The temperature-index (TI) method of estimating snowfall accumulation and melting is based on the National Weather Service River Forecasting System (NWSRFS) SNOW-17 model. This method takes into consideration the time of year, melt due to temperature, melt due to precipitation, and Heat Deficits within the snow pack. Two equations are used to calculate the amount of melt during a time step. Equation 7 is used in precipitation dominated time spans when the average precipitation over the previous 6 hours has exceeded 0.25 mm hr-1 and precipitation is occurring during the current time step. Equation 8 is used in all other times when the melt is considered temperature-dominated. The precipitation temperature, Tr, is assumed to be 0 °C or the air temperature, whichever is greater. Both melt routines only work when the air surface temperature is greater than 0 °C and only one melt routine is run per time step.
The TI method also keeps track of melt water being stored in the snowpack and water released from the snow pack. Although Equations 1-5 help simulate the “ripeness” of the snow pack by accounting for the heat deficit, Equations 18-21 are included in the TI method to help determine how much liquid water is being stored within the snow pack. The amount of melt that leaves the snow pack (MTI) is calculated in Equation 20 and is representative of the overall melt from the pack after the heat deficit and water storage capacity of the pack are accounted for.
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Mr = σ * dt * [(Ta + 273)4 - 2734] + 0.0125 * Px * fruse * Tr + 8.5 * fua * (dt/6) *
[(0.9 * esat - 6.11) + 0.00057 * Pa * Ta |
(14)
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Mnr = Mf * (Ta - MBASE) + 0.0125 * Px * fruse * Tr |
(15)
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Mf = (dt/6) * (Sv * (Av * (MFMAX - MFMIN) + MFMIN) |
(16)
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Sv = 0.5 * sin(<math>\tfrac{N * 2 * pi}{366}</math>) + 0.5 |
(17)
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Qw = Mr + Mnr + Px * fruse |
(19)
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MTI = Qw + Wq,n - Wqx - D2 - (PLWHC * D2) |
(20)
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Wq,n+1 = Wq,n - Qw - D2 |
(21)
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Mr = melt during precipitation-dominated time steps (mm)
σ = Stefan-Boltzman constant (6.12*10-10 mm/ºK/hr)
fruse = fraction of precipitation in the form of rain
fua = average wind function (mm/mb per 6hr)
Mnr = melt during temperature-dominated time steps (mm)
Mf = melt factor (mm/°C/dt)
MFMIN = minimum melt factor – Dec 21st (mm SWE/°C per 6 hrs)
MFMAX = maximum melt factor – June 21st (mm SWE/°C per 6 hrs)
MBASE = temperature at which snow begins to melt (°C)
Av = seasonal variation adjustment
Sv = seasonal sine curve melt variation
N = day number since March 21st
MTI = overall melt calculated using the temperature-index snow melt routine (mm SWE)
Wqx = liquid water capacity (mm)
Wq = liquid water held by the snow (mm)
Wi = water equivalent of the ice portion of the snow cover (mm)
Qw = liquid water available at the snow surface (mm)
PLWHC = percent liquid water holding capacity (decimal fraction)
The ice portion of the snow pack (Wi) is calculated based on the SWE of the snow pack and PLWHC. The calibration parameters when using the TI method include: SCF, MFMAX, MFMIN, fua, MBASE, fruse, TIPM, NMF, and PLWHC. For more information on the SNOW-17 model the reader is guided to Anderson, 1973; Anderson, 1976; and Melloh, 1999. The SNOW-17 model was originally intended for a 6-hour time step, but is compatible with an hourly time step. Although GSSHA employs a global variable time step which can be sub-minute, the TI method is always run at an hourly time step. The melt generated during the hour time step is distributed to the other GSSHA model processes at the global variable time step.
