Terrain-Driven Variability of Raindrop Size Distribution and Rainfall Kinetic Energy in Shaanxi, China and Implications for Microphysics Estimation

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Abstract The variability of raindrop size distribution (DSD) across terrain gradients plays a critical role in regulating rainfall microphysics and kinetic energy (KE), yet this variability remains under-explored in semi-arid regions. This study utilized six summers (2019–2024) of 92 disdrometer observations across Shaanxi Province, China, to demonstrate the pronounced south-north DSD gradient across terrains: while the site-averaged mass-weighted mean diameter ( D m ) increased, the normalized intercept parameter (log10 N w ) decreased rapidly from mountains to plateaus. The humid Qinling-Daba Mountains exhibits higher seasonal rainfall (>800 mm) dominated by a high concentration of small raindrops, while the semi-arid Loess Plateau shows frequent occurrences of large raindrops. This DSD shift drives higher KE in the Loess Plateau (25/28 stations >20 J m −2 mm −1 ) than in the Qinling-Daba Mountains (only 2/25 stations >20 J m −2 mm −1 ), thus amplifying soil erosion risks due to vulnerable loessal substrates. Despite the spatial heterogeneity, the site-averaged D m −log 10 N w pairs demonstrate consistent evolution throughout Shaanxi along with the increase in rain rate. We further establish D m as a universal microphysical constraint, deriving robust estimators for KE, accretion/evaporation rates, and mass-weighted terminal velocity of DSD. These relationships overcome the limitations of traditional methods by encoding terrain-mediated DSD heterogeneity through D m parameter. Consequently, they are practical for facilitating high-accuracy estimation of key microphysical quantities and process rates without full DSD resolution. Our findings offer critical semi-arid DSD benchmarks for improving model microphysics parameterization, advancing remote sensing-based KE retrievals, and designing targeted soil conservation strategies for erosion hotspots.

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