多层四流球谐函数算法的构建及在大气辐射传输模式中的应用

Construction of the multi-layers four-stream spherical harmonic expansion algorithm and its application to atmospheric radiative model

为了在不大幅度增加计算成本的情况下提高大气辐射传输计算的精度,利用单层四流球谐函数结合多层二流累加法,构造了可用于多层大气的四流球谐函数算法。为了比较与其他辐射传输算法的差异,引入48流离散纵坐标算法作为比较标准,Eddington近似、四流离散纵坐标算法作为比较对象。在真实大气廓线条件下,计算了晴空和有云大气顶向上辐射通量、地表向下辐射通量以及加热率廓线。得出以下结论:在晴空情况下,与作为标准的48流离散纵坐标法相比,Eddington近似、四流离散纵坐标法和新构造的四流球谐函数方法加热率绝对误差都小于0.3 K/d;向上、向下辐射通量的相对误差分别小于1%和0.6%。这表明在晴空情况下,3种算法对加热率的计算精度差别不大;对辐射通量的计算精度,两种四流近似算法比传统的Eddington近似更为精确。在有云情况下,与48流离散纵坐标法相比,四流球谐函数和四流离散纵坐标法计算的云顶加热率相对误差小于1%,而Eddington近似计算的云顶加热率相对误差大于5%。结果表明:新构造的四流球谐函数算法可用于大气辐射传输模式,在不大幅度增加计算成本的同时,提高了晴空大气的整体辐射计算精度和有云大气辐射加热率的计算精度。

In order to increase the accuracy of radiative transfer calculation without increasing calculation cost,a method using the singleˉlayer fourˉstream spherical harmonic expansion approximation combining with the twoˉstream adding algorithm has been built in this paper.Then,the fourˉstream spherical harmonic expansion approximation was compared with the traditional Eddington approximation and the fourˉstream discrete ordinate approximation by using the 48ˉstream discreteˉordinate approxiˉ mation method as a standard reference.The results of the upward and downward radiative fluxes as well as the heating rates in the real atmosphere have been shown.For clear sky,the differences between the Eddington method,fourˉstream spherical harˉ monic expansion approximation,fourˉstream discreteˉordinate approximation,and the standard results are all less than 0.3 K/d for heating rates,and less than 1% and 0.6% for the upward and downward radiative fluxes,respectively.It shows that the three methods have no large difference for heating rate calculations.The two fourˉstream approximations are a little more accuˉ rate than the Eddington method for flux calculation in clear sky.For cloudy sky,the differences of heating rates between the two fourˉstream methods and the standard results are all less than 1% at the top of the cloud,whereas these differences beˉ tween the Eddington method and the standard results are large than 5%.Therefore,the fourˉstream spherical harmonic expanˉ sion approximation built in this paper can be applied to the radiative transfer model to improve the accuracies of the whole radiaˉ tion calculation for clear sky and the heating rate calculation for cloudy sky without increasing large costs.