Thermal quality of a snowpack

From HydroWiki

The thermal quality of a snowpack is the unitless ratio of energy required to melt a unit mass of that snowpack relative to the energy required to melt a unit mass of ice at 0°C. The thermal quality of a snowpack depends on the water content and temperature of the snowpack. Thermal quality is often denoted by the symbolic term ‘B’.

Formula:

The thermal quality (B) of a snowpack is calculated as follows:

where λ_f is the latent heat of fusion at 0°C [ λ_f = 0.334 * 10⁶ J/kg ],

c_i is the specific heat of ice [ c_i = 2.1 * 10³ J/(kg °C) ],

θ is the liquid water content of the snowpack (θ = mass_water / mass_snow),

T_m is the melting temperature of ice [ T_m = 0°C ]

T_s is the average snowpack temperature (°C)

Relevance:

The thermal quality term is useful because it expresses the ‘melt readiness’ of a snowpack with respect to an important standard: the fully ripened snowpack. A snowpack is said to be ripe when it has reached isothermal 0°C, but has not yet melted. Once a snowpack is ripe, any additional energy input to the snowpack will act to melt the snow. When a snowpack is ripe, the energy required to melt a unit mass of the snow is equal to the latent heat of fusion (λ_f).

When the snowpack is ripe, B = 1. Substituting values of θ = 0 (no water in snowpack) and T_s = 0°C into the formula for thermal quality confirms this definition and demonstrates the simplicity of thermal quality:

B < 1 when a snowpack has water content. This water requires no further energy input to melt, so it subtracts from the required melt energy of a snowpack of a given mass. B > 1 when the snowpack is colder than 0°C, which means that more energy will be needed to heat the snowpack to isothermal 0°C before melting can begin.

Thermal quality is such a simple and important ratio that it is sometimes used as a term in snowpack energy balance equations.

Sources and links:

Use of ‘B’ in snowpack energy equations: http://www.wileywater.com/Contributor/Sample_3.htm