Snow melting and freezing

Snow melts in response to several climatic conditions, including air temperature, sun shine (solar radiation), the heat content of rain, and the heat transfer from condensing moisture in the air.

1. Snow moisture content

It is well known that melting snow does not immediately genenerate runoff. Rather, the snow gradually becomes wetter, like a sponge, until liquid water starts to drain out of the snow pack. If the temperature drops below freezing again, the liquid water will re-freeze. In MIKE SHE, this is conceptualized as two seperate snow storages - dry (or frozen) snow storage and wet (or liquid) snow storage.

Snow melt occurs by converting dry snow to wet snow. Surface runoff occurs when the ratio of dry to wet snow storage reaches a user specified maximum

- the maximum wet snow storage fraction, where the wet snow storage fraction, Wfrac, is calculated by

Equation 23.4:

\(W_{frac} = \frac{S_{wet}}{S_{wet}+S_{dry}}\)

where \(S_{wet}\) and \(S_{dry}\) are the wet and dry snow storages respectively.

2. Air temperature melting

If the air temperature is above the threshold melting temperature, then the snow will begin to melt and the snow storage will be reduced by

Equation 23.5:

\(M_T = C_T \cdot (T_{air} - T_0)\)

where \(M_T\) is the rate of melting due to the air temperature, \(C_T\) is the degree-day factor for snow melting (e.g in units of mm/day/C degree), \(T_{air}\) is the air temperature of the cell, and \(T_0\) is the threshold melting temperature. The air temperature melting will be positive if the air temperature is above the threshold temperature and negative if it is below. Thus, if the air temperature falls below the threshold melting temperature, then wet snow will be reconverted back to dry snow.

Note

In MIKE SHE, the degree-day factor is a time varying, spatially distributed value. This allows you to calibrate your snow melt over the winter season as the snow properties (e.g. albedo, density, etc) change.

3. Radiation melting

Solar radiation will cause the snow to melt at a rate proportional to the amount of incoming radiation. On cloudy days, the radiation intensity will be less, but still non-zero. Thus,

Equation 23.6:

\(M_R = -C_{rad} \cdot R_{SW}\)

where \(M_R\) is the rate of melting due to incoming short wave radiation, \(C_{rad}\) is the radiation melting factor for snow melting (e.g in units of mm/(kJ/m2)), \(R_{sw}\) is the amount of incoming solar radiation (e.g. in units of kJ/m2/hour).

4. Energy melting

The condensation of moist air on snow and the heat released from liquid rain as it cools are important contributors to snow melt. Even though these energy sources are not physically simulated, the following linear relationship allows these processes to be included.

Equation 23.7:

\(M_E = -C_E \cdot P \cdot (T_{air} - T_0)\)

where \(M_E\) is the rate of melting due to the energy in liquid rain, \(C_E\) is the energy melting coefficient for the energy in liquid rain (e.g in units of mm/mm rain/C degree), \(T_{air}\) is the air temperature of the cell, and \(T_0\) is the threshold melting temperature.

Energy melting only occurs if the air temperature is above the threshold melting temperature. In other words, the energy melting is aways positive. The temperature of the rain is assumed to be the same as the air temperature.

Note

The energy melting coefficient is a constant value for the entire model.

5. Snow balance

If the air temperature is above the threshold melting temperature, then dry snow storage will be reduced (converted to wet snow) by combining the three melting rates.

Equation 23.7:

\(M_{total} = M_T + M_R + M_E\)

If, on the other hand, the air temperature is below the threshold melting temperature, then the dry snow storage will be increased (wet snow converted to dry snow) by combining the freezing rate and the radiation melting rate, until the wet snow storage goes to zero

Equation 23.9:

\(M_{total} = M_T + M_R\)

In this case, the temperature melting will be positive (i.e. freezing) and radiation melting will be negative.

6. Snow pack area coverage

When the snow storage is small, snow will not cover the enter cell area. Rather, the snow will be concentrated in sheltered areas. If a small snow thickness was spread out over the entire cell area, then melting would occur too quickly. Thus, MIKE SHE also includes a snow coverage function, where you provide a minimum snow depth for which you can assume that the entire cell is covered with snow. For snow depths less than this minimum, the area fraction is linearly reduced to zero when the snow storage goes to zero. Thus, the area factor, Af, is

Equation 23.10:

\(A_f = \frac{S_T}{S_{min}}\)

where \(S_T\) is the total snow storage (wet + dry) and \(S_{min}\) is the minimum snow depth for full area coverage.

The melting/freezing rates are multiplied by the area factor before being applied. Furthermore, if the area factor is less than one, then the precipitation and ET is distributed between the snow and the normal ground surface based on the area factor.

7.ET from snow

The ET module will remove water from snow storage before any other ET is removed.

1. ET is removed first from wet snow as evaporation because the energy requirements for evaporation are lower than sublimation. The ET is removed from wet snow at the full rate, assuming that wet snow can be treated the same as ponded water.

2. If there is no wet snow (either because it is too cold or all the wet snow has been evaporated) then ET will be removed from dry snow as sublimation.

However, sublimation has a higher energy requirement than evaporation, so MIKE SHE includes a user defined factor for controlling sublimation. This is found on the Snow Melt dialog. The sublimation factor is a multiplier that reduces the actual ET rate from the snow. If the sublimation factor = 0, then the ET rate is 0. If the sublimation factor = 1.0, then the ET rate is the specified Reference ET rate. Thus,

\(Maximum ET = (Reference ET) \cdot (Crop Coefficient) \cdot (Sublimation Factor)\)

See Reference Evapotranspiration and the Crop Coefficient specified in the Vegetation Properties Editor.