Comparison of Cloud/Rain Band Structures of Typhoon Muifa (2022) Revealed in FY‐3E MWHS‐2 Observations With All‐Sky Simulations

All‐sky simulations of brightness temperature (TB) at Microwave Humidity Sounder‐2 (MWHS‐2) channel 15 from Fengyun‐3E (FY‐3E) are generated based on the European Center for Medium‐Range Weather Forecasts (ECMWF) reanalysis version 5 (ERA5) and the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) analysis for four typhoon cases. For Typhoon Muifa (2022), the MWHS‐2 TB observations have a strongest symmetric component within about 210‐km radial distances. Although much weaker, the symmetric component in the GFS all‐sky simulations compares more favorably with that of observations than the ERA5 all‐sky simulations. Due to ice scattering effects at 183.31 ± 7 GHz, spatial distribution patterns of TB observations and all‐sky simulations are quite similar to those of ice water path. The more cloud ice, the lower the TB. Deep convective systems within Muifa are captured by TB observations but not by simulations. Using an objective azimuthal‐spectral‐analysis based center‐fixing algorithm, the center positions of Typhoon Muifa can be well determined from both MWHS‐2 observations and GFS all‐sky simulations, but not from the ERA5 all‐sky TB simulations. Compared with the best track, the average center position errors for Muifa are 16.2, 24.9 and 74.4 km based on FY‐3E MWHS‐2 TB observations, the GFS all‐sky TB simulations, and the ERA5 all‐sky simulations, respectively. The conclusions of TC cloud/rain band structures and center positions of all‐sky simulations using the NCEP‐GFS analysis being better matching with those of FY‐3E MWHS‐2 observations than the ERA5 all‐sky simulations for Typhoon Muifa also hold true for three other typhoons.

BI AND ZOU 10.1029/2023JD039410 2 of 25 partly to their coarse resolutions (Hodges et al., 2017;Murakami, 2014;Schenkel & Hart, 2012).Tu et al. (2021) showed that the precipitable water vapor during the lifetime of Typhoon Lekima (2019) in the ERA5 reanalysis was closer to GPS observation than that in the Global Forecast System (GFS) analysis.Although there were other studies showing that the ERA5 reanalysis could also be superior to the NCEP GFS analysis for many other features of TCs besides TPW, little studies investigated TC cloud/rain band distributions in the ERA5 reanalysis and the NCEP GFS analysis.Satellite microwave humidity sounder observations of brightness temperature (TB) are strongly affected by cloud ice and water vapor distributions.One way to look at the TC cloud/rain band distributions in the ERA5 reanalysis and the NCEP GFS analysis is to examine the all-sky simulation of microwave humidity sounder TBs and compare them with microwave humidity sounder TB observations.
Microwave and infrared observations of TB from polar-orbiting and geostationary operational environmental satellites can reveal TC structures associated with temperature, water vapor, cloud liquid water and ice distributions in the atmosphere.A direct application of satellite TB observations is in atmospheric data assimilation (Geer et al., 2014).An inclusion of the ice scatter module in the fast radiative transfer model (RTTOV13.0)makes it possible to simulate TB observations under all sky conditions and thus to carry out all-sky data assimilation (Bauer et al., 2006;Eyre, 1991;Lawrence et al., 2018).It was found that the discrete dipole method can better characterize the scattering characteristics of snow particles, making all-sky simulations of humidity channels more accurate (Geer et al., 2017;Liu, 2008).Okamoto et al. (2021) examined the observation-minus-background (O-B) differences for Himawari-8 AHI observations, and pointed out that a poor forecast ability of high-altitude clouds caused a significant negative O-B bias in cloudy scenes.Realizing the importance of having a reasonably forecast accuracy of cloud hydrometeors, Li et al. (2021) assimilated Advanced Technology Microwave Sounder (ATMS) retrieved cloud liquid water path and ice water path to improve the accuracy of model predicted hydrometeors.The O-B biases for all-sky simulations of the Cross-track Infrared Sounder (CrIS) were successfully eliminated in all-sky conditions of both mei-yu rainfall cases and TCs.
Microwave temperature and humidity sounders carried on polar-orbiting operational environmental satellites can observe and reveal structures of TCs affected by water vapor, cloud/rain band distributions in the atmosphere.At present, applications of microwave humidity sounder observations to TC researches are mainly focused on obtaining the retrieval products of various atmospheric variables within TCs.Tian and Zou (2018) applied a refined hurricane warm-core retrieval algorithm to microwave temperature sounding observations of TB from either the ATMS or the Advanced Microwave Sounding Unit-A (AMSU-A) onboard multiple polar-orbiting operational environmental satellites that carry to examine the diurnal variability of the warm cores of Hurricanes Irma and Maria.These hurricanes occurred during the 2017 hyperactive Atlantic hurricane season.Compared with dropsondes data gathered within 1700-km radial distances of Hurricanes Irma and Harvey (2017), the means and standard deviations of the differences between ATMS-derived and dropsonde-measured temperature profiles were less than 0.7 and 1 K, respectively, in the vertical layer between ∼180 and 750 hPa.Zhang et al. (2019) used a backward propagation neural network to retrieve the sea level pressure in the TC inner-core regions, which has a root mean square error of less than 4 hPa when compared with the FNL analysis.The root mean square errors of the humidity profiles retrieved using a deep neural network and the ERA-Interim are less than 20%, with a maximum value of 18% at about 850 hPa (He et al., 2021).However, except for satellite data assimilation, there were very few studies that make a direct use of microwave TB distributions to studying structures of TCs.Using an objective method for TC center positioning based on an azimuth spectral analysis, Hu and Zou (2020, 2021, 2022) determined the symmetric center of TCs directly from a single channel TB observations of S-NPP ATMS channel 22 (183.31± 1.0 GHz) and CrIS channel 89 (703.75 cm) (Hu &Zou, 2020), of ATMS channel 18 (183.31 ± 7.0 GHz) andMHS humidity-sounding channel 5 (190.31 GHz) Hu &Zou, 2021), and of GOES-16 ABI channel 13 (10.3μm) (Hu & Zou, 2022).On average, the TC centers determined from satellite single channel TB observations deviate from the best track were less than 30 km.
This study aims at examining how well the TC cloud/rain band structures revealed by satellite microwave humidity TB observations are captured by the ERA5 reanalysis and the NCEP GFS analysis based on all-sky simulations FY-3E MWHS-2 TB observations, and are all-sky microwave TB simulations adequate for TC center positioning as TB observations did?Specifically, the structural evolutions of Typhoon Muifa revealed in FY-3E MWHS-2 TB observations are compared with the ERA and GFS all-sky simulations.Section 2 gives a brief description of Typhoon Muifa, which was a strong landfall typhoon in 2022 that occurred over Northwest Pacific.Section 3 introduces channel characteristics of the MWHS-2 onboard the FY-3E and evaluates the precision of an azimuth spectral analysis.Section 4 compares the structural differences among MWHS-2 TB observation and

A Brief Description of Typhoon Muifa (2022)
Typhoon Muifa that occurred in 2022 over the Northwest Pacific was selected for this study.Figure 1 shows the best track (Figure 1a) and temporal evolutions of the central sea level pressure (SLP) p c and the maximum sustained wind (V max ) from the best track data of the Regional Specialized Meteorological Center in Tokyo, the ERA5 reanalysis and the GFS analysis during the lifetime of Typhoon Muifa from 0600 UTC 7 to 0000 UTC 16 September 2022 (Figure 1b).It is noted that the maximum sustained wind from the best track data represents the maximum of 1-min average wind speed at 10 m (Landsea & Franklin, 2013), while the maximum sustained wind of the ERA5 reanalysis and the GFS analysis is calculated as the 10-m maximum wind speed near the center of Typhoon Muifa.The ERA5 reanalysis is the fifth generation ECMWF atmospheric reanalysis (Hersbach et al., 2018a(Hersbach et al., , 2018b) ) of the global climate with a temporal resolution of 1 hr, a horizontal resolution of 0.25° × 0.25°, and a total of 37 vertical layers from the surface to about 1 hPa.The NCEP GFS analysis has a temporal resolution of 6 hr, a horizontal resolution of 0.25° × 0.25°, and a total of 41 vertical layers from the surface to about 0.01 hPa (NCEP et al., 2015).
Muifa formed in a tropical cloud cluster and developed into a tropical storm (TS) at 0000 UTC 8 September 2022.It enhanced into a typhoon (TY) at 0000 UTC 10 September 2022, and quickly intensified into a severe typhoon (STY) at 1800 UTC 10 September 2022 with the maximum sustained wind of 44 m s −1 .Muifa maintained this intensity for almost four days while moving slowly.Based on the FY-4A satellite cloud image at 0000 UTC 11 September 2022 (Figure 1a), we know that the cloud structure of Muifa is quite symmetric and the outer cloud system is tight and thick.Muifa made its first landfall in Zhoushan, Zhejiang Province of China as a TY at around 1200 UTC 14 September 2022, followed by several landfalls over Shanghai, Shandong and Liaoning.The evolutions of the minimum SLP and the maximum sustained wind from the GFS analysis are much closer to those from the best track data than the ERA5 reanalysis (Figure 1b).The minimum SLP and the maximum sustained wind of the ERA5 reanalysis are weaker than both the best track data and the GFS analysis by more than 30 hPa and 20 m s −1 , respectively.
The TC movement is closely related to large-scale circulations.Figure 2 (left panels) shows the spatial distribution of the 500 hPa geopotential height and SLP of the ERA5 reanalysis when Muifa just reached TS intensity at 0000 UTC September 8 (Figure 2a), strengthened to the STY intensity at 1800 UTC September 10 (Figure 2c) and weakened to the STS at 1800 UTC September 14 that occurred about 6 hr after landfall (Figure 2e).Muifa was located within an inverted trough near (15°N, 133°E).A subtropical high was located to the northeast of the inverted trough (Figure 2a).Moving northwestward and intensified to STY by 1800 UTC September 10, Muifa was located to the southwest of a subtropic high and southeast of a mid-latitude trough.The anticyclonic circulation of the subtropic high and the cyclonic circulation of the mid-latitude trough resulted in a northwestward wind forcing and a southeastward wind forcing that of opposite directions near Muifa.Muifa thus moved slowly in the following 2 days.By 1800 UTC September 14, Muifa landed in Zhoushan, Zhejiang Province and was located in the east corner of the mid-latitude trough (Figure 2e).It is noted that as Muifa made landfall and started to weaken, and a new TC named Nanmadol formed near (139°N, 23°E).The landfall of Muifa brought huge wind and rain to the east coast of China.
The spatial distributions of the differences of large-scale circulations between the ERA5 reanalysis and the GFS analysis are provided in Figure 2 (right panels).The sea level pressure from the GFS analysis is generally lower (higher) than that of the ERA5 reanalysis in the areas of low (high) SLP values.The GFS SLPs near the center of Muifa are more than 15 hPa lower than the ERA5 at 1800 UTC September 10 and 1800 UTC 14 September 2022.Both the subtropical high located to the northeast and the mid-latitude trough located to the northwest of Muifa in the GFS analysis are stronger than those in the ERA5 reanalysis.The differences of large-scale circulations between the ERA5 and the GFS data may explain why the typhoon intensities determined by the ERA5 reanalysis are much weaker than those from the best-track and the GFS analysis.

FY-3E MWHS-2 Channel Characteristics and the Azimuth Spectral Analysis
The Chinese second-generation polar-orbit meteorological satellite Fengyun-3E (FY-3E) is currently the only dawn and dusk orbiting satellite in the world.It has a local equatorial crossing time at 0530 UTC for its descending nodes (Zhang et al., 2021).The Microwave Humidity Sounder-2 (MWHS-2) onboard the FY-3E is slightly different from the MWHS-2 onboard the FY-3C/3D.The 150-GHz window channel frequency was changed to 166 GHz.Using the 166-GHz and 89-GHz window channels, the ice water path (IWP) can be retrieved over oceans.Channels 11-15 are located at the water vapor absorption line (183.31GHz), which are designed to obtain atmospheric water vapor in different vertical layers of the atmosphere.The horizontal resolution of MWHS-2 channels is about 16 km.This study employs the low tropospheric water vapor channel 15 (183.31± 7 GHz) whose weighting function peaks at about 800 hPa.All-sky simulations of FY-3E MWHS-2 channel-15 TBs are generated from the ERA5 reanalysis and the NCEP GFS analysis by using the fast radiative transfer model RTTOV13.0 (Saunders et al., 2018).The input variables of RTTOV13.0 include three-dimensional temperature, specific humidity, pressure, specific cloud liquid water content, specific cloud ice water content, specific rain water content, specific snow water content, specific graupel water content (only GFS) and cloud fraction, as well as two-dimensional skin temperature, surface pressure, 2-m temperature, and 10-m wind vector (Table 1).Next, the TB field within a TC decomposed into azimuthal wavenumber components in the cylindrical coordinates (Hu & Zou, 2020;Zou et al., 2010).To do so, the TB field is firstly interpolated onto a cylindrical coordinate origin located at the TC center and a grid resolution of 3° azimuth interval and 15-km interval in radial direction.The discrete Fourier transform is then applied to a one-dimensional TB data sequence along the grid circle with a fixed radius to obtain the amplitude A and phase ∅ of wavenumbers from 0 to 60. Figures 3a and 3b show a spatial distribution of the sum of wavenumbers 0-60 accumulation of the channel-15 TB observations at 2119 UTC 10 September 2022 (Figure 3a) and the difference between Figure 3a and the TB observations (Figure 3b), respectively.It can be seen that differences between the sum of wavenumbers 0-60 and the original TB observations are less than 0.01 K.In other words, the sum of wavenumbers 0-60 accurately represents the original TB observations, and the azimuth spectral analysis does not lose useful information of TC structures captured by TB observations.A radial dependence of the root-mean-square errors of the sum of using limited wavenumber components from TB observations is presented in Figure 3c.Due to presences of small-scale features that are less symmetry in TB observations around 200-km radial distances, more wavenumber components are required at these radial distances than other radial distances to achieve the same precision.From Figure 3a, we find that the TB distributions are more symmetric at within 150-km radial distances and more homogeneous beyond 240-km radial distances than those near 210-km radial distances.The sum of the first 20 wavenumber components can well represent features in TB observations with a precision of higher than 0.5%.Figure 3d shows the amplitudes of wavenumbers 0 to 60 (color shading) and the averaged amplitude of wavenumbers 0 to 60 (black curve) at different radius.The later represents the total variance of TB observations.The amplitudes of TB observations rapidly with increasing wavenumbers.The amplitude of wavenumber zero is the largest.The total variance of TB observations within 30-270 km radial distances are much larger than elsewhere, implying that cloud and precipitation of Muifa are confined in this region at this time.

Comparison Between All-Sky Simulations and Observations
We compare the spatial distributions of MWHS-2 channel-15 TB observations, all-sky TB simulations from ERA5 reanalysis and GFS analysis at 2119 UTC 10, 2100 UTC 11 and 2203 UTC 13 September 2022 (Figure 4).The cloud/rain band structures with low TBs and the eye characterized by high TBs located at the center of the cloud/rain bands can be clearly seen in MWHS-2 TB observations at all three observing times (left panels in Figure 4).At 2119 UTC 10 September, the eye was the smallest among the three times shown.The eyewall and inner core cloud/rain bands of low TBs have circularly shaped structures, accompanied with 5-6 rainbands of short lengths at slightly larger radial distances between 105-and 225-km radial distances.The MWHS-2 TB revealed eye locations are consistent with the best track.The ERA5 simulated TBs (middle column) have wider and weaker eyewall that is farther away from the center.The eye is barely seen in the ERA5 TB simulations.The eyewall and inner core cloud/rain bands of low TBs from the GFS all-sky simulations (right column) have circularly shape structures and compared more favorably with observations (left column) scale-wise.Of course, having a horizontal resolution around 20-30 km, neither the MWHS-2 observations nor the ERA5 and GFS all-sky simulations could capture the actual cloud/rain bands within TCs, which requires a horizontal resolution higher than 3 km.
Using the azimuth spectral analysis method, we may decompose TB observations and their all-sky simulations into the symmetric and the asymmetric components at different wavenumbers.Taking the TB observations at about 2119 UTC 10 September 2022 (Figure 4a) as an example, Figure 5 shows the spatial distributions of wavenumbers 0 and 1 (Figure 5a), wavenumber 2 (Figure 5b), the sum of wavenumbers 0, 1 and 2, and the differences between TB observations and the sum of wavenumbers 0, 1 and 2 components.The wavenumber-0 symmetric TB component (Figure 5a) is more an order of magnitude larger than wavenumbers 1 and 2. There are two wavenumber-1 structures in TB observations shown in Figure 5a: the inner one is located at 90-km radial distances, and the outer at about 210-km radial distances.The two wavenumber-1 components have a 45° phase difference.The wavenumber-2 component is distributed along the circle of 105-km radius.A weak component of wavenumber 2 is found at a larger radial distance of about 210 km.The inner and outer wavenumber-2 structures have an opposite phase.The sum of the first three components of wavenumbers 0, 1 and 2 (Figure 5c) well represent the eye, eyewall and cloud/rain band structures in TB observations.The sum of the remaining asymmetric components (wavenumbers 3 to 60, Figure 5d) represents small scale variability in TB observations.
Figure 6 shows the temporal evolution of wavenumber-0 amplitudes from FY-3E MWHS-2 TB observations (Figure 6a) and all-sky simulations from the ERA5 reanalysis (Figure 6b) and the NCEP GFS analysis (Figure 6c) during the time period from 0911 UTC 9 September to 2144 UTC 14 September 2022.The amplitudes of wavenumber 0 in all-sky simulations are much weaker than those from TB observations.In other words, GFS and ERA5 underestimate the typhoon intensity significantly.Based on TB observations, Typhoon Muifa is highly  BI AND ZOU 10.1029/2023JD039410 9 of 25 symmetric within 210-km radial distances most of the times (Figure 6a), with the maximum symmetry near the radial distances around 60 km on 10-11 September and 75 km on 12-13 September 2022.The evolution of wavenumber-0 amplitude in the GFS all-sky simulations (Figure 6c) resembles more to that in TB observations (Figure 6a) than that in the ERA5 all-sky simulations (Figure 6b).
The microwave TBs at FY-3E MWHS-2 channel (183.31 ± 7 GHz) are strongly affected by ice scattering, which lowers TB values.We now examine if the differences among the MWHS-2 TB observations and the ERA5 reanalysis and GFS all-sky simulations are mainly caused by differences in ice among observation retrieval, the ERA5 reanalysis and GFS analysis.We present in Figure 7 the spatial distributions of the ice water path (IWP) retrieved from FY-3E MWHS-2 two window channels (Xu & Zou, 2019), in the ERA5 reanalysis, and calculated from the cloud ice water content of the GFS analysis at the same times as Figure 4, that is, 2119 UTC 10, 2100 UTC 11 and 2203 UTC 13 September 2022.The spatial distributions of IWP (Figure 7) are quite consistent with TB distributions (Figure 4).The low TB areas are highly correlated to large IWP areas.Similar to TB distribution, the high IWP regions in the GFS all-sky simulations and MWHS-2 observations are more compact and closer to the center than those in the ERA5 all-sky simulations.The larger the IWP, the lower the TB.At 2119 UTC 10 September 2022, the lowest TB value in observations and all-sky simulations from the ERA5 reanalysis and the GFS analysis in the inner core region of Muifa center is 164 K, 240 and 218 K, respectively, while the maximum IWP value in observations, the ERA5 reanalysis and the GFS analysis is 2.05 kg m −2 , 0.73 kg m −2 , 1.78 kg m −2 , respectively.It is noted that the ice water path in observations is much weaker on September 11 than September 10 and 13, which is probably associated with Typhoon Muifa (2022) being intensifying around 2100 UTC on both 10 and 13 September but weakening on 11 September (see Figure 1b).Such weakening in ice water path on 2100 UTC 11 September is not seen in all-sky simulations.
We may also look at the vertical and radial distribution of azimuth mean cloud ice water content in the ERA5 reanalysis and the GFS analysis within Typhoon Muifa. Figure 8 shows the cross-section of the cloud ice water content (color shading) as well as the radial variations of the azimuth mean TB observations (solid black curve) and all-sky simulations (dashed black curve) at 2119 UTC 10, 2100 UTC 11 and 2203 UTC 13 September 2022.Cloud ice water content is mainly distributed above the zero-degree temperature level near 500 hPa.The vertical band of ice water content of the GFS analysis near the center (right panels) is narrower and stronger than those of the ERA5 reanalysis (left panels).Cloud ice water content in the ERA5 reanalysis mainly confined within the vertical layer of 250-150 hPa, while that in the GFS analysis extends vertically from 400 to 150 hPa.An outward vertical tilt of the band of high cloud ice water content is found in the GFS analysis at 2100 UTC 11 and 2203 UTC 13 September 2022, while the band of high cloud ice water content of the ERA5 reanalysis titled vertically inwardly at 2203 UTC 13 September 2022.The vertical inward title of ice  water content is not quite natural.The azimuth radial profiles of TB observations differ greatly in magnitude from the all-sky simulations, while the maximum near the typhoon center and the minimum in the eyewall are seen in all three data sources.
Whether it's reanalysis and analysis, analysis variables (horizontal and vertical winds, humidity, potential vorticity, mixing ratios of hydrometeor variables, etc.) are made physically consistent.While the ice water path is a direct cause of the differences in TB simulations of cloud/rain band structures in TCs between the ERA5 reanalysis and GFS analysis, such differences in turn are related to the differences of various other meteorological factors within and around TCs (Malakar et al., 2020).Taking 1800 UTC 10 September 2022 as examples, the azimuthally averaged specific humidity within Muifa from the ERA5 reanalysis (Figure 9a) are obviously different from the GFS analysis (Figure 9b) near the center of Muifa.The GFS specific humidity is higher in the middle and low troposphere (below ∼450 hPa) and lower in the upper troposphere (above ∼450 hPa) near the typhoon center than its neighborhoods.The ERA5 specific humidity near the typhoon center is lower than its neighborhoods.
The spatial distribution of 10-m wind in the ERA5 reanalysis (Figure 9c) is much weaker than those in the GFS

Results of Typhoon Center Positioning Based on TB Observations and All-Sky Simulations
Hu and Zou (2020, 2021) developed an azimuthal-spectral-analysis based center-fixing algorithm to objectively determine the centers of tropical cyclones (TCs) using microwave humidity channel observations.These satellite observations have relatively high horizontal resolutions to provide structural information associated with cloud and atmospheric moisture within TCs.Simply speaking, the position in the observed TB field encompassing a TC that achieves the largest symmetric component with a specified radial distance is regarded as the TC center.
In this study, we would like to find out if a similar method that works successfully for TB observations would work for all-sky simulations of TB.
Figure 10 shows the center-positioning results for TBs (Figure 10a) and the radial variations of wavenumber-0 amplitude (Figure 10b) around Typhoon Muifa at 0852 UTC 10 September 2022.The first procedure consists Figure 11a presents the distances of the TB-determined centers from the best track of Typhoon Muifa using MWHS-2 TB observations (red) and simulations from the ERA5 (black) and the GFS (blue) all-sky simulations during the time period from 0000 UTC 9 to 1200 UTC 14 September 2022.The positions of the final centers are (circle symbol) are generally closer to the best track than the centers determined by the first azimuth spectral analysis (triangle symbol).The mean distance of TB determined typhoon center positions from the best track is 16.2, 74.4 and 24.9 km based on MWHS-2 observations, the ERA5, and the GFS all-sky simulations, respectively.The averaged center-positioning error based on FY-3E MWHS-2 TB observations is smallest, and that of the GFS all-sky simulations is much smaller than the ERA5 all-sky simulation.These are expected since the GFS TB simulations compared more favorably with TB observations than the ERA5 all-sky simulations in terms of the symmetry of the eyewall and inner core cloud/rain bands characterized by low TBs.Both GFS and ERA5 data have a 0.25 o x0.25° horizontal grid spacing and the MWHS-2 observations have a 16-km horizontal resolution, TC center position differences between the simulations and observations of about 10-20 km are expected.We may compare the location of the minimum SLP of Muifa between the NCEP GFS analysis and the ERA5 reanalysis.The Muifa's center positions from the ERA5 reanalysis deviate from the best track greatly for more than 90 km before Muifa reached STS intensity (Figure 11b).The locations of the minimum SLP from both the ERA5 and the GFS are close to the best track after Muifa reached STS intensity.The mean distance between the minimum SLP center positions of the ERA5 reanalysis and the GFS analysis and the best track are 30.7 and 28.2 km, respectively.In other words, the TB-determined centers from all-sky simulations, which are sensitive to cloud ice distributions within Muifa in the GFS analysis, are quite consistent with the minimum SLP centers in the GFS analysis.The ERA5 all-sky simulations do not well represent the structures of Typhoon Muifa in TB observations so that the TB-determined centers do not coincide with the minimum SLP centers in the ERA5 reanalysis.
We notice that the track differences from the best track based on the GFS all-sky simulations are smaller than observations from 1800 UTC 10 to 0000 UTC 12 September 2022.This is a time period during which the GFS wavenumber-0 amplitude compares more favorably with observations than other times (Figure 6c).Specifically, the center-positioning distance from the best track using the GFS all-sky simulations at 2100 UTC 11 September 2022 is about 20-km smaller than that determined by the TB observations.This is the time when the wavenumber-0 amplitude of TB observations is smaller than other times (see Figure 6a).In order to understand a possible reason, we show the TB observations and all-sky simulations at this time (Figure 12), as well as the best track (hurricane symbol) and TB determined center (open circle).It is seen that the best track deviates from the eye revealed in the TB observations (Figure 12a), which is why the distance between the TB-determined center from observations and the best track is relatively large at this particular time.The ERA5 all-sky simulations do not have a well-defined eye (Figure 12b).However, the best track coincides quite well with the eye revealed in the GFS all-sky simulations (Figure 12c).We believe that the best track can serve as a good reference, but it is not the truth and has some error with the actual typhoon centers.

Rainfall Products Within Muifa and Three Other Typhoon Cases
The rain bands over Muifa were observed by Global Precipitation Measurement (GPM) Microwave Imager (GMI) (Kummerow, 2022) and Dual-frequency Precipitation Radar (DPR) (Iguchi & Meneghini, 2021).The DPR consists of a Ku-band precipitation radar (KuPR) operating at 13.6 GHz and a Ka-band precipitation radar (KaPR) operating at 35.5 GHz.It provides altitude-dependent rain rates at 5-km horizontal resolution.The GMI has 13 microwave channels with their central frequencies located from 10 to 183 GHz, allowing a retrieval of the surface rain rate at 13-km horizontal resolutions.Since both DPR and GMI observations were available twice daily, Typhoon Muifa were observed fully only at 2035 UTC 11 and 0952 UTC 12 September 2022 during Muifa's lifetime.Figures 13a-13d present spatial distributions of the surface rain rate from GMI (Figures 13a and 13b) and DPR (Figures 13c and 13d).
Although detailed rain band structures are more clearly revealed in the surface rain rate from the high-resolution DPR observations, the surface rain rate from the low-resolution GPM observations did capture the broad features of rain bands (Figures 13a and 13b).We may compare the vertical cross-sections of the DPR rain rates with the MWHS-2 channel-15 TB observations (Figures 13e and 13f) and vertical cross-sections of cloud hydrometeors in  ERA5 and GFS with all-sky TB simulations of the ERA5 reanalysis and the GFS analysis (Figure 14).In general, low (high) TB observations (red curve in Figures 13e and 13f) are located in places with (without) DPR observed rain rates along the lines indicated in Figures 13c and 13d.Similarly, low (high) TB simulations are found in places with high (low) values of hydrometeors (Figure 14) in both the ERA5 reanalysis (Figures 14a and 14b) and the GFS analysis (Figures 14c and 14d) at 2035 UTC 11 and 0952 UTC 12 September 2022.Large structural differences are found between DPR height-dependent rain rate (Figures 13e and 13f) and model hydrometeors (Figure 14), which result in significant differences between observed and simulated TBs seen in these figures.
We may also carry out an azimuth-spectral analysis of GPM GMI rainfall, as we did for TBs.Results are presented in Figures 13a and 13b.The center positions of the GMI rain bands structures (square symbol) at 2035 UTC 11 and 0952 UTC 12 September 2022 are quite close to those determined by the MWHS-2 TB observations (cross symbol).The distances between the center determined from GMI rain bands and the TB-determined center is only 7.5 and 15.3 km at 2035 UTC 11 and 0952 UTC 12 September 2022, respectively.Such differences in center positioning are small enough given the observation resolutions of TB and GMI data at 16 and 13 km, respectively.MWHS-2 retrieved IWP can be used to estimate surface rain rate (RR) using the following formula (Weng et al., 2003): Although the cloud/rain structures are relatively well picked up in NCEP GFS-based all-sky TB simulations, the deep convective systems (DCS) are not.The detection of DCS can be done by directly using the channel differences of MWHS-2 TB observations.The method by Mathew et al. (2016), who used SAPHIR data to detect different layer deep convective clouds, is adapted in this study due to similar channel characteristics of FY-3E MWHS-2 to SAPHIR humidity channels.It consists of four layers of DCS points.The layer-1 DCS points are classified if they satisfy the following conditions: where the subscript represents MWHS-2 channel number, and the threshold value of T D is defined as a function of satellite viewing angle θ (Hong et al., 2005): The remaining points that do not satisfy Equation 2 are classified as layer-2 DCS points if the following conditions hold true: The layer-3 DCS points satisfy the following conditions but not Equations 2 and 3: The layer-4 DCS points satisfy the following conditions but not Equations 2-4: Figure 16 shows the spatial distributions of layer-1 to layer-4 DCS detected in FY-3E MWHS-2 TB observations as well as in all-sky simulations of the NCEP GFS analysis.It is seen that DCS points mainly distribute around center of Muifa in TB observations at 0852 UTC 10, 2119 UTC 10, 2203 UTC 13 September 2022 and the layer-1 DCS points correspond well with low TBs.However, there are very little DCS points in the GFS all-sky simulations.The ERA5 all-sky TB simulations also cannot capture DCS (figure omitted).A plausible reason is that the DCS in the GFS analysis at the resolution of 2.5° × 2.5°, which is about 1° × 1° coarser than MWHS-2 TB observations, is too weak.This causes smaller channel differences of MWHS TB observations used in the DCS detection algorithm.
The results presented so far are for one typhoon case during its lifetime.Three additional typhoon cases are added to confirm the conclusions whether the GFS all-sky simulations are more comparable to satellite observations for typhoon center positioning.Figure 17 presents the best tracks (Figure 17a) and the temporal variations of the maximum sustained wind (V max ) of Malakas from 0000 UTC 8 to 0600 UTC 16 April 2022, Hinnamnor from 0600 UTC 28 August to 0600 UTC 6 September 2022, Muifa from 0600 UTC 7 to 0000 UTC 16 September 2022, and Nanmadol from 1800 UTC 13 to 1200 UTC 19 September 2022 based on the RSMC best track data.
The four typhoons were fully covered by FY-3E MWHS-2 observations for a total of 52 times.The TB based center-positioning algorithm employs an azimuthal spectral analysis method and takes the position as the TC center when the TB field encompassing it achieves the largest axisymmetric component.Whether all-sky TB simulations are adequate for the TC center positioning depends mostly on if the TC axisymmetric component of cloud/rain bands are well captured.Figure 18 shows the radial variations of the azimuthal wavenumber-0 amplitudes of MWHS-2 TB observations and all-sky simulations from both the ERA5 and the GFS within the 360-km radial distances averaged within the lifetimes of the four typhoons shown in Figure 17.It is seen that the MWHS-2 observed typhoon axisymmetry is much stronger than all-sky simulations; and the axisymmetric component of the GFS TBs compares better with MWHS-2 observations than the ERA5 TBs for all four typhoons.As expected, the scatterplots of the deviations of the TB-determined typhoon centers from the best track (Figure 19) further confirm the accuracy of NCEP GFS analysis in terms of all-sky simulations of microwave humidity sounder to capture TC cloud/rain bands.The mean deviations are −3.0,−11.1, −6.1 km in the E-W direction and −2.6, −5.5, −4.6 km in the N-S direction for observation, ERA5 and GFS, respectively.The ±1 standard deviations are 13.9, 59.8, 27.0 km in E-W direction and 21.8, 65.5, 21.4 km in N-S direction for observation, ERA5 and GFS, respectively.The mean distances between the best track and TB-determined centers by observations, the ERA5 and the GFS all-sky simulations are 22.0, 76.5 and 29.9 km, respectively.The standard deviations TB-determined centers from the best track are 13.8, 45.3 and 18.2 km based on MWHS-2 observations and the ERA5 and the GFS simulations, respectively.

Summary and Conclusions
In this study, we evaluated the performance of the ERA5 reanalysis and the NCEP GFS analysis within Typhoon Muifa (2022) in terms of all-sky simulations of FY-3E MWHS-2 TB observations at channel 15 whose central frequency is located at 183.31 ± 7 GHz.The structures of Typhoon Muifa in TB observations and all-sky simulations were compared and the feasibility of using all-sky simulations to conduct TC center-positioning was attempted.The FY-3E MWHS-2 TB observations showed a significant symmetric component in the eyewall and inner core of Muifa, which are better captured by the GFS all-sky simulations than the ERA5 all-sky simulations.Such differences are closely associated with cloud ice distributions within Muifa.Similar to TBs, the spatial distributions of IWP from the GFS analysis compared more favorably with MWHS-2 retrieved IWP than the IWP distributions in the ERA5 reanalysis.In fact, the cloud ice water content in the GFS analysis has narrower, deeper and stronger distributions in the eyewall and inner core regions of strong convection than those of the ERA5 reanalysis.FY-3E MWHS-2 TB observations can capture DCS within Typhoon Muifa but neither the ERA5 reanalysis nor the GFS analysis can.We also showed that FY-3E MWHS-2 TB observations and the GFS all-sky simulations can be used successfully for typhoon center positioning applications.Since the symmetric components of Typhoon Muifa and other three typhoons are not well described by the ERA5 all-sky simulations, the center-positioning results are significantly degraded.This study only compared structural differences of FY-3E MWHS-2 TB observations and all-sky simulations for a few typhoons.We plan to extend the work to more TC cases and more microwave humidity sounders to obtain any statistically significant conclusions on evaluate performances of all-sky simulations.
Numerical TC forecasts at high resolutions adequate for cloud ice prediction will also be produced for evaluating performances of all-sky simulations.The purpose is to develop ideas for an improved all-sky data assimilation for TCs.

Figure 1 .
Figure 1.(a) FY-4A AGRI channel-1 (∼0.47 μm) reflectance observations at 0000 UTC 11 September 2022 (shading) and the best track (symbols) and (b) temporal evolutions of p c (open symbols) and the maximum sustained wind (V max ) (solid symbols) from the best track (red), the ERA5 reanalysis (black) and the GFS analysis (blue) during the lifetime of Typhoon Muifa from 0600 UTC 7 to 0000 UTC 16 September 2022.Intensity category is indicated by different symbols.

Figure 2 .
Figure 2. Spatial distributions of the ERA5 reanalysis (left panels) and differences between the ERA5 reanalysis and the GFS analysis (right panels, GFS minus ERA5) of SLP (color shading, unit: hPa) and 500-hPa geopotential height (contour, unit: m) at 0000 UTC September 8 (top panel), 1800 UTC September 10 (middle panel) and 1800 UTC September 14 (bottom panel), 2022.Also shown are the best track at the same time as the SLP (red symbol) and other times (black symbols) in each figure panel.

Figure 3 .
Figure 3. (a) Spatial distributions of the sum of azimuthal wavenumbers 0 to 60 of TB observations.(b) Differences between TB observations and those in (a).(c) Radial variations of the RMS errors of the wavenumbers 0, 0 + 1, 0 + 1+2, … from TB observations within 360-km radial distance.(d) Amplitudes of wavenumbers 0-60 (color shading) and the averaged amplitude of wavenumbers 0-60 (black curve) within 360-km radial distance of TB observations at 2119 UTC 10 September 2022.Also indicated in (a) and (d) are the 30-km and 210-km radial distance (black dashed line).

Figure 4 .
Figure 4. Spatial distributions of MWHS-2 channel-15 TB observations (left panels), ERA5 (middle panels) and NCEP GFS all-sky simulations (right panels) at 2119 UTC 10, 2100 UTC 11 and 2203 UTC 13 September 2022.Also indicated are the 105-and 225-km radial distance in the first panel (black dashed circle), the 360-km radial distance in the first column panel (black dashed circle), the sea level pressure (black contour) in the second and third columns and the best track center (hurricane symbol).

Figure 6 .
Figure 6.Temporal evolution of the wavenumber-0 amplitude of (a) TB observations, (b) the ERA5 and (c) the NCEP GFS all-sky simulations at FY-3E observation times (dotted vertical line) near the center locations of Typhoon Muifa during the time period from 0911 UTC 9 September 2022 to 2144 UTC 14 September 2022.

Figure 8 .
Figure 8. Azimuthally averaged cloud ice water mixing ratio (color shading) from the ERA5 reanalysis (left panels) and the NCEP GFS analysis (right panels) at 2119 UTC 10, 2100 UTC 11 and 2203 UTC 13 September 2022.Also shown are the azimuthally averaged TB observations (solid black curve), all-sky TB simulations (dashed curve) and zero-degree level (dotted black curve).

Figure 9 .
Figure 9. (a)-(b) Vertical cross-sections of the azimuthally averaged specific humidity and (c)-(d) spatial distributions of wind speed (color shading, unit: m s −1 ) and wind vector (black arrow) from the ERA5 reanalysis (left panels) and the GFS analysis (right panels) at 1800 UTC 10 September 2022.

Figure 10 .
Figure 10.(a) Spatial distribution of FY-3E MWHS-2 channel-15 TB observations (color shading) within and around Typhoon Muifa at 0852 UTC 10 September 2022, and (b) radial variations of the wavenumber-0 amplitudes of TBs in (a) in the second azimuthal spectral analysis procedure.Also indicated are the first-guess position (cross symbol), the best track position (hurricane symbol), the TB determined centers from the first (triangle symbol) and second (circle symbol) procedures of the azimuthal-spectral-analysis based center-fixing algorithm, as well as the first (large gray box) and second (small gray box) domains and second tryout centers (black dots).

Figure 11 .
Figure 11.(a) Distances between the best track of Muifa and the centers determined from the MWHS-2 TB observations (red) and the ERA5 (black) and GFS (blue) all-sky simulations by the first (triangle symbols) and second (circle symbols) procedures of the center-fixing algorithm and (b) distances between the best track and the minimum SLP (pc) location of ERA5 (black) and NCEP GFS (blue) of Typhoon Muifa during the time period from 0000 UTC 9 to 1200 UTC 14 September 2022.Also shown is the maximum sustained wind from the best track data (shading, unit: m s −1 ).

Figure 12 .
Figure 12.Spatial distributions of MWHS-2 channel-15 TB (a) observations and all-sky simulations from (b) ERA5 and (c) GFS at 2100 UTC 11 September 2022.Also indicated are the radial distance (black dashed circle) where wavenumber-0 amplitude reduces to 20% of the maximum amplitude, as well as the TB-determined center (circle symbol) and the best track (hurricane symbol).

Figure 13 .
Figure 13.(a)-(d) Spatial distributions of the surface rain rate (unit: mm hr −1 ) at 2035 UTC 11 (left panels) and 0952 UTC 12 (right panels) September 2022 from (a)-(b) GMI and (c)-(d) DPR.The center position of the GMI rain bands (square symbol), the best track (hurricane symbol), and the TB-determined center (cross symbol) and the tryout centers of the azimuth-spectral analysis at 0.05° resolution (gray points) are indicated in (a)-(b).(e)-(f) Vertical cross-sections of the DPR height-dependent rain rate along the black line in (c) and (d), respectively, and MWHS-2 TB observations (red curve) at (e) 2035 UTC 11 and (f) 0952 UTC 12 September 2022, and the 0°C height (black dashed curve) from DPR.

Figure 14 .
Figure 14.Vertical cross-sections of cloud hydrometeors (sum of liquid, ice, rain and snow) (shaded) and TB simulation (curve) along the same black line in Figures 13c and 13d from (a-b) ERA5 and (c-d) GFS at 2035 UTC 11 (left panels) and 0952 UTC 12 (right panels) September 2022.
Figure15compares the FY-3E MWHS-2 derived surface rain rate with that in ERA5 and GFS at 2100 UTC 11 (left panels) and 0955 UTC 12 September 2022 (right panels) within Typhoon Muifa.The spatial distributions of surface rain rate within Typhoon Muifa from both ERA5 (Figures15c and 15d) and GFS (Figures15e and 15f) differ greatly from those of FY-3E MWHS-2 derived surface rain rate (Figures15a and 15b) at both times.The correlation coefficient of surface rain rate between MWHS-2 and ERA5 (GFS) is as low as 0.53 (0.57) at 2100 UTC 11 September and 0.56 (0.61) at 0955 UTC 12 September 2022.Compared with MWHS-2 surface rain rates, the root mean square error of ERA5 (GFS) is as high as 4.2 (3.9) mm hr-1 at 2100 UTC 11 September and 4.0 (3.6) mm hr-1 at 0955 UTC 12 September 2022.

Figure 17 .
Figure 17.(a) The best tracks and (b) the maximum sustained wind (V max ) of Malakas from 0000 UTC 8 to 0600 UTC 16 April 2022 (blue symbols, upper x-axis), Hinnamnor from 0600 UTC 28 August to 0600 UTC 6 September 2022 (green symbols), Muifa from 0600 UTC 7 to 0000 UTC 16 September 2022 (black symbols), and Nanmadol from 1800 UTC 13 to 1200 UTC 19 September 2022 (red symbols) based on the RSMC best track data.The 52 FY-3E MWHS-2 observing times when the relevant typhoons were fully covered are indicated by the vertical lines in (b) using the same color convention as V max .

Figure 18 .
Figure 18.Radial variations of the mean (curve with open circles) and standard deviation (shaded in light color) of wavenumber-0 amplitudes of MWHS-2 TB observations (red) and all-sky simulations from the ERA5 (black) and the GFS (blue) within the 360-km radial distances during the lifetimes of Malakas, Hinnamnor, Muifa and Nanmadol.

Figure 19 .
Figure 19.Scatterplots of the deviations of the best track from the TB-determined typhoon centers by MWHS-2 observations and (b) the ERA5 and (c) the GFS all-sky simulations in the east-west (E-W) and the north-south (N-S) directions at the 52 times (see Figure 14b) for Malakas (blue symbols), Hinnamnor (green symbols), Muifa (black symbols) and Nanmadol (red symbols).Also indicated are the means (cross symbol in magenta color) and the ±one standard deviations (square box in magenta color).

Table 1
Input Variables and Geometry Parameters for All-Sky Simulations of Microwave Humidity Sounder All-Sky Simulations by RTTOV 13.0