Abstract. Electromagnetic signals commonly used in geodetical applications, such as the Global Navigation Satellite System (GNSS), undergo bending and delay in the neutral gas atmosphere of the Earth. The least-travel-time (LTT) concept is one of the approaches to model signal slant delays via a ray tracing (RT) procedure. In this study, we developed an LTT-based RT algorithm (LTT v2), where the 3-dimensional refractivity field of the atmosphere is based on the atmospheric model data. This representation is complete in a sense that the domain of the RT conforms to the native grid geometry of the atmospheric model. In addition, some physical and numerical approximations are improved compared to the previous version (LTT v1). The atmospheric states are generated using a global numerical weather prediction model, the Open Integrated Forecast System of the European Centre for Medium-Range Weather Forecasts. The slant delays of LTT v2 are compared with the products of the original least-travel-time GNSS delay model (LTT v1) and the products of the state-of-the-art VieVS Ray Tracer (RADIATE). The skill of slant delay estimation is assessed using metrics that are indicative of the quality of GNSS products derived using the GROOPS (Gravity Recovery Object Oriented Programming System) orbit solver software toolkit of the Graz University of Technology. Employment of slant delay products of the LTT RT algorithm shows radical improvement in GNSS processing. When using LTT v2 delay estimates, the GNSS orbit midnight discontinuities are reduced by more than 10 % compared to RADIATE, and more than 2 % compared to LTT v1. The residuals of ground station precise positioning are analysed with respect to the IGS14 reference positions. The RMS of residuals (accuracy) and standard deviation (precision) are substantialy reduced compared to RADIATE.