Simulation and sensitivity analysis for cloud and precipitation measurements via spaceborne millimeter wave radar

. This study presents a simulation framework for cloud and precipitation measurements via spaceborne millimeter 10 wave radar composed of nine sub modules. To demonstrate the influence of the assumed physical parameters and optimizing the microphysical modeling of the hydrometeors, we first conducted a sensitivity analysis. The results indicated that the radar reflectivity was highly sensitive to the particle size distribution (PSD) parameter of the median volume diameter and particle density parameter, which can cause reflectivity variations of several to more than 10 dB. The variation in the prefactor of the mass-power relations that related to riming degree may result in an uncertainty of approximately 30–45 %. 15 The particle shape and orientation also had a significant impact on the radar reflectivity. The spherical assumption may result in an average overestimation of the reflectivity by approximately 4–8 %, dependent on the particle shape and orientation modeling. Typical weather cases were simulated using optimal physical modeling accounting for the particle shapes, typical PSD parameters corresponding to the cloud precipitation types, mass-power relations for snow and graupel, and melting modeling. We present and validate the simulation results for a cold front stratiform cloud and a deep convective process with 20 observations from W-band cloud profiling radar (CPR) on the CloudSat satellite. The simulated brightness band features, echo structure, and intensity showed good agreement with the CloudSat observations; the average relative error in the vertical profile was within 20 %. Our results quantify the uncertainty in the millimeter wave radar echo simulation that may be caused by the physical model parameters and provide a scientific basis for optimal forward modeling. They also provide suggestions for prior physical parameter constraints for the retrieval of the microphysical properties of clouds and 25 precipitation. particles. The microphysical characteristic of each hydrometeor was substantially different, which affects the scattering properties and then the radar echo. The following introduces the microphysical modeling of the different hydrometeors. show the reflectivity change caused by D 0 and  under a conventional gamma PSD without constraints on the total number concentration. In the conventional gamma PSD, the D 0 and  vary independently; the reflectivity can change by 13 dB when D 0 varies from 0.2 to 0.8 mm. The results showed that the effect of PSD parameter variation on the reflectivity can be reduced by approximately 60 owing to constraints on the total number concentration for the PSD of cloud ice. approximately 45 30 to complex various microphysical shape and orientation frozen and mixed phase particles could lead to an average reflectivity difference of approximately 4–8 %. In addition to the PSD parameter and particle shape and orientation, this study emphasized the importance of the particle density parameters and PSD modeling constraints corresponding to different cloud precipitation types in the forward simulation and microphysical properties retrieval. Two typical cloud precipitation cases were presented. The simulation results were compared with the CloudSat 475 observations. During simulation, we considered the PSD parameter settings for typical cloud precipitation types, particle shapes, melting model, and influence of snow and graupel density relations. For snow and graupel microphysical modeling, unrimed snow particles was assumed in the stratiform clouds, and rimed snow with varying density-power relations was considered in the convective clouds. The simulation results with the optimization setting showed good agreement with the CloudSat observations; the average relative errors in the vertical profile between the simulation and CloudSat data were 480 within 20 %, which improved by 20–80 % compared with the conventional setting, i.e., not considering the melting model and riming effect for snow and graupel. The melting layer modeling for stratiform cloud could accurately reproduce the bright band structure after attenuation. The varying prefactor of density relations of snow and graupel considering the riming effects for convective cloud rendered the simulated echo structure consistent with the observations. The selection and modeling of cloud microphysical characteristics not only affects the forward simulation and numerical modeling, but also has a significant impact on physical parameter retrieval. This study contributes to a quantitative understanding of the uncertainties of forward simulations or radar retrievals due to variation in the microphysical properties of hydrometeors. They also provide a scientific basis for the analysis of millimeter wave radar observation data, the optimization of parameter settings in forward modeling, and microphysical constraints in parameter retrievals. The sensitivity test and simulation results suggest that accurate estimation of at least two parameters in the size distributions of hydrometeor particles including particle density factor is beneficial using certain methods, such as multiband measurements.


4
The complex refractive index of each hydrometeor was first calculated, which depends on their phase, composition, 95 density, and radar wavelength. For pure water and pure ice, such as raindrops, cloud water, and cloud ice, we calculated the refractive index according to Ray (1972). Dry snow is a mixture of air and ice, while wet snow and graupel are a mixture of air, ice, and water. The densities of air, ice, and water are generally 0.001, 0.917, and 1 g/cm 3 , respectively. The mixture has different densities according to the proportions of different components. Given the proportion of air, ice, and water (or riming fraction or melting fraction) in the hydrometeor, the refractive index of the mixture can be calculated using the 100 Maxwell-Garnet mixing formula.

Cloud water
Cloud water droplets form from the condensation of super-saturated water vapor onto cloud condensation nuclei. They are usually spherical due to surface tension, with a typical size of ~10 m  . As the size of cloud droplets is small relative to the wavelength, with an approximately spherical shape, their scattering characteristics can usually be calculated via Mie theory 105 or Rayleigh approximation based on the sphere assumption. The PSD of cloud water can generally be modeled with a normalized Gamma distribution: where Nw is the normalized intercept parameter, D0 is the median volume diameter, w  is the density of water, i.e. 1 g/cm 3 , 110  is the shape parameter, and  is the gamma function. Here, W in Eq. (2) is the water content of the cloud water, which is calculated by converting the mixing ratio of the hydrometeor from the WRF output: where Rgas is the gas state constant, P is the air pressure in hPa, T is the temperature in K, q is the mixing ratio of the hydrometeor based on the WRF output in kg/kg, and the units of W are g/m 3 . As W is the output of the WRF model, the PSD 115 of the gamma distribution was mainly determined by two parameters, i.e., D0 and  . According to Miles et al. (2000) and Yin et al. (2011), we simulated the PSD with a D0 and  ranging from 0.005-0.05 mm and 0-4, respectively.

Rain
Owing to the effects of surface tension, aerodynamic force, and hydrostatic gradient force, raindrops often take the shape of an oblate spheroid (horizontal axis (a0) > vertical axis (b0)), with an increase in the size of the raindrop. Here, we used the 120 axis ratio model proposed by Brandes (2002): where D is the equivolume diameter. The scattering and attenuation characteristics of raindrops were calculated using the Tmatrix method. Considering the influence of aerodynamics on the direction of raindrop particles, the canting angle of raindrops was assumed to be a Gaussian distribution with a mean value of 0 and a standard deviation (SD) of 7° (Zhang, 125 2017).
The PSD of raindrops was still modeled as the Gamma distribution shown in Eqs. (1) and (2), where W was calculated based on the rain mixing ratio from the WRF output. According to Bringi (2001), D0 and  were uniformly distributed in ranges of 0.5-2.5 mm and -1 to 4, respectively.

Cloud ice 130
Cloud ice is mainly composed of various non-spherical ice crystals; the size and shape of ice crystal particles are complex and diverse, which depend on the cloud temperature and whether the particles have experienced collision and merging processes in the cloud (Heysfield et al., 2013;Ryzhkov and Zrnic, 2019). The database in Liu (2008) can be used to examine the scattering characteristics of ice crystals with different shapes. Here, we used the T-matrix to calculate the scattering properties of ice crystals: spheroid and cylinder were mainly considered as the shapes. The spheroid was treated as a 135 horizontally aligned oblate spheroid with an axial ratio of 0.6 (Hogan et al., 2012); the relation between the larger and smaller dimension of cylinder was as follows (Fu, 1996): The distribution of the orientations in ice particles is variable, which depends on their falling behavior. According to Melnikov and Straka (2013), we set the ice crystal orientations as a Gaussian distribution, with a mean canting angle of 0° 140 and SD between 2° and 20°.
The PSD of cloud ice is similar to that of raindrops, mainly as an exponential or Gamma distribution. Here, the normalized Gamma distribution was adopted; the relation between the number concentration, NW, and D0 is as follows: where is 0.917 g/cm³ and W is the water content of cloud ice from WRF output. 145 According to Heymsfield et al. (2013), the total number concentration, Nt, is a function of the temperature, T: The maximum diameter, Dmax, is also dependent on T: where T is in º C, Nt is in m -3 , and Dmax is in mm. Given T and the water content of cloud ice, W, as well as the empirical 150 value of  , we can solve D0 from Eqs. (1), (6)-(8) and the following formula: Owing to the monotonicity of the functions, D0 can be easily solved numerically. For cloud ice,  usually ranges from 0 to 2 (Tinel et al., 2005;Yin et al., 2011).

Snow 155
Snowflakes are usually caused by the conglomeration and growth of ice crystals. Although the shapes of snowflakes are irregular, they can also be modeled as spheroids, typically with a constant axis ratio of 0.75 (Nowell et al., 2013;Zhang, 2017). As snowflakes fall with their major axis mainly aligned in the horizontal direction, the mean canting angle of snow is normally assumed to be 0 º and the SD of the canting angle is assumed to be 20 º (Zhang, 2017). The width of the canting angle distribution grows with an increase in aggregation. Garrett et al. (2015) showed that the average SD of moderate-to-160 heavy snow, consisting of dry aggregates, is approximately 40º .
The PSD of graupel is modeled as an exponential distribution; the distribution parameters are constrained by the masspower function relationship (Kneifel et al., 2011;Lin et al., 2011;Matrosov et al. 2007;Tomita, 2008): 165 where N0 is the intercept parameter ( usually between 10 3 -10 5 mm -1 m -3 ) and m(D) and () s D  are the mass and density of the particle, respectively.
Constants a and b strongly depend on the snow habit and microphysical process that determine snow growth, which are usually determined experimentally. The exponent value of b is generally a Gaussian distribution, with a mean of 2.1 170 (Heymsfield et al., 2010;Von et al., 2017). The prefactor of a can vary considerably, and the value of a increases with the aggregate density or riming degree (Huang et al., 2019;Ryzhkov and Zrnic, 2019;Sy et al., 2020;Wood et al., 2015). Most of the mass and density relations in previous studies (Brandes et al., 2007;Sy et al., 2020;Szyrmer and Zawadzki, 2010;Tiira et al., 2016) showed that the prefactor a between 0.005 and 0.014 cgs units (i.e., in g/cm b ), where D and m are in centimeters and grams; the mean value is approximately 0.009. The relations in different studies (Brandes et al., 2007;Mason et al., 2018;Tiira et al., 2016;Wood et al., 2015) vary slightly: the primary difference is the diameter expression for the maximum dimension diameter, Dm, median volume diameter, D0, or volume equivalent diameter, D. In this study, the diameter in the mass and density relations were converted to D according to the assumed axis ratio.

Graupel
Graupel is generated in convective clouds by the accretion of supercooled liquid droplets on ice particles or by the freezing 180 of supercooled raindrops lofted in updrafts. Actual graupel altitudes are highly variable because graupel is often observed in deep convection systems with strong up-and downdrafts. The density of graupel varies substantially depending on their formation mechanism, time of growth from the initial embryo, liquid water content, and ambient temperature. It is generally between 0.2 and 0.9 g/cm 3 ; the typical value is 0.4 g/cm 3 (Heymsfield et al., 2018;Ryzhkov and Zrnic, 2019).
Generally, graupels have irregular shapes. Here the shape of graupel was modeled as a spheroid, where the axis ratio 185 was modeled as (Ryzhkov et al., 2011): where w  is the axis ratio of raindrops, and fw is the mass water fraction. The SD of the canting angle, δ, was parameterized as a function of fw: where c is an adjustment coefficient , set usually as 0.8 (Jung et al., 2008).
The PSD of graupel is still assumed to be an exponential distribution, as shown in Eqs. (10)-(12). In convective clouds, a large part of graupel likely develops via collisions between frozen drops and smaller droplets; its bulk density decreases with an increasing graupel size (Khain and Pinsky, 2018). Similar mass relations can be found for graupel, but exponent b is higher compared with snow. Exponents for low-density graupel are approximately 2.3 (Erfani and Mitchell, 2017;von 195 Lerber et al., 2017) while lump graupel approaches 3.0 (Mace and Benson, 2017;Mason et al., 2019). The mean value of b is approximately 2.6 and prefactor a varies mainly between 0.002 and 0.006 g/cm b (Mason et al., 2018;Heymsfield et al., 2018), where the units for m and D are in grams and centimeters.

Melting modeling
Neglecting evaporation and the small amount of water that may collect on the particle owing to vapor diffusion, during the 200 evolution process of snow from dry snow to wet snow and complete melting into water, we assumed that the mass of snow was conserved:

205
If the mass fraction of melt water in the particle of fw is known, the density of melting snow can be obtained as follows ): (1 ) Besides, the density of snowflakes follows the power-law relation in Eq. (11). The exponent b in Eq. (11) can be approximately set as 2.1 and coefficient a can be obtained according to the exponential relationship between the density and 210 diameter, where density is calculated from Eq. (16) with an assumed fw value.
Due to melting, the uniform bin size set no longer applies, such that a new bin size must be calculated. According to Eqs. (11) and (15), the relation between the particle diameters can be obtained as follows: where the equivalent-mass melted diameter Dms corresponding to diameter Ds of each dry snow particle was calculated from 215 Eq. (15).
The bin size for rain (dDw) can be obtained by differentiating as follows According to the mass conservation model, the total liquid water content of a distribution is conserved. The number concentration of raindrops (Nw) in each size was calculated as follows 220 where ()

ms ms
NDis the number concentration of melting particles.

Radar equation
The signal power, Pr, received by the radar was calculated based on the radar equation: where Pt is the transmitted power, r0 is the range to the atmospheric target, C is the radar constant related to the instruments, and k is the attenuation coefficient. The radar equivalent reflectivity factor, Ze, was calculated from the scattering characteristics and the assumed PSD of the various hydrometeors: where () b D  is the backscattering cross section of the particle with a diameter D,  is the radar wavelength, and 230 where nw is the complex refractive index of water for a given wavelength and temperature. For spaceborne millimeter wave radar, the equivalent radar reflectivity factor (hereafter, radar reflectivity) observed by the radar is the attenuated radar reflectivity factor, Ze0: where the units of k are 1/km, Qt is the extinction section of the corresponding hydrometeor calculated by the T-matrix 235 (mm 2 ), the units of N(D) are m -3 mm -1 , and the unit of dD is mm. In the actual simulation process, a look-up table of backscattering and extinction cross-sections is established for reducing the calculation workload, which is under different diameters, temperatures, and liquid water volume ratios according to the physical models of the hydrometeors.
If there are many types of hydrometeors at the same height, the equivalent radar reflectivity of each hydrometeor is calculated based on the look-up table; then, the total radar reflectivity at this height is obtained by adding all types of 240 hydrometeors. Considering the difference between the resolution of the simulation data and the observation resolution of the instrument, the convolution of the simulation echo and antenna pattern were also performed during the coupling process of the simulation data and instrument parameters, in which the antenna pattern was set as a two-dimensional Gaussian distribution.
After coupling with the antenna pattern, the final radar reflectivity was obtained. Here, Ze has units of mm 6 /m 3 and it is 245 usually expressed in decibel form as 10 10*log ( ) ee dBZ Z = .

PSD parameters
The Gamma distribution is determined by three parameters. As one of the parameters is obtained from the water content, 255 W, of the hydrometeor in the WRF output, we mainly considered the effects of D0 and  on the radar reflectivity. Figure 2 shows the change in the radar reflectivity with variations in the gamma PSD parameters for cloud water and rain. Cloud water particles are relatively small in wavelength, which is in the linear growth stage in the Mie scattering region; the larger D0 corresponds to more large-size particles, which leads to stronger echoes. With a five-fold increase in D0, e.g., increasing from 10 to 50 m  , leads to an increase in the reflectivity of approximately 20 dB. For rain particles, the impact of D0 is not 260 as significant as that of cloud water: a five-fold change in D0 can lead to a change in the reflectivity within 5 dB. Owing to the Mie scattering effect on raindrops, the contribution from relatively small raindrops may be more than that from larger raindrops considering the influence of the number concentration. In the gamma PSD, the effect of  is relatively small; the change in the reflectivity caused by  is within 1.5 dB when using a constant D0.
For cloud ice, D0 is calculated from Eq. (9) given W and T;  is the only parameter that needs to be assumed. Figure 3a   265 and b show the reflectivity change with W and  , where Fig. 3a was obtained when T was -20 º C and Fig. 3b was obtained when T was -60 º C. As the PSD of cloud ice was constrained by the total number concentration, D0 and  are interrelated and D0 increases with an increase in  , W, and T. Based on Fig. 3a and b, we observed that when  varies from 0 to 2, the maximum reflectivity change is approximately 4 dB at -20 º C while that at -60 º C is approximately 5 dB. The reflectivity change was still affected by the D0 variation. Based on Eq. (9), D0 varied from 0.1-0.5 mm at -60 º C and 0.2-0.8 mm at -20 270 º C when W ranged from 0 to 0.5 g/m 3 . Figure 3c and d show the reflectivity change caused by D0 and  under a conventional gamma PSD without constraints on the total number concentration. In the conventional gamma PSD, the D0 and  vary independently; the reflectivity can change by 13 dB when D0 varies from 0.2 to 0.8 mm. The results showed that the effect of PSD parameter variation on the reflectivity can be reduced by approximately 60 % owing to constraints on the total number concentration for the PSD of cloud ice. 275 An exponential PSD with a power-law mass spectrum was used for snow and graupel. Figure 4 shows the effects of intercept parameter N0 and the mass power-law parameters of prefactor a and exponent b. With the mean mass-size relationships for snow and graupel, changing the dBN0 (dBN0 = log10(N0)) from 3 to 5 could cause a reflectivity increase of approximately 7-8 dB. With a constant N0 and mean value of exponent b, the reflectivity change caused by variation in prefactor a from 0.005 to 0.013 g/cm b for snow and 0.02 to 0.06 g/cm b for graupel can reach 8-9 dB. Using an average mass-280 power relation assumption, the variation in a may result in an uncertainty of approximately 45 % and 30 % for snow and graupel, respectively. For snow and graupel, exponent b is approximately 2.1 and 2.6, respectively. For analyzing the effect of the variation in b, a Gaussian distribution of b was modeled. According to the range in b, the standard deviation (SD) was assumed to be 0.5 and 0.3 for snow and graupel, respectively. The error bars in Fig. 4c and f represent the SD of the reflectivity change caused by variation in b, which was generally less than 2 dB for snow and 0.5 dB for graupel. The results 285 showed that the sensitivity of reflectivity to prefactor a was substantially greater than that of exponent b.

PSD models
The PSDs of hydrometeors can usually be represented as different models, such as the Gamma distribution and lognormal distribution, which are frequently used in cloud water PSDs. This section discusses the influence that the selection of different PSD models has on radar reflectivity factor, taking cloud water as an example. Figure 5a shows two PSD models of 290 cloud water, in which the black solid line represents the Gamma distribution, and the red-dotted line represents the lognormal distribution. The lognormal distribution uses the following formula: where Dm is the mass weighted diameter,  is the dispersion parameter.
The parameters in the PSD model in Fig. 5a are based on the typical parameter settings for cloud water in terrestrial 295 stratiform clouds (Mason, 1971;Miles et al., 2000;Niu and He, 1995), where D0 is 20 mm,  is 2 in the Gamma distribution, Dm is 20 mm,  is 0.5 in the lognormal distribution, and W in both PSD models are set to 1g/m 3 . The Gamma distribution (blue line) is the result of changing D0 (black line) from 20 to 30 mm; the objective is to obtain similarity between the Gamma and log-normal models. Corresponding to the typical parameter settings of the Gamma and log-normal distributions, the difference between the two PSDs was notable; the reflectivity caused by the different PSD models was approximately 4.5 300 dB. For the gamma distribution (D0 of 30 mm and log-normal distribution), there was still a difference in the radar reflectivity of approximately 0.8 dB. This result showed that the PSD model had a certain impact on echo simulation; it was necessary to carefully select the PSD model and set the parameters according to the type of cloud and precipitation.

Particle shape and orientation
The scattering properties of particles are sensitive to the hydrometeor shape and orientation. Previous studies (Marra et al., 305 2013;Masunaga et al., 2010;Seto et al., 2021;Wang et al., 2019) often assume that the hydrometeor particle is a sphere, but most particles are non-spherical. This section discusses the influence that cloud ice, snow, graupel, and rain particle shapes (cloud water is generally spherical) have on radar reflectivity. Figure 6 compares the backscattering cross-section and corresponding radar reflectivity under different shapes of cloud ice, dry snow, and rain. Three shape types, i.e., sphere, spheroid, and cylinder, for cloud ice were mainly considered, where 310 the shape parameter setting refers to section 2.2.3. The solid and dotted lines in Fig. 6a indicate that the SD of the canting angle (  ) is 2º and 20º , respectively. The radar reflectivity factor in Fig. 6b  sphere and non-sphere when the diameter was greater than 1 mm. Figure 6b shows that the spherical assumption may result in an average overestimation of the reflectivity by approximately 6 %. The reflectivity difference caused by  was 315 approximately 1 %. Figure 6c shows the backscattering section of dry snow with a constant density of 0.1 g/cm 3 , where the axis ratio of the spheroid was 0.75 and the SD of the canting angle was assumed to be 20º and 40º , respectively. When calculating the radar reflectivity factor, the corresponding exponential distribution parameter was N0 = 3 × 10 3 m -3 mm -1 and the average reflectivity difference between the sphere and spheroid reached approximately 8 % for a  of 20º and 4 % for a  of 40º . For raindrops, the apparent backscattering difference appeared after the equivalent diameter was 2 mm, as shown 320 in Fig. 6e. The reflectivity in Fig. 6f was obtained with a Gamma PSD parameter of D0 = 1.25 mm and =3  . The reflectivity difference caused by the particle shape was negligible. This is because particles less than 2 mm mostly contribute to the radar reflectivity for rain. The influence of shape on raindrops can be negligible.
The axis ratio and particle orientation change with variations in the density of snow and graupel. Figure 7 compares backscattering and corresponding radar reflectivity for graupel between spheres and spheroids at different densities and 325 orientations. The influence of particle shape on snow is similar to graupel (figures not shown here). The SD of the canting angle in Fig. 7a was calculated according to Eq. (14). Here,  was 54º at a density of 0.4 g/cm 3 while  was 20º at a density of 0.8 g/cm 3 . Based on Fig. 7a, the backscattering section difference increased with density, which may have been due to the stronger refractive index. Figure 7b shows the corresponding radar reflectivity for particles in (a), where the PSD was assumed to be an exponential distribution with N0 of 4 × 10 3 m -3 mm -1 . The spherical assumption may cause an average 330 overestimation of the reflectivity by approximately 4 % when the density is 0.8 g/cm 3 and  is 20º , whereas the reflectivity difference is negligible at  of 54º and density of 0.4 g/cm 3 . This result showed that, besides particle shape, the particle density and orientation should also be considered in the scattering simulation.

Simulation results for typical cases
Based on the sensitivity analysis of typical cloud physical parameters, we simulated the radar reflectivity of typical cloud 335 scenes by assuming appropriate physical parameters for different hydrometeors and cloud precipitation types with the hydrometeor mixture ratio from the WRF as input. The simulation results were compared with CloudSat observation data.
We then showed two typical weather cases: a cold front stratiform cloud and deep convective process.

WRF scenario simulation 340
From September 24 to 25, 2012, there was a large-scale low trough cold front cloud system in northwest China, which moved from the west to the east and entered Shanxi Province. The CloudSat satellite observed the stratiform cloud process https://doi.org/10.5194/egusphere-2022-886 Preprint. of CloudSat, this stratiform cloud process was simulated by the WRF model. This experiment adopted a one-way scheme with a quadruple nested grid. From the inside to the outside, the horizontal resolution was 1, 3, 9, and 27 km. It is divided 345 into 40 layers vertically and the top of the model was 50 hPa. Figure 8a shows the simulation area for the two internal layers (d03 and d04), in which the black line is the trajectory of the CloudSat CPR. Figure 8b shows the 3-D distribution of the total hydrometeor output of the WRF corresponding to the innermost grid. The hydrometeors were cloud water, snow, cloud ice, and rain. The hydrometeors were mainly distributed below 10 km; the maximum total water content was at approximately 3 km, ~0.9 g/m 3 . 350

Radar reflectivity simulation results
For comparison with CloudSat data, the two-dimensional (2-D) hydrometeor profile from the WRF model on the track matching CloudSat was selected as the input for the radar reflectivity simulation. The WRF data at 04:30 AM was selected.
Owing to the uneven output height layer of the WRF, data for the WRF simulation results were interpolated in the vertical direction; the vertical resolution of the interpolated data was 240 m, corresponding to the CloudSat CPR data. 365 Figure 9a-e shows the latitude-height cross-section of the hydrometeors in the stratiform case simulated by the WRF for cloud water, cloud ice, snow, rain, and the total hydrometeors. Snow is widely distributed, ranging from 3 to 10 km. Rain is widely distributed with water contents between 0.1 and 0.2 g/m 3 . At approximately 0 º C, the cloud water, snow, and rain were rich, which led to a high total water content, with a maximum of 0.57 g/m 3 .
For the stratiform case, the PSD parameters were assumed based on the typical empirical values of land stratiform 370 precipitation clouds (Mason, 1971;Niu and He, 1995;Yin et al., 2011). As snow in stratiform clouds are mainly unrimed particles (Yin et al., 2017), a mass-power relation representative of unrimed snow (Moisseev et al., 2017) was used in the simulation. In addition, a melting layer model with a width of 1 km was assumed below 0 º C and the PSD parameters of the raindrops were calculated according to the melting model. total hydrometeors, where Fig. 9f shows the reflectivity before attenuation, Fig. 9g shows attenuation, and Fig. 9h shows 375 reflectivity after attenuation. The reflectivity factor above 8 km was mainly a result of weak cloud ice and dry snow, which did not exceed -5 dBZ. The radar reflectivity caused by snow increased with an increase in the water content, up to approximately 10 dBZ. Melting led to an increase in the refractive index and density of snow, which resulted in a sharp increase in the radar reflectivity factor. Before attenuation, the radar reflectivity in the melting layer was equivalent to the reflectivity in the rain region. After attenuation, the radar reflectivity showed a rapid signal decline at the end of the melting 380 region, and the bright band became evident.
For the 94 GHz radar, the Mie scattering effect was dominant; the scattering efficiency tended to be stable when the particle reached a certain diameter. Although larger snowflakes melt and produce larger raindrops at depth in the melting layer, their contribution to the reflectivity factor was not significant owing to a decrease in their number concentration. Therefore, the bright band was not notable before attenuation; the reflectivity factor increased markedly in the upper part of 385 the melting layer but did not decrease considerably in the lower part. However, the bright band at the melting layer was highlighted after attenuation owing to strong attenuation caused by rain, melting snow, and exponential growth of the attenuation.  Figure 10c shows the observation results from the CloudSat CPR. The lines in Fig. 10d show the average vertical profiles of the reflectivity factor in Fig. 10a-c. The echo structure and echo intensity of the simulation results with the optimization setting showed good agreement with the CloudSat observations. The trends in the two profiles were basically identical; the relative error at each height was mostly within 15 %. The location and intensity of the brightness 395 band from the optimization simulation and CloudSat observation were highly consistent; the radar reflectivity peak for both were approximately 12 dBZ at 2.88 km with a bright band width of approximately 0.9 km. Without the melting model, the PSD parameters for raindrops were based on the assumed value. In Fig.10b, the radar reflectivity below 0 ℃ was evidently

Convective case 405
This case was a severe convective weather process that occurred in the Lower Yangtze-Huaihe river on June 23, 2016, in which strong winds and heavy rainfall occurred in Yancheng City, Jiangsu Province. The simulation area covered 32-36°N and 116-120.5°E. Triple nested grids were adopted, with horizontal resolutions of 13.5, 4.5, and 1.5 km. The model simulation results were compared with MODIS observation data and the cloud structure and cloud top temperature were consistent (figure not shown). 410 CloudSat observed this convective process at 04:30 AM on June 23, 2016, covering the cloud region from 32.43°N, 119.13°E to 36.11°N, and 118.10°E. For comparison with the CloudSat data, the vertical cross-section of the hydrometeor matching the CloudSat observation was selected for simulation. Figure 11a-f shows the latitude-height cross-section of the hydrometeor for the convective case simulated by the WRF for the total hydrometeors, cloud water, cloud ice, snow, graupel, and rain. The ice water content of the convective case was rich; the cloud ice, snow, and graupel particles were widely 415 distributed with high contents. Snow existed from 4 to 14 km, with a water content reaching approximately 1.5 g/m 3 .
Graupel particles mainly ranged from 4-8 km, with a maximum water content of 1.2 g/m 3 . Rain was mainly distributed between 34 and 36º N: the water content of the rain near 34.5 and 34.8º N reached 5 g/m 3 .
In the convective case, mixed phase particles, such as snow and graupel, were abundant while the components of snow and graupel were complex. Unlike stratiform clouds, a large percentage of heavily aggregated and/or rimed snow exist in 420 convective clouds (Yin et al., 2017); therefore, rimed particles were assumed for convective clouds modeling. As the prefactor a in the density-power relations increases with the riming degree (Mason et al., 2018;Moisseev et al., 2017;Ryzhkov and Zrnic, 2019), an adjustment factor f was considered in the simulation process, i.e., a=auf, where au is the density prefactor for unrimed snow, and f is obtained by f=1/(1-FR) where FR is the ratio of the rime mass to the snowflake mass. According to Mason et al (2018) and Moisseev et al (2017), we assumed that the rime mass fraction increased with 425 linearly with liquid water path. The exponent b was assumed as the mean value (a constant) based on the sensitivity analysis.
Then, the corresponding refractive index and PSD for snow and graupel were calculated according to the mass-power relations. The other physical parameters, such as the number concentration, were assumed according to the typical parameters of convective cloud precipitation (Ryu et al., 2021;Sun et al., 2020;Yang et al., 2019).  Fig. 11h is the attenuation, and Fig. 11i is the reflectivity after attenuation. Figure 11i shows that the internal vertical structure of the deep convective cloud can be accurately detected, but millimeter wave radar has difficultly penetrating the rainfall layer due to strong attenuation. Figure 12 shows a radar reflectivity comparison between the simulation results and CloudSat CPR observations for the deep convective case, where Fig. 12a-c shows the cross-sections of the reflectivity from simulations with optimization and conventional settings, as well as the CloudSat observations. The 435 main difference between the simulation processes in Fig. 12a and b is that the conventional setting used a constant density for snow and graupel while the density was varied according to the density-power relation of rimed particles in the https://doi.org/10.5194/egusphere-2022-886 Preprint. Discussion started: 22 September 2022 c Author(s) 2022. CC BY 4.0 License. optimization setting. The lines in Fig. 12d are the average profiles corresponding to Fig. 12a-c. Figure 12a and c show that the echo distribution and echo intensity of the simulation and CloudSat observation are in good agreement. The echo top heights were approximately 16 km and the maximum reflectivity factor was approximately 18 dBZ. The hydrometeors for 440 the cloud water, graupel, and rainfall particles were mainly concentrated between 34.5º N and 35.5º N, which produced strong echoes at middle heights and strong attenuation at lower heights. Comparing the profiles with the optimized simulation to that with the conventional simulation in Fig. 12d, the fixed density in the conventional simulation caused the echo at high altitudes to be stronger and the echo at low altitudes to be weaker.
To further illustrate the effect of snow and graupel, Fig. 13 shows the water content and reflectivity profiles for snow 445 and graupel corresponding to the black line in Fig. 12a. Figure 13a shows the vertical profile of the water content of snow and graupel. Figure 13b shows the simulation results corresponding to the hydrometeor profile in Fig. 13a. Relative to the reflectivity results with the conventional simulation, snow and graupel in the optimization simulation showed weak echo at high altitudes and strong echo at low altitudes. The trend in the profile for snow and graupel in Fig. 13b is the same as that in the average profiles shown in Fig. 12d. The vertical profile in the optimization simulation showed good consistency with that 450 of the CloudSat observation, with an average relative error of approximately 20 %. In contrast, the average relative error in the conventional simulation reached approximately 100 %. The simulation results demonstrated that the radar reflectivity is highly sensitive to the prefactor of the mass-power relation of snow and graupel; the effect of riming on the prefactor should be considered in the forward modeling simulations or microphysical parameter retrieval for convective clouds.

Conclusions 455
Active remote sensing with spaceborne millimeter wave radar is one of the most effective means of cloud and precipitation measurements. Many countries are developing next generation spaceborne cloud precipitation radar. During the design and demonstration stage of observation systems and in the interpretation of observation data, forward modeling simulations play a crucial role. The physical characteristics of hydrometeor particles, such as the shape, density, composition, PSD model and parameters, have an important impact on the simulation results. Based on establishing a simulation framework with nine sub 460 modules, we quantified the uncertainty of different physical model parameters for hydrometeors via a sensitivity analysis, presenting radar reflectivity simulations with optimized parameter settings.
The sensitivity of D0 in the Gamma distribution was approximately 5-10-fold greater than that of  ; the variation in  can cause reflectivity changes of less than 10 %. The constraints on PSD modeling from the empirical relationships in the observations using interconnected parameters, rather than independent variations, can significantly reduce the impact of PSD 465 variation. Owing to the constraint on the total number concentration for the PSD of cloud ice, the effect of D0 on the radar reflectivity can be reduced by approximately 60 %. The particle density not only affects the shape and orientation of particles, but also affects the size distribution of the particles. Using the exponential PSD with a power-law density spectrum for snow and graupel, we found that the effects of prefactor a were significantly greater than that of exponent b; variation in a may result in an uncertainty of approximately 45 % for snow and 30 % for graupel. Owing to complex physical characteristics 470 resulting from various microphysical processes, the shape and orientation of frozen and mixed phase particles are variable, which could lead to an average reflectivity difference of approximately 4-8 %. In addition to the PSD parameter and particle shape and orientation, this study emphasized the importance of the particle density parameters and PSD modeling constraints corresponding to different cloud precipitation types in the forward simulation and microphysical properties retrieval.
Two typical cloud precipitation cases were presented. The simulation results were compared with the CloudSat 475 observations. During simulation, we considered the PSD parameter settings for typical cloud precipitation types, particle shapes, melting model, and influence of snow and graupel density relations. For snow and graupel microphysical modeling, unrimed snow particles was assumed in the stratiform clouds, and rimed snow with varying density-power relations was considered in the convective clouds. The simulation results with the optimization setting showed good agreement with the CloudSat observations; the average relative errors in the vertical profile between the simulation and CloudSat data were 480 within 20 %, which improved by 20-80 % compared with the conventional setting, i.e., not considering the melting model and riming effect for snow and graupel. The melting layer modeling for stratiform cloud could accurately reproduce the bright band structure after attenuation. The varying prefactor of density relations of snow and graupel considering the riming effects for convective cloud rendered the simulated echo structure consistent with the observations. The selection and modeling of cloud microphysical characteristics not only affects the forward simulation and 485 numerical modeling, but also has a significant impact on physical parameter retrieval. This study contributes to a quantitative understanding of the uncertainties of forward simulations or radar retrievals due to variation in the microphysical properties of hydrometeors. They also provide a scientific basis for the analysis of millimeter wave radar observation data, the optimization of parameter settings in forward modeling, and microphysical constraints in parameter retrievals. The sensitivity test and simulation results suggest that accurate estimation of at least two parameters in the size distributions of 490 hydrometeor particles including particle density factor is beneficial using certain methods, such as multiband measurements.
Sensitivity to the particle shape and orientation demonstrates that increasing the polarization function is useful for analyzing the microphysical properties of frozen and mixed hydrometers. In future studies, we will consider establishing a cloud database for further optimizing prior information constraints by collecting a large amount of typical cloud precipitation