Short-term solar forecasting models based solely on global horizontal irradiance (GHI) measurements are often unable to discriminate the forecasting of the factors affecting GHI from those that can be precisely computed by atmospheric models. This study introduces a Physics-based Smart Persistence model for Intra-hour forecasting of solar radiation (PSPI) that decomposes the forecasting of GHI into the computation of extraterrestrial solar radiation and solar zenith angle and the forecasting of cloud albedo and cloud fraction. The extraterrestrial solar radiation and solar zenith angle are accurately computed by the Solar Position Algorithm (SPA) developed at the National Renewable Energy Laboratory (NREL). A cloud retrieval technique is used to estimate cloud albedo and cloud fraction from surface-based observations of GHI. With the assumption of persistent cloud structures, the cloud albedo and cloud fraction are predicted for future time steps using a two-stream approximation and a 5-min exponential weighted moving average, respectively. Our model evaluation using the long-term observations of GHI at NREL's Solar Radiation Research Laboratory (SRRL) shows that the PSPI has a better performance than the persistence and smart persistence models in all forecast time horizons between 5 and 60 min, which is more significant in cloudy-sky conditions. Compared to the persistence and smart persistence models, the PSPI does not require additional observations of various atmospheric parameters but is customizable in that additional observations, if available, can be ingested to further improve the GHI forecast. An advanced technology of cloud forecast is also expected to improve the future performance of the PSPI.