Snowpack Properties_ Evolution and Ablation by gjjur4356


									Snowpack Properties, Evolution
       and Ablation
• The discussion in the preceding lectures
  has emphasized the various processes of
  metamorphism that control the snow bulk

• Thermal properties that depend only on
  density (specific heat, latent heat) are well
• However, those that depend on conductivity or
  permeability of the snowpack are affected by
  sintering, particle size, ice layers and depth
• 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.

• The temperature dependence of the
  specific heat of ice given by Dorsey (1940)
• 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 0 oC and
  standard atmospheric pressure is 333.66
  kJ kg-1.

• 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.
• 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

• 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

• 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.
• 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
• ρs = ρw(w/s)
• where w (m) is the snow water equivalent,
  s (m) is the snow depth, and ρs and ρw are
  the snow and water densities,
Source: Sun et al. (2004)

• 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/(ρw 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
Source: Lynch-Stieglitz (1994)

• The energy balance of a snow volume
  depends upon whether it is a “cold” (<
  0oC) or a “wet” (0oC, often isothermal)
• Recall the energy balance of the
• Q* + QP = QH + QE + QG + ΔQS + QM.
• A term is added here to the energy
  balance to consider the heat transported
  by precipitation (QP), either snowfall or
• 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 ΔQS and QG are also
• The energy balance therefore reduces to
  that between a net radiative sink Q* and a
  convective sensible QH heat source.
• 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.

• In Canada, average ground temperatures
  are about 3oC warmer than average air
• 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.

• 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

• The important fluxes that can directly penetrate
  the snowpack are radiation, conduction,
  convection, and meltwater or rainwater
• 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.

• 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 50 oC
  m-1 in shallow subarctic and arctic
  snowpacks during early midwinter.

• 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.

• 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
• Subarctic and arctic snowpacks can
  undergo melt in upper layers whilst
  maintaining snow temperatures
  significantly below the freezing point in the
  lower layers.
• 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.

Ref: Bartelt and Lehning (2002)
Ref: Bartelt and Lehning (2002)
Source: Stieglitz
et al. (2003)

Source: Stieglitz et al. (2003)
Source: Pomeroy and Brun (2001)
          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.

• 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.

• 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.
• Any additional energy input produces melt
  water which subsequently drains to the
• 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
• The amount of energy available for melting
  snow is determined from the energy
  budget equation.
        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.

• 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
• 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.
• 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
• 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.

Source: Gray and Male (1981)
• 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.

• 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.

• 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 50 oN
  on April 1, a south-facing slope receives
  approximately 40% more direct beam
  radiation than a north-facing slope.

        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
• 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
• 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.

• 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* = σ(Tc4 - Ts4).
   Sensible, Latent, and Ground
           Heat Fluxes
• The convective and latent energy exchanges, Q h
  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.

• 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.
• However, QG does not normally change direction
  throughout the winter months and consequently
  its cumulative effects can be significant over a
• 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.

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

            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:

• 1) Rainfall on a melting snowpack where the rain
  does not freeze;
• 2) Rainfall on a pack with temperature < 0 oC
  where the water freezes and releases its latent
  heat of fusion.
• The first case can be described by the
• QP = ρw Cp(Tr - Ts)Pr/1000
• where QP is the energy supplied by rain to the
  snowpack, ρw 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.

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

• When rain falls on a snowpack which has
  a temperature <0oC, the situation is more
  complicated since the pack freezes some
  of the rain thereby releasing heat by the
  fusion process.

• The amount of meltwater can be
  calculated from:
• wm = QM /(ρw 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.

• 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.

• 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.

• 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.

       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
• 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.
• 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.

• 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.
• 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.

Ref: Barnett et al. (2005)
Annual Cycle of River Discharge

           Source: Yang et al. (2003), JGR.       63
        Source: Déry et al. (2005), J. Climate.
Annual cycle of mean daily discharge

Latitudinal Variation of HJUB Freshets

                    JD = 5(Latitude) -126

           Source: Déry et al. (2005), J. Climate.

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