Lim et al. (2025) Improved observed full raindrop size distributions and their normalization using double and triple moments

Identification

• Journal: Atmospheric Research
• Year: 2025
• Date: 2025-12-04
• Authors: Sanghun Lim, Wonbae Bang, Kyo‐Sun Sunny Lim, Merhala Thurai, GyuWon Lee
• DOI: 10.1016/j.atmosres.2025.108675

Research Groups

• Department of Atmospheric Sciences, Center for Atmospheric Remote sensing (CARE), Kyungpook National University, Daegu, Republic of Korea
• Jeonju Branch Office of Meteorology, Korea Meteorological Administration (KMA), Jeonju, Republic of Korea
• Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, USA

Short Summary

This study develops an optimized method for constructing full raindrop size distributions (DSDs) by statistically merging measurements from a 2D-Video Distrometer (2DVD) and a Meteorological Particle Spectrometer (MPS) based on instrumental uncertainty. The new method significantly improves DSD accuracy, reduces variability, and provides more stable generic functions compared to existing merging techniques.

Objective

• To develop an optimized method for constructing full raindrop size distributions (DSDs) by combining 2D-Video Distrometer (2DVD) and Meteorological Particle Spectrometer (MPS) measurements, based on instrumental uncertainty statistics rather than fixed critical diameters and weighting.
• To quantify the measurement uncertainty by size from MPS and 2DVD and derive optimal diameter-dependent weighting factors.
• To analyze the impact of the new merging method on DSD variability using double-moment scaling normalization to derive a stable generic function.
• To employ four different triple-moment normalization methods to further describe the reduction of DSD variability.

Study Configuration

• Spatial Scale: Collocated instruments at the Incheon Weather Observatory (37.476°N, 126.616°E), Republic of Korea, with the 2DVD installed 5 meters apart from the MPS.
• Temporal Scale:
  • Data for deriving merging parameters: 6 quasi-homogeneous stratiform rainfall cases from June to October 2022, comprising 121 three-minute averaged DSDs.
  • Data for complete DSD validation: 9 rainfall events (including monsoon, mesoscale convective systems, and a typhoon) from July to October 2022, comprising 575 three-minute averaged DSDs (selected from an initial 1372 DSDs where all four instruments provided data).
  • Time intervals for data processing: 6-second intervals for PLUVIO, converted to 60-second intervals; 300-second time lag for PLUVIO rainfall rate calculation; 3-minute averaging for DSDs.

Methodology and Data

• Models used:
  • Double-moment normalization (Lee et al., 2004)
  • Triple-moment normalization (Szyrmer (S05), Morrison (M19), Regression (Reg), Generic function moment regression (GF) methods)
  • Generalized gamma function for fitting normalized DSDs
  • Loglinear interpolation method for DSDs
  • Sequential Intensity Filtering Technique (SIFT) for identifying quasi-homogeneous microphysical processes
  • Empirical diameter-fall velocity relationship (Atlas et al., 1973) for particle filtering
• Data sources:
  • Meteorological Particle Spectrometer (MPS): Optical disdrometer, 64 photodiodes, 657 nanometers wavelength, diameter range 5.0 x 10⁻⁵ meters to 3.1 x 10⁻³ meters, diameter resolution 5.0 x 10⁻⁵ meters, sampling area approximately 6.2 x 10⁻⁴ square meters.
  • 2D-Video Distrometer (2DVD): Optical disdrometer, two line-scan cameras with 512 photodetectors each, diameter range 2.5 x 10⁻⁴ meters to 1.025 x 10⁻² meters, diameter resolution approximately 2.0 x 10⁻⁴ meters, sampling area 1.0 x 10⁻² square meters.
  • PLUVIO: Weighing-type rain gauge, used as a reference for rainfall rate (R).
  • Precipitation Occurrence Sensor System (POSS): Bistatic X-band (approximately 10 gigahertz) continuous-wave (CW) Doppler radar, used as a reference for radar reflectivity (Z), diameter range 3.4 x 10⁻⁴ meters to 5.34 x 10⁻³ meters.
  • Data collected during the Korea Precipitation Observation Program: International Collaborative Experiments for Mesoscale Convective System in Seoul Metropolitan Area (KPOP-MS).

Main Results

• Optimized DSD Merging: The weighting diameter range for merging MPS and 2DVD data was determined to be 0.7 x 10⁻³ meters to 1.2 x 10⁻³ meters, based on a median relative bias (RB) of number concentration within ±10%. Diameter-dependent weighting factors, derived from normalized standard deviations during quasi-homogeneous stratiform rain, showed MPS contributing more for diameters less than 0.7 x 10⁻³ meters and 2DVD for diameters greater than 0.7 x 10⁻³ meters.
• Improved DSD Representation: The new weighted complete DSD (NWCD(D)) method effectively resolved discontinuities and mitigated over/underestimation issues present in previous merging methods (NCD(D)) and individual 2DVD data (N2DVD(D)), particularly for small raindrops and during light rainfall or abrupt microphysical changes. For example, number concentrations in the weighting range improved from about 10⁵ m⁻⁴ to 300 m⁻⁴.
• Validation of Bulk Parameters:
  • Rainfall Rate (R): NWCD(D) exhibited lower Root Mean Square Error (RMSE) of 1.572 x 10⁻⁷ m s⁻¹ and Standard Deviation (STD) of 1.519 x 10⁻⁷ m s⁻¹, with a higher Correlation Coefficient (CORR) of 0.979, compared to N2DVD(D) (RMSE 1.664 x 10⁻⁷ m s⁻¹, STD 1.617 x 10⁻⁷ m s⁻¹, CORR 0.977) and NCD(D) (RMSE 1.617 x 10⁻⁷ m s⁻¹, STD 1.553 x 10⁻⁷ m s⁻¹, CORR 0.977) when validated against PLUVIO.
  • Radar Reflectivity (Z): NWCD(D) showed lower RMSE of 1.249 dBZ and STD of 1.007 dBZ, with a higher CORR of 0.989, compared to N2DVD(D) (RMSE 1.347 dBZ, STD 1.102 dBZ, CORR 0.988) and NCD(D) (RMSE 1.356 dBZ, STD 1.102 dBZ, CORR 0.985) when validated against POSS (for Z < 50 dBZ). A marked improvement was observed for weak rainfall (Z < 20 dBZ), with NWCD(D) RMSE of 1.321 dBZ, compared to N2DVD(D) RMSE of 1.573 dBZ and NCD(D) RMSE of 1.701 dBZ.
• DSD Variability and Normalization:
  • Double-moment normalization: NWCD(D) significantly reduced variability in the normalized generic function h(x) for small diameters (normalized diameter x < 0.5) and provided a more stable "S" shaped generic function across the entire range, indicating reduced measurement uncertainty.
  • Generalized Gamma Parameters: The kernel density distribution of the scale parameter (c) and shape parameter (μ) for hWCD(x) was narrower, with a mode at c = 4.04 and μ = -0.22, demonstrating a more stable and physically consistent generic function shape.
  • Triple-moment normalization: These methods significantly reduced estimation errors for lower-order moments (p ≤ 2.5) compared to double-moment normalization, especially when including the zeroth moment (M0) as a reference. Errors for higher-order moments (p ≥ 2.5) were generally comparable to double-moment normalization (except for the Szyrmer method).

Contributions

• Introduces a novel, statistically-driven framework for combining DSDs from multiple disdrometers with differing measurement sensitivities, using diameter-specific error characteristics to derive optimal weighting factors.
• Demonstrates that this optimized merging method (NWCD(D)) yields more accurate, continuous, and realistic full DSDs, particularly improving observations of small raindrops and during light precipitation or rapidly changing microphysical conditions.
• Quantitatively shows that the new method significantly reduces DSD variability and leads to a more stable and physically consistent generic function h(x) in double-moment normalization, which is crucial for DSD modeling.
• Provides a comprehensive evaluation of four triple-moment normalization methods, highlighting their effectiveness in further reducing estimation errors for lower-order moments, thus contributing to more precise control of DSD variability.
• The findings have significant implications for improving radar-based rainfall estimation, enhancing the understanding of microphysical processes (especially in light and extreme rain), and advancing microphysical parameterization in numerical weather prediction models by offering a stable generic h(x) as an alternative to assumed DSD models.

Funding

• Korea Meteorological Administration Research and Development Program “Observing Severe Weather in Seoul Metropolitan Area and Developing Its Application Technology for Forecasts” (Grant KMA2018-00125).
• National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2025-02242970).
• US National Science Foundation (award number 2418753).

Citation

@article{Lim2025Improved,
  author = {Lim, Sanghun and Bang, Wonbae and Lim, Kyo‐Sun Sunny and Thurai, Merhala and Lee, GyuWon},
  title = {Improved observed full raindrop size distributions and their normalization using double and triple moments},
  journal = {Atmospheric Research},
  year = {2025},
  doi = {10.1016/j.atmosres.2025.108675},
  url = {https://doi.org/10.1016/j.atmosres.2025.108675}
}