Numerical Methods For Determining Snow Accumulation

This section describes various methods used by models and post-processing techniques to accumulate snow at the surface. The techniques described below generally do not account for what happens to the snow after it reaches the ground, except where noted. Light snow falling onto a very warm surface might melt on contact completely, while snow falling at a heavier rate onto the same surface might cool the surface to freezing more rapidly, allowing accumulation to commence more quickly.

Users should be cognizant of the length of time represented in a snow accumulation graphic from a model or post-processing technique. With heavy snow falling over a long period, reduction of snow depth at the surface due to compaction would not be accounted for in some of these techniques. A warm air mass moving in or a high solar angle close to the vernal or autumnal equinox might lead to partial or complete melting with time not accounted for in these calculations. Even in cold conditions, a dry air mass moving in under sunny skies would encourage the sublimation process, reducing the snow depth at the surface over time.

Constant Snow:Liquid Ratio (SLR) Techniques

This simple technique multiplies the Quantitative Precipitation Forecast (QPF) or Snow Water Equivalent (SWE) by a fixed number to get a snow amount.

For example, a constant 10:1 SLR would yield 1" of snow for 0.1" of QPF or SWE. A constant 15:1 SLR would yield 1.5" of snow for the same 0.1" of QPF or SWE. The constant SLR to be used is determined by thickness values and/or the maximum temperature in the column. Lower SLRs (5:1 or 8:1) are often observed in marginally-warm environments or where sleet mixes with the snow. Higher SLRs (15:1 or 17:1) are often observed in very cold environments.

Limitation: the SLR is not uniform geographically or even in the same event at a fixed location. Different thermodynamic profiles can significantly affect the SLR (See Baxter et al. 2005), yielding potentially-substantial errors when using a constant SLR.

Variable SLR Techniques (Kuchera and Cobb Techniques, Variable Density, Snow Fraction)

Kuchera Technique:

• This technique identifies the maximum temperature (Tmax) in the column from the surface to 500 hPa:
  • If Tmax is greater than 271.16K (~28°F or -2°C), SLR = 12 + 2(271.16-Tmax)
  • If Tmax is less than or equal to 271.16K, SLR = 12 + (271.16-Tmax)
• Assuming primarily dendritic snow, this is generally superior to constant 10:1 SLR in areas of marginally warm or very cold temperature profiles
• Limitation: Can substantially overestimate accumulation in very cold air masses with strong winds/turbulence, as crystal branches break off due to collision of dendrites during descent, lowering the density of the accumulated snow at the surface
• Limitation: Can also substantially overestimate accumulation in very cold air masses where the primary crystal types are columns and plates instead of dendrites

Cobb Technique:

• This technique uses hourly model data and combines multiple techniques at a single point (Cobb and Waldstreicher 2005):
  • Looks at vertical velocity, wet- and dry-bulb temperatures, and relative humidity to create SLR at every model level from where the hydrometeor initiates to the surface
  • Calculates percentage of hydrometeors reaching the surface along with precipitation type and SLR at the lowest model level
    • Precipitation types are binned into snow, ice (sleet), or liquid (rain/freezing rain)
• This technique is difficult to implement within model code, so it is generally done in model post-processing
• A modification to the Cobb method is applied when using data from Convection Allowing Models to account for stronger vertical velocities in those models

Variable Snow Density (NOAA Tech Memorandum OAR GSL-66):

• Varies SLR from less than 5:1 to a maximum of 17:1 based on the lowest model level temperature
• Accumulation uses both snow and graupel/sleet, includes subtracting melting of fresh snow to estimate what is measured on a snowboard
• Limitation: Does not account for change in snow crystal type for various thermodynamic profiles, nor vertical motion profiles

Snow Fraction:

• Determines fraction of snow from the total precipitation over past hour
• Based on precipitation fall rate and liquid amount over previous hour, and the average 2 meter temperature in that hour
• Good for borderline cases of near-surface temperatures around 0°C/32°F
• Does not account for thermodynamic profile above the surface (e.g., warm nose)

Artificial Intelligence/Neural Networks

Roebber Method (Roebber et al. 2003):

• Artificial Neural Network technique using 28 radiosonde sites collocated with surface reports to from a dataset spanning 1973-1994
• Looks at low-to-mid level temperature and relative humidity, mid-to-upper level temperature, mid and upper level relative humidity, and the month (which is a proxy for insolation)
• Attempts to account for compaction using surface wind speed and liquid precipitation estimation
• Breaks out light/moderate/heavy snow density
• Limitation: Neglects in-cloud vertical motion, strong low-level wind, and early/late season ground temperature effects (like warm ground, wet snow)