Modeling and Validation Analysis of Sigmoid Function for Solar Radiation Diffuse Fraction

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. © 2020, Chinese Lasers Press. All right reserved.