The Aerosol Direct Radiative Effect (ADRE) is defined as the change in the solar radiation flux, F, due to aerosol scattering and absorption. The difficulty in determining ADRE stems mainly from the need to estimate F without aerosols, F0, with either radiative transfer modelling and knowledge of the atmospheric state, or regression analysis of radiation data down to zero aerosol optical depth (AOD), if only F and AOD are observed. This paper examines the regression analysis method by using modeled surface data products provided by the AErosol RObotic NETwork (AERONET). We extrapolated F0 by two functions: a straight linear line and an exponential nonlinear decay. The exponential decay regression is expected to give a better estimation of ADRE with a few percents larger extrapolated F0 than the linear regression. We found that, contrary to the expectation, in most cases the linear regression gives better results than the nonlinear. In such cases the extrapolated F0 represents an unrealistically low WVC, resulting in underestimation of attenuation caused by the water vapour, and hence too large F0 and overestimation of the magnitude of ADRE. The nonlinear ADRE is generally 40-50% larger in magnitude than the linear ADRE due to the extrapolated F0 difference. Since for a majority of locations, AOD and water vapour column (WVC) have a positive correlation, the extrapolated F0 with the nonlinear regression fit represents an unrealistically low WVC, and hence too large F0. The systematic underestimation of F0 with the linear regression is compensated by the positive correlation between AOD and water vapour, providing the better result.