An assessment of rainfall kinetic energy functional relationships with GPM DPR

The kinetic energy (KE) of rainfall is an important parameter in estimating the rainfall erosivity factor, an essential parameter in the soil erosion equation. The global precipitation measurement dual-frequency precipitation radar (GPM DPR) can provide radar reflectivity at Ku- and Ka-band frequencies (Z_ku and Z_ka), rainfall rate (I, mm h⁻¹), and drop size distribution parameters (mass-weighed mean diameter: D_m in mm and normalized intercept parameter: log₁₀N_w, N_w in m⁻³ mm⁻¹). The empirical relations between rainfall KE and GPM DPR parameters (KE_time–I, KE_mm–D_m, KE_time–Z_ku, and KE_time–Z_ka relations) can allow us to estimate the KE at the locations where there are no ground-based measurements. In the present work, long-term measurements of impact type disdrometers located at three different locations (Zhongli, Feitsui, and Hsiayun) in north Taiwan are used to collect the raindrop size distribution (RSD) information of six seasons (spring, mei-yu, summer, autumn, winter, and typhoon). Measured RSDs in six seasons are used to estimate the rainfall intensity, mass-weighted mean diameter, rainfall KE flux (KE_time, J m^–2 h⁻¹), KE content (KE_mm, J m⁻² mm⁻¹), radar reflectivity at Ku- and Ka-band frequencies. For the first time, present study establish and validate the rainfall KE functional relationships with GPM DPR data products (KE_time–I, KE_mm–D_m, KE_time–Z_ku, and KE_time–Z_ka relations). The empirical relations between rainfall KE and GPM DPR parameters (I, Dm, Zku, and Zka) are established for six seasons of each disdrometer location. Derived KE relations did not show any spatial disparity for a given season, especially the KE_mm–D_m, KE_time–Z_ku, and KE_time–Z_ka relations. On the other hand, a clear seasonal differences in the rainfall KE relations are noticed at each observational site. The established relations showed reasonable agreement in estimating the KE from the GPM DPR. However, in determining the KE, the KE_mm–D_m relation showed outperformance over the remaining three relations (KE_time–I, KE_time–Z_ku, and KE_time–Z_ka relations).