This work discusses the relevance of three sky cover (SC) indices for solar radiation modeling and forecasting. The three indices are global in the sense that they integrate relevant information from the whole sky and thus encode cloud cover information. However, the three indices also emphasize different specific meteorological processes and sky radiosity components. The three indices are derived from the observed cloud cover via total sky imager (TSI), via measurements of the infrared radiation (IR), and via pyranometer measurements of global horizontal irradiance (GHI). We enhance the correlations between these three indices by choosing optimal expressions that are benchmarked against the GHI SC index. The similarity of the three indices allows for a good qualitative approximation of the GHI irradiance when using any of the other two indices. An artificial neural network (ANN) algorithm is employed to improve the quantitative modeling of the GHI sky cover index, thus improving significantly the forecasting details of GHI when all three indices are used.