基于Stefan改进公式计算标准场地冻结深度的探讨

Based on Stefan improved formula calculate the freezing depth of the standard field

本研究依托于分布在全国季节冻土区600个气象台站,1971—2020年近50年实测季节冻土年最大冻结深度数据及温度观测数据,分别对600个台站的气温年变化趋势,气温冻结指数的年变化趋势等进行了探讨。并且在Stefan改进公式的基础上,进一步探讨了基于气温冻结指数的影响因子Ea与经度、纬度及海拔等因素在标准场地上的统计学关系,建立影响因子Ea与经纬度、海拔三者之间的相关关系式,将通过相关关系式计算得出的影响因子Ea与通过基于气温冻结指数的Stefan改进公式反推计算得到的影响因子Ea进行对比分析,验证相关关系的准确性。研究表明,因子在大多数点位拟合程度良好,但是一些位于多年冻土区边界处的点位,拟合差异较大。为解决这一问题,将研究区域重新划分为一般季节冻土区域及季节冻土区与多年冻土区边界处的过渡区域,分别进行相关性分析,再次建立影响因子Ea与经度、纬度、海拔之间的相关关系式。经过验证,点位拟合程度具有显著的提升。将相关关系式引入基于气温冻结指数的Stefan改进公式做进一步拓展,最终得到的经验公式将用于计算我国季节冻土区标准场地冻结深度。通常意义上由于Stefan公式中基于地表冻结指数的影响因子E本身计算较为繁复,应用于工程设计及施工并不简便,对难于计算或者难于获取到冻结深度的工程建设所在地,利用拓展后的经验公式计算得到的冻结深度值与气象台站观测值拟合度较高,能够较好地为工程建设提供冻结深度值作为参考。

This study is based on 600 meteorological stations distributed in seasonally frozen ground regions of China,the annual maximum freezing depth and temperature observation data were measured in the past 50 years from 1971 to 2020.In the 600 stations,the annual variation trends of temperature and freezing index were discussed respectively.On the basis of Stefan improved formula,the statistical relationship between the Ea factor(based on temperature freezing index)and factors such as longitude,latitude and altitude were further explored on the standard field,and established an empirical formula.Using the empirical formula to calculate the Ea factor,and verify the accuracy of it.The research shows that the Ea between the empirical formula and calculated by Stefan improved formula(based on temperature freezing index)have good fitting degree at most points,but some points at the boundary of permafrost regions have large fitting differences.In order to solve this problem,the research region was redivided into the general seasonally frozen regions and the transition regions at the boundary between the seasonally frozen regions and the permafrost regions.Correlation analysis was carried out respectively,and the relationship between the Ea and factors such as longitude,latitude,altitude were established.By comparing the observed values,it can be found that fitting degree of these points have been significantly improved.The correlation relationship was introduced into Stefan improved formula(based on temperature freezing index)for further expansion,and finally getting the empirical formula based on temperature freezing’s Stefan improved formula,which was used to calculate the freezing depth of the standard field in seasonally frozen ground regions of China.Since the E factor is relatively complicated to obtain,it is not easy to apply to engineering designs and constructions.For engineering construction sites where it is difficult to obtain the freezing depth,it calculated by using the empirical formula is similar to the observed values of meteorological stations.The combination degree is highly,which can be better provide the freezing depth as a reference for engineering constructions.