ERS 482/682 (Fall 2002) Lecture 9 - 1

Snow hydrology

ERS 482/682Small Watershed Hydrology

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

ERS 482/682 (Fall 2002) Lecture 9 - 29

Temperature-index approach

Figure 14.4 and Table 14.2 (Brooks et al. 1991)

ww

MM