A STUDY OF DUAL-FREQUENCY METHOD FOR SOLVING THE INTEGRAL SCATTERING EQUATION AT VARIOUS OPERATING WAVELENGTHS

• Published in: Radio physics and radio astronomy (Print) Vol. 30; no. 3; pp. 183 - 192
• Main Authors: Linkova, A., Dormidontov, A.
• Format: Journal Article
• Language: English
• Published: National Academy of Sciences of Ukraine, Institute of Radio Astronomy 01.09.2025
• Subjects: inverse problem; rain intensity; regularization
• ISSN: 1027-9636; 2415-7007; 2415-7007
• DOI: 10.15407/rpra30.03.183

Subject and Purpose. Remote sensing plays a key role in environmental monitoring. It effectively addresses urgent issues in atmospheric physics and socio-economic activities, such as flight safety and agriculture. In this work, the previously proposed method for solving the inverse problem of dual-frequency sensing in rainfall measurements is further developed, providing a sharper focus on the integral scattering equation solution using regularization techniques as applied to various combinations of operating wavelengths. Methods and Methodology. Numerical simulations are conducted for dual-frequency sensing at different operating wavelengths, wherein the integral scattering equation is solved using regularization techniques. Results. The numerical simulation of rain intensity retrieval in the range of up to 30 mm/h was carried out as applied to different operating wavelength pairs, 8.2 mm/ 3.2 cm, 8.2 mm/ 5.5 cm, 8.2 mm/10 cm, and 3.2 mm/10 cm, and considering various calculation errors present in the specific radar cross-section (RCS). Based on the numerical modeling, the most optimal regularization parameter value was determined, and the type of approximation for the free term of the integral equation was selected for each operating wavelength pair. It has been established that the proposed solution approach to the inverse problem of interest is not suitable for the wavelength pair 3.2 mm/10 cm due to excessive errors in rain intensity retrieval. The results for the pairs 8.2 mm/3.2 cm, 8.2 mm/5.5 cm, and 8.2 mm/10 cm are quite similar. However, the 8.2 mm/3.2 cm wavelength pair is distinguished for the smallest retrieval error and therefore best aligns with the proposed approach. Conclusions. The obtained results evidence that the maximum relative error in rain intensity retrieval does not exceed 35 % for the pair 8.2 mm/5.5 cm and 30 % for the pair 8.2 mm/ 10 cm provided that the rain intensity is higher than 5 mm/h and a relative error in the specific RCS calculation is within ±20 % for both wavelengths. For the same rain intensity over 5 mm/h, the maximum relative error in rain intensity retrieval for the pair 8.2 mm/3.2 cm does not exceed 20 %.