Snowpack Properties, Evolution and Ablation

1
Snowpack Properties, Evolution and Ablation

• The discussion in the preceding lectures has
  emphasized the various processes of metamorphism
  that control the snow bulk properties.
• Thermal properties that depend only on density
  (specific heat, latent heat) are well defined.

2

• However, those that depend on conductivity or
  permeability of the snowpack are affected by
  sintering, particle size, ice layers and depth
  hoar.
• The specific and latent heats of snow are the
  simplest thermal properties to determine since
  the contributions from air and water vapour can
  be discounted each property is simply the
  product of the snow density and the corresponding
  property for ice.

3

• The temperature dependence of the specific heat
  of ice given by Dorsey (1940) is
• C 2.115 0.00779T
• where C is the specific heat (kJ kg-1 K-1), and T
  (oC) is temperature.
• The latent heat of melting of ice at 0oC and
  standard atmospheric pressure is 333.66 kJ kg-1.

4

• For one-dimensional, steady-state heat flow by
  conduction in a solid the thermal conductivity is
  the proportionality constant of the Fourier
  equation
• F -K dT/dz
• where F is the heat flux (W m-2) and dT/dz is the
  temperature gradient.
• The thermal conductivity of snow (K) is a more
  complex property than specific heat because its
  magnitude depends on such factors as the density,
  temperature and the microstructure of the snow.

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• The thermal conductivity of ice varies inversely
  with temperature by about 0.17 oC-1 the same
  may be expected for snow.
• A temperature gradient could induce a transfer of
  vapour and the subsequent release of the latent
  heat of vapourization, thereby changing the
  thermal conductivity value.

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• In non-aspirated dry snow the heat transfer
  process involves conduction of heat in the
  network of ice grains and bonds, conduction
  across air spaces or pores, convection and
  radiation across pores (probably negligible) and
  vapour diffusion through the pores.
• Because of the complexity of the heat transfer
  processes, the thermal conductivity of snow is
  generally taken to be an apparent or
  effective conductivity Ke to embrace all the
  heat transfer processes.

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• The degree of surface packing (for example,
  hardness) also affects the flow of heat through
  snow, probably because a surface crust of low air
  permeability inhibits ventilation in the upper
  snow layer.
• The thermal conductivity of snow, even when
  dense, is very low compared to that of ice or
  liquid water therefore snow is a good insulator.
  
• This is an important factor affecting heat loss
  from buildings and the rate of freezing of lake
  and river ice.

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• Typical numerical models of snow use three
  prognostic variables to define a snowpack snow
  depth, snow water equivalent, and temperature.
• From snow depth and snow water equivalent, one
  can infer the snow density from
• ?s ?w(w/s)
• where w (m) is the snow water equivalent, s (m)
  is the snow depth, and ?s and ?w are the snow and
  water densities, respectively.

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Source Sun et al. (2004)
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• Apart from snow depth and snow water equivalent,
  the heat content or temperature of the snowpack
  is required to describe the system completely.
• The snow temperature is directly related to its
  heat content H (J) by
• T H/(?w w C).
• The energy balance of a snowpack is complicated
  not only by the fact that shortwave radiation
  penetrates the snow but also by water movement
  and phase changes.

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Source Lynch-Stieglitz (1994)
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• The energy balance of a snow volume depends upon
  whether it is a cold (lt 0oC) or a wet (0oC,
  often isothermal) snowpack.
• Recall the energy balance of the snowpack
• Q QP QH QE QG ?QS QM.
• A term is added here to the energy balance to
  consider the heat transported by precipitation
  (QP), either snowfall or rainfall.

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• In the case of a cold snowpack, such as is
  commonly found in mid-latitudes during winter
  with little or no solar input, QE and QM are
  likely to be negligible.
• Similarly, heat conduction within the snow will
  be small because of the low thermal conductivity
  of snow and the lack of solar heating, so that
  ?QS and QG are also negligible.
• The energy balance therefore reduces to that
  between a net radiative sink Q and a convective
  sensible QH heat source.

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• Although snowcover reduces the available energy
  at the surface because of its high albedo to
  solar radiation and high emissivity of longwave
  radiation, its insulative properties exert the
  greatest influence on soil temperature regime.
• Snow acts as an insulating layer that reduces the
  upward flux of heat, resulting in higher ground
  temperatures than would occur if the ground was
  bare.

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• In Canada, average ground temperatures are about
  3oC warmer than average air temperatures.
• In the case of a wet snowpack during the melt
  period, the surface temperature will remain close
  to 0oC, but the air temperature may be above
  freezing.
• Since snow is porous, liquid water infiltration
  is also important in transporting energy within
  the snowpack and into soils.

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• If meltwater freezes within the snowpack, there
  is latent release, warming snowpack layers to the
  freezing point.
• Most of the energy exchanges between snow and its
  environment occur at the atmosphere or ground
  interfaces however, because snow is porous, some
  radiation and convective fluxes that occur within
  the top few centimetres of the snowpack.

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• The important fluxes that can directly penetrate
  the snowpack are radiation, conduction,
  convection, and meltwater or rainwater
  percolation.
• Temperature regimes in dry snowpacks are
  exceedingly complex and are controlled by a
  balance of the energy regimes at the top and
  bottom of the snowpack, radiation penetration,
  effective thermal conductivity of the snow
  layers, water vapour transfer, and latent heat
  exchange during metamorphism.

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• Temperature stratification within dry snowpacks
  is usually unstable (warm temperatures below cold
  temperatures) from formation until late winter
  and spring, as energy inputs from the soil
  boundary exceed those from the atmosphere and
  upper layers.
• As a result, temperatures become warmer with
  depth, with gradients as high as 50oC m-1 in
  shallow subarctic and arctic snowpacks during
  early midwinter.

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• In cold climates with frozen soils, an inversion
  can develop in late winter where the upper
  snowpack warms to higher temperatures than the
  lower layers this reflects higher energy inputs
  from the atmosphere (often due to long sunlit
  periods in the northern spring) than from the
  frozen soil.
• For a given climate, the thermal regime in the
  snowpack strongly depends on the amount of
  snowfall early in the winter season.

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• Heavy snowfall early in the winter will tend to
  maintain the snowpack relatively warm, whereas
  shallow snowcovers will adjust more rapidly to
  the air temperatures.
• For a deep snowpack a midwinter rainfall would
  increase density and decrease depth.
• Subarctic and arctic snowpacks can undergo melt
  in upper layers whilst maintaining snow
  temperatures significantly below the freezing
  point in the lower layers.

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• Internal heat fluxes in wet snow, or in partially
  wet snow, are principally driven by conduction
  and by latent heat release due to refreezing of
  liquid water.

22
Ref Bartelt and Lehning (2002)
23
Ref Bartelt and Lehning (2002)
24
Source Stieglitz et al. (2003)
25
Source Stieglitz et al. (2003)
26
Source Pomeroy and Brun (2001)
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Snowpack Ablation

• In many countries snow constitutes a major water
  resource its release in the form of melt water
  can significantly affect agriculture,
  hydro-electric energy production, urban water
  supply and flood control.
• The ablation of a snowcover or the net volumetric
  decrease in its snow water equivalent is governed
  by the processes of snowmelt, evaporation and
  condensation, the vertical and lateral
  transmission of water within the snowcover and
  the infiltration of water to the underlying
  ground.

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• In turn, water yield and streamflow runoff
  originating from snow are governed by these same
  processes as well as the storage and the
  hydraulics of movement of water in channels.
• The rate of snowmelt is primarily controlled by
  the energy balance near the upper surface, where
  melt normally occurs.
• Shallow snowpacks may be considered as a box to
  which energy is transferred by radiation,
  convection, and conduction.

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• Early in the melt sequence vertical drainage
  channels develop in the snow contributing further
  to its heterogeneity.
• The internal structure significantly influences
  the retention and movement of melt water through
  the snow, making a detailed analysis of the
  transmission process extremely difficult.
• When the pack is primed to produce melt it is at
  a temperature of 0oC throughout and its
  individual snow crystals are coated with a thin
  film of water also, small pockets of water may
  be found in the angles between contacting grains,
  usually amounting to 3 to 5 of the snow by
  weight.

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• Any additional energy input produces melt water
  which subsequently drains to the ground.
• When melt rates are at their highest, 20 (by
  weight) of the pack or more may be liquid water,
  most of which is in transit through the snow
  under the influence of gravity.
• The amount of energy available for melting snow
  is determined from the energy budget equation.

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Shortwave Radiation

• There are two main types of radiation affecting
  snowmelt shortwave and longwave radiation.
• The amount of solar radiation penetrating the
  earth's atmosphere to be received at the surface
  varies widely depending on latitude, season, time
  of day, topography (slope and orientation),
  vegetation, cloud cover and atmospheric
  turbidity.

32

• While passing through the atmosphere radiation is
  reflected by clouds, scattered diffusely by air
  molecules, dust and other particles and absorbed
  by ozone, water vapour, carbon dioxide and
  nitrogen compounds.
• The absorbed energy increases the temperature of
  the air, which in turn, increases the amount of
  longwave radiation emitted to the earth's surface
  and to outer space.

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• Short-wave radiation reaching the surface of the
  earth has two components a direct beam component
  along the sun's rays and a diffuse component
  scattered by the atmosphere but with the greatest
  flux coming from the direction of the sun.
• Figure 9.1 shows the annual variation in daily
  values of solar radiation received by a
  horizontal surface at several latitudes assuming
  a mean transmissivity of unity, implying that all
  the energy reaches the surface.
• The influence of transmissivity is illustrated in
  Figure 9.2.

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36
Source Gray and Male (1981)
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• The time of year obviously is an important factor
  governing the solar radiation flux incident on
  the earth's surface, and hence on the melt rate.
• As a rule, the longer the spring melt is delayed
  the greater the danger of flooding.
• This is due partly to increases in the radiative
  flux and partly to the increased probability of
  rain.

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• The transmissivity is highest in winter and
  lowest in summer because the atmosphere contains
  more water vapour during summer.
• It also varies somewhat with latitude, increasing
  northwards.
• Snow on a south-facing slope melts faster than
  snow on a north-facing slope, the reason being
  that the orientation of the slope affects the
  amount of direct beam solar radiation the area
  receives.

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• The results are symmetric about a north-south
  line as might be expected the influence of
  orientation diminishes towards the summer
  solstice.
• Even on a 10o slope the effect of orientation can
  be significant e.g., at 50oN on April 1, a
  south-facing slope receives approximately 40
  more direct beam radiation than a north-facing
  slope.

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43
Longwave Radiation

• The net longwave radiation at the snow surface L
  is composed of the downward radiation L? and the
  upward flux L? emitted by the snow surface.
• Over snow L? is normally greater than L? so that
  L represents a loss from the snowpack.
• The longwave radiation emitted by the snow
  surface is calculated with the Stefan-Boltzmann
  law on the assumption that snow is a near perfect
  black body in the longwave portion of the
  spectrum.

44

• In alpine areas topographical variations have a
  significant influence on the longwave radiation
  received at a point, e.g., in a valley the
  atmospheric radiation is reduced because a part
  of the sky is obscured by its walls.
• However, the valley floor will gain longwave
  radiation from the adjacent slopes in amounts
  governed by their emissivities and temperatures
  the reflected longwave radiation from snow and
  most natural surfaces is almost negligible.
• Thus in areas of high relief the radiation
  incident at a site includes longwave emission
  from the atmosphere and the adjacent terrain.

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• To a first approximation the radiation emitted by
  cloud can be obtained by assuming black-body
  emission at the temperature of the cloud base.
• Hence, the net longwave radiation exchange
  between the overcast sky and the snow can be
  approximated as an exchange between two black
  bodies having temperatures Ts (snow surface) and
  Tc (cloud base), i.e., L s(Tc4 - Ts4).

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Sensible, Latent, and Ground Heat Fluxes

• The convective and latent energy exchanges, Qh
  and Qe, respectively, are of secondary importance
  in most snowmelt situations when compared to the
  radiation exchange, but still need to be
  considered to assess melt rates.
• Both Qh and Qe are governed by the complex
  turbulent exchange processes occurring in the
  first few metres of the atmosphere immediately
  above the snow surface.

47

• Heat is transferred to the snow by convection if
  the air temperature increases with height
  (commonly occurring when the snow is melting)
  and water vapour is condensed on the snow
  (accompanied by release of the latent heat of
  vapourization) if the vapour pressure increases
  with height.
• The ground heat flux QG is a negligible component
  in daily energy balances of a snowpack when
  compared to radiation, convection or latent heat
  components, so that the total snowmelt produced
  by QG over short periods of time can be ignored.

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• However, QG does not normally change direction
  throughout the winter months and consequently its
  cumulative effects can be significant over a
  season.
• In areas where snow temperatures remain near the
  freezing point and ground temperatures are
  relatively warm, melt can be produced as a result
  of QG.
• Although the amount of water produced may be
  small, its resultant effect on the thermal
  properties and infiltration characteristics of
  the underlying soil may be important.

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• Heat exchanges between soils and snow follow the
  simple Fourier equation for heat transfer used in
  heat transfer in snow alone.

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Rain on Snow

• The heat transferred to the snow by rain water is
  the difference between its energy content before
  falling on the snow and its energy content on
  reaching thermal equilibrium within the pack.
• Two cases must be distinguished in this energy
  exchange

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• 1) Rainfall on a melting snowpack where the rain
  does not freeze
• 2) Rainfall on a pack with temperature lt 0oC
  where the water freezes and releases its latent
  heat of fusion.
• The first case can be described by the
  expression
• QP ?w Cp(Tr - Ts)Pr/1000
• where QP is the energy supplied by rain to the
  snowpack, ?w is the density of water, Cp is the
  heat capacity of water, Tr the temperature of the
  rain, Ts is the snow temperature, Pr is the depth
  of rain or precipitation rate.

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Units

• QP (kJ m-2 d-1)
• ? (kg m-3)
• Cp (kJ kg-1 oC-1)
• Tr (oC)
• Ts (oC)
• Pr (mm d-1)

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• When rain falls on a snowpack which has a
  temperature lt0oC, the situation is more
  complicated since the pack freezes some of the
  rain thereby releasing heat by the fusion
  process.

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Snowmelt

• The amount of meltwater can be calculated from
• wm QM /(?w Lf B)
• where wm is the meltwater (m), Lf (J kg-1) is the
  latent heat of fusion, and B is the fraction of
  ice in a unit mass of wet snow.
• B usually has a value of 0.95 to 0.97.

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• Net radiation and sensible heat largely govern
  the melt of shallow snowpacks in open
  environments.
• At the beginning of the melt, radiation is the
  dominant flux with sensible heat growing in
  contribution through the melt.

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• If a complete set of meteorological measurements
  is not available, then temperature index models
  may be used to predict snowmelt. Index models
  relate melt to air temperatures such that
• wm Mf (TA - TB)
• where TA (oC) is the mean air temperature over a
  given time period and TB is a base temperature
  below which melt does not occur (usually 0oC).
• The melt factor Mf varies from 6 to 28 mm oC-1
  day-1 for snowmelt on the Canadian Prairies.

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• Although index models are simple, they should be
  used with caution as the melt factors tend to
  vary from year to year and with location.

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Streamflow Generation

• Streamflow generated by snowmelt water that
  directly runs off rather than infiltrating or
  from water that infiltrates and then moves
  downslope through a shallow subsurface soil of
  high permeability.
• During snowmelt, frozen or saturated soils
  restrict infiltration and evaporation is
  relatively low this promotes a water excess over
  a basin and permits relatively large runoff
  generation for the amount of water applied to the
  ground.

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• As a result, peak annual streamflows often occur
  directly after snowmelt.
• The constituent water of this freshet comprise
  both snowmelt water and water expelled from soils
  by infiltrating snowmelt water, with important
  implications for stream chemistry.
• For point scales, the influence of snow water
  equivalent on infiltration and runoff generation
  varies for different soil types.

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• The effect of a deep forest environment snowpacks
  in promoting warm soils causes forest runoff to
  drop with increasing snow water equivalent for
  deep snow and dry soils.
• In northern forests, from 40 to 60 of annual
  streamflow is derived from snowmelt, with
  increases in snowmelt runoff of from 24 to 75
  when the forest is removed by harvesting or fire.
  
• In cold, semiarid environments (arctic, northern
  prairies, steppes), greater than 80 of annual
  streamflow is derived from snowmelt, even though
  snowfall accounts for less than 50 of the annual
  precipitation.

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• Snowmelt in the western cordillera of North
  America and mountain systems of central Asia is
  the major source of water when carried as
  streamflow to semiarid regions downstream.
• Snowmelt water sustains arctic, alpine, prairie,
  and boreal forest lakes and wetlands, which are
  primary aquatic habitats in their respective
  ecosystems.

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Ref Barnett et al. (2005)
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Annual Cycle of River Discharge
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Annual cycle of mean daily discharge
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Latitudinal Variation of HJUB Freshets
JD 5(Latitude) -126
Source Déry et al. (2005), J. Climate.