One of the major challenges confronting the widespread adoption of solar energy is the uncertainty of production. The energy generated by photovoltaic systems is a function of the received solar irradiance which varies due to atmospheric and weather conditions. A key component required for forecasting irradiance accurately is the clear sky model which estimates the average irradiance at a location at a given time in the absence of clouds. Current methods for modelling clear sky irradiance are either inaccurate or require extensive atmospheric data, which tends to vary with location and is often unavailable. In this paper, we present a data-driven methodology, Blue Skies, for modelling clear sky irradiance solely based on historical irradiance measurements. Using machine learning, Blue Skies is able to generate clear sky models that are more accurate spatio-temporally compared to the state of the art, reducing errors by almost 50%.