1. Snowmelt runoff generation Snowmelt modeling
ATM 301 Lecture #15 (sections )
Snowmelt: Processes and modeling
Snowmelt processes
Snowmelt runoff generation
Snowmelt modeling

2. Seasonal cycle of a snowpack:
Accumulation Period: the period of general increase in snowpack
water equivalent prior the melt period.
Melt Period: the period with generally positive net input of energy:
- Warming phase: T increases to oC
- Ripening phase: meltwater is retained in the snowpack
- Output phase: part of the meltwater leaves the snowpack

3. Measurements from one snow season (Danville, VT)
Dingman Fig. 5-23

4. Snowmelt modeling: Energy Budget Approach
Measure / estimate / predict the various energy inputs and outputs
Calculate snow warming and melting based on the net energy input
Often we don’t have sufficient measurements, so need to estimate some of the terms
Rn, LE, H, Precip., …
Marks et al. (1999)

5. Energy Balance Over a Snow Cover
Pomeroy and Brun (2001)

6. Energy budget components [MJ m-2] (Danville, VT)19
Energy budget components [MJ m-2] (Danville, VT)
Dingman Table 5-5

7. Snowmelt Stages:
1. Warming Phase
2. Ripening Phase
3. Output Phase

8. Energy Balance: Warming Phase
Snowpack Temperature increases with net energy input (FE):
where ci = 2,102 J/(kg K) is the heat capacity of ice. hswe is the snow-water
equivalent depth of the snowpack.
Cold content (or internal energy) of a snowpack is the amount of energy per unit area required to raise its mean temperature from Ts to 0oC (i.e., to complete the warming phase):

9. Structure inside a snowpack during the ripening phase:

10. Energy Balance: Ripening Phase
Snowpack T stays at the freezing point (0oC), liquid water depth (hw) forms when a net energy flux (FE) applied to it over a period t:
where f = 334 J/kg is the latent heat of freezing.
At the end of the ripening phase (i.e., just before output phase), the snowpack reaches its liquid water holding capacity:
where hs is snow depth, ret is the maximum volumetric water content of the snowpack, and it is related to snow density s (in kg/m3):
The net energy input required to complete the ripening phase is :

11. Snow Porosity () and Maximum Water-holding Capacity (ret)
As a Function of Snow Density (s)

12. Energy Balance: Output Phase
Once the snowpack is ripe, further net energy input produces output of
meltwater
The net energy required to complete the output phase (i.e., melt all the
snow) is
The amount of water output (w) for a given amount of input of energy
(Qmelt) during the output phase is

13. Example of Energy Balance Calculations for a Snowpack
Snowpack survey data:
Site Site 2
Depth (cm)
Water equivalent (cm)
Mean temperature (oC)
Compute 1) the snow density and cold content
2) the amount of the energy required to complete the ripening phase
(i.e., before water output begins)
3) the amount of energy required to melt the whole snowpack
4) the total amount water output from the melting of the snowpack
1). From hswe = (s/ w) hs , we have s=(hswe/hs) w = 28/100 * 1000kg/m3=380kg/m3
cold content
2). The energy amount = Ucc + Ur (the amount to complete the ripening phase)

14. Snowmelt modeling: Temperature-Index Approach
Since meteorological data are often very limited, this method uses daily averaged air temperature alone to predict snowmelt.
Δw=0 ; Ta < Tm (0°C)
Δw=M (Ta – Tm) ; Ta > Tm
M is called the “melt factor/coefficient” or the “degree-day factor”
When M is tuned to specific location (based on albedo, slope, vegetation, etc.) this method can work well
This method neglects the actual processes that control snowmelt, so it can sometimes be very wrong
Dingman Fig. 5-31
slope= M

15. Snowmelt modeling: Hybrid Approach
If we have some information about radiation, we can improve on the realism of the temp.-index approach.
Δw = 0 ; Ta < Tm ( 0°C)
Δw = (K+L)/(ρwλf) + Mr (Ta – Tm) ; Ta > Tm
Mr is called the “restricted melt factor”, and has a constant value of 2 mm day-1
λf=0.334 MJ/kg is the latent heat of freezing.

16. Comparing snowmelt models and observations

17. Comparing snowmelt models and observations

18. Snowmelt Runoff Generation What happens to water after snowmelt?
Percolation through snowpack
Snowmelt Runoff
Generation
There are time delays between snowmelt and stream response:
Water takes time to travel to bottom of snowpack
Time lag (hrs)
Dingman Fig. 5-30

19. What happens to water after snowmelt?
Unsaturated soil
There are time delays between snowmelt and stream response:
Water takes time to move trough soil/snowpack into stream
The delay between snowmelt and stream response depends on which of these situations is occurring
Impermeable soil (frost, rock)
Partially saturated soil
Dingman Fig. 5-25

20. Homework #5 (Snow and groundwater) Due Thursday, 11/9/2017
Ex. 1 on p. 251 (copied on next slide) (20%)
Ex. 2 on p. 251 (only need to compute density only in 2a. In 2b, use the bulk sample from station 3 to calculate the density) (see next slide). (15%)
What are the impacts of global warming on snowfall and snowpack? Why should we be concerned about these impacts? (15%)
What is groundwater? Why groundwater is important for humans? (15%)
Describe the typical relationships between streams and groundwater. (20%)
What are the challenges in managing our groundwater resources in the U.S. and around the world? (15%)