The present study numerically investigates the turbulent nonpremixed hydrogen jet flames. The turbulent combustion processes are represented by the reaction progress variable model coupled with the presumed joint probability density function. The reaction progress variables are derived assuming the radicals O, H, and OH to be in partial equilibrium and additional species HO2 and H2O2 in Steady state. The turbulent combustion model is extended to nonadiabatic flame by introducing additional variable for the transport equation of enthalpy and radiative heat loss is calculated using a local, geometry independent model. The predictive capability of the RPV combustion model has been validated against the detailed experimental data involving the distribution of temperature, major species, radicals, and NO. Effects of the HO2/H2O2 chemistry and radiative heat loss on the thermal NO formation are discussed in detail. In order to examine the validity of the optically thin radiation model in conjunction with the improved RPV model, the present numerical results for the radiant fraction have been compared with measurements and other computational results. Furthermore the capability of the present RPV model reproducing the NOx emission index (EINOx) is critically evaluated.