黄河内蒙古段典型河段河冰介电常数率定及冰厚监测

Dielectric constant calibration and ice thickness monitoring of river ice in the Inner Mongolia section of the Yellow River

摘要

为提升凌汛期河冰厚度监测精度并揭示其时空分布规律，利用无人机探地雷达技术，在黄河内蒙古段典型弯道、直道和桥梁河段开展实测与反演研究。采用最小相对误差法率定不同河段与时段的最优介电常数，并用于冰厚反演与验证。结果表明：河冰介电常数存在显著差异，弯道波动幅度最大（介电常数最大值与最小值差约2.446），1月主河槽较浅滩高约0.991，2月整体下降且差异减弱；直道分布最为集中（差约0.476），时段间变化较小，表现稳定；桥梁区介于二者之间，1月挤压带显著高于邻近冰盖，2月趋于集中。率定后冰厚反演精度显著提高，回归拟合度（R²）均在0.949以上，均方根误差为0.61～5.03 cm。冰厚分布整体呈增厚趋势，但局部差异显著，弯道与桥梁区空间离散性强于直道。研究揭示了典型河段介电常数与冰厚分布的空间差异及时段变化特征，为凌汛期冰情监测与风险防控提供了可靠的技术支撑。

Abstract

Understanding ice processes, evaluating flood risks, and assisting with winter river management in cold climates all depend on accurate river-ice thickness monitoring throughout the ice-flood season. The spatial variability of river morphology and hydrodynamic conditions significantly complicates ice-thickness inversion, especially when uniform dielectric parameters are utilized across various channel types. In the Inner Mongolia section of the Yellow River, the processes of ice formation, accumulation, and deformation during freeze-up and mid-winter stages are very different in river bends, straight reaches, and bridge-constricted sections. These differences present challenges for achieving consistent and reliable ice-thickness estimation using ground-penetrating radar (GPR). To address these limitations, this study aims to improve ice-thickness inversion accuracy and to clarify the spatial and temporal variability of river-ice dielectric properties by integrating unmanned aerial vehicle (UAV)–based GPR evaluations with reach-specific dielectric calibration. Field measurements were carried out in typical river bends, straight reaches, and bridge-constrained sections of the Yellow River's Inner Mongolia reach. UAV-mounted GPR systems were deployed to collect high-resolution radar profiles throughout the ice-flood season, covering both January and February observation periods. Borehole drilling was carried out synchronously to obtain in-situ ice-thickness measurements for validation. To reduce systematic errors and improve comparability among different reaches and periods, the minimum relative error (E_MR) method was applied to calibrate optimal dielectric constants for river ice at each channel type and observation stage. These calibrated dielectric values were then used for ice-thickness inversion, and the inverted results were quantitatively evaluated against borehole measurements using the coefficient of determination (R²) and root mean square error (E_RMS). To describe variations between channel types and seasonal stages, spatial patterns of dielectric characteristics and ice thickness were further examined. The findings show that river-ice dielectric properties exhibit significant temporal and spatial heterogeneity. Among the three channel types, bend sections exhibited the largest variability, with the difference between maximum and minimum dielectric constants reaching approximately 2.446. In January, the dielectric constant of main-channel ice in bends was about 0.991 higher compared with that of shallow marginal ice, reflecting enhanced ice accumulation and deformation under complex flow conditions. By February, dielectric constants generally decreased, and inter-zone differences proved less distinct. Straight reaches showed the most concentrated dielectric distribution, with a range of only about 0.476, and displayed minimal variation between January and February, indicating relatively stable ice growth conditions. Bridge sections showed intermediate features: in February, the spatial distribution tended to converge, whereas in January, the constricted zone beneath bridges had much higher dielectric constants than nearby ice cover. After dielectric calibration, ice-thickness inversion accuracy improved considerably, withR² values consistently exceeding 0.949 and E_RMS ranging from 0.61 to 5.03 cm. Ice-thickness generally increased from early to mid-winter, but local spatial variability remained evident, particularly in bends and bridge sections, whereas straight reaches maintained more uniform thickness distributions. This study shows that for accurate ice-thickness inversion in complex river environments, adopting dielectric constants specific to reach and period are crucial. The findings confirm that river-ice dielectric properties and ice-thickness distributions are strongly controlled by channel morphology, hydrodynamic conditions, and seasonal evolution. UAV-based GPR surveys, combined with targeted dielectric calibration, provide an effective and high-precision approach for large-scale ice-thickness monitoring during the ice-flood season. By elucidating the spatial heterogeneity and temporal dynamics of dielectric characteristics across typical channel types, this research offers robust technical support for winter ice-condition monitoring, ice-flood hazard assessment, and risk management in the Inner Mongolia section of the Yellow River.

关键词

黄河内蒙古段 / 河冰 / 探地雷达 / 介电常数率定 / 冰厚反演

Key words

Inner Mongolia section of the Yellow River / river ice / ground penetrating radar / dielectric constant calibration / ice thickness inversion

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基金资助

国家自然科学基金项目(52379014)

国家自然科学基金联合基金项目(U23A2012)

内蒙古自然科学基金青年基金项目(2023QN05026)