Early Detection of Convective Echoes and Their Development Using a Ka-Band Radar Network

: Cumulonimbus clouds, which cause local heavy rainfall and urban ﬂoods, can develop within 20min after being detectedby operational centimeter-wavelength(X-,C-, or S-band)weatherradars.To detect such cloudswith greater lead times, Ka-band radars at a wavelength of 8.6mm together with operational X-band radars were used in this study. The vertically averaged radar reﬂectivity (VAR) of convective echoes detected by the Ka-band and X-band radars were deﬁned as mesoscale cloud echoes (MCEs) and mesoscale precipitation echoes (MPEs), respectively. The time series of each echo was analyzed by an echo tracking algorithm. On average, MCEs that developed into MPEs (denoted as developed MCEs) were detected 17min earlier than the MPEs and 33min earlier than the peak time of the area-averaged VAR (VARa) for MPEs. Some MCEs dissipated without developing into MPEs (denoted as non-developed MCEs). There were statistically signiﬁcant differences between the developed and non-developed MCEs in terms of the maximum VARa values, maximum MCEs areas, and increase amounts of the VARa values and MCE areas for the ﬁrst 6–12min after their detection. Among these indicators, themaximumVARafortheﬁrst9 minshowedthemostsigniﬁcantdifferences. Therefore, an algorithmfor predicting MCE development using this indicator is discussed.


Introduction
In summer, meso-g-scale (spatial scale 2-20 km) cumulonimbus clouds can cause localized heavy rainfall. If such a heavy rainfall event occurs in an urban area, even over a short time, it can result in flooding. Because cumulonimbus clouds develop very quickly, heavy rainfall sometimes occurs only 20 min after such clouds are detected by conventional (S-, C-, or X-band) weather radars (Ishihara 2012;Kim et al. 2012). For flood warning systems, it is therefore important to detect cumulonimbus clouds as early as possible.
Recently, operational X-band radars have been used in Japan to observe cumulonimbus clouds in urban areas. The Japanese Ministry of Land, Infrastructure, Transport, and Tourism installed an extended radar information network (XRAIN) consisting of 39 X-band (wavelength of about 3 cm) multiparameter (MP-X) radars. XRAIN can obtain the distribution of rainfall intensity at the surface every minute in major urban areas and can perform a volumetric scan every 5 min. Nowcasts (short-term precipitation forecasts using XRAIN) based on the vertically integrated liquid (VIL) water content (Hirano andMaki 2010, 2018), vertical vorticity estimated from Doppler velocity (Nakakita et al. 2013), and tracking algorithms for precipitation systems (Yoshida et al. 2012) have been proposed. In recent years, X-band phased array weather radars (PAWRs), which can obtain a threedimensional observation within 30 s, have been developed (Yoshikawa et al. 2013;Yoshida et al. 2013;Ushio et al. 2015).
More recently, a polarimetric PAWR has been developed (Takahashi et al. 2019). The fast observation by PAWRs makes it possible to capture the detailed vertical structure of rapidly developing cumulonimbus clouds. A nowcasting method based on PAWRs that includes vertical advection has also been proposed (Otsuka et al. 2016).
The main target of X-band radars such as MP-X and PAWR is precipitation particles. The X-band radar wavelength cannot be used to observe cloud droplets. To detect cumulonimbus clouds earlier, it is necessary to use millimeter-wave radars. The U.S. Department of Energy has acquired scanning Ka-band (wavelength of 8.5 mm) radars in the Atmospheric Radiation Measurement (ARM) Program . Borque et al. (2014) showed the advantages of the ARM Kaband radar for observing clouds without precipitation. The Korean Meteorological Administration also operates a scanning Ka-band radar in combination with microwave radiometers to study cloud water content estimation (Oh et al. 2018). A scanning Ka-band radar has also been developed in Japan (Hamazu et al. 2003) to observe fog (Uematsu et al. 2005) and the development of cumulonimbus clouds (Sakurai et al. 2012;Nishiwaki et al. 2013;Misumi et al. 2018). Sakurai et al. (2012) showed that the Ka-band radar can detect the first echoes about 15-25 min earlier than X-band radars, and that a rapid increase of radar reflectivity could be an indicator of cumulonimbus development. Nakakita et al. (2017) showed that a Kaband radar can predict the possibility of local heavy rainfall more than 10 min earlier than X-band radars. Few studies have been conducted on short-term precipitation forecasts using millimeter-wave radars because these radars are easily affected by attenuation and it is difficult to apply them to scan the wide areas necessary for tracking the movement of echoes. Another important reason is that an operational network has not yet been deployed.
Denotes content that is immediately available upon publication as open access.
Recently, the National Research Institute for Earth Science and Disaster Resilience has deployed five Ka-band radars in the Tokyo metropolitan area (Maesaka et al. 2015;. This radar network enables the tracking of convective echoes from the initial to the mature stages with a plan position indicator (PPI). The radar network reduces the influence of rain attenuation by observing one cumulonimbus cloud with multiple radars. The Ka-band radar network overlaps the XRAIN observation range, and thus different-wavelength radars can observe the formation and development of cumulonimbus clouds simultaneously.
Another problem in short-term precipitation forecasting using millimeter-wave radars is that it is not known whether the detected early radar echoes will develop into heavy precipitation echoes. The early stage echoes detected by millimeterwave radars may dissipate without causing any precipitation on the ground. Therefore, an indicator is necessary to predict whether the detected radar echoes will develop.
In this study, we observed convective echoes using the Kaband radar network and propose an indicator for predicting the development of early echoes. XRAIN was used for tracking convective echoes in the developing and mature stages. The case studies consisted of local heavy rainfall events in the Tokyo metropolitan area in 2016 and 2017. The algorithm for the identification and tracking of convective cells (AITCC, Shimizu and Uyeda 2012) was used to obtain the statistical characteristics of individual convective echoes. Based on the results, a practical indicator for predicting the development of convective echoes is discussed.

a. Radars
In this study, five Ka-band radars located at Tsukuba (TKB), Ota (OTA), Hanno (HNO), Nishitokyo (NTK), and Matsudo (MTD) were used. These radars were installed to cover densely populated areas in the Tokyo metropolitan area (Fig. 1). The analysis domains correspond to the observation areas of HNO   Fig. 1). The Ka-band radars use frequencies between 34.8 and 34.9 GHz and have a beamwidth of 0.318. A pulse width of 55 ms (long pulse) is usually used with pulse compression technology to improve range resolution and sensitivity. However, such long pulses cannot be used to observe radar echoes within 8.7 km of a radar; this range is covered by short pulses (1.0 ms). The maximum observation range is 30 km and the range resolution is 150 m. The minimum detectable reflectivity is about 217 dBZ in dual-polarization mode (TKB, OTA, and HNO) and about 220 dBZ in singlepolarization mode (NTK and MTD) at the 20-km distance. Each radar performs PPI observations at 4-6 elevation angles every 3 min (TKB: 5.28,8.08,11.58,15.78,20.88,27.28;OTA: 1.68,4.58,7.58,10.68,15.08;HNO: 5.08,7.08,10.58,14.98,20.38;NTK: 6.88,10.38,14.48,19.58,26.218;MTD: 2.78,5.88,10.08,16.48). The outputs are the radar reflectivity Z, Doppler velocity V, and spectrum width W for NTK and MTD, and the differential reflectivity Z DR , specific differential  phase shift K dp , and correlation coefficient r hv , as well as Z, V, and W, for the other radars. The specifications of the Ka-band radars are listed in Table 1.
In general, Ka-band radars are strongly affected by attenuation because of their short wavelengths compared to those of conventional weather radars. Here, attenuation correction for the atmosphere was performed by assuming an attenuation rate of 0.15 dB km 21 (one way). Generally, the specific attenuation depends on temperature and humidity, so it is necessary to consider their time and space variations for accurate correction. However, it is difficult to obtain their temporal and spatial distributions within the observation range. Therefore, the correction was made using a constant value.
Attenuation corrections for Ka-band reflectivity for precipitation particles or cloud droplets have been proposed using dual-wavelength radars (Chandrasekar et al. 2003), a vertical pointing radar (Matrosov 2005), and dual Ka-band radars (Nishikawa et al. 2016). However, the main target of this study is early convective echoes, which appear in environments where the attenuation due to other convective echoes is negligible. Moreover, the networked Ka-band radars reduce the influence of attenuation by observing one echo with multiple radars. Therefore, no correction was made for precipitation particles or cloud droplets.
To remove non-meteorological echoes (such as insects), we regarded cloud echoes when the 5 bins 3 5 rays moving average of the received power P r was larger than a certain noise level: where P r is the received power from the targets. This procedure is adopted because the spatial fluctuations differ between meteorological and non-meteorological echoes. Polarimetric methods (e.g., r hv thresholding) would be more reliable, but two of the five Ka-band radars are non-polarimetric and these methods were not applied in this study. The noise level in Eq.
(1) was calculated by adding the dispersion (4 dB) to the average value of the received power for a clear sky. The noise levels are approximately #2110 dBm for short pulses and #2123 dBm for long pulses, though the values slightly vary with radar. Furthermore, data that included spurious echoes such as range side lobes and second trips were excluded.
The PPI obtained at each radar site was converted to a constant altitude PPI (CAPPI) of Z using the Cressman interpolation method. The horizontal and vertical grid resolutions for the interpolation were 150 and 100 m, respectively, considering the beam spread (162 m) at 30 km from the radar. After interpolation, horizontal smoothing with a 3 3 3 mesh median filter was applied. For grids that could not be interpolated by available data, a 5 3 5 mesh Gaussian filter was applied. Figures 2a and 2b show the CAPPI of Z. Because the interval of the elevation angles is large compared to the beamwidth, the interpolation gaps are conspicuous. Therefore, to fill these gaps and utilize the reflectivity at all levels, we calculated the vertically averaged reflectivity (VAR) from the CAPPI data as VAR i,j 5 10 log 1 where the subscripts i, j, and k represent the grid points along the x, y, and z axes of the CAPPI data, respectively; z ijk is the  radar reflectivity at (i, j, k) (mm 6 m 23 ); and n is the number of vertical grids where z ijk . 0 at (i, j). The unit of the VAR is dBZ. By adopting VAR, a continuous horizontal distribution for the reflectivity was obtained (Fig. 2c). However, because VAR projects three-dimensional information onto a horizontal plane, it should be noted that the data at different elevations may be mixed in each horizontal grid. The number of PPIs that contribute to VAR varies depending on the distance from the radar; it is more than 10 in the analysis domains (Fig. 2d). VAR is similar to VIL, which was not used in this study because it is difficult to obtain the cloud water content from the reflectivity of a Ka-band radar, especially when drizzle is present (Khain et al. 2008).

b. Definition of echoes
For the statistical analysis, radar echoes were classified as follows. In the VAR derived from Ka-band radars, if an area enclosed by a contour line of 220 dBZ was between 3 and 400 km 2 , these echoes are denoted mesoscale cloud echoes (MCEs). For X-band radars, the threshold for the VAR was set to 5 dBZ and the echoes are denoted mesoscale precipitation echoes (MPEs). These thresholds almost correspond to the minimum detectable reflectivity for both radars. The MCE and MPE areas were automatically calculated by the AITCC by counting the number of grids within the outermost contours. The upper limit of the MCE (MPE) area was defined to exclude echoes larger than the meso-g-scale (2-20 km). However, there were no such large echoes in this study. The lower limit of the area was defined to exclude non-precipitation echoes such as ground clutter, which could not be removed by the moving target indication (MTI) method. The MCEs that developed into MPEs are denoted as developed MCEs and those that did not develop into MPEs are denoted as nondeveloped MCEs in this paper.

c. Detection and tracking of echoes
The AITCC was used for the detection and tracking of MCEs and MPEs. This algorithm identifies individual convective cells (CCs) and their groups (convective cell groups, CCGs). First, the AITCC extracts the regions enclosed by contour lines at a certain threshold of reflectivity. The region is defined as a CCG. Then, the CCG is divided into CCs, which consist of a single reflectivity peak and its surrounding areas. In the present study, CCGs derived from the VAR are defined as MCEs or MPEs. They were detected every 3 and 5 min, respectively.
The CCG tracking method in the AITCC is as follows. First, the average movement vectors (MVs) of all CCGs are calculated by the cross-correlation method using radar echoes at successive time steps. Next, MVs for individual CCGs are identified by linking the past and current CCGs using the average MVs. If there are multiple links to one CCG, the similarity is evaluated based on the area, shape, and reflectivity (maximum and average) between the past and current CCGs. If there are multiple CCGs with high similarity, they are determined to be merged/separated. In this study, the tracking results were manually checked; when the characteristics of an MCE (MPE) at a certain time differed significantly from those at the previous time step, they were treated as the formation of a new MCE or MPE. In addition, the MCEs (MPEs) that formed or extended outside of the study area, or that dissipated within two time steps, were excluded from the analysis. Figure 3 shows an example of the MCE detection/tracking results obtained with the AITCC.

d. Cases
We studied local heavy rainfall events that occurred in the study area in August 2016 and 2017. Nakakita et al. (2016) defined a local heavy rainfall event as rainfall with an intensity of 50 mm h 21 observed within 30 min of its onset. In 2016 and 2017, there were four local heavy rainfall events in the study area (Table 3, Fig. 4). All of the cases were in August because deep convection frequently occurs under weak synoptic-scale forcing in the study area. In these cases, local heavy rainfall occurred after the convergence of sea breezes from the east and south (Fig. 4). Such conditions are frequently observed when local heavy rainfall occurs around Tokyo (Fujibe et al. 2002;Saito et al. 2018). Therefore, the study cases are typical of convective events in the Tokyo metropolitan area.

a. Characteristics of developed MCEs
In this section, the characteristics of MCEs are examined based on the time variation of the VAR. Figure 5 shows the horizontal distribution of VAR for developed MCEs observed on 4 August 2016. Two MCEs (M1, M2) were detected at 1403 JST (UTC 1 9 h), and another MCE (M3) formed to the east of M2 at 1412 JST. MPEs for M1 and M2 were detected at 1415 JST, and the MPE for M3 formed at 1420 JST. They continued to develop, reaching their peak VAR at 32 min after their first detection. Figure 6 shows the time series of the area-averaged VAR (VARa) of the MCEs and MPEs. The thresholds for the VAR of MCEs and MPEs are 220 and 5 dBZ, respectively, as described above. VAR varied about two orders of magnitude within a MCE (MPE) (unit: mm 26 m 23 ), and VARa values were close to the 75th percentile of VAR in the early stages of MCEs (MPEs). The time differences (t 1 ) of the first detection between the MCE and MPE were 12 min for M1 and M2 and 8 min for M3, and the time differences (t 2 ) between the first detection of the MCE and the first VARa peak of the MPE (hereafter referred to as the peak time) were 32 min for M1 and M2 and 28 min for M3. At the time when the MCEs formed, their VARa values differed greatly (213.5, 23.4, and 26.6 dBZ for M1, M2, and M3, respectively). However,  the areas of initial MCEs were similar (4.6, 3.6, and 4.8 km 2 , respectively). The areas increased to 20 km 2 when the MPEs were detected. In this case, six developed MCEs were detected. Table 4 shows the characteristics of 15 developed MCEs. The mean values of t 1 and t 2 were 16.7 and 32.7 min, respectively. On average, the increase amount of VARa (DVARa) in the period between the first detection of MCEs and MPEs was 19.2 dB and the average of the maximum VARa (MaxVARa) during this period was 12.9 dBZ. The average increment of the MCE areas (DAREA) was 27.4 km 2 , and the average of the maximum MCE areas (MaxAREA) was 33.6 km 2 in this period.

b. Indicator of MCE development
In this section, we compare the developed MCEs with nondeveloped MCEs to find an indicator to predict MCE development. There were 39 non-developed MCEs. The mean values of the initial VARa and the areas of these MCEs were 210.4 dBZ and 4.6 km 2 , respectively, which are comparable to those of the developed MCEs (28.6 dBZ and 6.2 km 2 ). Therefore, there is no significant difference at the initial stage of MCEs. However, the MaxVARa before the dissipation of MCEs was 23.7 dBZ on average, which is much smaller than that of the developed MCEs (12.9 dBZ before the detection of MPEs). Similarly, the MaxAREA was 8.5 km 2 on average for non-developed MCEs, which is smaller than that of the developed MCEs (33.6 km 2 ). Here, we define elapsed time Dt as the time after the first detection of an MCE. Figure 7 shows histograms of DVARa, MaxVARa, DAREA, and MaxAREA for Dt 5 15 min. There are differences between the developed and non-developed MCEs in terms of these variables. The MaxVARa values show a clear difference; they are always greater than 0 dBZ for developed MCEs and always smaller than 5 dBZ for nondeveloped MCEs. The mean values of the MaxVARa were 13.4 and 23.3 dBZ for the developed and non-developed MCEs, respectively. Differences are also clear for Dt 5 9 min (Fig. 8), but not clear for Dt 5 3 min (Fig. 9). Table 5 shows the results of the Lepage test for Dt 5 15, 12, 9, 6, and 3 min to examine whether the differences between the developed and non-developed MCEs were statistically significant. Except for some variables for Dt 5 3 and 15 min, the differences were significant at the 99% confidence level. Among them, the highest value is for the MaxVARa for Dt 5 9 min. Table 6 shows the threat score (TS) for the prediction of MPEs using each indicator, where the thresholds for predicting developed and non-developed MCEs for each indicator were chosen to maximize the TSs. MCEs whose t 1 was less than Dt were excluded from the calculation of the TSs. The TSs are relatively high when the MaxVARa values were used as an indicator (57.1%, 83.3%, 90%, and 85.7% for Dt 5 6, 9, 12, and 15 min, respectively). The TS is the highest for DAREA (58.8%) when Dt 5 3 min. The mean lead times to the first detection of MPEs are 13.7, 10.7, 7.7, 4.7, and 1.7 min for Dt 5 3, 6, 9, 12, and 15 min, respectively. There is a trade-off between TSs and the lead time, which makes it difficult to declare the best indicator. Nevertheless the MaxVARa produces a TS of greater than 80% and thus provides reliable predictions. Therefore, the MaxVARa for Dt 5 9 min (threshold: 0 dBZ) would be the best indicator for practical forecasting.

Discussion
In the previous section, we examined several variables that characterize the developed and non-developed MCEs. Among them, the MaxVARa for Dt 5 9 min was found to be the best indicator that clearly distinguishes the developed and nondeveloped MCEs. In this section, we discuss a practical application of this indicator for predicting MCE development.
Here, we suppose that MCEs are detected based on the VAR field obtained from Ka-band radars at t 5 t 0 2 Dt (Fig. 10). The VARa values of the MCEs are calculated from this time. After a time period Dt, forecasting starts only for MCEs whose MaxVARa value exceeds a certain threshold at time t 5 t 0 . The MVs are calculated using the movements of MCEs for t 5 t 0 2 Dt and t 0 , and the locations of the MCEs are extrapolated to T minutes ahead along the MV. Finally, the potential regions of heavy rainfall caused by MPEs are forecast along the movement area of the MCEs.
This algorithm aims to detect developing cumulonimbus clouds as early as possible and forecast their rainfall area. The time difference between the first detection of MCEs and MPEs is about 17 min, and that between the first detection of MCEs and the peak time of MPEs is about 33 min. Therefore, if Dt 5 9 min is used, the lead times for the detection of MPEs and their peak time will be 8 and 24 min, respectively. The algorithm is also feasible to C-or S-band radars instead of X-band radars. In such cases, the lead time may vary depending on radar sensitivity.
Next, we discuss the restrictions of the forecast using this indicator. First, this indicator is only applicable to convective echoes formed near Ka-band radar sites because the minimum detectable reflectivity decreases with the distance from radar sites due to attenuation. Because the observation area of Ka-band radars is narrow compared to that of centimeterwavelength radars, a network of many Ka-band radars is required. A wide observation area also makes it possible to apply this algorithm to fast-moving echoes. Second, the target of this algorithm is limited to isolated cumulonimbus clouds. For convective echoes accompanied by large precipitation systems such as squall lines, typhoon rainbands, or cold fronts, strong rain attenuation would affect the VAR value. In such cases, accurate observation of the VAR for weak echoes would be difficult.
In the present study, cumulonimbus clouds initiated by updrafts associated with the local convergence of sea breezes were considered. The investigation of other types of convective clouds that develop under different conditions, such as orographically induced convection, should also be undertaken. Unlike the case for the convergence of sea breezes, the updraft would be maintained for a relatively long time in mountainous areas, which may affect the VAR time variation. In future studies, we plan to evaluate the algorithm for more cases while taking into account the limitations mentioned above.

Conclusions
To detect cumulonimbus clouds in their early development stages and forecast their development, local heavy rainfall was observed by multiple Ka-band radars and operational X-band radars. The VAR was used to analyze the development of convective echoes. MCEs and MPEs were defined based on the VAR derived from Ka-band and X-band radars, respectively, and statistical analyses of the echoes and tracking information were performed. The results are summarized as follows: 1) The first detection time of MCEs was 17 min earlier than that of MPEs and 33 min earlier than the peak time of the VARa of MPEs on average. 2) There were statistically significant differences between developed and non-developed MCEs in terms of the MaxVARa, MaxAREA, DVARa, and DAREA for 6-12 min after their first detection. Among these indicators, the MaxVARa showed the most statistically significant differences. A nowcast algorithm for predicting MCE development was proposed using the MaxVARa as an indicator. This method is expected to forecast local heavy rainfall earlier than conventional X-band radars, although there are some restrictions on its use.