On 2--4 July 2004, unusually severe convective systems developed over Taiwan area, following the passage of Typhoon Mindulle (10W, T0407). During the lifetime of these storms, total lightning was detected by the TPC SAFIR total lightning detection system, infrared cloud-top temperatures were measured by the NOAA GOES-9 satellite, radar reflectivity was observed by the CWB Doppler network, and hourly surface rainfall was measured by a network of high-density raingauge stations. Using these data, we find that proxies published in previous research are useful for studying the evolution of convection in the July 2004 storm. This paper focuses on a 6-hour portion of the "oceanic" storm's lifetime. Our study shows the following: (1) Middle-level (at 6 km altitude) 40-dBZ radar reflectivity and high-level (at 12 km altitude) 20-dBZ radar reflectivity are good indicators for tracking deep convective cells and total lightning. (2) Areas with infrared cloud-top temperatures lower than -77¿C, areas covered by 6-km 40-dBZ contours and 12-km 20-dBZ contours, and areas with intense surface rainfall are closely related to each other. (3) Column maximum radar reflectivities are good indicators for surface rainfall. The motion of the rain fields can be tracked by following the leading portion of areas defined by infrared cloud-top temperatures lower than -72¿C. The correlation between lightning, radar reflectivity, infrared cloud-top temperatures, and heavy surface rainfall found in this work will be a critical test for models of storm processes.