Standoff detection of hazardous materials using infrared backscattering spectroscopy shows promise due to its speed of detection, sensitivity, chemical specificity, eye safety, and the ability to perform detection in a stealthy manner. However, infrared diffuse reflectance spectra of trace particles on substrates exhibit a strong dependence on substrate type, particle size, and mass loading. This has a negative impact on the performance of detection algorithms and false alarm rates when using commercially available spectral databases. We present two models that are quickly computed yet capture most of the observed spectral features. Model I is best suited for calculating the diffuse reflectance spectra of trace amounts of particles on relatively smooth substrates, while model II extends the applicability of model I to particles on very rough substrates. The models can be used for algorithm development and training. The main inputs to the models are the analyte and substrate optical constants as a function of wavelength, and the particle size distribution and average mass loading. The accuracy of the models was checked by comparing to experimentally measured diffuse reflectance spectra of several carefully prepared samples.