Uncertainty quantification of solar diffuse irradiation on inclined surfaces for building energy simulation

Traditional uncertainty quantification (UQ) in the design of energy efficient buildings is limited to the propagation of parameter uncertainties in model input variables.  Some models inside building simulation are inherently inaccurate, which introduces additional uncertainties in model predictions. Therefore, quantification of this type of uncertainty (i.e., modelling, or more strictly speaking model form uncertainty) is a necessary step toward the complete UQ of model predictions.  This paper quantifies the model form uncertainty of a widely used sky model developed by Perez (1990), which computes solar diffuse irradiation on inclined surfaces.  We collect a dataset from measured solar irradiation on surfaces with multiple tilt angles and orientations, covering a wide spectrum of sky conditions. We first show statistical evidence for the model inadequacy based on our collected data and some results in published studies. Then, we develop a two-phase regression model, quantifying the model form uncertainty, which de facto constitutes an alternative for the Perez model. Model validation results show that model bias errors and root mean square errors are considerably reduced by the new model formulation for every tilted surface. Lastly, we study the significance of this model form uncertainty in the energy consumption predictions obtained with whole building simulation.