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This paper reports on the refinement (building on Ref.~\cite{hatch_22}) andapplication of simple formulas for electron heat transport from electrontemperature gradient (ETG) driven turbulence in the pedestal. The formulas areimproved by (1) improving the parameterization for certain key parameters and(2) carefully accounting for the impact of geometry and shaping in theunderlying gyrokinetic simulation database. Comparisons with nonlineargyrokinetic simulations of ETG transport in the MAST pedestal demonstrate themodel's applicability to spherical tokamaks in addition to standard aspectratio tokamaks. We identify bounds for model applicability: the model isaccurate in the steep gradient region, where the ETG turbulence is largelyslab-like, but accuracy decreases as the temperature gradient becomes weaker inthe pedestal top and the instabilities become increasingly toroidal in nature.We use the formula to model the electron temperature profile in the pedestalfor four experimental scenarios while extensively varying input parameters torepresent uncertainties. In all cases, the predicted electron temperaturepedestal exhibits extreme sensitivity to separatrix temperature and density,which has implications for core-edge integration. The model reproduces theelectron temperature profile for high $\eta_e = L_{ne}/L_{Te}$ scenarios butnot for low $\eta_e$ scenarios in which microtearing modes have beenidentified. We develop a proof-of-concept model for MTM transport and explorethe relative roles of ETG and MTM in setting the electron temperature profile.We propose that pedestal scenarios predicted for future devices should betested for compatibility with ETG transport.

Modeling electron temperature profiles in the pedestal with simple formulas for ETG transport