14 snow hydrology-part1

Riccardo Rigon, Stefano Endrizzi, Matteo Dall’Amico

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Snow, Ice, Permafrost

Thursday, November 18, 2010

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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




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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.

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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


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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



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The formation of snowfalls


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Necessary conditions:

•Presence of water vapour

•Vapour pressure greater than equilibrium pressure

•Temperature T < 0 ºC

•Presence of condensation nuclei





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Le montagne influenzano le precipitazioniVersante sopravento: nubi, pioggia, neve (stau)

Versante sottovento: tempo asciutto (föhn)

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9The formation of snowfalls

Mountains effect precipitations:

•Windward side: clouds, rain, snow (stau)

•Leeward side: dry weather (föhn)


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If the condensation process is triggered

There are various formation phases:

•Nucleation

•Formation of ice crystals

•Formation of snow crystals

Crystal growth AggregationRiming




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Snow crystals


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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

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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)


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Snow!



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Snowfalls are linked by particular synoptic situations

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9The formation of snowfalls


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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

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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



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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.



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The statistics of snowfalls

Snow on the ground

Immagine in italiano


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Gli spessori di neve più elevatinel 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)

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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)


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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.



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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

020406080

100120140160180200

1787

1807

1827

1847

1867

1887

1907

1927

1947

1967

1987

2007

cm

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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


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Snow at the microscale


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Snow crystals

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Ken

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atri

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Column Dendrite

The overall shape depends on temperature and water availability.

basic shapes


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Snow, Ice, PermafrostK

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Snow crystals


http://www.its.caltech.edu/%7Eatomic/

http://www.its.caltech.edu/%7Eatomic/

http://www.its.caltech.edu/~atomic/snowcrystals/primer/primer.htm




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Photographs of snow crystals

Rime on Plate Crystal Early Rounding Faceted Growth Early Sintering (Bonding)

Wind-Blown Grains Melt-Freeze withNo Liquid Water

Melt-Freeze withLiquid Water

Faceted Layer Growth Hollow, Faceted Grain(Depth Hoar)


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Characteristic dimensions

Term Size[mm]

Very fine ≤ 0.2Fine 0.2-0.5Medium 0.5 - 1.0Coarse 1.0 -2.0Very coarse 2.0 -5.0Extreme ≥ 5


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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


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Areal Distribution

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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



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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


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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



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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 SnowAccumulation

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Effects of vegetation

Areal Distribution



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Open environments

Together, vegetation distribution and topography can cause differences in snow

distribution patterns.


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Areal Distribution



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Open environments

Areal Distribution



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Snow redistribution processes

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Blowing Snow

The transport of snow by the wind has a relevant effect on snow

distribution.

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Blowing Snow

Four factors:

1 - Drag speed

2 - Windspeed thresholds

3 - Types of transport

4 - Rate of transport


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Blowing SnowDrag 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/sAntartic Ice Sheet u10/26.5 0.19Snow-covered lake u1.18

10 /41.7 0.16Snow-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 SpeedAntarctic Lake Field


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Blowing SnowWindspeed 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


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Blowing Snow3 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


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Blowing Snow

The transport rate depends on the conditions of the

surface of the snow but it is approximately:

∝ u310

By doubling the windspeed, the transport rate increases eightfold;

quadrupling the windspeed, the transport increases by a factor of 64


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Blowing Snow

During transportation, the snow particles are more

affected by sublimation rather than if they were still.

30

25

252216

225020

Mean Annual Blowing Snow Sublimation

CANADA, 1970-1976Loss in mm SWE over 1 km


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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


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Blowing Snow

Overall, transport by wind produces forms that are

easily recognisable from space.


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The snowpack


Water (Liquid)

Ice

Air

Massa Volume

Vag

ViMi

Mag

The column of snow

Mw Vw

M∗ V∗



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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


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Basic notation

M∗ = Mag + Mw + Mi

M∗ = Mv + Mw + Mi



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Mass of snow

Basic notation


M∗ = Mv + Mw + Mi



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Mass of snow

Mass of air

Basic notation


M∗ = Mv + Mw + Mi



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Mass of liquid water

Mass of snow

Mass of air

Basic notation


M∗ = Mv + Mw + Mi



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Mass of vapour

Mass of snow

Mass of air

Basic notation


M∗ = Mv + Mw + Mi



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Mass of vapourMass of ice

Mass of snow

Mass of air

Basic notation


M∗ = Mv + Mw + Mi



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The volumes, with the same indices as the masses

V∗ = Vag + Vw + Vi

Vtw = Vv + Vw + Vi


Basic notation


Ice density

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Snow bulk density

ρi :=Mi

Vi


ρ∗ :=M∗V∗

=M∗

Vag + Vw + Vi

Basic notation


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Variation of density in time


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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


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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


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Snow porosity

Relative saturation

φ∗ :=Vag + Vw

Vag + Vw + Vi

S∗ :=θw

φ∗


Basic notation


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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

ρwVi(A)

A


Basic notation


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Qualitative characteristics of the snowpack

Term Size θ∗Dry Usually T ≤ 0 ◦C 0

Little tendency for snow grain to stick togetherMoist T = 0 ◦C ≤ 0.03

Grains stick togetherWet T = 0 ◦C 0.03 - 0.08

Water can be seen in meniscus, but not squeezed out from snowPendular regime

Very wet T = 0 ◦C 0.08 - 0.15Water can be pressed out by squeezing snowAppreciable amount of air (funicular regime)

Slush T = 0 ◦C ≥ 0.15The snow is flooded with water. No air


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Other characteristics of the snowpack

•Shape of the grains of snow

•Size of the grains of snow

•Albedo

•Temperature

•Hardness

•Mechanical properties


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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)


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Thermal properties of snow

It is assumed that the heat flux is according to Fourier’s law:

�Jh = Kh�∇T


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�Jh = Kh�∇T

Heat fluxW m-2


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�Jh = Kh�∇T

Heat fluxW m-2

Thermal conductivity

W m-1 K-1


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�Jh = Kh�∇T

Heat fluxW m-2

Thermal conductivity

W m-1 K-1

Temperature gradient

K m-1


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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.



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�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∗



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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.


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Temperature

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


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050

100

150

Snow

Dep

th [c

m]

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SnowD simFlux to ground

Nov 97 Feb 98 May 98 Aug 98 Nov 98

030

6090

120

150

Flux

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● SnowD meas

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Temperaturewith and without snow


Snow metamorphism

•Gravitational settling

•Destructive metamorphism

•Constructive metamorphism

•Melting metamorphism

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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)

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Neve, Ghiaccio, Permafrost



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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:


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“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)


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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


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Reduces the free energy of the system to its stable state

This energy depends of the local radius of curvature of the ice crystal


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elevated radius of

curvature implies

g rea t e r vapour

pressure


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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



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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.




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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.



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“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



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Melting metamorphismor “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.


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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.



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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).



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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)


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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


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R↓ sw

R↓ lw

R↑ sw

R↑ lw

Pe

λs EvH

∆U∗

G



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∆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



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Spectral signature of snow


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Albedo


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The radiative balance of snow

SNOW, T = 0oC

CLEAR DRY AIR, T = 0oC

Net Energy LossFrom Snow Pack No Net Energy Loss

From Snow Pack

�a ≈ 0.6− 0.7�w,i,∗ ≈ 0.92− 0.97

R = � σ T 4


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The radiative balance of snow


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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

INSTABILITYln(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



99SW 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.U

lric

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101


14 snow hydrology-part1

Education

snow stauleeward

snow storm

characteristics of snow

snow crystalsthursday

snow coverthe

stefano endrizzi

various formation phases

figura della neve