The Snow Melting Process


Home	The Shuswap Lake	Runoff Report 1999

The Snow Melting Process

It happens every year, with the beginning of the warmer spring the snow in the mountains starts to melt. To understand the physics during the snow melt you just have to look at your lawn after a rain. The water source is different but the result is the same. Forced by gravity the water is pulled to the ground. At first, the dry ground is able to absorb the water, holding it in its upper layers. After a while the ground gets saturated and unable to bind the water. At this point you would recognize the building of puddles in your lawn. For the mountain region this means that the water starts to flow towards the deepest point. This happens at about 10 to 15 cm below the surface, just below the roots of the low vegetation. I don't get further into the physics of that but you may easily see this by pulling up a square of grass including its roots and surrounding ground. The flow of water is slow but steady facing a high resistance. Only if the supply of water is larger than the subsurface flow can carry, the water will flow on the surface. The water eventually will end up in a creek or stream and gets carried it away.

The following stages apply for the spring runoff:

Progress	Season	Applies to
Initial Runoff	Early Spring	Low level snow pack	Daytime temperatures are high enough to start the snow melt process. The ground absorbs the water, allows a slow subsurface flow. Cooler night temperatures interrupt the melting process and the supply of water, but subsurface flow continues throughout the night.
	Early Spring	Low level snow pack	As the temperatures get higher the melting process intensifies. During daytime the saturation point of the ground is reached, increasing the water pressure and speed of the subsurface flow. Exceptional hot days or rain may result in temporary surface flow.
Main Runoff	Late Spring / Early Summer	Low level and medium level snow pack	Warmer weather causes a constant supply of water during day and night. Subsurface flow reaches its maximum, surface flow starts. The amount of water produced by the melting process reaches its maximum and runoff continues into late night. Rain showers add water to the surface flow, which reaches the stream system very fast and can cause critical peaks.
	Summer	Medium and high level snow pack	Low level snow is gone, medium level snow continues to melt. The runoff slows down since temperatures in higher elevations are lower and the total snow surface is much smaller. Subsurface flow is slower because of the increased resistance due to larger flow distances. Also hot weather heats up the ground in lower elevations and vaporizes part of snow water.
Final Runoff	Late Summer / Early Fall	High level snow pack	Usual very limited visual indications of the runoff other than slowly decreasing snow pack. Snow melts only during daytime on hot days. Subsurface flow only, much of the water gets absorbed in lower elevations. Stream network is back to normal levels.

The Physics of Snow Melt

Two primary factors control the melting of snow:

Air temperature
Intensity of the sun

Secondary factors are

Wind, wind speed and wind temperature
Rain, rain water temperature and quantity
Heat absorption properties of the ground (i.e. rocks, vegetation, loose soil)
Angle of the sun in relation to the snow surface
Snow density and consistence

There are also some additional factors that may influence the melting process. But at this point I will concentrate on the primary factors.

Snow on the ground melts from top to bottom. Heat converts the snow particles into water and gravity pulls the water to the ground. Ignoring topics like energy and temperatures of the converted water the process is as follows.

The top layer of the snow pack absorbs the heat energy and causes the snow crystals to break down. At first surrounding snow crystals are able to bind the fine water drops. As they grow the gravitational force is gets stronger than the adhesive force and the drops start flow to the ground. This progress is actually far more complicated but not of importance here. The warmer water drops cause some pre-melting in the upper layers but eventually leak through the snow with no major effect to its consistency. The air temperature should be at least 5 degree Celsius to initiate that process. Heat absorption from direct sun light is usually much larger than from the surrounding air.

Temperature and Altitude

With increase of the altitude the air temperature decreases. This happens in a rate of 1.944444444-degree Celsius for each 1000 ft (304.8 m).

It can be calculated using the following formula:

Tc - ((Ax - Am) * (1.944444444 / 304.8))

where

Tc = current temperature (Celsius)
Ax = altitude for the questioned temperature (metres)
Am = altitude where the temperature was measured (metres)

The following example shows the temperature differences for some altitudes.

Altitude in Metres	Temperature in degree Celsius
300	20
500	18.8
800	16.8
1000	15.6
1500	12.4
2000	9.2
2500	6.0
3000	2.8

This example shows that, based on the air temperature, no snow is melting above 2500 m even if it's a nice warm day in the valley below.

The height of the now pack normally increases with the altitude. The temperature / altitude sheet clearly indicates the reason for that. Because of the cooler temperature in upper elevations a rainy day in the valley means snow conditions in the mountains. It simply snows earlier in the year and lasts longer. Snow accumulates and increases the snow pack.

Another effect of the temperature differences comes with the runoff season. The lower the altitude of the snow pack, the faster the snow melt and the more intense the runoff. Disregarding the temperature decrease for a moment, the heat energy of sun and air acts everywhere on the top layer of the snow pack at the same time. The height of the snow pack is not an important factor here, only the surface area. Snow melts at the surface in a fixed rate as defined by the laws of physics (I will come back to that in a later update). This is best explained using the following example.

Let's assume that the total runoff area of 10,000 square km is divided into portions of 50% low altitude, 40% medium altitude, and 10% high altitude. And let's further assume that height of the snow pack is 1 metre at low altitude, up to 2 metres in the medium altitude, and up to 3 metres in the higher regions. To make this example as easy as possible I will now ignore the factor of temperature differences in certain altitudes completely.
At the beginning of the runoff season the heat energy of sun and air acts on the snow surface of the complete region. This means that snow water is produced everywhere in an area of 10,000 sq. km, at any given point. This continues until the low altitude snow pack is melted away. What remains is a snow pack of 1 m in medium altitude and 2 metres in the higher elevations. The snow-covered area has decreased to 50%, which means that the amount of snow water permanently produced during the runoff is now reduced to the half of its potential. Now the medium altitude snow pack is melting leaving just a snow pack of 1 metre in higher elevation behind. The remaining area covered by snow is just 10%, producing only 1/10th of initial water.

This shows that for the day-to-day runoff observation and forecast the height of the snow pack is not the crucial factor but only the snow surface area. It differs from long term forecasting where the height of the snow pack allows some indications for the accumulated effect on lakes and reservoirs. A typical example of this misconception was the 1999 runoff season for the Shuswap Lake region where information about the total snow pack of about 130% to 160% above normal caused some scare among local residents. This kind of prophecy simply has been proven false.

The next page will give a closer insight in the runoff characteristics for the Shuswap Lake region.

=== Top of Page ===