用气温和冰厚修正黄河冰内雷达波速的物理机理和参数化

黄河平封冰和立封冰中冰晶体间以水膜形式存在有未冻结的自由水和非自由水，其含量随冰温变化。理论上冰内雷达波速取决于冰体自身的晶体结构和组分，但冰内未冻水含量可对其产生明显的影响；冰内未冻水含量取决于冰温，冰温又受控于气温、辐射和冰厚。分析了黄河什四份子2020—2021年冬季气温和雷达探测冰厚数据，发现气温主导的未冻水含量变化是影响雷达准确探测平封冰厚度的首要因子。通过确定黄河冰-水界面热通量，并引入含有气温、辐射、风速、云量的一维冰热力学模型，结合13个钻孔实测冰厚，计算了与雷达探测冰厚时刻一致的1251个热力学模拟冰厚。在此基础上，分别获得了气温升高过程和降低过程中粒状冰、柱状冰内雷达波速受气温影响以及受气温和冰厚联合影响的统计关系。最终确定将气温和冰厚对雷达波速联合影响的统计关系作为平封冰雷达波速动态修正的参数化方案，依此将固定式雷达冰内雷达波速由常数更换为函数，从而提高了平封冰雷达冰厚探测的精度。根据黄河存在非冻结冰花和堆积碎冰块，建议开展不同类型冰厚探测研究。

Physical scheme and parametrization by using air temperature and ice thickness to improve accuracy of GPR propagation velocity in Yellow River ice

The unfrozen free and unfree water occur in water film among the ice crystals in thermal growth ice and consolidated ice blocks in the Yellow River,and its content varies e with the ice temperature.Theoretically,the propagation velocity of radar wave depends on the ice crystal construction and compositions,however,the unfrozen water amount affects the velocity observably.The unfrozen water amount depends on ice temperature;and the ice temperature is controlled by air temperature,radiation and ice thickness mainly.After the analyzing of local air temperature and the GPR ice thickness at Shensifenzi,Yellow River in the winter of 2020-2021,it was confirmed that the air temperature is the key factor affecting the unfrozen water amount.An array of 1251 simulated ice thickness by using a 1-D thermal ice model with air temperature,solar radiation,wind speed and cloud amount after obtaining the heat flux between ice-water for the Yellow River ice relied on 13 drilled ice thickness data.Based on these studies,the statistical relationships of the propagation velocities in granular and columnar ice with air temperature,and with air temperature as well as ice thickness for air temperature increasing and decreasing processes were performed.Finally,these relationships can become parametrizations of a dynamical error correction algorithm of propagation velocity of GPR combined with air temperature and ice thickness was proposed.Theses formula could be used as the parameterization function instead of a constant propagation velocity of GPR for the suspended fixed-point radar to obtain higher accurate radar measured ice thickness.Following the facts of frazil under ice and non-consolidated ice blocks in ice jams along the Yellow River,the different research cases for the radar ice thickness measurements were suggested.