Freezing degree-day ($N=\int \max (T_f-T_a,0)dt$)

A freezing degree-day accumulates air temperature below a declared reference freezing temperature, with time in days and temperature difference in degrees Celsius or kelvins. The reference temperature and averaging convention must match the empirical sea ice thermodynamics formula using it. Warming by a constant $\Delta T$ subtracts $\Delta T$ times the number of days only if those days remain below the reference threshold.