1. Ice Formation and Ice Cover Hydraulics 2004 Cold Regions Workshop
Steven F Daly
ERDC/CRREL
US Army Corps
of Engineers ®
Engineer Research and Development Center

2. Outline Ice formation Evolution of river ice Formation of ice covers
River Ice Hydraulics
Steven F Daly (603)

3. Cold Problem Solvers for the Nation
CRREL
Cold Problem Solvers for the Nation

4. Two contrasting cases:
Ice Formation
Two contrasting cases:
Turbulent parcel of water. Ideal case of ice formation in rivers.
Quiescent parcel of water. Ideal case of ice formation in lakes, ponds, slow-moving rivers.

5. Here the heat loss rate from the water is less than the latent heat released by growing ice.
Water cools with no ice
Here the heat loss rate from the water is greater than the latent heat released by growing ice.
Here the heat loss rate from the water is equal to the latent heat released by growing ice.

6. Where does the ice come from?
Nucleation?: Spontaneous Appearance
Homogeneous nucleation: Pure water
Heterogeneous nucleation: due to the action of catalysts (nucleating agents) such as silver iodide, organic particles, bacterial

7. Secondary Nucleation
Seed crystals introduced from outside the waterbody. Sources: bubble bursting, wave breaking; snow; ice; etc.
Secondary nucleation is the formation of new crystals due to the presence of ice crystals. We think it is through the removal of nuclei through collisions with other crystals and hard boundaries.

11. Frazil Ice Formation Formed only in areas of open water
Formed in turbulent water
Flow velocity
Wind mixing
Formed in supercooled water
-.01°C to -.02°C

12. Formation of Ice in Quiescent Water
Start with an (ideal) quiescent parcel of water losing heat to the air
Heat loss stratifies water due to temperature dependence of water density. Remember that water is most dense at 39F (4C)
Substantial gradients of temperature can exist with coldest water at the surface. Maximum temperature at depth: 4C

13. Ice Cover Formation Static Ice Cover Formation
Typical of ponds, small lakes, and slow flowing rivers
Dominated by thermal growth
Air
Heat transfer
Ice
Ice Growth
Water
Interface temperature always at the ice/water equilibrium
temperature: 0C for freshwater.

14. Ice Cover Growth To model ice cover growth:
Various heat transfer modes
Solar penetration of ice cover
Insulating effects of snow cover
Heat transfer from underlying waterbody
Temperature profile within ice

15. Ice Cover Growth -Stefan Eq
To estimate ice cover growth
Assume heat transfer linear function of difference between air and melting temperature
Ignore solar penetration of ice cover
Account for Insulating effects of snow cover through calibration
Ignore heat transfer from underlying waterbody
Assume linear temperature profile

16. Ice Cover Growth- Stefan equation:
Accumulated Freezing Degree Days

17. Ice Cover Growth
AFDD: Accumulated Freezing Degree Days. The FDD for a single day is found by
subtracting the mean temperature for the day from 0C (32F). The AFDD are found
by summing the FDD for all days from the onset of freezing. FDD can be positive, if
the mean temperature is below freezing, or negative (if the mean temp is above)
Generally, the melting process is much more complicated than freezing.
Table
Ice Cover Condition *  †
Windy lake w/no snow
Average lake with snow
Average river with snow
Sheltered small river
* AFDD calculated using degrees Celsius. The ice thickness is in centimeters.
† AFDD calculated using degrees Fahrenheit. The ice thickness is in inches.

21. Grand Forks, ND

22. Problems with the ideal cases
Turbulent
Gravity: Particles rise to the surface
Flocculation: Particles bond together
Deposition: Anchor ice
Flow conditions change as ice is transported
Quiescent
Wind mixing
Heat transfer from water
Snow loading and flooding of the ice cover
Quasi-steady assumption not appropriate

23. Evolution of frazil ice
Formation
1. Seeding.
2. Frazil ice dynamics.
3. Flocculation and Deposition.
4. Transport and Mixing
5. Floe formation and induration
6. Ice cover formation and under ice cover transport.
Supercooled water, turbulence, the creation
of disk crystals through secondary nucleation
Transformation and transport
Water at equilibrium. Frazil in the form of flocs,
slush, floes, and anchor ice. Largely moving
Stationary ice covers
Fine grained ice. Can be quite large.

25. Ice Crystals Nucleated
FRAZIL ICE IN RIVERS
Entrainment
Seed Crystals
Supercooled
Water
Surface Growth and Surface Flocculation
Stable Ice Cover
Deposited
Slush
Disks
Buoyant
Anchor Ice
Transported Frazil
Ice Crystals Nucleated
in Cold Air

28. Frazil Slush

30. Anchor Ice Stationary Ice Covers Frazil Disks Frazil Slush Ice Pans
(Pancake ice)
Large Floes
~width of channel
Stationary Ice
Covers
Intermediate Form
Final Form

31. Anchor Ice

32. Anchor Ice

33. Anchor Ice Dominated by deposition of crystals
Thermal growth can occur but produces only small volumes
Can be highly transitory - often breaks free of substrate at dawn
Most stable in shallow, fast flowing streams
Most observations suggest that it does not penetrate gravel very deeply
Form of anchor ice is influenced by flow velocity
Anchor ice dams

34. frazil ice blockage of
water intake
trash racks

35. If supercooled water is entering trash rack, frazil will adhere to
trash rack bars. Blockage will occur when ice can bridge between
bars.
Head loss with time

37. Frazil Evolution: Ice Floes
Frazil Slush
Large Floes
Frazil Slush
Pancake Ice
“Low Energy”
“High Energy”
Steep Rivers
Large Waves
Rivers with
Mild Slopes
Mountain Streams

41. Border ice growth along river edge

43. Ice Cover Formation Dynamic Ice Cover Formation
Dominated largely by the interaction between ice floes and the flowing water
An ice cover may initially form dynamically and later thicken due to thermal growth

44. Dynamic Ice Cover Formation
Froude
Number
Bridging
Juxtaposition of Floes
Underturning of floes
Shoving of ice cover
Under-ice transport
No ice-cover progression
Increasing
flow Velocity
Increasing
flow depth

45. Juxtaposition of floes
Static analysis: The ice floe will underturn when the underturning moment produced
by the water exceeds the maximum righting moment the block can produce

46. River Ice Covers
Wide covers always float at hydrostatic equilibrium except under rare occasions
Hydraulically river ice:
Blocks flow area
Reduces hydraulic radius (area/wetted perimeter)
Modifies effective channel roughness (Manning’s n value)
Additionally, river ice can
Inter-act with “short” period waves

47. Ice Cover Crystal Structures
Fine grained ice
Frazil or snow
“White” ice
Resists solar penetration
Columnar ice
Thermally grown
“Black” ice
Transparent, allows solar penetration,”candle ice”

49. Summary
Ice formation
Evolution of river ice
Formation of ice covers

50. River Ice Hydraulics Additional stationary boundary
Modifies vertical flow profile
Changes flow conditions
Flow Area
Hydraulic Radius
Hydraulic Roughness
Ice cover has mass and stiffness
Resists bending and vertical motion
Potential impact on wave propagation

54. Changes in vertical profile
Modifies discharge calculations
Modifies vertical transport
Temperature
Trace materials
sediment
Shear stress distribution around boundaries

55. Ice cover has mass and stiffness
The mass and stiffness of an ice cover impacts only relative short waves
Order of the characteristic length of the ice cover
Period of a few seconds
We usually don’t measure such waves
In flow calculations we can ignore the mass & stiffness and assume the ice is always floating. NO PRESSURIZED FLOW

56. Wave Velocity Ice Covered vs. Open
Relatively short
~ characteristic length
(2/L)

57. Manning’s Equation with IceB d
In practice: River ice covers are
always floating at hydrostatic equilibrium.
Or more exactly
Non-hydrostatic pressure will always be temporary and
relatively short lived and for practical applications can be ignored.

58. Manning’s Equation
Substituting the expression for Manning’s n we arrive at the
Manning equation for steady flow, expressed for the flow
velocity or the total discharge, Q

59. Manning’s Equation with Ice: Area and Hydraulic RadiusB d
Adjust the terms of the Manning’s equation to account for the presence of ice
Recall that for open water R ~ d

60. Composite Roughness value
Ice region
Bed region
Max velocity
Velocity Profile
under steady flow conditions
If we assume that the average flow velocity in the ice region and the bed region are equal;
And we assume Manning’s equation applies to each;
And we assume the energy grade line is the same in both; ni nb
Sabaneev Formula

61. Type of Ice Condition Manning’s n value
Suggested Range of Manning’s n Values for Ice Covered Rivers The suggested range of Manning’s n values for a single layer of ice
Type of Ice Condition Manning’s n value
Sheet ice Smooth to 0.012
Rippled ice to 0.03
Fragmented single layer to 0.025
Frazil ice New 1 to 3 ft thick to 0.03
3 to 5 ft thick to 0.06
Aged to 0.02

62. The suggested range of Manning’s n values for ice jams
Thickness Manning’s n value
ft Loose frazil Frozen frazil Sheet ice
The suggested range of Manning’s n values for ice jams

64. Manning’s Equation with Ice for Rectangular Channels
Same form as open water. Modify
Roughness coefficient
Flow area
Hydraulic Radius

65. Manning’s Equation with Ice for Rectangular Channels
Open water
Ice Covered
Potential 32% increase in total depth due to ice cover at uniform flow

66. Partially Covered Rivers

67. Practical Implications of River Ice Hydraulics
Open water rating curve is not accurate
Relationship between discharge and stage can change continuously as ice cover evolves
Stage Up
Stage Down
Anchor ice
Examples from Stuart Hamilton, Environment Canada

68. Stage-up
A good place to study stage-up processes is on the Fraser river, as shown on the map.
Flows from high elevation continental climate to coastal climate.
Flows north before it heads south
Fraser at Red Pass is ice-free year round, groundwater fed
South Fort George is below the confluence with the Nechako
Upper fraser timing of stage-up is typical upstream migration from Shelley
Lower Fraser sequence is in reverse – downstream freezes last
Valid open water downstream data to validate and quantify magnitude and duration of discharge depressions
Dan Moore and Taha are now working with this data to answer a variety of questions

69. Stage-down
Everybody knows about stage-up discharge depressions, but how many of you have seen evidence in support of a stage-down discharge enhancement.
It follows that all of the water lost to storage at stage-up must be found again in the spring, but the signal is usually lost in noisy data at break-up.

70. Stage-down
Another example of a stage-down discharge enhancement

71. Anchor Ice

72. Hanging frazil dams
Hanging frazil dams can be quite transient, accumulating and then disappearing. Often they can disappear before the first winter measurement so there is no record of them for some streams, however, they add a lot of uncertainty to the interpretation of stage data for the purpose of discharge estimation.

73. Summary Ice formation Evolution of river ice Formation of ice covers
River Ice Hydraulics