Recent advances in development of photoionization models in air based on radiative transfer and Helmholtz equations open new perspectives for efficient solution of nonthermal gas discharge problems involving complex geometries. Many practical applications require accurate modeling of streamer discharges developing in weak electric fields, in which the photoionization process significantly contributes to discharge dynamics. This paper (1) reports original studies, which demonstrate the validity and accuracy of the recently proposed photoionization models for studies of streamers in weak electric fields, and (2) introduces efficient boundary conditions for the photoinization models based on radiative transfer theory.