lecture 9 - 1 ers 482/682 (fall 2002) snow hydrology ers 482/682 small watershed hydrology
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ERS 482/682 (Fall 2002) Lecture 9 - 2
• ~13% of average precipitation in US is snow
Significance of snow
Figure 4.16 (Manning 1987)
ERS 482/682 (Fall 2002) Lecture 9 - 3
• ~13% of average precipitation in US is snow
Significance of snow
Figure 5-11 (Dingman 2002)
ERS 482/682 (Fall 2002) Lecture 9 - 4
• ~13% of average precipitation in US is snow
Significance of snow
• In some areas, snowmelt is main source of water supply
• Can affect water quality
ERS 482/682 (Fall 2002) Lecture 9 - 5
Snow properties
• Granular
icepore spaces
• If T<0°C: ice, air• If T=0°C: ice, water, air
ERS 482/682 (Fall 2002) Lecture 9 - 6
Snow properties
• Snow density
wi
s
wwii
s
wis V
VVV
MM 1
porosity water content
i = icew = water
ERS 482/682 (Fall 2002) Lecture 9 - 7
Definitions• precipitation
– depth of rainfall plus water equivalent of snow, sleet, and hail
• snowfall– incremental depth of snow and solid precipitation
• snowpack– accumulated snow on the ground
• snowmelt– amount of liquid water produced by melting leaving the snowpack
• ablation– total loss of water substance from snowpack (includes
evaporation/sublimation)
• water output– total of liquid water leaving snowpack
All typically expressed in units of depth [L]All typically expressed in units of depth [L]
ERS 482/682 (Fall 2002) Lecture 9 - 8
Snow measurement
• Precipitation gages
Figure 3-5 (Linsley et al. 1982)
ERS 482/682 (Fall 2002) Lecture 9 - 9
Snow measurement
• Precipitation gages• Snow board/snow stake
Figure 4.18 (Manning 1987)
ERS 482/682 (Fall 2002) Lecture 9 - 10
Snow measurement
• Precipitation gages• Snow board/snow stake• Universal gage (Fig. 5-6)• Snow survey
Federal sampler
Depth probe
ERS 482/682 (Fall 2002) Lecture 9 - 11
Snow measurement
• Precipitation gages• Snow board/snow stake• Universal gage (Fig. 5-6)• Snow survey• Snow pillow (Fig. 5-8)
ERS 482/682 (Fall 2002) Lecture 9 - 12
Snow measurement
• Precipitation gages• Snow board/snow stake• Universal gage (Fig. 5-6)• Snow survey• Snow pillow (Fig. 5-8)• Lysimeter
ERS 482/682 (Fall 2002) Lecture 9 - 13
Snow measurement
• Acoustics• Radar• Satellite
Table 5-1 summarizes methodsTable 5-1 summarizes methods
ERS 482/682 (Fall 2002) Lecture 9 - 14
Snowmelt processes
• Snowpack metamorphism– Involves changes in
• Snow structure• Density• Temperature• Albedo• Liquid water content
ERS 482/682 (Fall 2002) Lecture 9 - 15
Snowmelt processes
• Accumulation period– hm increases
– net energy input is negative– average snowpack temperature decreases
• Melt period net energy input is positivenet energy input is positive
snowpack snowpack TTss increases to 0increases to 0°C°C
melting occurs, but no water output; melting occurs, but no water output; TTss = 0 = 0°C°C
– Warming phase– Ripening phase– Output phase energy input energy input water output water output
ERS 482/682 (Fall 2002) Lecture 9 - 16
Warming phase
msmwicc TThcQ
where Qcc = cold content ci = heat capacity of ice w = density of water hm = snow water equivalence Ts = temperature of the snowpack Tm = melting point temperature
2102 J kg2102 J kg-1-1 °°CC-1-1
1000 kg m1000 kg m-3-3
0 0 °C°C
[°C][°C]
[m][m]
[J m[J m-2-2]]
Snowpack temperature increases to Ts = 0°C
Note: Qm1 = Qcc at beginning of melt period
ERS 482/682 (Fall 2002) Lecture 9 - 17
Ripening phase
fwsretm hQ 2
where Qm2 = net energy to complete ripening phase ret = maximum volumetric water content f = latent heat of fusion
Figure 5-20Figure 5-20
0.334 MJ kg0.334 MJ kg-1-1
[J m[J m-2-2]]
Before water output when the snowpack is isothermal at Ts = 0°C
ERS 482/682 (Fall 2002) Lecture 9 - 18
Output phase
fwwretmm hhQ 3where Qm3 = net energy to melt the rest of the snow hwret = liquid water-retaining capacity of snowpack [m][m]
[J m[J m-2-2]]
Water output after snowpack is ripe
Equations 5-14 and 5-15Equations 5-14 and 5-15
fwm
tShw
where w = incremental water output from snowpack S = net rate of energy exchanges into snowpack t = time period
[J m[J m-2-2 day day-1-1]]
[day][day]
[m][m]
ERS 482/682 (Fall 2002) Lecture 9 - 19
Energy exchange processes
S = K + L + H + LE + R + G
Equation 5-26
where K = shortwave (solar) radiation input L = longwave radiation H = turbulent exchange of sensible heat with atmosphere LE = turbulent exchange of latent heat with atmosphere R = heat input by rain G = conductive exchange of sensible heat with ground
All expressed in units of [E LAll expressed in units of [E L-2-2 T T-1-1]]
ERS 482/682 (Fall 2002) Lecture 9 - 20
Shortwave radiation input, K
• Energy input due to sun’s energy– Depends upon slope, aspect, cloud cover,
vegetation cover, albedo
Figure 14.1 (Brooks et al. 1991)Figure 13-10 (Dunne & Leopold 1978)
ERS 482/682 (Fall 2002) Lecture 9 - 21
Shortwave radiation input, K
• Energy input due to sun’s energy– Depends upon slope, aspect, cloud cover,
vegetation cover, albedo
Figure 14.2 (Brooks et al. 1991)Figure 5-23 (Dingman 2002)
ERS 482/682 (Fall 2002) Lecture 9 - 22
Shortwave radiation input, K
• Energy input due to sun’s energy– Depends upon slope, aspect, cloud cover,
vegetation cover, albedo
1inKKwhere Kin = amount of shortwave radiation reaching snow = albedo (fraction reflected back to atmosphere)
Table D-6
ERS 482/682 (Fall 2002) Lecture 9 - 23
Longwave radiation, L
• Terrestrial radiation, reflected solar radiation– Depends on temperature of earth’s surface,
air temperature, canopy cover, cloud cover
3.272.273 4 aat TL
where at = effective emissivity of the atmosphere = Stefan-Boltzmann constant Ta = 2-m air temperature
4.904.901010-9-9 MJ m MJ m-2-2 day day-1-1 K K-4-4
°C°C
Equation 5-38, 5-39 or 5-40Equation 5-38, 5-39 or 5-40
Adjusts for snowsurface Tss = 0°C
Equation 5-42
ERS 482/682 (Fall 2002) Lecture 9 - 24
Turbulent sensible heat exchange, H
• Occurs whenever there is temperature difference between surface and air– Assumes neutral atmospheric conditions,
wind speed and air temperature measured at 2 m above snow surface in clear non-forested area ssaa TTvH 348.0where va = wind speed at 2 m above snow surface Ta = 2-m air temperature Tss = temperature at snow surface
m sm s-1-1
°C°C
Equation 5-43
°C°C
If there is a temperature inversion, should apply stability correction factors
ERS 482/682 (Fall 2002) Lecture 9 - 25
Turbulent latent heat exchange, LE
• Occurs whenever there is vapor pressure difference between surface and air– Assumes neutral atmospheric conditions,
wind speed and air temperature measured at 2 m above snow surface in clear non-forested area
Equations 5-45 or 5-46
cold snow (cold snow (TTssss < 0 < 0°C)°C) melting snow (melting snow (TTssss = 0 = 0°C)°C)
ERS 482/682 (Fall 2002) Lecture 9 - 26
Heat input by rain, R
• Rainwater gives up heat due to cooling to freezing point and/or freezing
Equation 5-47
usually assumed = usually assumed = TTaa
C0for msmrww TTTTrcR
where cw = heat capacity of water r = rainfall rate Tr = temperature of rain Tm = melting temperature
msfwmrww TTrTTrcR for
4.194.191010-3-3 MJ kg MJ kg-1-1 K K-1-1
[L T[L T-1-1]]
°C°C
0 °C0 °C
ERS 482/682 (Fall 2002) Lecture 9 - 27
Sensible heat exchange with ground, G
• Occurs whenever there is a temperature difference between snow and ground
Usually negligible, but can be significantduring accumulation period
ERS 482/682 (Fall 2002) Lecture 9 - 28
Modeling snowmelt
• Energy balance approach (Figure 5-29)• Temperature-index approach
C0for mama TTTTMw
ma TTw for 0
where w = snowmelt for a certain time period M = melt coefficient Ta = air temperature Tm = melting temperature