 and IWP >1000 g m-2.

The performance of the different channel combinations (all the auxiliary information is added) is presented in Table 4. Since the 183 GHz channels (CH.3–5) of MHS have proven to have good sensitivity to CloudSat IWP, the influence of the 150 GHz channel and its PD were mainly focused on here. The results of cases 2 and 3 in Table 4 show that adding the 150 GHz window channel (CH.2) gives an improvement to all the metrics. Considering the contribution of PD in the retrieval, the results show that the addition of PD alone (case 4) contributes to the retrieval of IWP, while the combination including both H and V polarization channels has the best performance (case 1). Figure 9b illustrates the MAPE of different channels. Comparing case 3 with case 4 in Table 4, the addition of PD gives an obvious improvement in the retrieval results at IWP >2000 g m-2. In general, all channels of MWHS contribute to ice cloud retrieval.

The final retrieval models (case 1 in Table 2 and case 8 in Table 3) were selected according to the metrics. Combining the cloud filtering network and the IWP retrieval network with the test data, the final results are shown in Table 5. The performance over the ocean and land is also listed. After adding the cloud filtering network, the accuracy of the IWP retrieval decreased significantly for MAPE and BIAS and slightly for CC and RMSE. The results are better over the ocean than over land, especially the correlation. Figure 10 shows the scatterplot between MWHS IWP and 2C-ICE IWP in January 2015. The result shows relative agreement, but the MWHS IWP has significant dispersion at low IWPs, which may be due to the lack of sensitivity of the MWHS to thin ice clouds. Although the MWHS channels are sensitive to the IWP when it is around 100 g m-2, the cloud filtering network shows large FAR, which will lead to unsatisfactory results at the IWP threshold. The final model underestimates the true value overall but overestimates it when the IWP <300 g m-2.

Ice cloud misidentification is an important and unavoidable problem in this study. One reason is that the microwave channels detect ice clouds through the large decrease in TB. However, the low temperature in high-altitude regions or other temperature anomaly phenomena can also lead to low TB. In the final results above, although geographic information is added to the training data, there are still many misclassification cases, such as on the Tibetan Plateau in winter. Therefore, knowing the surface temperature or the near-surface air temperature will help ice cloud detection. Holl et al. (2014) show that infrared channels show good performance. The other reason is due to the mismatch between the CloudSat and the MWHS footprints spatially and temporarily. Since the CloudSat pixels cover less than 15 % of the MWHS pixels, the 2C-ICE scenes cannot fully represent the MWHS observations, especially in the case of thin clouds.

For the IWP retrieval, the 150 GHz window channel has a significant ice cloud response which, in combination with 183 GHz channels, provides a better retrieval of IWP. The PD at 150 GHz, although contaminated by polarization from the ocean surface, also contributes positively to the retrieval especially when the IWP is larger than 1000 g m-2. In addition, the PD of quasi-polarization channels from MWHS is related to the scan angle and does not fully represent the polarization information of the ice particles, especially near the 45∘ scan angle. From the perspective of polarization measurements only, a cross-track scanner does not provide as much polarization information as a conical scanner.

In terms of the retrieval using the neural network, the results of this paper are basically consistent with Holl et al. (2014). The error between the retrieval results and 2C-ICE is approximately 100 %. The latitude and ocean/land mask are important auxiliary information for DNN retrieval. Holl et al. (2014) used angle information that contains geometric observations of the local zenith and azimuth and showed a significant improvement. However, the results in Table 3 show that the scan angle is of limited help for retrieval, which may be due to the fact that the scan angle is not fully representative of the geometry of the observed radiance, and it works better when used in conjunction with the latitude and land/sea mask.

However, there are some limitations to using neural networks for IWP retrieval. Collocation is the first limitation, since there are some uncertainties in the field of view of MWHS and CloudSat due to the large resolution difference. These uncertainties are represented in the training data and can be better predicted using, for example, quantile regression neural networks (Pfreundschuh et al., 2018). The most important issue is the real sample (2C-ICE) used in training, which has uncertainties that are difficult to quantify. Therefore, it is also impossible to make accurate error estimates of the model results. In the absence of access to a large number of real samples, the use of neural networks can only converge to a certain product with the highest accuracy (such as 2C-ICE). An alternative approach is to use simulation results (typical profiles) of radiative transfer models, where the generalization ability of the network will strongly depend on the model itself and the input field. In addition, the microwave band below 200 GHz is sensitive only to large ice particles and thick clouds and is relatively less effective for cloud detection.