Degree-Day Snowmelt

The degree-day method is a temperature-index model, and it is an empirical shortcut, not physics. Melting really takes energy (see the latent heat page), and the heat the snow actually receives is what drives it, but air temperature is measured everywhere and stands in well for that heat. So each degree above the base temperature is assumed to melt a fixed depth of water, the degree-day factor. It is the oldest and simplest model of snowmelt and is still widely used in river forecasting. Hock (2003) reviews temperature-index melt modelling in mountain areas.

In $M = \mathrm{DDF}\,\max(T - T_b,\ 0)$, $T$ is the mean air temperature of the day, the mean of the highest and lowest or of the hourly values, and $T_b$ is the base temperature, 0 °C unless a basin has been calibrated otherwise. The $\max$ means a day at or below the base melts nothing: the formula never gives a negative melt. The degree-day factor is a depth of water per degree per day, about 2 for a snowpack under forest, 4 as a middling value, and 7 or more for open, sunny snow. The answer is a depth of water, not of snow.

With a factor of 4, a mean of 2.5 °C and a base of 0 °C, the melt is 4 × 2.5 = 10 mm/day. Open, sunny snow with a factor of 7 and a mean of 5.2 °C melts 7 × 5.2 = 36.4 mm/day. A mean of $-3$ °C with a base of 0 °C melts nothing. Run backward, 10 mm/day at 2.5 °C above the base gives a factor of 4, which is the way to find a factor from a measured melt.

Because only air temperature enters, the method cannot tell a sunny day from a cloudy one at the same temperature, and the factor has to absorb the difference. That is why it runs from about 2 under forest to 7 or more in the open. Treat a factor as a calibrated value for the setting it came from, and turn to the latent heat page when the full energy balance matters. The snow-water-equivalent page gives the depth of water the pack holds, which a day's melt is taken from.