一种数值积分方案用于球函数分析的试验

Experiment of a Numerical Integral Scheme for Spherical Function Analysis

针对半球月平均位势高度场球函数分析的实际问题,分析比较了吴新元提出的数值积分公式与常用的梯形积分公式、辛卜生积分公式在标准化缔合勒让德函数■mm+2k模、交角计算中的误差。结果表明:对m=0,1,吴新元数值积分公式的■mm+2k模、交角计算精度明显高于常用的两种积分公式;对m≥2,吴新元数值积分公式的精度虽低于梯形积分公式,但其模、交角误差低于10-4、2×10-3°。由于半球月平均位势高度场球函数方差谱具有低维、低阶的基本特征,故用吴新元数值积分公式替代常用积分公式可明显提高月平均位势高度场球函数分析精度。

Aiming at the practical spherical function analysis of monthly mean hemispherical potential hight field,it was compared and analyzed that calculation errors of the modulus and cross angle of the standardized associated Legendre function ■mm＋2k using common trapeziod formula,Simpson integral formula and WU Xin-yuan′s numerical integral expression.The results are given as follow：when m=0,1,the calculation precision of the modulus and cross angle of ■mm＋2k by WU Xin-yuan′s expression is better than those by the other two common integral formula;when m≥2,the precision of trapeziod integral formula is higher than that of WU Xin-yuan′s expression,whose errors for the modulus and cross angle calculation is still below 10-4 and 2×10-3°,respectively.Because the variance spectrum of monthly mean hemispherical potential hight field spherical function has the basic character of reduced dimensionality and low order,using WU Xin-yuan′s expression is able obviously to improve the spherical function analysis precision of monthly mean hemispherical potential hight field.