Difference between revisions of "Radiation-derived Temperature Index"

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(Created page with "The Radiation-derived Temperature-Index (RTI) is based on the SNOW-17 snow model (TI method in GSSHA), but replaces Air Temperature (T<sub>a</sub>, °C) with a radiation-de...")
 
 
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The Radiation-derived Temperature-Index (RTI) is based on the SNOW-17 snow model (TI method in GSSHA), but replaces Air Temperature (T<sub>a</sub>, &deg;C) with a radiation-derived proxy temperature (T<sub>rad</sub>, &deg;C)
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The Radiation-derived Temperature-Index (RTI) snow model is based on the SNOW-17 snow model (TI method in GSSHA), but replaces Air Temperature (T<sub>a</sub>, &deg;C) with a radiation-derived proxy temperature (T<sub>rad</sub>, &deg;C) in the melt equations (see below).  T<sub>rad</sub> is calculated using a simple energy balance at the surface of the snowpack, allowing for contributions from shortwave and long wave radiation, which includes the impacts of topography, cloud cover, vegetation, and atmosphere.  All of the calculations are internal within GSSHA, limiting the need for additional inputs.  Because T<sub>rad</sub> includes contributions from the snowpack, the need to calibrate tow melt factors (M<sub>f,min</sub> and M<sub>f,max</sub>) can be replaced with a constant melt factor (M<sub>f</sub>).
  
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The RTI snow model is based on Follum et al. (2015).
  
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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<sup>-1</sup> 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, T<sub>r</sub>, is assumed to be 0 &deg;C or the air temperature, whichever is greater.  Both melt routines only work when the air surface temperature is greater than 0 &deg;C and only one melt routine is run per time step.
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The RTI model has been tested at several locations, with the RTI model showing to more accurately capture spatial heterogeneity within the snowpack.
  
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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 (M<sub>TI</sub>) 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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| width=550 | ''M<sub>r</sub> = '''σ''' * dt * [(T<sub>a</sub> + 273)<sup>4</sup> - 273<sup>4</sup>] + 0.0125 * P<sub>x</sub> * fr<sub>use</sub> * T<sub>r</sub> + 8.5 * fua * (dt/6) * <br>[(0.9 * e<sub>sat</sub> - 6.11) + 0.00057 * P<sub>a</sub> * T<sub>a</sub> || (14)
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| width=550 | ''M<sub>r</sub> = '''σ''' * dt * [(T<sub>rad</sub> + 273)<sup>4</sup> - 273<sup>4</sup>] + 0.0125 * P<sub>x</sub> * fr<sub>use</sub> * T<sub>r</sub> + 8.5 * fua * (dt/6) * <br>[(0.9 * e<sub>sat</sub> - 6.11) + 0.00057 * P<sub>a</sub> * T<sub>rad</sub> || (14)
 
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| width=550 | ''M<sub>nr</sub> = M<sub>f</sub> * (T<sub>a</sub> - MBASE) + 0.0125 * P<sub>x</sub> * fr<sub>use</sub> * T<sub>r</sub> || (15)
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| width=550 | ''M<sub>nr</sub> = M<sub>f</sub> * (T<sub>rad</sub> - MBASE) + 0.0125 * P<sub>x</sub> * fr<sub>use</sub> * T<sub>r</sub> || (15)
 
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| width=550 | ''M<sub>f</sub> = (dt/6) * (S<sub>v</sub> * (A<sub>v</sub> * (MF<sub>MAX</sub> - MF<sub>MIN</sub>) + MF<sub>MIN</sub>) || (16)
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| width=550 | ''M<sub>f</sub> = constant value defined by user || (16)
 
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| width=550 | ''S<sub>v</sub> = 0.5 * sin(<math>\tfrac{N * 2 * pi}{366}</math>) + 0.5 || (17)
 
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| width=550 | ''W<sub>qx</sub> = PLWHC * W<sub>i</sub> || (18)
 
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| width=550 | ''Q<sub>w</sub> = M<sub>r</sub> + M<sub>nr</sub> + P<sub>x</sub> * fr<sub>use</sub> || (19)
 
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| width=550 | ''M<sub>TI</sub> = Q<sub>w</sub> + W<sub>q,n</sub> - W<sub>qx</sub> - D2 - (PLWHC * D2) || (20)
 
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| width=550 | ''W<sub>q,n+1</sub> = W<sub>q,n</sub> - Q<sub>w</sub> - D2 || (21)
 
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M<sub>r</sub> = melt during precipitation-dominated time steps (mm)
 
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'''σ''' = Stefan-Boltzman constant (6.12*10<sup>-10</sup> mm/ºK/hr)
 
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fr<sub>use</sub> = fraction of precipitation in the form of rain
 
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fua = average wind function (mm/mb per 6hr)
 
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M<sub>nr</sub> = melt during temperature-dominated time steps (mm)
 
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M<sub>f</sub> = melt factor (mm/&deg;C/dt)
 
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MF<sub>MIN</sub> = minimum melt factor – Dec 21<sup>st</sup> (mm SWE/&deg;C per 6 hrs)
 
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MF<sub>MAX</sub> = maximum melt factor – June 21<sup>st</sup> (mm SWE/&deg;C per 6 hrs)
 
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MBASE = temperature at which precipitation begins to fall as snow (&deg;C)
 
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A<sub>v</sub> = seasonal variation adjustment
 
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S<sub>v</sub> = seasonal sine curve melt variation
 
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N = day number since March 21<sup>st</sup>
 
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M<sub>TI</sub> = overall melt calculated using the temperature-index snow melt routine (mm SWE)
 
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W<sub>qx</sub> = liquid water capacity (mm)
 
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W<sub>q</sub> = liquid water held by the snow (mm)
 
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W<sub>i</sub> = water equivalent of the ice portion of the snow cover (mm)
 
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Q<sub>w</sub> = liquid water available at the snow surface (mm)
 
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PLWHC = percent liquid water holding capacity (decimal fraction)
 
  
  
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The ice portion of the snow pack (W<sub>i</sub>) is calculated based on the SWE of the snow pack and PLWHC. The calibration parameters when using the TI method include: SCF, MF<sub>MAX</sub>, MF<sub>MIN</sub>, fua, MBASE,  f<sub>ruse</sub>, TIPM, NM<sub>F</sub>, 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.
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The main cards used in the RTI snow model include:
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:RTI_SNOW                  => Tells GSSHA to use the RTI snow model
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:NWSRFS_MF_CONSTANT 1.3    => Constant Melt Factor
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:NWSRFS_TIPM 1.0          => Same as TI Snow Method
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:NWSRFS_NMF 0.2            => Same as TI Snow Method
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:NWSRFS_FUA .5            => Same as TI Snow Method
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:NWSRFS_PLWHC 0.002        => Same as TI Snow Method
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:NWSRFS_FR_USE 0.0        => Same as TI Snow Method

Latest revision as of 19:21, 25 September 2018

The Radiation-derived Temperature-Index (RTI) snow model is based on the SNOW-17 snow model (TI method in GSSHA), but replaces Air Temperature (Ta, °C) with a radiation-derived proxy temperature (Trad, °C) in the melt equations (see below). Trad is calculated using a simple energy balance at the surface of the snowpack, allowing for contributions from shortwave and long wave radiation, which includes the impacts of topography, cloud cover, vegetation, and atmosphere. All of the calculations are internal within GSSHA, limiting the need for additional inputs. Because Trad includes contributions from the snowpack, the need to calibrate tow melt factors (Mf,min and Mf,max) can be replaced with a constant melt factor (Mf).

The RTI snow model is based on Follum et al. (2015).

The RTI model has been tested at several locations, with the RTI model showing to more accurately capture spatial heterogeneity within the snowpack.


Mr = σ * dt * [(Trad + 273)4 - 2734] + 0.0125 * Px * fruse * Tr + 8.5 * fua * (dt/6) *
[(0.9 * esat - 6.11) + 0.00057 * Pa * Trad 		(14)
Mnr = Mf * (Trad - MBASE) + 0.0125 * Px * fruse * Tr (15)
Mf = constant value defined by user (16)



The main cards used in the RTI snow model include:

RTI_SNOW => Tells GSSHA to use the RTI snow model
NWSRFS_MF_CONSTANT 1.3 => Constant Melt Factor
NWSRFS_TIPM 1.0 => Same as TI Snow Method
NWSRFS_NMF 0.2 => Same as TI Snow Method
NWSRFS_FUA .5 => Same as TI Snow Method
NWSRFS_PLWHC 0.002 => Same as TI Snow Method
NWSRFS_FR_USE 0.0 => Same as TI Snow Method
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