This paper presents a statistical signature model that accounts for variability in the measured radiance spectrum from a target, based on an extensive physical model. Spectral variability is simulated in Modtran using a target’s reflectance spectrum and the resulting set of possible radiance spectra are represented by a statistical distribution function. The model incorporates the likely signature variability, taking into account estimates of variability and uncertainty in the physical imaging conditions. Estimates of the adjacency effect and secondary illumination are included. The model is tested on hyperspectral data by performing signature-specific detection. A simple method for combining signature and background information for detection purposes is also presented and tested. Good detection results are obtained, even for targets in difficult illumination conditions.