14 snow hydrology-part1

Riccardo Rigon, Stefano Endrizzi, Matteo Dall’Amico
Turner,SnowStorm,1842
Snow, Ice, Permafrost
Thursday, November 18, 2010

2
Yes, still the snow
...
What will be of the snow, of the garden,
what will be of free will and of destiny
and of those who have lost their way in the snow
....
Andrea Zanzotto (La beltà, 1968)
Rigon, Endrizzi, Dall’Amico

Goals:
•To introduce the phenomenon of snowfalls
•To describe the characteristics of snow on the ground and its
metamorphism
•To introduce the difference between snow and ice and introduce some
elements of glacial hydrology
•To introduce the thematics relative to frozen soils and permafrost
3

4
Snow
Snowfalls are an important element of the water cycle: in arctic and alpine
catchments they can contribute over 95% of the hydric balance and cause
over 50% of floods, when melting.
Snow modifies the energy balance of the Earth’s surface in an essential way,
with relevant consequences on climate and ecosystems.
DonCline,1999

5
it is important to understand
•the mechanisms of precipitation and accumulation of snow
•the mechanisms of ablation and movement of snow
•the mechanisms of runoff generation
In order to understand the phenomena that have been listed

6
It is important to quantify
•the amount of snow that precipitates and its redistribution due to the
wind
•the amount of water in the snow cover
•the amount of snow lost through sublimation
•the quantity and timescales of melting
•the modalities of meltwater flow aggregation

7
The formation of snowfalls
DonCline,1999

8
Necessary conditions:
•Presence of water vapour
•Vapour pressure greater than equilibrium pressure
•Temperature T < 0 ºC
•Presence of condensation nuclei

9
Le montagne influenzano le precipitazioni
Versante sopravento: nubi, pioggia, neve (stau)
Versante sottovento: tempo asciutto (föhn)
DanieleCatBerro,2009
Mountains effect precipitations:
•Windward side: clouds, rain, snow (stau)
•Leeward side: dry weather (föhn)

10
If the condensation process is triggered
There are various formation phases:
•Nucleation
•Formation of ice crystals
•Formation of snow crystals
Crystal growth AggregationRiming

11

12
Snow crystals

13
Forma di base del cristallo di neve: esagonale
135 a.C. - prime osservazioni documentate in Cina
1635 – Cartesio, primi disegni delle forme dei cristalli
1681 – Trattato “La figura della neve” del livornese Donato Rossetti
1820 – Classificazione di William Scoresby jr.
1845 – Ricerca sulle proprietà della neve di Faraday
1885 – Prima fotografia al microscopio, Wilson Bentley
(collezione al Museo delle Scienze di Buffalo, USA)
W. Bentley
www.bentley.sciencebuff.org
On snow crystals
Snow crystals
Basis shape of the snow crystal: hexagonal
135 BC - first documented observations in China
1635 AD - Descartes, the first diagrams of snow crystal shapes
1681 - Essay “The Shape of Snow” by Donato Rossetti
1821 - Classification by William Scoresby Jr.
1845 - Studies on the properties of snow by Faraday
1885 - First microscopic photograph by Wilson Bentley
(Buffalo Science Museum collection, USA)

14
Snow!

15
Snowfalls are linked by particular
synoptic situations
D.Cline,1999The formation of snowfalls

16
Prevedere la neve (quantità, limite nevicata): una sfida…
- Effetto valle
- Quota inferiore sul basso Piemonte
- Effetto rovesci / isotermie verticali
- Quantità difficili da prevedere in prossimità di 0 °C
But locally it is difficult
To forecast snow (quantity, snow limit) is a challenge....
•Valley effect
•Lower altitude in southern Piedmont
•Storm effects / vertical isotherms
•Quantities difficult to forecast in proximity of 0 ºC

17
In hydrological modelling
Usually, the rule of the U.S. Corps of Engineers is used:
•if the temperature is below -6º C, the precipitation is all snow
•if the temperature is above 6º C, the precipitation is all liquid
•for intermediate temperatures, only a fraction is snow, the rest is liquid.
Modern models, however, use satellite data to correct the rule.

18
The statistics of snowfalls
Snow on the ground
Immagine in italiano

19
Gli spessori di neve più elevati
nel mondo e nelle Alpi italiane
1140 cm l'11 marzo 1911 a Tamarack, California (USA)
1035 cm il 28 marzo 1937 al Piccolo San Bernardo (Aosta)
850 cm il 14 marzo 1972 al Lago Valsoera (Torino)
600 cm il 13 febbraio 1951 al Lago Toggia (Verbania)
Le nevicate più abbondanti
in un giorno nel mondo e in Italia
193 cm il 15 aprile 1921 a Silver Lake, Colorado (USA)
340 cm nel dicembre 1961 a Roccacaramanico (L'Aquila),
record non omologato
198 cm il 30 dicembre 1917 a Gressoney-La Trinité
155 cm l'11 marzo 2004 a Gares (Belluno)
The greatest depths of snow recorded in the world
and in the Italian Alps
1140 cm, 11th march 1911 at Tamarack California (USA)
1035 cm, 28th March 1937 at Little Saint Bernard, Aosta (Italy)
850 cm, 14th March 1972 at Lake Valsoera, Turin (Italy)
600 cm, 13th March 1951 at Lake Toggia, Verbania (Italy)
The greatest snowfalls recorded in one day
in the world and in Italy
193 cm, 15th April 1921 at Silver Lake, Colorado (USA)
340 cm, in December 1961 at Roccacaramanico, L’Aquila (Italy)
(unapproved record)
198 cm, 30th December 1917 at Gressoney-la Trinité, Aosta (Italy)
155 cm, 11th March 2004 at Gares, Belluno (italy)

20

21
There has been a drastic reduction in snowfalls since the end of
the 1980s. The winter of 2007-08 was the warmest and least
snowy on record.

22
La misura della neve a Torino iniziò nel 1787,
si tratta di una tra le serie nivometriche più lunghe al mondo.
L’inverno più nevoso, il 1882-83, accumulò ben 172 cm di neve fresca.
Altri tempi… mentre fino al 1989 la media storica era di 50 cm di neve all’anno,
dal 1990 la media si è ridotta a soli 17 cm.
Torino, quantità annua neve fresca (anno idrologico) dal 1787-88 al 2008-09
0
20
40
60
80
100
120
140
160
180
200
1787
1807
1827
1847
1867
1887
1907
1927
1947
1967
1987
2007
cm
Snow measurements in Turin began in 1787, the records there represent the longest nivometric series in the world.
The snowiest winter was the winter of 1882-83 when there was a cumulative depth of 172 cm of fresh snow.
Times have changed ... up to 1989 the historical average was a cumulative depth of 50 cm per year
Since 1990, this average has been reduced to only 17 cm

23
Snow at the microscale

24
Snow crystals
Plate
from:TheSnowflake:Winter’sSecretBeauty,
KennethLibbrechtandPatriciaRasmussen
Column Dendrite
The overall shape depends on temperature and water availability.
basic shapes

25
Snow, Ice, PermafrostKennethG.Libbrecht,:http://www.its.caltech.edu/~atomic/snowcrystals/
primer/primer.htm
Snow crystals

26
Photographs of snow crystals
Rime on Plate Crystal Early Rounding Faceted Growth Early Sintering (Bonding)
Wind-Blown Grains Melt-Freeze with
No Liquid Water
Melt-Freeze with
Liquid Water
Faceted Layer Growth Hollow, Faceted Grain
(Depth Hoar)

27
Characteristic dimensions
Term Size
[mm]
Very ﬁne ≤ 0.2
Fine 0.2-0.5
Medium 0.5 - 1.0
Coarse 1.0 -2.0
Very coarse 2.0 -5.0
Extreme ≥ 5

28
Snow on the ground
Modis Snow, tiles 500 m, 21 Aprile 2002

29Modis, Alta Valsugana, 24 ottobre 2003
Snow on the ground

30Modis, Alta Valsugana, 17 Novembre 2003
Snow on the ground

31Modis, Alta Valsugana, 17 Gennaio 2004
Snow on the ground

32Modis, Alta Valsugana, 16 Maggio, 2004
Snow on the ground

Seasonal trend of snow
33
and its temperature in temperate environments

34
in tropical areas
With current climatic conditions, snow can only accumulate at high altitudes.
This accumulation is particularly dependant on the alternation of wet and dry
seasons (for example, as a consequence of phenomena such as El Niño and La
Niña).
During the dryer seasons, snow tends to melt, while it tends to accumulate
during the wet seasons.
Seasonal trend of snow

35
Areal Distribution
DonCline,1999

36
DonCline,1999
Spatial Scales
Microscale
10 - 100 m
Mesoscale
100 m - 10 km
Macroscale
> 10 km
Differences in
accumulation due to
individual plants and
micro-topography
Small-scale
turbulence
Differences in
accumulation due to
vegetation cover
plants and micro-
topography
Characteristics of
the terrain
Meteorological
dynamics
Areal Distribution

37
DonCline,1999
Effects of topography
•Locally, snow cover increases with altitude
- in fact, the quantity of precipitation events increases
- evapotranspiration and melting decreases
•The increase varies greatly from year to year
•Other topographical factors that affect snow cover:
- slope, aspect
Areal Distribution

38
DonCline,1999
Effects of vegetation
•Conifers and deciduous species obviously accumulate different
amounts of snow
•Snow gathered on treetops sublimates faster than snow on the ground
Areal Distribution

39
Most studies show that snow accumulation occurs prevalently in open spaces
rather than within the forested areas.
The clearings are not generally subject to a great redistribution of snow due to
the wind, therefore the major factor contributing to the difference in
accumulation is sublimation, which is favoured by the heating of the tree trunks.
20-45%
Greater Snow
Accumulation
DonCline,1999
Effects of vegetation
Areal Distribution

40
Open environments
Together, vegetation distribution and topography can cause differences in snow
distribution patterns.
DonCline,1999
Areal Distribution

41
DonCline,1999
Open environments
Areal Distribution

42
Snow redistribution processes
Lenhing,2005

43
Blowing Snow
The transport of snow by the wind has a relevant effect on snow
distribution.
DonCline,1999

44
Blowing Snow
Four factors:
1 - Drag speed
2 - Windspeed thresholds
3 - Types of transport
4 - Rate of transport

45
Blowing Snow
Drag speed
The drag speed of the wind u* is usually calculated from the wind profile,
but it can be estimated on the basis of a single windspeed measurement
taken at 10 m from the ground:
where red. factor u∗
(u10 = 5) m/s
Antartic Ice Sheet u10/26.5 0.19
Snow-covered lake u1.18
10 /41.7 0.16
Snow-covered fallow ﬁeld u1.30
10 /44.2 0.18
0
0.3750
0.7500
1.1250
1.5000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
u*
10-m Wind Speed
Antarctic Lake Field

46
Blowing Snow
Windspeed thresholds at which transport begins.
The thresholds depend on the characteristics of the snow.
Type of snow u∗
t m s−1
Old, wind-hardened 0.25 -1
dense, or wet
Fresh, loose, dry snow 0.07-0.25
and during snowfall

47
Blowing Snow
3 types of movement
Type of movement Motion Typical Height u∗
[m] [m s−1
]
Creep Roll ≤ 0.01 ≤ 5
Saltation Bounce 0.01-0.1 5-10
Turbulent Supended 1-100 10
Diﬀusion

48
Blowing Snow
The transport rate depends on the conditions of the
surface of the snow but it is approximately:
∝ u3
10
By doubling the windspeed, the transport rate increases eightfold;
quadrupling the windspeed, the transport increases by a factor of 64

49
Blowing Snow
During transportation, the snow particles are more
affected by sublimation rather than if they were still.
30
25
2522
16
22
5020
Mean Annual Blowing Snow Sublimation
CANADA, 1970-1976
Loss in mm SWE over 1 km

50
Blowing Snow
Transport causes the modification of the ice crystals
- it makes them rounder
As a consequence, the snow cover that has
accumulated because of transport is denser than that
which precipitated in situ.
Snow crystals
collected after a
snowfall with
little wind
Snow crystals
collected
during
transportation
2 mm

51
Blowing Snow
Overall, transport by wind produces forms that are
easily recognisable from space.

52
The snowpack
Water (Liquid)
Ice
Air
Massa Volume
Vag
ViMi
Mag
The column of snow
Mw Vw
M∗
V∗

53
The snowpack is:
- a porous medium (as shown in the preceding slide)
Generally, it is composed of different layers, which are typically
homogeneous, of different thicknesses and of different types of snow.
The layers are composed of crystals and grains that are usually bound
together by some sort of cohesion.
The snowpack

54
Basic notation
M∗ = Mag + Mw + Mi
M∗ = Mv + Mw + Mi

54
Mass of snow
Basic notation
M∗ = Mv + Mw + Mi

54
Mass of snow
Mass of air
Basic notation
M∗ = Mv + Mw + Mi

54
Mass of liquid
water
Mass of snow
Mass of air
Basic notation
M∗ = Mv + Mw + Mi

54
Mass of liquid
water
Mass of vapour
Mass of snow
Mass of air
Basic notation
M∗ = Mv + Mw + Mi

54
Mass of liquid
water
Mass of vapour
Mass of ice
Mass of snow
Mass of air
Basic notation
M∗ = Mv + Mw + Mi

55
The volumes, with the same indices as the masses
V∗ = Vag + Vw + Vi
Vtw = Vv + Vw + Vi
Basic notation

Ice density
56
Snow bulk density
ρi :=
Mi
Vi
ρ∗ :=
M∗
V∗
=
M∗
Vag + Vw + Vi
Basic notation

57
Variation of density in time

58
Typical densities of snow
Snow Type Density
[kg m−3
]
Wild snow 10-30
New snow 50-60
falling in still air
Settling snow 70-90
Average wind-toughened 280
snow
Hard wind slab 400-500
New ﬁrn snow 550-650
Thawing ﬁrn snow 600-700

59
Volume fraction of liquid water in snow
pores (dimensionless)
θw :=
Vw
Vag + Vw + Vi
Volume fraction of frozen water (ice) in snow
θi :=
Vi
Vag + Vw + Vi
Basic notation

60
Snow porosity
Relative saturation
φ∗ :=
Vag + Vw
Vag + Vw + Vi
S∗ :=
θw
φ∗
Basic notation

61
Water equivalent of snow
Volume of water due to the complete melting of the snow on a
corresponding horizontal area.
h∗ =

θw + (1 − φ∗)
ρi
ρw

V∗
A
=

θw + (1 − φ∗)
ρi
ρw

hsn
hsn :=
V∗
A
h∗ :=
Vw(A) + ρi
ρw
Vi(A)
A
Basic notation

62
Qualitative characteristics
of the snowpack
Term Size θ∗
Dry Usually T ≤ 0 ◦
C 0
Little tendency for snow grain to stick together
Moist T = 0 ◦
C ≤ 0.03
Grains stick together
Wet T = 0 ◦
C 0.03 - 0.08
Water can be seen in meniscus, but not squeezed out from snow
Pendular regime
Very wet T = 0 ◦
C 0.08 - 0.15
Water can be pressed out by squeezing snow
Appreciable amount of air (funicular regime)
Slush T = 0 ◦
C ≥ 0.15
The snow is ﬂooded with water. No air

63
Other characteristics
of the snowpack
•Shape of the grains of snow
•Size of the grains of snow
•Albedo
•Temperature
•Hardness
•Mechanical properties

64
Variation of the albedo in time
Albedo as a function of snow surface (i.e., time since last snowfall).
From U.S. Army Corps of Engineers (1956)

65
Thermal properties of snow
It is assumed that the heat flux is according to Fourier’s law:
Jh = Kh
∇T

65
Jh = Kh
∇T
Heat flux
W m-2

65
Jh = Kh
∇T
Heat flux
W m-2
Thermal
conductivity
W m-1 K-1

65
Jh = Kh
∇T
Heat flux
W m-2
Thermal
conductivity
W m-1 K-1
Temperature
gradient
K m-1

66
The thermal conductivity, Kh, is a measure of the capacity of a material to transfer
heat. A good heat conductor has an elevated value of K, while an insulator has a
low value of K.
Fresh snow 0.03 (better than glass wool!)
Old snow 0.4
Ice 2.1
Jh = Kh
∇T
Snow attenuates the thermal changes of the atmosphere. For example, a
change of 1 degree in air temperature, in 15 minutes, causes a change of only
0.1 degrees at a depth of 20 cm in the snowpack and of only 0.01 degrees at
a depth of one metre.

67
Jh = Kh
∇T
Kh grows with the metamorphosis of the snow. For example, Sturm, 1997 gives
the following parametric formula:
Kh = 0.138 − 1.01 ρ ∗ +3.233 ρ2
∗

68
Temperature
Generally two different situations are found in the snowpack:
- there is a variation of temperature between the surface and the
ground upon which the snowpack is lying: the temperature is typically
dominated by the temperature at the surface and the ground is usually
at 0ºC … unless, of course, we find ourselves in the presence of
permafrost.
- there is no temperature gradient: the snowpack is in an isothermic
state.

69
Temperature
Snow is a good thermal insulator. Large temperature gradients can be observed in
proximity of the surface.

70
050100150
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SnowD sim
Flux to ground
Nov 97 Feb 98 May 98 Aug 98 Nov 98
0306090120150
Fluxtoground[W/m^2]
●
SnowD meas
summerwinter
about 50 W/m2about 5 W/m2
Temperature
with and without snow

Snow metamorphism
•Gravitational settling
•Destructive metamorphism
•Constructive metamorphism
•Melting metamorphism
71

72
The name indicates the changes to the morphology of the grains that occur
due to variations in temperature and pressure to which they are subjected
following their deposition.
Snow metamorphism changes:
•density
•porosity
•albedo
•thermal conductivity
•cohesion
Snow metamorphism

Metamorphism occurs because:
•the grains have relatively large surface area with respect to their volume
and they tend towards a more stable geometric configuration (the
spherical surface is the one with minimum energy)
•the temperature, during the season, exceeds the melting point
•the pressure in the lower layers causes a compaction of the snow (and
approaches melting conditions)
73
Neve, Ghiaccio, Permafrost

74
Two categories of metamorphism can be identified:
In the presence of liquid water:
- T = 0 (usually)
In the absence of liquid water:
- T 0
- ice is in equilibrium with vapour
- prevalently determined by the flux of vapour
Metamorphism occurs because:

75
“Dry” metamorphism
It is linked to the movement of vapour in the pores
The movement of vapour is linked to the vapour pressure gradient
The pressure gradient is controlled by:
•Temperature (on the basis of what has been seen so far, the
equilibrium vapour pressure depends on the temperature according to
the Clausius-Clapeyron law)
•Local radius of curvature of the ice crystals (the Clausius-Clapeyron
law must be modified when the air-ice interface is curved. The
equilibrium vapour pressure increases with increasing radius of
curvature)

76
Destructive metamorphism
Constructive metamorphism
Two types
It occurs at constant temperature and it is due to the demolition of
the cusps of the grains. The process is particularly intense for freshly
fallen snow and brings about increases in density at rates greater
than 1% per hour. It comes to a halt when the density is of the order
of 0.25 g cm-3
Depends on the temperature from point to point. In the warmer points
sublimation of the snow occurs. The vapour then moves following the
pressure gradients.
“Dry” metamorphism

77
Reduces the free energy of the system to its stable state
This energy depends of the local radius of curvature of the ice crystal

77
elevated radius of
curvature implies
greater vapour
pressure

78
A negative radius
o f c u r v a t u r e
implies a lower
vapour pressure in
t h e r m o d y n a m i c
equilibrium

79
The difference in vapour pressure between two point implies a vapour
transfer (from “+” to “-”).
In this way there is
an excess of vapour
over the “-” point
and , consequently,
condensation.
+
-
The ideal equilibrium
configuration is a sphere.
The real equilibrium
configuration depends on
the interaction of the
single crystal with
surrounding
environment.

80
The macroscopic effect of destructive
metamorphism is that of :
- reducing the surface / volume ratio of the
crystals and therefore increasing the
density of the snow (by filling the pores);
- increasing the cohesion between grains.

81
“dry” but dictated by the temperature gradient
It can be very efficient if the gradient is at least 10 ºC/m and the snow
density is low (less than 350 kg/m3)
It creates faceted grains with weak reciprocal bonds
It tends to reduce the density

82
Melting metamorphism
or “wet” metamorphism
It occurs in the presence of water and, therefore, in proximity of T=0 ºC
There are two main mechanisms:
•surface melting followed by percolation of the meltwater
•an acceleration of the “dry” processes which brings about the formation of
large, rounded grains.

83
The first of these mechanisms is caused by surface melting or by the
introduction of rainwater which freezes within the snowpack at lower
temperature. In this way a layer of compact ice can form within the
snowpack, which can extend even over large distances.
The freezing of water within the snowpack causes the liberation of
latent heat, which contributes to the generation of vapour and the
acceleration of its transfer.

84
T h e s e c o n d m e t a m o r p h i c
process that accompanies
melting processes is the rapid
disappearance of the smaller
grains and the formation of
larger grains, which occurs in the
presence of liquid water. Because
of this phenomenon, a snowpack
that is melting is formed by an
aggregation of grains with
diameters of 1-2 millimetres
(Colbeck, 1978).

85
The energy balance of snow
It occurs by:
• radiation (energy transfer by means of electromagnetic waves)
• conduction (heat transfer by direct contact between molecules)
• convection (sublimation and transfer of sensible heat due of atmospheric
turbulence)
• advection (due to mass transfer: precipitation, vapour, meltwater)

86
Factors contributing to the energy exchange
• The Wind (it is the manifestation of atmospheric turbulence that controls
the transfer of sensible and latent heat at the surface)
• The presence of water vapour (its gradients control the transfer of
sensible heat)
• The amount of radiation (across the spectrum)
• The energy content of rainwater which alters the state of the snow

87
DonCline,1999,Jordan,1991
R↓ sw
R↓ lw
R↑ sw
R↑ lw
Pe
λs EvH
∆U∗
G

88
∆U∗ = Rn lw + Rn sw − H − λs Ev + G + Pe
Rn lw := R↓ lw − R↑ lw Rn sw := R↓ sw − R↑ sw
R↓ sw
R↓ lw
R↑ sw
R↑ lw
Pe
λs EvH
∆U∗
G

89
Spectral signature of snow

90
Albedo

91
The radiative balance of snow
SNOW, T = 0oC
CLEAR DRY AIR, T = 0oC
Net Energy Loss
From Snow Pack No Net Energy Loss
From Snow Pack
a ≈ 0.6 − 0.7
w,i,∗ ≈ 0.92 − 0.97
R = σ T4

92
The radiative balance of snow

93
On rainy and cloudy days, exchanges of sensible and latent heat dominate
the balance.
However, these exchanges are always important due to the high albedo of
snow which does not allow for large storage of radiative energy, except
maybe in the summertime.
Generally, a large-scale melting of snow requires that the “turbulent”
exchanges of energy be rather intense.
Turbulent fluxes

94
Stable atmospheric conditions reduce turbulence and, therefore, the turbulent energy
transfer. Vice versa, atmospheric instability increases the transfers.
Aerodynamic roughness
length
INSTABILITY
ln(z-d0)
STABILITY
q-qs
Turbulent fluxes

95
The theory that describes this process is known by the name of its authors:
Monin-Obukhov
Turbulent fluxes

96
Over snow it is easy for stable atmospheric conditions to prevail: it is a
feedback effect caused by the elevated albedo of the snow.
Therefore, the same condition that minimises radiative storage also
minimises the turbulent energy transfers.
Turbulent fluxes

97
However, given that snow cover is not uniform across the landscape, and that
vegetation constitutes an element that absorbs and emits energy with great
efficiency, there are parts of the landscape where snowmelt is greater than in
others.
Turbulent fluxes

98
FoehnAccumulation season - the Tonale Pass

99
SW radiation tends to zero when the sky is cloudy
Accumulation season - the Tonale Pass

100
Latent and sensible heat:
• there are increases when
windspeed is high.
• they increase and decrease in
antiphase, except that...
• they both increase when it rains
or there is high humidity in the
atmosphere
Accumulation season - the Tonale Pass

Riccardo Rigon
Thank you for your attention!
G.Ulrici,2000?
101

14 snow hydrology-part1

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