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中文摘要：
在温度随高度线性递减的假定下,根据加权平均温度和函数内积的定义,推导出加权平均温度Tm与地表温度Ts存在非线性函数关系,这突破了传统的加权平均温度Tm与地表温度Ts近似为一次函数关系的认识。利用2010年中国78个无线电探空站数据对线性函数和非线性函数的系数项进行拟合,其结果证实了加权平均温度Tm与地表温度Ts的非线性关系。
英文摘要：
Based on the premise that temperature decreases with height, the relationship between weighted mean temperature （Tm） and surface temperature （Ts） are deduced, from the inner product of the function and mathematical statistics, and the existence of nonlinear functions, which breaks through the traditional expressions of approximately linear functions between the Tm and Ts. This article uses the 2010 China 78 sounding station data to fit the coefficients of the two models,the results demonstrate that the deduced nonlinear relationships works well.
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