Cecil Moore wrote:
"The definition of irradiance is "the average energy per unit time. Any
deviation away---."

As energy per unit time is power, Cecil`s definition agrees with what my
dictionary says:
"Irradiance-The incident radiated power per unit area of a surface; the
radiometric counterpart of illumination, usually expressed in watts/cm,
squared."

This is different from Poynting which uses instantaneous values.

Best regards, Richard Harrison. KB5WZI