为研究太阳辐射散射分布对日照时数测量的影响,基于大气辐射传输理论,利用泰勒级数展开,建立了散射分数、晴空指数和大气光学质量的Sigmoid函数模型。利用不同时间尺度的辐射数据训练集,通过非线性拟合得到了散射分数与晴空指数和大气光学质量的变化关系的数学模型,给出了一维模型S0和二维模型S1。利用不同地域观测站点的太阳辐射数据建立验证数据集,利用Sigmoid模型计算了散射分数,分析了实测值与计算值之间的相关系数、平均偏差、均方根误差和t-统计量等。结果表明,采用Sigmoid模型计算的散射分数值与实测值相关系数在0.8以上,平均偏差在±0.2以内,均方根误差在0.25以内,t-统计量最小低至0.0172。本研究为散射辐射分布模型的构建提供了新的方向,下一步需引入更为广泛的辐射数据进行模型跨地域的适用性研究。

In order to study the influence of the solar radiation diffuse distribution on the measurement of sunshine duration, based on atmospheric radiation transmission theory, the Sigmoid function models of diffuse fraction, clearness index, and atmospheric optical quality are established by Taylor series expansion. Using the training dataset of radiation data with different time scales, the mathematical model of the diffuse fraction varying with the clearness index and the atmospheric optical mass is obtained by nonlinear fitting, and the one-dimensional model S0 and the two-dimensional model S1 are given. Based on the solar radiation data from different observation sites, the diffuse fraction is calculated by the Sigmoid model. The correlation coefficient between the measured and calculated values, mean deviation, root mean square error, and t-statistic are analyzed. The results show that the correlation coefficient between the diffuse fraction calculated with the Sigmoid model and the measured value is above 0.8, the average deviation is within ±0.2, the root mean square error is within 0.25, and the minimum t-statistic is as low as 0.0172. This study provides a new thought for the construction of the solar radiation diffuse distribution model, and the next step should introduce more extensive radiation data to study the applicability of the model across regions.