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Transcript of Water movement Movement of water through through a ... 1 Movement of water through snow GEO 4430,...

  • 1

    Movement of water through snow

    GEO 4430, snow hydrology 21.03.2006

    Thomas V. Schuler t.v.schuler@geo.uio.no

    Vs = 1 m3 Ts = -1 °C

    Tw = 0 °Cmelt-water

    snow

    cold content = the energy needed to bring the snow/ ice volume to 0°C

    density of snow, ρs = 400 kg m-3 density of water, ρw = 1000 kg m-3 specific heat of snow, cs = 2100 J kg-1 K-1 latent heat of fusion, L = 0.333 x 106 J kg-1

    How much water is needed to overcome the cold content?

    Hs = ∆T ms cs (cold content) Hrf = mw L (heat release

    while refreezing)

    Hs = Hrf = 840 kJ Solving for Vw= mw ρw-1 yields Vw = 2.5 l

    Water movement through a snowpack

    melting surface wetting front

    T distribution

    0C

    wet processes

    dry processes

    Motion of water through a snowpack

    Snow metamorphism

    (a) Constructive metamorphosis (faceting),

    (b) Destructive metamorphosis (rounding),

    (c) Sintering

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    Infiltration into snowpack and percolation driven by gravity

    …after the cappilary water capacity is filled

    dt dm 3/2

    ⎟ ⎠ ⎞

    ⎜ ⎝ ⎛

    effθ 3

    melt rate

    eff. poros

    depends on snow density

    Stages of snowpack evolution from a hydrological point of view

    • Warming phase: increase T until isothermal conditions: T = 0 C

    • Ripening phase: filling the field capacity / retention capacity

    • Output phase: outflow from the snowpack occurs

    layers of different permeability

    How does the water move?

    ”fingering”

    ice lenses

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    Albert et al., 1999

    Albert et al., 1999

    Image processing

    Snow temperature distribution after two rainfall events

    Conway & Benedict, 1994

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    Snow lysimeter array

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    heterogeneity

    permeability

    delay of runoff after onset of the melting season

    Anyway, water moves slowly through snowpack Efficient storage mechanism

    time

    warming ripening outflow

    depending on site conditions

    Modelling: Discharge routing

    Photo: R. Pettersson

    Photo: R. Pettersson

    Linear reservoir

    Q Linear

    reservoir

    Q = k * V

    Q – discharge V – storage volume k – storage konstant

    P

    )1()()1()( k t

    tn k

    t

    tntn eIeQQ ∆−

    ∆−

    −∆∆ −+⋅=

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    V

    Linear reservoir I

    t

    Q

    Q proportional to V kt t eQQ

    − ⋅= 0)(

    )1()()1()( k t

    tn k

    t

    tntn eIeQQ ∆−

    ∆−

    −∆∆ −+⋅=

    Water movement: summary

    • Snowpack similar to a porous aquifer after removal of cold content

    • 3 stages of snowpack hydrological evolution: warming, ripening, outflow

    • Snowpack permeability depends on density, grain size, temperature... highly heterogeneous

    • With maturing of the snowpack, the permeability becomes larger and more homogeneous