Analysis of the influences of uncertainties in input variables on the outcomes of the Heliosat-2 method

Abstract

The Heliosat-2 method, which employs satellite images to assess solar irradiance at ground level, is one of the most accurate among the available operational methods. Its input variables have uncertainties which impact on the final result. The General Law of Uncertainty Propagation is employed to analyze the impact of these uncertainties on a single pixel with Meteosat-7 inputs in various stages, beginning with the sensitivity coefficients and the changes induced in the clear-sky index ( K C ) by each independent variable. Once these coefficients are known, the partial combined standard uncertainty (CSU) is calculated for K C from each independent variable and albedo. Finally, the total CSU of K C is calculated. All of the results are in agreement and show that the most influential variables in the uncertainty of estimation of cloudy skies are, in this order, the Linke turbidity factor (54% of K C value), terrain elevation (33%) , the calibration coefficient of the satellite sensor (13%) and the ground albedo (5%). What causes the initial uncertainty in the ground albedo is its variation over time and the difficulty in assessing it from a reflectance time-series for mixed clear and cloudy skies. The Linke turbidity factor is the most influential variable on the width of the uncertainty interval, not only because of its own uncertainty (17% in this study), but because it is also used in numerous intermediate calculations. For clear skies, the partial CSUs are considerably lower, except for ground albedo (5% also).