The PR was the first spaceborne precipitation radar onboard the TRMM. It is a single-frequency microwave radar operating at 13.8 GHz (Kummerow et al., 1998; Kozu et al., 2001). PR scans in the cross-track direction at a scanning inclination of 17°. There are 49 pixels on each scanning line. The horizontal resolution is about 4.3 km at nadir (5.0 km after the orbital boost), and the scanning width is 215 km (245 km after the orbital boost). It can detect the three-dimensional structure of precipitation from mean sea level to 20 km (a total of 80 layers) with a vertical resolution of 0.25 km.

The 2A25 data are the second-level data product of the TRMM PR, which are generated by inverting the echo signals detected by the PR. This dataset mainly includes scanning time, geographic information, three-dimensional rain rate, rain type and so on (Awaka et al., 1997). The detection sensitivity of the PR is about 17 dBZ, corresponding to the rain rate of about 0.4 mm h⁻¹ (Schumacher and Houze, 2003). Therefore, when the rain rate of the pixels is lower than 0.4 mm h⁻¹, a default value is assigned, and those pixels are not included in the calculation.

The VIRS scans in the cross-track direction with a scanning angle of 45°. There are 261 pixels on each scanning line. The scanning width is 720 km (833 km after the orbital boost), and the horizontal resolution is 2.2 km at nadir (2.4 km after the orbital boost). It has five channels from the visible to the far infrared band: CH1 (0.63 µm), CH2 (1.6 µm), CH3 (3.7 µm), CH4 (10.8 µm) and CH5 (12.0 µm). The 1B01 is a first-level data product of VIRS, which includes the reflectance at CH1 and CH2, the infrared radiation brightness temperature at CH3, CH4, and CH5 after correcting and calibrating the VIRS detection results.

The TMI is a nine-channel passive microwave radiometer with five frequencies spanning from 10 to 85 GHz. The microwave signal frequencies are 10.65, 19.35, 21.3, 37.0, and 85.5 GHz, with 21.3 GHz being a single vertical polarization channel. The other four frequencies are dual horizontal (H) and vertical (V) polarization channels. The scanning width is 760 km (878 km after the orbital boost). The horizontal resolution of each frequency channel (effective field of view of beam, Kummerow et al., 1998) varies from 63 km × 37 km at 10.65 GHz to 7 km × 5 km at 85.5 GHz. The 1B11 data contain the calibrated TMI-detected microwave brightness temperature at multiple channels.

To comprehensively analyze the parameters of precipitation, cloud top spectral signal and particle phase in precipitation systems, the rain rate profile and echo profile of 2A25, the reflectance and infrared temperature of 1B01, and the microwave brightness temperature of 1B11 were collocated in PR horizontal resolution to produce a merged dataset. The reason for that is the difference spatial resolutions of the three instruments, but the time lag of observation among the three instruments to the same target is less than 1 min, i.e., the quasi-synchronous observations (Liu et al., 2008; Fu et al., 2011; Sun and Fu, 2021). Statistics show about 7 VIRS pixels within 1 PR pixel. It was found that the spectral signals of VIRS changed weakly after merging; the mean change was less than 0.7 %, and the mean square deviation was less than 2.5 % (Fu et al., 2011). Because TMI channels have different spatial resolutions that are larger than PR pixel resolution, the nearest neighbor method was used to obtain microwave brightness temperature at PR pixel resolution, i.e., each PR pixel was assigned the microwave brightness temperatures of nine channels from a TMI pixel closest to the PR pixel (Liu et al., 2008).

The definition of rain cell in this study is the same as that proposed by Fu et al. (2020), i.e., a rain cell consists of at least four connected rain pixels within the swath of PR's scan. This also eliminates those tiny rain cells smaller than four rain pixels. In the process of identifying rain cells, the eight-connected domain method is used. According to the working mode of PR, its swath consists of 49 pixels (from number 1 to 49), so if the identified rain cell has pixels at the PR swath edge (the first pixel and 49th pixel), the rain cell is not included. If the identified rain cell is at the beginning or end of the PR swath, the rain cell is also eliminated. The advantage of this is to avoid the truncation effect of PR swath. For the identified rain cells, this study utilizes the minimum bounding rectangle (MBR) fitting method and the best fit ellipse (BFE) fitting method to calculate the geometric parameters. The two methods can fit an ellipse and a rectangle frame with the smallest area covering the target object (rain cell), as done by Nesbitt et al. (2006) and Fu et al. (2020), respectively. There are differences in the geometric parameters calculated by the MBR and BFE fitting methods, such as the area of the external frame and spatial morphology index of rain cell. However, the physical parameters are unaffected by both methods. The rain cell parameters calculated in this study by the two fitting methods can be used by studies according to their own preferences.

The definitions of geometric and physical parameters describing the identified rain cell were almost the same as that of Fu et al. (2020). The specific geometric parameters are listed in Table 1, in which the first six parameters describe the horizontal geometry of rain cells and the rest describe the vertical geometry. These parameters have a clear physical meaning, such as α, which represents the horizontal shape of a rain cell, a small (large) α indicates that the horizontal shape of rain cell is more like a strip (square) precipitation system, and it has more (less) correlation with a frontal precipitation system. The variable β expresses the ratio of a rain cell's area (Srain) to the area of a rectangle or ellipse frame (S), and characterizes the effectiveness of both methods used to fit the external frame of rain cells. A large (small) β indicates a larger (smaller) number of rain pixels inside the rectangle or ellipse frame. The variables γmax and γav represent the three-dimensional spatial shape of a rain cell. Small γmax (γav) indicates a “squatty” appearance of a rain cell, in contrast to a “lanky” appearance for larger γmax (γav).

The physical parameter definitions of rain cells are listed in Table 2 including rain type, rain rate profile, reflectivity factor profile, mean rain rate, visible reflectance and infrared brightness temperature, microwave brightness temperature and so on. These parameters are significant for characterizing the intensity, the inhomogeneity, and the evolution stage of rain cell.

In order to better understand the geometric and physical parameters of rain cells using the MBR and BFE fitting methods, two rain cells are analyzed below. One identified rain cell A occurred on 2 June 1999 in the southern Tibetan Plateau (TRMM orbit 08691), and the other, rain cell B, on 13 June 2003 in the eastern Tibetan Plateau (TRMM orbit 31787). Figure 1 shows the distribution of rain rate and rain type for the two rain cells. The frames of both methods are also plotted, which clearly shows the length and width of the frame from the MBR fitting method, and the long and short axes of the frame from the BFE fitting method. Table 3 lists the statistics of parameters for the two rain cells. Figure 1a shows that rain cell A applying the MBR fitting method has length 291.25 km (Lr), width 140.68 km (Wr), rain area 10 223.50 km² (Srain), MBR area 40 971.84 km² (Sr), and filling ratio 0.25 (βr). The horizontal shape index is 0.48 (αr), which indicates rain cell A with a strip like shape. The rain cell A applying the BFE fitting method (Fig. 1c) has length 345.88 km (Le), width 144.08 km (We), rain area 10 223.50 km² (Srain), BFE area 39 140.42 km² (Se), and filling ratio 0.26 (βe). The horizontal shape index is 0.42 (αe), which also indicates rain cell A with a strip like shape. Rain cell B, shown in Fig. 1b and d applying the MBR and BFE fitting method, has parameters listed in Table 3 that show it is slightly strip-shape.

The vertical parameters of both rain cells are also listed in Table 3. The variables γmax and γav are affected by the fitting method. Comparing rain cell A and B, the latter has higher echo tops (Hmax=17.75 km, Hav=9.47 km), and shows a “lanky” appearance (γmax=0.11, γav=0.08 in the MBR fitting method; γav=0.07 in the BFE fitting method). In rain cell B, the mean echo top height of convective precipitation (10.39 km) and stratiform precipitation (7.96 km) is also higher than those in rain cell A (Havc=5.76 km, Havs=5.58 km), which indicates that rain cell B has stronger updraft velocity and a deeper precipitating cloud. The ratio of the maximum reflectivity factor height to the maximum echo top height, μ, is 0.37 and 0.15 for rain cell A and B, respectively. By combining γmax and μ, it can be concluded that rain cell B is a deep precipitation system with large particles in the lower part of the cloud.

The physical parameters of both rain cells are listed in Table 4. PR observation shows that the mean rain rate RRave and the maximum rain rate RRmax of rain cell B are 11.64 and 113.14 mm h⁻¹, respectively, while rain cell A is a relatively weak rain cell. The defined physical parameters also show that the mean convective rain rate of rain cell A is 5.52 mm h⁻¹, and that of rain cell B is 17.35 mm h⁻¹. Meanwhile, the mean stratiform rain rate of rain cell A and rain cell B are 1.16 and 2.31 mm h⁻¹, respectively. The convective area fraction to total precipitation area (CAF) and stratiform area fraction to total precipitation area (SAF) are 2.56 % and 97.3 % for rain cell A, and 62.01 % and 37.99 % for rain cell B, respectively. The convective precipitation contribution to total precipitation (CPC) and stratiform precipitation contribution to total precipitation (SPC) are 11.14 % and 88.79 % for rain cell A, and 92.46 % and 7.54 % for rain cell B, respectively. This indicates that rain cell B is a convective rain cell while rain cell A is a stratiform rain cell. Rain cell B reaches the maximum reflectivity factor at an altitude of 2.75 km, while rain cell A reaches its maximum at 3.25 km. However, the dBZmax of rain cell B is 57.81 dBZ, which is much higher than that of rain cell A (36.38 dBZ). This reflects that there are relatively large particles at the bottom of rain cell B in the cloud.

Since TRMM PR, VIRS, and TMI observed the same target in spatiotemporal synchronization, the spatial distributions of visible reflectance (0.63 µm) and far-infrared brightness temperature (10.8 µm) for the two rain cells are shown in Fig. 2. The figure also shows the external frames of rain cells using the MBR and BFE fitting methods. It indicates many strips of reflectance (larger than 0.8) and a uniform distribution of brightness temperature (varying from 240 to 250 K) for rain cell A, while rain cell B consists of two convective clouds with reflectance greater than 0.85 and brightness temperature lower than 220 K. Table 4 also shows the calculated mean visible reflectance RF1ave for the two rain cells (0.72 for rain cell A and 0.69 for rain cell B, respectively). The RF1avc (RF1avs) for rain cell A is 0.73 (0.72), and for rain cell B, it is 0.66 (0.73). The large reflectance values indicate that the cloud optical thickness at the top of the two rain cells is large. The mean brightness temperature at VIRS channel 10.8 µm (TB10.8_ave) is 253.65 and 222.96 K for the two rain cells, indicating that rain cell B has a higher cloud top, i.e., the ice phase is distributed at the cloud top, while the cloud top of rain cell A has an ice-liquid mixed phase. The values of TB10.8_avc are lower than those of TB10.8_avs, which indicates that the cloud top height of convective rain pixels is higher than that of stratiform rain pixels. The signals of VIRS channels can be used to retrieve cloud parameters. The retrieval algorithms have been studied and reviewed by many authors (Nakajima and King, 1990; Rossow and Garder, 1993; Han et al., 1994; Rossow and Schiffer, 1999; Fu, 2014). In addition, the relationship between the precipitation of PR and the brightness temperature of VIRS can be extended to the infrared brightness temperature of geostationary satellites, thereby improving the precipitation forecasting capability of geostationary satellites.

Similar to Fig. 2, the distribution of microwave brightness temperature observed by nine channels of TMI is shown. However, for simplicity, Fig. 3 only plots the distribution of brightness temperature at the TMI horizontal polarization channels 19.4 and 85 GHz. At channel 19.4 GHz, rain cell A shows relatively lower brightness temperature (from 250 to 280 K), while rain cell B has higher brightness temperature (from 260 to 290 K). Because the low-frequency microwave channel is easily affected by the radiation from the land surface, it can be judged that the temperature of land surface in rain cell A is lower than that in rain cell B. The brightness temperature of microwave high frequency channels is mainly affected by the composition of ice phase inside cloud, such as ice particles and supercooled water, while the influence of land surface radiation on these channels is weak. The more content of ice phase composition inside the cloud, the lower brightness temperature at these high frequency channels. According to this principle, rain cell B shows low brightness temperature at 85 GHz in Fig. 3d because the rain cell belongs to a deep convective precipitation system. Because rain cell A has more stratiform precipitation and fewer ice particles, its brightness temperature at the same channel is higher. In Table 4, the mean brightness temperature at channel 19.4 and 85 GHz also indicates the difference between the two rain cells and between the two rain types. The microwave brightness temperature of TMI channels can be used to retrieve cloud parameters such as ice water, liquid water, or rain rate based on retrieval algorithms of previous studies (Grody, 1976; Grody et al., 1980; Liu and Curry, 1993; Petty, 1994a, b; Wang et al., 2009; Fu, 2021). The rain rate from PR can also help optimize the passive microwave inversion of precipitation results. The related algorithms can be extended to the same microwave instruments on different platforms in the future.

In order to visually display the parameter distributions of rain cells A and B using the MBR and BFE fitting methods, Fig. 4 shows the distribution of rain rate, reflectance at VIRS visible channel, brightness temperature at VIRS thermal infrared channel, and microwave brightness temperatures at TMI low-frequency and high-frequency channels. It must be pointed out that both VIRS and TMI signals in Fig. 4 correspond to PR precipitation pixels (that is, signals corresponding to each PR pixel's resolution), and these signals are not provided if no precipitation exists in the rain cell. Therefore, the rain cell data established in this study facilitate the study of the relationships among precipitation, visible/infrared, and microwave signals. The combination of multi-source data can effectively enhance the understanding of precipitation systems.

A simple application is shown in Fig. 5, which displays the multi-parameter distribution along the AB line and EF line in Fig. 4a and b, respectively. The vertical cross sections of reflectivity factor (Fig. 5a and b) show that rain cell A is a shallow and weak precipitation system, while rain cell B is deep convective precipitation system. The strong echo (greater than 38 dBZ) of rain cell B reaches higher altitude, nearly 16 km. The visible reflectance (Fig. 5c and d) from the cloud tops of the two rain cells varies between 0.4 and 0.8, and the reflectance of the strong echo region in rain cell B is higher (greater than 0.6). The near-infrared reflectance (Fig. 5c and d) varies from 0.1 to 0.4, which means there are a lot of ice particles inside the cloud of the two rain cells. The infrared brightness temperature at VIRS channel 3.7 µm (Fig. 5e and f) shows higher values in rain cell A, relatively lower in rain cell B. At VIRS channels 10.8 and 12.0 µm, rain cell A has uniform brightness temperatures, while rain cell B exhibits the characteristics of a deep convective cloud top, with low brightness temperature. For the four horizontal polarization channels of TMI (Fig. 5i and j), the microwave brightness temperature of rain cell A is uniformly distributed, and the brightness temperature of each channel has little difference. In rain cell B, the brightness temperature at low-frequency channels, 10 and 19 GHz, is also evenly distributed, and the brightness temperature at the two channels is higher than that in rain cell A, but the brightness temperature at the 37 and 85 GHz channels changes significantly. Corresponding to the strong echo region in Fig. 5b, the brightness temperature of these two channels is low, indicating that there are more ice particles inside the cloud in strong echo region of rain cell B. The results indicate that the established new data can be used to analyze the spectral signals and microwave characteristics of precipitating clouds.