The Bias in Moment Estimators for Parameters of Drop Size Distribution Functions: Sampling from Exponential Distributions

A Synthetic Quantitative Precipitation Estimation by Integrating S- and C-Band Dual-Polarization Radars over Northern Taiwan

The key factors, namely, the radar data quality, raindrop size distribution (RSD) variability, and the data integration method, which significantly affect radar-based quantitative precipitation estimation (QPE) are investigated using the RCWF (S-band) and NCU C-POL (C-band) dual-polarization radars in northern Taiwan. The radar data quality control (QC) procedures, including the corrections of attenuation, the systematic bias, and the wet-radome effect, have large impact on the QPE accuracy. With the proper QC procedures, the values of normalized root mean square error (NRMSE) decrease about 10~40% for R(ZHH) and about 5~15% for R(KDP). The QPE error from the RSD variability is mitigated by applying seasonal coefficients derived from eight-year disdrometer data. Instead of using discrete QPEs (D-QPE) from one radar, the synthetic QPEs are derived via discretely combined QPEs (DC-QPE) from S- and C-band radars. The improvements in DC-QPE compared to D-QPE are about 1.5–7.0% and 3.5–8.5% in R(KDP) and R(KDP, ZDR), respectively. A novel algorithm, Lagrangian-evolution adjustment (LEA), is proposed to compensate D-QPE from a single radar. The LEA-QPE shows 1–4% improvements in R(KDP, ZDR) at the C-band radar, which has a larger scanning temporal gap (up to 10 min). The synthetic LEA-QPEs by combining two radars have outperformed both D-QPEs and DC-QPEs.

Characteristics of Raindrop Size Distribution on the Eastern Slope of the Tibetan Plateau in Summer

Precipitation microphysics over the Tibetan Plateau (TP) remain insufficiently understood, due to the lack of observations and studies. This paper presents a comprehensive investigation of the raindrop size distribution (DSD) for rainfall that happened on the eastern slope of TP in summer. DSD differences between different rain types and under different rain rates are investigated. Confidential empirical relationships between the gamma shape and slope parameters, and between reflectivity and rain rate are proposed. DSD properties in this area are also compared with those in other areas. The results indicate that the stratiform and convective rains contribute to different rain duration and amount, with diverse rainfall macro- and microphysical properties. The rain spectra of two rain types can become broader with higher concentrations as the rain rate increases. DSDs in this area are different to those in other areas. The stratiform DSD is narrower than that in the non-plateau area. The two rain types of this area both have higher number concentrations for 0.437–1.625 mm raindrops than those of the mid-TP. The relationships of shape–slope parameters and reflectivity–rain rate in this area are also different from those in other areas. The rain spectra in this area can produce a larger slope parameter under the same shape parameter than in the mid-TP. The convective rain can produce a smaller rain rate under the same reflectivity. The accuracy proposed reflectivity–rain rate relationship in application to quantitative rainfall estimation is also discussed. The results show that the relationship has an excellent performance when the rain rate exceeds 1 mm h−1.