Recent high-speed imaging of ignition processes in spray-guided gasoline engines has motivated the development of the physically-based spark channel ignition monitoring model SparkCIMM, which bridges the gap between a detailed spray/vaporization model and a model for fully developed turbulent flame front propagation. Previously, both SparkCIMM and high-speed optical imaging data have shown that, in spray-guided engines, the spark plasma channel is stretched and wrinkled by the local turbulence, excessive stretching results in spark re-strikes, large variations occur in turbulence intensity and local equivalence ratio along the spark channel, and ignition occurs in localized regions along the spark channel (based upon a Karlovitz-number criteria). In this paper, SparkCIMM is enhanced by: (1) an extended flamelet model to predict localized ignition spots along the spark plasma channel, (2) a detailed chemical mechanism for gasoline surrogate oxidation, and (3) a formulation of early flame kernel propagation based on the G-equation theory that includes detailed chemistry and a local enthalpy flamelet model to consider turbulent enthalpy fluctuations. In agreement with new experimental data from broadband spark and hot soot luminosity imaging, the model establishes that ignition prefers to occur in fuel-rich regions along the spark channel. In this highly-turbulent highly-stratified environment, these ignition spots burn as quasi-laminar flame kernels. In this paper, the laminar burning velocities and flame thicknesses of these kernels are calculated along the mean turbulent flame front, using tabulated detailed chemistry flamelets over a wide range of stoichiometry and exhaust gas dilution. The criteria for flame propagation include chemical (cross-over temperature based) and turbulence (Karlovitz-number based) effects. Numerical simulations using ignition models of different physical complexity demonstrate the significance of turbulent mixture fraction and enthalpy fluctuations in the prediction of early flame front propagation. A third paper on SparkCIMM (companion paper to this one) focuses on the importance of molecular fuel properties and flame curvature on early flame propagation and compares computed flame propagation with high speed combustion imaging and computed heat release rates with cylinder pressure analysis. The goals of SparkCIMM development are to (a) enhance our fundamental understanding of ignition and combustion processes in highly-turbulent highly-stratified engine conditions, (b) incorporate that understanding into a physically-based submodel for RANS engine calculations that can be reliably used without modification for a wide range of conditions (i.e., homogeneous or stratified, low or high turbulence, low or high dilution), and (c) provide a submodel that can be incorporated into a future LES model for physically-based modeling of cycle-to-cycle variability in engines. Published by Elsevier Inc. on behalf of The Combustion Institute.