Predictive code simulations of high density scenarios of ITER and other reactor-grade devices require an experimentally validated scaling relation for the one-fluid effective heat diffusivity chi in the ELMy H mode regime. A comprehensive empirical chi scaling compatible with the ITERH92-P ELMy H mode scaling of the thermal energy confinement time is presented. It follows from a power law ansatz for chi and integration of the single-fluid energy equation and recovers all the exponents of the global confinement law. The numerical factor of the global scaling is used to calibrate the heat diffusivity. The dependences of chi on the temperature and temperature gradient, connected with the power degradation of confinement, are inferred from profile information of a high density H mode discharge. The scaling law obtained is successfully tested against JET, ASDEX and ASDEX Upgrade H mode discharges covering a wide parameter range. It is found to predict the strong rise of the experimental chi profiles with increasing effective radius