The Nowcast of Atmospheric Ionizing Radiation for Aviation Safety (NAIRAS) is a real-time, global, physics-based model used to assess radiation exposure to commercial aircrews and passengers. The model is a free-running physics-based model in the sense that there are no adjustment factors applied to nudge the model into agreement with measurements. The model predicts dosimetric quantities in the atmosphere from both galactic cosmic rays (GCR) and solar energetic particles, including the response of the geomagnetic field to interplanetary dynamical processes and its subsequent influence on atmospheric dose. The focus of this paper is on atmospheric GCR exposure during geomagnetically quiet conditions, with three main objectives. First, provide detailed descriptions of the NAIRAS GCR transport and dosimetry methodologies. Second, present a climatology of effective dose and ambient dose equivalent rates at typical commercial airline altitudes representative of solar cycle maximum and solar cycle minimum conditions and spanning the full range of geomagnetic cutoff rigidities. Third, conduct an initial validation of the NAIRAS model by comparing predictions of ambient dose equivalent rates with tabulated reference measurement data and recent aircraft radiation measurements taken in 2008 during the minimum between solar cycle 23 and solar cycle 24. By applying the criterion of the International Commission on Radiation Units and Measurements (ICRU) on acceptable levels of aircraft radiation dose uncertainty for ambient dose equivalent greater than or equal to an annual dose of 1 mSv, the NAIRAS model is within 25% of the measured data, which fall within the ICRU acceptable uncertainty limit of 30%. The NAIRAS model predictions of ambient dose equivalent rate are generally within 50% of the measured data for any single-point comparison. The largest differences occur at low latitudes and high cutoffs, where the radiation dose level is low. Nevertheless, analysis suggests that these single-point differences will be within 30% when a new deterministic pion-initiated electromagnetic cascade code is integrated into NAIRAS, an effort which is currently underway.