A wavelet variability model (WVM) for simulating solar photovoltaic (PV) power plant output given a single irradiance point sensor timeseries using spatio-temporal correlations is presented. The variability reduction (VR) that occurs in upscaling from the single point sensor to the entire PV plant at each timescale is simulated, then combined with the wavelet transform of the point sensor timeseries to produce a simulated power plant output. The WVM is validated against measurements at a 2-MW residential rooftop distributed PV power plant in Ota City, Japan and at a 48-MW utility-scale power plant in Copper Mountain, NV. The WVM simulation matches the actual power output well for all variability timescales, and the WVM compares well against other simulation methods.