A dimensionless-entropy weight method for determining cloud physical parameter responses induced by aircraft cloud seeding

To address the challenges in evaluation of aircraft cloud seeding effect, this study proposes a physical evaluation method that integrates multiple key techniques to achieve an integrated quantitative evaluation based on multiple indicators. This evaluation approach was applied to six aircraft cloud seeding operations conducted in Henan Province of China during 2023–2024. Results show that the six operations exhibited nonlinear growth patterns for dispersion in both the target and control areas, with rapid expansion at the initial stage followed by a slower rate. The dispersion rate, distance, extent and concentration of the seeding agent vary significantly depending on the meteorological conditions, such as atmospheric turbulence, wind speed, stability and humidity. For the six operations, the vertically integrated liquid water content (VIL) showed notably high entropy weights (0.06–0.43) in multiple operations (No. 2, 3 and 6), making it a relatively stable indicator for evaluating the cloud seeding effects. Due to complex cloud microphysical processes such as latent heat release from deposition, downdrafts, cloud dissipation and cloud development, the responses of cloud-top temperature to seeding varied considerably (− 44.56 °C ~ − 6 °C). The effects of cloud seeding on cloud effective radius and optical thickness are complex and vary substantially depending on specific seeding conditions. The responses of liquid water path were time-dependent, the seeding-induced responses of radar reflectivity exhibited distinct patterns, including delayed manifestation, strong enhancement, and ineffectiveness or being masked. The strong-echo area and the VIL in the target areas fluctuated and generally decreased over time, respectively. The change rates of hourly precipitation induced by seeding varied from 3.82% to 8.91%. The integrated physical inspection dimensionless index (PIDI, a physical evaluation index for evaluating cloud seeding effects) values for the seven indicators ranged from 15.0% to 69.7%, showing a smaller variation magnitude compared with the change rates of individual indicators, which reflects the synergistic effects of multiple indicators. This study provides a quantifiable and robust algorithm that mitigates the interference of natural variability, and its application to six case studies demonstrates its potential for advancing cloud seeding techniques and improving effect evaluation capabilities.