In this paper a new hybrid Model Output Statistics (MOS), named MOS cascade, is developed to refine the day-ahead forecast of the global horizontal irradiance provided by the Weather Research and Forecast (WRF) model. The proposed approach is based on a sequence of two different MOS. The first, called MOSRH, is a new physically based algorithm, built to correct the treatment of humidity in the WRF radiation schemes. The second, called MOSNN, is based on artificial intelligence techniques and aims to correct the main systematic and learnable errors of the Numerical Weather Prediction output. The 1-day and 2-day forecast accuracies are analyzed via direct comparison with irradiance data measured in two sites, Rome and Lugano. The paper shows that a considerable reduction in error was achieved using MOSRH model and MOS cascade. The differences between the two sites are discussed in details. Finally, the results obtained are compared with the benchmark accuracy reached for the data available for the average climate in Southern Spain and Switzerland.