where RF and RM are the freezing and melting rate, respectively, La the latent heat of fusion of ice (3.34 x 105 J kg-1) and cp,i the specific heat capacity of ice (2.1 x 103 J kg-1 K-1); ps is the snow density and Ts is the snow temperature,2 both at height z. The integral is over the snowpack depth HS and is often referred to as the snowpack's cold content. Freezing and melting rates couple the energy balance through Equation (3.2) to the mass M per unit area of the snowpack which, neglecting the mass of air, is given by:

z where Q\ and Qi are the volumetric fractions of ice and water taken at height z with densities p; and pi, respectively. The mass balance of the snowpack is given in units of kg m-2 s-1 by (see Fig. 3.2):

dt where dM/dt is the snowpack mass change rate (positive in the case of accumulation); P is the precipitation rate (accumulation) and E = Esubl + Eevap

1 Here energy fluxes are the dot product of energy flux densities and the unit normal to the surface. Using the coordinate system shown in Fig. 3.1, energy flux densities directed away from a surface lead to a positive energy flux.

2 Because 0°C (273.15 K) is the melting point of ice, the Celsius scale is the natural choice for describing temperature conditions. However, the absolute Kelvin scale is used in the equations unless stated otherwise.


Sum of sublimation and evaporation rate at surface

Precipitation rate



Snow mass per unit area M

Runoff rate .t snow-soil interface^

R runoff

Runoff rate .t snow-soil interface^

R runoff

Figure 3.2. Mass balance for an open snowpack.

Snow depth

Figure 3.2. Mass balance for an open snowpack.

z y is the sum of sublimation and evaporation rates at the surface that may contribute either positively or negatively to the mass balance. The runoff rate, Rrunoff, is strongly coupled to the melting rate of so-called isothermal snowpacks (Ts = 0 °C throughout the snowpack) and contributes to ablation only.

A further coupling of energy and mass balances arises because the latent heat flux is simply related to both sublimation and evaporation rates through:

where Lvi is the latent heat of sublimation for ice (2.838 x 106 J kg-1 at 0 °C) and Lvi is the latent heat of evaporation for water (2.505 x 106 J kg-1 at 0 °C).

3.3 The fluxes involved in the energy balance

John C. King, John W. Pomeroy, Donald M. Gray, and Charles Fierz

In the following sections, these fluxes will be discussed in greater detail and schemes for modeling them will be presented.

Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

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