Snowcover Structure and
Metamorphism
• Snow stratification results from successive
snowfalls over the winter and processes
that transform the snow cover between
snowfalls.
• Snow metamorphism depends on
temperature, temperature gradient, and
liquid water content.
• The size, type, and bonding of snow
crystals are responsible for pore size and
permeability of the snowpack.
1
• In low wind speed environments, fresh
snowfall has low hardness and density (50
to 120 kg m-3).
• Temperature gradients induce water
vapour pressure gradients, vapour
diffusion from the warmest crystals, and
consequent change in the shape of the
crystals.
• If persistent temperature profiles exist,
then distinctive crystal shapes develop
within the snowpack.
2
Source: DeWalle & Rango (2008)
3
• First, crystals may be transformed into
faceted crystals and eventually into depth
hoar over time.
• The grain shape of these crystals does not
allow an efficient compaction of the
snowpack.
• Depth hoar may take a number of shapes
including cups, needles, scrolls and plates.
• A layer of depth hoar has very low
strength.
4
Source: DeWalle & Rango (2008)
5
Source: DeWalle & Rango (2008)
6
• Metamorphism can also result from compaction
caused by the pressure of overlying layers of
snow that leads to its densification.
• This process is responsible for transforming
snow into glacial ice whose crystals sometimes
attain sizes of the order of 1 cm.
• During its early stages, the refreezing of melt
water can accelerate the densification process.
• Snow density is often assumed to increase
exponentially with time (e.g. Verseghy, 1991).
7
8
Source: DeWalle & Rango (2008)
9
Summary of snow metamorphosis
processes
Source: DeWalle & Rango (2008)
10
Snowpack Properties and
Evolution
• The preceding slides 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.
11
• 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.
12
• 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.
13
• 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.
14
• 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.
15
• 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.
16
• 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.
17
• Typical numerical models of snow use
three prognostic variables to define a
snowpack: snow depth, snow water
equivalent (SWE), and temperature.
• From snow depth and snow water
equivalent, one can infer the snow density
from:
• ρs = ρw(w/s)
• where w (m) is SWE, s (m) is the snow
depth, and ρs and ρw are the snow and
water densities, respectively.
18
Source: Sun et al. (2004)
19
• Apart from snow depth and SWE, 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
changes.
20
Sleepers
River
watershed,
Vermont
Source: Lynch-Stieglitz (1994)
21
• The energy balance of a snow volume
depends upon whether it is a “cold” (<
0oC) or a “wet” (0oC, often isothermal)
snowpack.
• Recall the energy balance of the
snowpack:
• 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
rainfall.
22
• 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
negligible.
• The energy balance therefore reduces to
that between a net radiative sink Q* and a
convective sensible QH heat source.
23
Source: Armstrong & Brun (2008)
24
• 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.
25
Source: Armstrong & Brun (2008)
26
• In Canada, average near-surface soil
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.
27
• 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.
28
• 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.
29
• 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.
30
• 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 (a stable regime).
• 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.
31
• 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.
32
• 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.
33
Ref: Bartelt and Lehning (2002)
34
Ref: Bartelt and Lehning (2002)
35
Source: Pomeroy and Brun (2001)
36
Snowpack Ablation
• In many countries snow constitutes a major
water resource; its release in the form of melt
water can significantly affect agriculture, hydroelectric energy production, urban water supply
and flood control.
• The ablation of a snowcover or the net
volumetric decrease in its SWE 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.
37
• 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.
38
• Early in the melt sequence vertical
drainage channels develop in the snow
contributing further to its heterogeneity.
• The flow of water is affected by
impermeable layers, zones of preferential
flow called flow fingers, and large
meltwater drains.
• Meltwater drains are usually large and end
at the base of the snowpack, whereas flow
fingers occur between two snow layers
only.
39
Source: DeWalle & Rango (2008)
40
• 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.
41
Source: DeWalle & Rango (2008)
42
• 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.
43
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.
44
• 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.
45
• 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.
46
47
48
Source: Gray and Male (1981)
49
• 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.
50
• 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.
51
• The results are symmetric about a northsouth 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.
52
53
54
55
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.
56
• 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.
57
• 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).
58
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.
59
• 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.
60
• 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.
61
• Heat exchanges between soils and snow
follow the simple Fourier equation for heat
transfer used in heat transfer in snow
alone.
62
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:
63
• 1) Rainfall on a melting snowpack where the rain
does not freeze;
• 2) Rainfall on a pack with temperature < 0oC
where the water freezes and releases its latent
heat of fusion.
• The first case can be described by the
expression:
• 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.
64
Units
•
•
•
•
•
•
QP (kJ m-2 d-1)
ρ (kg m-3)
Cp (kJ kg-1 oC-1)
Tr (oC)
Ts (oC)
Pr (mm d-1)
65
• 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.
66
Snowmelt
• 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.
67
• 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.
68
• 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.
69
• 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.
70