TROPICAL GEOGRAPHY ›› 2015, Vol. 35 ›› Issue (6): 852-859.

Mathematical Expectation of the Surface Solar Irradiance Estimation Error under the Combined Uncertainty Impact of Multi Remotely Sensed Atmospheric Parameters in Hong Kong

RAO Junfeng，ZHANG Xianfeng

1. （Institute of Remote Sensing and Geographical Information System，Peking University，Beijing 100871，China）
• Online:2015-11-05 Published:2015-11-05

Abstract:

The radiative transfer equation simulation method is an accurate and effective way to estimate the surface solar irradiance, however, as the input data, the satellite remotely sensed atmospheric parameters have some uncertainty because of the retrieval algorithm and the sensors. The atmospheric parameters uncertainty effect brings error to the estimation of the surface solar shortwave irradiance using the radiative transfer equation method which takes the satellite remotely-sensed atmospheric parameters as input data. It is obviously more creditable to consider the combined uncertainty effect of multi atmospheric parameters than to take single atmospheric parameter uncertainty effect into consideration alone. The Multi-angle Imaging SpectroRadiometer (MISR) Aerosol optical depth (AOD) product and Moderate Resolution Imaging Spectroradiometer (MODIS) water vapor column product (WVC) uncertainty calculation formulas are derived from comparing satellite remote sensing products with the surface measured data in Hong Kong. By analyzing MISR/AOD and MODIS/WVC product values distribution in Hong Kong in the period from 2005 to 2013, the combined probability density distribution function of MISR/AOD and MODIS/WVC is obtained. Using the combined probability density distribution function as a weight function, which is multiplied with the relative error distribution function of the estimation of surface solar shortwave irradiance, the mathematical expectation of the surface solar irradiance calculation relative error under the multi remotely sensed atmospheric parameters’ combined uncertainty impact is worked out. The conclusion shows that when the solar zenith angle is 0° in the summer, the relative error mathematical expectation of the surface solar irradiance estimation is 3.17%, and with a 90% confidence that the relative error mathematical expectation will be lower than 3.53%. Besides the situation that the solar zenith angle is 0° in the summer, the relative error mathematical expectations under various solar zenith angle in different seasons are also obtained which provide the scientists and engineers a look up table for checking that if the accuracy of the surface solar shortwave irradiance estimation results satisfy their application requirements, especially for the application in the subtropical climate area.