Heat Deficits

The heat deficit is defined as the amount of heat that must be added to return the snow pack from below 0 ºC to an isothermal state (0 °C) (Anderson 1973; Anderson 1976; Melloh 1999). The equations to calculate the heat deficit within this report are based on the National Weather Service River Forecasting System (NWSRFS) SNOW-17 model (Anderson 1973). There are two types of heat defi-cit, one caused by temperature and one caused by precipitation. It is important to include the heat deficit because melt and rain continue to refreeze within the snow cover until the heat deficit reaches zero (Melloh 1999). The heat deficit described below is in units of mm of SWE, making it easily incorporated into most snow melt routines by simply reducing the amount of melt (in mm of SWE) calculated in the melt routine by the heat deficit.

TEMPERATURE BASED HEAT DEFICIT When the air surface temperature drops below 0 °C the snow pack drops in tem-perature as well, creating a temperature deficit that is a portion of the heat deficit. By not considering the temperature deficit of the snow, the simulated snow melts too quickly when temperatures rise from below 0 °C to above 0 °C. The SNOW-17 model incorporates a method where temperature indices, essentially a term to consider snow pack temperature, are calculated based on Equation 1, and then are used in Equation 2 to calculate the change in snow cover heat deficit due to tem-perature. Equations 1, 2, and 3 are used to account for the temperature deficit within the snow pack. The weighting multiplier (TIPM) and the proportionality factor (NM_F) are calibration parameters, but the results section will show that they are relatively insensitive when compared to the parameters and algorithms per-taining to the melting processes.

ATI2 = ATI1 + TIPMdt * (Ta - ATI1)

(1)

ΔDt = NMF * (ATI1 - (Ta)

(2)

TIPMdt = 1.0 - (1.0 - TIPM)dt/6

(3)

ATI₁ = temperature indices at the beginning of time step (ºC) ATI₂ = temperature indices at the end of time step (ºC)

       Ta = air temperature (ºC)

dt = time step (hours) TIPM_dt = weighting multiplier (0.1 to 1.0) for previous time period TIPM = weighting multiplier (0.1 to 1.0) for previous 6-hr period ΔD_t = change in heat deficit due to a temperature gradient, expressed in water equivalent (mm SWE) NM_F = proportionality factor, also known as the negative melt factor (mm/ºC per 6hr)

PRECIPITATION BASED HEAT DEFICIT