## 2 Weather Radars, Wind Retrieval Algorithm and EDR Calculation  
A network of four S-band weather radars with two installed at Tai Mo Shan (TMS) and Tate's Cairn (TC), respectively, in Hong Kong, one at Qiu Yu Tan (QYT) in Shenzhen, China, and one in Zhuhai near Macao provide essential radar observations of the squall line that affected Hong Kong on 15 March 2025. Data from these S-band weather radars together with an X-band Phased Array Weather Radar (PAWR) installed at Sha Lo Wan (SLW) in Hong Kong are used for the retrieval of 3D winds associated with the squall line. The antenna heights of the weather radars at TMS, TC, QYT, Zhuhai and SLW are 968 m, 588 m, 328 m, 257 m and 34 m above sea level, respectively.  
The radar-based wind retrieval was based on a pythonic library, PyDDA, using Doppler velocity data from the above five sets of weather radars and the 3D variational data assimilation (3 DVAR) wind retrieval method as suggested by [PERSON] et al. [7], [PERSON] et al. [8,9], [PERSON] et al. [10], [PERSON] et al. [11] and [PERSON] et al. [12]. For the calculation of EDR which is used as a quantitative measure of convective turbulence, it is based on the signal-to-noise ratio (SNR) and spectral width (W) data from the weather radars using a fuzzy logic approach and details of the algorithm can be found in [PERSON] et al. [13].  
The retrieval of 3D wind field using variational multiple Doppler radar analysis is a very useful method for diagnosing atmospheric wind flow and the dynamical features of weather systems. It basically combines radar velocity observations, initial analysed wind fields from the Weather Research and Forecasting (WRF) model and other optional constraints from different sources to produce a more accurate wind analysis. The optimal wind analysis is obtained through minimization of a cost function using the Limited Memory Broyden-Fletcher-Goldfarb-Shanno Bounded (L-BFGS-B) method [14] and details are described in [15]. The 3D wind field retrieval technique has been successfully applied for studying a number of severe weather events occurring in Hong Kong, including vertical motion and cloud electrification in convective systems [15], cross-mountain wavy wind flow caused by terrain-induced windshear [16], thunderstorm-induced windshear and microbursts [4] and waterspouts [17], etc. In 2025, the 3D wind retrieval technique was used by HKO on a real-time basis for operational forecasting of severe weather [18]. Low-level horizontal wind fields at 2 km and 3 km heights as well as the corresponding vertical velocities are made available at every 6 min for monitoring of low-altitude weather. The 3D wind fields show the potential for nowcasting of intense convective weather although there are uncertainties in the retrieval method [19] and further improvement efforts can be made on deriving the vertical velocity.  
There have been developments of 3D wind retrieval that can account for orographic effects such as topographic forcing triggering convective activity [20; 21; 22; 23]. Further improvement is made using the Spline Analysis at Mesoscale Utilizing Radar and Aircraft Instrumentation (SAMURAI) analysis technique in which the finite element method is used to handle complex boundary geometries directly without interpolation to a Cartesian grid and the method has demonstrated good results as evidenced by previous studies [11; 24; 25; 26]. More recent studies deal with retrievals over complex terrain like the ones by [PERSON] et al. [27] using the ghost cell immersed boundary method (GCIBM) and [PERSON] and [PERSON] [19] introducing the immersed boundary method (IBM) have gained positive results in advancing the knowledge of orographic precipitation dynamics and convective initiation with topographic forcing.